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Artykuły w czasopismach na temat "Scalar Linear Codes"
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Connelly, Joseph, and Kenneth Zeger. "Linear Network Coding Over Rings – Part I: Scalar Codes and Commutative Alphabets." IEEE Transactions on Information Theory 64, no. 1 (2018): 274–91. http://dx.doi.org/10.1109/tit.2017.2697421.
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Etzion, Tuvi, and Antonia Wachter-Zeh. "Vector Network Coding Based on Subspace Codes Outperforms Scalar Linear Network Coding." IEEE Transactions on Information Theory 64, no. 4 (2018): 2460–73. http://dx.doi.org/10.1109/tit.2018.2797183.
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Ross, Molly, and Hitesh Bindra. "Statistical Mechanics-Based Surrogates for Scalar Transport in Channel Flow." Fluids 6, no. 2 (2021): 79. http://dx.doi.org/10.3390/fluids6020079.
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Thermal hydraulics, in certain components of nuclear reactor systems, involve complex flow scenarios, such as flows assisted by free jets and stratified flows leading to turbulent mixing and thermal fluctuations. These complex flow patterns and thermal fluctuations can be extremely critical from a reactor safety standpoint. The component-level lumped approximations (0D) or one-dimensional approximations (1D) models for such components and subsystems in safety analysis codes cannot capture the physics accurately, and may introduce a large degree of modeling uncertainty. On the other hand, high-fidelity computational fluid dynamics codes, which provide numerical solutions to the Navier–Stokes equations, are accurate but computationally intensive, and thus cannot be used for system-wide analysis. An alternate way to improve reactor safety analysis is by building reduced-order emulators from computational fluid dynamics (CFD) codes to improve system scale models. One of the key challenges in developing a reduced-order emulator is to preserve turbulent mixing and thermal fluctuations across different-length scales or time-scales. This paper presents the development of a reduced-order, non-linear, “Markovian” statistical surrogate for turbulent mixing and scalar transport. The method and its implementation are demonstrated on a canonical problem of differentially heated channel flow, and high-resolution direct numerical simulations (DNS) data are used for emulator or surrogate development. This statistical surrogate model relies on Kramers–Moyal expansion and emulates the turbulent velocity signal with a high degree of accuracy.
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Thomas, Anoop, and Balaji Sundar Rajan. "Generalized Index Coding Problem and Discrete Polymatroids." Entropy 22, no. 6 (2020): 646. http://dx.doi.org/10.3390/e22060646.
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The connections between index coding and matroid theory have been well studied in the recent past. Index coding solutions were first connected to multi linear representation of matroids. For vector linear index codes, discrete polymatroids, which can be viewed as a generalization of the matroids, were used. The index coding problem has been generalized recently to accommodate receivers that demand functions of messages and possess functions of messages. In this work we explore the connections between generalized index coding and discrete polymatroids. The conditions that need to be satisfied by a representable discrete polymatroid for a generalized index coding problem to have a vector linear solution is established. From a discrete polymatroid, an index coding problem with coded side information is constructed and it is shown that if the index coding problem has a certain optimal length solution then the discrete polymatroid is representable. If the generalized index coding problem is constructed from a matroid, it is shown that the index coding problem has a binary scalar linear solution of optimal length if and only if the matroid is binary representable.
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Nesseris, Savvas. "The Effective Fluid Approach for Modified Gravity and Its Applications." Universe 9, no. 1 (2022): 13. http://dx.doi.org/10.3390/universe9010013.
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In this review, we briefly summarize the so-called effective fluid approach, which is a compact framework that can be used to describe a plethora of different modified gravity models as general relativity (GR) and a dark energy (DE) fluid. This approach, which is complementary to the cosmological effective field theory, has several benefits, as it allows for the easier inclusion of most modified gravity models into the state-of-the-art Boltzmann codes that are typically hard-coded for GR and DE. Furthermore, it can also provide theoretical insights into their behavior since in linear perturbation theory it is easy to derive physically motivated quantities such as the DE anisotropic stress or the DE sound speed. We also present some explicit applications of the effective fluid approach with f(R), Horndeski and scalar–vector–tensor models, namely, how this approach can be used to easily solve the perturbation equations and incorporate the aforementioned modified gravity models into Boltzmann codes so as to obtain cosmological constraints using Monte Carlo analyses.
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Kim, Dohyun, Jong-Hoon Ahn, Jongshill Lee, Hoon Ki Park, and In Young Kim. "A Linear Transformation Approach for Estimating Pulse Arrival Time." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/643653.
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We propose a new mathematical framework for estimating pulse arrival time (PAT). Existing methods of estimating PAT rely on local characteristic points or global parametric models: local characteristic point methods detect points such as foot points, max points, or max slope points, while global parametric methods fit a parametric form to the anacrotic phase of pulse signals. Each approach has its strengths and weaknesses; we take advantage of the favorable properties of both approaches in our method. To be more precise, we transform continuous pulse signals into scalar timing codes through three consecutive transformations, the last of which is a linear transformation. By training the linear transformation method on a subset of data, the proposed method yields results that are robust to noise. We apply this method to real photoplethysmography (PPG) signals and analyze the agreement between our results and those obtained using a conventional approach.
