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Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
For many inverse parameter problems for partial differential equations in which the domain contains only well-separated objects, an asymptotic solution to the forward problem involving 'polarization tensors' exists. These are functions of…
We study a stochastic model of a copolymerization process that has been extensively investigated in the physics literature. The main questions of interest include: (i) what are the criteria for transience, null recurrence, and positive…
Physical models often contain unknown functions and relations. In order to gain more insights into the nature of physical processes, these unknown functions have to be identified or reconstructed. Mathematically, we can formulate this…
A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
We investigate the crystallization of a single, flexible homopolymer chain using transition path sampling (TPS). The chain consists of N identical spherical monomers evolved according to Langevin dynamics. While neighboring monomers are…
We use a recently developed lattice model to study the percolation of particles of different sizes and shapes in the presence of a polymer matrix. The polymer is modeled as an infinitely long semiflexible chain. We study the effects of the…
In this paper, we suggest a novel sampling method for Monte Carlo molecular simulations. In order to perform efficient sampling of molecular systems, it is advantageous to avoid extremely high energy configurations while also retaining the…
Ring polymers remain a major challenge to our current understanding of polymer dynamics. Experimental results are difficult to interpret because of the uncertainty in the purity and dispersity of the sample. Using both equilibrium and…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
A strategy is developed for generating equilibrated high molecular-weight polymer melts described with microscopic detail by sequentially backmapping coarse-grained (CG) configurations. The microscopic test model is generic but retains…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number of ways a permutation can be decomposed into a product of a given number of 2-cycles, 3-cycles, etc.…
The reversible kinetics of copolymerization is solved analytically for the multistate mechanism proposed by B. D. Coleman and T. G. Fox [J. Chem. Phys. 38, 1065 (1963)] under low conversion conditions where the concentrations of monomeric…
From a detailed analysis of cone-jet cross sections in effective field theory, we obtain novel factorization theorems which separate the physics associated with different energy scales present in such processes. The relevant low-energy…
A new generalized cyclic symmetric structure in the factor matrices of polyadic decompositions of matrix multiplication tensors for non-square matrix multiplication is proposed to reduce the number of variables in the optimization problem…
The research is important for a molecular theory of liquid and has a wide interest as an example solving the problem when dynamic parameters of systems can be indirectly connected with their equilibrium properties. In frameworks of the…
We consider the problem of packing congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex…
We present a scaling theory describing the collapse of a homopolymer chain in poor solvent. At time t after the beginning of the collapse, the original Gaussian chain of length N is streamlined to form N/g segments of length R(t), each…