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Journal articles on the topic 'Scalar Linear Codes'
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1
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 (January 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 (April 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 (February 10, 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 (June 10, 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 (December 24, 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 (September 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 (January 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 (December 1, 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.
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Lepori, Francesca, Julian Adamek, and Ruth Durrer. "Cosmological simulations of number counts." Journal of Cosmology and Astroparticle Physics 2021, no. 12 (December 1, 2021): 021. http://dx.doi.org/10.1088/1475-7516/2021/12/021.
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Abstract In this paper we present for the first time the angular power spectra C ℓ(z,z') for number counts from relativistic N-body simulations. We use the relativistic N-body code gevolution with its exact integration of lightlike geodesics which include all relativistic scalar contributions to the number counts. We compare our non-perturbative numerical results with the results from class using the hmcode approximation for the non-linear matter power spectrum. We find that this simple description is excellent for both, the density and the convergence. On the other hand, the current implementation of redshift-space distortions in Boltzmann codes is not accurate. We also find that the largest contribution to the unequal-redshift power spectra is the cross-correlation of the density and the lensing contribution to the number counts, especially for redshift bins that are far apart. Correlating the number counts with the convergence map we find that the signal is dominated by the lensing-lensing term when the convergence field redshift is not higher than the number counts one, while it is dominated by the density-lensing term in the opposite case. In the present study, the issue of galaxy bias is deliberately left aside by considering only unbiased samples of matter particles from the simulations.
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Brando, Guilherme, Kazuya Koyama, and Hans A. Winther. "Revisiting Vainshtein screening for fast N-body simulations." Journal of Cosmology and Astroparticle Physics 2023, no. 06 (June 1, 2023): 045. http://dx.doi.org/10.1088/1475-7516/2023/06/045.
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Abstract We revisit a method to incorporate the Vainshtein screening mechanism in N-body simulations proposed by R. Scoccimarro in [1]. We further extend this method to cover a subset of Horndeski theories that evade the bound on the speed of gravitational waves set by the binary neutron star merger GW170817. The procedure consists of the computation of an effective gravitational coupling that is time and scale dependent, G eff (k,z), where the scale dependence will incorporate the screening of the fifth-force. This is a fast procedure that when contrasted to the alternative of solving the full equation of motion for the scalar field inside N-body codes, reduces considerably the computational time and complexity required to run simulations. To test the validity of this approach in the non-linear regime, we have implemented it in a COmoving Lagrangian Approximation (COLA) N-body code, and ran simulations for two gravity models that have full N-body simulation outputs available in the literature, nDGP and Cubic Galileon. We validate the combination of the COLA method with this implementation of the Vainshtein mechanism with full N-body simulations for predicting the boost function: the ratio between the modified gravity non-linear matter power spectrum and its General Relativity counterpart. This quantity is of great importance for building emulators in beyond-ΛCDM models, and we find that the method described in this work has an agreement of below 2% for scales down to k ≈ 3h/Mpc with respect to full N-body simulations.
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Aboutorabian, Elham, and Morteza Raissi Dehkordi. "New Extended Quantitative Local and Global Regularity Index for Single- and Multiframe RC Bridges Based on Modal Vector Correlation." Shock and Vibration 2021 (June 25, 2021): 1–17. http://dx.doi.org/10.1155/2021/6860335.
