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Mon Sep 09

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Emergent behavior in collective dynamics
Eitan Tadmor, University of Maryland

Collective dynamics is driven by alignment that tend to self-organize the crowd and by different external forces that keep the crowd together. Different emerging equilibria are self-organized into clusters, flocks, tissues, parties, etc.

I will overview recent results on the hydrodynamics of large-time, large-crowd collective behavior, driven by different “rules of engagement”. In particular, I address the question how short-range interactions lead, over time, to the emergence of long-range patterns, comparing geometric vs. topological interactions.

Mon Oct 07

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Nonuniqueness in Dynamical Systems
Richard McGehee, University of Minnesota

Discontinuous vector fields arise naturally in some applications. In this presentation, a simple classical model of ocean circulation is introduced as an example of how discontinuities give rise to nonunique solutions. Standard bifurcation techniques often fail when the vector field is not smooth, and certainly fail when the vector field is discontinuous. However, some topological techniques seem to carry over, and a crude birfurcation theory can be extended to a large class of discontinuous systems.

Mon Dec 02

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Towards personalized computer simulation of breast cancer treatment
 Arnoldo Frigessi  ,  University of Oslo  

Current personalized cancer treatment is based on biomarkers which allow assigning each patient to a subtype of the disease, for which treatment has been established. Such stratifiedpatient treatments represent a first important step away from one-size-fits-all treatment.However, the accuracy of disease classification comes short in the granularity of thepersonalization: it assigns patients to one of a few classes, within which heterogeneity inresponse to therapy usually is still very large. In addition, the combinatorial explosivequantity of combinations of cancer drugs, doses and regimens, makes clinical testingimpossible. We propose a new strategy for personalised cancer therapy, based on producing acopy of the patient’s tumour in a computer, and to expose this synthetic copy to multiplepotential therapies. We show how mechanistic mathematical modelling, patient specificinference and simulation can be used to predict the effect of combination therapies in a breastcancer. The model accounts for complex interactions at the cellular and molecular level, andis able of bridging multiple spatial and temporal scales. The model is a combination ofordinary and partial differential equations, cellular automata and stochastic elements. Themodel is personalised by estimating multiple parameters from individual patient data,routinely acquired, including histopathology, imaging and molecular profiling. The resultsshow that mathematical models can be personalized to predict the effect of therapies in eachspecific patient. The approach is tested with data from five breast tumours collected in arecent neoadjuvant clinical phase II trial. The model predicted correctly the outcome after 12weeks treatment and showed by simulation how alternative treatment protocols would haveproduced different, and some times better, outcomes. This study is possibly the first onetowards personalized computer simulation of breast cancer treatment incorporating relevantbiologically-specific mechanisms and multi-type individual patient data in a mechanistic andmultiscale manner: a first step towards virtual treatment comparison.Xiaoran Lai, Oliver Geier, Thomas Fleischer, Øystein Garred, Elin Borgen, Simon Funke,Surendra Kumar, Marie Rognes, Therese Seierstad, Anne-Lise Børressen-Dale, VesselaKristensen, Olav Engebråten, Alvaro Köhn-Luque, and Arnoldo Frigessi, Tow

Mon Dec 09

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Gradient Flows: From PDE to Data Analysis
Franca Hoffman, Caltech

Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.

Mon Feb 03

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium
Anders Hansen, Cambridge
Mon Feb 24

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium
Brittany Froese Hamfeldt, NJIT
Mon Mar 16

Applied and Computational Math Colloquium

3:35pm - TBA
Applied and Computational Math Colloquium
Mauro Maggioni, Johns Hopkins
Mon Mar 16

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium
Mauro Maggioni, Johns Hopkins
Mon Apr 13

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium
Dio Margetis, Maryland
Mon May 04

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium
Eric Bonnetier, Université Joseph Fourier