2,366 results match your criteria Algebra & Number Theory[Journal]

Applications of Artificial Intelligence and Machine Learning Algorithms to Crystallization.

Chem Rev 2022 Jun 27. Epub 2022 Jun 27.

School of Chemical Engineering, National Technical University of Athens, Heroon Polytechniou 9, 15780 Zografou, Greece.

Artificial intelligence and specifically machine learning applications are nowadays used in a variety of scientific applications and cutting-edge technologies, where they have a transformative impact. Such an assembly of statistical and linear algebra methods making use of large data sets is becoming more and more integrated into chemistry and crystallization research workflows. This review aims to present, for the first time, a holistic overview of machine learning and cheminformatics applications as a novel, powerful means to accelerate the discovery of new crystal structures, predict key properties of organic crystalline materials, simulate, understand, and control the dynamics of complex crystallization process systems, as well as contribute to high throughput automation of chemical process development involving crystalline materials. Read More

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On reducing and finding solutions of nonlinear evolutionary equations via generalized symmetry of ordinary differential equations.

Math Biosci Eng 2022 May;19(7):6962-6984

AGH University of Science and Technology, Faculty of Applied Mathematics, aleja Adama Mickiewicza 30, 30-059 Kraków, Poland.

We study symmetry reductions of nonlinear partial differential equations that can be used for describing diffusion processes in heterogeneous medium. We find ansatzes reducing these equations to systems of ordinary differential equations. The ansatzes are constructed using generalized symmetries of second-order ordinary differential equations. Read More

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Biol Cybern 2022 Jun 21. Epub 2022 Jun 21.

Idiap Research Institute, Martigny, Switzerland.

In Bourlard and Kamp (Biol Cybern 59(4):291-294, 1998), it was theoretically proven that autoencoders (AE) with single hidden layer (previously called "auto-associative multilayer perceptrons") were, in the best case, implementing singular value decomposition (SVD) Golub and Reinsch (Linear algebra, Singular value decomposition and least squares solutions, pp 134-151. Springer, 1971), equivalent to principal component analysis (PCA) Hotelling (Educ Psychol 24(6/7):417-441, 1993); Jolliffe (Principal component analysis, springer series in statistics, 2nd edn. Springer, New York ). Read More

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A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions.

Lett Math Phys 2022 11;112(3):58. Epub 2022 Jun 11.

Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120 Heidelberg, Germany.

We focus on functional renormalization for ensembles of several (say ) random matrices, whose potentials include multi-traces, to wit, the probability measure contains factors of the form for certain noncommutative polynomials in the matrices. This article shows how the "algebra of functional renormalization"-that is, the structure that makes the renormalization flow equation computable-is derived from ribbon graphs, only by requiring the one-loop structure that such equation (due to Wetterich) is expected to have. Whenever it is possible to compute the renormalization flow in terms of -invariants, the structure gained is the matrix algebra with entries in , being the free algebra generated by the Hermitian matrices of size (the flowing random variables) with multiplication of homogeneous elements in given, for each , by which, together with the condition for each complex , fully define the symbol . Read More

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Implication in finite posets with pseudocomplemented sections.

Soft comput 2022 19;26(13):5945-5953. Epub 2022 Apr 19.

Faculty of Science Department of Algebra and Geometry, Palacký University Olomouc, 17. listopadu 12, Olomouc, 771 46 Czech Republic.

It is well-known that relatively pseudocomplemented lattices can serve as an algebraic semantics of intuitionistic logic. To extend the concept of relative pseudocomplementation to non-distributive lattices, the first author introduced so-called sectionally pseudocomplemented lattices, i.e. Read More

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Differential and shared genetic effects on kidney function between diabetic and non-diabetic individuals.

Commun Biol 2022 Jun 13;5(1):580. Epub 2022 Jun 13.

Division of Kidney, Urologic and Hematologic Diseases, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD, USA.

