Related papers: Frequent universality criterion and densities
We study the rates of convergence of the posterior distribution for Bayesian density estimation with Dirichlet mixtures of normal distributions as the prior. The true density is assumed to be twice continuously differentiable. The bandwidth…
We improve the best known upper bound on the density of a planar measurable set A containing no two points at unit distance to 0.25442. We use a combination of Fourier analytic and linear programming methods to obtain the result. The…
We study generalized density-based clustering in which sharply defined clusters such as clusters on lower-dimensional manifolds are allowed. We show that accurate clustering is possible even in high dimensions. We propose two data-based…
In this paper I will approach the computation of the maximum density of regular lattices in large dimensions using a statistical mechanics approach. The starting point will be some theorems of Roger, which are virtually unknown in the…
This invited paper proposes and discusses several Bayesian attempts at nonparametric and semiparametric density estimation. The main categories of these ideas are as follows: 1) Build a nonparametric prior around a given parametric model.…
Recent work on the use of dimensional reduction for the regularisation of non--supersymmetric theories is reviewed. It is then shown that there exists a class of theories for which a universal form of the soft supersymmetry breaking terms…
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…
A frequentist definition of sensitivity of a search for new phenomena is discussed, that has several useful properties. It is based on completely standard concepts, is generally applicable, and has a very clear interpretation. It is…
When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…
The time-frequency uncertainty principle states that the product of the temporal and frequency extents of a signal cannot be smaller than $1/(4\pi)$. We study human ability to simultaneously judge the frequency and the timing of a sound.…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…
In order to construct a general density-functional theory for nonuniform fluid mixtures, we propose an extension to multicomponent systems of the weighted-density approximation (WDA) of Curtin and Ashcroft [Phys. Rev. A 32, 2909 (1985)].…
We generalize the validity criterion for the infinitary proof system of the multiplicative additive linear logic with fixed points. Our criterion is designed to take into account axioms and cuts. We show that it is sound and enjoys the cut…
We generalize the ordinary aggregation process to allow for choice. In ordinary aggregation, two random clusters merge and form a larger aggregate. In our implementation of choice, a target cluster and two candidate clusters are randomly…
Universality is one of the most important ideas in computability theory. There are various criteria of simplicity for universal Turing machines. Probably the most popular one is to count the number of states/symbols. This criterion is more…
Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling…
We study multiply recurrent and hypercyclic operators as a special case of $\mathcal F$-hypercyclicity, where $\mathcal F$ is the family of subsets of the natural numbers containing arbitrarily long arithmetic progressions. We prove several…
We introduce the notion of the algebraic overshear density property which implies both the algebraic notion of flexibility and the holomorphic notion of the density property. We investigate basic consequences of this stronger property, and…
We define a general method for finding a quasi-best approximant in sup-norm to a target density belonging to a given model, based on independent samples drawn from distributions which average to the target (which does not necessarily belong…