2,140 results match your criteria Algebra Colloquium[Journal]


Method for the Manual Analysis of Moiré Structures in STM images.

Chemphyschem 2021 May 4;22(9):870-884. Epub 2021 May 4.

Department Chemie, Ludwig-Maximilians-Universität München, Butenandtstr. 5-13, 81377, Munich, Germany.

A method is presented to manually determine the lattice parameters of commensurate hexagonal moiré structures resolved by STM. It solves the problem that lattice parameters of moiré structures usually cannot be determined by inspection of an STM image, so that computer-based analyses are required. The lattice vector of a commensurate moiré structure is a sum of integer multiples both of the two basis vectors of the substrate and of the adsorbed layer. Read More

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Predicting Middle School Profiles of Algebra Performance Using Fraction Knowledge.

Child Dev 2021 Apr 30. Epub 2021 Apr 30.

Temple University.

Fraction knowledge and algebraic skill are closely linked. Algebra is a gatekeeper for advanced courses (Booth & Newton, 2012; Brown & Quinn, 2007). This study uses the person-centered approach of latent profile analysis to examine individual differences in middle schoolers' (N = 350) algebra performance at the end of the year (EOY). Read More

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Three-Dimensional Unified Motion Control of a Robotic Standing Wheelchair for Rehabilitation Purposes.

Sensors (Basel) 2021 Apr 27;21(9). Epub 2021 Apr 27.

Departamento de Eléctrica y Electrónica, Universidad de las Fuerzas Armadas-ESPE, Sangolquí 171103, Ecuador.

Technological advances in recent years have shown interest in the development of robots in the medical field. The integration of robotic systems in areas of assistance and rehabilitation improves the user's quality of life. In this context, this article presents a proposal for the unified control of a robotic standing wheelchair. Read More

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Direct statistical inference for finite Markov jump processes via the matrix exponential.

Authors:
Chris Sherlock

Comput Stat 2021 Apr 19:1-25. Epub 2021 Apr 19.

Department of Mathematics and Statistics, Lancaster University, Lancaster, UK.

Given noisy, partial observations of a time-homogeneous, finite-statespace Markov chain, conceptually simple, direct statistical inference is available, in theory, via its rate matrix, or infinitesimal generator, , since is the transition matrix over time . However, perhaps because of inadequate tools for matrix exponentiation in programming languages commonly used amongst statisticians or a belief that the necessary calculations are prohibitively expensive, statistical inference for continuous-time Markov chains with a large but finite state space is typically conducted via particle MCMC or other relatively complex inference schemes. When, as in many applications arises from a reaction network, it is usually sparse. Read More

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Constructing Compact Signatures for Individual Fingerprinting of Brain Connectomes.

Front Neurosci 2021 6;15:549322. Epub 2021 Apr 6.

Department of Computer Science, Purdue University, West Lafayette, IN, United States.

Recent neuroimaging studies have shown that functional connectomes are unique to individuals, i.e., two distinct fMRIs taken over different sessions of the same subject are more similar in terms of their connectomes than those from two different subjects. Read More

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IDENTIFYING THE NUMBER OF COMPONENTS IN GAUSSIAN MIXTURE MODELS USING NUMERICAL ALGEBRAIC GEOMETRY.

J Algebra Appl 2020 Nov 21;19(11). Epub 2019 Oct 21.

Department of Mathematics, University of Hawai'i at Mānoa, 2565 McCarthy Mall, Honolulu, Hawaii 96822, USA.

Using Gaussian mixture models for clustering is a statistically mature method for clustering in data science with numerous successful applications in science and engineering. The parameters for a Gaussian mixture model are typically estimated from training data using the iterative expectation-maximization algorithm, which requires the number of Gaussian components a priori. In this study, we propose two algorithms rooted in numerical algebraic geometry, namely an area-based algorithm and a local maxima algorithm, to identify the optimal number of components. Read More

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November 2020

Feature Selection Using Approximate Conditional Entropy Based on Fuzzy Information Granule for Gene Expression Data Classification.

