Related papers: Bounded m-ary Patch-Width Are Equivalent For m > 2
We discuss how to construct open membranes in the recently proposed matrix model of M theory. In order to sustain an open membrane, two boundary terms are needed in the construction. These boundary terms are available in the system of the…
We prove the lower bound R(M_m) \geq 3/2 m^2 - 2 on the border rank of m x m matrix multiplication by exhibiting explicit representation theoretic (occurence) obstructions in the sense of the geometric complexity theory (GCT) program. While…
Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the…
Categorical structures and their pseudomaps rarely form locally presentable 2-categories in the sense of Cat-enriched category theory. However, we show that if the categorical structure in question is sufficiently weak (such as the…
We present a Rice-like complexity lower bound for any MSO-definable problem on binary structures succinctly encoded by circuits. This work extends the framework recently developed as a counterpoint to Courcelle's theorem for graphs encoded…
The mim-width of a graph is a powerful structural parameter that, when bounded by a constant, allows several hard problems to be polynomial-time solvable - with a recent meta-theorem encompassing a large class of problems [SODA2023]. Since…
Properties of two classes of generally convex sets in the n-dimentional real Euclidean space, called m-semiconvex and weakly m-semiconvex, 1<=m<n, are investigated in the present work. In particular, it is established that an open set with…
We establish the choice property, a weak analogue of definable choice, for certain tame expansions of o-minimal structures. Most noteworthily, dense pairs of real closed fields have this property.
Let $n_q(M,d)$ be the minimum length of a $q$-ary code of size $M$ and minimum distance $d$. Bounding $n_q(M,d)$ is a fundamental problem that lies at the heart of coding theory. This work considers a generalization $n^\bx_q(M,d)$ of…
Given a weakly o-minimal structure $\mathcal M$ and its o-minimal completion $\bar {\mathcal M}$, we first associate to $\bar {\mathcal M}$ a canonical language and then prove that $Th(\mathcal M)$ determines $Th(\bar {\mathcal M})$. We…
We introduce a notion of mean cohomological independence dimension for actions of discrete amenable groups on compact metrizable spaces, as a variant of mean dimension, and use it to obtain lower bounds for the radius of comparison of the…
Consider the following one-player game. Take a well-formed sequence of opening and closing brackets. As a move, the player can pair any opening bracket with any closing bracket to its right, erasing them. The goal is to re-pair (erase) the…
We give a classification of all multiple intersections of D-branes in ten dimensions and M-branes in eleven dimensions that corresponds to threshold BPS bound states. The residual supersymmetry of these composite branes is determined. By…
We show that any second-countable \'etale groupoid with polynomial growth is topologically amenable. If its unit space is compact and metrizable, we show that the groupoid has weak $m$-comparison. Thus if the groupoid is also ample and…
In this paper we prove a new Myers' type diameter estimate on a complete connected Reimannian manifold which admits a bounded vector field such that the Bakry-\'Emery Ricci tensor has a positive lower bound. The result is sharper than…
We show that for a Banach algebra $A$ with a bounded approximate identity, the amenability of the projective tensor product of A with A, the amenability of the projective tensor product of A with A^{op}and the amenability of A are…
We show that the m-fold connected sum $m\#\mathbb{C}\mathbb{P}^{2n}$ admits an almost complex structure if and only if m is odd.
This paper is concerned with "nice" compactifications of manifolds. Siebenmann's iconic dissertation characterized open manifolds M^m (m>5) compactifiable by addition of a manifold boundary. His theorem extends easily to cases where M^m is…
We say that a graph $G$ is $(2,m)$-linked if, for any distinct vertices $a_1,\ldots, a_m, b_1,b_2$ in $G$, there exist vertex disjoint connected subgraphs $A,B$ of $G$ such that $\{a_1, \ldots, a_m\}$ is contained in $A$ and $\{b_1,b_2\}$…
A graph $G$ is cyclically $c$-edge-connected if there is no set of fewer than $c$ edges that disconnects $G$ into at least two cyclic components. We prove that if a $(k, g)$-cage $G$ has at most $2M(k, g) - g^2$ vertices, where $M(k, g)$ is…