Mathematical Biology

If Space Turned out to be Time: Resonances and Patterns in the Visual Cortex

Speaker: 
Bard Ermentrout
Date: 
Wed, Oct 9, 2019 to Thu, Oct 10, 2019
Location: 
PIMS, University of Manitoba
Conference: 
PIMS-UManitoba Distinguished Lecture
Abstract: 

When subjects are exposed to full field flicker in certain frequencies, they perceive a variety of complex geometric patterns that are often called flicker hallucinations. On the other had, when looking at high contrast geometric patterns like op art, shimmering and flickering is observed. In some people, flicker or such op art can induce seizures. In this talk, I describe a simple network model of excitatory and inhibitory neurons that comprise the visual area of the brain. I show that these phenomena are reproduced and then give an explanation based on symmetry breaking bifurcations and Floquet theory. Symmetric bifurcation theory also shows why one expects a different class of patterns at high frequencies from those at low frequencies.

 

On the other hand, the visual system is also very sensitive to specific spatial frequencies and this sensitivity can be pathological in the case of so-called pattern-senstive epilepsy. It has been shown that certain types of "op art"can cause visual discomfort. We show that the network that we used in flicker is also sensitive to spatially periodic inputs and suggest that a Hopf bifurcation instability is responsible for the discomfort and seizures.

 

Speaker Biography

Bard Ermentrout received his PhD in Theoretical Biology at the University of Chicago and was a postdoctoral fellow at the NIH from 1979-1982. He has been at the University of Pittsburgh since then. He is the author of over 200 papers and two books as well as the simulation package, XPPAUT. He is a Sloan Fellow and a SIAM Fellow and received the Mathematical Neuroscience Prize in 2015.

Class: 

DINOSAUR WARS: Extinction by Asteroid or Volcanism? Are we the Dinosaurs of the 6th Mass Extinction?

Speaker: 
Gerta Keller
Date: 
Thu, Jul 25, 2019
Location: 
PIMS, University of Victoria
Conference: 
Hugh C. Morris Lecture
Abstract: 

For the past 40 years the demise of the dinosaurs has been attributed to an asteroid impact on Yucatan, a theory that is imaginative, popular and even sexy. From the very beginning, scientists who doubted this theory were threatened into silence or their careers destroyed by the main theory proponents. Thus began the Dinosaur wars in 1980 – and still continuing. As in any war, there are two sides to the Dinosaur wars. The majority believes an asteroid hit Yucatan and instantaneously wiped out 75% of all life including the dinosaurs in a global firestorm and nuclear type winter. A small minority tested this theory and found contrary evidence that supported Deccan volcanism in India that caused rapid climate warming due to greenhouse gases (CO2), environmental stress, acid rain and ocean acidification culminating in the mass extinctions. This lecture highlights the four decades of the dinosaur wars, the increasing acceptance of volcanism’s catastrophic effects and likely cause of the mass extinction and the resulting ad hoc revisions to accommodate the impact theory. The talk ends with the ongoing 6th mass extinction initiated by rapid fuel burning that is causing the most rapid climate warming in Earth’s history and ocean acidification, which is predicted to reach the 6th mass extinction in as little as 50-75 years and maximum of 250 years. We could be the Dinosaurs of the 6th mass extinction.

 

Speaker Biography

Gerta Keller is Professor of Paleontology and Geology in the Geosciences Department of Princeton University since 1984. She was born on March 7, 1945 in Liechtenstein. She grew up on a small farm in Switzerland as the sixth of a dozen children with no prospect for education. At age 14 she entered apprenticeship as dressmaker, at 17 she worked for the DIOR Fashion House in Zurich. With no prospect for advancement she began her adventure travels through North Africa and the Middle East, supporting herself by waitressing. She immigrated to Australia at 21, was shot by a bank robber and nearly died at 22. After recovery, she resumed her adventure travels through Southeast Asia and arrived in San Francisco in 1968. There she found the first opportunity for education and entered City College, continued her undergraduate studies at San Francisco State College majoring in Anthropology and Geology, concentrating on climate and environmental changes and their effects on mass extinctions. She was awarded a Danforth Fellowship for her graduate studies at Stanford University in 1974 and received her PhD in 1978. She continued her work at Stanford University and the U.S. Geological Survey in Menlo Park and steadily researched climatic and environmental effects on life all the way back to the dinosaur mass extinction 66 million years ago. In 1984 she was hired as tenured faculty at Princeton University.

