“…Each fiber can then be collapsed into a single representative base node through an information-preserving transformation called “symmetry fibration,” introduced by Grothendieck in the context of algebraic geometry. We exemplify the symmetry fibrations in gene regulatory networks and then show that they universally apply across species and domains from biology to social and infrastructure networks. …”
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“…Our NMODL framework has been tested against a large number of previously published user models and offers high-level domain-specific optimizations and symbolic algebraic simplifications before target code generation. …”
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“…Unlike the classical model, the slack model naturally mods out projective transformations. It is inherently algebraic, arising as the positive part of a variety of a saturated determinantal ideal, and provides a new computational tool to study classical realizability problems for polytopes. …”
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“…DEBay estimates Normalized Gene Expression Coefficient (NGEC), which is a relative measure of the expression of the target gene in each cell type in a population. NGEC has a direct algebraic correspondence with the normalized fold change in gene expression measured by qPCR. …”
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“…TDA uses principles from algebraic topology to comprehensively measure shape in data sets. …”
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“…In contrast to the accepted theory for (2 + 1) surfaces, we found that the crossover point from a BKT (logarithmic) rough surface to a KPZ (algebraic) rough surface is different from the kinetic roughening point for the (001) surface. …”
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“…The type of a data stream is captured formally by a monoid, an algebraic structure with a distinguished binary operation and a unit. …”
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“…We analyze the adiabatic liquid dynamics, within which, following the general approach, the nature of the related Poissonian structure on the fluid motion phase space as a semidirect Banach groups product, and a natural reduction of the canonical symplectic structure on its cotangent space to the classical Lie-Poisson bracket on the adjoint space to the corresponding semidirect Lie algebras product are explained in detail. We also present a modification of the Hamiltonian analysis in case of a flow governed by isothermal liquid dynamics. …”
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“…For image reconstruction we employ Algebraic Reconstruction Techniques (ART) as well as standard Fourier methods. …”
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“…We generalize combinatorial coverage to the richer world of algebraic data types by formalizing a class of sparse test descriptions based on regular tree expressions. …”
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“…These collocated equations yield a system of algebraic equations containing shifted Legendre coefficients, which can be obtained by solving this system of equations. …”
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“…The aim of this paper is to present a game-based algorithm of controlling behaviours in the relation between an operator (OP) and a technical object (TO), based on the assumption that the game is logistics-oriented and the algorithm is to support ML applied in e-commerce optimization management. Algebraic methods, including matrices, Lagrange functions, systems of differential equations, and set-theoretic notation, have been used as the main tools. …”
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“…By splitting the bearing noise term from the pseudomeasurement matrix and performing some algebraic manipulations, their cross-covariance can be calculated and incorporated into the filtering process to account for their effects on estimation. …”
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“…The hybrid algorithms were found to not perform better than the single algorithms, and the SART (simultaneous algebraic reconstruction technique) algorithm from CAT (computer assisted tomography) yielded better performances in the accuracy and stability of source strength identification. …”
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“…Using well-developed concepts from simplicial algebraic topology, we define a distance between models based on their simplicial representations. …”
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“…The map promotes a dynamical description based on algebraic equations with a reduced number of variables and, due to its simplicity, it is easier to perform parameter adjustments. …”
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“…Two novel structures, i.e., fuzzy parameterized intuitionistic fuzzy hypersoft set (fpifhs-set) and fuzzy parameterized neutrosophic hypersoft set (fpnhs-set), are developed by employing algebraic techniques like theoretic, analytical, pictorial, and algorithmic techniques. …”
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“…Our procedure is computationally efficient and provably correct, accounts for constrained interaction types, and allows to concurrently assign multiple desired functional patterns. Further, we derive algebraic and graph-theoretic conditions to guarantee the feasibility and stability of target functional patterns. …”
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“…By integrating artificial intelligence (AI), viral genomes isolated from patients, tens of thousands of mutational data, biophysics, bioinformatics, and algebraic topology, the SARS-CoV-2 evolution was revealed to be governed by infectivity-based natural selection. …”
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“…In computer experiments, sharing BDD-based occupancy data was successfully demonstrated in the ROS-based simulator with the linked list-based BDD. Algebraic operations in exchanged BDDs effectively managed future interactions such as data insertion and timing of collision avoidance in the LDM. …”
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