A continuation of the workshop Few-Body Dynamics in Atoms, Molecules, and Planetary Systems, held between June 28 and July 1, 2010, at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, CEMAD-2013 aims to bring together experts in celestial mechanics and semi-classical theory, as applied to the study of atoms and molecules, for the benefit of all those involved. The main emphasis is on the mathematical aspects of these research fields. This event is part of the initiative Mathematics of the Planet Earth (MPE-2013) as well as a satellite meeting of the Mathematical Congress of the Americas (MCA-2013). For more information on how to participate see the CEMAD 2013 website.

Announcing PACIFIC NORTHWEST THEORY DAYS in Victoria!

We proudly invite you to attend the 3^rd Pacific Northwest Theory Days in Victoria, BC on May 4-5, Saturday and Sunday, with a special focus on Theory of Algorithmic Networks and Randomization.

We have a fabulous list of distinguished invited speakers, from member institutions  as well as guest speakers from IBM Almaden and 3(!) different research groups (theory, crypto, and systems) at Microsoft Research in Redmond, INRIA Rennes, University of Washington and ETH.

Topics include communication complexity, streaming, sampling and approximation algorithms, electronic voting, computational biology and distributed computing.

Registration is free but please register so we can provide enough lunch and beverages: http://www.pims.math.ca/scientific-event/130504-t3pntd

See this site for local information. Students are especially welcome; a limited amount of travel expenses is available.

This event is sponsored by the  Pacific Institute of Mathematical Sciences (PIMS) CRG on Algorithmic Theory of Networks and Randomization.

Tentative Schedule

Saturday May 4 in David Strong Building C103

10:00 Coffee

11:00 "Spectrally Thin Trees" Nick Harvey (UBC)

12:00  "Vertex Sparsifiers"  Konstantin Makarychev (Theory, Microsoft Research)

Lunch 1-2

2:00 "Low Rank Approximation and Regression in Input Sparsity Time" David Woodruff (IBM Almaden)

3:00 A Randomized Rounding Approach for the Traveling Salesman Problem" Mohit Singh  (Theory, Microsoft Research)

Break

4:15 "Tight Lower Bounds for Greedy Routing in Higher- Dimensional Small-World Grids"  Philipp Woelfel (U. Calgary)

Sunday May 5 in David Strong Building C103

9:00  "Communication complexity and parallel query processing" Paul Beame (U Washington)

10:00 "Direct Products in Communication Complexity"  Anup Rao (U Washington)

Break

11:15   "Distributed Complexity" Roger Wattenhofer (ETH Zurich/Systems and Networks, Microsoft Research)

Lunch 12:15

1:30  "Rumor spreading and graph expansion" George Giakkoupis (INRIA Rennes)

2:30  "Verifiable Election Technologies," Josh Benaloh (Cryptography, Microsoft Research)

Break

3:45  "Algorithms for Structural Aberration Discovery in Cancer Genomes" Cenk Sahinalp (SFU)

A copy of the thesis will be available for viewing in the General Office of the
Department of Mathematics and Statistics SSM A425 at least one week prior to the
oral examination.

A Prognostat tool was developed to predict survival for palliative care patients. The Cox proportional hazards model was fitted to the survival outcomes incorporating several clinical characteristics together with some demographic variables. The significance of Prognostat components were assessed using Wald tests for the corresponding (log)-hazard ratios. A backwards elimination process was used to formulate a final survival prediction model. Survival nomograms were generated using Harrell’s Design  library for R which incorporates Cox model analyses to compute weights that are applied to the Prognostat components to determine an overall Prognostat Score.

In my talk I will first review some modeling concepts describing the behavior of individuals in an animal swarm of e.g. fish or birds, and focus on a model of self-propelled interacting particles. It is a well-known fact that even minimalistic interactions rules allow for the emergence of coherent macroscopic patterns observed in nature, when applied to all members of a swarm. In the mean-field limit approach, a kinetic PDE is used to model the evolution of a particle density rather than tracing individuals separately. Its macroscopic closure allows for a compact description of some coherent patterns, such as flocks or mills.
I will then discuss the possibility to explicitly compute the stationary density profile of such states using a particular type of interaction potential called Quasi-Morse. Flock and mill profiles can be predicted with a cheap numerical procedure that does not necessitate particle simulations.
Finally, I will present a result on the stability of flock solutions, where we are able to show that under mild assumptions the stability of the interaction potential (in a first-order aggregation model) inherits to the family of flock solutions in our second-order model.