Authors:
Hengyi Zhang

Front Genet 2021 30;12:631505. Epub 2021 Mar 30.

College of Animal Science and Technology, Northwest A&F University, Yangling, China.

Classification is widely used in gene expression data analysis. Feature selection is usually performed before classification because of the large number of genes and the small sample size in gene expression data. In this article, a novel feature selection algorithm using approximate conditional entropy based on fuzzy information granule is proposed, and the correctness of the method is proved by the monotonicity of entropy. Read More

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Simultaneous Detection of Six Isoforms of Tau Protein in Human Cerebrospinal Fluid by Multidimensional Mass Spectrometry-Based Targeted Proteomics.

J Proteome Res 2021 Apr 12. Epub 2021 Apr 12.

School of Pharmacy, Nanjing Medical University, Nanjing 211166, China.

Abnormal expression of Tau protein can cause the development of Alzheimer's disease (AD). So far, much evidence has demonstrated that Tau has multiple isoforms. These isoforms are suggested to have distinct physiological roles and contribute unequally to the progress of AD. Read More

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Effects of optical activity to Mueller matrix ellipsometry of composed waveplates.

Opt Express 2021 Mar;29(7):10434-10450

Mueller matrix ellipsometry has been used to precisely characterize quartz waveplates for demanding applications in the semiconductor industry and high precision polarimetry. We have found this experimental technique to be beneficial to use because it enables us to obtain absolute and precise measurement of retardation in a wide spectral range, waveplate orientation, and compound waveplate adjustment. In this paper, the necessity of including the optical activity in the Mueller matrix model and data treatment is demonstrated. Read More

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Testing short distance anisotropy in space.

Sci Rep 2021 Apr 2;11(1):7474. Epub 2021 Apr 2.

Theoretical Physics Lab, THEPI Division, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung, 40132, Indonesia.

The isotropy of space is not a logical requirement but rather is an empirical question; indeed there is suggestive evidence that universe might be anisotropic. A plausible source of these anisotropies could be quantum gravity corrections. If these corrections happen to be between the electroweak scale and the Planck scale, then these anisotropies can have measurable consequences at short distances and their effects can be measured using ultra sensitive condensed matter systems. Read More

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Influence of the dissipation on the N-level atom interacting with a two two-level atoms in presence of qubit-qubit interaction.

Sci Rep 2021 Apr 1;11(1):7345. Epub 2021 Apr 1.

Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, 11884, Egypt.

The interacting of two qubits and an N-level atom based on su(2) Lie algebra in the presence of both qubit-qubit interaction and dissipation term is considered. The effects of the qubit-qubit interaction and the dissipation term on the dynamics of the proposed system are discussed in detail for certain values of the number of levels. The dynamical expressions of the observable operators are obtained using the Heisenberg equation of motion. Read More

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Mathematical modelling of the conductivity in CZTiS-CZSnS as a function of synthesis temperature.

J Phys Condens Matter 2021 Apr 26;33(19). Epub 2021 Apr 26.

Instituto para la Investigación e Innovación en Ciencia y Tecnología de Materiales (INCITEMA), Universidad Pedagógica y Tecnológica de Colombia, Tunja, Av. Central del Norte 39-115, Colombia.

The electrical behavior of photovoltaic materials related with CuZnTiSand CuZnSnSmaterials were analyzed as function of synthesis temperature in accordance with a new mathematical model based on the Kramers-Kronig equations with a high reliability. The samples were obtained through a hydrothermal route and a subsequent thermal treatment of solids at 550 °C for 1 h under nitrogen flow (50 ml min). The characterization was done by x-ray diffraction, ultraviolet spectroscopy (UV), Raman spectroscopy, atomic force microscopy (AFM) and solid state impedance spectroscopy (IS) techniques. Read More

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Optimal Solution to the Torsional Coefficient Fitting Problem in Force Field Parametrization.

