Related papers: Proof of the Most Informative Boolean Function Con…
This note considers a finite dimensional statistical model for the Calder\'on problem with piecewise constant conductivities. In this setting it is shown that injectivity of the forward map and its linearisation suffice to prove the…
A transmitter Alice may wish to reliably transmit a message to a receiver Bob over a binary symmetric channel (BSC), while simultaneously ensuring that her transmission is deniable from an eavesdropper Willie. That is, if Willie listening…
In this paper, we study the value distributions of perfect nonlinear functions, i.e., we investigate the sizes of image and preimage sets. Using purely combinatorial tools, we develop a framework that deals with perfect nonlinear functions…
We present a new example of a partial boolean function whose one-way quantum communication complexity is exponentially lower than its one-way classical communication complexity. The problem is a natural generalisation of the previously…
Many nonlinear filters used in practise are stack filters. An algorithm is presented which calculates the output distribution of an arbitrary stack filter S from the disjunctive normal form (DNF) of its underlying positive Boolean function.…
We prove that for any pair of i.i.d. random variables $X,Y$ with finite moment of order $a \in (0,2]$ it is true that $E |X-Y|^a \leq E |X+Y|^a$. Surprisingly, this inequality turns out to be related with bifractional Brownian motion. We…
Alice and Bob want to run a protocol over a noisy channel, where a certain number of bits are flipped adversarially. Several results take a protocol requiring $L$ bits of noise-free communication and make it robust over such a channel. In a…
Let $(X_1 , \ldots , X_d)$ be random variables taking nonnegative integer values and let $f(z_1, \ldots , z_d)$ be the probability generating function. Suppose that $f$ is real stable; equivalently, suppose that the polarization of this…
To resist algebraic attack, a Boolean function should possess good algebraic immunity (AI). Several papers constructed symmetric functions with the maximum algebraic immunity $\lceil \frac{n}{2}\rceil $. In this correspondence we prove that…
The reliability function gives the rate of exponential convergence to zero of the error probability in a communication channel. In this paper bounds for the reliability function of a quantum pure state channel are given, reminiscent of the…
In this paper, a generalization of the traditional point-to-point to communication setup, which is named as "reliable communications with asymmetric codebooks", is proposed. Under the assumption of independent identically distributed…
We study an extension of the standard two-party communication model in which Alice and Bob hold probability distributions $p$ and $q$ over domains $X$ and $Y$, respectively. Their goal is to estimate \[ \mathbb{E}_{x \sim p,\, y \sim…
An extremal point of a positive threshold Boolean function $f$ is either a maximal zero or a minimal one. It is known that if $f$ depends on all its variables, then the set of its extremal points completely specifies $f$ within the universe…
We prove a conjecture of Lalley and Sellke [Ann. Probab. 15 (1987)] asserting that the empirical (time-averaged) distribution function of the maximum of branching Brownian motion converges almost surely to a double exponential, or Gumbel,…
In a 2016 ArXiv posting F. Bergeron listed a variety of symmetric functions $G[X;q]$ with the property that $G[X;1+q]$ is $e$-positive. A large subvariety of his examples could be explained by the conjecture that the Dyck path LLT…
This paper introduces a novel algorithmic solution for the approximation of a given multivariate function by a nomographic function that is composed of a one-dimensional continuous and monotone outer function and a sum of univariate…
In this paper, we investigate the problem of deciding whether two standard normal random vectors $\mathsf{X}\in\mathbb{R}^{n}$ and $\mathsf{Y}\in\mathbb{R}^{n}$ are correlated or not. This is formulated as a hypothesis testing problem,…
The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability…
Various AI models are increasingly being considered as part of clinical decision-support tools. However, the trustworthiness of such models is rarely considered. Clinicians are more likely to use a model if they can understand and trust its…
Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval…