Related papers: Densities, spectral densities and modality

A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…

Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…

A practical measure for the complexity of sequences of symbols (``strings'') is introduced that is rooted in automata theory but avoids the problems of Kolmogorov-Chaitin complexity. This physical complexity can be estimated for ensembles…

With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…

Speckle patterns are used in a broad range of applications including microscopy, imaging, and light-matter interactions. Tailoring speckles' statistics can dramatically enhance their performance in applications. We present an experimental…

To address the challenge of quantifying uncertainty in the outputs generated by language models, we propose a novel measure of semantic uncertainty, semantic spectral entropy, that is statistically consistent under mild assumptions. This…

Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known…

Measuring inter-dataset similarity is an important task in machine learning and data mining with various use cases and applications. Existing methods for measuring inter-dataset similarity are computationally expensive, limited, or…

There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types…

We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which…

The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…

The spectral representation is an effecient tool to explore electrical properties of material mixtures. It separates the contributions of geometrical topology and intrinsic properties of the constituents in the system. The aim of this paper…

Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable $\mathbf{x}$ and a dependent variable $\mathbf{y}$ by modeling their conditional probability…

Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them…

We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…

We introduce a new form of density functional theory for the {\em ab initio} description of electronic systems in contact with a molecular liquid environment. This theory rigorously joins an electron density-functional for the electrons of…

The modality is important topic for modelling. Using parametric models is an efficient way when real data set shows trimodality. In this paper we propose a new class of trimodal probability distributions, that is, probability distributions…

A new method of matrix spectral factorization is proposed which reliably computes an approximate spectral factor of any matrix spectral density that admits spectral factorization

Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…

We consider the estimation of the global mode of a density under some decay rate condition around the global mode. We show that the maximum of a histogram, with proper choice of bandwidth, achieves the minimax rate that we establish for the…