Related papers: Parametrized Measuring and Club Guessing
Complex signed measures of finite total variation are a powerful signal model in many applications. Restricting to the $d$-dimensional torus, finitely supported measures allow for exact recovery if the trigonometric moments up to some order…
We establish a general method for proving bounds on the information that can be extracted via arbitrary entangled measurements on tensor products of hidden subgroup coset states. When applied to the symmetric group, the method yields an…
Under mild assumptions, the SRB measure $\mu$ associated to an Axiom A attractor $A$ has the following properties: (i) the empirical measure starting at a typical point near $A$ converges weakly to $\mu$; (ii) the pushforward of any…
Our purpose is to obtain a very effective and general method to prove that certain $C_0$-semigroups admit invariant strongly mixing measures. More precisely, we show that the Frequent Hypercyclicity Criterion for $C_0$-semigroups ensures…
In this paper, we introduce several geometric characterizations for strong minima of optimization problems. Applying these results to nuclear norm minimization problems allows us to obtain new necessary and sufficient quantitative…
We examine homogeneous metrics on spheres and determine which ones have positive sectional curvature. The answer is subtle and surprisingly difficult to prove. In some cases we also determine their pinching constants. This completes the…
Strong mixing property holds for a broad class of linear and nonlinear time series models such as ARMA and GARCH models. In this article we study correlation structure of strong mixing sequences, and some asymptotic properties are…
We develop a theory of \emph{sharp measure zero} sets that parallels Borel's \emph{strong measure zero}, and prove a theorem analogous to Galvin-Myscielski-Solovay Theorem, namely that a set of reals has sharp measure zero if and only if it…
Menger conjectured that subsets of R with the Menger property must be ${\sigma}$-compact. While this is false when there is no restriction on the subsets of R, for projective subsets it is known to follow from the Axiom of Projective…
We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show…
Measurement in quantum mechanics is generally described as an irreversible process that perturbs the wavefunction describing a quantum system. In this work we establish a formal connection between the measurement description within the…
Concentration of measure is a phenomenon in which a random variable that depends in a smooth way on a large number of independent random variables is essentially constant. The random variable will "concentrate" around its median or…
We prove that if there exists a simplified $(\omega_1,2)$-morass, then there is a ccc forcing which adds an $\omega_3$-chain in P($\omega_1$) mod finite and a ccc forcing which adds a family of $\omega_3$-many strongly almost disjoint…
The theory of majorizing measures, extensively developed by Fernique, Talagrand and many others, provides one of the most general frameworks for controlling the behavior of stochastic processes. In particular, it can be applied to derive…
Let $M$ be a multimeasure defined on a $\sigma$-algebra and taking values in the family of bounded non-empty subsets of a Banach space $X$. We prove that $M$ admits a control measure whenever $X$ contains no subspace isomorphic to…
It is demonstrated that the the statistics for a joint measurement of two conjugate variables in Quantum Mechanics are expressed through an equation identical to the classical one, provided that joint classical probabilities are substituted…
While coresets have been growing in terms of their application, barring few exceptions, they have mostly been limited to unsupervised settings. We consider supervised classification problems, and non-decomposable evaluation measures in such…
Several performance measures are used to evaluate binary and multiclass classification tasks. But individual observations may often have distinct weights, and none of these measures are sensitive to such varying weights. We propose a new…
A generalization of the classical Sard theorem in the plane is the following. Let $f$ be a function defined on a subset $A\subset{\mathbb R}^2$. If $f$ has modulus of continuity $\omega(r)\lesssim r^2$, then $f(A)\subset{\mathbb R}$ has…
Useful quantum metrology requires nonclassical states with a high particle number and (close to) the optimal exploitation of the state's quantum correlations. Unfortunately, the single-particle detection resolution demanded by conventional…