Tootfinder

This https://arxiv.org/abs/2112.04290 has been replaced.
link: https://scholar.google.com/scholar?q=a

Partial Okounkov bodies and Duistermaat--Heckman measures of non-Archimedean metrics
Let $X$ be a smooth projective variety. We construct partial Okounkov bodies associated to Hermitian pseudo-effective line bundles $(L,ϕ)$ on $X$. We show that partial Okounkov bodies are universal invariants of the singularity of $ϕ$. As an application, we generalize the theorem of Boucksom--Chen and construct Duistermaat--Heckman measures associated with finite energy metrics on the Berkovich analytification of an ample line bundle.

This https://arxiv.org/abs/2310.00172 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A physics-informed deep learning approach for solving strongly degenerate parabolic problems
In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning frameworks for solving initial-boundary value problems involving nonlinear PDEs. Recently, PINNs have shown promising results in several application fields. Motivated by applications to gas filtration problems, here we present and evaluate a PINN-based approach to…

This https://arxiv.org/abs/2302.11604 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Monge-Ampere Geometry and Vortices
We introduce a new approach to Monge-Ampere geometry based on techniques from higher symplectic geometry. Our work is motivated by the application of Monge-Ampere geometry to the Poisson equation for the pressure that arises for incompressible Navier-Stokes flows. Whilst this equation constitutes an elliptic problem for the pressure, it can also be viewed as a non-linear partial differential equation connecting the pressure, the vorticity, and the rate-of-strain. As such, it is a key diagnostic…

This https://arxiv.org/abs/2307.10917 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Efficient quantum amplitude encoding of polynomial functions
Loading functions into quantum computers represents an essential step in several quantum algorithms, such as quantum partial differential equation solvers. Therefore, the inefficiency of this process leads to a major bottleneck for the application of these algorithms. Here, we present and compare two efficient methods for the amplitude encoding of real polynomial functions on $n$ qubits. This case holds special relevance, as any continuous function on a closed interval can be uniformly approxim…

The order-theoretical foundation for data flow security
Luigi Logrippo
https://arxiv.org/abs/2403.07226 https://arxiv.org/pdf/2403.07…

The order-theoretical foundation for data flow security
Some theories on data flow security are based on order-theoretical concepts, most commonly on lattice concepts. This paper presents a correspondence between security concepts and partial order concepts, by which the former become an application of the latter. The formalization involves concepts of data flow, equivalence classes of entities that can access the same data, and labels. Efficient, well-known algorithms to obtain one of these from one of the others are presented. Security concepts su…

Clunie lemma in several complex variables and application in PDEs
Wenjie Hao, Qingcai Zhang
https://arxiv.org/abs/2403.05008 https://…

Clunie lemma in several complex variables and application in PDEs
Two purposes will be shown in this paper. The first one is to extend the classic Tumura-Clunie type theorem for meromorphic functions of one complex variable to meromorphic functions of several complex variables by using Clunie lemma. The second one is to characterize entire solutions of certain partial differential equations in $\mathbb{C}^{m}$. Our results are extensions and generalizations of the previous theorems by Liao-Ye \cite{Liao-Ye} and Li \cite{Li11}.

This https://arxiv.org/abs/2201.09074 has been replaced.
link: https://scholar.google.com/scholar?q=a

Product of some large sets near idempotent
We characterize when the finite Cartesian product of central sets near idempotent is central near idempotent. Moreover, we provide a partial characterization for the infinite Cartesian product of the same. Then, we study the abundance of some large sets near idempotent. Also, we investigate the effect of tensor product near idempotent. Finally, as an application we provide the polynomial extension of Milliken-Taylor theorem near zero.

Multiple elliptic integrals and differential equations
John M. Campbell, M. Lawrence Glasser, Yajun Zhou
https://arxiv.org/abs/2403.07298 https://

Multiple elliptic integrals and differential equations
We introduce and prove evaluations for families of multiple elliptic integrals by solving special types of ordinary and partial differential equations. As an application, we obtain new expressions of Ramanujan-type series of level 4 and associated singular values for the complete elliptic integral $\mathbf K$ with integrals involving $\mathbf K$.

