Applied Math Seminar

Optimization problems on planar lattice transmitter networks

10/26/2015 - 4:15pm
10/26/2015 - 5:15pm
Speaker: 
Lenny Fukshansky (CMC)
Abstract: 

Consider a network of radio transmitters of equal power placed at points of a two-dimensional lattice. On the one hand, we would like to choose a lattice that would maximize the coverage area of our network; on the other, we want to maximize the signal-to-noise ratio. We present some results and conjectures in the direction of these optimization problems and their relation to each other on some particularly interesting classes of planar lattices, as well as discuss some counting results on the number of possible such lattice networks of fixed determinant. This work came out of a Fletcher Jones Fellowship project in 2011.

Where: 
Emmy Noether Room Millikan 1021 Pomona College

Optimal control for chemotherapy scheduling

09/28/2015 - 4:00pm
09/28/2015 - 5:00pm
Speaker: 
Minaya Villasana (Universidad Simón Bolívar)
Abstract: 

In this talk some advances on the optimal control model formulation and resolution for chemotherapy scheduling is presented.  Firstly, a DDE model is introduced for tumor progression with immune response upon which a suitable optimal control problem formulation is devised and several heuristic algorithms are evaluated.  A second model that incorporates two drugs: cytotoxic and cytostatic is presented.  We show numerically that the optimal scheduling on this new model corresponds to an asynchronous delivery. 

Where: 
Emmy Noether Room, Millikan 1021, Pomona College

Topological data analysis for investigation of dynamics and networks

11/09/2015 - 4:15pm
11/09/2015 - 5:15pm
Speaker: 
Heather Harrington (Oxford University)
Abstract: 

Persistent homology (PH) is a technique in topological data analysis that allows one to examine features in data across multiple scales in a robust and mathematically principled manner, and it is being applied to an increasingly diverse set of applications. We investigate applications of PH to dynamics and networks, focusing on two settings: dynamics {\em on} a network and dynamics {\em of} a network.

Dynamics on a network: a contagion spreading on a network is influenced by the spatial embeddedness of the network. In modern day, contagions can spread as a wave and through the appearance of new clusters via long-range edges, such as international flights. We study contagions by constructing Œcontagion maps¹ that use multiple contagions on a network to map the nodes as a point cloud. By analyzing the topology, geometry, and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modelling, forecast, and control of spreading processes.

Dynamics of a network: one can construct static graph snapshots to represent a network that changes in time (e.g. edges are added/removed). We show that partitionings of a network of random-graph ensembles into snapshots using existing methods often lack meaningful temporal structure that corresponds to features of the underlying system. We apply persistent homology to track the topology of a network over time and distinguish important temporal features from trivial ones. We define two types of topological spaces derived from temporal networks and use persistent homology to generate a temporal profile for a network. We show that the methods we apply from computational topology can distinguish temporal distributions and  provide a high-level summary of temporal structure.

Together, these two investigations illustrate that persistent homology can be very illuminating in the study of networks and their applications.

 

 

Where: 
Emmy Noether Room, Millikan 1021, Pomona College

Incorporating Sustainability into Mathematics Courses

11/23/2015 - 4:15pm
11/23/2015 - 5:15pm
Speaker: 
Victor J. Donnay (Bryn Mawr College)
Abstract: 

Abstract: How to link the math with the real world? Professor Donnay will discuss his experiences of incorporating issues of environmental sustainability into his math teaching.  He will present a variety of approaches ranging from easy to adapt extensions of standard homework problems to elaborate service learning projects. He will share some of the educational resources that he helped collect as chair of the planning committee for Mathematics Awareness Month 2013: the Mathematics of Sustainability, as well as his TED Ed video on Tipping Points and Climate Change. He has used these approaches in a variety of courses including Calculus, Differential Equations, Mathematical Modeling, and a Senior Seminar.

