JAS

332

Volume 103

Number 1

Spring 2017

Journal of the

MCZ

WASHINGTON LIBRARY

MAY 25 2017

HARVARD

UNIVERSITY

ACADEMY OF SCIENCES

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Description of a New Species of Pentorchis Meggitt S. Banerjee, B. Manna, and.........

Bi Vi OUST ON coche 2 pies Ne eA ee 1

Generalized Extensivity J. E. Gray and S. R. AAGiISON.L ..eceseccssessssssssessssvesssscesssesssiessssessssneessseee 9

Work Functions of Thermally Roughened Surfaces Ni(111) and Pd(111)

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Attention-Deficit/Hyperactivity Disorder J. J. Stephens and D. L. By? eceecccssseessssvee-- 37

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ISSN 0043-0439 Issued Quarterly at Washington DC

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Journal of the

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Volume 103. Number1 = Spring 2017

Contents

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EX QeRtCh oan CITE MUTI ME CHINGIINS Oe. hl 8 eeentheia tyad Bard sta. aan cdedeE A Ue howe eens ill

Description of a New Species of Pentorchis Meggitt S. Banerjee, B. Manna, and

AIS SES CVV) alles tite 8 a jhe tet in Nr cre eB sec eledon cage Sus teiaeeins che stauneslocelieus toads Ott l

Generdized Extensivity J. .nGray and So RAAGISON i isbaucesesvshsssesesthevcstes elbseodes 3)

Work Functions of Thermally Roughened Surfaces Ni(111) and Pd(111)

Gale Derty, Ball. Worth MaOGross, and MIE, Wert. dicate eect ttae PAY

Attention-Deficit/Hyperactivity Disorder J. J. Stephens and D. L. Byrd ..........06. 37

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PCE EUI Abe Gh MOONE UIOMON A eb aSaugh gare sc al pest ciatea valet MON ig as veo melavohineanuan eUacmarnd ea eceutes enna 59

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ISSN 0043-0439 Issued Quarterly at Washington DC

Spring 2017

Editor’s Remarks

Welcome to the spring issue. In keeping with past issues we continue to

offer an eclectic selection of papers. Special thanks go to the reviewers who

bravely reviewed this particular mixture.

The sciences remain at the forefront of human progress. This Journal

is part of that effort. Without a wide variation in what we study we step

backward. One never can tell what useful result will come from an

otherwise rare study. I offer one example. Radio astronomers receive

signals from the Universe that have static in them. Some years ago the radio

community wrote a software program to clean the data, and thereby draw

out a clear signal. This program wended its way through the astronomical

community and was improved by programmers at the Space Telescope

Science Institute. From there, with the help of the National Science

Foundation, it was noticed by the medical community who adapted it for

use 1n ultrasounds, especially mammograms. One reason ultrasound images

are cleaner and clearer than they were years ago 1s because of the static filled

data of the radio astronomers. Such a result cannot be predicted. Science

must wander where it will. Out of those wanderings come solutions to today

and tomorrows’ problems.

In this issue we wander first to India for a paper that describes a new

species of tapeworm. Then we come back to the United States for a paper

that discusses the mathematics underlying generalized extensivity.

Following that we have a physics paper describing the work functions of

nickel and palladium. To close we have a paper that delves into an issue of

importance to many parents: ADHD — attention-deficit/hyperactivity

disorder.

I hope you enjoy these selections.

Sethanne Howard

Washington Academy of Sciences

il

Journal of the Washington Academy of Sciences

Editor Sethanne Howard showard@washacadscl.org

Board of Discipline Editors

The Journal of the Washington Academy of Sciences has an 11-member

Board of Discipline Editors representing many scientific and technical

fields. The members of the Board of Discipline Editors are affiliated with a

variety of scientific institutions in the Washington area and beyond —

government agencies such as the National Institute of Standards and

Technology (NIST); universities such as Georgetown; and professional

associations such as the Institute of Electrical and Electronics Engineers

(LEEE).

Anthropology Emanuela Appetiti eappetiti@hotmail.com

Astronomy Sethanne Howard sethanneh@msn.com

Biology/Biophysics Eugenie Mielczarek mielczar@physics.gmu.edu

Botany Mark Holland maholland@salisbury.edu

Chemistry Deana Jaber djaber@marymount.edu

Environmental Natural

Sciences Terrell Erickson terrell.erickson] @wdc.nsda.gov

Health Robin Stombler rstombler@auburnstrat.com

History of Medicine Alain Touwaide atouwaide@hotmail.com

Operations Research Michael Katehakis mnk@rci.rutgers.edu

Science Education Jim Egenrieder jim@deepwater.org

Systems Science Elizabeth Corona elizabethcorona@gmail.com

Spring 2017

Description of a new species of Pentorchis Meggitt,

1927 tapeworm from the bird Cissa chinensis in

Arunachal Pradesh, India

Suranjana Banerjee', Buddhadeb Manna’, and A. K. Sanyal!

‘Zoological Survey of India, India

"University of Calcutta, India

Abstract

In 2008 two birds (Cissa chinensis) were caught in Arunachal Pradesh, India

with the help of a bird trap. One of them was infected with a new cestode

species of the genus Pentorchis Meggitt, 1927. The genus Pentorchis Meggitt,

1927 had contained only two known species. The newly described species

named Pentorchis arunachalensis is characterized by an elongated scolex;

absence of neck; five testes; pear-shaped cirrus sac; multilobulated ovary, and a

sac-like uterus that differentiates it from the rest of the described species in the

genus. This is also the first report of the genus Pentorchis Meggitt, 1927 from

Arunachal Pradesh, India.

Introduction

THE GENUS PENTORCHIS was established by Meggitt in 1927. The type

species of this genus is Pentorchis arkteios Meggitt, 1927 collected from

the host Ursus malayanus from Victoria Memorial Park in Rangoon,

Myannmar. Ashfaq ef al. (1991) recorded a new species Pentorchis

shindei from the host Acridotheres ginginianus from the Aurangabad

district in Maharashtra, India. At present only two known species are

present under the genus Pentorchis Meggitt, 1927.

1. Pentorchis arkteios Meggitt, 1927

2. Pentorchis shindei Ashfaq et al., 1991

The aim of this paper is to add a new cestode species found in a vertebrate

host from Arunachal Pradesh, India.

Material and Methods

During a study tour during the months of October-November, 2008

to collect cestode parasites from vertebrate hosts in Arunachal Pradesh

(India) two birds (Cissa chinensis) were caught in Daporijo, Upper

Subansiri district of Arunachal Pradesh. One bird was released after

Spring 2017

identification while the other bird, which was listless and drooping, was

examined for parasites. The birds were caught in a bird trap with the help

of local men. The bird trap used is locally known as ‘Tawan’ (Atyadurai,

2012) a crude form of a mist net. The infected bird was euthanized with

ethanol in a closed jar following the protocol of Ghosh and Kundu (1999).

A cotton swab of a few drops of ethanol was used for the anaesthetization

of the bird. The necropsy was performed under a stereoscopic microscope.

The bird was dissected and the entire alimentary canals were removed and

internal organs such as liver, heart, lung, kidney, urinary bladder were

placed into normal saline (Justine ef al., 2012) and examined separately in

different petri dishes. We found that the bird was infected with two

cestode specimens of the genus Pentorchis. The cestode specimens were

collected from the intestine of the host, pressed and flattened between two

slides, and preserved in 70% alcohol in a glass vial. They were then

dehydrated in increasing concentrations of alcohol, stained in alcoholic

borax carmine, cleared in xylol, and mounted on slides in Canada balsam

(Ghosh and Kundu, 1999). The specimens were studied under a

microscope (Magnus MLX-Trinoculor from Olympus, Japan) and camera

lucida drawings and photomicrographs were made to describe the species.

Results

We have isolated a new species of Pentorchis arunachalensis

(Figs. 1, 2) with the characteristics of the genus Pentorchis Meggitt, 1927.

The strobila consists of a few proglottids. The body of the mature parasite

consists of a scolex, neck, immature, mature, and gravid proglottids. All

the proglottids are broader than they are long. Segmentation is craspedote.

All the measurements given are in millimeters unless otherwise mentioned

in the text. The parasite measures 28.71-29.07 in length and 0.29 in

breadth. The immature proglottids measure 0.25-0.29 in length and 0.46-

0.52 in breadth. The mature proglottids measure 0.34-0.4 in length and

(.63-0.65 in breadth. The gravid proglottids measure 0.1-0.2 in length and

0.2-0.29 in breadth. The scolex is elongated, measures 0.27 in length and

0.20 in breadth; it bears an unarmed rostellum and four suckers. The

rostellum is 0.06 in length and 0.11 in breadth. The four suckers are round

in shape and muscular, extending from the base of the rostellum to the

base of the scolex and measure 0.09 in length and 0.06 in breadth. The

neck is absent, and segmentation begins immediately behind the scolex.

Washington Academy of Sciences

The testes are round, 5-7 in number, located on both sides of the ovary,

variable in size and measure 0.1-0.14 in length and 0.1-0.13 in breadth.

Three of the testes are poral while the rest are aporal. The cirrus sac is

pear-shaped, extends up to 1/3 rd distance of the proglottid crossing the

osmoregulatory canals and measures 0.2 in length and 0.06 in width. The

vas deferens remains coiled at the base of the cirrus sac. There are no

internal and external seminal vesicles. The cirrus sac opens in the middle

of the lateral margin of the proglottid through the genital pore which is

unilateral and not surrounded by a sphincter muscle; genital atrium absent.

The ovary is multilobate and situated in the middle of the segment close to

the posterior margin of the proglottid. It measures 0.03-0.05 in length and

0.08-0.1 in transverse diameter. The vagina opens posterior to the cirrus

sac. It 1s a narrow tube that dilates into a small seminal receptacle

immediately after leaving the ovary. The seminal receptacle measures

0.04-0.05 in length and 0.07-0.1 in breadth. The uterus is sac-like. In

mature proglottids it is divided by a few incomplete septa, but in fully

gravid proglottids it extends to the anterior margin of the segment and

occupies the whole proglottid. The gravid proglottids remain filled with

eggs and the uterine septa gradually disappear. The vitellaria is small,

lobed, and post ovarian situated on the posterior margin of the segment

and measures 0.02-0.03 in length and 0.04-0.05 in breadth. The eggs are

round in shape and measure 0.01-0.06 in width.

Data Summary

Type specimens. Holotype (One specimen in two slides with the

Zoological Survey of India Accession numbers W9932/1 and W9933/1

respectively) and one Paratype (One specimen in | slide with the

Zoological Survey of India Accession number W9934/1)

Deposition. Deposited in Platyhelminthes Section, Zoological Survey of

India, New Alipur, Kolkata-53, India

Type host. Cissa chinensis (Green Magpie)

Site of infection. Intestine

Type locality. Daporijo (27.9863° N, 94.2205° E), Upper Subansir1,

Arunachal Pradesh, India

Prevalence. 1/2

Spring 2017

Etymology. The specific epithet is derived from the name of the state of

Arunachal Pradesh where it had been recovered.

wuwe'd

Fig.1. Camera lucida drawings of Pentorchis arunachalensis n. sp.

(a)Scolex (b) Mature proglottids (c) Gravid proglottids

Washington Academy of Sciences

Fig.2. Photomicrographs of Pentorchis arunachalensis n. sp.