This https://arxiv.org/abs/2303.03531 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Null Hamiltonian Yang-Mills theory: Soft symmetries and memory as superselection
Soft symmetries for Yang-Mills theory are shown to correspond to the residual Hamiltonian action of the gauge group on the Ashtekar-Streubel phase space, which is the result of a partial symplectic reduction. The associated momentum map is the electromagnetic memory in the abelian theory, or a nonlinear, gauge-equivariant, generalization thereof in the nonabelian case. This result follows from an application of Hamiltonian reduction by stages, enabled by the existence of a natural normal subg…

This https://arxiv.org/abs/2305.07148 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Fully quantum algorithm for lattice Boltzmann methods with application to partial differential equations
Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speedup traditional algorithms for flow simulations. We show that lattice-based mesoscale numerical methods can be executed as efficient quantum algorithms due to their statistical features. This approach revises a quantum algorithm for lattice gas automata to eliminate classical computations and measurements at every time step. For this, …

Deep reinforcement learning of airfoil pitch control in a highly disturbed environment using partial observations
Diederik Beckers, Jeff D. Eldredge
https://arxiv.org/abs/2404.01506

Deep reinforcement learning of airfoil pitch control in a highly disturbed environment using partial observations
This study explores the application of deep reinforcement learning (RL) to design an airfoil pitch controller capable of minimizing lift variations in randomly disturbed flows. The controller, treated as an agent in a partially observable Markov decision process, receives non-Markovian observations from the environment, simulating practical constraints where flow information is limited to force and pressure sensors. Deep RL, particularly the TD3 algorithm, is used to approximate an optimal cont…

Gauge Theoretical Method in Solving Zero-curvature Equations I. -- Application to the Static Einstein-Maxwell Equations with Magnetic Charge
Takahiro Azuma (Dokkyo University), Takao Koikawa (Institute of Human Culture Studies, Otsuma Women's University)
https://arxiv.org/abs/2403.12375<…

Gauge Theoretical Method in Solving Zero-curvature Equations I. -- Application to the Static Einstein-Maxwell Equations with Magnetic Charge
The inverse scattering problem is applied to 2-dimensional partial differential equations called soliton equations such as the KdV equation and so on. It is also used to integrate the Einstein equations with axial symmetry. These inverse scattering problems look different. We show that they can be understood in a unified way. As an application to the Einstein equation, we find solutions of the Einstein-Maxwell equations with magnetic charge.

Mean values of multiplicative functions and applications to residue-class distribution
Paul Pollack, Akash Singha Roy
https://arxiv.org/abs/2402.16266 http…

Mean values of multiplicative functions and applications to residue-class distribution
We provide a uniform bound on the partial sums of multiplicative functions under very general hypotheses. As an application, we give a nearly optimal estimate for the count of $n \le x$ for which the Alladi-Erdős function $A(n) = \sum_{p^k \parallel n} k p$ takes values in a given residue class modulo $q$, where $q$ varies uniformly up to a fixed power of $\log x$. We establish a similar result for the equidistribution of the Euler totient function $ϕ(n)$ among the coprime residues to the "co…

A second-order semi-Lagrangian exponential scheme with application to the shallow-water equations on the rotating sphere
Jo\~ao Guilherme Caldas Steinstraesser, Pedro da Silva Peixoto, Martin Schreiber
https://arxiv.org/abs/2405.02237

A second-order semi-Lagrangian exponential scheme with application to the shallow-water equations on the rotating sphere
In this work, we study and extend a class of semi-Lagrangian exponential methods, which combine exponential time integration techniques, suitable for integrating stiff linear terms, with a semi-Lagrangian treatment of nonlinear advection terms. Partial differential equations involving both processes arise for instance in atmospheric circulation models. Through a truncation error analysis, we first show that previously formulated semi-Lagrangian exponential schemes are limited to first-order acc…

This https://arxiv.org/abs/2307.16197 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Cauchy problem associated to the logarithmic Laplacian with an application to the fundamental solution
Let $\lnlap$ be the logarithmic Laplacian operator with Fourier symbol $2\ln |ζ|$, we study the expression of the diffusion kernel which is associated to the equation $$\partial_tu+ \lnlap u=0 \ \ {\rm in}\ \, (0,\tfrac N2) \times \R^N,\quad\quad u(0,\cdot)=0\ \ {\rm in}\ \, \R^N\setminus \{0\}.$$ We apply our results to give a classification of the solutions of $$\left\{ \arraycolsep=1pt \begin{array}{lll} \displaystyle \partial_tu+ \lnlap u=0\quad \ &{\rm in}\ \ (0,T)\times \R^N\\[…

