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The modeling of solid-state transformations, such as polymorphic transitions and chemical reactions in molecular crystals, is vital for many applications including drug design or the development of new synthesis methods. However, a…
This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions in two/three dimensions. The method is obtained by combining…
In this work, we propose a new training method for finding minimum weight norm solutions in over-parameterized neural networks (NNs). This method seeks to improve training speed and generalization performance by framing NN training as a…
Subgraph matching is to find all subgraphs in a data graph that are isomorphic to an existing query graph. Subgraph matching is an NP-hard problem, yet has found its applications in many areas. Many learning-based methods have been proposed…
In this paper, we study adaptive neuron enhancement (ANE) method for solving self-adjoint second-order elliptic partial differential equations (PDEs). The ANE method is a self-adaptive method generating a two-layer spline NN and a numerical…
This paper proposes a new approximation algorithm for the offline Virtual Network Embedding Problem (VNEP) with latency constraints. Given is a set of virtual networks with computational demands on nodes and bandwidth demands together with…
Shortest path algorithms have played a key role in the past century, paving the way for modern day GPS systems to find optimal routes along static systems in fractions of a second. One application of these algorithms includes optimizing the…
This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…
We consider the shortest path routing (SPR) of a network with stochastically time varying link metrics under potential adversarial attacks. Due to potential denial of service attacks, the distributions of link states could be stochastic…
We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a unified methodology for constructing optimal first-order methods for convex and nonconvex optimization. BnB-PEP poses the problem of finding the optimal…
Feature selection is an important and active research area in statistics and machine learning. The Elastic Net is often used to perform selection when the features present non-negligible collinearity or practitioners wish to incorporate…
Graph representation learning has achieved great success in many areas, including e-commerce, chemistry, biology, etc. However, the fundamental problem of choosing the appropriate dimension of node embedding for a given graph still remains…
Attributed networks are ubiquitous since a network often comes with auxiliary attribute information e.g. a social network with user profiles. Attributed Network Embedding (ANE) has recently attracted considerable attention, which aims to…
We provide new tradeoffs between approximation and running time for the decremental all-pairs shortest paths (APSP) problem. For undirected graphs with $m$ edges and $n$ nodes undergoing edge deletions, we provide four new approximate…
We consider the classical single-source shortest path problem in directed weighted graphs. D.~Eppstein proved recently an $\Omega(n^3)$ lower bound for oblivious algorithms that use relaxation operations to update the tentative distances…
Analyzing the physical and chemical properties of single DNA based molecular machines such as polymerases and helicases often necessitates to track stepping motion on the length scale of base pairs. Although high resolution instruments have…
We propose two sparsity-aware normalized subband adaptive filter (NSAF) algorithms by using the gradient descent method to minimize a combination of the original NSAF cost function and the l1-norm penalty function on the filter…
This paper studies graph-based active learning, where the goal is to reconstruct a binary signal defined on the nodes of a weighted graph, by sampling it on a small subset of the nodes. A new sampling algorithm is proposed, which…
Stochastic electronic structure theories, e.g., Quantum Monte Carlo methods, enable highly accurate total energy calculations which in principle can be used to construct highly accurate potential energy surfaces. However, their stochastic…
The alternating direction method of multipliers (ADMM) is a powerful algorithm for solving decentralized optimization problems including networked microgrid energy management (NetMEM). However, its performance is highly sensitive to the…