Abstract and announcement (pdf file)

A copy of his Dissertation is available for perusal in SSM A425.

It is common to encounter situations where the choice of an estimator or test is predicated on the outcome of some prior statistical test. When this is the case, the properties of the resulting estimator (or second test) are usually affected in quite complex ways. For example, estimators that are unbiased under standard assumptions may become biased when a preliminary test precedes their selection and application.

"Preliminary test inference" has been explored widely since at least 1944. However, the implications of this important literature are frequently overlooked by practitioners. Recently, there has been a renewed interest in this problem.

In this talk I give a brief overview of some of the issues associated with inference after a preliminary test, and illustrate these issues with some simple examples that have been selected to be accessible to students.

Abstract: Algebra and topology are old friends.  Many topological problems are solved by applying algebraic methods.  But sometimes the relationship can work the other way.  My talk will discuss how the topological viewpoint can be used to establish the basic facts regarding orderability of groups. These facts can be used, in turn, to show that certain groups of interest to topologists are orderable, for example knot groups and the group of PL homeomorphisms of a disk fixed on the boundary.

Abstract: I will discuss how the concept of orderability of a group can be applied to problems in topology, particularly in the theory of 3-dimensional manifolds.

Abstract (PDF file)

Abstract: I will review the Sylvester Equation AX+XB  = C in finite and
infinite dimensions leading to recent results about solutions subject to
side conditions which are suggested by certain applications.

A copy of the thesis will be available for viewing in the General Office of the Department of Mathematics and Statistics at least one week prior to the oral examination.

Abstract:
In this talk, I will discuss the problem of studying  billiard
trajectories in a polygon whose interior angles are  rational
multiples of pi.  This leads naturally to the study of
translation surfaces, which is another term for the notion  of a
holomorphic 1-form on a (closed) Riemann surface.   The moduli
space of such objects admits an action of  SL(2,R) with a finite
invariant measure that can be used  to give information about the
dynamics of billiard trajectories  in the original polygon; for
example, a theorem of  Kerckhoff-Masur-Smillie tells us that for
almost every  direction theta, every trajectory with initial
direction theta  will be uniformly distributed.  In this talk, I
will describe some  refinements of the general technique of
exploiting dynamics  on the moduli space to obtain information
about dynamics of  billiard trajectories. This talk is intended
for a general audience.

Abstract: A right Hilbert A-module, E, for some C*-algebra, A, is a generalization of a Hilbert space. Instead of the usual complex-valued inner product, we have an A-valued inner product. We also add a right action of A on E. While these slight modifications seem innocuous, many results of Hilbert space theory that one might expect to carry over, do not. Just as with Hilbert spaces, it is a certain class of operators which act on Hilbert A-modules which are of particular interest, as they form a C*-algebra. I will present an introduction to these modules and their corresponding operators.

Abstact: Suppose that infinitely many red and blue points occur at random locations in Euclidean space, and consider translation-invariant schemes for perfectly matching red points to blue points. (Translation- invariance can be interpreted as meaning that the matching is constructed without favouring one spatial location over another.) What is the best possible cost of such a matching, measured in terms of the edge lengths? What happens if we insist that the matching is constructed without extra randomness, or if we forbid edge crossings, or if the points act as selfish agents? This last restriction can be formalized via the concept of stable marriage, the topic of the 2012 Nobel Prize in Economics.

I will review recent progress and open problems on these questions, as well as variants including fair allocation, multi-colour matching and multi-edge matching.

Alexander Holroyd received his Ph.D. from the University of Cambridge in 2000. After post-doctoral positions at UCLA and Berkeley, he became a faculty member at UBC. Holroyd won the Rollo Davidson prize (awarded to an outstanding young probabilist) and the Andre-Aisenstadt Prize (for an outstanding young mathematician in Canada). In 2010, he moved to the Theory Group at Microsoft Research in Redmond, Washington.

Download poster (PDF file)

Abstract: This talk will discuss the use of mathematical models to analyze how cells behave based on the activation of intracellular signalling pathways. Specifically, the mitogen activated protein (MAP) kinase pathway is one of the best understood cellular signal transduction pathways and functions in promoting cell survival, growth and division. The first part of the talk will detail a kinetic analysis of this pathway that could predict the behavior of embryonic stem cell derived neural progenitor cells in response to treatment with the growth factor neurotrophin-3. The second part of the talk will focus on reprogramming cancer cells to chose cell death instead of proliferation through the use of chimeric proteins that manipulate the MAP kinase pathway.

