Mathematics

Stochastic Organization in the Mitotic Spindle

Speaker: 
Christopher Miles
Date: 
Wed, May 19, 2021
Location: 
Zoom
Online
PIMS, University of British Columbia
Conference: 
Mathematical Biology Seminar
Abstract: 

For cells to divide, they must undergo mitosis: the process of spatially organizing their copied DNA (chromosomes) to precise locations in the cell. This procedure is carried out by stochastic components that manage to accomplish the task with astonishing speed and accuracy. New advances from our collaborators in the New York Dept of Health provide 3D spatial trajectories of every chromosome in a cell during mitosis. Can these trajectories tell us anything about the mechanisms driving them? The structure and context of this cutting-edge data makes utilizing classical tools from data science or particle tracking challenging. I will discuss my progress with Alex Mogilner on developing analysis for this data and mathematical modeling of emergent phenomena.

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Changing the Culture Panel Discussion: How has Coronavirus changed the teaching of Mathematics?

Speaker: 
Kseniya Garaschuk
Dan Laitsch
Cameron Morland
Rob Lovell
Date: 
Fri, May 14, 2021
Location: 
Zoom
Online
Conference: 
Changing the Culture 2021
Changing the Culture
Abstract: 

The title for the panel discussion at this year's Changing the Culture conference was "How has Coronavirus changed the teaching of Mathematics?". In the video, each of our panelists addresses that question from their perspective. Following these opening remarks, the panelists respond to questions posed by the Changing the Culture community.

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PIMS Education Prize 2021: Bruce Dunham

Speaker: 
Bruce Dunham
Date: 
Fri, May 14, 2021
Location: 
Zoom
Online
Conference: 
Changing the Culture 2021
Changing the Culture
Abstract: 

PIMS is pleased to announce that the winner of the 2021 Education Prize is Dr. Bruce Dunham, Professor of Teaching in the Statistics Department of the University of British Columbia.

Dr. Dunham is an internationally respected expert in statistics education, and has contributed to education in the mathematical sciences by developing and providing resources for evidence-based teaching. He has also provided training and expert advice on statistics teaching and curriculum. He has served in a range of leadership roles at UBC and at the provincial and national level.

Dr. Dunham has served on the British Columbia Committee on the Undergraduate Program in Mathematics (BCCUPMS) since 2006 and has been the chair of the BCCUPMS Statistics sub-committee since that time. He has played a major role in the new BC Statistics 12 high school course, from defining the vision of the course, to the development of the curriculum and currently, in his continued role in teacher support and training, including offering five training workshops for teachers. At the national level, Dr. Dunham has served in various roles in the Statistical Society of Canada. He has served on the executive committee of the Society’s Education Section, having previously been secretary and president and currently president-elect. He has served on the Society’s Education Committee.

The evaluation committee was particularly impressed by the direct public impact of his curriculum work in the BC school system, and the development of free software for the community. Dr. Dunham is a tremendous advocate for mathematics and statistics, his leadership contributes to public awareness, fostering communication among various groups concerned with mathematical training. We are very pleased to celebrate him, and his achievements with the PIMS Education prize.

Dr. Dunham's prize was awarded as part of the 2021 Changing the Culture event.

How to fold things into thirds, sevenths, and thirty-sevenths!

Speaker: 
James Tanton
Date: 
Fri, May 14, 2021
Location: 
Online
Zoom
Conference: 
Changing the Culture 2021
Changing the Culture
Abstract: 

Come with something floppy in hand--a string, a shoelace, a tie, or perhaps a floppy zucchini. Not only will we fold the object into strange fractional lengths, but we’ll also see how folding it into fractions leads to famous unsolved mathematics! Can you solve an unsolved problem?

Subject: 

Mathematics of diffusive signaling and the role of receptor clustering in chemoreception.

Speaker: 
Alan Lindsay
Date: 
Wed, May 12, 2021
Location: 
UBC
Online
Conference: 
PIMS Workshop on New Trends in Localized Patterns in PDES
Abstract: 

Cells receive chemical signals at localized surface receptors, process the data and make decisions on where to move or what to do. Receptors occupy only a small fraction of the cell surface area, yet they exhibit exquisite sensory capacity. In this talk I will give an overview of the mathematics of this phenomenon and discuss recent results focusing on receptor organization. In many cell types, receptors have very particular spatial organization or clustering - the biophysical role of which is not fully understood. In this talk I will explore how the number and configuration of receptors allows cells to deduce directional information on the source of diffusing particles. This involves a wide array of mathematical techniques from asymptotic analysis, homogenization theory, computational PDEs and Bayesian statistical methodologies. Our results show that receptor organization plays a large role in how cells decode their environmental situation and infer the location of distant sources.

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Subject: 

Non-hexagonal lattices from a two species interacting system

Speaker: 
Xiaofeng Ren
Date: 
Wed, May 12, 2021
Location: 
UBC
Online
Conference: 
PIMS Workshop on New Trends in Localized Patterns in PDES
Abstract: 

A two species interacting system motivated by the density functional theory for triblock copolymers contains long range interaction that affects the two species differently. In a two species periodic assembly of discs, the two species appear alternately on a lattice. A minimal two species periodic assembly is one with the least energy per lattice cell area. There is a parameter b in [0,1] and the type of the lattice associated with a minimal assembly varies depending on b. There are several thresholds defined by a number B=0.1867... If b is in [0, B), a minimal assembly is associated with a rectangular lattice; if b is in [B, 1-B], a minimal assembly is associated with a square lattice; if b is in (1-B, 1], a minimal assembly is associated with a rhombic lattice. Only when b=1, this rhombic lattice is a hexagonal lattice. None of the other values of b yields a hexagonal lattice, a sharp contrast to the situation for one species interacting systems, where hexagonal lattices are ubiquitously observed.