This https://arxiv.org/abs/2309.15326 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

Structural identifiability analysis of linear reaction-advection-diffusion processes in mathematical biology
Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Approaches to assess the so-called structural identifiability of models are well-established for ordinary differential equation models, yet there are no commonly adopted approaches that can be applied to assess the structural identifiability of the partial differential equation (PDE) models that are requisite to capture spatial features i…

Verco: Learning Coordinated Verbal Communication for Multi-agent Reinforcement Learning
Dapeng Li, Hang Dong, Lu Wang, Bo Qiao, Si Qin, Qingwei Lin, Dongmei Zhang, Qi Zhang, Zhiwei Xu, Bin Zhang, Guoliang Fan
https://arxiv.org/abs/2404.17780

Verco: Learning Coordinated Verbal Communication for Multi-agent Reinforcement Learning
In recent years, multi-agent reinforcement learning algorithms have made significant advancements in diverse gaming environments, leading to increased interest in the broader application of such techniques. To address the prevalent challenge of partial observability, communication-based algorithms have improved cooperative performance through the sharing of numerical embedding between agents. However, the understanding of the formation of collaborative mechanisms is still very limited, making d…

This https://arxiv.org/abs/2402.02238 has been replaced.
link: https://scholar.google.com/scholar?q=a

Silicon nitride bent asymmetric coupled waveguides with partial Euler bends
Waveguide geometries combining bent asymmetric coupled structures and adiabatic transitions shaped as partial Euler bends are put forward and theoretically analyzed in this work. Designs aiming to reduce the radiation loss, with application in curved waveguide sections and Q-enhanced microresonators, and polarization selection geometries, both for the silicon nitride platform, are studied using highly accurate numerical techniques.

Quasi-intermediate value theorem and outflanking arc theorem for plane maps
Jiehua Mai, Enhui Shi, Kesong Yan, Fanping Zeng
https://arxiv.org/abs/2402.16076

Quasi-intermediate value theorem and outflanking arc theorem for plane maps
For a disk $D$ in the plane $\mathbb R^2$ and a plane map $f$, we give several conditions on the restriction of $f$ to the boundary $\partial D$ of $D$ which imply the existence of a fixed point of $f$ in some specified domain in $D$. These conditions are similar to those appeared in the intermediate value theorem for maps on the real line. As an application of the main results, we establish a fixed point theorem for plane maps having an outflanking arc, which extends the famous theorem due to …

Mean values of multiplicative functions and applications to residue-class distribution
Paul Pollack, Akash Singha Roy
https://arxiv.org/abs/2402.16266 http…

Mean values of multiplicative functions and applications to residue-class distribution
We provide a uniform bound on the partial sums of multiplicative functions under very general hypotheses. As an application, we give a nearly optimal estimate for the count of $n \le x$ for which the Alladi-Erdős function $A(n) = \sum_{p^k \parallel n} k p$ takes values in a given residue class modulo $q$, where $q$ varies uniformly up to a fixed power of $\log x$. We establish a similar result for the equidistribution of the Euler totient function $ϕ(n)$ among the coprime residues to the "co…

This https://arxiv.org/abs/2309.05877 has been replaced.
initial toot: https://mastoxiv.page/@…

Choosing restart strategy at partial knowledge of process statistics
Optimization of a random processes by restart is a subject of active theoretical research in statistical physics and has long found practical application in computer science. Meanwhile, one of the key issues remains largely unsolved: when should we restart a process whose detailed statistics are unknown to ensure that our intervention will improve performance? Addressing this query here we propose several constructive criteria for the effectiveness of various protocols of non-instantaneous rest…

This https://arxiv.org/abs/2307.08867 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Spectral-infinite element method approach for computing asymptotically flat initial data sets in general relativity
In this work, we introduce a spectral-infinite element method for solving Einstein's constraint equations in hyperbolic form. As an application of this, we use this method for computing asymptotically flat perturbations of a Kerr black hole with small angular momentum. Our numerical infrastructure is based on the use of a spin-weighted spherical harmonic transform combined with an infinite element method for solving partial differential equations in unbounded domains.