J Phys Chem A 2021 Apr 24;125(12):2673-2681. Epub 2021 Mar 24.

Department of Computational Biophysics and Bioinformatics, Faculty of Biochemistry, Biophysics and Biotechnology, Jagiellonian University, ul. Gronostajowa 7, 30-387 Cracow, Poland.

Molecular modeling is an excellent tool for studying biological systems on the atomic scale. Depending on objects, which may be proteins, nucleic acids, or lipids, different force fields are recommended. The phospholipid bilayers constitute an example, in which behavior is extensively studied using molecular dynamics simulations due to limitations of experimental methods. Read More

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Cluster Algebras for Feynman Integrals.

Phys Rev Lett 2021 Mar;126(9):091603

DESY Theory Group, DESY Hamburg, Notkestrasse 85, 22607 Hamburg, Germany.

We initiate the study of cluster algebras in Feynman integrals in dimensional regularization. We provide evidence that four-point Feynman integrals with one off-shell leg are described by a C_{2} cluster algebra, and we find cluster adjacency relations that restrict the allowed function space. By embedding C_{2} inside the A_{3} cluster algebra, we identify these adjacencies with the extended Steinmann relations for six-particle massless scattering. Read More

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Tropical Tensor Network for Ground States of Spin Glasses.

Phys Rev Lett 2021 Mar;126(9):090506

CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.

We present a unified exact tensor network approach to compute the ground state energy, identify the optimal configuration, and count the number of solutions for spin glasses. The method is based on tensor networks with the tropical algebra defined on the semiring of (R∪{-∞},⊕,⊙). Contracting the tropical tensor network gives the ground state energy; differentiating through the tensor network contraction gives the ground state configuration; mixing the tropical algebra and the ordinary algebra counts the ground state degeneracy. Read More

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Superconformal Bondi-Metzner-Sachs Algebra in Three Dimensions.

Phys Rev Lett 2021 Mar;126(9):091602

Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia 5090000, Chile.

The conformal extension of the BMS_{3} algebra is constructed. Apart from an infinite number of "superdilatations," in order to incorporate superspecial conformal transformations, the commutator of the latter with supertranslations strictly requires the presence of nonlinear terms in the remaining generators. The algebra appears to be very rigid, in the sense that its central extensions as well as the coefficients of the nonlinear terms become determined by the central charge of the Virasoro subalgebra. Read More

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Duality Hierarchies and Differential Graded Lie Algebras.

Commun Math Phys 2021 18;382(1):277-315. Epub 2021 Feb 18.

Institute for Physics, Humboldt University Berlin, Zum Großen Windkanal 6, D-12489 Berlin, Germany.

The gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies: generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require higher-form gauge fields. Recently, we proposed that the algebraic structure allowing for consistent tensor hierarchies is axiomatized by 'infinity-enhanced Leibniz algebras' defined on graded vector spaces generalizing Leibniz algebras. It was subsequently shown that, upon appending additional vector spaces, this structure can be reinterpreted as a differential graded Lie algebra. Read More

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February 2021

Real-Time Thinning Algorithms for 2D and 3D Images using GPU processors.

Authors:
Martin G Wagner

J Real Time Image Process 2020 Oct 28;17(5):1255-1266. Epub 2019 May 28.

Department of Medical Physics, University of Wisconsin, 1111 Highland Avenue, Madison, WI 53705.

The skeletonization of binary images is a common task in many image processing and machine learning applications. Some of these applications require very fast image processing. We propose novel techniques for efficient 2D and 3D thinning of binary images using GPU processors. Read More

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October 2020

Zero forcing number of graphs with a power law degree distribution.

Authors:
Alexei Vazquez

Phys Rev E 2021 Feb;103(2-1):022301

Cancer Research UK Beatson Institute, Glasgow, United Kingdom and Institute for Cancer Sciences, University of Glasgow, G611BD Glasgow, United Kingdom.

