2,153 results match your criteria Algebra & Number Theory[Journal]


Diffeomorphic Respiratory Motion Estimation of Thoracoabdominal Organs for Image-Guided Interventions.

Med Phys 2021 Jun 11. Epub 2021 Jun 11.

Department of Mechanical Engineering and Automation, Harbin Institute of Technology, Shenzhen, 518055, China.

Purpose: Percutaneous image-guided interventions are commonly used for the diagnosis and treatment of cancer. In practice, physiological breathing-induced motion increases the difficulty of accurately inserting needles into tumors without impairing the surrounding vital structures. In this work, we propose a data-driven patient-specific hierarchical respiratory motion estimation framework to accurately estimate the position of a tumor and surrounding vital tissues in real time. Read More

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Heterogeneous Effects of Early Algebra across California Middle Schools.

J Policy Anal Manage 2020 23;39(3):772-800. Epub 2020 Feb 23.

University of California at Irvine, 4181 Social Science Plaza A, Irvine, CA 92697.

How should schools assign students to more rigorous math courses so as best to help their academic outcomes? We identify several hundred California middle schools that used 7th-grade test scores to place students into 8th-grade algebra courses and use a regression discontinuity design to estimate average impacts and heterogeneity across schools. Enrolling in 8th-grade algebra boosts students' enrollment in advanced math in ninth grade by 30 percentage points and eleventh grade by 16 percentage points. Math scores in tenth grade rise by 0. Read More

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February 2020

Correction: Gill, R.D. Does Geometric Algebra Provide a Loophole to Bell's Theorem? 2020, , 61.

Entropy (Basel) 2021 May 19;23(5). Epub 2021 May 19.

Mathematical Institute, Leiden University, Rapenburg 70, 2311 EZ Leiden, The Netherlands.

Corrections are made to my paper "Gill, R.D. Does Geometric Algebra Provide a Loophole to Bell's Theorem? 2020, , 61" [. Read More

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FOCUSED-Short-Term Wind Speed Forecast Correction Algorithm Based on Successive NWP Forecasts for Use in Traffic Control Decision Support Systems.

Sensors (Basel) 2021 May 13;21(10). Epub 2021 May 13.

Faculty of Information Studies in Novo Mesto, 8000 Novo Mesto, Slovenia.

In this paper, we propose a new algorithm, called FOCUSED (FOrecast Correction Using Successive prEDictions), for forecast correction of short-term wind speed predictions. We developed FOCUSED with the aim of improving the forecast of bora gusts, which frequently result in high-speed wind situations dangerous for traffic. The motivation arises from occasionally ambiguous results of the currently deployed decision support system, which aids traffic management in strong and gusty wind conditions at the coast of Croatia. Read More

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Entropy of Quantum States.

Entropy (Basel) 2021 May 21;23(6). Epub 2021 May 21.

Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy.

Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a minimality property of the von Neumann entropy of a density matrix with respect to its possible decompositions into pure states, we give a purely algebraic definition of entropy for states of an algebra of observables, thus solving the above ambiguity. Read More

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Interference between naïve and scientific theories occurs in mathematics and is related to mathematical achievement.

Cognition 2021 May 29;214:104789. Epub 2021 May 29.

University of Graz, Graz, Austria.

When students learn a scientific theory that conflicts with their earlier naïve theories, the newer and more correct knowledge does not always replace the older and more incorrect knowledge. Both may coexist in a learner's long-term memory. Using a new speeded reasoning task, Shtulman and Valcarcel (2012) showed that naïve theories interfere with retrieving scientific theories. Read More

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Switching Spinless and Spinful Topological Phases with Projective PT Symmetry.

Phys Rev Lett 2021 May;126(19):196402

Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore.

A fundamental dichotomous classification for all physical systems is according to whether they are spinless or spinful. This is especially crucial for the study of symmetry-protected topological phases, as the two classes have distinct symmetry algebra. As a prominent example, the spacetime inversion symmetry PT satisfies (PT)^{2}=±1 for spinless/spinful systems, and each class features unique topological phases. Read More

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Current Status of e-Health in Burkina Faso.