Abstract:

The main objects of interest of this talk are topological
dynamical systems on measure metric spaces that are
equicontinuous with respect to a measure. We will talk about
different notions of continuity and equicontinuity with respect
to a measure and characterize them. We will see how to check for
weak convergence of sequences of measures of a certain family.

MARK LEWIS is a Professor in the Department of Mathematical and Statistical Sciences at the University of Alberta. He holds a Canada Research Chair in Mathematical Biology and a Killam Research Fellowship. His research is mathematical biology, with a focus in spatial ecology and his mathematical models include nonlinear partial differential equations, integrodifference equations and related stochastic spatial processes. Biological problems include modeling the process of territorial pattern formation in wolves, predicting population spread in biological invasions, calculating optimal strategies for biocontrol and assessing the effect of habitat fragmentation on species survival. A significant part of his research involves the formulation and verification of quantitative models, in collaboration with biologists. His mathematical approaches include analytical methods for dynamical systems, perturbation theory and computational methods.

View poster (PDF)

PIMS DISTINGUISHED SPEAKER: MARK LEWIS

Mathematics behind stream population dynamics

Human activities change the natural flow regimes in streams and rivers and this impacts ecosystems. In this talk I will mathematically investigate the impact of changes in water flow on biological populations.  The approach I will take is to develop process-oriented advection-diffusion-reaction equations that couple hydraulic flow to population growth, and then to analyze the equations so as to assess the effect of impacts of water flow on population dynamics. The mathematical framework is based on new theory for the net reproductive rate R_o as applied to advection-diffusion-reaction equations. I will then connect the theory to populations in rivers under various flow regimes. This work lays the groundwork for connecting R_o to more complex models of spatially structured and interacting populations, as well as more detailed habitat and hydrological data. This is achieved through explicit numerical simulation of two dimensional depth-averaged models for river population dynamics.

MARK LEWIS is a Professor in the Department of Mathematical and Statistical Sciences at the University of Alberta. He holds a Canada Research Chair in Mathematical Biology and a Killam Research Fellowship. His research is mathematical biology, with a focus in spatial ecology and his mathematical models include nonlinear partial differential equations, integrodifference equations and related stochastic spatial processes. Biological problems include modeling the process of territorial pattern formation in wolves, predicting population spread in biological invasions, calculating optimal strategies for biocontrol and assessing the effect of habitat fragmentation on species survival. A significant part of his research involves the formulation and verification of quantitative models, in collaboration with biologists. His mathematical approaches include analytical methods for dynamical systems, perturbation theory and computational methods.

View poster (PDF)

Abstract: A configuration is merely a set of points and a set of lines (or blocks) along with an incidence relation that prescribes at most one line between any pair of points. This subject originated in ancient Greece, with Euclid and Pappus, but considering its age, very little has been uncovered. After the preliminaries, I'll present my own findings on the topic. As is typical of my talks, there will be plenty of pretty math pictures and animations. As a not-very-secret-anymore surprise, there will be a brief pseudo-mathematical performance as well. It's about as mathematical as astrology, but I'll make any excuse to shorten my talk.

This talk is the first in a series on Dispersive PDEs that will continue Saturday, March 9. Please see the full list of speakers and the schedule details.

Organizer: S. Ibrahim: ibrahims@uvic.ca

Friday, March 8:

2:00-2:50 T. Akahori (Shizuoka): Remarks on the energy-critical nonlinear Schrodinger equation


Saturday, March 9:

8:30-9:00 Welcome

9:00-9:50 H. Nawa (Osaka): Nelson diffusions and Nonlinear Schrodinger equations

10:00-10:30 Coffee break

10:30-11:20  T.-P. Tsai (UBC) On the existence and uniqueness of fast-moving multi-solitons for energy-subcritical nonlinear Schrodinger equations

11:30-12:20 W. Sun (SFU) Dispersive systems derived from kinetic equations with an entropy structure

12:30-1:30 Lunch break

1:30-2:20 R. Schweyer (France) Blow up dynamics for the 1-corotational energy critical harmonic heat flow

2:30-3:20 N. Boussaid (France & UVic): On spectral stability of the nonlinear Dirac equation

Abstract: Recently, Peter Dukes alerted me to a way of computing
the digits of Pi via a "billiard" game. I will use this
remarkable process to introduce the collision transformation,
discuss its properties and provide a geometric proof that the
number of collisions in a system of N hard spheres (any N,
arbitrary diameters and masses) in all space is always finite.
This answers a question originally asked by Sinai.

