Related papers: Product Space Models of Correlation: Between Noise…
The Kaczmarz algorithm is an iterative method to reconstruct an unknown vector $f$ from inner products $\langle f , \varphi_{n} \rangle $. We consider the problem of how additive noise affects the reconstruction under the assumption that…
We study the long-time effect of noise on pattern formation for the aggregation model. We consider aggregation kernels that generate patterns consisting of two delta-concentrations. Without noise, there is a one-parameter family of…
A statistical model is said to be un-normalised when its likelihood function involves an intractable normalising constant. Two popular methods for parameter inference for these models are MC-MLE (Monte Carlo maximum likelihood estimation),…
The aim of this expository article is to present recent developments in the centuries old discussion on the interrelations between continuous and differentiable real valued functions of one real variable. The truly new results include,…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
Correlation self-testing of quantum theory involves identifying a task or set of tasks whose optimal performance can be achieved only by theories that can realise the same set of correlations as quantum theory in every causal structure.…
Let $F\in\mathbb{C}[x,y,z]$ be a constant-degree polynomial,and let $A,B,C\subset\mathbb C$ be finite sets of size $n$. We show that $F$ vanishes on at most $O(n^{11/6})$ points of the Cartesian product $A\times B\times C$, unless $F$ has a…
Given a subset $A \subseteq \{0,1\}^n$, let $\mu(A)$ be the maximal ratio between $\ell_4$ and $\ell_2$ norms of a function whose Fourier support is a subset of $A$. We make some simple observations about the connections between $\mu(A)$…
A large variety of microscopic or mesoscopic models lead to generic results that accommodate naturally within Boltzmann-Gibbs statistical mechanics (based on $S_1\equiv -k \int du p(u) \ln p(u)$). Similarly, other classes of models point…
Using the calculus of variations, we prove that a Euclidean set of fixed Gaussian measure that nearly maximizes Gaussian noise stability is close to a half space. The main result proves a modification of a conjecture of Eldan from 2013: a…
We consider the convolution model where i.i.d. random variables $X_i$ having unknown density $f$ are observed with additive i.i.d. noise, independent of the $X$'s. We assume that the density $f$ belongs to either a Sobolev class or a class…
Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…
Using first principles from inference, we design a set of functionals for the purposes of \textit{ranking} joint probability distributions with respect to their correlations. Starting with a general functional, we impose its desired…
We discuss conformal manifolds for conformal field theories with boundaries or defects. Using conformal perturbation theory we derive constraints on coefficients appearing in the boundary operator product expansion and three-point functions…
We study the robustness of conformal prediction, a powerful tool for uncertainty quantification, to label noise. Our analysis tackles both regression and classification problems, characterizing when and how it is possible to construct…
We examine measure preserving mappings $f$ acting from a probability space $(\Omega, F,\mu) $ into a probability space $% (\Omega ^{*},F^{*},\mu ^{*}) ,$ where $\mu ^{*}=\mu (f^{-1})$. Conditions on $f$, under which $f$ preserves the…
The aim of this chapter is to describe two situations where positive noise correlations can be directly monitored using a transport experiment, either with a superconductor or with a correlated electron system. To be more precise, the…
Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…
An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit…
We study the steady state properties of a phenomenological two-state predator model in presence of correlated Gaussian white noise. Based on the corresponding Fokker-Planck equation for probability distribution function the steady state…