(a) Scolex (b) Mature proglottids (c) Gravid proglottids

Spring 2017

Discussion

The present observed species measures 28.71-29.07 in length and

0.29 in breadth; the scolex elongated, measuring 0.27 in length and 0.20 in

breadth; an unarmed rostellum is present, 0.06 in length and 0.11 in

breadth; suckers measure 0.09 in length and 0.06 in breadth; the neck

absent; testes are five in number; cirrus sac pear-shaped, measuring 0.2 in

length and 0.06 in width; the ovary is multilobulated; the seminal

receptacle elongated; the uterus sac-like; genital pores are unilateral, not

surrounded by a sphincter muscle; the genital atrium is absent; the

vitellaria are small, compact, and postovarian; eggs are round in shape.

The observed species differs from P. arkteios Meggitt, 1927 in

which the scolex has a diameter of 0.38; diameter of the rostellum is 0.07;

the genital pore is surrounded by a distinct sphincter muscle; the cirrus sac

measures 0.25-0.35 x 0.03-0.04; the seminal receptacle is large and coiled;

the ovary is sac-like; from P. shindei Ashfaq et al., 1991 we have a small

and globose scolex; suckers have a diameter of 0.14-0.15; rostellum 1s

oval-shaped, measuring 0.18 x 0.07-0.11; cirrus sac measures 0.1 x 0.001;

ovary is bilobed and the lobes are unequal; the seminal receptacle is

absent; the vitelline gland triangular; genital atrium is present; genital

pores irregularly alternate.

New Key to the species of the genus Pentorchis Meggitt, 1927

1. Seminal receptacle present, genital pores umilatetal........2 5... 22.s..a.e. 2

-Seminal receptacle absent, genital pores irregularly alternate........... 2)

2. Ovary imdistinetiy OMOWEd as 6.4... 2.0.52. cence P. arkteios Meggitt, 1927

“Ovary-ttilO DULAC. ee ysge caine sie eas tasee atone P. arunachalensis n. sp.

3. Distinctly bilobed Ov ary.n. 24... eaee- 4p ae P.shindei Ashfaq et al., 1991

Acknowledgements

The authors are thankful to the Director, Zoological Survey of India for

providing necessary facilities for this work. The authors would also like to

express their deepest thanks to Library Division of Zoological Survey of

India, Kolkata - HQ for providing necessary facilities.

Washington Academy of Sciences

References

Ashfaq, S., Shinde, G. B. and Jadhav, B. V.(1991). A new cestode

Pentorchis shindei sp. nov.from Acridotheres ginginianus from

Aurangabad, Maharashtra, India. Indian Journal of Helminthology

1992, 43(2): 159-161.

Aiyadurai, A. (2012). Bird hunting in Mishmi Hills of Arunachal Pradesh,

north-eastern India. Indian Birds 7 (5): 134 -137.

Ghosh, R.K. and Kundu, D.K. (1999). Fauna of Meghalaya

(Cestoda).Zoological Survey of India, State Fauna Series 4 (Part

9):247-281.

Meggitt, F.J. (1927). A list of cestodes collected in Rangoon during the

years 1923-26. Journal of the Burma Research Society Rangoon

16:200-201.

Justine, J.L., Briand, M., Rodney, A. and Bray, R.A. (2012). A quick and

simple method, usable in the field, for collecting parasites in suitable

condition for both morphological and molecular studies. Parasitology

Research, Springer Verlag (Germany), 111 (1): 341-351.

Bios

Dr. Suranjana Banerjee M.Sc., Ph.D. in Zoology 1s a Senior Zoological

Assistant in the Zoological Survey of India. Her field of interest includes

research in morphology, taxonomy and systematics of cestodes. She

acquired her Ph.D. degree on her work on Taxonomy of Cestodes from

Eastern and North Eastern States of India. She has discovered several new

species of cestodes from India. Apart from her major field of interest in

cestode taxonomy, her other areas of interest include taxonomy of soil

nematodes and insects of the order Odonata. She has published more than

15 research papers in national journals.

Dr. Buddhadeb Manna, Emeritus Professor and Head (Ret.), Department

of Zoology, University of Calcutta, is engaged in research in Parasitology.

As many as seven students got a Ph.D. from Calcutta University under his

able guidance. He has published nearly 216 research articles in different

journals of International repute.

Spring 2017

Dr. Asok Kanti Sanyal M.Sc., Ph.D. in Zoology was retired Director-in-

charge and Emeritus Scientist in Zoological Survey of India. He received

training on EIA, Biodiversity Conservation and SEM in U.K. and

Singapore. He has 40 years of working experience on taxonomy and

ecology of soil microarthropods, Acarology, Nematology, Wildlife,

Biodiversity and has discovered over 130 species of mites and nematodes

from India and Antarctica. He has published several books and more than

220 scientific papers in national and international journals. He is also

amongst the very few to have made an Expedition to Antarctica from the

Zoological Survey of India. Several scholars have been awarded the

M.Phil. and Ph.D.degree under his supervision.

Washington Academy of Sciences

Generalized Extensivity, Generalized Superposition

and the Principle of Parsimony

John E. Gray

Naval Surface Warfare Center, Dahlgren

Stephen R. Addison

University of Central Arkansas

Abstract

In order to apply thermodynamics to systems in which entropy is not

extensive, it has become customary to define generalized entropies. While this

approach has been effective, it is not the only possible approach. We suggest

that some systems can be investigated by instead generalizing the concept of

extensivity. We begin by reexamining the role of linearity in the definition of

complex physical systems. We show that there is a generalized form of

extensivity that can be defined for a number of non-linear systems. We further

show that a generalization of the principle of linear superposition is the basis

for defining generalized extensivity. We introduce a definition for the degree

of non-extensivity for systems. We show that generalized extensivity can be

used as a means of understanding complex physical systems, and we propose

extending the idea of extensivity beyond thermodynamics to other physical

systems. We then explore generalized superposition principles in terms of the

principle of parsimony and provide examples where generalized superposition

principles can be found in phenomenological and statistical models of nature.

The current methods can be applied in situations in which we do not need to

consider quantum effects; we will probe the limitations imposed by quantum

effects in a later paper.

1. Introduction

WE BEGIN BY NOTING EFFORTS to understand thermodynamic systems

through considering entropy and its generalizations. We suggest that

systems can be investigated by instead focusing on extensivity and its

generalizations. We then consider the linkages between extensivity and

linear superposition and between generalized extensivity and generalized

superposition principles. Finally we link generalized extensivity and

superposition to the Principle of Parsimony. We note that superposition

principles can be used to organize knowledge arising from

phenomenological or statistical models, while variational principles are

used in mathematical models in which the underlying structure can be

expressed in terms of differential equations.

Spring 2017

A number of authors have proposed generalizations of entropy to

address the problem of providing a universal measure of complexity or

disorder; examples include Tsallis entropy, and Renyi entropy [1]. One of

the properties of entropy that remains controversial is the issue of

extensivity — the appearance of linear or additive behavior of the

subcomponents of a system when taken as a whole. Extensivity is not a

universal feature of entropy, though it is often treated as if it is [2, 3].

However, a variety of sources have demonstrated that entropic extensivity

cannot be one of the fundamental axioms of thermodynamics, see Addison

and Gray [4] for further discussions.

Examples that illustrate that extensivity is not fundamental to

thermodynamics can be found in many places. Consider a familiar

example: entropy was defined phenomenologically by Clausius as an

integral over a reversible path, but as Jaynes [5] observed the Clausius

definition says nothing about extensivity, since the size of the system does

not vary over the integration path. Furthermore, Hill, in pioneering work

in the 1960s noted that extensivity does not apply to all entropic systems,

particularly those that exist at small scales [6-8]. Thus, extensivity is a

notion independent of entropy. The subject of the next section of this paper

is how we can generalize extensivity so it applies to more general complex

systems. There is an advantage in attempting to generalize what can be

thought of as a purely mathematical concept. Extensivity can be

generalized in a straightforward manner without bringing along the

physical ideas associated with entropy; in this way we avoid the confusion

that often arises from mixing the physical and mathematical aspects of

entropy.

We take a contrarian viewpoint to the proposed generalization of

entropy by Tsallis [9] as well as many subsequent ideas that are

summarized in Tsallis [10]. This approach allows us to suggest an

approach to addressing the following the point made by Boon and Tsallis

i:

Asking whether the entropy of a system is or is not

extensive without indicating the composition law of its

elements, is like asking whether some body 1s or is not in

movement without indicating the referential with regard to

which we are observing the velocity.

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1]

The formalism of generalized superposition can be used to ask

what types of functions allow a nonlinear combination to give the

appearance of superposition.

We suggest several different forms of generalized extensivity can

be defined, including one associated with power laws, which is connected

to Tsallis entropy. As part of this exploration, we cast Tsallis entropy in a

manner that is consistent within the framework of generalized extensivity.

Thus, instead of being concerned whether Tsallis entropy has the

appearance of extensivity or when it is inherently non-extensive, we

propose that it can be viewed as having the property of extensivity in the

same context that a law of generalized superposition can be found, e.g.

when it can be related to power laws. We also discuss the role generalized

superposition plays in the understanding of power laws.

In complex, compound systems, the meaning of extensivity needs

to be explored in order to gain insight into the meaning of complexity.

Instead of proposing yet another generalization of entropy, we will

demonstrate the notion of extensivity can be generalized. Generalized

extensivity allows us to replace the classical notion of extensivity by

considering a more general notion of superposition. By choosing to

broaden the notion of what constitutes an extensive system rather than

changing the notion of what classical entropy means, we choose to

economize the physical interpretation of entropy; this serves the principle

of parsimony in a manner consistent with Occam’s razor.

2. The Principle of Superposition and Generalized Extensivity

The notion of extensivity can be developed mathematically by

relating it to the theory of linear systems. For a linear system with inputs

x;(n), scalars c;, and a system transform T(- ) there is always a rule for

combining inputs to give outputs. This system will be linear, provided the

system obeys the principle of superposition (where + denotes ordinary

addition)

T[ x,(n)+x,(n)]=T7[ x(n) ]+T[x,()]. (1)

and - denotes scalar multiplication

Spring 2017

eis ea lp (2)

There are many physical quantities where combinations behave

like linear systems and obey the principle of superposition. Mass and

energy are examples of quantities that exhibit this property; when

individual components of mass and energy are combined, the result is the

combination of the individual masses and energies. Thus both mass and

energy are extensive variables. On the other hand, both temperature and

pressure are not extensive because they are not additive over sub-systems.

The most familiar example of a combination of components that 1s

not extensive is multiplication. For a system with a law of combination

defined by multiplication:

x(n) =[x,(n)]-[()] 3)

with the introduction of a separator function for multiplication, the

logarithm,

log x(n) =log([ x, (n) }-[ x, (”) ]) = log] x, (7) ]+log[ x, (7) J. (4)

We have the appearance of superposition. For example, the Boltzmann

definition of entropy is S=kInQ, so under the circumstances that the

microstates are multiplicative Q=Q,Q,, then the entropy of the

combined states is S = S, +5; so the Boltzmann entropy obeys the

principle of generalized extensivity. We then introduce the definition

S= log| x(n) ], (5)

so that Eq. (4) becomes

S=S, +5). (6)

This is an example of a non-linear combination of components that can be

re-interpreted as obeying the superposition principle. This suggests that we

can look for an underlying generalized superposition principle — that 1s

extensivity — in many complex systems. Such a principle exists in signal

processing and in the analysis of homomorphic systems that provides

wider applications in complex systems.