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Seismic demand and performance of bridges are highly dependent upon the level of irregularity. Although previous studies have proposed methodologies so as to quantify the irregularity of the bridges in terms of global regularity index, it still remains unclear how to determine the distribution of irregularity along a bridge, as well as to discover the irregularity sources. This research project is intended to develop a quantitative vector regularity criterion for single- and multiframe bridges based on the modified correlation function for spatial locations of scaled mode shapes of deck-alone and whole bridge. The proposed criterion calculates two types of regularity indices, namely, local (LRI) and global regularity indices (GRI). The GRI is a scalar value representing the overall regularity of the entire bridge, whereas the LRI highlights vector irregularity distribution along the bridge. Since the deck discontinuity due to the in-span hinges is one of the leading causes for irregularity, the proposed index has been employed in case of multiframe bridges as well. Furthermore, the current study aims to investigate the correlation between the proposed irregularity indicators and the nonlinear to linear demand ratio. Therefore, the appropriate analysis method can be chosen based on irregularity extent of bridges. Obtained results of the proposed indices reveal that in-span hinge is one of the main parameters affecting the distribution of local irregularity along a bridge. Therefore, multiframe bridges need to be investigated in detail so as to validate the special design requirements recommended by design codes.
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Hunana, P., T. Passot, E. Khomenko, D. Martínez-Gómez, M. Collados, A. Tenerani, G. P. Zank, Y. Maneva, M. L. Goldstein, and G. M. Webb. "Generalized Fluid Models of the Braginskii Type." Astrophysical Journal Supplement Series 260, no. 2 (June 1, 2022): 26. http://dx.doi.org/10.3847/1538-4365/ac5044.
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Abstract Several generalizations of the well-known fluid model of Braginskii (1965) are considered. We use the Landau collisional operator and the moment method of Grad. We focus on the 21-moment model that is analogous to the Braginskii model, and we also consider a 22-moment model. Both models are formulated for general multispecies plasmas with arbitrary masses and temperatures, where all of the fluid moments are described by their evolution equations. The 21-moment model contains two “heat flux vectors” (third- and fifth-order moments) and two “viscosity tensors” (second- and fourth-order moments). The Braginskii model is then obtained as a particular case of a one ion–electron plasma with similar temperatures, with decoupled heat fluxes and viscosity tensors expressed in a quasistatic approximation. We provide all of the numerical values of the Braginskii model in a fully analytic form (together with the fourth- and fifth-order moments). For multispecies plasmas, the model makes the calculation of the transport coefficients straightforward. Formulation in fluid moments (instead of Hermite moments) is also suitable for implementation into existing numerical codes. It is emphasized that it is the quasistatic approximation that makes some Braginskii coefficients divergent in a weakly collisional regime. Importantly, we show that the heat fluxes and viscosity tensors are coupled even in the linear approximation, and that the fully contracted (scalar) perturbations of the fourth-order moment, which are accounted for in the 22-moment model, modify the energy exchange rates. We also provide several appendices, which can be useful as a guide for deriving the Braginskii model with the moment method of Grad.
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Cacuci, Dan Gabriel. "The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (nth-CASAM-L): I. Mathematical Framework." Energies 14, no. 24 (December 10, 2021): 8314. http://dx.doi.org/10.3390/en14248314.
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This work presents the mathematical framework of the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as “nth-CASAM-L”), which is conceived for obtaining the exact expressions of arbitrarily-high-order (nth-order) sensitivities of a generic system response with respect to all of the parameters (including boundary and initial conditions) underlying the respective forward/adjoint systems. Since many of the most important responses for linear systems involve the solutions of both the forward and the adjoint linear models that correspond to the respective physical system, the sensitivity analysis of such responses makes it necessary to treat linear systems in their own right, rather than treating them as particular cases of nonlinear systems. This is in contradistinction to responses for nonlinear systems, which can depend only on the forward functions, since nonlinear operators do not admit bona-fide adjoint operators (only a linearized form of a nonlinear operator admits an adjoint operator). The nth-CASAM-L determines the exact expression of arbitrarily-high order sensitivities of responses to the parameters underlying both the forward and adjoint models of a nonlinear system, thus enable the most efficient and accurate computation of such sensitivities. The mathematical framework underlying the nth-CASAM is developed in linearly increasing higher-dimensional Hilbert spaces, as opposed to the exponentially increasing “parameter-dimensional” spaces in which response sensitivities are computed by other methods, thus providing the basis for overcoming the “curse of dimensionality” in sensitivity analysis and all other fields (uncertainty quantification, predictive modeling, etc.) which need such sensitivities. In particular, for a scalar-valued valued response associated with a nonlinear model comprising TP parameters, the 1st-−CASAM-L requires 1 additional large-scale adjoint computation (as opposed to TP large-scale computations, as required by other methods) for computing exactly all of the 1st-−order response sensitivities. All of the (mixed) 2nd-order sensitivities are computed exactly by the 2nd-CASAM-L in at most TP computations, as opposed to TP(TP + 1)/2 computations required by all other methods, and so on. For every lower-order sensitivity of interest, the nth-CASAM-L computes the “TP next-higher-order” sensitivities in one adjoint computation performed in a linearly increasing higher-dimensional Hilbert space. Very importantly, the nth-CASAM-L computes the higher-level adjoint functions using the same forward and adjoint solvers (i.e., computer codes) as used for solving the original forward and adjoint systems, thus requiring relatively minor additional software development for computing the various-order sensitivities.