Reduced glomerular filtration rate (GFR) can progress to kidney failure. Risk factors include genetics and diabetes mellitus (DM), but little is known about their interaction. We conducted genome-wide association meta-analyses for estimated GFR based on serum creatinine (eGFR), separately for individuals with or without DM (n = 178,691, n = 1,296,113). Read More

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Quantum-Safe Group Key Establishment Protocol from Lattice Trapdoors.

Sensors (Basel) 2022 May 30;22(11). Epub 2022 May 30.

Division of Industrial Systems, RISE-Research Institutes of Sweden, 852 33 Sundsvall, Sweden.

Group communication enables Internet of Things (IoT) devices to communicate in an efficient and fast manner. In most instances, a group message needs to be encrypted using a cryptographic key that only devices in the group know. In this paper, we address the problem of establishing such a key using a lattice-based one-way function, which can easily be inverted using a suitably designed lattice trapdoor. Read More

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The SHARK integral generation and digestion system.

Frank Neese

J Comput Chem 2022 Jun 9. Epub 2022 Jun 9.

Department of Molecular Theory and Spectroscopy, Max Planck Institut für Kohlenforschung, Mülheim an der Ruhr, Germany.

In this paper, the SHARK integral generation and digestion engine is described. In essence, SHARK is based on a reformulation of the popular McMurchie/Davidson approach to molecular integrals. This reformulation leads to an efficient algorithm that is driven by BLAS level 3 operations. Read More

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Systematic Dimensional Analysis of the Scaling Relationship for Gradient and Shim Coil Design Parameters.

Magn Reson Med 2022 Jun 6. Epub 2022 Jun 6.

Department of Radiology, Mayo Clinic, Rochester, Minnesota, USA.

Purpose: To demonstrate systematic, linear algebra-based, dimensional analysis to derive a scaling relationship among the design parameters of MRI gradient and harmonic shim coils.

Theory And Methods: The dimensions of five physical quantities relevant for gradient coil design (inductance, gradient amplitude, inner diameter [ ], current, and the permeability of free space) were decomposed into fundamental units, and their exponents were arranged into a dimensional matrix. The resulting set of homogenous equations was solved using standard linear algebraic methods. Read More

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ArboAlvo: stratification method for territorial receptivity to urban arboviruses.

Rev Saude Publica 2022 27;56:39. Epub 2022 May 27.

Fundação Oswaldo Cruz. Escola Nacional de Saúde Pública. Rio de Janeiro, RJ, Brasil.

Objective: To present the urban arboviruses (dengue, zika and chikungunya) stratification methodology by the territorial receptivity Index, an instrument for the surveillance and control of these diseases, which considers the heterogeneity of an intra-municipal territory.

Methods: Ecological study that uses as unit of analysis the areas covered by health centers in Belo Horizonte. For the development of a territorial receptivity index, indicators of socio-environmental determination of urban arboviruses were selected in order to integrate the analysis of main components. Read More

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Prediction of ocular magnification and aniseikonia after cataract surgery.

Acta Ophthalmol 2022 Jun 1. Epub 2022 Jun 1.

Augen- und Laserklinik Castrop-Rauxel, Castrop-Rauxel, Germany.

Background: Ocular magnification and aniseikonia after cataract surgery has been widely ignored in modern cataract surgery. The purpose of this study was to analyse ocular magnification and inter-individual differences in a normal cataract population with a focus on monovision.

Methods: From a large dataset containing biometric measurements (IOLMaster 700) of both eyes of 9734 patients prior to cataract surgery, eyes were indexed randomly as primary (P) and secondary (S). Read More

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Family and Individual Quality of Life in Parents of Children with Developmental Disorders and Diabetes Type 1.

J Clin Med 2022 May 19;11(10). Epub 2022 May 19.

Department of Public Health, University of Split School of Medicine, 21000 Split, Croatia.

Background: This cross-sectional study assessed both family and individual quality of life (QOL), and their association with self-esteem, optimism, chronic psychological stress, anxiety, and depression in parents of children with chronic conditions.

Methods: Parents of children with Down syndrome (DS), autistic spectrum disorder (ASD), cerebral palsy (CP), diabetes mellitus type 1 (DMT1), and parents of children without chronic diseases with typical development (TD) were included. Multivariate linear regression analysis was used to assess parental characteristics associated with the domains of individual and family QOL. Read More

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Entropy Treatment of Evolution Algebras.