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2.1 Generalized Extensivity

In order to generalize the idea of superposition in linear systems to

non-linear systems, Oppenheim [12] proposed a modification of Eq. (1)

and Eq. (2). The summation sign in Eq. (1) must be replaced with two

different symbols: a rule for combining inputs designated by @, and a rule

for combining outputs designated by @. We then write the generalized

superposition principle for such a system with a system transform H(-) as

H| x,(n)®x,(n)]=H|x,(n)]®H| x, (n)] (7)

which is the generalization of Eq. (1) for nonlinear systems. A similar

replacement is required for scalar multiplication by a constant, c, so the

generalization of Eq. (2) is

H| c®x(n)|=coH| x(n) | (8)

where ®& replaces the input scalar multiplication and o replaces the output

scalar multiplication. The notation we have adopted is an adaptation of the

notation used in the signal processing literature [13].

Systems with inputs and outputs that satisfy both Eqs. (7) and (8)

are called homomorphic systems since they can be represented as

algebraically linear (homomorphic) mappings between the input and

output signal spaces. Oppenheim and Schafer have written a brief history

of signal processing background for solving certain non-linear signal

processing problems that are the origin of their classification scheme [14].

They summarized this informally, by stating that all homomorphic systems

can be thought of in the following manner:

"... all homomorphic — systems have — canonical

representation consisting of a cascade of three systems.

The first system is an invertible nonlinear characteristic

operator (system) that maps a nonadditive combination

operation such as a convolution into ordinary addition. The

second system is a linear system obeying additive

superposition, and the third system is the inverse of the first

nonlinear system."

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The logarithmic function is a separator function for multiplication.

That is why there is confusion about entropy being extensive; for many

systems the total entropy is achieved by the multiplication of subsystems,

but this is not always true. Hill includes examples where multiplication

over subsystems does not yield the true entropy of the composite system.

Most non-linear functions M(x,vy) do not separate with a

superposition principle, for example a separator function, S, does not exist

such that

S| N(x,y)]=A(x)+B(y). (9)

The mathematical details for determining if the rule for combining systems

can be deconstructed so that a valid separator function S exists are

discussed by Tretiak and Eisenstein [15].

An informal argument is sufficient for our purposes to capture the

flavor of the conditions for S to be a separator function. By taking the

partial derivative Te 22) of Eq. (9) with respect to each of the

individual arguments, we have

S'| N(x) |N, (x)=, (2), (10)

and

SN Gay) oy) = Bay), (11)

combining we find

=, (2)

Then, by defining

cane

(sy) =| RAE) tn, (0)-I98, (9). (13)

ant y)

we see that

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A,, (x)

H (x,y)=— :

wea ae) ch

and

B,(¥)

H (x, y)=-=——;; (13

> ( y) B,(y) )

thus the first partials of H(x,y) are functions of a single variable and

separation has been achieved. This provides the means for finding a

separator function for N(x, y). In thermodynamic language, the existence

of a separator function means that there is a Maxwell relation between the

variables A and B.

When it exists generalized superposition provides an interpretation

of the extensivity property of entropy. In fact, generalized superposition

can be used as a guiding principle to look for extensive variables in a

generalized setting [16, 17] of determining the thermodynamics of

complex systems. More general types of entropy-like variables can be

defined using this form of generalized superposition. Since the rule for

combining subsystems into the whole is nonlinear, the principle of

generalized superposition allows us to look for a rule that gives the

appearance of linearity, and hence extensivity. Linearity on a macroscopic

scale gives us a generalized thermodynamics of complex systems. The

realization that the counting functions that enumerate the states have an

underlying separator function that obeys this generalized form of

superposition allows us to generalize the concept of extensivity. Thus, we

define a system as obeying a principle of generalized extensivity if it obeys

Eqs. (7) and (9) rather than Eqs. (1) and (2).

2.2 Other Forms of Extensivity

A second possibility that allows us to consider another type of

extensivity is illustrated by considering a relaxation of the linearity

requirement. An enumeration function need not be strictly linear either. An

example of this is illustrated by attempting to linearize a counting function

such as the factorial n!. While In(n!) is not linear, it is approximately linear

for a physical system that has a large number of components; thus for all

practical purposes

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In((n+m)!) = nln (n)+mIn(m) = In(n!)+In(m!); (16)

so n! has been linearized with respect to the logarithm. We have omitted a

factor O(1/n) in Eq. (16); this term is ignorable in systems that consist of

a significant number of interacting units. The only time this factor plays a

role is when trying to determine the transition point between collective and

individual behavior, such as in the question of how many atoms are

required before a system acts like a liquid or solid, or at the nanoscale

where collective behavior starts to break down. (We will discuss this

question further in a subsequent paper — it is largely outside of the purview

of this paper.) The difference between approximately linear and linear is a

point that is not emphasized which is illustrated by examining the factorial

function. There are a number of different functions that are linear in the

Stirling approximation. This notion of extensivity is captured by what we

term Ulam extensivity that is related to the mathematical properties of

functions that are termed approximately linear [18-20]. Consider

Tee yh) =e nO Gi), (17)

where g(x) tends to 0 as x becomes large, which is the reason the

logarithm of a factorial gives the appearance of linearity for large n. Vogt

[21] has discussed form isometry, which could be considered as a means

to generalize Ulam extensivity.

2.3 Power Laws, Homogeneity, and Extensivity

Generalized extensivity connects power laws and homogeneity

together. To illustrate the concept of generalized extensivity we consider

an example of a system that has a power-law like combination rule for

counting combinations of states which is defined by

x(n)=[x,(n) |" -[5(n)] (18)

where @ and f are constants. Notice that with the introduction of a

separator function for multiplication, the logarithm, we have

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log(x(n)) = log([, (n) |" | x, (n)}"]

= a(log| x, (n) |) + B(log| x, (n) |).

Thus recovering a familiar superposition principle. If we then choose

a = B, we have

log(x(7)) = @(log| x, (2) |+log] x, (n) ]). (20)

This equation reminds us of the basic definition of extensivity through the

theory of homogeneous functions. We will now review the basic ideas

through which we can analyze power laws using generalized extensivity.

(19)

The functional equations appropriate to the study of homogenous

functions were developed by Euler [22, 23]. Davis [24], Stanley [25], and

Widder [26] provide modern introductions of varying degrees of

sophistication to functional equations. In general, a function f(x) is a

homogenous function, if for all values of the parameter A,

Uae eae (2)

Stanley [25] has shown that g is not arbitrary function, instead it is

the parameter raised to a power of n. Thus a homogenous function f (x)

is one that satisfies

f (xa) =A" f(x) (22)

This definition can be extended to any finite number of variables.

The degree, n, is restricted to integer values only. It is possible for

multidimensional functions to be homogenous of different degrees for

different variables. This is common occurrence in thermodynamics. For a

function in the variables x, y, and z; the function satisfies

ja EP a eae aati CN cae (23)

we say this function is homogenous of degree n in the variables x and y,

it is not homogenous in the variable z. A definition introduced by Stanley

[25] of a generalized homogeneous function, is that it 1s a function that

satisfies the equation

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KiAveay) =A (8). (24)

It is this formulation of homogenous functions that is widely used

in the analysis of critical point phenomena and phase transitions using the

static scaling hypothesis. Functions that are homogenous obey the

principle of generalized superposition since f(xA)=A" f(x) and

f(yA)=A" f(y) so in general A” f(x)+A"f(y)# f(AxtAy),

however for n = 1, we have

Af (x)+Af (y) =f (xA)+ f (yA) = f (AxtAy) =f (x+y), (25)

so homogeneity and extensivity are the same for some types of functions.

This form of extensivity is what we term homogenous extensivity.

2.4 Symbolic Extensivity

The concept of symbolic extensivity arises naturally from

dimensional analysis. Three approaches can be taken based on the

common aegis of dimensional analysis codified by Bridgman [27]. You

take all the physical units that are required for a complete system

specification of a physical group of functions such as length L, time T, and

mass M; so the dimensional symbols action under the operations of

arithmetic constitute a mathematical group. For example, consider the

symbol for length L. Combinations of L form a group G;: there is an

identity, Lo = 1; there is an inverse, 1/L or L~*; and L raised to any

rational power p is a member of G, which has an inverse L~?. The group

operation is multiplication, with the usual rules for handling exponents

(L” x L™ = ["™*™). For example in classical mechanics, any physical

quantity can be expressed dimensionally in terms of base units, which have

dimensions M, L, and T.

~ From this group specification we note that by replacing a variable

x in f(x) by (x + 6,) it is natural to define f(x) to be translationally

extensive 1f

fis Od STAs (On) (26)

The degree of non-extensivity &(x,6,) of a function f (x) is then

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Wak 9 daca God bay)

F(x)

so = (x, 6,) = 0 for an extensive function. For a function that is Ulam

extensive,

= (x.0. ): (27)

C

g(x)

which is effectively zero for almost all g(x), especially those that scale

with the number of objects. As an example, the area of a square of side x

. = 5 oe

isms scyi(x)= 27 then 2a dy): = <=, so for 6, << x, 5(x,5,) = 0 and

ke ol

(28)

the area of the square is approximately extensive; however, when x

becomes comparable in size to 6x the area is non-extensive. This behavior

is potentially observable at the transition region between macrosystems

and nanosystems. To extend the definition to multiple dimensions, we

define the degree of non-extensivity as

idee 0, »X, rO. prea Xp, 17, )-F(¥)-F | :)

I (%)

A multidimensional function 1s translationally extensive if & (%, dz) = 0.

The volume of a cylinder is lr’, so the degree of non-extensivity is

Dae tO) peek ed (eae)

wen) (30)

ESP TS.

=2—~4£4—42—"+.

he CHEN yh ip

= (a, 0, |) 129)

2 (7,0,).0,)=

It is only when the fractional terms scale with the dimensional

ratios, or and that the degree of non-extensivity is not effectively zero.

For mat volumes for which we have an analytical formula, they can be

translationally extensive until the dimensional ratios, ~ and at, are of

similar size, then extensivity breaks down in a non-linear fashion.

The dimensional specification group, Gs, is constituted from the

individual units of the dimensional quantities that constitute the units of

the overall complex system which are labeled U;, U2,...,U,, in the system

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20

specification which are specified by the groups Gy,, Guz>--+» Gun: The

complex system group is obtained by taking the direct product, &, of these

groups :

Gs = Gu, ® Gu, ® - @ Gu, (31)

It is possible to use the complex system group to formulate a

dimensionless specification for each complex system units provided they

are specified by scaling factors. Thus, for a complex physical system

specified by variables x,, Xz, ...,%,,can be represented as

P(x1,X>,..,X_). The way to remove the dimensions from a physical

: : c ; aL

variable is to replace x, > 6,,x; where 6,,has units proportional = a

al

function that satisfies

f (Ex,%1) = gE, )f Or) (32)

which is scaling or homogenous extensivity. Necessarily, since

dim f(éx,%1) = f@) (33)

eal

we have anv Sola ee = 1. So by an argument similar to the one used

by Stanley, we have g ~ x”. So this type of extensivity reduces essentially

to earlier work.

The notion of extensivity extends beyond physics to the entire

subject of complex systems [28]. While the survey by Tsallis and Gell-

Mann discusses many non-physics applications of Tsallis entropy [29], we

would argue that the same applies to generalized extensivity for much the

same reasons. Furthermore, extensivity and its generalizations apply to a

new area of physics that is just starting to be explored:

nanothermodynamics, a name that has been proposed by Hill [30, 31].

Nanothermodynamics requires that a chemical potential as well as

variables that are extensive require a reformulation by scaling them, not

relative to one scaling component N, but rather rescaling the multiple

components relative to scales of different sizes N;. The appearance of

collective behavior, e.g. nanothermodynamics, emerges only if the

collective components act together in a unified manner, a type of

generalized extensivity [32].