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Tritschler, V. K., B. J. Olson, S. K. Lele, S. Hickel, X. Y. Hu, and N. A. Adams. "On the Richtmyer–Meshkov instability evolving from a deterministic multimode planar interface." Journal of Fluid Mechanics 755 (August 19, 2014): 429–62. http://dx.doi.org/10.1017/jfm.2014.436.
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AbstractWe investigate the shock-induced turbulent mixing between a light and a heavy gas, where a Richtmyer–Meshkov instability (RMI) is initiated by a shock wave with Mach number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Ma}= 1.5$. The prescribed initial conditions define a deterministic multimode interface perturbation between the gases, which can be imposed exactly for different simulation codes and resolutions to allow for quantitative comparison. Well-resolved large-eddy simulations are performed using two different and independently developed numerical methods with the objective of assessing turbulence structures, prediction uncertainties and convergence behaviour. The two numerical methods differ fundamentally with respect to the employed subgrid-scale regularisation, each representing state-of-the-art approaches to RMI. Unlike previous studies, the focus of the present investigation is to quantify the uncertainties introduced by the numerical method, as there is strong evidence that subgrid-scale regularisation and truncation errors may have a significant effect on the linear and nonlinear stages of the RMI evolution. Fourier diagnostics reveal that the larger energy-containing scales converge rapidly with increasing mesh resolution and thus are in excellent agreement for the two numerical methods. Spectra of gradient-dependent quantities, such as enstrophy and scalar dissipation rate, show stronger dependences on the small-scale flow field structures as a consequence of truncation error effects, which for one numerical method are dominantly dissipative and for the other dominantly dispersive. Additionally, the study reveals details of various stages of RMI, as the flow transitions from large-scale nonlinear entrainment to fully developed turbulent mixing. The growth rates of the mixing zone widths as obtained by the two numerical methods are ${\sim } t^{7/12}$ before re-shock and ${\sim } (t-t_0)^{2/7}$ long after re-shock. The decay rate of turbulence kinetic energy is consistently ${\sim } (t-t_0)^{-10/7}$ at late times, where the molecular mixing fraction approaches an asymptotic limit $\varTheta \approx 0.85$. The anisotropy measure $\langle a \rangle _{xyz}$ approaches an asymptotic limit of ${\approx }0.04$, implying that no full recovery of isotropy within the mixing zone is obtained, even after re-shock. Spectra of density, turbulence kinetic energy, scalar dissipation rate and enstrophy are presented and show excellent agreement for the resolved scales. The probability density function of the heavy-gas mass fraction and vorticity reveal that the light–heavy gas composition within the mixing zone is accurately predicted, whereas it is more difficult to capture the long-term behaviour of the vorticity.
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Wan, Kai, Hua Sun, Mingyue Ji, Daniela Tuninetti, and Giuseppe Caire. "Cache-Aided General Linear Function Retrieval." Entropy 23, no. 1 (December 26, 2020): 25. http://dx.doi.org/10.3390/e23010025.
