arXiv subjects

Chang Yang

Publications and source records attributed to Chang Yang.

At least 55 records · Page 3Linked to original sources

arXiv2022

Light quark decays of doubly heavy baryons in light front approach

We explore the semileptonic and nonleptonic decays of doubly heavy baryons $(Ω_{cc}^ {(*) +}, Ω_{bb}^ {(*)0}, Ω_{bc}^ {(*) -}, Ω_{bc}^ {\prime 0}) $ induced by the $s\to u$ transition. Hadronic form factors are parametrized by transition matrix elements and are calculated in the light front quark model. With the form factors, we make use of helicity amplitudes and analyze semileptonic and nonleptonic decay modes of doubly heavy baryons. Benchmark results for partial decay widths, branching fractions, forward-backward asymmetries and other phenomenological observables are derived. We find that typical branching fractions for semileptonic decays into $\ell\barν$ are at the order $10^ {-7}-10^ {-8} $ and the ones for nonleptonic decays are at the order $10^ {-5} $, which are likely detectable such as in LHCb experiment. With the potential data accumulated in future, our results may help to shape our understanding of the decay mechanism in the presence of two heavy quarks.

hep-ph↗

arXiv2022

A Game-Theoretic Perspective of Generalization in Reinforcement Learning

Generalization in reinforcement learning (RL) is of importance for real deployment of RL algorithms. Various schemes are proposed to address the generalization issues, including transfer learning, multi-task learning and meta learning, as well as the robust and adversarial reinforcement learning. However, there is not a unified formulation of the various schemes, as well as the comprehensive comparisons of methods across different schemes. In this work, we propose a game-theoretic framework for the generalization in reinforcement learning, named GiRL, where an RL agent is trained against an adversary over a set of tasks, where the adversary can manipulate the distributions over tasks within a given threshold. With different configurations, GiRL can reduce the various schemes mentioned above. To solve GiRL, we adapt the widely-used method in game theory, policy space response oracle (PSRO) with the following three important modifications: i) we use model-agnostic meta learning (MAML) as the best-response oracle, ii) we propose a modified projected replicated dynamics, i.e., R-PRD, which ensures the computed meta-strategy of the adversary fall in the threshold, and iii) we also propose a protocol for the few-shot learning of the multiple strategies during testing. Extensive experiments on MuJoCo environments demonstrate that our proposed methods can outperform existing baselines, e.g., MAML.

cs.LG↗

arXiv2022

Linear periods for unitary representations

Let $F$ be a local non-Archimedean field of characteristic zero with a finite residue field. Based on Tadić's classification of the unitary dual of $\mathrm{GL}_{2n}(F)$, we classify irreducible unitary representations of $\mathrm{GL}_{2n}(F)$ that have nonzero linear periods, in terms of Speh representations that have nonzero periods. We also give a necessary and sufficient condition for the existence of a nonzero linear period for a Speh representation.

math.RT↗

arXiv2022

A new collision avoidance model with random batch resolution strategy

Research on crowd simulation has important and wide range of applications. The main difficulty is how to lead all particles with a same and simple rule, especially when particles are numerous. In this paper, we firstly propose a two dimensional agent-based collision avoidance model, which is a $N$-particles Newtonian system. The collision interaction force, imminent interaction force and following interaction force are designed, so that particles can be guided to their respective destinations without collisions. The proposed agent-based model is then extended to the corresponding mean field limit model as $N\to\infty$. Secondly, notice that direct simulation of the $N$-particles Newtonian system is very time-consuming, since the computational complexity is of order $\mathcal{O}(N^2)$. In contrast, we propose an efficient hybrid resolution strategy to reduce the computational complexity. It is a combination of the Random Batch method (Shi Jin, Lei Li, and Jian-Guo Liu. Random batch methods (RBM) for interacting particle systems. Journal of Computational Physics, 400:108877, 2020.) and the method based on local particles Newtonian system. Thanks to this hybrid resolution strategy, the computational complexity is reduced to $\mathcal{O}(N)$. Finally, various tests are presented to show robustness and efficiency of our collision avoidance model and the hybrid resolution strategy.

math.NA↗

arXiv2022

A Unified Perspective on Deep Equilibrium Finding

Extensive-form games provide a versatile framework for modeling interactions of multiple agents subjected to imperfect observations and stochastic events. In recent years, two paradigms, policy space response oracles (PSRO) and counterfactual regret minimization (CFR), showed that extensive-form games may indeed be solved efficiently. Both of them are capable of leveraging deep neural networks to tackle the scalability issues inherent to extensive-form games and we refer to them as deep equilibrium-finding algorithms. Even though PSRO and CFR share some similarities, they are often regarded as distinct and the answer to the question of which is superior to the other remains ambiguous. Instead of answering this question directly, in this work we propose a unified perspective on deep equilibrium finding that generalizes both PSRO and CFR. Our four main contributions include: i) a novel response oracle (RO) which computes Q values as well as reaching probability values and baseline values; ii) two transform modules -- a pre-transform and a post-transform -- represented by neural networks transforming the outputs of RO to a latent additive space (LAS), and then the LAS to action probabilities for execution; iii) two average oracles -- local average oracle (LAO) and global average oracle (GAO) -- where LAO operates on LAS and GAO is used for evaluation only; and iv) a novel method inspired by fictitious play that optimizes the transform modules and average oracles, and automatically selects the optimal combination of components of the two frameworks. Experiments on Leduc poker game demonstrate that our approach can outperform both frameworks.