The zero forcing number is the minimum number of black vertices that can turn a white graph black following a single neighbor color forcing rule. The zero forcing number provides topological information about linear algebra on graphs, with applications to the controllability of quantum dynamical systems. Here, I investigate the zero forcing number of undirected graphs with a power law degree distribution p_{k}∼k^{-γ} by means of numerical simulations. Read More

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February 2021

Infinite combinatorics in mathematical biology.

Biosystems 2021 Jun 14;204:104392. Epub 2021 Mar 14.

Institute of Mathematical Biology, Faculty of Computer Sciences, Mannheim University of Applied Sciences, 68163, Mannheim, Germany. Electronic address:

Is it possible to apply infinite combinatorics and (infinite) set theory in theoretical biology? We do not know the answer yet but in this article we try to present some techniques from infinite combinatorics and set theory that have been used over the last decades in order to prove existence results and independence theorems in algebra and that might have the flexibility and generality to be also used in theoretical biology. In particular, we will introduce the theory of forcing and an algebraic construction technique based on trees and forests using infinite binary sequences. We will also present an overview of the theory of circular codes. Read More

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ACE: the Advanced Cohort Engine for searching longitudinal patient records.

J Am Med Inform Assoc 2021 Mar 13. Epub 2021 Mar 13.

Center for Biomedical Informatics Research, School of Medicine, School of Medicine, Stanford University, Stanford, California, USA.

Objective: To propose a paradigm for a scalable time-aware clinical data search, and to describe the design, implementation and use of a search engine realizing this paradigm.

Materials And Methods: The Advanced Cohort Engine (ACE) uses a temporal query language and in-memory datastore of patient objects to provide a fast, scalable, and expressive time-aware search. ACE accepts data in the Observational Medicine Outcomes Partnership Common Data Model, and is configurable to balance performance with compute cost. Read More

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A question of Mazurov on groups of exponent dividing 12.

Commun Algebra 2020 8;48(12):5372-5373. Epub 2020 Jul 8.

Department of Mathematical and Statistical Sciences, Marquette University, Wisconsin, USA.

Mazurov asked whether a group of exponent dividing 12, which is generated by , and subject to the relations has order at most 12. We show that if such a group is finite, then the answer is yes. Read More

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Sparse data embedding and prediction by tropical matrix factorization.

BMC Bioinformatics 2021 Feb 25;22(1):89. Epub 2021 Feb 25.

Faculty of Computer and Information Science, University of Ljubljana, Večna pot 113, 1000, Ljubljana, Slovenia.

Background: Matrix factorization methods are linear models, with limited capability to model complex relations. In our work, we use tropical semiring to introduce non-linearity into matrix factorization models. We propose a method called Sparse Tropical Matrix Factorization (STMF) for the estimation of missing (unknown) values in sparse data. Read More

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February 2021

Analytic evaluation of energy first derivatives for spin-orbit coupled-cluster singles and doubles augmented with noniterative triples method: General formulation and an implementation for first-order properties.

J Chem Phys 2021 Feb;154(6):064110

Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA.

A formulation of analytic energy first derivatives for the coupled-cluster singles and doubles augmented with noniterative triples [CCSD(T)] method with spin-orbit coupling included at the orbital level and an implementation for evaluation of first-order properties are reported. The standard density-matrix formulation for analytic CC gradient theory adapted to complex algebra has been used. The orbital-relaxation contributions from frozen core, occupied, virtual, and frozen virtual orbitals to analytic spin-orbit CCSD(T) gradients are fully taken into account and treated efficiently, which is of importance to calculations of heavy elements. Read More

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February 2021

Resolution of the identity approximation applied to PNOF correlation calculations.

J Chem Phys 2021 Feb;154(6):064102

Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, Mexico City C.P. 04510, Mexico.

