Gauss
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Related Articles from SNS
Effective Constrained Scalar--Gauss--Bonnet Inflation Motivated by $f(R,\mathcal{G})$ Gravity
arXiv:2606.05212v1 Announce Type: new Abstract: We develop an effective framework for inflation in a constrained scalar--Gauss--Bonnet theory motivated by a restricted sector of $f(R,\mathcal{G})$ gravity. Using unified parametrizations of the Hubble expansion rate and the Gauss--Bonnet coupling function within a generalized slow-roll formalism, we derive analytical expressions for the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$, and study their dependence on the model parameters.
Optimality of quasi-Monte Carlo methods and suboptimality of the sparse-grid Gauss--Hermite rule in Gaussian Sobolev spaces
Announce Type: replace Abstract: Optimality of several quasi-Monte Carlo methods and suboptimality of the sparse-grid quadrature based on the univariate Gauss--Hermite rule is proved in the Sobolev spaces of mixed dominating smoothness of order $\alpha$, where the optimality is in the sense of worst-case convergence rate. For sparse-grid Gauss--Hermite quadrature, lower and upper bounds are established, with rates coinciding up to a logarithmic factor. The dominant rate is found to be only...
Producing Quality Pseudorandomness with a Generalized Gauss Continued-Fraction Map
Announce Type: replace-cross Abstract: Well-known chaotic maps, such as the logistic and tent maps, have been used to generate cryptographically secure pseudorandomness, yet we know of no efforts which attempt to utilize the Gauss continued-fraction map, a known chaotic map, as a starting point for producing quality pseudorandom output. In this paper, we consider the family of $r$-continued-fraction maps, which generalize the Gauss map, and use them to generate pseudorandom output which...
Producing Quality Pseudorandomness with a Generalized Gauss Continued-Fraction Map
arXiv:2605.05378v3 Announce Type: replace-cross Abstract: Well-known chaotic maps, such as the logistic and tent maps, have been used to generate cryptographically secure pseudorandomness, yet we know of no efforts which attempt to use the Gauss continued-fraction map, a known chaotic map, as a starting point for producing quality pseudorandom output. In this paper, we consider the family of $r$-continued-fraction maps, which generalize the Gauss map, and use them to generate pseudorandom...
Approximation by short exponential sums with geometric error decay based on Gauss quadrature
Announce Type: new Abstract: We present new short exponential sum approximations of length $N$ for $f_1(x)=\frac{1}{a+x}$ with $a>0$ on $[0, \infty)$ and for $f_2(x)= {\mathrm e}^{-x^2/2\sigma}$ with $\sigma>0$ on ${\mathbb R}$ with geometric error decay ${\rho}^{-2N}$ for user-defined $N \ge 2$ and $\rho > The approximations are built over consecutive intervals $[b_j, \, b_{j+1}) \subset [0, \infty)$, $j \in {\mathbb N}_{0}$, with interval lengths that depend on $\rho$ and grow...
Gauss Circle Lattices with Geometric Convolutions for Synthesizing High Dimensional Image-Source Room Impulse Responses
arXiv:2606.04358v1 Announce Type: new Abstract: The image-source model (ISM) is a widely adopted method for efficiently simulating acoustic room impulse responses (RIRs) under specular reflection assumptions. Acoustic paths between source and receiver are traced to lattice points computed from successive reflections over bounding planes of the room.
Residual-Weighted Randomized Jacobi: Sharpened Bounds via Residual Concentration and Asynchronous Extension
arXiv:2606.01232v1 Announce Type: new Abstract: We study randomized stationary methods for symmetric positive definite linear systems in which component $j$ is selected with probability proportional to $|r_j|^\ell$. This power-weighted family interpolates continuously between uniform randomized Jacobi as $\ell \to 0$ and Gauss--Southwell greedy relaxation as $\ell \to \infty$. For the central case $\ell = 2$, we sharpen the standard one-step convergence analysis using the inverse...
Neural Spectral Element Methods for stiff multiphysics PDEs with electrochemical transport benchmarks
arXiv:2606.02335v1 Announce Type: cross Abstract: The Neural Spectral Element Method (NSEM) evaluates each network only at fixed Legendre-Gauss-Lobatto quadrature nodes and replaces all derivative calls with precomputed spectral differentiation matrices. The resulting deterministic loss enables limited-memory BFGS (L-BFGS) to reach residuals of 10^-9 to 10^-10. A Kosloff-Tal-Ezer coordinate map resolves electrochemical boundary layers, while a mesh-free neural mortar framework couples...
An Efficient Solver for the Richards Equation for Variably Saturated Flows in Porous Media
Announce Type: new Abstract: We present a nonlinear multigrid solver for the Richards equation in variably saturated porous media with strongly nonlinear hydraulic conductivity and water-retention relationships. The governing equation is discretized using a second-order conservative finite-difference scheme in space and an implicit backward differentiation formula in time. The core component of the solver is a nonlinear Gauss--Seidel (NGS) smoother based on a triangular splitting of the...
Algebraic and FFT-Based Methods for Discrete-Time Matrix Convolutions with Applications to Semi-Markov Models
arXiv:2605.30379v2 Announce Type: replace Abstract: We study the convolution product of matrix-valued sequences and its role in the computation of Markov renewal equations. Explicit representations and recursive formulae for the convolutional inverse are derived and used to construct FFT-accelerated convolution and Newton-type inversion schemes, together with a Gauss--Jordan alternative in truncated power-series rings. The proposed framework is also applied to discrete approximations of...