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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…
In this paper, we study the localization phenomena in a slender cylinder composed of an incompressible hyperelastic material subjected to axial tension. We aim to construct the analytical solutions based on a three-dimensional setting and…
We develop a unified scaling framework for the end-position distributions of tethered polymers confined in finite cylindrical geometries. Two observables are analysed: the longitudinal distribution P(x), along the confinement axis, and the…
We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke)…
As distributed systems increase in size, the need for scalable algorithms becomes more and more important. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to…
We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems effectively lie in a…
The dynamics of two-dimensional fluids confined within a random matrix of obstacles is investigated using both colloidal model experiments and molecular dynamics simulations. By varying fluid and matrix area fractions in the experiment, we…
Deflation techniques are typically used to shift isolated clusters of small eigenvalues in order to obtain a tighter distribution and a smaller condition number. Such changes induce a positive effect in the convergence behavior of Krylov…
Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…
Subspace recycling techniques have been used quite successfully for the acceleration of iterative methods for solving large-scale linear systems. These methods often work by augmenting a solution subspace generated iteratively by a known…
Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to…
This paper proposes a robust, high-precision positioning methodology to address localization failures arising from complex background interference in large-scale flight navigation and the computational inefficiency inherent in conventional…
The tacnode process is a universal behavior arising in nonintersecting particle systems and tiling problems. For Dyson Brownian bridges, the tacnode process describes the grazing collision of two packets of walkers. We consider such a Dyson…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
For distributions over discrete product spaces $\prod_{i=1}^n \Omega_i'$, Glauber dynamics is a Markov chain that at each step, resamples a random coordinate conditioned on the other coordinates. We show that $k$-Glauber dynamics, which…
Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. This amounts to a generalization from 2-point to point-link-point interactions. An associated graph theory with…
Motivated by the `subgraphs world' view of the ferromagnetic Ising model, we develop a general approach to studying mixing times of Glauber dynamics based on subset expansion expressions for a class of graph polynomials. With a canonical…
Models of complex systems often consist of multiple interconnected subsystem/component models that are developed by multi-disciplinary teams of engineers or scientists. To ensure that such interconnected models can be applied for the…
We study the convergence in total variation and $V$-norm of discretization schemes of the underdamped Langevin dynamics. Such algorithms are very popular and commonly used in molecular dynamics and computational statistics to…
Understanding and predicting the glassy dynamics of polymers remain fundamental challenges in soft matter physics. While the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory has been successful in describing relaxation…