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Coded Caching, proposed by Maddah-Ali and Niesen (MAN), has the potential to reduce network traffic by pre-storing content in the users’ local memories when the network is underutilized and transmitting coded multicast messages that simultaneously benefit many users at once during peak-hour times. This paper considers the linear function retrieval version of the original coded caching setting, where users are interested in retrieving a number of linear combinations of the data points stored at the server, as opposed to a single file. This extends the scope of the authors’ past work that only considered the class of linear functions that operate element-wise over the files. On observing that the existing cache-aided scalar linear function retrieval scheme does not work in the proposed setting, this paper designs a novel coded caching scheme that outperforms uncoded caching schemes that either use unicast transmissions or let each user recover all files in the library.
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Yan, Qifa, and Daniela Tuninetti. "Robust, Private and Secure Cache-Aided Scalar Linear Function Retrieval From Coded Servers." IEEE Journal on Selected Areas in Communications 40, no. 3 (March 2022): 968–81. http://dx.doi.org/10.1109/jsac.2022.3142360.
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Kişi, Emre, Murat Sarduvan, Halim Özdemir, and Nurgül Kalaycı. "On the spectrum of linear combinations of finitely many diagonalizable matrices that mutually commute." Special Matrices 9, no. 1 (January 1, 2021): 305–20. http://dx.doi.org/10.1515/spma-2020-0138.
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Abstract We propose an algorithm, which is based on the method given by Kişi and Özdemir in [Math Commun, 23 (2018) 61], to handle the problem of when a linear combination matrix X = ∑ i = 1 m c i X i X = \sum\nolimits_{i = 1}^m {{c_i}{X_i}} is a matrix such that its spectrum is a subset of a particular set, where ci , i = 1, 2, ..., m, are nonzero scalars and Xi , i = 1, 2, ..., m, are mutually commuting diagonalizable matrices. Besides, Mathematica implementation codes of the algorithm are also provided. The problems of characterizing all situations in which a linear combination of some special matrices, e.g. the matrices that coincide with some of their powers, is also a special matrix can easily be solved via the algorithm by choosing of the spectra of the matrices X and Xi , i = 1, 2, ..., m, as subsets of some particular sets. Nine of the open problems in the literature are solved by utilizing the algorithm. The results of the four of them, i.e. cubicity of linear combinations of two commuting cubic matrices, quadripotency of linear combinations of two commuting quadripotent matrices, tripotency of linear combinations of three mutually commuting tripotent matrices, and tripotency of linear combinations of four mutually commuting involutive matrices, are presented explicitly in this work. Due to the length of their presentations, the results of the five of them, i.e. quadraticity of linear combinations of three or four mutually commuting quadratic matrices, cubicity of linear combinations of three mutually commuting cubic matrices, quadripotency of linear combinations of three mutually commuting quadripotent matrices, and tripotency of linear combinations of four mutually commuting tripotent matrices, are given as program outputs only. The results obtained are extensions and/or generalizations of some of the results in the literature.
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Bhowmick, Sauradeep, and Gui-Rong Liu. "Three Dimensional CS-FEM Phase-Field Modeling Technique for Brittle Fracture in Elastic Solids." Applied Sciences 8, no. 12 (December 4, 2018): 2488. http://dx.doi.org/10.3390/app8122488.
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The cell based smoothed finite element method (CS-FEM) was integrated with the phase-field technique to model brittle fracture in 3D elastic solids. The CS-FEM was used to model the mechanics behavior and the phase-field method was used for diffuse fracture modeling technique where the damage in a system was quantified by a scalar variable. The integrated CS-FEM phase-field approach provides an efficient technique to model complex crack topologies in three dimensions. The detailed formulation of our combined method is provided. It was implemented in the commercial software ABAQUS using its user-element (UEL) and user-material (UMAT) subroutines. The coupled system of equations were solved in a staggered fashion using the in-built non-linear Newton–Raphson solver in ABAQUS. Eight node hexahedral (H8) elements with eight smoothing domains were coded in CS-FEM. Several representative numerical examples are presented to demonstrate the capability of the method. We also discuss some of its limitations.
