“…For a year-long course, core chapters (1-4) are accessible to those who have taken a year of univariate differential and integral calculus; matrix algebra, multivariate calculus, and engineering mathematics are needed for the latter, more advanced chapters. …”
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“…A special feature of this book is the inclusion of detailed guidance regarding the use of the computer algebra system Maple™ to perform many of the computations involved in the exercises. …”
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“…Mathematical areas explored include combinatorics, logic, graph theory, linear algebra, geometry, topology, computer science, operations research, probability, game theory, and music theory. …”
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“…The sole prerequisite for reading this text is high school algebra. Topics covered include: * mathematical induction * modular arithmetic * the Fundamental Theorem of Arithmetic * Fermat's Little Theorem * RSA encryption * the Euclidean algorithm * rational and irrational numbers * complex numbers * cardinality * Euclidean plane geometry * constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)* infinite series * higher dimensional spaces. …”
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“…In places, some knowledge of analysis or algebra, number theory or probability will be helpful. …”
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“…To fill this gap, in this work, we elaborate on novel algorithms to adapt the linear algebra operations of DL layers to PHE. Concretely, we focus on Convolutional Neural Networks. …”
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“…Keywords: Automata Theory/ Sequential Machines, Bioinformatics, Complex Biological Systems, Complex Systems Biology, Computer Simulations and Modeling, Dynamical Systems , Quantum Dynamics, Quantum Field Theory, Quantum Groups,Topological Quantum Field Theory (TQFT), Quantum Automata, Quantum Dots, Cognitive Systems, Graph Transformations, Logic, Mathematical Modeling; applications of the Theory of Categories, Functors and Natural Transformations; pushouts, pullbacks, presheaves, sheaves, Categories of sheaves, Topos, n-valued Logic, N-categories/ higher dimensional algebra, Homotopy theory; applications to quantum field theories, quantum gravity, complex systems biology, bioengineering, informatics, Bioinformatics, Computer simulations, Mathematical Biology of complex systems and phenomena in various types of Dynamical Systems; bioengineering, Computing, Neurosciences, Bioinformatics, biological and/or social networks; quantitative ecology and quantitative biology/…”
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“…We also utilized medical subject heading (MeSH) terms and Boolean algebra operators to refine our search. We included articles that compared cardiovascular outcomes between patients receiving bempedoic acid and those receiving a placebo. …”
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“…Exhibiting a deep connection between purely geometric problems and real algebra, the complexity class [Formula: see text] plays a crucial role in the study of geometric problems. …”
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“…To outline the complex biological rhythms underlying the time-to-action of goal-oriented behavior in the adult brain, we employed a Boolean Algebra model based on Control Systems Theory. This suggested that “timers” of the brain reflect a metabolic excitation-inhibition balance and that healthy clocks underlying goal-oriented behavior (optimal range of signal variability) are maintained by XOR logic gates in parallel sequences between cerebral levels. …”
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“…The approach is further validated for statistical significance where it emerges better than other state-of-the-art approaches.Clinical and Translational Impact Statement—The mathematical concepts of low rank and rank decomposition in matrix algebra are translated to remove specularities in the endoscopic images The result shows the impact of the proposed method in removing specular reflections from endoscopic images indicating improved diagnosis efficiency for both endoscopists and computer-aided diagnosis systems…”
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“…Using this, we give an algebraic proof for the cancellation of double poles in the KLT formula for gravity amplitudes. …”
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“…Radiographic projections were generated using linear algebra for combinations of axial and coronal rotation from −20° to +20°. …”
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“…The full set of possible trajectories for objects thrown in rotating environments is provided and a simplified approach to the Coriolis and centrifugal force differential equation using complex algebra is demonstrated. Experimentation reported in this article was conducted on parabolic flights and an analog weightlessness and rotating apparatus. …”
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“…In the analogous formalism for describing chiral algebras of class [Formula: see text] , the vertex algebra associated to the sphere has been dubbed the chiral universal centraliser. …”
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“…By use of permutation groups in algebra, we propose an [Formula: see text] (n(2)) time algorithm to efficiently compute and obtain a minimum series of fusions, fissions and block-interchanges required to transform one circular multi-chromosomal genome into another, where n is the number of genes shared by the two studied genomes. …”
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“…However they have limited applicability to some areas such as data mining because MapReduce has poor performance on problems with an iterative structure present in the linear algebra that underlies much data analysis. Such problems can be run efficiently on clusters using MPI leading to a hybrid cloud and cluster environment. …”
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“…We then study and prove some properties of dual model by exploiting its relationship with algebra. Based on these properties, we propose a four coverage axis line method based on four sensing coverage and prove that four sensing coverage always yields two dual correct answers; usually one of them is infeasible. …”
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“…In this study, we use permutation groups in algebra to design an O(δn) time algorithm for solving the weighted sorting problem by CCLP operations when the weight ratio between reversals and non-reversal CCLP operations is 1:2, where n is the number of genes in the given chromosome and δ is the number of needed CCLP operations. …”
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“…By dispensing with the standard unitary transformations on state vectors in Hilbert space and using instead rotors and multivectors, based on Clifford’s geometric algebra (GA), it is shown how the N-player case becomes tractable. …”
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