towards a graph theoretical approach to study gender

7/30/2019 Towards a Graph Theoretical Approach to Study Gender

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Gender differences inmathematical abilities Gender differences in mathematical abilities,

still concern the scientists who are trying to

investigate the females underrepresentationat

difficult mathematics [1-2]. Both parents and teachers report that males

seem to perform better in complex

mathematics compared to females. Whats going on the brain?

BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus


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Anatomical Differences


Males have larger cerebra compared to femalesof the same age and health status [6].

This difference is most prominent in the frontal andthe occipital lobes, bilaterally [7]

Males brain have a thicker right hemisphere

Females have larger corpus callosum in contrastto males [8-10]

The larger corpus callosum allows more information toflow between the left and the right hemisphere.

women use their both hemispheres, they tend tocreate more synapses between them


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Graph Theory


We have used Graph Theory to check the

aforementioned assumption.

Graph is a mathematical representation of a

set of objects where some of them areconnected by links. These interconnected

objects are called vertices or nodes while the

links that connect some pairs of vertices arecalled edges.


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Participants


11 Males & 11 Females

Normal or corrected to normal vision

They were refrained from any alcohol or caffeine

consumption the day before the experiment. They were also asked to sleep as adequately and

comfortably as possibly achievable the nightbefore the experiment.

They also signed an informed consent form, whilethe experimental protocol was approved by theethics committee of the medical department.


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Experimental Design (1/2)


The EEG recordings were performed in darkelectrical and sound attenuated room.

They were lying in a comfortable chair and the

stimuli were given with a laptop about 80 cm infront of the individual.

The EEG signals were recorded with 31electrodes placed on the scalp according to

10/20 International System). The signals were amplified and then digitized

at 500 Hz and online filtered (1-200 Hz)


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Experimental Design (2/2)


In order to examine the cerebral responses tomathematical stimuli, two different tasks wereused during the EEG recordings.

The first one, which was served as the controlone, appears a white cross to a black screen forthirty seconds (CTRL)

The second one included eight trials of twodigitmultiplications (MULT) (e.g.31x24)

10 secs segments, without any visible artifactswere chosen for further analysis.


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Cortical Activity Cortical Activity was computed by

using an average head modelfrom the reconstruction of 152normal MRI scans(http://www.loni.ucla.edu/ICBM/)

The four different compartments ofthe head model (scalp, outer andinner skull, cortex) were extractedusing the Boundary ElementMethod (BEM). BEM isimplemented in the Brainstormtoolbox

Regarding the regularized solutionof the linear inverse problem, wehave used the column-normnormalization, resulting to atransition kernel from our 28 scalp

signals to 258 cortical signalsBIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus


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Our Cortex Model



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More Graph Theory (1/5)


The 258 dipoles are the nodes of our graph.

In order to setup the graph we have to clarify

the connections among the nodes.

The functional connectivity of the cortical sourceswas computed using the Mutual Information

Yy Xx ypxp

yxpyxpYXI

)()(

),(log),(),(

functionondistributiyprobabilitjointThe:),( yxp

functionondistributiyprobabilitmarginalThe:)(xp


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For every subject we have formed a 258x258

adjacency matrix, using the mutual informationindex.

In the current analysis we used binary andundirected graphs.

Binary means that two nodes will be connected or

not.

Undirected means that we have not any

information about the direction of the connection

among two nodes.


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More Graph Theory (3/5) In order to pass

from the AMs to

binary and

undirected graphs,having a

representation of the

populations

behaviour, we haveemployed a methodproposed by [19].



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More Graph Theory (4/5) Then we split the

hemispheres taking

the graph of each

hemisphereseparately



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Graph Parameters:

Density: The density (K) of a graph is the ratio of thenumber of edges across the number of possible

edges.

Global Efficiency: Latora and Marchiori [22] definedthe efficiency of the path between two vertices as the

inverse of their shortest distance. So the Global

Efficiency is the mean of the efficiencies of all paths.

Local efficiency: Local efficiency of a graph is theaverage of the global efficiencies of each subgraph.

The subgraphs are formed by removing the ith node,

and taking the rest nodes which were connected to

the removed one.