Abstract (PDF file)

ABSTRACT: In this talk, I introduce the restricted normal cone, which is a novel generalization of the Mordukhovich (also known as basic or limiting) normal cone. Basic properties are presented. Restricted normal cones are useful in extending work by Lewis, Luke and Malick on the method of alternating projections for two (possibly nonconvex) sets. An application to the problem of sparse optimization will also be presented.

Based on joint work with: Heinz Bauschke (UBC Okanagan), Russell Luke (Goettingen, Germany), and Shawn Wang (UBC Okanagan).

Abstract:  The dimension of a linear space is the maximum integer d such that any d points are contained in a proper subspace.  Regarding pairwise balanced designs as linear spaces, I’ll show how some standard design-theoretic constructions carry an asymptotic existence theory for designs with prescribed minimum dimension.  This is joint work with Alan C.H. Ling.

Abstract: Persistent homology is a relatively new effort by algebraic topologists, in a sense it represents the idea that classical homology, due to Poincare over 100 year ago, when married with modern computers should produce novel ways of describing the shape of large, high-dimensional data sets.   This idea has been gaining popularity recently.  I will describe some experiments that William Sethares and I have done, applying persistent homology to musical data.  It seems persistent homology can be useful for discovering some hard-to-see non-linear aspects of data, as well as some rather subtle metrical aspects of data.    There are many foundational questions that are still open in this rather young field, some of which will be mentioned.

Announcement and abstract (PDF file)

Abstract

An edge ordering of a graph G = (V,E) is an injection f : E → R, where R denotes the set of real numbers. A path in G for which the edge ordering f increases along its edge sequence is called an f-ascent; an f-ascent is maximal if it is not contained in a longer f -ascent. The depression of G is the smallest integer k such that any edge ordering f has a maximal f -ascent of length at most k. In this dissertation we discuss various results relating to the depression of a graph. We determine a formula for the depression of the class of trees known as double spiders. A k-kernel of a graph G is a set of vertices U⊆V(G) such that for any edge ordering f of G there exists a maximal f -ascent of length at most k which neither starts nor ends in U. We study the concept of k-kernels and discuss related depression results, including an improved upper bound for the depression of trees. We include a characterization of the class of graphs with depression three and without adjacent vertices of degree three or higher, and also construct a large class of graphs with depression three which contains graphs with adjacent vertices of high degree. Lastly, we apply the concept of ascents to edge colourings using possibly fewer than ∥E(G)∥ colours (integers). We consider the problem of determining the minimum number of colours for which there exists an edge colouring such that the length of a shortest maximal path of edges with increasing colors has a given length.

Abstract: Higher-rank graphs are a higher-dimensional analogue of
directed graphs introduced by Kumjian and Pask in 2000 as a
combinatorial model of Robertson and Steger's higher-dimensional
Cuntz-Krieger algebras associated to families of commuting matrices.
Formally, a higher-rank graph is a category satisfying some special
conditions. We will show some of the analogues of results for directed
graphs, and show a construction of higher-rank graphs in terms of
directed graphs that provides a different and potentially more intuitive
way of thinking them.

A graph is independent domination bicritical, or i-bicritical, if the removal of any two vertices decreases the independent domination number. A graph is called i-superbicritical if the deletion of any two independent vertices reduces the independent domination number by exactly two. Structural results and construction techniques for i-bicritical graphs will be presented. It can be shown that i-superbicritical graphs are also i-bicritical, and this special class will be investigated.

The empirical likelihood is a modern non-parametric method of inference with many applications in statistics. It combines modern computing power with the classical asymptotic approach to yield a powerful and versatile inference tool, and it continues to find new applications and surprising new theoretical results.

Empirical likelihood ratio confidence regions are known to suffer from an undercoverage problem in that their observed coverage probabilities tend to be lower than the desired nominal levels. In this talk, I will give a brief introduction to the general idea of the empirical likelihood and review the undercoverage problem described in the previous talk. Then, I will discuss two well-known high order methods for dealing with this problem and talk about my own recent work on a geometric solution for this problem.

