Abstract (click to read)

The problem of constructing "fair" political districts and related disputes around detecting intentional gerrymandering have received a significant amount of attention in recent years. A key question in this area is determining the expected properties of a representative districting plan as a function of the input geographic and demographic data. One natural approach is to generate a comparison ensemble of plans using MCMC and I will present successful applications of this approach in both court cases and legislative reform efforts. However, our recent work has demonstrated that the commonly used boundary-node flip proposal can mix poorly on real-world examples. In this talk, I will present some new proposal distributions for this setting and discuss some related open problems concerning mixing times and spanning trees. I will also discuss some generic hardness results for sampling problems on partitions of planar graphs.

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Spatiotemporally complex data arise in a wide variety of systems such as the formation of coral reefs, evolution of weather, or nanodot formation on semiconductors. Irregularity of time-varying structures, complexity of patterns, and sensitivity to initial conditions, among other things can make quantifying and distinguishing patterns difficult. Persistent homology is a promising tool for characterizing such systems, providing a low-dimensional summary of the geometric and topological structure of data. These summaries retain a remarkable amount of information that allows for the investigation of the influence of nonlinear parameters, classification of data by parameters, and study of defect evolution. In this talk, I will give several examples of how topological techniques can be used to quantify order, study model parameters, and quantify and track the evolution of defects, focusing on ion bombarded systems.

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This talk aims to connect five keywords in statistics/probability—ranks, (degenerate) U-statistics, combinatorial (non-)CLT, optimal transport theory, and Le Cam's contiguity lemma—through one theme, nonparametric independence testing. The corresponding results show the existence of consistent rate-optimal distribution-free tests of two null hypotheses, mutual independence and independence of two random vectors, both for the first time. In technical terms, we give (1) the first Cramer-type moderate deviation theorem for degenerate U-statistics, (2) a new type of combinatorial non-central limit theorem for double- and multiple-indexed permutation statistics, and (3) a nontrivial use of Le Cam's third lemma with elements of non-normal limits.

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The past decade has seen an ever increasing interest in the application of statistical tools developed in the interdisciplinary field of network analysis to enhance our understanding of complex systems and critical infrastructures, e.g., power grids, telecommunication platforms, and brain connectome. However, most modern approaches in network studies still largely focus on global topological characteristics, and the role of local geometry and topology in network functionality, along with its associated statistical properties, still remain largely under-investigated. In turn, the emerging tools of topological data analysis (TDA), and in particular, persistent homology, associated with the systematic study of progressively finer simplical complexes, enable to unveil some critical characteristics behind organization of complex networks and interactions of their components at multi-scale levels, which are otherwise largely inaccessible with conventional analytical approaches. In this talk we discuss utility of integrating the machinery of TDA and network motifs for more systematic, data-driven and geometrically enhanced inference for complex networks in a broad range of real-world scenarios, from analysis of power grid resilience to cryptocurrency price dynamics to clustering and vulnerability zoning of multilayer climate-insurance networks.

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Deep learning achieves tremendous success in image and speech recognition and machine translation. However, deep learning is not trustworthy. 1. How to improve the robustness of deep neural networks? Deep neural networks are well known to be vulnerable to adversarial attacks. For instance, malicious attacks can fool the Tesla self-driving system by making a tiny change on the scene acquired by the intelligence system. 2. How to compress high-capacity deep neural networks efficiently without loss of accuracy? It is notorious that the computational cost of inference by deep neural networks is one of the major bottlenecks for applying them to mobile devices. 3. How to protect the private information that is used to train a deep neural network? Deep learning-based artificial intelligence systems may leak the private training data. Fredrikson et al. recently showed that a simple model-inversion attack can recover the portraits of the victims whose face images are used to train the face recognition system.

In this talk, I will present some recent work on developing PDE-principled robust neural architecture and optimization algorithms for robust, accurate, private, and efficient deep learning. I will also present some potential applications of the data-driven approach for bio-molecule simulation and computer-aided drug design.