 

Prof. Gerta Keller’s major research and discoveries ranged from climate change and its effects on ocean circulation, ocean anoxic events, polar warming, Deccan volcanism, comet showers, extraterrestrial impacts, the dinosaur mass extinction, the age of the Chicxulub impact and the 6th mass extinction. Her research frequently challenged accepted scientific dogma and placed her at the center of acrimonious debates fighting for survival of truth-based evidence. All but the cause of the Chicxulub impact were soon accepted by scientists and integrated into new research. After four decades, impact proponents still fiercely defend the impact theory, deny contrary evidence and at best incorporate volcanism as ad hoc revisions, proclaiming the impact triggered volcanism that caused the mass extinction.

 

Gerta Keller has over 260 scientific publications in international journals and is a leading authority on catastrophes and mass extinctions, and the biotic and environmental effects of impacts and volcanism. She has co-authored and edited several books and she has been featured in many films and documentaries by very popular TV channels and Film Corporations, including BBC, The History Channel, and Hollywood.

Class: 

Public Goods, from Biofilms to Societies.

Speaker: 
Simon Levin
Date: 
Sat, Jun 15, 2019
Location: 
PIMS, University of Victoria
Conference: 
Levin Fest
Abstract: 

Ecological and economic systems are alike in that individual agents compete for limited resources, evolve
their behaviors in response to interactions with others, and form exploitative as well as cooperative interactions as a result. In these complex adaptive systems, macroscopic properties like the flow patterns of resources like nutrients and capital emerge from large numbers of microscopic interactions, and feed back to affect individual behaviors. In this talk, I will explore some common features of these systems, especially as they involve the evolution of cooperation in dealing with public goods, common pool resources and collective movement. I will describe examples from bacteria and slime molds to vertebrate groups to insurance arrangements in human societies and international agreements on environmental issues.

Class: 

Mathematical ecology: A century of progress, and challenges for the next century

Speaker: 
Simon Levin
Date: 
Sat, Jun 15, 2019
Location: 
PIMS, University of Victoria
Conference: 
Levin Fest
Abstract: 

The subject of mathematical ecology is one of the oldest and most exciting
in mathematical biology, and has helped in the management of natural
systems and infectious diseases. Though many problems remain in those
areas, we face new challenges today in finding ways to cooperate in
managing our Global Commons. From behavioral and evolutionary
perspectives, our societies display conflict of purpose or fitness across
levels, leading to game-theoretic problems in understanding how
cooperation emerges in Nature, and how it might be realized in dealing with
problems of the Global Commons. This lecture will attempt to weave these
topics together, tracing the evolution from earlier work to challenges for the
future.


 



Simon Levin is the J.S. McDonnell distinguished university professor in Ecology and Evolutionary Biology at Princeton University. He is a recipient of the National Medal of Science, the Kyoto Prize and a Robert H. MacArthur Award.

Class: 

Optimizing Biogas Generation Using Anaerobic Digestion

Speaker: 
Gail Wolkowicz
Date: 
Tue, Nov 27, 2018
Location: 
PIMS, University of Manitoba
Conference: 
PIMS-UManitoba Distinguished Lecture
Abstract: 

Anaerobic digestion is a complex, naturally occurring process during which organic matter is broken down into biogas and various byproducts in an oxygen-free environment. It is used for bioremediation and the production of methane which can be used to produce energy from animal waste. A system of differential equations modelling the interaction of microbial populations in a chemostat is used to describe three of the four main stages of anaerobic digestion: acidogenesis, acetogenesis, and methanogenesis. To examine the effects of the various interactions and inhibitions, we study both an inhibition-free model and a model with inhibition.

