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Mar 16, 2017
Dynamical Systems

Equilibrium states for Mañé diffeomorphisms

We study thermodynamic formalism for the family of robustly transitive diffeomorphisms introduced by Ma\~n\'e, establishing existence and uniqueness …
Aug 01, 2017
Combinatorics

The inverse eigenvalue problem of a graph: Multiplicities and minors

The inverse eigenvalue problem of a given graph $G$ is to determine all possible spectra of real symmetric matrices whose off-diagonal entries are go…
Oct 15, 2015
Combinatorics

Equitable Decompositions of Graphs

We investigate connections between the symmetries (automorphisms) of a graph and its spectral properties. Whenever a graph has a symmetry, i.e. a non…
Jul 26, 2015
Mathematical Physics

Self-Limiting Trajectories of a Particle Moving Deterministically in …

We study the motion of a particle moving on a two-dimensional honeycomb lattice, whose sites are randomly occupied by either right or left rotators, …
Dec 01, 2015
Geometric Topology

Every hyperbolic group that is the fundamental group of a compact special cube complex has a Gromov boundary that is the quotient of a compact subset of R3 with connected preimages.

All finite subdivision rules are combinatorially equivalent to thre…

Finite subdivision rules in high dimensions can be difficult to visualize and require complex topological structures to be constructed explicitly. In…
Jun 10, 2018
Machine Learning
Computers and Society
Applications

ActiveRemediation: The Search for Lead Pipes in Flint, Michigan

We detail our ongoing work in Flint, Michigan to detect pipes made of lead and other hazardous metals. After elevated levels of lead were detected in…
Mar 31, 2017
Dynamical Systems

Unique equilibrium states for geodesic flows in nonpositive curvature

We study geodesic flows over compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the s…
Mar 06, 2018
Physics and Society
Disordered Systems and Neural Networks
Social and Information Networks

Hidden Symmetries in Real and Theoretical Networks

Symmetries are ubiquitous in real networks and often characterize network features and functions. Here we present a generalization of network symmetr…
May 23, 2015
Dynamical Systems

Unique equilibrium states for Bonatti-Viana diffeomorphisms

We show that the robustly transitive diffeomorphisms constructed by Bonatti and Viana have unique equilibrium states for natural classes of potential…
Dec 22, 2016
Fluid Dynamics

Error propagation dynamics of PIV-based pressure field calculations: …

A recent study analyzed the dynamic propagation of error in a PIV-based pressure field calculation by directly analyzing the pressure Poisson equatio…
Jul 06, 2017
Machine Learning
Applications

A Data Science Approach to Understanding Residential Water Contaminat…

When the residents of Flint learned that lead had contaminated their water system, the local government made water-testing kits available to them fre…
Jun 18, 2019
Combinatorics

Characterizing cospectral vertices via isospectral reduction

Two emerging topics in graph theory are the study of cospectral vertices of a graph, and the study of isospectral reductions of graphs. In this paper…
Feb 03, 2017
Combinatorics

Extensions and Applications of Equitable Decompositions for Graphs wi…

We extend the theory of equitable decompositions, in which, if a graph has a particular type of symmetry, i.e. a uniform or basic automorphism $\phi$…
Apr 16, 2019
Dynamical Systems

We prove Theorem 3.10. Let φt:M→M be a topologically transitive Anosov flow on a compact manifold and let T>0. We find an open set of diffeomorphisms with flow type and minimal strong foliations accumulating on φT. We first use structural stability …

A dichotomy for measures of maximal entropy near time-one maps of t…

We show that time-one maps of transitive Anosov flows of compact manifolds are accumulated by diffeomorphisms robustly satisfying the following dicho…
Aug 22, 2016
Adaptation and Self-Organizing Systems
Combinatorics
Dynamical Systems

Mechanisms for Network Growth that Preserve Spectral and Local Struct…

We introduce a method that can be used to evolve the topology of a network in a way that preserves both the network's spectral as well as local struc…
Dec 05, 2017
Social and Information Networks
Combinatorics

Uncovering Hierarchical Structure in Social Networks using Isospectra…

We employ the recently developed theory of isospectral network reductions to analyze multi-mode social networks. This procedure allows us to uncover …
Jan 01, 2016
Numerical Analysis

A Refinement Algorithm for Generalized B-splines

In this paper we present a method for knot insertion and degree elevation of generalized B-splines (GB-splines) via the local representation of these…
May 14, 2013
Geometric Topology

Braiding link cobordisms and non-ribbon surfaces

We define the notion of a braided link cobordism in $S^3 \times [0,1]$, which generalizes Viro's closed surface braids in $\mathbb{R}^4$. We prove th…
Oct 14, 2015
Numerical Analysis

A New Algorithm for the Evaluation of Generalized B-splines

In this paper we present a method for direct evaluation of generalized B-splines (GB-splines) via the local representation of these curves as piecewi…
Feb 15, 2011
Group Theory
Differential Geometry
Dynamical Systems
Metric Geometry

A `transversal' for minimal invariant sets in the boundary of a CAT(0…

We introduce new techniques for studying boundary dynamics of CAT(0) groups. For a group $G$ acting geometrically on a CAT(0) space $X$ we show there…
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