Entropy (Basel) 2022 Apr 24;24(5). Epub 2022 Apr 24.

Department of Mathematical, Faculty of Science, Tafila Technical University, P.O. Box 179, Tafila 66110, Jordan.

In this paper, by introducing an entropy of Markov evolution algebras, we treat the isomorphism of -evolution algebras. A family of Markov evolution algebras is defined through the Hadamard product of structural matrices of non-negative real -evolution algebras, and their isomorphism is studied by means of their entropy. Furthermore, the isomorphism of -evolution algebras is treated using the concept of relative entropy. Read More

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Understanding the interaction among enablers of quality enhancement of higher business education in Pakistan.

PLoS One 2022 26;17(5):e0267919. Epub 2022 May 26.

Faculty of Administrative Science, Taiz University, Taiz City, Yemen.

This study aims to generate a list of enablers of quality enhancement of higher business education in Pakistan and build a structural model of enablers to prioritize them. It also intends to impose direction and hierarchy on the inter-relationships of the enablers. The study's design consists of a literature review, data collection from primary sources, and qualitative analysis. Read More

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Algebra of diffeomorphism-invariant observables in Jackiw-Teitelboim gravity.

J High Energy Phys 2022 16;2022(5):97. Epub 2022 May 16.

Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA.

In this paper we use the covariant Peierls bracket to compute the algebra of a sizable number of diffeomorphism-invariant observables in classical Jackiw-Teitelboim gravity coupled to fairly arbitrary matter. We then show that many recent results, including the construction of traversable wormholes, the existence of a family of SL(2 ℝ) algebras acting on the matter fields, and the calculation of the scrambling time, can be recast as simple consequences of this algebra. We also use it to clarify the question of when the creation of an excitation deep in the bulk increases or decreases the boundary energy, which is of crucial importance for the "typical state" versions of the firewall paradox. Read More

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An Improved Particle Swarm Optimization Algorithm and Its Application to the Extreme Value Optimization Problem of Multivariable Function.

Min Cai

Comput Intell Neurosci 2022 13;2022:1935272. Epub 2022 May 13.

School of Mathematical and Statistics, Xuzhou University of Technology, Xuzhou 221008, China.

It is proposed to improve the study of particle optimization and its application in order to solve the problem of inefficiency and lack of local optimization skills in the use of particle herd optimization. Firstly, the basic principle, mathematical description, algorithm parameters, and flow of the original (Particle Swarm Optimization, PSO) algorithm are introduced, and then the standard PSO algorithm is introduced; thirdly, over the last 10 years, four types of improvements have been proposed through the study of improved particle algorithms. The improved algorithm is applied to the extreme value optimization problem of multivariable function. Read More

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Sparse Angle CBCT Reconstruction Based on Guided Image Filtering.

Front Oncol 2022 27;12:832037. Epub 2022 Apr 27.

Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier (LIRMM), Unité Mixte de Recherche (UMR) 5506, French National Center for Scientific Research (CNRS) - University of Montpellier (UM), Montpellier, France.

Cone-beam Computerized Tomography (CBCT) has the advantages of high ray utilization and detection efficiency, short scan time, high spatial and isotropic resolution. However, the X-rays emitted by CBCT examination are harmful to the human body, so reducing the radiation dose without damaging the reconstruction quality is the key to the reconstruction of CBCT. In this paper, we propose a sparse angle CBCT reconstruction algorithm based on Guided Image FilteringGIF, which combines the classic Simultaneous Algebra Reconstruction Technique(SART) and the Total p-Variation (TpV) minimization. Read More

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Quantum Relativity of Subsystems.

Phys Rev Lett 2022 Apr;128(17):170401

Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA.

One of the most basic notions in physics is the partitioning of a system into subsystems and the study of correlations among its parts. In this Letter, we explore this notion in the context of quantum reference frame (QRF) covariance, in which this partitioning is subject to a symmetry constraint. We demonstrate that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. Read More

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Fluorescence Lifetime Phasor Analysis of the Decamer-Dimer Equilibrium of Human Peroxiredoxin 1.

