Related papers: Upper bound for the counting function of interior …
A new upper bound on the relative entropy is derived as a function of the total variation distance for probability measures defined on a common finite alphabet. The bound improves a previously reported bound by Csisz\'ar and Talata. It is…
We prove that the density of any covering single-insertion code $C\subseteq X^r$ over the $n$-symbol alphabet $X$ cannot be smaller than $1/r+\delta_r$ for some positive real $\delta_r$ not depending on $n$. This improves the volume lower…
We develop a novel framework for proving converse theorems for channel coding, which is based on the analysis technique of multicast transmission with an additional auxiliary receiver, which serves as a genie to the original receiver. The…
The purpose of this note is to establish a Central Limit Theorem for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on the correct aymptotics of the variance of the eigenvalue counting function of GUE matrices…
Given a random matrix A with eigenvalues between -1 and 1, we analyze the number of iterations needed to solve the linear equation (I-A)x=b with the Neumann series iteration. We give sufficient conditions for convergence of an upper bound…
Bayesian inference requires approximation methods to become computable, but for most of them it is impossible to quantify how close the approximation is to the true posterior. In this work, we present a theorem upper-bounding the KL…
In this paper, we introduce the concept of Z$_1$-eigenvalue to infinite dimensional generalized Hilbert tensors (hypermatrix) $\mathcal{H}_\lambda^{\infty}=(\mathcal{H}_{i_{1}i_{2}\cdots i_{m}})$, $$ \mathcal{H}_{i_{1}i_{2}\cdots…
The goal of this paper is to develop numerical methods computing a few smallest elasticity transmission eigenvalues, which are of practical importance in inverse scattering theory. The problem is challenging since it is nonlinear,…
We present novel bounds on the capacity of the independent and identically distributed binary deletion channel. Four upper bounds are obtained by providing the transmitter and the receiver with genie-aided information on suitably-defined…
Let $\phi(n)$ be the Euler totient function and $\phi_k(n)$ its $k$-fold iterate. In this note, we improve the upper bound for the number of positive $n\leqslant x$ such that $\phi_{k+1}(n)\geqslant cn$. Comparing with the upper bound which…
We propose a universal analysis for static routings on networks and describe the congestion characteristics by the theory. The relation between average transmission time and transmission capacity is described by inequality T0Rc0<=1. For…
We show that any quantum algorithm deciding whether an input function $f$ from $[n]$ to $[n]$ is 2-to-1 or almost 2-to-1 requires $\Theta(n)$ queries to $f$. The same lower bound holds for determining whether or not a function $f$ from…
A subset $\mathcal{C}\subseteq\{0,1,2\}^n$ is said to be a $\textit{trifferent}$ code (of block length $n$) if for every three distinct codewords $x,y, z \in \mathcal{C}$, there is a coordinate $i\in \{1,2,\ldots,n\}$ where they all differ,…
For bound states of atoms and molecules of $N$ electrons we consider the corresponding $K$-particle reduced density matrices, $\Gamma^{(K)}$, for $1 \le K \le N-1$. Previously, eigenvalue bounds were obtained in the case of $K=1$ and…
We use a method developed by Bj\"orklund and Gorodnik to show a central limit theorem (as $T$ tends to $\infty$) for the counting functions $\# \left( \Lambda \cap \Omega_T \right)$ where $\Lambda$ ranges over the space $Y_{2d}$ of…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state…
We consider transmission over a wireless multiple antenna communication system operating in a Rayleigh flat fading environment with no channel state information at the receiver and the transmitter with coherence time T=1. We show that,…
By considering the prime zeta function, the author intended to demonstrate in that the Riemann zeta function zeta(s) does not vanish for Re(s)>1/2, which would have proven the Riemann hypothesis. However, he later realised that the proof of…
Let ${H}=(V, {E})$ be a hypergraph on the vertex set $V$ and edge set ${E}\subseteq 2^V$. We show that number of distinct {\it traces} on any $k-$ subset of $V$, is most $k.{\hat \alpha}(H)$, where ${\hat \alpha}(H)$ is the {\it degeneracy}…
We derive an exponentially decaying upper-bound on the unnormalized amount of information leaked to the wire-tapper in Wyner's wire-tap channel setting. We characterize the exponent of the bound as a function of the randomness used by the…