In addition to students and faculty, secondary math and science teachers are invited to attend.
Where: 
Emmy Noether Room, Millikan 1021, Pomona College

Constrained Adaptive Sensing

10/12/2015 - 4:15pm
10/12/2015 - 5:15pm
Speaker: 
Tina Woolf (CGU)
Abstract: 

Traditional signal processing schemes sample signals at a high rate and immediately discard most of the information during the compression process. Compressed sensing is a new field that improves this by directly sensing the signal in compressed form using few nonadaptive, linear measurements. Adaptive sensing, which allows the selection of the next measurement based on previous observations, significantly improves signal recovery when arbitrary linear measurements can be constructed. However, in practice, the types of measurements that can be acquired are limited. In this talk, we will discuss recent results on the limitations and advantages of adaptive sensing when the measurements are constrained to belong to a finite set of allowable measurement vectors.

Where: 
Emmy Noether Room (Pomona), Millikan 1021

Modeling Electrical Capacitance Tomography with Complete Electrode Model

10/05/2015 - 4:15pm
10/05/2015 - 5:15pm
Speaker: 
Weifu Fang (Mathematics and Statistics, Wright State University)
Abstract: 

We will discuss the modeling of electrical capacitance tomography with the use of different electrode models, in comparison with the study of electrical impedance tomography.

 

Where: 
Emmy Noether Room, Millikan 1021, Pomona College

On a "Lethargic" Theorem

09/21/2015 - 4:00pm
09/21/2015 - 5:00pm
Speaker: 
Asuman Aksoy (Claremont McKenna College)
Abstract: 

One of the most important theorems used in constructive theory of functions is called Berstein's "lethary" theorem [3]. The theorem states that if $ \{d_i\}  $ is a sequence of nonnegative numbers with $ \lim d_i =0 $ then there exists a function $ f\in C[0,1] $ such that dist$ (f, P_i) = d_i $ for $ i=0,1,2,3,\dots $, where C[0,1] denotes the Banach space of all continuous, real-valued functions defined on the interval $ [0,1] $ with supremum norm, and $ P_i $ denotes the space of all polynomials of degree $  \leq i $. In this talk, after examining the developments in this theory [1], we present a lethargic theorem for Fr ́echet spaces [2]. This is joint work with G. Lewicki.

References

[1] J. Almira and A. G. Aksoy On Shapiro’s Lethargy Theorem and Some Appli- cations, Jean. J. Approx. 6(1), 87 − 116, 2014.

[2] A. G. Aksoy and G. Lewicki Bernstein’s Lethargy Theorem in Fr ́echet spaces, arXiv:1503.06190.

[3] S. N. Bernstein, Collected Works, II Moskow,: Akad Nauk SSR. 1954.

Where: 
Emmy Noether Room, Millikan 1021, Pomona College

Lecture 2. Finite speed support propagation of solutions for nonlinear parabolic equations.

06/25/2015 - 1:00pm
06/25/2015 - 4:00pm
Speaker: 
Professor Roman Taranets (UCLA)
Abstract: 

Lecture Series for Graduate Students on Applied PDE Analysis
Lecture 1: Applications of Stampacchia's Lemma in qualitative analysis of solutions for elliptic PDEs.
Lecture 2. Finite speed support propagation of solutions for nonlinear parabolic equations.
Lecture 3. Waiting time phenomenon of interface for nonlinear parabolic equations.

Where: 
CGU Math. North

Lecture 1: Applications of Stampacchia's Lemma in qualitative analysis of solutions for elliptic PDEs.

06/24/2015 - 1:00pm
06/24/2015 - 4:00pm
Speaker: 
Professor Roman Taranets (UCLA)
Abstract: 

Lecture Series for Graduate Students on Applied PDE Analysis
Lecture 1: Applications of Stampacchia's Lemma in qualitative analysis of solutions for elliptic PDEs.
Lecture 2. Finite speed support propagation of solutions for nonlinear parabolic equations.
Lecture 3. Waiting time phenomenon of interface for nonlinear parabolic equations.

Where: 
CGU Math. North

Nonlinear Diffusions of Image Processing

04/24/2015 - 3:00pm
04/24/2015 - 4:00pm
Speaker: 
Patrick Guidotti (UC Irvine)
Abstract: 

In this talk the speaker will give an overview on the use of nonlinear diffusions as image processing tools by starting with the seminal Perona-Malik equation. Particular emphasis will be given to regularizations proposed by the speaker which exhibit enhanced practical effectiveness and allow for rigorous mathematical justification of the numerical behavior of their solution.

Where: 
CGU Math South (710 N. College Ave)
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