Related papers: Locally anti-blocking $\mathbf{g}$-polytopes for f…

We address the problem of learning the topology of directed acyclic graphs (DAGs) from nodal observations, which adhere to a linear structural equation model. Recent advances framed the combinatorial DAG structure learning task as a…

We study localized plasmonic excitations in bilayer graphene (BLG) nanodisks, comparing AA-stacked and AB-stacked BLG and contrasting the results to the case of two monolayers without electronic hybridization. The electrodynamic response of…

The Navier-Stokes equations for compressible barotropic flow in the stationary three dimensional case are considered. It is assumed that a fluid occupies a bounded domain and satisfies the no-slip boundary condition. The existence of a weak…

We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows.…

A lattice polytope $\mathcal{P} \subset \mathbb{R}^d$ is called a locally anti-blocking polytope if for any closed orthant $\mathbb{R}^d_{\varepsilon}$ in $\mathbb{R}^d$, $\mathcal{P} \cap \mathbb{R}^d_{\varepsilon}$ is unimodularly…

Gelfand-Tsetlin polytopes are prominent objects in algebraic combinatorics. The number of integer points of the Gelfand-Tsetlin polytope $\mathrm{GT}(\lambda)$ is equal to the dimension of the corresponding irreducible representation of…

We report a nano-infrared (IR) imaging study of trilayer graphene (TLG) with both ABA (Bernal) and ABC (rhombohedral) stacking orders using the scattering-type scanning near-field optical microscope (s-SNOM). With s-SNOM operating in the…

Recovering underlying Directed Acyclic Graph (DAG) structures from observational data is highly challenging due to the combinatorial nature of the DAG-constrained optimization problem. Recently, DAG learning has been cast as a continuous…

Let L^1(G) and M(G) be group algebra and measure algebra of a locally compact group G, respectively and D:L^1(G)-->M(G) be a continuous linear map. We consider D behaving like derivation or anti-derivation at orthogonal elements for several…

The symplectic vortex equations admit a variational description as global minimum of the Yang-Mills-Higgs functional. We study its negative gradient flow on holomorphic pairs $(A,u)$ where $A$ is a connection on a principal $G$-bundle $P$…

We show that the Ehrhart h-vector of an integer Gorenstein polytope with a regular unimodular triangulation satisfies McMullen's g-theorem; in particular, it is unimodal. This result generalizes a recent theorem of Athanasiadis (conjectured…

A comprehensive study has been undertaken on the dimensional swelling of graphene-reinforced elastomers in liquids. Anisotropic swelling was observed for samples reinforced with graphene nanoplatelets (GNPs), induced by the in-plane…

We reprove the $\lambda$-Lemma for finite dimensional gradient flows by generalizing the well-known contraction method proof of the local (un)stable manifold theorem. This only relies on the forward Cauchy problem. We obtain a rather…

We study polytopes defined by inequalities of the form $\sum_{i\in I} z_{i}\leq 1$ for $I\subseteq [d]$ and nonnegative $z_i$ where the inequalities can be reordered into a matrix inequality involving a column-convex $\{0,1\}$-matrix. These…

Let $G$ be a connected center-free simple real algebraic group of rank one and $\Gamma < G$ be a Zariski dense torsion-free convex cocompact subgroup. We prove that the frame flow on $\Gamma \backslash G$, i.e., the right translation action…

Let $X = G/\Gamma$, where $G$ is a Lie group and $\Gamma$ is a lattice in $G$, let $O$ be an open subset of $X$, and let $F = \{g_t: t\ge 0\}$ be a one-parameter subsemigroup of $G$. Consider the set of points in $X$ whose $F$-orbit misses…

We present an experimental investigation of turbulent drag reduction with flexible and rigid polymer solutions. The flexible polymer is partially hydrolyzed polyacrylamide (HPAM) and the rigid polymer is xanthan gum (XG). The experiments…

In great contrast to the numerous discoveries of superconductivity in layer-stacked graphene systems, the absence of superconductivity in the simplest and cleanest monolayer graphene remains a big puzzle. Here, through realistic computation…

For a finite dimensional algebra $A$ over a field $k$, the 2-term silting complexes of $A$ gives a simplicial complex $\Delta(A)$ called the $g$-simplicial complex. We give tilting theoretic interpretations of the $h$-vectors and…

We compute the de Rham cohomology of the weak stable foliation of the geodesic flow of a connected orientable closed hyperbolic surface with various coefficients. For most of the coefficients, we also give certain "Hodge decompositions" of…