Stud Health Technol Inform 2021 May;281:755-756

Algebra, discrete Mathematics and Informatics laboratory (LAMDI), Bobo-Dioulasso.

The term e-health refers to all areas where information and communication technologies (ICT) are used for health. E-health appears more and more as a relevant solution to meet the challenges health systems are facing. However, despite its interest, e-health has long remained underexploited in Burkina Faso even if many softwares have been the subject of investments in hospitals as part of a modernization of administrative operations, which does not directly contribute to the quality of care. Read More

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CLUE: Exact maximal reduction of kinetic models by constrained lumping of differential equations.

Bioinformatics 2021 May 25. Epub 2021 May 25.

IMT School for Advanced Studies, Lucca, 55100, Italy.

Motivation: Detailed mechanistic models of biological processes can pose significant challenges for analysis and parameter estimations due to the large number of equations used to track the dynamics of all distinct configurations in which each involved biochemical species can be found. Model reduction can help tame such complexity by providing a lower-dimensional model in which each macro-variable can be directly related to the original variables.

Results: We present CLUE, an algorithm for exact model reduction of systems of polynomial differential equations by constrained linear lumping. Read More

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Conceptual knowledge of the associativity principle: A review of the literature and an agenda for future research.

Trends Neurosci Educ 2021 Jun 27;23:100152. Epub 2021 Feb 27.

Department of Psychology, Portsmouth University, PO1 2UP, United Kingdom.

Individuals use diverse strategies to solve mathematical problems, which can reflect their knowledge of arithmetic principles and predict mathematical expertise. For example, '6 + 38 - 35' can be solved via '38 - 35 = 3' and then '3 + 6 = 9', which is a shortcut-strategy derived from the associativity principle. The shortcut may be critical for understanding algebra, however approximately 50% of adults fail to use it. Read More

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Explicit volume-preserving numerical schemes for relativistic trajectories and spin dynamics.

Phys Rev E 2021 Apr;103(4-1):043310

Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.

A class of explicit numerical schemes is developed to solve for the relativistic dynamics and spin of particles in electromagnetic fields, using the Lorentz-Bargmann-Michel-Telegdi equation formulated in the Clifford algebra representation of Baylis. It is demonstrated that these numerical methods, reminiscent of the leapfrog and Verlet methods, share a number of important properties: they are energy conserving, volume conserving, and second-order convergent. These properties are analyzed empirically by benchmarking against known analytical solutions in constant uniform electrodynamic fields. Read More

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State estimation and nonlinear tracking control simulation approach. Application to a bioethanol production system.

Bioprocess Biosyst Eng 2021 May 16. Epub 2021 May 16.

Instituto de Ingeniería Química, Universidad Nacional de San Juan (UNSJ), CONICET, Av. Lib. San Martín Oeste 1109, J5400ARL, San Juan, Argentina.

Tracking control of specific variables is key to achieve a proper fermentation. This paper analyzes a fed-batch bioethanol production process. For this system, a controller design based on linear algebra is proposed. Read More

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Unified Analysis on the Global Dissipativity and Stability of Fractional-Order Multidimension-Valued Memristive Neural Networks With Time Delay.

IEEE Trans Neural Netw Learn Syst 2021 May 5;PP. Epub 2021 May 5.

The unified criteria are analyzed on the global dissipativity and stability for the delayed fractional-order systems of multidimension-valued memristive neural networks (FSMVMNNs) in this article. First, based on the comprehensive knowledge about multidimensional algebra, fractional derivatives, and nonsmooth analysis, we establish the unified model for the studied FSMVMNNs in order to propose a more uniform method to analyze the dynamic behaviors of multidimensional neural networks. Then, by mainly applying the Lyapunov method, employing several new lemmas, and solving some mathematical difficulties, without any separation, we acquire the unified and concise criteria. Read More

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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 05 12;20(5):2299-2307. 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