Table Of ContentAssociation for Women in Mathematics Series
Ami Radunskaya · Rebecca Segal
Blerta Shtylla E ditors
Understanding
Complex
Biological
Systems with
Mathematics
Association for Women in Mathematics Series
Volume 14
SeriesEditor
KristinLauter
MicrosoftResearch
Redmond,Washington,USA
Association for Women in Mathematics Series
Focusingonthegroundbreakingworkofwomeninmathematicspast,present,and
future,Springer’sAssociationforWomeninMathematicsSeriespresentsthelatest
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Mathematicshasbeenanon-profitorganizationdesignedtohelpencouragewomen
and girls to study and pursue active careers in mathematics and the mathematical
sciencesandtopromoteequalopportunityandequaltreatmentofwomenandgirls
inthemathematicalsciences.Currently,theorganizationrepresentsmorethan3000
members and 200 institutions constituting a broad spectrum of the mathematical
community,intheUnitedStatesandaroundtheworld.
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Ami Radunskaya (cid:129) Rebecca Segal (cid:129) Blerta Shtylla
Editors
Understanding Complex
Biological Systems with
Mathematics
123
Editors
AmiRadunskaya RebeccaSegal
MathematicsDepartment DepartmentofMathematics
PomonaCollege VirginiaCommonwealthUniversity
Claremont,CA,USA Richmond,VA,USA
BlertaShtylla
MathematicsDepartment
PomonaCollege
Claremont,CA,USA
ISSN2364-5733 ISSN2364-5741 (electronic)
AssociationforWomeninMathematicsSeries
ISBN978-3-319-98082-9 ISBN978-3-319-98083-6 (eBook)
https://doi.org/10.1007/978-3-319-98083-6
LibraryofCongressControlNumber:2018959746
MathematicsSubjectClassification:92-06,92-B05
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Women Advancing Mathematical Biology
Workshop
Aim andScope
Informationaboutbiologicalsystemsiscollectedatafastrate.Whileitisbecoming
clearthatbiologicalsystemsarehighlyinterconnectedandcomplex,itisnotalways
clearhowtoorganizetheavailableinformationanddataaboutthesesystemsinorder
to make conclusions and predictions. Using mathematical formulations to frame
questions, explore patterns, and synthesize information can be quite powerful. To
advance our understanding of a rich array of biological systems, fifty researchers
cametogethertoworkonsixdifferentresearchproblemsinaworkshopheldatthe
MathematicalBiosciencesInstituteonthecampusofOhioStateUniversityWomen
AdvancingMathematicalBiology:UnderstandingComplexBiologicalSystemswith
MathematicswasheldonApril24–28,2017,inColumbus,Ohio,andwasorganized
by Ami Radunskaya, Rebecca Segal, and Blerta Shtylla. This volume contains
articles with results from each team, produced during the intensive one-week
workshopandthefollow-upcollaborationsthatemergedafterit(Fig.1).
HistoryandContext
Although progress has occurred in the representation of women in mathematical
sciences, the numbers are still unbalanced. In the most recent American Mathe-
matical Society Survey from 2015, only 24% of tenure-track mathematics faculty
are female (http://www.ams.org/profession/data/annual-survey/demographics). A
specific breakdown of distribution within different types of institutions (https://
www.womendomath.org/research/) gives an even more compelling picture of why
research workshops such as this one can be so valuable for the mathematics
community. Research mentoring and support from senior mentors is one key to
success, and a workshop environment provides a significant amount of interaction
inaconcentratedamountoftime.
v
vi WomenAdvancingMathematicalBiologyWorkshop
Fig.1 Groupphotographoftheworkshopparticipants
TheprimaryaimoftheWomeninMathematicalBiology(WIMB)workshopsis
tofosterresearchcollaborationamongwomeninmathematicalbiology.Participants
spend a week making progress on a research project and encouraging innovation
in the application of mathematical, statistical, and computational methods in the
resolutionofsignificantproblemsinthebiosciences.Theworkshopshaveaspecial
format designed to maximize the opportunities to collaborate. The groups are
structured to facilitate tiered mentoring. Each group has a senior researcher who
presents a problem. This person is matched with a co-leader, a researcher in their
fieldbutwithwhomtheyhavenotpreviouslycollaborated.Thegroupsarerounded
outwithresearchersatvariouscareerstages.Bymatchingseniorresearchmentors
with junior mathematicians, we expand and support the community of scholars in
themathematicalbiosciences.
To date, WIMB workshops have occurred at the IMA, NIMBioS, and MBI.
These workshops have been a part of the AWM’s NSF ADVANCE grant which
hassupported11ResearchCollaborationWorkshopsasof2018andhascommitted
tosupportingatleast9moreinavarietyofmathematical fields including control,
commutativealgebra,geometrydatascience,materials,operatoralgebras,analysis,
number theory, shape, topology numerical analysis, and representation theory. For
the Mathematical Biology workshops, each group continues their project together
toobtainresultsthataresubmittedtothepeer-reviewedAWMProceedingsvolume
for the workshop. The benefit of such a structured program with leaders, projects,
and working groups planned in advance is based on the successful WIN (Women
In Numbers) conferences and works in both directions: senior women will meet,
WomenAdvancingMathematicalBiologyWorkshop vii
mentor,and collaborate withthe brightestyoung women intheir fieldon apartof
theirresearchagendaoftheirchoosing,andjuniorwomenandstudentswilldevelop
their network of colleagues and supporters and encounter important new research
areastoworkin,therebyimprovingtheirchancesforsuccessfulresearchcareers.