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3. Generalized Extensivity as a Principle of Parsimony in Physics

The Principle of Parsimony in physics is most often observed in

variational principles such as Hamilton’s Principle. We propose that the

Principle of Parsimony in physics means the development of a large

number of consequences from a small number of assumptions. Examples

include Newton’s second law and Maxwell’s Equations. Indeed, much of

the structure of physical theories in use today is based on the parsimony of

variational principles [33-35]. But, in addition to laws and the variational

principles from which they can be derived, we must also consider

phenomenological and statistical models as possible models the exhibit

parsimony. Phenomenological and statistical models play important roles

in theoretical physics, and they play even more important roles in applied

physics and engineering. The principle of parsimony has not often been

applied to, or considered in, these areas; however if we examine some

examples, we quickly realize that the principle of parsimony is often

present in the guise of a superposition principle.

In phenomenology and statistical physics the most natural form of

parsimony is counting. In statistical physics we develop an understanding

of macrostates by counting accessible microstates, and we see how

emergent macroscopic properties arise from microscopic states. The

properties of the macrostate (the whole) emerge from combinations of

microstates (the parts.) The concept of the whole as a sum of the parts is

at the heart of the concept of generalized extensivity. Entropy is one

example of an emergent property arising from a superposition principle;

other superpositions will lead to different emergent properties.

Macroscopic observables emerge from superposition principles in much

the same way that laws emerge from variational principles. Thus we can

view generalized superposition as an organizing principle.

We can develop a deeper understanding of generalized

superposition as an organizing principle by considering information

theory. Shannon’s formulation of information theory [36] has led to the

information revolution upon which our modern technological society is

built. Gell-Mann and Tsallis [29] have argued that information theory is

the key concept in physics. In parallel with Jaynes [37, 38] it is possible to

reformulate quantum mechanics and quantum field theory using

information theory resulting in a quantum information theory. One method

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of building a quantum information theory is to follow Wheeler and his “it

from bit” methodology [40]. An alternative method can be based on

generalized superposition methods, as is well known superposition

principles form the core of the Dirac formulation of quantum mechanics

[40].

Before the development of Shannon’s information theory, it was

not known that messages could be compressed. Compression 1s usually

considered possible as a result of redundancy within languages [41].

However, compression can also be considered as a type of superposition

of the information content of a structured alphabet [42, 43]. The existence

of a generalized superposition principle in this context allows us to move

from an alphabet level of description to a language level of description.

Gravity can be thought of as obeying a generalized superposition

with respect to its basis in the extensivity (i.e. additivity) of mass. When

there is a sufficient mass present in a system, entropy emerges as a function

of area rather than volume [44]. Other systems can be expected to

transition from one law of generalized superposition to another.

Ultimately, we are able to understand nature through models, as we

are able to discover methods of expressing relationships between

collections of entities rather than individual entities. The existence of laws

that describe collective behavior of systems is the ultimate form of the

principle of parsimony in phenomenological descriptions. In modern

physics we have realized that laws that describe collective behavior are

ultimately more important than tracking individual entities. Predicting the

future state of systems with any degree of complexity 1s computationally

infeasible, thus we have laws that model collective behavior, in a statistical

sense, than the trajectories of individual particles in such systems.

4. Discussion and Conclusions

In conclusion we have proposed a means of extending the concept

of extensivity to a wider variety of physical systems as well as to the wider

subject area of complex systems. As a result of this, we suggest that the

Tsallis entropy could be interpreted as a form of generalized superposition

for some power laws. Further, we have noted that generalized

superposition principles are present in phenomenological, and statistical

descriptions of nature, and that such descriptions can be considered as

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phe,

examples of the principle of parsimony in action. The further development

of the understanding of generalized superposition principles can be

expected to provide a common framework that will enable the use of

common methodologies to a number of seemingly unrelated statistical and

phenomenological models.

5. Acknowledgements

The authors would like to thank Fransisco Santiago (NSWCDD)

for being a sounding board for discussion of new ideas to extend the

concept of generalized extensivity to the nanodomain. The first author

would like to thank Harold Szu for many useful discussions about the

mathematical and physical aspects of entropy that helped form the author’s

attempt to separate the purely mathematical from the physical in

understanding entropy.

6. References

[1] Mark P. Wachowiak, Renata Smolikova, Georgia D. Tourassi and Adel S.

Elmaghraby, Estimation of generalized entropies with sample spacing, Pattern

Analysis & Applications, 8, 95-101, 2005

[2] H.B. Callen, Thermodynamics, |st Ed., Wiley, 1960.

[3] H.B. Callen, Thermodynamics and an Introduction to Thermostatics, 2nd Ed.,

Wiley, 1985.

[4] S.R. Addison and J. E. Gray, Is extensivity a fundamental property of entropy?, J.

Phys. A: Math. Gen., 34, 7733-7737, 2001.

[5] E. T. Jaynes, in Maximum Entropy and Bayesian Methods, edited by C.R. Smith,

G. J. Erickson, and P.O. Neudorfer, Kluwer Academic, 1992.

[6] T. L. Hill, Thermodynamics of Small Systems J. Chem. Phys., 36, 3182, 1962.

[7] T. L. Hill, Statistical Mechanics; Dover: New York, 1987.

[8] T. L. Hill, Thermodynamics of Small Systems, Dover: New York, 1994.

[9] C. Tsallis, Possible Generalization of Boltzmann-Gibbs Statistics J. Stat. Phys., 52,

479-487, 1988.

[10] C. Tsallis, Entropic Nonextensivity: A Possible Measure of Complexity, Santa Fe

Research Institute Research Papers, 2001.

[11]J. P. Boon and C. Tsallis, Special issue overview Nonextensive statistical

mechanics: new trends, new perspectives, Europhysics News,

November/December, 2005.

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[12] A. V. Oppenheim, Generalized Superposition, Information and Control, 11, 528-

536, 1967,

[13] A. V. Oppenheim and R. W. Schafer, Digital Signal Processing, Prentice-Hall, Inc,

Englewood Cliffs, New Jersey, 1975.

[14] A. V. Oppenheim and R. W. Schafer, From frequency to quefrency: a history of the

cepstrum, Signal Processing Magazine, IEEE, Volume 21, Issue 5, pp 95 — 106,

Sept. 2004.

[15]O. J. Tretiak and B. A. Eisenstein, Separator Functions for Homomorphic Filtering,

IEEE Trans. on Acoustics, Speech, and Signal Processing, AASP-24, No. 5, 1976.

[16]J. E. Gray, Advances in Synergetics: System Research on Emergence, Volume 1,

Edited by G. E. Lasker and G. L. Farre, (The International Institute for Advanced

Studies in Systems Research and Cybernetics, 1994).

[17] J. E. Gray, Actes du Symposium ECHO, eds. Andre Ehresmann, G. L. Farre, J.

Vanbremeersch, Amiens (France), 21-23 Auot 1996.

[18] D. H. Hyers and S. M. Ulam, On approximate isometries, Bull. Amer. Math. Soc.,

vol. 51, pp. 288-92 1945.

[19] D. H. Hyers and S. M. Ulam, Approximate isometries of the space of continuous

functions, Ann. of Math., Vol. 48,pp.285-289, 1947.

[20] D. H. Hyers and S. M. Ulam, Approximately convex functions, Proc. Am. Math.

Soc., vol. 3 pp. 821-8, 1952

[21] A. Vogt, On the Linearity of Form Isometries, S/AM J. Appl. Math., Vol 23, No. 4,

1973.

[22] Leonhard Euler, Institutiones Calculi Differentialis, (Reprinted as Opera Omina, Sr.

Vole erpzic 1913);

[23] Leonhard Euler, Institutiones Calculi Differentialis II, (Reprinted as Opera Omina,

Simi, Vol i3.beipae 1925):

[24] Harold T. Davis, Introduction to Non-Linear Differential and Integral Equations

(Dover, New York 1962), pp. 1956.

[25]H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, Oxford

University Press, New York, 1971.

[26] D. V. Widder, Advanced Calculus, 2nd. Edition, (Prentice-Hall, Englewood Cliffs,

New Jersey), pp. 520.

[27] P. W. Bridgman, Dimensional Analysis, Yale University Press, 1922.

[28] Y. Bar-Yam, Dynamics of Complex Systems, Addison-Wesley Press, 2003.

[29] M. Gell-Mann and C. Tsallis, Nonextensive Entropy-Interdisciplinary Applications,

Edited by Murray Gell-Mann, Oxford University Press, New York, 2004.

[30] T. L. Hill, Pespective: Nanothermodynamics, Nano Letters, Vol. 1, #3, 111-112,

2001.

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[31] T. L. Hill, Extension of Nanothermodynamics to Include a One-Dimensional

Surface Excess, Nano Letters, Vol. 1, #3, 159-160, 2001.

[32] T. L. Hill, A Different Approach to Nanothermodynamics, Nano Letters, Vol. 1,

fds Zl o=2 105, 2001,

[33] Jean-Louis Basdevant, Variational Principles in Physics, Springer-Verlag, 2007.

[34] Cornelius Lanczos, The Variational Principles of Mechanics, 4" Ed., University of

Toronto Press, 1970

[35] Herbert Goldstein, Classical Mechanics, Addison-Wesley, 1950.

[36] Claude E. Shannon and Warren Weaver, The Mathematical Theory of

Communication, University of Illinois Press, 1949.

[37] E.T. Jaynes, Information Theory and Statistical Mechanics, The Physical Review,

106, 620-630, 1957.

[38] E.T. Jaynes, Information Theory and Statistical Mechanics II, The Physical Review,

108, 171-190, 1957.

[39] J A Wheeler. Sakharov revisited: “It from Bit”. Proceedings of the First

International A. D. Sakharov Memorial Conference on Physics, Moscow, USSR,

1991, May 27-31, ed M Man’ko, Nova Science Publishers, Commack, NY, 1991.

[40] P.A.M. Dirac, The Principles of Quantum Mechanics, 4" Ed., Oxford University

Press, 1958.

[41] Jacob Ziv and Adrian Lempel, A Universal Algorithm for Sequential Data

Compression, IEEE Transaction on Information Theory, IT-23, 337-243, 1977.

[42] P.C.W. Davies, Why is the physical world so comprehensible? CTNS Bulletin,

12,2, Spring 1992.

[43] Neri Merhav, Physics of the Shannon Limits, IEEE Transactions On Information

Theory, Vol. 56, 4274-4285, September 2010.

[44] Jakob D. Bakenstein, Black Holes and Entropy, Phys Rev D7, 2333-2346, 1973.

Biographies

John E. Gray received BS degrees in mathematics and physics in 1977

followed by an MS in physics in 1980, all degrees were taken at the

University of Mississippi. Additionally he has taken electrical engineering

courses from the Catholic University and physics courses from VPI. He

has worked at the Naval Surface Warfare Center for more than 34 years.

He has worked in radar, electromagnetics, signal processing, track

filtering, weapon's control systems, and guidance algorithms. He has over

one hundred and sixty technical publications in these areas as well as in

mathematics and physics. He is a senior member of the IEEE, a member

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26

of Society for Industrial and Applied Mathematics (SIAM), a Life Member

of the American Physical Society (APS), and a member of Sigma Pi

Sigma, the Washington Evolutionary Systems Society (WESS), and the

Washington Academy of Sciences.

Stephen R. Addison received the B.Sc (Hons) from the University of

Wales (now Cardiff University) in 1978, followed by an MS (1982) and

PhD (1984), all in physics. He has been on the faculty of the University of

Central Arkansas since 1984 where he currently serves as Professor of

Physics and Dean of the College of Natural Sciences and Mathematics. He

has been an active researcher in underwater acoustics, signal processing,

thermal physics, and nonlinear systems. He is a member of the Acoustical

Society of America, the American Association of Physics Teachers, the

Arkansas Academy of Sciences, IEEE, the Seismological Society of

America, Sigma Pi Sigma and Sigma Xi. Past offices include service as

President of the Arkansas-Oklahoma-Kansas Section of AAPT.

