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

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…

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

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, …

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.

Finite subdivision rules in high dimensions can be difficult to visualize and require complex topological structures to be constructed explicitly. In…

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…

We study geodesic flows over compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the s…

Symmetries are ubiquitous in real networks and often characterize network features and functions. Here we present a generalization of network symmetr…

We show that the robustly transitive diffeomorphisms constructed by Bonatti and Viana have unique equilibrium states for natural classes of potential…

A recent study analyzed the dynamic propagation of error in a PIV-based pressure field calculation by directly analyzing the pressure Poisson equatio…

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

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…

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 $\phi$…

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 …

We show that time-one maps of transitive Anosov flows of compact manifolds are accumulated by diffeomorphisms robustly satisfying the following dicho…

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…

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

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…

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…

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…

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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