In this work, the required algebra to employ the resolution of the identity approximation within the Piris Natural Orbital Functional (PNOF) is developed, leading to an implementation named DoNOF-RI. The arithmetic scaling is reduced from fifth-order to fourth-order, and the memory scaling is reduced from fourth-order to third-order, allowing significant computational time savings. After the DoNOF-RI calculation has fully converged, a restart with four-center electron repulsion integrals can be performed to remove the effect of the auxiliary basis set incompleteness, quickly converging to the exact result. Read More

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February 2021

Effect of Age and Embryo Morphology on Live Birth Rate After Transfer of Unbiopsied Blastocysts.

JBRA Assist Reprod 2020 Nov 5. Epub 2020 Nov 5.

Division of Reproductive Endocrinology and Infertility, Department of Obstetrics and Gynecology, Keck School of Medicine, University of Southern California, Los Angeles, California.

Objective: To determine the rate of live birth per blastocyst based on morphology and oocyte age using data from a single center.

Methods: This is a mathematical analysis and model building study of autologous blastocyst stage embryo transfers at a University-affiliated center. A total of 448 blastocyst stage embryos were transferred in 244 fresh and frozen embryo transfers from May 2015 through April 2018. Read More

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November 2020

A compression strategy for particle mesh Ewald theory.

J Chem Phys 2021 Feb;154(5):054112

Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA.

Particle Mesh Ewald (PME) has become a standard method for treating long-range electrostatics in molecular simulations. Although the method has inferior asymptotic computational complexity to its linear scaling competitors, it remains enormously popular due to its high efficiency, which stems from the use of fast Fourier transforms (FFTs). This use of FFTs provides great challenges for scaling the method up to massively parallel systems, in large part because of the need to transfer large amounts of data. Read More

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February 2021

Quantum Grothendieck rings as quantum cluster algebras.

Authors:
Léa Bittmann

J Lond Math Soc 2021 Jan 27;103(1):161-197. Epub 2020 Jul 27.

Faculty of Mathematics Universität Wien Oskar-Morgenstern-Platz 1 Wien 1090 Austria.

We define and construct a quantum Grothendieck ring for a certain monoidal subcategory of the category of representations of the quantum loop algebra introduced by Hernandez-Jimbo. We use the cluster algebra structure of the Grothendieck ring of this category to define the quantum Grothendieck ring as a quantum cluster algebra. When the underlying simple Lie algebra is of type , we prove that this quantum Grothendieck ring contains the quantum Grothendieck ring of the category of finite-dimensional representations of the associated quantum affine algebra. Read More

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January 2021

The Continuum Between Temperament and Mental Illness as Dynamical Phases and Transitions.

Authors:
William Sulis

Front Psychiatry 2020 18;11:614982. Epub 2021 Jan 18.

Collective Intelligence Laboratory, Department of Psychiatry and Behavioural Neuroscience, McMaster University, Hamilton, ON, Canada.

The full range of biopsychosocial complexity is mind-boggling, spanning a vast range of spatiotemporal scales with complicated vertical, horizontal, and diagonal feedback interactions between contributing systems. It is unlikely that such complexity can be dealt with by a single model. One approach is to focus on a narrower range of phenomena which involve fewer systems but still cover the range of spatiotemporal scales. Read More

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January 2021

Progressive gray matter hypertrophy with severity stages of insomnia disorder and its relevance for mood symptoms.

Eur Radiol 2021 Feb 3. Epub 2021 Feb 3.

Department of Medical Imaging, Guangdong Second Provincial General Hospital, Guangzhou, China.

Objective: To investigate the gray matter (GM) alterations in patients with insomnia disorder (ID) at different severity stages and the relationship between GM alterations and sleep, mood, and cognitive measures.

Methods: One hundred one ID patients and 63 healthy controls (HC) were included. Each patient underwent structural MRI and completed sleep-, mood-, and cognitive-related questionnaires. Read More

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February 2021