The CUNY Data Science and Applied Topology Reading Group is joint between the Mathematics and Computer Science programmes. We meet Fridays 11.45 -- 12.45 in GC 4419. You can contact us at cunygc@appliedtopology.nyc.

Our plan is to primarily read and discuss seminal papers in data science, in applied topology and in topological data analysis. Each seminar one participant takes the responsibility to present a paper and prepare items for discussion. We expect occasionally to be able to invite external speakers.

## Schedule

Current schedule can be found here.

We will be sending out announcements through a mailing list; you can subscribe here.

## Organizers

- Mikael Vejdemo-Johansson, Computer Science Programme, CUNY Graduate Center; Department of Mathematics, CUNY College of Staten Island
- Azita Mayeli, Mathematics Programme, CUNY Graduate Center; Department of Mathematics, CUNY Queensborough Community College

## Suggested papers

We have compiled a list of papers that might be interesting to present.

# Schedule

### Multiplierless iteration for the resolution of semidefinite linear systems

Algorithms of numerical analysis assume by default that all numbers manipulated by the computer are real numbers. We introduce for the first time in this talk a numerical method that accommodates the internal coarse binary operations of a computer to increase the efficiency of the algorithm. We show that a linear system of equations with a matrix that is symmetric and positive semidefinite can be iteratively solved with an algorithm where every multiplication is reduced to a scaling by a power of 2, which simply amounts to bit shifts in binary.

We will then see how this multiplierless algorithm can be used in various problems, such as least squares, l1-regularized least squares and the minimal-norm resolution of any consistent linear system. A particular application of focus will be the minimal-norm reconstruction of a bandlimited signal from generalized nonuniform samples.

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### Reading Group

Azita Mayeli launches the reading group for the spring, reading Vershynin: High-dimensional probability.

The book can be accessed from the author's website at https://www.math.uci.edu/~rvershyn/papers/HDP-book/HDP-book.html

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### Periodic Minimizers of a Ternary Non-Local Isoperimetric Problem

We study a two-dimensional ternary inhibitory system derived as a sharp-interface limit of the Nakazawa-Ohta density functional theory of triblock copolymers. This free energy functional combines an interface energy favoring micro-domain growth with a Coulomb-type long range interaction energy which prevents micro-domains from unlimited spreading. Here we consider a limit in which two species are vanishingly small, but interactions are correspondingly large to maintain a nontrivial limit. In this limit two energy levels are distinguished: the highest order limit encodes information on the geometry of local structures as a two-component isoperimetric problem, while the second level describes the spatial distribution of components in global minimizers. We provide a sharp rigorous derivation of the asymptotic limit, both for minimizers and in the context of Gamma-convergence. Geometrical descriptions of limit configurations are derived; among other results, we will show that, quite unexpectedly, coexistence of single and double bubbles can arise. The main difficulties are hidden in the optimal solution of two-component isoperimetric problem: compared to binary systems, not only it lacks an explicit formula, but, more crucially, it can be neither concave nor convex on parts of its domain.

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