A hands-on introduction to Physics-Informed Neural Networks for solving partial differential equations with benchmark tests taken from astrophysics and plasma physics
Hubert Baty
https://arxiv.org/abs/2403.00599

A hands-on introduction to Physics-Informed Neural Networks for solving partial differential equations with benchmark tests taken from astrophysics and plasma physics
I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the equation evaluated at various points within the domain. Boundary conditions are incorporated either by introducing soft constraints with corresponding boundary data values in the minimization process or by strictly enforcing the solution with hard constraints. …

This https://arxiv.org/abs/2312.00489 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs
We analyze a goal-oriented adaptive algorithm that aims to efficiently compute the quantity of interest $G(u^\star)$ with a linear goal functional $G$ and the solution $u^\star$ to a general second-order nonsymmetric linear elliptic partial differential equation. The current state of the analysis of iterative algebraic solvers for nonsymmetric systems lacks the contraction property in the norms that are prescribed by the functional analytic setting. This seemingly prevents their application in …

This https://arxiv.org/abs/2403.10904 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSD_…

Urban Sound Propagation: a Benchmark for 1-Step Generative Modeling of Complex Physical Systems
Data-driven modeling of complex physical systems is receiving a growing amount of attention in the simulation and machine learning communities. Since most physical simulations are based on compute-intensive, iterative implementations of differential equation systems, a (partial) replacement with learned, 1-step inference models has the potential for significant speedups in a wide range of application areas. In this context, we present a novel benchmark for the evaluation of 1-step generative le…

Coupled-cluster approach to Coster-Kronig decay and Auger decay in hydrogen sulfide and argon
Jan Philipp Drennhaus, Anthuan Ferino-P\'erez, Florian Matz, Thomas-C. Jagau
https://arxiv.org/abs/2402.17368

Coupled-cluster approach to Coster-Kronig decay and Auger decay in hydrogen sulfide and argon
We perform ab initio simulations of the total and partial Auger decay widths of 1s^-1, 2s^-1, and 2p^-1 ionized hydrogen sulfide and 2s^-1 ionized argon with non-Hermitian quantum chemistry. We use coupled cluster theory with single and double substitutions (CCSD) and equation of motion CCSD (EOM-CCSD) and discuss the novel application of (equation of motion-) second order Møller-Plesset perturbation theory (MP2). We find good agreement between the methods for the 1s^-1 hole of H2S, whereas fo…

This https://arxiv.org/abs/2312.00489 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs
We analyze a goal-oriented adaptive algorithm that aims to efficiently compute the quantity of interest $G(u^\star)$ with a linear goal functional $G$ and the solution $u^\star$ to a general second-order nonsymmetric linear elliptic partial differential equation. The current state of the analysis of iterative algebraic solvers for nonsymmetric systems lacks the contraction property in the norms that are prescribed by the functional analytic setting. This seemingly prevents their application in …

This https://arxiv.org/abs/2305.01065 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An Inverse Problem With the Final Overdetermination for the Mean Field Games System
The mean field games (MFG) theory has broad application in mathematical modeling of social phenomena. The Mean Field Games System (MFGS) is the key to the MFG theory. This is a system of two nonlinear parabolic partial differential equations with two opposite directions of time 0

Urban Sound Propagation: a Benchmark for 1-Step Generative Modeling of Complex Physical Systems
Martin Spitznagel, Janis Keuper
https://arxiv.org/abs/2403.10904

Urban Sound Propagation: a Benchmark for 1-Step Generative Modeling of Complex Physical Systems
Data-driven modeling of complex physical systems is receiving a growing amount of attention in the simulation and machine learning communities. Since most physical simulations are based on compute-intensive, iterative implementations of differential equation systems, a (partial) replacement with learned, 1-step inference models has the potential for significant speedups in a wide range of application areas. In this context, we present a novel benchmark for the evaluation of 1-step generative le…

Unique continuation for a gradient inequality with $L^n$ potential
Adam Coffman, Yifei Pan, Yuan Zhang
https://arxiv.org/abs/2402.15503 https://

Unique continuation for a gradient inequality with $L^n$ potential
We establish a unique continuation property for solutions of the differential inequality $|\nabla u|\leq V|u|$, where $V$ is locally $L^n$ integrable on a domain in $\mathbb R^n$. A stronger uniqueness result is obtained if in addition the solutions are locally Lipschitz. One application is a finite order vanishing property in the $L^2$ sense for the exponential of $W^{1,n}$ functions. We further discuss related results for the Cauchy-Riemann operator $\bar\partial$ and char…

Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations
Daniel Doehring, Gregor J. Gassner, Manuel Torrilhon
https://arxiv.org/abs/2402.12140

Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations
A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge-Kutta method is devised. Intended for semidiscretizations of hyperbolic partial differential equations, the herein developed approach allows the optimization of stability polynomials with more than hundred stages. A potential application of these high degree stability polynomials are problems with locally varying characteristic speeds as found in non-uniformly refined meshes and different wav…

This https://arxiv.org/abs/2309.02156 has been replaced.
link: https://scholar.google.com/scholar?q=a

Subspace Acceleration for a Sequence of Linear Systems and Application to Plasma Simulation
We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different approaches to leverage the subspace containing the history of solutions computed at previous time steps in order to generate a good initial guess for the iterative solver. In particular, we propose a novel combination of reduced-order projection with randomized…

Wave-front tracking for a quasi-linear scalar conservation law with hysteresis
Fabio Bagagiolo, Stefan Moreti
https://arxiv.org/abs/2404.11405 https://

Wave-front tracking for a quasi-linear scalar conservation law with hysteresis
In this article we deal with the Cauchy problem for the quasi-linear scalar conservation law \[u_t+ {\cal F}(u)_t+u_x=0,\] where ${\cal F}$ is a specific hysteresis operator, namely the Play operator. Hysteresis models a rate-independent memory relationship between the input $u$ and its output. Its presence in the partial differential equation gives a particular non-local feature to the latter allowing us to capture phenomena that may arise in some application fields. Riemann problems and the i…

This https://arxiv.org/abs/2402.12140 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations
A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge-Kutta methods is devised. Intended for semidiscretizations of hyperbolic partial differential equations, the herein developed approach allows the optimization of stability polynomials with more than hundred stages. A potential application of these high degree stability polynomials are problems with locally varying characteristic speeds as found in non-uniformly refined meshes and different wa…

This https://arxiv.org/abs/2208.02767 has been replaced.
link: https://scholar.google.com/scholar?q=a

Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration
We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal control problems subject to parabolic partial differential equation (PDE) constraints under uncertainty: the state in our setting is the solution of a parabolic PDE with a random thermal diffusion coefficient, steered by a control function. To account for the presence of uncertainty in the optimal control problem, the objective function is composed with a risk measure. We focus on two risk measures, both…

This https://arxiv.org/abs/2206.02217 has been replaced.
link: https://scholar.google.com/scholar?q=a

Learning Mesh Motion Techniques with Application to Fluid-Structure Interaction
Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shape optimization via the method of mappings. In both cases, an appropriate mesh motion technique is required. The choice is typically based on heuristics, e.g., the solution operators of partial differential equations (PDE), such as the Laplace or biharmonic equation. Especially the latter, which shows good numerical performance for large displacements, is expensive. Moreover, from a continuous perspec…

This https://arxiv.org/abs/2402.12140 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations
A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge-Kutta method is devised. Intended for semidiscretizations of hyperbolic partial differential equations, the herein developed approach allows the optimization of stability polynomials with more than hundred stages. A potential application of these high degree stability polynomials are problems with locally varying characteristic speeds as found in non-uniformly refined meshes and different wav…

This https://arxiv.org/abs/2304.12377 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Efficient and Scalable Path-Planning Algorithms for Curvature Constrained Motion in the Hamilton-Jacobi Formulation
We present a partial-differential-equation-based optimal path-planning framework for curvature constrained motion, with application to vehicles in 2- and 3-spatial-dimensions. This formulation relies on optimal control theory, dynamic programming, and Hamilton-Jacobi-Bellman equations. We develop efficient and scalable algorithms for solutions of high dimensional Hamilton-Jacobi equations which can solve these types of path-planning problems efficiently, even in high dimensions, while maintaini…

This https://arxiv.org/abs/2304.12377 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Efficient and Scalable Path-Planning Algorithms for Curvature Constrained Motion in the Hamilton-Jacobi Formulation
We present a partial-differential-equation-based optimal path-planning framework for curvature constrained motion, with application to vehicles in 2- and 3-spatial-dimensions. This formulation relies on optimal control theory, dynamic programming, and Hamilton-Jacobi-Bellman equations. We develop efficient and scalable algorithms for solutions of high dimensional Hamilton-Jacobi equations which can solve these types of path-planning problems efficiently, even in high dimensions, while maintaini…