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Zt

Work Functions of

Thermally Roughened Surfaces of

Ni(111) and Pd(111)

G. N. Derry, E. H. Worth, M. Gross, and M. E. Kern

Loyola University Maryland

Abstract

The work functions of clean and microscopically well-ordered surfaces of

nickel and palladium single-crystal samples oriented to the (111) crystal

face were measured in ultrahigh vacuum using the photoelectron threshold

yield technique, resulting in @ = 5.68+0.03 eV for the Pd(111) surface and

d = 5.60+0.06 eV for the Ni(111) surface. The samples, although

microscopically ordered, were macroscopically roughened by the thermal

annealing process used during the preparation of the clean surfaces in

vacuo. The difference between the work functions of the two surfaces was

also found independently by measuring their contact potential difference

with a Kelvin probe, resulting in Ad = 0.15+0.08 eV. The Pd(111) result is

consistent with previous measurements in the literature, but the Ni(111)

result is not. The relationship between this inconsistency and the thermal

roughening of the surfaces is discussed.

Introduction

THE WORK FUNCTION OF A SOLID SURFACE depends on both the bulk

electronic structure of the solid and the locally relaxed electron density

distribution at the surface of the solid'. For this reason the work functions

of different crystal faces of a material differ from each other, and

considerable effort has been expended to obtain precise knowledge

concerning these work functions for the low index surface structures of

many metals*>. Despite this effort, reliable measurements are not available

for many metal surfaces®, and we have embarked on a program to measure

a number of these cases. In order to compare measurements with theoretical

calculations of the work function, the sample surface needs to be as close as

possible to ideal (i.e. perfectly ordered and free of contamination). In

technological applications, such as electrochemistry and microelectronics,

metal surfaces and interfaces may be far from ideal, making the effects of

such departures from ideality of some interest. In the present paper we

report on the work functions of two metal surfaces that are free of

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contamination and show evidence of microscopic crystalline order, but are

macroscopically disordered due to thermal roughening.

The samples used in this study are the (111) crystal surfaces of

nickel and palladium. The work function of Ni(111) has previously been

reported in twelve publications’'*, and most of the reported work functions

are fairly consistent with each other. The work function of Pd(111) has been

measured less extensively, reported in six publications'?** and with

somewhat larger scatter. The original intention of this study, which will

eventually be accomplished using re-polished surfaces, was to improve the

reliability and precision of both work function measurements, with a focus

on the palladium surface for which the existing data is sparser. The

unintended thermal roughening of the surfaces during the surface cleaning

and preparation procedures, however, presented the opportunity to examine

the effects of such roughening on the work functions of these metals under

otherwise controlled conditions. We report here the results of these

measurements.

Methods

All of the work reported here was performed in ultrahigh vacuum at

a system pressure of ~ 3x10° Pa. The analysis chamber is equipped with an

electron gun and a four-grid retarding field electron optics with which to

perform low energy electron diffraction (LEED) and Auger electron

spectroscopy studies of the surfaces. To measure contact potential

differences between the sample surfaces and a stainless steel probe head we

use a vibrating capacitor Kelvin probe. The Kelvin probe is mounted on the

chamber using a bellows so that it can be retracted when not in use. The

actual work function of each surface is measured using threshold yield

photoemission. Light from a monochromator mounted on a xenon arc lamp

is introduced into the chamber through a sapphire window and arrives at the

sample surface through a small aperture in a biased electron collector. The

relative light intensity as a function of wavelength had been previously

determined for this lamp, and these calibration data were used in the present

work. The emitted photocurrent is measured using an electrometer

connected to the otherwise isolated sample. The work function of the

sample is found from the dependence of the photocurrent yield on the

photon energy, using the method developed by Fowler’>.

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Phe

The samples are cleaned in vacuo using successive cycles of argon ion

sputtering and annealing at elevated temperatures, with a final “flashing” to

high temperature just prior to data acquisition. A large number of such

cycles is typically required before a clean and well-ordered surface, as

demonstrated by the Auger spectroscopy and electron diffraction results, is

obtained. The samples are heated by mounting them onto a potted ceramic

button heater using a tantalum cap. The heater is large enough to

accommodate both samples simultaneously. The entire unit, consisting of

the heater and both samples, is mounted on a manipulator that has XYZ

translational motion and polar angle rotation, allowing us to position either

sample for sputter cleaning, characterization by electron diffraction or

Auger spectroscopy, contact potential difference measurement, or

photocurrent measurement.

After both sample surfaces are simultaneously clean and well-

ordered, the work function of each surface can be measured using the

photoelectron yield. As an additional test, the difference between the work

functions of the two surfaces can be measured independently using the

Kelvin probe. This is accomplished by measuring the contact potential

difference between the probe and the sample surface for each surface,

followed by subtraction to eliminate the unknown work function of the

probe surface. By measuring the contact potential differences under

virtually identical conditions, we are able to minimize problems due to stray

capacitance efc.

The two samples used in this work are single crystals of nickel and

of palladium. Both samples are cut to expose the (111) Miller index of these

face-centered-cubic crystals. Preparation of the surfaces prior to insertion

into the vacuum system consisted of polishing with diamond paste of

successively smaller particle size from 10 pL to 0.1 w. Surface quality was

monitored by using an optical microscope and by reflection of a laser beam

from the surface. The samples were also rinsed with acetone and deionized

water before insertion into the chamber. The quality of the polished

surfaces, based on the methods mentioned, appeared to be very good at the

time they were installed and the chamber was pumped down. After ultrahigh

vacuum was achieved using turbomolecular pumping and _ titanium

sublimation pumping, the surfaces were cleaned and characterized in vacuo

as described above. Presumably due to residual stresses left over from the

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mechanical polishing process, the surfaces of both samples gradually

developed a macroscopically roughened morphology during the iterative

high-temperature annealing cycles.

Results

Both surfaces required extensive iterative cycling of ion

bombardment and thermal annealing. The primary contaminant that

segregated to the surface during the annealing process was sulfur, but this

was eventually eliminated after approximately fifty cleaning cycles

performed in ultrahigh vacuum over about three months. Microscopic

disorder caused by ion sputtering is healed by several hours of annealing at

approximately 900 K (the precise temperature 1s not known due to the

detachment of the thermocouple spot weld), after which both clean surfaces

were observed by electron diffraction to have microscopic order. The two

surfaces were judged clean by the absence of observed contaminants in their

Auger spectra, and the degree of microscopic order 1s documented in Figure

1 and Figure 2, showing typical LEED images for the surfaces during the

time period that the data was being acquired. As stated above, however, the

macroscopic morphology of both surfaces had slowly degraded over the

course of the annealing cycles, with the optically polished appearance

evolving into a dull matte appearance, despite the observed increase in

microscopic order. All of the results reported here were obtained using these

thermally roughened matte surfaces.

Threshold photocurrent data were obtained for each of the two clean

and annealed surfaces in eleven separate experimental runs, five for Ni(111)

and six for Pd(111). Cleaning cycles and surface characterization were

continued throughout this work, and each of these experimental runs was

preceded by a final flashing to eliminate any residual adsorbed gases, then

cooling to room temperature for data acquisition. The photoelectron yields

are fit to a Fowler curve” to obtain the work function. In this method we

use the dependence of the photoelectron yield Y on the photon energy near

the threshold, log(Y) < F(hf/kT). In this expression, F(x) is a universal

function derived by Fowler (the so-called “Fowler curve”) and f= v— gh

is the photon frequency shifted by an amount equal to the threshold

frequency. The amount of the shift (in energy) needed to obtain a good fit

to the data is equal to the work function of the sample surface. This

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procedure was performed both by using the traditional method”° of simply

rigidly shifting the horizontal axis and also by doing a least square fit to the

data, with these two methods never differing by more than 10 meV. Typical

examples of the results for each surface are shown in Figure 3 and Figure

4. Averaging the results of all experimental runs to obtain a final work

function value, we have for the Pd(111) surface @= 5.68+0.03 eV. For the

Ni(111) surface, the final work function value is @= 5.60+0.06 eV.

Figure 1—Low energy electron diffraction image for the clean Ni(111)

surface, incident beam normal to surface, incident beam energy 278 eV.

The Kelvin probe was used to measure the difference between the

work functions of the two surfaces in three separate data acquisition runs,

each preceded by the same final surface treatment described above. For each

measurement the probe was moved to several different lateral positions on

the sample surface to explore the degree of scatter that this caused. As

mentioned above, the actual output of each measurement was the difference

between the work function of the sample and the work function of the

(unknown) probe tip. By performing this measurement sequentially on each

of the two surfaces, the probe tip work function can be subtracted yielding

the desired difference between the Pd(111) and Ni(111) work functions.

The net result of all these measurements was Ag= 0.15+0.08 eV.

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Figure 2—Low energy electron diffraction image for the clean Pd(111)

surface, incident beam normal to surface, incident beam energy 276 eV.

Discussion

The most striking feature of these results is that the work functions

of the Ni(111) and Pd(111) samples are very close to each other. In the

threshold yield experiments the difference between the work functions is

only Ag = 0.08+0.09 eV. This small difference is surprising based on the

results available in the literature. For Pd(111) the average result for the work

function is @ = 5.67£0.12 eV based on previous measurements in the

literature’? **, which is very consistent with the results obtained here. For

Ni(111), on the other hand, the average result for the work function is ¢=

5.24+0.07 eV based on previous measurements in the literature’'®,

considerably smaller than the value obtained here. The Ag result from the

contact potential difference experiments also indicates that these two work

functions are closer to each other than their literature values suggest. The

difference between the values from the literature is Ag = 0.43+0.19 eV, in

contrast to the difference value of Ag= 0.15+0.08 eV measured here. While

this contact potential difference measurement is somewhat larger than the

difference between the threshold yield work function measurements, the

work function difference values are still consistent with each other given

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their uncertainties. In contrast, neither of these difference measurements is

consistent with the literature results.

Obviously the discrepancy is in the Ni(111) work functions. Equally

obvious is the possible explanation for such discrepancy, namely that the

macroscopically roughened surface used in the present work might have a

different work function than a smooth and well-polished surface. What

makes this question more interesting, however, is the excellent agreement

between the present results and the literature results for Pd(111), which is

also a macroscopically roughened surface. Why such thermal roughening

should affect the work function so differently in the two samples is

extremely unclear. An alternative explanation might be that the Ni(111)

values in the literature are subject to some systematic error; this is possible,

given that the majority of those measurements are based on ultraviolet

photoemission valence band cutoffs, and these measurements are subject to

several potential problems*’?*. However, three of those measurements*!*"'7

use the same technique used in the present work; moreover, it seems

unlikely that a systematic bias of this sort should be present in such a large

number of independent studies. The question of why this discrepancy exists

is very intriguing, and a key part of solving this mystery will be to re-

measure the Ni(111) and Pd(111) work functions using the same

methodology employed in the present work with samples that retain their

highly polished smooth surface morphology. This work is presently

underway in our laboratory.

In most practical device applications (such as energy conversion and

microelectronics) where there is an important dependence of device

behavior on the work function at some interface, the morphology of the

interfacial surfaces is more complex than that of a smooth surface/vacuum

interface. Theoretical understanding of the work functions of such complex

morphologies is not highly developed. For these reasons, the issues

broached by the results of this study, and their ultimate resolution, are of

considerable interest and importance.

