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Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…
It is often useful to have polynomial upper or lower bounds on a one-dimensional function that are valid over a finite interval, called a trust region. A classical way to produce polynomial bounds of degree $k$ involves bounding the range…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
This paper presents an efficient and comprehensive MATLAB code to solve two-dimensional structural topology optimization problems, including minimum mean compliance, compliant mechanism synthesis and multi-load compliance problems. The…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
We provide a new method for constructing equiangular tight frames (ETFs). The construction is valid in both the real and complex settings, and shows that many of the few previously-known examples of ETFs are but the first representatives of…
Interactive Imitation Learning deals with training a novice policy from expert demonstrations in an online fashion. The established DAgger algorithm trains a robust novice policy by alternating between interacting with the environment and…
We show here how, using Euler's integration method and an associated function bounding the error in function of time, one can generate structures closely surrounding the invariant tori of dynamical systems. Such structures are constructed…
Benefiting from the continuous representation ability, deep implicit functions can represent a shape at infinite resolution. However, extracting high-resolution iso-surface from an implicit function requires forward-propagating a network…
Acquiring plausible pathways on high-dimensional structural distributions is beneficial in several domains. For example, in the drug discovery field, a protein conformational pathway, i.e. a highly probable sequence of protein structural…
Recurrent All-Pairs Field Transforms (RAFT) has shown great potentials in matching tasks. However, all-pairs correlations lack non-local geometry knowledge and have difficulties tackling local ambiguities in ill-posed regions. In this…
We introduce a variant of the proximal gradient method in which the quadratic term is diagonal but may be indefinite, and is safeguarded by a trust region. Our method is a special case of the proximal quasi-Newton trust-region method of…
A rapidly convergent series, based on Taylor expansion of the imaginary part of the complex error function, is presented for highly accurate approximation of the Voigt/complex error function with small imaginary argument (Y less than 0.1).…
In this paper, we present an approach to enhance interpolation and approximation error estimates. Based on a previously derived first-order Taylor-like formula, we demonstrate its applicability in improving the $P_1$-interpolation error…
The paper [1] shows that simple linear classifier can compete with complex deep learning algorithms in text classification applications. Combining bag of words (BoW) and linear classification techniques, fastText [1] attains same or only…
Correctness of results from mixed-integer linear programming (MILP) solvers is critical, particularly in the context of applications such as hardware verification, compiler optimization, or machine-assisted theorem proving. To this end,…
Intelligent document processing pipelines extract structured entities (tables, images, and text) from documents for use in downstream systems such as knowledge bases, retrieval-augmented generation, and analytics. A persistent limitation of…
Video-text retrieval (VTR) aims to locate relevant videos using natural language queries. Current methods, often based on pre-trained models like CLIP, are hindered by video's inherent redundancy and their reliance on coarse, final-layer…
Steiner Tree Problem (STP) in graphs aims to find a tree of minimum weight in the graph that connects a given set of vertices. It is a classic NP-hard combinatorial optimization problem and has many real-world applications (e.g., VLSI chip…
In this paper, we investigate numerical solutions for inverse singular value problems (for short, ISVPs) arising in various applications. Inspired by the methodologies employed for inverse eigenvalue problems, we propose a Cayley-free…