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The conserved Swift-Hohenberg equation and crystallization

Speaker: 
Edgar Knobloch
Date: 
Wed, May 12, 2021
Location: 
UBC
Online
Conference: 
PIMS Workshop on New Trends in Localized Patterns in PDES
Abstract: 

The phase-field model, also known as the conserved Swift-Hohenberg equation, provides a useful model of crystallization that is derivable from the more accurate dynamical density functional theory. I will survey the properties of this model focusing on spatially localized structures and their organization in parameter space. I will highlight the role played by conserved mass and discuss the role played by these structures in the thermodynamic limit in both one and two spatial dimensions. I will then discuss dynamic crystallization via a propagating crystallization front. Two types of fronts can be distinguished: pulled and pushed fronts, with different properties. I will demonstrate, via direct numerical simulation, that the crystalline structures deposited by a rapidly moving front are not in thermodynamic equilibrium and so become disordered as they age. I will conclude with a discussion of a two-wavelength generalization of the model that exhibits quasicrystalline order in both two and three dimensions and of the associated spatially localized structures with different quasicrystalline motifs. The possible role of metastable spatially localized structures in nucleating crystallization will be highlighted.

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Subject: 

Traveling pulses with oscillatory tails, figure-eight stack of isolas, and dynamics in heterogeneous media

Speaker: 
Yasumasa Nishiura
Date: 
Wed, May 12, 2021
Location: 
UBC, Vancouver, Canada
Online
Conference: 
PIMS Workshop on New Trends in Localized Patterns in PDES
Abstract: 

The interplay between 1D traveling pulses with oscillatory tails (TPO) and heterogeneities of bump type is studied for a generalized three-component FitzHugh-Nagumo equation. We first present that stationary pulses with oscillatory tails (SPO) forms a “snaky" structure in homogeneous space, then TPO branches take a form of "figure-eight-like stack of isolas" located close to the snaky structure of SPO. Here we adopt voltage-difference as a bifurcation parameter. A drift bifurcation from SPO to TPO can be found by introducing another parameter at which these two solution sheets merge. As for the heterogeneous problem, in contrast to monotone tail case, there appears a nonlocal interaction between the TPO and the heterogeneity that creates infinitely many saddle solutions. The response of TPO shows a variety of dynamics including pinning and depinning processes in addition to penetration and rebound. Stable/unstable manifolds of these saddles interact with TPO in a complex way, which causes a subtle dependence on the initial condition and a difficulty to predict the behavior after collision even in one-dimensional space. Nevertheless, for 1D case, a systematic global exploration of solution branches (HIOP) induced by heterogeneities, and the reduction method to finite-dimensional ODEs allow us to clarify such a subtle dependence of initial condition and detailed mechanism of the transitions from penetration to pinning and pinning to rebound from dynamical system view point. It turns out that the basin boundary between two different outputs against the heterogeneities forms an infinitely many successive reconnections of heteroclinic orbits among those saddles as the height of the bump is changed, which causes the subtle dependence of initial condition. This is a joint work with Takeshi Watanabe.

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Subject: 

Symmetries and bifurcations in non-local cell adhesion models

Speaker: 
Thomas Hillen
Date: 
Thu, May 13, 2021
Location: 
UBC
Online
Conference: 
PIMS Workshop on New Trends in Localized Patterns in PDES
Abstract: 

Cellular adhesion is one of the most important interaction forces between cells and other tissue components. In 2006, Armstrong, Painter and Sherratt introduced a non-local PDE model for cellular adhesion, which was able to describe known experimental results on cell sorting and pattern formation. The pattern formation arises through non-local attractive interactions of the cells. In this talk I will analyse the underlying symmetries and bifurcations that lead to the observed patterns. (joint work with A. Buttenschoen).

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Patterns, waves and bufurcations in cell migration

Speaker: 
Leah Edelstein-Keshet
Andreas Buttenschoen
Date: 
Thu, May 13, 2021
Location: 
UBC
Online
Conference: 
PIMS Workshop on New Trends in Localized Patterns in PDES
Abstract: 

Cell migration plays a central roles in embryonic development, wound healing and immune surveillance. In 2008, Yoichiro Mori, Alexandra Jilkine and LEK published a reaction-diffusion model for the initial step of cell migration, the front-back chemical polarization that sets a cell's directionality. (More detailed mathematical properties of this model were described by the same group in 2011.) Since then, progress has been made in investigating how that simple "wave-pinning" mechanism is shaped and tuned by feedback from other proteins, from the cell's environment (extracellular matrix), from interplay with larger signaling networks, and from cell-cell interactions. In this talk, we will describe some of this progress and mathematical questions that arise. In particular, AB will demonstrate how his numerical PDE bifurcation analysis has helped us to understand how cells repolarize to reverse their direction of motion.

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