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Hou, Junsheng, Robert K. Mallan, and Carlos Torres-Verdín. "Finite-difference simulation of borehole EM measurements in 3D anisotropic media using coupled scalar-vector potentials." GEOPHYSICS 71, no. 5 (2006): G225—G233. http://dx.doi.org/10.1190/1.2245467.
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This paper describes the implementation and successful validation of a new staggered-grid, finite-difference algorithm for the numerical simulation of frequency-domain electromagnetic borehole measurements. The algorithm is based on a coupled scalar-vector potential formulation for arbitrary 3D inhomogeneous electrically anisotropic media. We approximate the second-order partial differential equations for the coupled scalar-vector potentials with central finite differences on both Yee’s staggered and standard grids. The discretization of the partial differential equations and the enforcement of the appropriate boundary conditions yields a complex linear system of equations that we solve iteratively using the biconjugate gradient method with preconditioning. The accuracy and efficiency of the algorithm is assessed with examples of multicomponent-borehole electromagnetic-induction measurements acquired in homogeneous, 1D anisotropic, 2D isotropic, and 3D anisotropic rock formations. The simulation examples consider vertical and deviated wells with and without borehole and mud-filtrate invasion regions. Simulation results obtained with the scalar-vector coupled potential formulation favorably compare in accuracy with results obtained with 1D, 2D, and 3D benchmarking codes in the dc to megahertz frequency range for large contrasts of electrical conductivity. Our numerical exercises indicate that the coupled scalar-vector potential equations provide a general and consistent algorithmic formulation to simulate borehole electromagnetic measurements from dc to megahertz in the presence of large conductivity contrasts, dipping wells, electrically anisotropic media, and geometrically complex models of electrical conductivity.
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Bavier, Eric, Mark Hoemmen, Sivasankaran Rajamanickam, and Heidi Thornquist. "Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems." Scientific Programming 20, no. 3 (2012): 241–55. http://dx.doi.org/10.1155/2012/243875.
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Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples the algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.
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Fowler, Paul J., Xiang Du, and Robin P. Fletcher. "Coupled equations for reverse time migration in transversely isotropic media." GEOPHYSICS 75, no. 1 (2010): S11—S22. http://dx.doi.org/10.1190/1.3294572.
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Reverse time migration (RTM) images reflectors by using time-extrapolation modeling codes to synthesize source and receiver wavefields in the subsurface. Asymptotic analysis of wave propagation in transversely isotropic (TI) media yields a dispersion relation describing coupled P- and SV-wave modes. This dispersion relation can be converted into a fourth-order scalar partial differential equation (PDE). Increased computational efficiency can be achieved using equivalent coupled second-order PDEs. Analysis of the corresponding dispersion relations as matrix eigenvalue systems allows one to characterize all possible coupled linear second-order systems equivalent to a given linear fourth-order PDE and to determine which ones yield optimally efficient finite-difference implementations. Setting the shear velocity along the axis of symmetry to zero yields a simpler approximate TI wave equation that is more efficient to implement. This simpler approximation, however, can become unstable for some plausible combinations of anisotropic parameters. The same eigensystem analysis can be applied using finite vertical shear velocity to obtain solutions that avoid these instability problems.
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Caravano, Angelo, Eiichiro Komatsu, Kaloian D. Lozanov, and Jochen Weller. "Lattice simulations of inflation." Journal of Cosmology and Astroparticle Physics 2021, no. 12 (2021): 010. http://dx.doi.org/10.1088/1475-7516/2021/12/010.
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Abstract The scalar field theory of cosmological inflation constitutes nowadays one of the preferred scenarios for the physics of the early universe. In this paper we aim at studying the inflationary universe making use of a numerical lattice simulation. Various lattice codes have been written in the last decades and have been extensively used for understating the reheating phase of the universe, but they have never been used to study the inflationary phase itself far from the end of inflation (i.e. about 50 e-folds before the end of inflation). In this paper we use a lattice simulation to reproduce the well-known results of some simple models of single-field inflation, particularly for the scalar field perturbation. The main model that we consider is the standard slow-roll inflation with an harmonic potential for the inflaton field. We explore the technical aspects that need to be accounted for in order to reproduce with precision the nearly scale invariant power spectrum of inflaton perturbations. We also consider the case of a step potential, and show that the simulation is able to correctly reproduce the oscillatory features in the power spectrum of this model. Even if a lattice simulation is not needed in these cases, that are well within the regime of validity of linear perturbation theory, this sets the basis to future work on using lattice simulations to study more complicated models of inflation.