Abstract: Graph C*-algebras are a generalisation of Cuntz and Kriegers C*-algebras associated to topological Markov chains from their seminal work in 1980. We may associate a C*-algebra to a directed graph in such a way that many properties of the C*-algebra may be deduced from simpler combinatorial properties of the graph. There are several different methods of associating a C*-algebra to a directed graph. I will outline how we do this using groupoids, as a universal object, and as a couniversal object. I will present the two most frequently used results:

the gauge invariant uniqueness theorem, and the Cuntz-Krieger uniqueness theorem. I will then show compute some examples and present some interesting structure results.

Abstract: The Krieger generator theorem says that every
invertible measure- preserving system with finite
measure-theoretic entropy can be embedded into a full shift with
strictly greater topological entropy. In joint work with Anthony
Quas, we extend Krieger’s theorem to include toral automorphisms
(which are not necessarily hyperbolic) to give a positive answer
to a question of Lind and Thouvenot.

This alternative math education event will take place

6:30 - 8:00 p.m.
Thursday, February 7, 2013
Strawberry Vale School
4109 Rosedale Avenue
Victoria, BC

Fun methods to teach math and computer science concepts to students, teachers and parents through games and art will be demonstrated. Lots of hands on activities!

• a Sorting Network
• an Impossible Balancing Act
• "Get Your Goat" game
• Mathematical Puzzles
• the Guessing Game
• Sudoku
• the Penny Game
• the Set Game
• and lots more!

For more information please contact the PIMS UVic Site Office in the Department of Mathematics and Statistics at the University of Victoria at (250) 472-4271 Email pims@uvic.ca

Abstract: In the 1960's, Stephen Smale initiated an ambitious program to
understand the dynamics of a certain class maps on smooth manifolds, which he
called Axiom A. David Ruelle gave a definition of a Smale space to describe,
in purely topological terms, the dynamics of an Axiom A system on its
non-wandering set. I will discuss these definitions and give several concrete
examples. Later, Anthony Manning proved that the zeta function for such
systems was rational and Rufus Bowen conjectured that this was due to the
existence of an underlying homology theory. A partial solution to this was
given by Krieger and also Bowen and Franks when they constructed a very
beautiful invariant for shifts of finite type. I will discuss this invariant
and then show how it can be extended to all Smale spaces as a homology theory,
as predicted by Bowen.

Abstract:
Here we discuss a scheduling problem that has its root in scheduling actors. In particular we are interested in enumerating elements of the product of sets such that individual elements do not appear too frequently in the listing of the elements of the product. This problem (eventually) reduces to finding an appropriate Hamilton path in a appropriately defined graph. We show bounds for some basic parameters of the problem and describe conditions for the existence of such a path.

Abstract: In the 1960's, Stephen Smale initiated an ambitious program to understand the dynamics of a certain class maps on smooth manifolds, which he called Axiom A. David Ruelle gave a definition of a Smale space to describe, in purely topological terms, the dynamics of an Axiom A system on its non-wandering set. I will discuss these definitions and give several concrete examples. Later, Anthony Manning proved that the zeta function for such systems was rational and Rufus Bowen conjectured that this was due to the existence of an underlying homology theory. A partial solution to this was given by Krieger and also Bowen and Franks when they constructed a very beautiful invariant for shifts of finite type. I will discuss this invariant and then show how it can be extended to all Smale spaces as a homology theory, as predicted by Bowen.

Pathogen transmission between domesticated animals and wildlife presents a challenge for both wildlife conservation and farming.  Mathematical models of transmission dynamics can be used to better understand the sources of pathogens and optimize treatments of domestic animals to reduce the spill-over and spill-back of pathogens between domesticated and wild populations of animals.

In Pacific Canada, the expansion of open-net salmon farming has brought concern about pathogen transmission between farm and wild salmon. In particular, the spill-over of parasitic sea lice from farm salmon to out-migrating juvenile wild salmon has been implicated in declines of wild salmon populations in regions of salmon farming.  Over the past decade, political and scientific controversy has brought attention to the issue and spurred better management of parasites on farm salmon. We present a mechanistic model of sea louse transmission dynamics between farm and wild salmon that considers parasiticide treatments on salmon farms. The model was fit to data (with some challenges!) and used to evaluate farm management scenarios that reduce sea lice on wild juvenile salmon.  The model predicts that locating farms distal to salmon rivers greatly reduces infections of wild juvenile salmon. Treating farm salmon with parasiticides before outbreaks occur also reduces louse transmission, although frequent treatments may accelerate the evolution of parasiticide resistance in sea lice. These results may help inform management of salmon farms in regions with sympatric wild fish populations.

