This paper introduces a full discretization procedure to solve wave beam propagation in random media modeled by a paraxial wave equation or an Itô-Schrödinger stochastic partial differential equation. This m...
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We study a temporal step size control of explicit Runge-Kutta(RK)methods for com-pressible computational fluid dynamics(CFD),including the Navier-Stokes equations and hyperbolic systems of conservation laws such as th...
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We study a temporal step size control of explicit Runge-Kutta(RK)methods for com-pressible computational fluid dynamics(CFD),including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler *** demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy(CFL)*** numerical examples show that the error-based step size control is easy to use,robust,and efficient,e.g.,for(initial)transient periods,complex geometries,nonlinear shock captur-ing approaches,and schemes that use nonlinear entropy *** demonstrate these properties for problems ranging from well-understood academic test cases to industrially relevant large-scale computations with two disjoint code bases,the open source Julia pack-ages *** with *** and the C/Fortran code SSDC based on PETSc.
Many applications of computer vision rely on the alignment of similar but non-identical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed...
The purpose of this short note is to fill a gap in the literature: Frobenius reciprocity in the theory of doctrines is closely related to modular connections in projective homological algebra and the notion of a princ...
The purpose of this short note is to fill a gap in the literature: Frobenius reciprocity in the theory of doctrines is closely related to modular connections in projective homological algebra and the notion of a principal element in abstract commutative ideal theory. These concepts are based on particular properties of Galois connections which play an important role also in the abstract study of group-like structures from the perspective of categorical/universal algebra; such role stems from a classical and basic result in group theory: the lattice isomorphism theorem.
We prove Lp-Hardy inequalities with distance to the boundary for domains in the Heisenberg group Hn, n ≥ 1. Our results are based on a geometric condition. This is first implemented for the Euclidean distance in cert...
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Let G be a simple graph and let L ( G ) denote the line graph of G . A p - independent set in G is a set of vertices S ⊆ V ( G ) such that the subgraph induced by S has maximum degree at most p . The p - independence ...
Let G be a simple graph and let L ( G ) denote the line graph of G . A p - independent set in G is a set of vertices S ⊆ V ( G ) such that the subgraph induced by S has maximum degree at most p . The p - independence number of G , denoted by α p ( G ) , is the cardinality of a maximum p -independent set in G . In this paper, and motivated by the recent result that independence number is at most matching number for regular graphs Caro et al., (2022), we investigate which values of the non-negative integers p , q , and r have the property that α p ( G ) ≤ α q ( L ( G ) ) for all r-regular graphs. Triples ( p , q , r ) having this property are called valid α -triples . Among the results we prove are: • ( p , q , r ) is valid α -triple for p ≥ 0 , q ≥ 3 , and r ≥ 2 . • ( p , q , r ) is valid α -triple for p ≤ q < 3 and r ≥ 2 . • ( p , q , r ) is valid α -triple for p ≥ 0 , q = 2 , and r even. • ( p , q , r ) is valid α -triple for p ≥ 0 , q = 2 , and r odd with r = max { 3 , 17 ( p + 1 ) 16 } . We also show a close relation between undetermined possible valid α -triples, the Linear Aboricity Conjecture, and the Path-Cover Conjecture.
In this paper, we study the Lp-estimates for the solution to the 2D-wave equation with a scaling-critical magnetic potential. Inspired by the work of [6], we show that the operators (I+LA)−γeit√LA is bounded in Lp(2...
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Differential privacy (DP) is a mathematical framework for releasing information with formal privacy guarantees. Despite the existence of various DP procedures for performing a wide range of statistical analysis and ma...
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Real–world mathematical models often manifest as systems of non-linear differential equations, which presents challenges in obtaining closed-form analytical solutions. In this paper, we study the diffusion-driven ins...
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Real–world mathematical models often manifest as systems of non-linear differential equations, which presents challenges in obtaining closed-form analytical solutions. In this paper, we study the diffusion-driven instability of an activator–inhibitor–type reaction–diffusion (RD) system modeling the GEF–Rho–Myosin signaling pathway linked to cellular contractility. The mathematical model we study is formulated from first principles using experimental observations. The model formulation is based on the biological and mathematical assumptions. The novelty is the incorporation of Myo9b as a GAP for RhoA, leading to a new mathematical model that describes Rho activity dynamics linked to cell contraction dynamics. Assuming mass conservation of molecular species and adopting a quasi-steady state assumption based on biological observations, model reduction is undertaken and leads us to a system of two equations. We adopt a dual approach of mathematical analysis and numerical computations to study the spatiotemporal dynamics of the system. First, in absence of diffusion, we use a combination of phase-plane analysis, numerical bifurcation and simulations to characterize the temporal dynamics of the model. In the absence of spatial variations, we identified two sets of parameters where the model exhibit different transition dynamics. For some set of parameters, the model transitions from stable to oscillatory and back to stable, while for another set, the model dynamics transition from stable to bistable and back to stable dynamics. To study the effect of parameter variation on model solutions, we use partial rank correlation coefficient (PRCC) to characterize the sensitivity of the model steady states with respect to parameters. Second, we extend the analysis of the model by studying conditions under which a uniform steady state becomes unstable in the presence of spatial variations, in a process known as Turing diffusion–driven instability. By exploiting the necessary condit
With the soaring demand for high-performing integrated circuits, 3D integrated circuits (ICs) have emerged as a promising alternative to traditional planar structures. Unlike existing 3D ICs that stack 2D layers, a fu...
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