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2.8

2.4

log(Y)

0.8

0.4

0 5 10 15 20 25

hf/kT

Figure 3—Fowler plot for typical Ni(111) photocurrent data; points are

logarithm of the measured yield near threshold; line is the theoretical

curve predicted by Fowler; horizontal axis is adjusted for best fit between

the data and the curve, resulting in the work function measurement.

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2.5

>

wer 1.5

it 0)

=)

ae

1 e

0.5 e

)

0 2 4 10 12 14

6 8

ht/kT

Figure 4—Fowler plot for typical Pd(111) photocurrent data; points are

logarithm of the measured yield near threshold; line is the theoretical

curve predicted by Fowler; horizontal axis is adjusted for best fit between

the data and the curve, resulting in the work function measurement.

Bio

Gregory N. Derry is Professor of Physics at Loyola University

Maryland. His research areas are ultrahigh vacuum surface physics,

nonlinear dynamics, and epistemological studies of science/religion issues.

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References

J. Holzl and F. K. Schulte, Work Functions of Metals, in Solid Surface Physics, ed.

by G. Hohler (Springer-Verlag, Berlin, 1979), pp. 1-150.

J.C. Riviere, Work Function: Measurements and Results, in Solid State Surface

Science (Vol. 1), ed. by M. Green (Decker, New York, 1969), pp. 179-289.

V. S. Fomenko, Emissive Properties of Materials, 3" ed. (Naukova Dumka, Kiev,

1970).

H. B. Michaelson, J. Appl. Phys. 48, 4729 (1977).

H. Kawano, Prog. Surf. Sci. 83, 1 (2008).

G. N. Derry, M. E. Kern, and E. H. Worth, J. Vac. Sci. Technol. A 33, 060801

(2015).

B. Lescop, A. Galtayries, and G. Fanjoux, J. Phys. Chem. B 108, 13711 (2004).

T. A. Callcott and A. U. MacRae, Phys. Rev. 178, 966 (1969).

F. J. Himpsel, J. A. Knapp, and D. E. Eastman, Phys. Rev. B 19, 2872 (1979).

. J. E. Demuth, Surf Sci. 65, 369 (1977).

. K. Giesen, F. Hage, F. J. Himpsel, H. J. Riess, and W. Steinmann, Phys. Rev. B 33, 5241

(1986).

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9691 (1992).

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(1997).

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Rey. Lett. 43, 966 (1979).

. P. Dolle, M. Tommasini, and J. Jupille, Surf Sci. 211/212, 904 (1989).

. J. A. Barnard, J. J. Ehehardt, H. Azzouzi, and M. Alnot, Surf, Sci. 211/212, 740 (1989).

. B. G. Baker, B. B. Johnson, and G. L. C. Maire, Surf. Sci. 24, 572 (1971).

. K. Gurtler and K. Jacobi, Surf Sci. 134, 309 (1983).

. W. Sesselmann, B. Woratschek, J. Kuppers, G. Ertl, and H. Haberland, Phys. Rev. B

35, 1547 (1987).

. J. Hulse, J. Kuppers, K. Wandelt, and G. Ertl, Appl. Surf. Sci. 6, 453 (1980).

. J. E. Demuth, Surf. Sci. 65, 369 (1977).

. R. Fischer, S. Schuppler, N. Fischer, Th. Fauster, and W. Steinmann, Phys. Rey. Lett.

70, 654 (1993).

. K. Wandelt and J. E. Hulse, J. Chem. Phys. 80, 1340 (1984).

. G.D. Kubiak, J. Vac. Sci. Technol. A 5, 731 (1987).

. R.F. Fowler, Phys. Rev. 38, 45 (1931).

A. L. Hughes and L. A. DuBridge, Photoelectric Phenomena, \* ed. (McGraw-Hill,

New York, 1932).

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. M. G. Helander, M. T. Greiner, Z. B. Wang, and Z. H. Lu, Appl. Surf. Sci. 256, 2602

(2010).

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Attention-Deficit/Hyperactivity Disorder (ADHD):

Reviewing the Neurocognitive Characteristics of an

American Epidemic

Jessica J. Stephens and Dana L. Byrd

Texas A&M University - Kingsville

Abstract

The childhood-onset symptom of inattention, often coupled with

hyperactivity and/or impulsivity, as well as the occurrence of its severity

beyond what is developmentally appropriate, have for decades been a

sufficient basis for a psychological or psychiatric diagnosis of Attention

Deficit Disorder (ADD) or Attention-Deficit/Hyperactivity Disorder

(ADHD). The distinction between symptoms and the variation of their

onset, severity, combination, and maturation course have resulted in marked

differences in the diagnostic prevalence and medical treatment of attention-

deficit disorder in children and adults. Many differences in the features of

ADHD have varied by country and over time, as well. The combination of

1) the core aspect of ADD/ADHD as being self-inhibiting behaviors typical

of an individual of younger age, 2) the diagnostic guides allowing for the

possibility of change and/or disappearance of some or all symptoms with

maturation, and 3) the evolution of our general view of these disorders as

having valid diagnosis and treatment-worthy presentation in adulthood,

leads to an interesting question: To what extent is ADD/ADHD a

developmental delay versus a life-long impairment? This manuscript

reviews research findings on the neural basis of attention-deficit disorder or

other disorders across childhood and on into adulthood, especially as they

pertain to the default mode network. The ultimate goal is to shed light on

the neurological, maturational, and genetic influences on the disorder.

Background

WHEN ASKED TO LABEL the typical behavioral traits of an average child,

common replies might describe impulsiveness, impatience, and heightened

energy. These mannerisms are shared by many children, possibly giving

insight into the present complications and criticisms associated with

accurately identifying and diagnosing Attention-Deficit Hyperactivity

Disorder (ADHD). These shared mannerisms are an impediment to the

functioning of those diagnosed with ADHD. In addition, the strength and

duration of symptoms may be key in accurately distinguishing between

children behaving within a normal developmental spectrum and those who

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are in need of treatment. In America, 12% of children between the ages of

12 and 17 have been reported as receiving a current or former diagnosis of

ADHD (NSCH, 2007). Adult prevalence of ADHD has been reported to

be only 4.4%, less than half the rate seen in children [1]. This fact

indicates a potential developmental issue at the core of the ADHD

phenomenon.

Some questions may arise regarding precisely when and how

certain characteristics seen in those diagnosed with ADHD cease to be a

part of the normal developmental process. To better understand the

prognosis of ADHD in those affected, we must understand the differences

between those diagnosed and those not diagnosed, including alterations in

the brain, especially of the default neural networks, over the course of the

disorder from childhood to adulthood. Findings from neurological testing

techniques may provide a window into the disorder, showing the ways in

which the brain’s structure and activity are different across certain

populations diagnosed with ADHD. These tests also give an understanding

of how behaviors and thinking patterns that are integral to the disorder can

be separated from those associated with simple immaturity. An

understanding of the theories around ADHD may give additional insights

into how we currently explain the disorder, and as such, some of these

theories will be included in this review. Finally, findings on the genetic

basis of the disorder have recently come to light, potentially offering

psychological professionals a better understanding of both the biological

underpinnings and course of the disorder, as well as the opportunity to

develop new methods of objectively diagnosing ADHD in the future. An

overview of the disorder is necessary for understanding some of its

mechanisms and manifestations, therefore, some notes on what a diagnosis

of ADHD signifies and how it is identified will follow.

- The Diagnostic and Statistical Manual of Mental Disorders

Description of ADHD

In the United States, the current version of the Diagnostic and

Statistical Manual of Mental Disorders (DSM), a diagnostic guide for all

psychological disorders, outlines characteristic symptom criteria of

ADHD. The DSM is written by a committee of experts under the

supervision of the American Psychiatric Association and has been updated

to a fifth edition, known as the DSM -V as of May 2013.

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The DSM-V listed the same basic symptomatic behaviors and

patterns of thought required for an Attention Deficit/Hyperactivity

Disorder diagnosis as was set by the previous DSM-IV edition [3]. These

include: symptoms being present in at least two environments that the

child is commonly exposed to; proof of a disturbance in the child’s ability

to maintain a routine quality of life or to complete tasks necessary for their

optimal growth and functioning; and/or the presence of symptoms that are

not better explained by a separate diagnosis. Patients must display at least

six features from one of two columns for a period greater than six months.

Column | lists nine criteria for inattention; column 2 lists nine criteria for

heightened activity/impulsive behavior.

The most striking addition to the diagnosis of ADHD made in the

DSM-V may be in the area of sub-categories for the disorder, which have

been entirely reformed. The term “ADD”, Attention Deficit Disorder

without hyperactivity, will no longer be used by physicians to diagnose a

child who clearly displays a significantly increased level of activity and

impulsive behavior. Rather, there are now specific emphases that can

define the predominant symptoms present in an ADHD child. Those who

display a maximum of two items in column 2 and at least six items in

column | will be diagnosed as “Predominantly Inattentive Presentation,”

while those who display at least six symptoms in column 2 without the

presence of at least six symptoms from column | for over six months will

be treated as “Predominantly Hyperactive/Impulsive.” Those with six or

more shared symptoms present from both columns will be diagnosed as

‘““Combined Presentation.”

While the symptoms of heightened activity and inattention remain

unchanged, the DSM-V has raised the minimum age at which symptoms

must have been present from 7 to 12.

Childhood ADHD

The first step of a child’s diagnostic process is usually initiated

when a lay adult reports a child’s aberrant behaviors to a health care

professional. It is often a school psychologist or a teacher who suggests

the potential diagnosis to the child’s parent. The parent may then seek out

confirmation of a formal diagnosis by their physician [2]. However, a

child sometimes displays abnormal behavior consistent with ADHD while

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in a physician’s office and will, therefore, be referred by their pediatrician

or general practitioner. In a sample of 3,483,089 children diagnosed with

ADHD, Zarin and colleagues (1998) discovered that an ADHD diagnosis

was much more likely to be given by a primary physician (75.4%) than a

psychiatrist (12.4%) or other mental health specialist (12.2%).

Prevalence rates for the diagnosis of childhood ADHD have varied

widely over the years from between 3% to 11% in 1997, 4.2% to 6.3% in

2003, and 5.29% listed in 2008, with a mean score of 5.96% over the

course of eleven years. The Centers for Disease Control and Prevention

[5] revealed in their findings from national survey compilations that the

diagnosis increased in prevalence from 5.5% in 2003 to 11% 1n 2011.

Adult ADHD

According to the DSM-V (2013) the difference between adult and

childhood ADHD is that, for adults to be diagnosed, ADHD symptoms

must have been present during childhood before the age of 12, even if the

disorder was not treated. While many symptoms, especially those of

hyperactivity and impulsivity, were typically reported as declining with

age, inattention deficits remained relatively constant. Similarly, the

majority of the 60% of individuals who were reported as going through a

remission of the disorder were said to display too few symptoms to garner

a formal diagnosis [19]. These findings are consistent with much of the

research in the area of maturation and ADHD, specifically regarding the

age-related decline of hyperactivity and impulsivity symptoms and the

steady or increased levels of inattention often reported in diagnosed adults.

Other findings on the adult manifestations of this disorder included

unusually high rates of mobility between jobs as well as abnormalities in

self-care, both of which might be indicators of impaired executive control,

including increased instances of substance abuse and inadequate nutrition

intake.

By the time a child who warrants a diagnosis becomes an adult, all

symptoms of ADHD were found to be less severe, more varied, and less

obvious. This population retained a slightly diminished level of efficiency

in prolonging concentration on tasks, yet displayed far Jess symptom

severity in regards to fidgeting, lack of impulse regulation, fleeting

interest, and stillness in structured settings for extended periods [1].

