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
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
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
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
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
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
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)
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
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)
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
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)
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
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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More Graph Theory (2/5)
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
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].
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
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More Graph Theory (4/5) Then we split the
hemispheres taking
the graph of each
hemisphereseparately
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
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More Graph Theory (5/5)
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
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)
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
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)
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
REGARDINGTHE GE WEOBSERVETHAT BOTHMALES ANDFEMALESSEEM TOHAVE MOREEFFICIENTGRAPHS INTHE LEFTHEMISPHERECOMPAREDTO THE RIGHTONE.HOWEVERTHEDIFFERENCEBETWEEN
THE GEAMONG THE
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Results (3/8)
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
THIS GIVESUS AFURTHEREVIDENCETO
SUPPORTTHATFEMALESUSE THEIRBOTHHEMISPHERES TO BEARON TWO-DIGITMULTIPLICATIONS,
THATS WHYBOTH
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Results (4/8)
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
SAMELY, WECANCONCLUDEFOR MALESTHAT THEIRRIGHTHEMISPHERES GLOBALEFFICIENCYIS TOO LOW,COMPAREDTO THELEFTS ONE,BECAUSETHEY ARENOT BASEDON THEIRRIGHTHEMISPHERE TO SOLVEDIFFICULTARITHMETIC
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Results (6/8)
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
SO IT SEEMSTHAT FORBOTHMALES ANDFEMALES
RIGHTHEMISPHERE IS MOREFAULTSTOLERANTIN
CONTRASTTO THE LEFTONE,BECAUSETHE RIGHTHEMISPHER
E IS NOTTHE
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Results (7/8)
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
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)
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
THE
FEMALES
USE BOTH
HEMISPHER
ES, SO THERIGHT
HEMISPHER
E IS LESS
FAULTS
TOLERANT
COMPARED
TO THERIGHT ONE.
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References
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
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
BIBE 2012 | 11-13 Nov. 2012 | Larnaca Cyprus
Any Questions?Manousos KladosPhD Candidate -- Research Assistant
Group of Applied NeurosciencesLab of Medical Informatics
School of Medicine
Aristotle University of Thessaloniki
mklados@med.auth.gr
___________________________________
Tel: +30-2310-999332
Fax:+30-2310-999263
Website: http://www.manousosklados.
eu/
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