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Results (1/8)


HYPOTHESIS

CONFIRMED

MALES GRAPHOF THE LEFT

HEMISPHERE

IS MORE

DENSE

COMPARED TO

THE RIGHTONE

FEMALES

GRAPHS OF

BOTH

HEMISPHERES

DOESNT SEEMTO HAVE ANY


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Results (2/8)


REGARDINGTHE GE WEOBSERVETHAT BOTHMALES ANDFEMALESSEEM TOHAVE MOREEFFICIENTGRAPHS INTHE LEFTHEMISPHERECOMPAREDTO THE RIGHTONE.HOWEVERTHEDIFFERENCEBETWEEN

THE GEAMONG THE


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Results (3/8)


THIS GIVESUS AFURTHEREVIDENCETO

SUPPORTTHATFEMALESUSE THEIRBOTHHEMISPHERES TO BEARON TWO-DIGITMULTIPLICATIONS,

THATS WHYBOTH


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Results (4/8)


SAMELY, WECANCONCLUDEFOR MALESTHAT THEIRRIGHTHEMISPHERES GLOBALEFFICIENCYIS TOO LOW,COMPAREDTO THELEFTS ONE,BECAUSETHEY ARENOT BASEDON THEIRRIGHTHEMISPHERE TO SOLVEDIFFICULTARITHMETIC


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Results (6/8)


SO IT SEEMSTHAT FORBOTHMALES ANDFEMALES

RIGHTHEMISPHERE IS MOREFAULTSTOLERANTIN

CONTRASTTO THE LEFTONE,BECAUSETHE RIGHTHEMISPHER

E IS NOTTHE


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Results (7/8)


WE ALSO

OBSERVE THAT

MALES SEEM

TO HAVE

GREATER

DIFFERENCEOF THEIR

LOCAL

EFFICIENCY

AMONG THE

TWO

HEMISPHERES

COMPARED TOFEMALES,

WHICH IS

EXPLAINED BY

THE FACT THAT

MALES USE

MORE THEIR

LEFT


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Results (8/8)


THE

FEMALES

USE BOTH

HEMISPHER

ES, SO THERIGHT

HEMISPHER

E IS LESS

FAULTS

TOLERANT

COMPARED

TO THERIGHT ONE.


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References


1. National Academy of Sciences, Beyond Bias and Barriers: Fulfilling the Potential ofWomen in Academic Science and Engineering. National Academies Press,Washington DC, 2006.

2. DF Halpern, CP Benbow, DC Geary, RC Gur, JS Hyde, and MA Gernsbacher TheScience of Sex Differences in Science and Mathematics. Psychological Science inthe Public Interest, August 2007 8, pp.1-51.

3. ZF Zaidi. Gender Differences in Human Brain: A Review, The Open Anatomy

Journal, 2010 2, pp.37-554. ER Sowell, BG Peterson,E Kan, et al. Sex differences in cortical thickness mapped

in 176 healthy individuals between 7 and 87 years of age. Cereb Cortex 2007 17,pp.1550-1560.

5. CM Leonard, S Towler, S Welcome, et al. Size matters: cerebral volume influencessex differences in neuroanatomy. Cereb Cortex 2008 18(12), pp. 2920-2931

6. KM Bishop, D Wahlsten. Sex differences in the human corpus callosum: myth orreality? Neurosci Biobehav Rev 1997 21(5), pp.58- 60.

7. E Luders, KL Narr, PM Thompson, et al. Gender effects on cortical thickness andthe influence of scaling. Hum. Brain Mapp 2006 27(4),pp.314-324

8. V Latora and M Marchiori. Efficient Behavior of Small-World Networks Phys. Rev.Lett. 2001 87, 198701


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Thank You Very Much


Any Questions?Manousos KladosPhD Candidate -- Research Assistant

Group of Applied NeurosciencesLab of Medical Informatics

School of Medicine

Aristotle University of Thessaloniki

[email protected]

___________________________________

Tel: +30-2310-999332

Fax:+30-2310-999263

Website: http://www.manousosklados.

eu/

towards a graph theoretical approach to study gender

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