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Based upon the National Co-morbidity Survey Replication of

9,282 American participants, adults are deemed far less likely to be

diagnosed with ADHD than U.S. children, despite their diagnostic rates

remaining much higher than adults in other nations [1]. The diagnostic

frequency of adult ADHD was 4.4% of those sampled. This figure makes

up less than half of those individuals estimated as being currently

diagnosed with childhood ADHD. This is partially explained by the fact

that, until May of 2013, individuals diagnosed with Adult ADHD must

have had symptoms present in childhood before the age of 7 (now 12).

Other studies have found even lower rates of an ADHD clinical diagnosis

in adults. In a meta-regression analysis on the prevalence of adult ADHD

diagnosis done by Simon and colleagues [7], it was reported that only

2.5% adults were clinically diagnosed with the disorder. The rather stark

difference in prevalence rates for children and adults is most likely

indicative of a maturation change during the course of the illness.

ADHD and Gender

A remaining commonality between childhood and adult ADHD is

the population most affected: Caucasian males. Boys are nearly two and a

half times more likely than girls to receive a formal diagnosis, with rates

of 13.2% versus 5.6%, respectively [5]. It was found by Bruchmiiller ef al.

[9] that, despite both genders obtaining an ADHD diagnosis, a boy would

be 2-3 times more likely to receive treatment for the disorder than would a

girl. Some advocate the point of view that biological differences between

the two sexes influence their differences in the prevalence and course of

ADHD. Obrien ef al. [10] provide evidence that developmental and

biological distinctions may be the key to understanding the gender divide.

For instance, it is more common for boys to display problems with

working memory and motor skills than it is for girls. Additionally, male

children commonly manifest more pronounced problems with behavioral

inhibition and, as a result, receive more reprimanding for acting out

inappropriately. All this contributes to the greater likelihood of diagnosing

the predominantly hyperactive or combined subtype of the disorder.

Girls, conversely, tend to display symptoms more closely

associated with atypical planning, organizing, and using higher order

cognitive skills. Female children with ADHD often exhibit more

symptoms in the areas of goal setting and task completion, leading to a

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more common diagnosis of the predominantly inattentive variety of the

disorder.

Girls and boys tend to have very different courses of maturation in

brain areas such as the frontal lobes, temporal lobes, parietal lobes, and

grey matter of the cerebral cortex. In general, differences in symptoms

may be linked with developmental differences in prefrontal areas,

somatosensory cortex, and parietal lobes. This may explain the findings by

Skogi ef al. [11] concerning the differences found in the executive

functioning (EF) task performance of girls and boys who share an ADHD

diagnosis. They were assessed as having significantly different

performance scores in certain EF tasks, such as behavioral inhibition,

cognitive flexibility, word fluency, and working memory. The

performance of each gender on working memory tasks was determined to

be the EF measure showing the most substantial gender difference.

Structural MRI’s have shown that some of the aforementioned

areas of a boy’s brain typically mature at a rate 1 to 3 years behind the rate

seen in girls, especially in areas of high order cognitive functioning in the

cerebral cortex. These areas are associated with motor task coordination,

organizing sensory information, and perceptual responses to the

environment. Differences between the genders in these areas, which are

minimized over time, may lead to reduced symptom expression in boys as

they develop into adolescents and adults. To further investigate the role of

age, maturation, and the brain in Attention Deficit Hyperactivity Disorder,

we explore the findings of researchers who have studied the structural and

functional nature of the brain for child, adolescent, and adult populations.

Neurology of ADHD: Default Mode Network Research

Fair et al. [12] proposed that age-related symptom differences

found in children, adolescents, and adults diagnosed with ADHD could be

due to the developmental differences in default mode networks, or those

involved in attentional tasks associated with working memory. Working

memory describes both problem-solving and awareness, functions that are

created, in part, by associating retrieved and relevant long-term memories

with our current environmental perceptions. Children at age six had

significantly more trouble maintaining focus and reducing conscious

disruption than did adults. This was believed to be related to the fewer

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43

overall connections between networks in the fronto-parietal areas, which

are associated with higher order cognitive functioning and somatosensory

awareness, and those in the rest of the brain.

Adolescent brains develop midway through childhood and

adulthood in respect to neural network development, with connections

becoming strongest and most numerous in adult neural networks [12].

This finding might imply that with adulthood comes an overall greater

ability to maintain attention for extended periods due to enhanced

development of these networks within the brain.

Neurology of ADHD: Diffusion Tensor Imaging Studies

The brain’s grey matter predominately consists of neuronal (nerve)

cell bodies, unmyelinated axon terminals, dendrites, and synapses. Grey

matter cells are responsible for perceptual and sensory functions, motor

tasks, and activation of recall and communication. White matter in the

brain 1s composed almost entirely of fatty glial cells, which are responsible

for nourishment and insulation of cell bodies, as well as myelinating

axons. White matter plays a major role in the quick and coordinated

transmission of neuronal signals sent to and from grey matter all over the

nervous system. While grey matter serves many important functions in the

brain that could play a role in ADHD, including verbal expression,

emotional regulation, and sensory perception; white matter may play a

prominent role in higher order cognitive functions within the brain, due to

its part in the efficiency and speed of transmitting neural impulses. White

matter tends to be the focus of most Diffusion Tensor Imaging (DTI)

studies of ADHD.

Both white and grey matter can be studied extensively using DTI

technology. The test, which measures the flow of water through connected

nervous system tissue, provides a structural view of a neural region,

especially of interconnected tracts. An approximation of the degree of

connectivity may thus be achieved.

In a study using DTI technology on children with ADHD, Ashtari

et al. [13] found that a reduction of white matter volume was related to

diminished ability to prolong one’s concentration. A white matter volume

reduction was also found to relate to inhibited executive functioning in

abilities such as organizing, verbalizing speech, linguistic memory, and

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44

kinesthetic functioning. A lesion in the cerebellum revealed a similar

association. This led researchers to propose that the cerebellum may be of

much greater value to those trying to understand the underlying functional

problems associated with ADHD expression.

DTI studies have proposed that ADHD may be associated with

disrupted maturation of white matter pathways during adolescent and adult

development as well. These pathways connect distant areas of the central

nervous system, including those within the brain, to each other for

message transference. Grey matter communication 1s believed to be more

localized. After a DTI investigation on this notion Konrad and Eickhoff

[15] found that the normal developing brain follows a pattern of

maturation in a healthy child that is disturbed in a child with ADHD. This

design involves maturation of the brain’s default mode network (DMN),

which is partly related to spontaneous and self-referential thoughts

becoming more integrated and interconnected to the executive network as

a child matures into an adolescent and then an adult. They propose that

this may be one area where the ADHD brain differs from others. The

neurological connections in these pathways may be more highly

fragmented and segregated, therefore impeding top down control from the

executive centers of the cortex. Thus, more mature integration and top-

down control may be hindered by dysfunction or dysregulation of ADHD

individuals’ DMN, though it is unclear if this dysfunction is a life-long

disordered dysfunction, a developmental delay in the maturation of the

DMN in those with ADHD, or some combination of disordered

dysfunction and developmental delay.

Neurology of ADHD: Volumetric Studies

Irregular cross-communication and size disparities in particular

regions of the brain of those diagnosed with ADHD were discussed by

Krain and Castellanos [14] in their meta-review of literature on brain

development in diagnosed children. Of the differences between healthy

cohorts and those with the disorder the most significant were the

disruptions between the prefrontal lobe and basal ganglia, which work

conjointly to regulate responses to environmental stimuli. When compared

to control children, it was found that the combined cerebral volume in

children diagnosed with ADHD was reduced by 3.2% and that 48% of this

difference was due to the reduction of volume in the prefrontal cortex of

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the frontal lobes, an area linked with modulating impulses planning,

reasoning, judgment, memory, and higher order cognitive functions (i.e.,

“executive functions”’).

They also reported reduced grey matter and white matter volumes

in areas such as the corpus callosum, the right posterior areas, the

cerebellum, and a large portion of the left hemisphere. The corpus

callosum is a band of axons and other supporting tissue connecting the two

brain hemispheres, which allows for cross-communication between them.

The right posterior parietal cortex is thought to be responsible for spatial

perception, sensory-motor coordination, recall, and attention relevant to

physically navigating one’s environment. The cerebellum is the area of the

brain that is believed to be responsible for repetitive or synchronized

motor tasks, internal timing, and responsiveness shifts. It has also been

consistently found to be of smaller volume in children diagnosed with

ADHD. Durston ef al. [16] found similar substantial volume differences in

ADHD versus non-ADHD afflicted children (-4%) in cerebral regions and

the cerebellum.

Krain and Castellanos [14] discovered another group difference in

the brains of three sets of children: control children without ADHD,

children with ADHD who were medicated, and children with ADHD who

were not medicated. Prescription stimulant usage was identified as the

primary source of influence in regards to volume differences in the

cerebrums of these children. Both groups of children with ADHD had a

smaller volume than the control children of the same sex and age (-3.2%)

and this statistically significant difference remained constant throughout

adolescence. Furthermore, the group which differed in brain volume from

the control group was clearly the medicated group [14]. It should be noted

that it is possible the children on stimulant medications had smaller brain

volumes than their cohorts before initiating stimulant use, as this was not

accounted for in this study.

Neurology of ADHD: Positron Emission Tomography

Positron Emission Tomography (PET) scans have isolated glucose

level disparities between those with ADHD and healthy controls. It is

believed that the frontal regions of the brain in non-medicated adults with

ADHD contain reduced glucose levels when completing tasks associated

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with higher cognitive functions [17]. These brain metabolism differences

were seen largely in the frontal lobe during tasks requiring working

memory, task-switching, self-inhibition, and filtering interference, all of

which were considered executive functioning (EF) measures. Executive

functioning has long been an area of interest in studies which focus on

symptomology of ADHD. It was consistently found that the most common

performance differences between Adults with ADHD and Adults without

ADHD were measures of response time, cognitive planning and

organization, as well as working memory storage and manipulation tasks.

Magnetic Resonance Imaging Studies

In a healthy child the developing brain follows a pattern of

maturation that is believed to involve a reduction in connectivity between

short-term neural network pathways, which are thought to be responsible

for processing sensory information in the present moment [14]. The

pruning of these pathways may decrease the capacity of working memory

input. Short-term neural pathways are typically minimized as a child

develops into an adolescent, allowing for the long term pathways to

become fully mature and replace them. Long term pathways are believed

to allow for a stronger and more efficient relay of information stored 1n

permanent memory sites across the brain.

To uncover possible associations between ADHD and _ neural

pathway connectivity Konrad and Eickhoff [15] investigated findings from

18 structural and functional brain studies on participants with and without

ADHD. They determined that short-term neural pathway reduction may be

underused in the ADHD brain during maturation into adolescence. This

reduced pruning of short-term pathways may relate to low-level resting

sensory processing overwhelming the processing of higher-order cognitive

information, leading to difficulties in sustaining attention and solving

complex problems.

Due to limits on the capacity of functional and structural studies on

brain maturation, little can be conclusively said about how these

connections form and communicate. It has been discussed, however, that

after maturation, adolescents diagnosed with ADHD were commonly

atypical from healthy controls in a number of ways [14]. These included

hormonal influences on the brain at puberty, myelination (white matter

Washington Academy of Sciences

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development), connection distances of neural pathways, and_ the

connection strengths and numbers in various areas of the brain that

involve concentration and working memory, such as the fronto-cerebellar

region.

