David Uminsky

• Boston University, PhD (Mathematics)
• Managing Director at University of Chicago

We propose an adaptive version of the total variation algorithm proposed in [3] for computing the balanced cut of a graph. The algorithm from [3] used a sequence of inner total variation minimizations to guarantee descent of the balanced cut energy as well as convergence of the algorithm. In practice the total variation minimization step is never s...

Large systems of particles interacting pairwise in d dimensions give rise to extraordinarily rich patterns. These patterns generally occur in two types. On one hand, the particles may concentrate on a co-dimension one manifold such as a sphere (in 3D) or a ring (in 2D). Localized, space-filling, co-dimension zero patterns can occur as well. In this...

Pairwise particle interactions arise in diverse physical systems ranging from insect swarms to self-assembly of nanoparticles. In the presence of long-range attraction and short-range repulsion, such systems can exhibit bound states. We use linear stability analysis of a ring equilibrium to classify the morphology of patterns in two dimensions. Con...

Societal Impact Statement Genetically modified (GM) crops have the potential to address multiple challenges for African smallholder farmers but are limited by several institutional constraints. Public–private partnerships (PPPs) are seen as an organizational fix to one such constraint, bringing privately held intellectual property rights on key cro...

Genetically modified (GM) crops can be a tool to address food security, climate change, and environmental sustainability in Africa. However, despite nearly three decades of developing GM crops for explicit use on the African continent, very little is known about this research, and very few crop varieties have moved from development to use by farmer...

Through a series of case studies, we review how the unthinking pursuit of metric optimization can lead to real-world harms, including recommendation systems promoting radicalization, well-loved teachers fired by an algorithm, and essay grading software that rewards sophisticated garbage. The metrics used are often proxies for underlying, unmeasurab...

Differential cell counts is a challenging task when applying computer vision algorithms to pathology. Existing approaches to train cell recognition require high availability of multi-class segmentation and/or bounding box annotations and suffer in performance when objects are tightly clustered. We present differential count network (“DCNet”), an an...

We present LUMÁWIG, a novel efficient algorithm to compute dimension zero bottleneck distance between two persistence diagrams of a specific kind which outperforms all other publicly available algorithm in runtime and accuracy. We bypass the overwhelming matching problem in previous implementations of the bottleneck distance, and prove that the zer...

Stability of persistence diagrams under slight perturbations is a key characteristic behind the validity and growing popularity of topological data analysis in exploring real-world data. Central to this stability is the use of Bottleneck distance which entails matching points between diagrams. Instances of use of this metric in practical studies ha...

Stability of persistence diagrams under slight perturbations is a key characteristic behind the validity and growing popularity of topological data analysis in exploring real-world data. Central to this stability is the use of Bottleneck distance which entails matching points between diagrams. Use of this metric in practical studies has, however, b...

We address the question of how to quantify the contributions of groups of players to team success. Our approach is based on spectral analysis, a technique from algebraic signal processing, which has several appealing features. First, our analysis decomposes the team success signal into components that are naturally understood as the contributions o...

We address the question of how to quantify the contributions of groups of players to team success. Our approach is based on spectral analysis, a technique from algebraic signal processing, which has several appealing features. First, our analysis decomposes the team success signal into components that are naturally understood as the contributions o...

Optimizing a given metric is a central aspect of most current AI approaches, yet overemphasizing metrics leads to manipulation, gaming, a myopic focus on short-term goals, and other unexpected negative consequences. This poses a fundamental contradiction for AI development. Through a series of real-world case studies, we look at various aspects of...

Atrial Fibrillation is a heart condition characterized by erratic heart rhythms caused by chaotic propagation of electrical impulses in the atria, leading to numerous health complications. State-of-the-art models employ complex algorithms that extract expert-informed features to improve diagnosis. In this note, we demonstrate how topological featur...

We present a new $O(k^2 \binom{n}{k}^2)$ method for generating an orthogonal basis of eigenvectors for the Johnson graph $J(n,k)$. Unlike standard methods for computing a full eigenbasis of sparse symmetric matrices, the algorithm presented here is non-iterative, and produces exact results under an infinite-precision computation model. In addition,...

