相关论文: Transfer current and pattern fields in spanning tr…

For $d\ge 2$ and an odd prime power $q$, consider the vector space $\mathbb{F}_q^d$ over the finite field $\mathbb{F}_q$, where the distance between two points $(x_1,\ldots,x_d)$ and $(y_1,\ldots,y_d)$ is defined as $\sum_{i=1}^d…

The performance of a classifier trained on data coming from a specific domain typically degrades when applied to a related but different one. While annotating many samples from the new domain would address this issue, it is often too…

The connected tree-width of a graph is the minimum width of a tree-decomposition whose parts induce connected subgraphs. Long cycles are examples of graphs that have small tree-width but large connected tree-width. We show that a graph has…

Let $G$ be a connected graph in which almost all vertices have linear degrees and let $T$ be a uniform spanning tree of $G$. For any fixed rooted tree $F$ of height $r$ we compute the asymptotic density of vertices $v$ for which the…

In order to use the Gaussian representation for propagators in Feynman amplitudes, a representation which is useful to relate string theory and field theory, one has to prove first that each $\alpha$- parameter (where $\alpha$ is the…

An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an…

Domain transfer (DT) maps source to target distributions and supports tasks such as unsupervised image-to-image translation, single-cell analysis, and cross-platform medical imaging. However, DT is fundamentally ill-posed: push-forward…

Considering the wired uniform spanning forest on a nonunimodular transitive graph, we show that almost surely each tree of the wired uniform spanning forest is light. More generally we study the tilted volumes for the trees in the wired…

We use Stein's method to obtain distributional approximations of subgraph counts in the uniform attachment model or random directed acyclic graph; we provide also estimates of rates of convergence. In particular, we give uni- and…

We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…

Many modern learning tasks require models that can take inputs of varying sizes. Consequently, dimension-independent architectures have been proposed for domains where the inputs are graphs, sets, and point clouds. Recent work on graph…

We examine how conformal boundaries encode energy transport coefficients -- namely transmission and reflection probabilities -- of corresponding conformal interfaces in symmetric orbifold theories. These constitute a large class of…

We present a twistor-like formula for the complete tree-level S matrix of 6D $(2,0)$ supergravity coupled to $21$ abelian tensor multiplets. This is the low-energy effective theory that corresponds to Type IIB superstring theory…

Let $G$ be the Cartesian product of a regular tree $T$ and a finite connected transitive graph $H$. It is shown in arXiv:2006.06387 that the Free Uniform Spanning Forest ($\mathsf{FSF}$) of this graph may not be connected, but the…

We use the duality between color and kinematics to obtain scattering amplitudes in non-minimal conformal N=0,1,2,4 (super)gravity theories. Generic tree amplitudes can be constructed from a double copy between (super-)Yang-Mills theory and…

We study the noise sensitivity of the minimum spanning tree (MST) of the $n$-vertex complete graph when edges are assigned independent random weights. It is known that when the graph distance is rescaled by $n^{1/3}$ and vertices are given…

A model is developed describing the energy distribution of quasi-particles in a quasi-one dimensional, normal metal wire, where the transport is diffusive, connected between equilibrium reservoirs. When an ac bias is applied to the wire by…

We show that $\N=1$ gauge theories with an adjoint chiral multiplet admit a wide class of large-N double-scaling limits where $N$ is taken to infinity in a way coordinated with a tuning of the bare superpotential. The tuning is such that…

We consider the spectra of excitations around diagonal and intersecting D-brane configurations on tori. These configurations are described by constant curvature connections in a dual gauge theory description. The low-energy string…

We study the electron transmission through the domain boundary on bilayer graphene separating AB and BA stacking regions. Using the effective continuum model, we calculate the electron transmission probability as a function of the electron…