Related papers: On the Duality between Sampling and Interpolation

We propose a "decomposition method" to prove non-asymptotic bound for the convergence of empirical measures in various dual norms. The main point is to show that if one measures convergence in duality with sufficiently regular observables,…

We show that extremely simple systems of a not too large number of particles can be simultane- ously thermally stable and complex. To such an end, we extend the statistical complexity's notion to simple configurations of non-interacting…

Complete proofs of Schur-Weyl duality in positive characteristic are scarce in the literature. The purpose of this survey is to write out the details of such a proof, deriving the result in positive characteristic from the classical result…

Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…

In this work we study if the norms rotund, uniformly rotund, weakly uniformly rotund, locally uniformly rotund or weakly locally uniformly rotund interpolate in the complex or the real interpolation spaces. We will see that the properties…

We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…

We study the permutation complexity of finite-state stationary stochastic processes based on a duality between values and orderings between values. First, we establish a duality between the set of all words of a fixed length and the set of…

In this paper, we prove that the property of being a grape (in any of its variants) is invariant under Alexander duality. The explicitly determined (simple-)homotopy type of a grape can be transferred to its Alexander dual via Combinatorial…

In [18] Fournier and Printems establish a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with H\"{o}lder continuous coefficients. This is of course out of reach by using…

We present another proof for the well-known {\em small model property} of two-variable logic. As far as we know, existing proofs of this property rely heavily on model theoretic concepts. In contrast, ours is purely combinatorial and uses…

By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.

This article extends the hypotheses assessment method to the case with two competing simple hypotheses. In doing so we further clarify the benefits that hypotheses assessments can bring to classical statistical analyses. Given that…

We propose a new method for hierarchical clustering based on the optimisation of a cost function over trees of limited depth, and we derive a message--passing method that allows to solve it efficiently. The method and algorithm can be…

We study multiple sampling, interpolation and uniqueness for the classical Fock spaces in the case of unbounded multiplicities. We show that there are no sequences which are simultaneously sampling and interpolating when the multiplicities…

This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from…

Basing on invariant properties of universal multifractals we propose a simple algorithm for interpolation of multifractal densities. The algorithm admits generalization to a multidimensional case. Analitically obtained are multifractal…

Uniform interpolation properties are defined for equational consequence in a variety of algebras and related to properties of compact congruences on first the free and then the finitely presented algebras of the variety. It is also shown,…

Given a large set of measurement sensor data, in order to identify a simple function that captures the essence of the data gathered by the sensors, we suggest representing the data by (spatial) functions, in particular by polynomials. Given…

Let X be a countably infinite set of real numbers and let Y_x, x \in X, be an independent family of stationary random subsets of the real numbers, e.g. homogeneous Poisson point processes. We give criteria for the a.s. existence of various…

A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the…