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In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…
A rational triangle has rational edge-lengths and area; a rational tetrahedron has rational faces and volume; either is Heronian when its edge-lengths are integer, and proper when its content is nonzero. A variant proof is given, via…
The evolutionary trajectory of a protein through sequence space is constrained by function and three-dimensional (3D) structure. Residues in spatial proximity tend to co-evolve, yet attempts to invert the evolutionary record to identify…
Proteins perform much of the work in living organisms, and consequently the development of efficient computational methods for protein representation is essential for advancing large-scale biological research. Most current approaches…
Predicting the structure of multi-protein complexes is a grand challenge in biochemistry, with major implications for basic science and drug discovery. Computational structure prediction methods generally leverage pre-defined structural…
Protein structure tokenization converts 3D structures into discrete or vectorized representations, enabling the integration of structural and sequence data. Despite many recent works on structure tokenization, the properties of the…
Cracks in concrete structures are very common and are an integral part of this heterogeneous material. Characteristics of cracks induced by standardized tests yield valuable information about the tested concrete formulation and its…
We introduce a lattice model of protein conformations which is able to reproduce second structures of proteins (alpha--helices and beta--sheets). This model is based on the following two main ideas. First, we model backbone parts of amino…
We present an efficient algorithm to recover the three dimensional structure of a protein from its contact map representation. First we show that when a physically realizable map is used as target, our method generates a structure whose…
High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product…
Predicting the three-dimensional (3D) structure of a protein from its primary sequence of amino acids is known as the protein folding (PF) problem. Due to the central role of proteins' 3D structures in chemistry, biology and medicine…
Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable at present on classical architectures. Here, we discuss…
The ability to precisely visualize the atomic geometry of the interactions between a drug and its protein target in structural models is critical in predicting the correct modifications in previously identified inhibitors to create more…
The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several authors have reported that in numerical experiments the generating vector sometimes…
Rod-based structures are commonly used in practical applications in science and engineering. However, in many design, analysis, and manufacturing tasks, handling the rod-based structures in three dimensions directly is generally…
Three dimensional (3D) toric codes are a class of stabilizer codes with local checks and come under the umbrella of topological codes. While decoding algorithms have been proposed for the 3D toric code on a cubic lattice, there have been…
We address protein structure prediction in the 3D Hydrophobic-Polar lattice model through two novel deep learning architectures. For proteins under 36 residues, our hybrid reservoir-based model combines fixed random projections with…
Overlaying commensurate optical lattices with various configurations called superlattices can lead to exotic lattice topologies and, in turn, a discovery of novel physics. In this study, by overlapping the maxima of lattices, a new isolated…
We propose an ion trap configuration such that individual traps can be stacked together in a three dimensional simple cubic arrangement. The isolated trap as well as the extended array of ion traps are characterized for different locations…
Today, hardware constraints are an important limitation on quantum adiabatic optimization algorithms. Firstly, computational problems must be formulated as quadratic unconstrained binary optimization (QUBO) in the presence of noisy coupling…