All of the survey respondents said that the workshop was a good use of their
time. The group dynamics were overwhelmingly listed as a positive experience:
“The participants’ attitude: everyone was willing to learn and to teach, without
judgment.Thevarietyofexpertisepergroupseemedtobebalancedandefficient.”
Participantslefttheworkshopsatisfiedwiththeircontribution:“WhataPOSITIVE,
AFFIRMING experience! The group leaders were all very supportive, working
within their groups to find ways people could contribute even if the topic and
methodswerenewandsharingadviceandinsightwith*all*participants.”Groups
continuedtomeetinpersonorremotelyandmaintainedtheworkshopmomentum:
“Mygroupwasproductiveandenthusiasticthewholeweekanditwasagreatwork
environment. Doing math in an all-female group was a really positive experience
and I left feeling super motivated.” The participants enjoyed the energetic and
supportive research environment and the opportunity to connect with so many
researchers across all career levels. Almost all of the participants learned new
mathematics, new biology, or new computation tools to move the research project
inaproductivedirection.
Research
Within this volume are mathematical research papers covering a wide range of
applicationareas.Theworkcanbelooselygroupedintoafewgeneralapplication
areas:diseasespread,cancer,andflowoffluidsinandaroundorganisms.
Two groups examined the spread of disease under different scenarios. One
group looked at the importance of a unique individual (a superspreader) and
one group looked at the importance of the community network. To investigate
the impact of superspreaders on epidemic dynamics, the researchers formulated
deterministicandstochasticmodelsthatincorporateddifferencesinsuperspreaders
versusnonsuperspreaders.Inparticular,continuous-timeMarkovchainmodelswere
usedtoinvestigateepidemicfeaturesassociatedwiththepresenceofsuperspreaders
inapopulation.Inaseparateresearcheffort,anotherteamlookedattheimportance
and impact of the social network on disease spread. The network’s structure,
including group stability clustering, and an individual’s behavior and affiliation
choice all have some impact on the effect of disease spread. They considered
the impact of network structure on the circulation of ectoparasitic infections in
a population using two ODE models that each approximate a simplified network
model: one with uniform social contacts, and one with a few highly connected
individuals.
viii WomenAdvancingMathematicalBiologyWorkshop
AsafirststeptoexploreinfectiondynamicsandpossiblemanagementofAfrican
swinefever,athirdgroupdevelopedtwomathematicalmodelsofthelifecycleofthe
softbodiedtickO.moubata.Oneisacontinuous-timedifferentialequationmodel
that simplifies the tick life cycle to two stages, and the second is a discrete-time
differenceequationmodelthatusesfourstages.Bothmodelsusedtwohosttypes:
smallhostsandlargehosts,andbothmodelsfindthateitherhosttypealonecould
supportthetickpopulationandthatthefinaltickdensityisafunctionofhostdensity.
One research team worked on a mathematical model of multiple myeloma and
the role of the immune system in possible therapeutic interventions. The model
examined three distinct populations of the innate and adaptive immune system:
cytotoxic T cells, natural killer cells, and regulatory T cells. The system was
exploredcomputationallyandtheoreticallyandthelong-termbehaviorofthesystem
wasanalyzedtoidentifyequilibriaandtheirassociatedstability.
Tworesearchteamsworkedonfluidflowproblems:onelookedatthedynamics
of flow around an organism and one looked at internal blood flow. A nematocyst
is a specialized organelle within cells of jellyfish and other Cnidarians that sting.
It contains a barbed, venomous thread that accelerates faster than almost anything
else in the animal kingdom. A model of the fluid-structure interaction of the
barbedthreadacceleratingthroughwatertopunctureitspreywascreatedusingthe
immersed boundary method. This work is important for understanding the regime
of flow velocities needed to hit prey and the implications for the design of the
nematocyst.
Ourfinalteamlookedatthevasculatureoftheplacentatoexploretherelationship
between vessel networks in control placenta compared to placentas of individuals
at risk for autism. They developed a mechanistic model using a Monte-Carlo
simulation to mimic three mechanisms for controlling vascular growth: vessels
grow faster/longer, vessels terminate more frequently before branching, and flow
directions are more tightly controlled. For each mechanism, they analyzed simu-
lated vascular networks based on structural properties and blood flow, assuming
Poiseuille’slawanddistensiblevessels.Furthermore,thisstudyrequiresareliable
andautomatedmechanismtoextractthevascularnetworks.Sothegroupdeveloped
twoalgorithmstoextractthevascularnetworkfrommedicalimages.Onewasbuilt
upon a directional multiscale mathematical framework based on a combination of
shearletsandLaplacian eigenmaps andisabletoisolatevesselswithhighsuccess
inhigh-contrastimagessuchasthoseproducedinCTscans.Thesecondalgorithm,
which applies a conditional generative adversarial neural network (cGAN), was
trained to simulate a human-traced PCSVN given a digital photograph of the
placentalchorionicsurface.
WomenAdvancingMathematicalBiologyWorkshop ix
ConcludingRemarks
The groups are continuing to work on furthering the projects and presenting their
work at conferences. Past workshops have had successful research collaborations
that last for years following the workshop. The more community building we can
accomplish,thehighertherateofsuccessforwomenandmathematics.Thismeans
moreinnovativeresearchwillbeproducedandbuiltuponbytheentiremathematics
community.
Claremont,CA,USA AmiRadunskaya
Richmond,VA,USA RebeccaSegal
Claremont,CA,USA BlertaShtylla
June14,2018