In this paper, we address the fundamental statistical question: how can you assess the power of an A/B test when the units in the study are exposed to interference? This question is germane to many scientific and industrial practitioners that rely on A/B testing in environments where control over interference is limited. We begin by proving that in...

We investigate the role of anisotropy in two classes of individual-based models for self-organization, collective behavior and self-assembly. We accomplish this via first-order dynamical systems of pairwise interacting particles that incorporate anisotropic interactions. At a continuum level, these models represent the natural anisotropic variants...

In this paper we study the pattern formation of a kinematic aggregation model for biological swarming in two dimensions. The swarm is represented by particles and the dynamics are driven by a gradient flow of a non-local interaction potential which has a local repulsion long range attraction structure. We review and expand upon recent developments...

The purpose of this panel is to discuss the creation and implementation of a data science degree program at the undergraduate level. The panel includes representatives from three different universities that each offers an undergraduate degree in Data Science as of fall 2013. We plan to share information on the logistics of how the data science prog...

Ideas from the image processing literature have recently motivated a new set of clustering algorithms that rely on the concept of total variation. While these algorithms perform well for bi-partitioning tasks, their recursive extensions yield unimpressive results for multiclass clustering tasks. This paper presents a general framework for multiclas...

The classical inverse statistical mechanics question involves inferring properties of pairwise interaction potentials from exhibited ground states. For patterns that concentrate near a sphere, the ground states can range from platonic solids for small numbers of particles to large systems of particles exhibiting very complex structures. In this set...

In this paper we consider the linear stability of a family of exact collapsing similarity solutions to the aggregation equation ρt = ∇ · (ρ∇K * ρ) in d, d ⩾ 2, where K(r) = rγ/γ with γ > 2. It was previously observed [Y. Huang and A. L. Bertozzi, “Self-similar blowup solutions to an aggregation equation in Rn,” J. SIAM Appl. Math. 70, 2582–2603 (2...

This paper presents a theory describing the fluid mechanics of whale flukeprints. It contains excerpts of a longer paper recently published in the International Journal of Non-Linear Mechanics special issue on biological structures. Whale flukeprints are smooth oval-shaped water patches that form on the surface of the ocean behind a swimming or div...

Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Tight continuous relaxations of balanced cut problems have recently been shown to provide excellent clustering results. In this paper, we present an explicit-implicit gradient flow scheme for the relaxed ratio cut problem, and prove t...

In this paper we derive evolution equations for the two-dimensional active scalar problem when the solution is supported on one-dimensional curves. These equations are a generalization of the Birkhoff-Rott equation when vorticity is the active scalar. The formulation is Lagrangian and it is valid for nonlocal kernels K that may include both a gradi...

Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Continuous relaxations of balanced cut problems yield excellent clustering results. This paper provides rigorous convergence results for two algorithms that solve the relaxed Cheeger Cut minimization. The first algorithm is a new stee...

Whale flukeprints are an often observed, but poorly understood, phenomenon. Used by whale researchers to locate whales, flukeprints refer to a strikingly smooth oval-shaped water patch which forms behind a swimming or diving whale on the surface of the ocean and persists up to several minutes. In this paper we provide a description of hydrodynamic...

In this paper we introduce simplified, combinatorially exact formulas that arise in the vortex interaction model found in (Nagem, et al., SIAM J. Appl. Dyn. Syst. 2009). These combinatorial formulas allow for the efficient implementation and development of a new multi-moment vortex method (MMVM) using a Hermite expansion to simulate 2D vorticity. T...

We study quantum chromodynamics from the viewpoint of untruncated Dyson–Schwinger equations turned to an ordinary differential equation for the gluon anomalous dimension. This non-linear equation is parameterized by a function P(x) which is unknown beyond perturbation theory. Still, very mild assumptions on P(x) lead to stringent restrictions for p...

We study quantum chromodynamics from the viewpoint of untruncated Dyson-Schwinger equations turned to an ordinary differential equation for the gluon anomalous dimension. This nonlinear equation is parameterized by a function P(x) which is unknown beyond perturbation theory. Still, very mild assumptions on P(x) lead to stringent restrictions for po...

