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The problem of measuring an unbounded system attribute near a singularity has been discussed. Lenses have been introduced as formal objects to study increasingly precise measurements around the singularity and a specific family of lenses…
We have developed a theory of polymer entanglement using an extended Cahn-Hilliard functional, with two extra terms. One is a nonlocal attractive term, operating over mesoscales, which is interpreted as giving rise to entanglement, and the…
We establish the sharpness of the percolation phase transition for a class of infinite-range weighted random connection models. The vertex set is given by a marked Poisson point process on $\mathbb{R}^d$ with intensity $\lambda>0$, where…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…
Density-based clustering methodology has been widely considered in the statistical literature for classifying Euclidean observations. However, this approach has not been contemplated for directional data yet. In this work, directional…
This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects,…
Distortions in a family of conjugated polymers are studied within two complementary approaches, i.e. within a many-body Valence Bond (VB) approach using a transfer matrix technique to treat the Heisenberg model of the systems, and also in…
A novel clustering technique based on the projection onto convex set (POCS) method, called POCS-based clustering algorithm, is proposed in this paper. The proposed POCS-based clustering algorithm exploits a parallel projection method of…
We develop a clustering framework for observations from a population with a smooth probability distribution function and derive its asymptotic properties. A clustering criterion based on a linear combination of order statistics is proposed.…
A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation…
Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some…
Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as obtained from particle tracking experiments. Recent work in this context highlights the application of graph-based approaches,…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
Abstract polymer models are systems of weighted objects, called polymers, equipped with an incompatibility relation. An important quantity associated with such models is the partition function, which is the weighted sum over all sets of…
We study numerical integration over bounded regions in $\mathbb{R}^s, s\ge1$ with respect to some probability measure. We replace random sampling with quasi-Monte Carlo methods, where the underlying point set is derived from deterministic…
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,…
This paper proposes an uncertain data clustering approach to quantitatively analyze the complexity of prefabricated construction components through the integration of quality performance-based measures with associated engineering design…
The present work proposes the concept of induced percolation over multiple-object systems, so that features such as the number of merged clusters can be used as a relevant measurement. The suggested approach involves the expansion of the…
We discuss a new approach to data clustering. We find that maximum likelyhood leads naturally to an Hamiltonian of Potts variables which depends on the correlation matrix and whose low temperature behavior describes the correlation…