Int J Mol Sci 2022 May 9;23(9). Epub 2022 May 9.

Laboratorio de Fisicoquímica Biológica, Instituto de Química Biológica, Facultad de Ciencias, Universidad de la República, Montevideo 11400, Uruguay.

Protein self-assembly is a common feature in biology and is often required for a myriad of fundamental processes, such as enzyme activity, signal transduction, and transport of solutes across membranes, among others. There are several techniques to find and assess homo-oligomer formation in proteins. Naturally, all these methods have their limitations, meaning that at least two or more different approaches are needed to characterize a case study. Read More

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Modular Structure of the Weyl Algebra.

Roberto Longo

Commun Math Phys 2022 19;392(1):145-183. Epub 2022 Mar 19.

Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, 00133 Rome, Italy.

We study the modular Hamiltonian associated with a Gaussian state on the Weyl algebra. We obtain necessary/sufficient criteria for the local equivalence of Gaussian states, independently of the classical results by Araki and Yamagami, Van Daele, Holevo. We also present a criterion for a Bogoliubov automorphism to be weakly inner in the GNS representation. Read More

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Encouraging research on recursive thinking through the lens of a model of the spread of contagious diseases.

ZDM 2022 May 3:1-13. Epub 2022 May 3.

University of California San Diego, La Jolla, CA USA.

Recursive reasoning is a powerful tool used extensively in problem solving. For us, recursive reasoning includes iteration, sequences, difference equations, discrete dynamical systems, pattern identification, and mathematical induction; all of these can represent how things change, but in discrete jumps. Given the school mathematics curriculum's later emphasis on calculus-the mathematics of change in continuous contexts-it is surprising that the curriculum seems to neglect recursive thinking after the early grades. Read More

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On the role of continuous symmetries in the solution of the three-dimensional Euler fluid equations and related models.

Philos Trans A Math Phys Eng Sci 2022 Jun 9;380(2226):20210050. Epub 2022 May 9.

School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland.

We review and apply the continuous symmetry approach to find the solution of the three-dimensional Euler fluid equations in several instances of interest, via the construction of constants of motion and infinitesimal symmetries, without recourse to Noether's theorem. We show that the vorticity field is a symmetry of the flow, so if the flow admits another symmetry then a Lie algebra of new symmetries can be constructed. For steady Euler flows this leads directly to the distinction of (non-)Beltrami flows: an example is given where the topology of the spatial manifold determines whether extra symmetries can be constructed. Read More

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Electronic energies from coupled fermionic "Zombie" states' imaginary time evolution.

J Chem Phys 2022 May;156(17):174116

School of Chemistry, University of Leeds, Leeds LS2 9JT, United Kingdom.

Zombie states are a recently introduced formalism to describe coupled coherent fermionic states that address the fermionic sign problem in a computationally tractable manner. Previously, it has been shown that Zombie states with fractional occupations of spin orbitals obeyed the correct fermionic creation and annihilation algebra and presented results for real-time evolution [D. V. Read More

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A new algebraic approach to genome rearrangement models.

J Math Biol 2022 05 5;84(6):49. Epub 2022 May 5.

Discipline of Mathematics, School of Natural Sciences, University of Tasmania, Private Bag 37, Sandy Bay, TAS, 7001, Australia.

We present a unified framework for modelling genomes and their rearrangements in a genome algebra, as elements that simultaneously incorporate all physical symmetries. Building on previous work utilising the group algebra of the symmetric group, we explicitly construct the genome algebra for the case of unsigned circular genomes with dihedral symmetry and show that the maximum likelihood estimate (MLE) of genome rearrangement distance can be validly and more efficiently performed in this setting. We then construct the genome algebra for a more general case, that is, for genomes that may be represented by elements of an arbitrary group and symmetry group, and show that the MLE computations can be performed entirely within this framework. Read More

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Bond topology of chain, ribbon and tube silicates. Part I. Graph-theory generation of infinite one-dimensional arrangements of (TO) tetrahedra.