cs.GT↗

arXiv2021

Block preconditioning methods for asymptotic preserving scheme arising in anisotropic elliptic problems

Efficient and robust iterative solvers for strong anisotropic elliptic equations are very challenging. In this paper a block preconditioning method is introduced to solve the linear algebraic systems of a class of micro-macro asymptotic-preserving (MMAP) scheme. MMAP method was developed by Degond {\it et al.} in 2012 where the discrete matrix has a $2\times2$ block structure. By the approximate Schur complement a series of block preconditioners are constructed. We first analyze a natural approximate Schur complement that is the coefficient matrix of the original non-AP discretization. However it tends to be singular for very small anisotropic parameters. We then improve it by using more suitable approximation for boundary rows of the exact Schur complement. With these block preconditioners, preconditioned GMRES iterative method is developed to solve the discrete equations. Several numerical tests show that block preconditioning methods can be a robust strategy with respect to grid refinement and the anisotropic strengths.

math.NA↗

arXiv2021

Asymptotic preserving scheme for anisotropic elliptic equations with deep neural network

In this paper, a new asymptotic preserving (AP) scheme is proposed for the anisotropic elliptic equations. Different from previous AP schemes, the actual one is based on first-order system least-squares for second-order partial differential equations, and it is uniformly well-posed with respect to anisotropic strength. The numerical computation is realized by a deep neural network (DNN), where least-squares functionals are employed as loss functions to determine parameters of DNN. Numerical results show that the current AP scheme is easy for implementation and is robust to approximate solutions or to identify anisotropic strength in various 2D and 3D tests.

math.NA↗

arXiv2020

Distinguished representations, Shintani base change and a finite field analogue of a conjecture of Prasad

Let $E/F$ be a quadratic extension of fields, and $G$ a connected quasi-split reductive group over $F$. Let $G^{op}$ be the opposition group obtained by twisting $G$ by the duality involution considered by Prasad. Assume that the field $F$ is finite. Let $π$ be an irreducible generic representation of $G(E)$. When $π$ is a Shintani base change lift of some representation of $G^{op}(F)$, we give an explicit nonzero $G(F)$-invariant vector in terms of the Whittaker vector of $π$. This shows particularly that $π$ is $G(F)$-distinguished. When the field $F$ is $p$-adic, the paper also proves that the duality involution takes an irreducible admissible generic representation of $G(F)$ to its contragredient. As a special case of this result, all generic representations of $G_2,\ F_4$ or $E_8$ are self-dual.

math.RT↗

arXiv2019

Preserving the accuracy of numerical methods discretizing anisotropic elliptic problems

In this paper we study the loss of precision of numerical methods discretizing anisotropic problems and propose alternative approaches free from this drawback. The deterioration of the accuracy is observed when the coordinates and the mesh are unrelated to the anisotropy direction. While this issue is commonly addressed by increasing the scheme approximation order, we demonstrate that, though the gains are evident, the precision of these numerical methods remain far from optimal and limited to moderate anisotropy strengths. This is analysed and explained by an amplification of the approximation error related to the anisotropy strength. We propose an approach consisting in the introduction of an auxiliary variable aimed at removing the amplification of the discretization error. By this means the precision of the numerical approximation is demonstrated to be independent of the anisotropy strength.

math.NA↗

arXiv2019

A Whittaker-Plancherel Inversion Formula for $\mathrm{SL}_2(\mathbb{C})$

In this paper, we establish a Whittaker-Plancherel inversion formula for $\mathrm{SL}_2(\mathbb{C})$ from the analytic perspective of the Bessel transform of Bruggeman and Motohashi. The formula gives a decomposition of the Whittaker-Fourier coefficient of a compactly supported function on $\mathrm{SL}_2(\mathbb{C})$ in terms of its Bessel coefficients attached to irreducible unitary tempered representations of $\mathrm{SL}_2(\mathbb{C})$.

math.RT↗

arXiv2019

Gamma factors of level zero supercuspidal representations

We give an explicit formula for the twisted gamma factor for a pair of irreducible supercuspidal representations of level zero. We also obtain an explicit formula for the unramified base change of level zero supercuspidal representations.

