Related papers: Quadratic Programming Approach to Fit Protein Comp…
Optimal Morse matchings reveal essential structures of cell complexes which lead to powerful tools to study discrete geometrical objects, in particular discrete 3-manifolds. However, such matchings are known to be NP-hard to compute on…
In the post-Moore era, the need for efficient solutions to non-deterministic polynomial-time (NP) problems is becoming more pressing. In this context, the Ising model implemented by the probabilistic computing systems with probabilistic…
A frame is a generalization of a basis of a vector space to a redundant overspanning set whose vectors are linearly dependent. Frames find applications in signal processing and quantum information theory. We present a genetic algorithm that…
Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…
In this paper, we discuss the solution of a Quadratic Eigenvalue Complementarity Problem (QEiCP) by using Difference of Convex (DC) programming approaches. We first show that QEiCP can be represented as dc programming problem. Then we…
The graph partitioning problem is a well-known NP-hard problem. In this paper, we formulate a 0-1 quadratic integer programming model for the graph partitioning problem with vertex weight constraints and fixed vertex constraints, and…
This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…
We present a convex mixed-integer programming formulation for non-rigid shape matching. To this end, we propose a novel shape deformation model based on an efficient low-dimensional discrete model, so that finding a globally optimal…
Accurately modeling and designing protein complex structures is a central problem in computational structural biology, with broad implications for understanding cellular function and developing therapeutics. This thesis investigates two…
We consider a parametric convex quadratic programming, CQP, relaxation for the quadratic knapsack problem, QKP. This relaxation maintains partial quadratic information from the original QKP by perturbing the objective function to obtain a…
We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…
Protein structure determination has long been one of the primary challenges of structural biology, to which deep machine learning (ML)-based approaches have increasingly been applied. However, these ML models generally do not incorporate…
Solving point-wise feature correspondence in visual data is a fundamental problem in computer vision. A powerful model that addresses this challenge is to formulate it as graph matching, which entails solving a Quadratic Assignment Problem…
We show NP-hardness of a generalized quadratic programming problem, which we called Unconstrained N-ary Quadratic Programming (UNQP). This problem has recently become practically relevant in the context of novel memristor-based neuromorphic…
Binary embedding is the problem of mapping points from a high-dimensional space to a Hamming cube in lower dimension while preserving pairwise distances. An efficient way to accomplish this is to make use of fast embedding techniques…
This paper examines the nonconvex quadratically constrained quadratic programming (QCQP) problems using an iterative method. One of the existing approaches for solving nonconvex QCQP problems relaxes the rank one constraint on the unknown…
Many problems of interest in computer vision can be formulated as a problem of finding consistent correspondences between two feature sets. Feature correspondence (matching) problem with one-to-one mapping constraint is usually formulated…
In this paper, we consider the quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces. By using the Legendre property of quadratic forms or the compactness of operators in the presentations of…
Protein structure prediction can be shown to be an NP-hard problem; the number of conformations grows exponentially with the number of residues. The native conformations of proteins occupy a very small subset of these, hence an exploratory,…
In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of…