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Hasan, Hussain S. "Building a New Software of Electromagnetic Lenses (CADTEL)." International Letters of Chemistry, Physics and Astronomy 9 (September 2013): 46–55. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.9.46.
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The Computer Aided designing Tools for Electromagnetic Lenses (CADTEL) is a new software as application package of programs concept to aid both users and professionals in symmetric and asymmetric electromagnetic lenses with single, double, and multipole piece in electron microscope of electron optics field. The CADTEL software has been designed to run on several computer platforms and includes two types of design procedure. The first one named, analysis procedure (which is based on trial and error) where consist of three sorts called; H1 programs for magnetic scalar potential by solving Laplace's equation [1,2], H2 and H3 programs for magnetic vector potential by solving Poisson's equation [3,4] in linear and non linear media respectively. While the second part, named H4 programs for the synthesis procedure (inverse design). The previous types differ by the obtaining the magnetic flux density, and poles shape, while it is analog by compute and plot the lens properties which are operating at zero, low, high, and infinite magnification conditions (operation modes). CADTEL software consist of computational and plot steps of magnetic field, equipotential surfaces, flux lines, objective and projector properties, and poles shape for proposed lens design which are appear in auto visual interfaces, that are coded in visual basic language [5].
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Hasan, Hussain S. "Building a New Software of Electromagnetic Lenses (CADTEL)." International Letters of Chemistry, Physics and Astronomy 9 (March 3, 2013): 46–55. http://dx.doi.org/10.56431/p-681k4r.
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The Computer Aided designing Tools for Electromagnetic Lenses (CADTEL) is a new software as application package of programs concept to aid both users and professionals in symmetric and asymmetric electromagnetic lenses with single, double, and multipole piece in electron microscope of electron optics field. The CADTEL software has been designed to run on several computer platforms and includes two types of design procedure. The first one named, analysis procedure (which is based on trial and error) where consist of three sorts called; H1 programs for magnetic scalar potential by solving Laplace's equation [1,2], H2 and H3 programs for magnetic vector potential by solving Poisson's equation [3,4] in linear and non linear media respectively. While the second part, named H4 programs for the synthesis procedure (inverse design). The previous types differ by the obtaining the magnetic flux density, and poles shape, while it is analog by compute and plot the lens properties which are operating at zero, low, high, and infinite magnification conditions (operation modes). CADTEL software consist of computational and plot steps of magnetic field, equipotential surfaces, flux lines, objective and projector properties, and poles shape for proposed lens design which are appear in auto visual interfaces, that are coded in visual basic language [5].
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Jia-Chen He, Jia-Chen He, Ming-Jian Fu Jia-Chen He, and Li-Qun Lin Ming-Jian Fu. "Multi-scale Fusion Residual Network For Single Image Rain Removal." 電腦學刊 34, no. 2 (April 2023): 129–40. http://dx.doi.org/10.53106/199115992023043402010.
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<p>Deep learning has been widely used in single image rain removal and demonstrated favorable universality. However, it is still challenging to remove rain streaks, especially in the nightscape rain map which exists heavy rain and rain streak accumulation. To solve this problem, a single image nightscape rain removal algorithm based on Multi-scale Fusion Residual Network is proposed in this paper. Firstly, based on the motion blur model, evenly distributed rain streaks are generated and the dataset is reconstructed to solve the lack of nightscape rain map datasets. Secondly, according to the characteristics of the night rain map, multi-scale residual blocks are drawn on to reuse and propagate the feature, so as to exploit the rain streaks details representation. Meanwhile, the linear sequential connection structure of multi-scale residual blocks is changed to a u-shaped codec structure, which tackles the problem that features cannot be extracted effectively due to insufficient scale. Finally, the features of different scales are combined with the global self-attention mechanism to get different rain streak components, then a cleaner restored image is obtained. The quantitative and qualitative results show that, compared to the existing algorithms, the proposed algorithm can effectively remove rain streaks while retaining detailed information and ensuring the integrity of image information.</p> <p> </p>
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Patle, Bhumeshwar, Shyh-Leh Chen, Brijesh Patel, Sunil Kumar Kashyap, and Sudarshan Sanap. "Topological drone navigation in uncertain environment." Industrial Robot: the international journal of robotics research and application 48, no. 3 (April 8, 2021): 423–41. http://dx.doi.org/10.1108/ir-10-2020-0218.