Acta Crystallogr A Found Adv 2022 May 4;78(Pt 3):212-233. Epub 2022 Apr 4.

Department of Earth Sciences, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada.

Chain, ribbon and tube silicates are based on one-dimensional polymerizations of (TO) tetrahedra, where T = Si plus P, V, As, Al, Fe and B. Such polymerizations may be represented by infinite graphs (designated chain graphs) in which vertices represent tetrahedra and edges represent linkages between tetrahedra. The valence-sum rule of bond-valence theory limits the maximum degree of any vertex to 4 and the number of edges linking two vertices to 1 (corner-sharing tetrahedra). Read More

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Online Strategies To Improve Quantitative Skills in Microbiology Laboratory Classes.

J Microbiol Biol Educ 2022 Apr 28;23(1). Epub 2022 Mar 28.

Department of Biology, Virginia Commonwealth University, Richmond, Virginia, USA.

Biology is an increasingly quantitative science. Thus, it is important that undergraduate biology curricula include frequent opportunities for students to practice their quantitative skills. This can create a substantial grading burden for faculty teaching online and/or large enrollment courses, but the "formula question" feature present in many learning management systems (LMS) offers a solution. Read More

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Lcapy: symbolic linear circuit analysis with Python.

Michael Hayes

PeerJ Comput Sci 2022 18;8:e875. Epub 2022 Feb 18.

Electrical and Computer Engineering, University of Canterbury, Christchchurch, New Zealand.

Lcapy is an open-source Python package for solving linear circuits symbolically. It uses a superposition of DC analysis, AC (phasor) analysis, transient (Laplace) analysis, and noise analysis. Expressions are evaluated using the computer algebra system SymPy. Read More

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February 2022

Realization of multi-configurable logic gate behaviour on fluorescence switching signalling of naphthalene diimide congeners.

RSC Adv 2021 Oct 1;11(56):35274-35279. Epub 2021 Nov 1.

Physical Sciences Division, Institute of Advanced Study in Science and Technology Paschim Boragaon Guwahati-781035 Assam India

Organic entities like suitably functionalized naphthalene diimide (NDI) exhibited logical behaviours in response to various external stimuli and can be used to develop digital logic operations. The present findings include utilization of two congeners of NDI , N1 and N2 for the successive turning ON/OFF of fluorescence with inclusion of acid and base. The recognition of the switching phenomenon of the probes N1 and N2 are applied to construct fundamental digital logic gates such as NOT, YES, IMPLICATION, INHIBIT, The inputs to each of the logic gates are defined by the presence or absence of acid and base. Read More

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October 2021

Research priorities to reduce the impact of COVID-19 in low- and middle-income countries.

J Glob Health 2022 15;12:09003. Epub 2022 Apr 15.

National Yang Ming Chiao Tung University, Taipei, Taiwan.

Background: The COVID-19 pandemic has caused disruptions to the functioning of societies and their health systems. Prior to the pandemic, health systems in low- and middle-income countries (LMIC) were particularly stretched and vulnerable. The International Society of Global Health (ISoGH) sought to systematically identify priorities for health research that would have the potential to reduce the impact of the COVID-19 pandemic in LMICs. Read More

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Swiss knife partial least squares (SKPLS): One tool for modelling single block, multiblock, multiway, multiway multiblock including multi-responses and meta information under the ROSA framework.

Anal Chim Acta 2022 May 30;1206:339786. Epub 2022 Mar 30.

Faculty of Science and Technology, Norwegian University of Life Sciences, 1430, Ås, Norway.

In the domain of chemometrics and multivariate data analysis, partial least squares (PLS) modelling is a widely used technique. PLS gains its beauty by handling the high collinearity found in multivariate data by replacing highly covarying variables with common subspaces spanned by orthogonal latent variables. Furthermore, all can be achieved with simple steps of linear algebra requiring minimal computation power and time usage compared to current high-end computing and substantial hyperparameter tuning required by methods such as deep learning. Read More

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