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Synthetic polymeric materials underpin fundamental technologies in the energy, electronics, consumer goods, and medical sectors, yet their development still suffers from prolonged design timelines. Although polymer informatics tools have…
We consider the problem of generating uniformly random partitions of the vertex set of a graph such that every piece induces a connected subgraph. For the case where we want to have partitions with linearly many pieces of bounded size, we…
Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific…
Model selection, via penalized likelihood type criteria, is a standard task in many statistical inference and machine learning problems. Progress has led to deriving criteria with asymptotic consistency results and an increasing emphasis on…
In this article we present an algorithm to compute bounds on the marginals of a graphical model. For several small clusters of nodes upper and lower bounds on the marginal values are computed independently of the rest of the network. The…
The method of regions, which provides a systematic approach for computing Feynman integrals involving multiple kinematic scales, proposes that a Feynman integral can be approximated and even reproduced by summing over integrals expanded in…
Maximum entropy methods, rooted in the inverse Ising/Potts problem from statistical physics, are widely used to model pairwise interactions in complex systems across disciplines such as bioinformatics and neuroscience. While successful,…
High-fidelity simulations, such as computational fluid dynamics and finite element analysis, are essential for modeling complex engineering systems but are often prohibitively expensive for tasks including parametric studies, optimization,…
Given a hypergraph, influence maximization (IM) is to discover a seed set containing $k$ vertices that have the maximal influence. Although the existing vertex-based IM algorithms perform better than the hyperedge-based algorithms by…
We derive and introduce anisotropic effective pair potentials to coarse-grain solutions of semiflexible rings polymers of various lengths. The system has been recently investigated by means of full monomer-resolved computer simulations,…
One of the very few mathematically rigorous nonlinear model reduction methods is the restriction of a dynamical system to a low-dimensional, sufficiently smooth, attracting invariant manifold. Such manifolds are usually found using local…
Simulations of knotting and unknotting in polymers or other filaments rely on random processes to facilitate topological changes. Here we introduce a method of \textit{topological steering} to determine the optimal pathway by which a…
This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…
This work introduces a method for generating generalized structures of amorphous polymers using simulated polymerization and molecular dynamics equilibration, with a particular focus on amorphous polymers. The techniques and algorithms used…
We investigate symmetric edge polytopes generated by Erd\H{o}s--R\'enyi random graphs in a high-dimensional regime. These objects provide a natural and largely unexplored model of random lattice polytopes, in which geometric properties are…
The hybrid high-order method is a modern numerical framework for the approximation of elliptic PDEs. We present here an extension of the hybrid high-order method to meshes possessing curved edges/faces. Such an extension allows us to…
Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly,…
We prove a distributional limit theorem conjectured in [Journal of Statistical Physics 174, No. 6, 1372-1403 (2019)] for partition functions defining models of directed polymers on diamond hierarchical graphs with disorder variables placed…
Probabilistic graphical models (PGMs) serve as a powerful framework for modeling complex systems with uncertainty and extracting valuable insights from data. However, users face challenges when applying PGMs to their problems in terms of…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…