I shall talk about a way of adjusting parametric failure-time distributions which allows for much greater flexibility in the shape of the hazard-rate function, including the possibility of a bathtub shape.  The adjustment involves the introduction of one extra parameter, so that the power-law adjusted forms of the common two-parameter distributions such as the Weibull, lognormal, gamma etc. are three-parameter distributions.

To motivate the talk (and to make it last 50 minutes!) I shall trace a path that I followed over perhaps the last ten years of my career to produce this work.  This may give some idea to graduate students of how research can progress.  The results and applications may be far from what one originally anticipated!

An open dynamical system is a measure preserving transformation
on a state space with a 'hole'. As orbits enter the hole, they
are lost from the system. Example: a billiard table.  Typically,
Lebesgue almost every orbit enters the hole eventually, so there
can be no absolutely continuous invariant measure. Instead we
look for a quasi-invariant measure, meaning, a measure stationary
after conditioning on the state of not being in the hole.  In
this setting one has a Perron-Frobenius operator and P-F equation
whose solution gives the density of a quasi-invariant measure.

Borrowing shamelessly from Anthony's careful setup last week in
the closed dynamics setting, I hope to describe the basic
functional analysis setup and a fundamentally different method
for calculating (= approximating) the quasi-invariant density
using optimization instead of discretization and projection.

Keywords:  Open dynamics, Perron-Frobenius operator, density,
maximum entropy principle, moment constraints.

Prof. Deirdre McCloskey is an economic historian of great distinction—and a gracious but energetic contrarian. She has written fourteen books, edited seven more, and published more than 350 articles on economic theory, economic history, philosophy, rhetoric, feminism, ethics and law. Her most recent book is Bourgeois Dignity: Why Economics Can’t Explain the Modern World (2010).

McCloskey has written that "most of what appears in the best journals of economics is unscientific rubbish." Whatever your views may be, she will stretch your intellectual horizons and challenge your pet beliefs about ethics and economics.

Free and open to the public

The Economics Department, the Peter B. Gustavson School of Business, and the Department of Mathematics and Statistics  are cohosting a seminar by Deirdre McCloskey (University of Illinois, Chicago). The seminar is free and open to the public.

Abstract: We describe a method of constructing finitely summable
Fredholm modules over the reduced C*-algebra of
a Gromov hyperbolic group. The method is to utilize the
action of the group on a certain geometrically defined `boundary'.

In the first talk we will introduce Gromov hyperbolic groups and
their boundaries, and the first major ingredient of the construction:
an analogue of the Poisson transform for hyperbolic groups.
In the second talk we will go into K-theory and K-homology and
derive the main result.

One of the difficulties in studying the intitiation and spacing of organs is finding tractable eukaryotic systems. We investigated phenotypic variation of physiological and morphological traits in cloned embryos of Larix x marschlinsii (hybrid larch)and Pseudotsuga menziesii (Douglas-fir). Embryos are multiplied in vitro and then matured in a stepwise controlled manner. By raising the embryos in different expermimental conditions their physiology, biochemistry and morphology can be altered. Since genotypic variation has been eliminated in such cloned systems, the variation we see is almost entirely phenotypic. We focused on the initiation and differentiation of cotyledons, which are the first lateral organs in the plant embryo. These appear simultaneously as a whorl of organs. We established treatments that reliably varied the number of lateral organs per whorl. By focusing on phenotype, we can use these studies to test physico-chemical models for the spatial patterning underlying morphogenesis. Our data indicate that cotyledon spacing is controlled by a wave-forming mechanism. We discuss the experimental results in terms of our ongoing mathematical and computational work on reaction-diffusion dynamics in growing systems.

Abstract

Mixed models are useful for modelling the dependence among response variables
inherent in repeated measures studies. Classical goodness-of-fit and model checking
methods for such models can be vague due to the complexity of their error structures.
Formal assessment tools available in the literature range from graphical checks of the
distributional assumptions to likelihood based and cross validation tests.
The talk focuses on measures used to check and compare mixed models regardless of
their distributional assumptions. Such methods include concordance relation measures,
penalized likelihood criteria and Bayesian based model checking. Their application is
illustrated with clustered dataset examples containing multiple random effects.