We discuss the structure of beta functions as determined by the recursive nature of Dyson–Schwinger equations turned into an analysis of ordinary differential equations, with particular emphasis given to quantum electrodynamics. In particular we determine when a separatrix for solutions to such ODEs exists and clarify the existence of Landau poles...

The crocodilia have multiple interesting characteristics that affect their population dynamics. They are among several reptile species which exhibit temperature-dependent sex determination (TSD) in which the temperature of egg incubation determines the sex of the hatchlings. Their life parameters, specifically birth and death rates, exhibit strong...

After the pioneering work on complex dynamics by Fatou and Julia in the early 20th century, Noel Baker went on to lay the foundations of transcendental complex dynamics. As one of the leading exponents of transcendental dynamics, he showed how developments in complex analysis such as Nevanlinna theory could be applied. His work has inspired many ot...

The two-dimensional Navier-Stokes equations are rewritten as a system of coupled nonlinear ordinary differential equations. These equations describe the evolution of the moments of an expansion of the vorticity with respect to Hermite functions and of the centers of vorticity concentrations. We prove the convergence of this expansion and show that...

An approximate solution to the two-dimensional incompressible fluid equations is constructed by expanding the vorticity field in a series of derivatives of a Gaussian vortex. The expansion is used to analyze the motion of a corotating Gaussian vortex pair, and the spatial rotation frequency of the vortex pair is derived directly from the fluid vort...

We study the properties of a logconcavity operator on a symmetric, unimodal subset of finite sequences. In doing so we are able to prove that there is a large unbounded region in this subset that is ∞-logconcave. This problem was motivated by the conjecture of Boros and Moll [cf. G. Boros and V.H. Moll, Irresistible integrals. Symbolics, analysis a...

We describe how basic voting data and simple ideas from linear algebra can be used to pinpoint voting coalitions in small voting bodies. The approach we use is an example of (generalized) spectral analysis, which is a nonmodel-based method for doing exploratory data analysis. As a proof of concept, we show how important coalitions of justices on th...

In this paper we consider the family of rational maps of the complex plane given by z 2 + λ z 2 where λ is a complex parameter. We regard this family as a singular perturbation of the simple function z 2. We show that, in any neighborhood of the origin in the parameter plane, there are infinitely many open sets of parameters for which the Julia set...

We describe the behavior of the family of rational maps of the form f λ (z)=λz + 1 z· We show that, in every neighborhood of the origin in parameter space, there are infinitely many copies of the Mandelbrot set as well as infinitely many “blowup” points, i.e., parameters for which the critical orbits map to ∞ so the Julia set is the entire plane.

In this paper we consider the dynamical behavior of the family of complex rational maps given by Fλ(Z) = Zn + Z d/λ where n ≥ 2, d ≥ 1. Despite the high degree of these maps, there is only one free critical orbit up to symmetry. Also, the point at oo is always a superattracting fixed point. Our goal is to consider what happens when the free critica...

This paper introduces a new method, noncommutative harmonic analysis, as a tool for political scientists. The method is based on recent results in mathematics which system-atically identify coalitions in voting data. The first section shows how this new approach, noncommutative harmonic analysis is a generalization of classical spectral analysis. T...

Abstract This work explores voting trends by analyzing how individuals form their polit- ical aliations,during a presidential campaign. Using a variation of the traditional epidemiological model, we construct an ODE model that represents the transition of potential voters through various levels of political interest in either the Republican or Demo...

The idea of splitting integrals of rational functions into its even and odd parts is used to improve a new method of integration. It has been shown that the even part of a function is easier to deal with. The integration of the odd part yields the map F(R(x)) = R( p x) R( p x) 2 p x on the space of rational functions. The properties of F are examin...

We study the dynamics of the mapF(R(x)) = R( p x) R( p x) 2 p x on the space of rational functions, in the context of a new method of integration. We give a recursive formula for the iterates of a model family of rational functions, which is closed under the action ofF. We give a class of rational functions that are mapped to zero by two iterations...