math.RT↗

arXiv2018

Numerical Simulations to the Vlasov-Poisson System with a Strong Magnetic Field

In this paper, we present an efficient Particle-In-Cell algorithm for the simulation of the three dimensional Vlasov-Poisson system in the presence of a strong external magnetic field. When the intensity of the magnetic field is sufficiently large and for any time step, the numerical scheme provides formally a consistent approximation of the drift-kinetic model, which corresponds to the asymptotic model. Numerical results show that this new Particle-In-Cell method is efficient and accurate large time steps.

math.NA↗

arXiv2015

A hybrid finite volume method for advection equations and its applications in population dynamics

We present in this paper a very adapted finite volume numerical scheme for transport type-equation. The scheme is an hybrid one combining an anti-dissipative method with down-winding approach for the flux and an high accurate method as the WENO5 one. The main goal is to construct a scheme able to capture in exact way the numerical solution of transport type-equation without artifact like numerical diffusion or without "stairs" like oscillations and this for any regular or discontinuous initial distribution. This kind of numerical hybrid scheme is very suitable when properties on the long term asymptotic behavior of the solution are of central importance in the modeling what is often the case in context of population dynamics where the final distribution of the considered population and its mass preservation relation are required for prediction.

math.NA↗

arXiv2014

Morita's Theory for the Symplectic Groups

We construct and study the holomorphic discrete series representation and the principal series representation of the symplectic group $\mathrm{Sp}(2n,F)$ over a $p$-adic field $F$ as well as a duality between some sub-representations of these two representations. The constructions of these two representations generalize those defined in Morita and Murase's works. Moreover, Morita built a duality for $\mathrm{SL}(2, F)$ defined by residues. We view the duality we defined as an algebraic interpretation of Morita's duality in some extent and its generalization to the symplectic groups.

math.RT↗

arXiv2014

Mixed semi-Lagrangian/finite difference methods for plasma simulations

In this paper, we present an efficient algorithm for the long time behavior of plasma simulations. We will focus on 4D drift-kinetic model, where the plasma's motion occurs in the plane perpendicular to the magnetic field and can be governed by the 2D guiding-center model. Hermite WENO reconstructions, already proposed in \cite{YF15}, are applied for solving the Vlasov equation. Here we consider an arbitrary computational domain with an appropriate numerical method for the treatment of boundary conditions. Then we apply this algorithm for plasma turbulence simulations. We first solve the 2D guiding-center model in a D-shape domain and investigate the numerical stability of the steady state. Then, the 4D drift-kinetic model is studied with a mixed method, i.e. the semi-Lagrangian method in linear phase and finite difference method during the nonlinear phase. Numerical results show that the mixed method is efficient and accurate in linear phase and it is much stable during the nonlinear phase. Moreover, in practice it has better conservation properties.

math.NA↗

arXiv2013

Conservative and non-conservative methods based on hermite weighted essentially-non-oscillatory reconstruction for Vlasov equations

We introduce a WENO reconstruction based on Hermite interpolation both for semi-Lagrangian and finite difference methods. This WENO reconstruction technique allows to control spurious oscillations. We develop third and fifth order methods and apply them to non-conservative semi-Lagrangian schemes and conservative finite difference methods. Our numerical results will be compared to the usual semi-Lagrangian method with cubic spline reconstruction and the classical fifth order WENO finite difference scheme. These reconstructions are observed to be less dissipative than the usual weighted essentially non- oscillatory procedure. We apply these methods to transport equations in the context of plasma physics and the numerical simulation of turbulence phenomena.

math.NA↗

arXiv2013

Numerical Simulations of Kinetic Models for chemotaxis

We present a new algorithm based on a Cartesian mesh for the numerical approximation of kinetic models for chemosensitive movements set in an arbitrary geometry. We investigate the influence of the geometry on the collective behavior of bacteria described by a kinetic equation interacting with nutrients and chemoattractants. Numerical simulations are performed to verify accuracy and stability of the scheme and its ability to exhibit aggregation of cells and wave propagations. Finally some comparisons with experiments show the robustness and accuracy of such kinetic models.

math.NA↗

arXiv2012

Inverse Lax-Wendroff method for boundary conditions of Boltzmann type models

In this paper we present a new algorithm based on a Cartesian mesh for the numerical approximation of kinetic models on complex geometry boundary. Due to the high dimensional property, numerical algorithms based on unstructured meshes for a complex geometry are not appropriate. Here we propose to develop an inverse Lax-Wendroff pro- cedure, which was recently introduced for conservation laws [S. Tan & C.W. Shu, JCP (2010)], to the kinetic equations. Applications in 1Dx3D and 2Dx3D of this algorithm for Boltzmann type operators (BGK, ES-BGK models) are then presented and numerical results illustrate the accuracy properties of this algorithm.

math.NA↗