A case study illustrates the importance of including inhibition on the regions of stability. Implications for optimizing biogas production are then explored. In particular, which control parameters and changes in initial conditions the model predicts can move the system to, or from, the optimal state are then considered. An even more simplified model proposed in Bornh\”{o}ft, Hanke-Rauschenback, and Sundmacher [Nonlinear Dynamics 73, 535-549 (2013)], claimed to capture most of the qualitative dynamics of the process is then analyzed. The proof requires considering growth in the chemostat in the case of a general class of response functions including non-monotone functions when the species death rate is included.

Class: 

The Mathematics of Social Evolution

Speaker: 
Troy Day
Dave McLeod
Date: 
Thu, Mar 22, 2018
Location: 
PIMS, University of Manitoba
Conference: 
PIMS-UManitoba Distinguished Lecture
Abstract: 

How social traits evolve remains an open question in evolutionary biology. Two traits of particular interest are altruism (where an individual incurs a cost to help others) and spite (where an individual incurs a cost to harm others). Both traits should be evolutionarily disadvantageous because any benefits arising from these behaviours are also available to “cheaters” who do not pay the cost of displaying altruism or spite themselves. In this talk I will show how stochasticity can sometimes reverse the direction of evolution and drive the emergence of these behaviours. I will start with an individual-based evolutionary model and then approximate it using a system of stochastic differential equations (SDEs). These SDEs are then be reduced to a single SDE on a “slow manifold” governing the evolutionary dynamics. A rather complete analysis of this SDE is then possible, showing exactly when and how stochasticity can drive the evolution of altruism and spite.

Biography:

Tryo Day is a Professor and former CRC in the Department of Mathematics and Statistics at Queen’s University. His research interests involve evolutionary theory, including the evolution of pathogen virulence, drug resistance, social traits, and epigenetic inheritance.

Dr. Day is coauthor (with James Stewart) of the textbooks “Biocalculus: Calculus, Probability and Statistics for the Life Sciences”, and (with Sarah P. Otto) “A Biologist’s Guide to Mathematical Modeling”. He is an Elected Fellow of the Royal Society of Canada and the AAAS, and is the recipient of a Killam Research Fellowship, a Steacie Fellowship, the CAIMS Research Prize, and the Steacie Prize.

Class: 

The Emerging Roles and Computational Challenges of Stochasticity in Biological Systems

Speaker: 
Linda Petzold
Date: 
Fri, Mar 28, 2014
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 

In recent years it has become increasingly clear that stochasticity plays an important role in many biological processes. Examples include bistable genetic switches, noise enhanced robustness of oscillations, and fluctuation enhanced sensitivity or “stochastic focusing". Numerous cellular systems rely on spatial stochastic noise for robust performance. We examine the need for stochastic models, report on the state of the art of algorithms and software for modeling and simulation of stochastic biochemical systems, and identify some computational challenges.

Class: 

Using epidemiological data to understand within-host parasite dynamics of malaria infection

Speaker: 
Miles Davenport
Date: 
Sat, Jan 19, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Disease Dynamics 2013
Abstract: 

Using epidemiological data to understand within-host parasite dynamics of malaria infection.

Class: 

Public Health Decision-Making in Global HIV/STIs

Speaker: 
David Wilson
Date: 
Fri, Jan 18, 2013 to Sat, Jan 19, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Disease Dynamics 2013
Abstract: 

Public Health Decision-Making in Global HIV/STIs

Class: 

Combatting Neglected Disease Leishmaniasis in India: Identifying True Burden & Designing Efficient Control Policy

Speaker: 
Anuj Mubayi
Date: 
Sat, Jan 19, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Disease Dynamics 2013
Abstract: 

Combatting Neglected Disease Leishmaniasis in India: Identifying True Burden & Designing Efficient Control Policy

Class: 

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