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Join me in exploring some paradoxical results that arise when people imagine infinite processes, including Ross Urns and Aristotle's Wheel. We will analyze the mental acts we perform as we seek to resolve these paradoxes, and what this tells us about ways that important mathematical distinctions can emerge.

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TDA software is becoming more mainstream and accessible to both mathematicians in the field and to data scientists at large. Recently, I worked as part of a small team of open source software developers to create a Python library known as scikit-tda. In addition to using this library in myriad research applications, I have also been developing a compendium of examples for pedagogical purposes, some of which are in a repository I call "TDALabs" (https://github.com/ctralie/TDALabs). In this talk, I will interactively go through a number of these examples, including a demo of the stability theorem, sliding windows in time series and video, the natural space of image patches, diffusion maps and TDA, lower star image filtrations for cell segmentation in images, mesh reconstruction via alpha shapes, and isometry blind 3D shape clustering. It is the hope that people will be inspired to use these materials in their own courses and workshops, and it is also the hope that some will help me build on them and contribute additional concise examples that showcase their work. Pull requests are welcome!

We will join the seminar online via BlueJeans.

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Vivek will present empirical findings from his two research projects on product recall, one each in vehicles and medical devices. Both projects address current public policy-related changes

1. A problem that plagues vehicle recalls in the U.S. is the excessive time taken by the manufacturer to investigate the defect. Prolonged investigation delays the manufacturer's initiation of the recall, keeping the driving public at risk. In response, lawmakers and business press have demanded the regulators to investigate the defective products themselves. The demand assumes that such regulatory investigation will pressurize the manufacturer to promptly initiate the recall. The authors show that regulatory investigations delay, rather than expedite, recall initiation. They also find that recalls that are preceded with a regulatory investigation—what the regulator calls influenced recalls—take longer to complete than their uninfluenced counterparts. The delayed completion occurs because the regulatory investigation cuts short the manufacturer's recall planning.


2. Does the speed of product innovation hurt product quality? Although speedy innovation is a celebrated firm practice, recent incidents in the medical devices industry suggest that speedy innovation can have a dark side. The authors show that speedy innovation indeed increases the incidence of quality failures. They reason that speed decreases the firm's attention to safety testing, thus increasing the failure incidence. Drawing on the attention-based view of the firm (ABV), the authors show that two strategic decisions by the firm—CEO compensation structure and marketing investment—moderate the firm attention to product testing. Specifically, they document that CEO's pay-performance sensitivity aggravates, whereas the CEO's risk-taking incentive alleviates the speed-quality trade-off. Similarly, marketing myopia exacerbates whereas marketing stock allays the effect. The research not only cautions managers against the celebrated mindset of rush-to-innovate but also helps firms alleviate the speed-quality trade-off through their strategic decisions on CEO compensation and marketing investment.

Abstract (click to read)

Prime integers play a critical role in securing the internet. They are used, primarily, in the key exchanges and signatures (i.e., Public Key Cryptography) used to create secure links. Attacks against these systems often target the primes themselves, making the search for, or generation of, primes an important tool for securing our information centric world.

Abstract (click to read)

We investigate forest biomass dynamics in USA using autoregressive models from financial mathematics, and how biomass in USA is affected by various climatic characteristics. The models predict biomass and evaluate forest growth rate in USA ecological regions and reveal the most influential climatic characteristics for biomass. The analysis involves Bayesian techniques to treat irregular data. In the absolute majority of ecological regions, biomass yearly averages behave as geometric random walks with normal increments. In California Coastal Province, geometric random walk with normal increments adequately describes dynamics of both biomass yearly averages and biomass on individual forest plots. Bayesian approach allowed us to evaluate forest growth rate within each USA ecological region. Precipitation Seasonality turns out to explain the majority of biomass variation in all USA domains (Humid, Dry and Humid Tropical).

In this work, we have implemented statistical time series models for biomass in USA. The developed models account stochastic effects of environmental disturbances and allow to predict future biomass dynamics. We have obtained that precipitation is the most crucial climatic characteristic for forest biomass in USA.