Durston ef al. [16] reviewed the literature summarizing

developmental changes found consistently in structural MRI studies. It

appears that, although the size of the brain does not increase after age: 3;

there are changes in the proportion of white and grey matter throughout

childhood and into adolescence. Myelination of the axons, which are

responsible for speed and efficiency of neuronal message transmission in

the white matter of the frontal and parietal areas, increases substantially

between the ages of 5 and 17 years. Symptoms of demyelination, or a

reduction in the myelin surrounding neurons, include cognitive disruptions

and difficulty with control of muscular movements.

Theories of ADHD: The Dynamic Developmental Theory

The Dynamic developmental theory of ADHD has been discussed

by Sagdvolden et al. [20], who propose that ADHD 1s caused by a lack of

appropriate nervous system directing of GABA, the most commonly

occurring inhibitory neurotransmitter of the nervous system, as well as a

lack of appropriate directing of glutamate, the most commonly occurring

excitatory neurotransmitter of the nervous system. They stated that this

was due to deficient levels of dopamine. Inadequate dopamine activation

was related to a reduction in the regulation of GABA and Glutamate in

maintaining neurological homeostasis. This was proposed as potentially

impairing self-reinforcing of the basic cognitive tasks and related

behaviors, such as motivation, attention, impulses, planning, and

excitation. The behavioral variables most closely associated with cortical

dopamine abnormalities are said to be sustained attention deficits and

improper organization of goals.

Theories of ADHD: The Executive Dysfunction Theory

The Executive Dysfunction theory is supported by many ADHD

researchers, including Barkely, Casstellanos and Tannock, Pennington and

Ozonoff, and Schaechar. This theory describes the central characteristics

of the disorder as being involved in deficits of behavioral appropriateness,

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rationality, short-term memory retention and processing, attentiveness, and

forethought. In their review of the theories of ADHD Johnson, Weirsema,

and Kuntsi [23] explain that executive function theory accepts that

disparities in the functioning of the basal ganglia, thalamus, and parietal

cortices, which are involved in neurological cross-communication,

processing movement, and environmental details, are abnormal in those

with ADHD. Irregularities in the fronto-striatal and fronto-parietal

cortices, which are associated with motor coordination and attentional

processing, respectively, have also been proposed as being related to

executive dysfunction.

Performance of executive functioning (EF) tasks, such as reward

postponement, short-term memory capacity, goal regulation, sustained

attention, and planning, is usually irregular in those diagnosed with

ADHD. Several cognitive functioning differences were found in a Meta-

Analysis of EF measures in the ADHD population [21]. Strong group

differences were found between those with and without a formal ADHD

diagnosis in areas of response inhibition, working memory, and planning,

with the diagnosed group displaying poorer capabilities in all areas.

Theories of ADHD: Working Memory Model

Baddeley initiated a model of working memory after attempting to

resolve the issues of how short-term memory works [22]. It was theorized

that a triad of working memory systems is in place which functions by the

simultaneous processing of information via visual-spatial, auditory, and

episodic interaction, thus leading to integration of stored long-term

memories with immediate memories being consolidated in the

hippocampus. This three category system overlaps with the cognitive tasks

being performed in the present moment, especially those involved with

logical assessment, recollection, and rationalization. Thus, Baddeley’s

working memory model gives insight into the immediate processing of

details as they are associated with stored information. This theory gives

insight into the attentional and EF measured differences which are

symptomatic of ADHD.

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Theories of ADHD: State Regulation Model

Another concept asserted as a possible explanation for ADHD that

has been investigated by Johnson, Weirsema, and Kuntsi [23] is the State

Regulation Model. This theory is based upon Sander’s model of Cognitive

Energy, where task efficiency in remembering, sensory encoding, and

motor reflexes are found to be irregular in those with ADHD. This means

the irregular cognitive energy distribution in the brain leads to task

performance disruptions [23].

State Regulation Model predicts that individuals diagnosed with

ADHD are prone to difficulties in regulating and organizing effortful

cognitions, especially when information is presented to the child in a slow

or periodic manner and when a response is required. This is most

specifically referred to as problems in activation, or in the effort needed to

incline an individual to act. The model concludes that problems in

allocating effortful cognitive resources to stimuli in the environment often

cause problems with the ability to properly evaluate environmental events

as well as slower response times during cognitive tasks.

Johnson et al. found that studies could reverse these effortful

deficits by having a reward stimulus incentive for ADHD diagnosed

individuals, as they showed comparable measures to controls without

ADHD who also received an incentive. This could indicate that the

effortful attentional processes of the ADHD brain may be in need of more

meaningful or motivational stimuli in order to act in a comparable way to

those individuals without the disorder. It is also possible that reducing the

arousal of cortisol, a steroid associated with stress responses and not a

problem of energy distribution and activation levels within the brain, leads

to inhibited activation of certain cognitive responses meant to act on

external stimuli [23].

ADHD Biomarkers: DRD4 Gene

Faraone ef al. [24], in their meta-analysis, compared the findings

of numerous studies on genetic influences of ADHD. It was concluded

that the most prominent genetic basis for ADHD 1s likely the 7 repeat

alleles of the Dopamine D4 receptor (DRD4) gene. DRD4 genes were

likened to those of a moderator for dopaminergic activity and act as

dopamine receptor agonists, while simultaneously reducing the synthesis

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of dopamine within the brain. It was discovered that there was a

significant relationship between the DRD4 gene and the risk of developing

ADHD in childhood: it is 14% greater than the average population. As

genes tend to interact and work together in concert when expressing

singular traits, the relative influence of only one gene for any given trait is

typically small. The expression of various symptoms of ADHD may

involve the DRD4 gene working simultaneously with several other

expressed genes which, in combination, assert characteristics of this

developmental disorder.

Faraone ef al. [24] reported that when DRD4 was inhibited in mice

bred without the gene, aka “Knockout mice,” dopamine was created in

excess within the brain, leading to both a reduction in the desire to seek

out novelty in environments and a hypersensitivity to mind altering

substances like alcohol, cocaine, and amphetamines. Both of these

discoveries are consistent with behavioral findings among many studies on

heightened novelty exploration and substance use in those with ADHD.

Those with the DRD4 gene, as opposed to the knockout mice without it,

might have a reduced overall synthesis of dopamine within the brain, and

may therefore seek out novelty and psychoactive substances to counter the

effects of the brain’s reduced dopamine creation. Dopamine and

noradrenaline are believed to play a role in the onset and expression of

ADHD symptoms, including deficits in those behavioral and executive

cognitive tasks possibly related to noradrenergic and dopaminergic

dysregulation [24].

ADHD and Biomarkers: Adrenergic Genes

In addition to dopaminergic genes other alleles related to the stress

hormone adrenaline are believed to play a role in symptomatic behavior of

ADHD. Comings [25] concluded from his meta-analysis that

hyperadrenergic genes relate more strongly to behaviors typical of ADHD

than do dopaminergic genes. Adrenergic genes play a role in the

transmission of and relationship between dopamine and noradrenaline in

the same areas of the brain where symptoms of ADHD manifest. When

adrenergic receptor cells were stimulated to fire in steady succession, it

was discovered that animals would display aberrant behavior such as

irritability, reduced attentiveness, proneness to diversion, and heightened

sensitivity to stimuli, all concurrent with ADHD symptoms.

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ADHD Biomarkers: Diagnostic Marker Genes

Pingault ef a/. [26] studied the genetic markers and behavioral

development of 8395 twin pairs in England and Wales for a longitudinal

comparison over the span of 8 years. Average scores for hyperactivity and

impulsivity declined from 6.0 to 2.9 after being measured at age 8 and age

16, respectively. Most of the inter-individual developmental differences

were linked with additive gene differences found within the genomes of

these individuals. Over half of the genes studied were isolated and found

to be related to the developmental course of ADHD from age 8 to age 16,

rather than the quality or quantity of the symptoms of ADHD. This could

reveal that most genes responsible for the behavior of the disorder relate to

the genetically predisposed development of the brain. This finding may be

crucial to understanding the differences in the developmental course of the

illness between populations. Also discussed was the diagnostic potential of

identifying vulnerability marker genes that relate to persisting symptoms.

These genes could be mapped and isolated from a blood, urine, or saliva

sample. If doctors can identify them in patients, they could inform parents

of children with an increased likelihood of being predisposed with the

disorder. This could lead to preventative measures to reduce the risk of

expressing symptoms in the future.

Diagnosing ADHD with Neuroimaging

Researchers [15, 16] have, by now, understood that ADHD 1s a

disorder that impairs response inhibition, or the ability to stop oneself

from performing an action. This symptom of ADHD has most often been

assessed using behavioral task monitoring, or “stop-task monitoring,”

which measures the speed of participant reaction and the errors

accumulated on an activity which primes users to make quick motor

decisions. By using this task monitoring test, it was proposed that the

brains of adolescents with ADHD would show physical indicators of the

disorder in some of its areas. Hart ef al. [17] discovered that fMRI

mapping of patterns in the brain can indicate differences not present in

those without the disorder. A 77% diagnostic rate was claimed by the

researchers. This diagnostic rate was found to be 90% accurate for the 30

ADHD diagnosed adolescents and 63% accurate for the 30 control

adolescents used. A subsequent study, which used the same brain mapping

and behavioral monitoring methods, found similar results [17]. Low

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52

activation during stop-task monitoring indicated physical differences in

the brains, specifically in the prefrontal, striatal, and temporo-parietal

regions of adolescents with ADHD. These differences were not present in

healthy controls and were only intermediately present in unaffected

siblings. If perfected, this type of physical examination of the brain may

be a more accurate way of observing and diagnosing the disorder than

more traditional subjective assessment of symptoms have been.

Conclusions

We found that separate studies varied drastically in the ongoing

clinical diagnosis of ADHD from childhood into adulthood, with ranges of

4-66% retention rates [7]. We think this is due to methodological

differences among studies. We propose that such differences are due to the

studies not using the same diagnostic instruments. Some studies used

quantitative assessments, while others used qualitative assessments of

symptoms. These qualitative methods included symptom check-lists, self-

reports, peer-reports, or professional reports used by caregivers and care

providers of the child. Such methods may have led to disparities in

measurements of inattention, hyperactivity, and impulsivity, which could

depend upon the diagnostic instruments and individuals administering

them for an assessment of symptoms.

Results from comparison studies of those with and without Adult

ADHD can be rife with differences in type, onset, quantity, and severity of

symptoms, suggesting possible reliability problems in current diagnostic

practices [1]. Future studies may want to control this by isolating and

using the diagnostic tools when comparing individuals who have been

formally diagnosed with ADHD.

Diagnosing ADHD may continue to become more objective as

ADHD marker genes and alleles are continuously studied and understood.

Genes may play a larger role in symptom type and severity as well as

symptom changes over the course of development and remission. It is also

becoming increasingly more likely that we will develop new testing

methods for identifying maturational markers of the disorder, potentially

present in white matter tracts and the default mode network. Further

insight into the basis of the disorder could give the diagnosed, their

Washington Academy of Sciences

53

families, and their physician new tools for preventing or managing the

Symptom trajectory of ADHD.

Bios

Jessica Stephens is currently a lecturer of Psychology courses at Texas

A&M University- Kingsville, where she completed her Master of Science

in Psychology. Ms. Stephens has been accepted into the Experimental

Psychology Health- PHD program at the University of Texas

at Arlington for the 2017 Fall semester, where she will pursue

comparative research on psychoactive drugs and related behavioral

variables.

Dana Byrd is an assistant professor in the Department of Psychology and

Sociology at Texas A&M University — Kingsville. Dr. Byrd’s research

focus is investigates the nature and development of higher-level cognitive

functions, using psychophysiological and neuroscientific measures.

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