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Purpose With the increasing demand for surveillance and smart transportation, drone technology has become the center of attraction for robotics researchers. This study aims to introduce a new path planning approach to drone navigation based on topology in an uncertain environment. The main objective of this study is to use the Ricci flow evolution equation of metric and curvature tensor over angular Riemannian metric, and manifold for achieving navigational goals such as path length optimization at the minimum required time, collision-free obstacle avoidance in static and dynamic environments and reaching to the static and dynamic goals. The proposed navigational controller performs linearly and nonlinearly both with reduced error-based objective function by Riemannian metric and scalar curvature, respectively. Design/methodology/approach Topology and manifolds application-based methodology establishes the resultant drone. The trajectory planning and its optimization are controlled by the system of evolution equation over Ricci flow entropy. The navigation follows the Riemannian metric-based optimal path with an angular trajectory in the range from 0° to 360°. The obstacle avoidance in static and dynamic environments is controlled by the metric tensor and curvature tensor, respectively. The in-house drone is developed and coded using C++. For comparison of the real-time results and simulation results in static and dynamic environments, the simulation study has been conducted using MATLAB software. The proposed controller follows the topological programming constituted with manifold-based objective function and Riemannian metric, and scalar curvature-based constraints for linear and nonlinear navigation, respectively. Findings This proposed study demonstrates the possibility to develop the new topology-based efficient path planning approach for navigation of drone and provides a unique way to develop an innovative system having characteristics of static and dynamic obstacle avoidance and moving goal chasing in an uncertain environment. From the results obtained in the simulation and real-time environments, satisfactory agreements have been seen in terms of navigational parameters with the minimum error that justifies the significant working of the proposed controller. Additionally, the comparison of the proposed navigational controller with the other artificial intelligent controllers reveals performance improvement. Originality/value In this study, a new topological controller has been proposed for drone navigation. The topological drone navigation comprises the effective speed control and collision-free decisions corresponding to the Ricci flow equation and Ricci curvature over the Riemannian metric, respectively.
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Dankelmann, Peter, Jennifer D. Key, and Bernardo G. Rodrigues. "A Characterization of Graphs by Codes from their Incidence Matrices." Electronic Journal of Combinatorics 20, no. 3 (August 16, 2013). http://dx.doi.org/10.37236/2770.
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We continue our earlier investigation of properties of linear codes generated by the rows of incidence matrices of $k$-regular connected graphs on $n$ vertices. The notion of edge connectivity is used to show that, for a wide range of such graphs, the $p$-ary code, for all primes $p$, from an $n \times \frac{1}{2}nk$ incidence matrix has dimension $n$ or $n-1$, minimum weight $k$, the minimum words are the scalar multiples of the rows, there is a gap in the weight enumerator between $k$ and $2k-2$, and the words of weight $2k-2$ are the scalar multiples of the differences of intersecting rows of the matrix. For such graphs, the graph can thus be retrieved from the code.
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Ma, Yinbin, and Daniela Tuninetti. "A General Coded Caching Scheme for Scalar Linear Function Retrieval." IEEE Journal on Selected Areas in Information Theory, 2022, 1. http://dx.doi.org/10.1109/jsait.2022.3182706.
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