Related papers: Cluster Estimates and Analytic Wavefunctions
Clustering algorithms became an essential part of the neurophysiological data analysis toolbox in the last twenty five years. Many problems, from the definition of cell types/groups based on morphological, molecular and physiological data…
The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…
This paper develops a novel hybrid approach for estimating the mixture model of $t$-factor analyzers (MtFA) that employs multivariate $t$-distribution and factor model to cluster and characterize grouped data. The traditional estimation…
We consider a stationary random field indexed by an increasing sequence of subsets of $\mathbb{Z}^d$ obeying a very broad geometrical assumption on how the sequence expands. Under certain mixing and local conditions, we show how the tail…
We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behaviour of a coupled cluster wavefunction representation…
In the modal approach to clustering, clusters are defined as the local maxima of the underlying probability density function, where the latter can be estimated either non-parametrically or using finite mixture models. Thus, clusters are…
We prove two-sided inequalities between the integral moduli of smoothness of a function on $\mathbb{R}^d/\mathbb{T}^d$ and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is…
A sufficient condition for a cluster point of a planar harmonic function to be an asymptotic value is given, based on a partitioning into regions of constant valence. A sufficient condition for the cluster set of a planar harmonic function…
Dynamical behavior of the clusters during relaxation is studied in two-dimensional Potts model using cluster algorithm. Average cluster size and cluster formation velocity are calculated on two different lattice sizes for different number…
Arclets in clusters of galaxies can be used to determine the lens mapping and not only to constrain the mass density of the cluster. Multiply imaged arclets are therefore easily identified without further modelling.
The key to the proof of the Ohsawa-Takegoshi Extension Theorem is a certain $\bar{\partial}$-estimate. The purpose of this note is to show that the 'curvature term' that arises in the Kohn-Morrey-H\"{o}rmander inequality (or the…
The occurrence of successive extreme observations can have an impact on society. In extreme value theory there are parameters to evaluate the effect of clustering of high values, such as the extremal index. The estimation of the extremal…
In [7], a cluster expansion method has been developed to study the fluctuations of the hard sphere dynamics around the Boltzmann equation. This method provides a precise control on the exponential moments of the empirical measure, from…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
In a Newtonian system with localized interactions the whole set of particles is naturally decomposed into dynamical clusters, defined as finite groups of particles having an influence on each other's trajectory during a given interval of…
A new method for the determination of open cluster membership based on a cumulative effect is proposed. In the field of a plate the relative x and y coordinate positions of each star with respect to all the other stars are added. The…
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…
Through Ecological Momentary Assessment (EMA) studies, a number of time-series data is collected across multiple individuals, continuously monitoring various items of emotional behavior. Such complex data is commonly analyzed in an…
A straightforward expansion of Edwards' functional integral representation of the grand partition function for a polymer liquid as an infinite set of Feynman diagrams is shown to yield a cluster expansion that is closely related to the…
Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are…