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We demonstrate a new algorithm for finding protein conformations that minimize a non-bonded energy function. The new algorithm, called the difference map, seeks to find an atomic configuration that is simultaneously in two constraint…

Image segmentation is the process of partitioning the image into significant regions easier to analyze. Nowadays, segmentation has become a necessity in many practical medical imaging methods as locating tumors and diseases. Hidden Markov…

In this work, following the Discrete de Rham (DDR) paradigm, we develop an arbitrary-order discrete divdiv complex on general polyhedral meshes. The construction rests 1) on discrete spaces that are spanned by vectors of polynomials whose…

This paper addresses the problem of natural image segmentation by extracting information from a multi-layer array which is constructed based on color, gradient, and statistical properties of the local neighborhoods in an image. A Gaussian…

We present a hierarchical optimization architecture for large-scale power networks that overcomes limitations of fully centralized and fully decentralized architectures. The architecture leverages principles of multigrid computing schemes,…

In this review we identify a new category of structural optimization methods that has emerged over the last 20 years, which we propose to call feature-mapping methods. The two defining aspects of these methods are that the design is…

We describe an approach for segmenting an image into regions that correspond to surfaces in the scene that are partially surrounded by the medium. It integrates both appearance and motion statistics into a cost functional, that is seeded…

We introduce an energy-based model, which seems especially suited for constrained systems. The proposed model provides an alternative to the popular port-Hamiltonian framework and exhibits similar properties such as energy dissipation as…

We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise…

We propose to apply several gradient estimation techniques to enable the differentiation of programs with discrete randomness in High Energy Physics. Such programs are common in High Energy Physics due to the presence of branching processes…

In intensity-modulated radiation therapy, optimal intensity distributions of incoming beams are decomposed into linear combinations of leaf openings of a multileaf collimator (segments). In order to avoid inefficient dose delivery, the…

A levelset free but a hybrid image segmentation approach based on a modified version of the piece wise constant shape gradient of an Mumford Shah shape functional and a repulsive function is considered. The segmentation is performed a…

Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient…

Shortening quantum circuits is crucial to reducing the destructive effect of environmental decoherence and enabling useful algorithms. Here, we demonstrate an improvement in such compilation tasks via a combination of using hybrid…

Deep learning has led to significant advances in artificial intelligence, in part, by adopting strategies motivated by neurophysiology. However, it is unclear whether deep learning could occur in the real brain. Here, we show that a deep…

We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect…

A computational method is presented which is capable to obtain low lying energy structures of topological amorphous systems. The method merges a differential mutation genetic algorithm with simulated annealing. This is done by incorporating…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem…

In recent years, deep-networks-based hashing has become a leading approach for large-scale image retrieval. Most deep hashing approaches use the high layer to extract the powerful semantic representations. However, these methods have…