Abstract: Ulam's method is a very successful and practical method
for computing densities of absolutely continuous invariant
measures of transformations. In this talk, we recall our recent
work on Multiplicative ergodic theorems and indicate how this
work can be used to give a version of Ulam's method for
non-autonomous dynamical systems.  (This is joint work with
Gary Froyland and Cecilia Gonzalez-Tokman)

We consider various characterizations of discrete-time pursuit games, a collection of combinatorial games that includes Cops and Robbers and all of its variants. There are two players, Left and Right, who may move via prescribed rules. If Left can ensure that Right enters into a fixed set of final positions, then Left wins; otherwise, Right wins. In a wide variety of cases a relational characterization of such games is provided for when Left wins. In the case that the set of positions is finite, a precise formula is given for the length of the game, along with an algorithm for computing if Left has a winning strategy whose complexity is a function of the parameters of the game.

Everyone is welcome to join in for refreshments at the Grad Center after this talk.

Abstract: We describe a method of constructing finitely summable
Fredholm modules over the reduced C*-algebra of
a Gromov hyperbolic group. The method is to utilize the
action of the group on a certain geometrically defined `boundary'.

In the first talk we will introduce Gromov hyperbolic groups and
their boundaries, and the first major ingredient of the construction:
an analogue of the Poisson transform for hyperbolic groups.
In the second talk we will go into K-theory and K-homology and
derive the main result.

An \emph{edge ordering} of a graph $G$ is an injection $f:E(G)\rightarrow
\mathbb{R}$, the set of real numbers. A path in $G$ for which the edge
ordering $f$ increases along its edge sequence is called an
$f$-\emph{ascent}; an $f$-ascent is \emph{maximal} if it is not contained
in a longer $f$-ascent. The \emph{depression} of $G$, denoted
$\varepsilon(G)$, is the smallest integer $k$ such that any edge ordering
$f\ $has a maximal $f$-ascent of length at most $k$. We apply the concept
of ascents to edge colourings using possibly less than $|E(G)|$ colours
(integers) and consider the following question: What is the smallest
integer $r$ such that there exists a proper edge colouring
$c:E(G)\rightarrow \{1,2,...,r\}$ for which a shortest maximal $c$-ascent
has length $\varepsilon(G)$?

We consider an arbitrary directed graph on finitely many vertices, on which each edge is assigned a positive length and a positive weight.  The asymptotic growth is given for the weighted count of paths of length at most t, as t approaches infinity.

Abstract: The aim of the talk is to give an overview of recent
developments in semigroup C*-algebras. The emphasis will lie on two
aspects: Amenability and K-theory. We will also discuss several concrete
examples.

Abstract: Local field potentials recorded from groups of neurons often
display prominent oscillations in various frequency ranges. The amplitude of
oscillations in the gamma band (30-80 Hz) is modulated by perception and
cognition and is the object of many modeling and experimental studies. Here
we present and analyze a simple stochastic model of the interactions of
populations of excitatory and inhibitory neurons, which may explain gamma
oscillations. We show how the irregularly changing amplitude of such
oscillations, called "gamma bursts" may arise from the intrinsic dynamics of
the model. This is joint work with Mark McDonnell of Dept of Communications
Engineering, UniSA, Adelaide, and Lawrence Ward of Dept of Psychology, UBC,
Vancouver.

We consider two graph colouring problems in which edges at distance at most $t$ are given distinct colours, for some fixed positive integer $t$. We give two upper bounds for the distance-$t$ chromatic index, the least number of colours necessary for such a colouring. One is a bound of $(2-\eps)\Delta^t$ for graphs of maximum degree at most $\Delta$, where $\eps$ is some absolute positive constant independent of $t$. The other is a bound of $O(\Delta^t/\log \Delta)$ (as $\Delta\to\infty$) for graphs of maximum degree at most $\Delta$ and girth at least $2t+1$. The first bound is an analogue of Molloy and Reed's bound on the strong chromatic index. The second bound is tight up to a constant multiplicative factor, as certified by a class of graphs of girth at least $g$, for every fixed $g \ge 3$, of arbitrarily large maximum degree $\Delta$, with distance-$t$ chromatic index at least $\Omega(\Delta^t/\log \Delta)$.

This talk includes joint work with Tomas Kaiser (Pilsen) and also Putra Manggala (McGill).