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Peng Zhao

Publications and source records attributed to Peng Zhao.

232 records · Page 13Linked to original sources
arXiv2014

New Construction of Algebro-Geometric Solutions to the Modified Kadomtsev-Petviashvili Hierarchy

We extend Gesztesy-Holden's method to 2+1 dimensional case to obtain a unified construction to the algebro-geometric solutions of the whole modified Kadomtsev-Petviashvili (mKP) hierarchy. Our tools include the relations between solutions of the Gerdjikov-Ivanov (GI) and mKP hierarchy, the Baker-Akhiezer functions in 2+1 dimensions, a special function $ψ_1(P)ψ_2(P^*)$ on $X\times \mathbb{R}^3$ and Dubrovin-type equations for auxiliary divisors.

nlin.SI↗
arXiv2014

Algebro-Geometric Solutions for the Kadomtsev-Petviashvili Hierarchy

Based on the idea of symmetric constraint, we apply the Gesztesy-Holden's method to derive explicit representations of the Baker-Ahkiezer function $ψ_1$ of the KP hierarchy, from which we provide theta function representations of algebro-geometric solutions for the whole Kadomtsev-Petviashvili (KP) hierarchy. This provides a approach to obtain some special subclasses of algebro-geometric solutions for the KP hierarchy and other high dimensional hierarchy of equations.

nlin.SI↗
arXiv2014

Cluster algebras from dualities of 2d N=(2,2) quiver gauge theories

We interpret certain Seiberg-like dualities of two-dimensional N=(2,2) quiver gauge theories with unitary groups as cluster mutations in cluster algebras, originally formulated by Fomin and Zelevinsky. In particular, we show how the complexified Fayet-Iliopoulos parameters of the gauge group factors transform under those dualities and observe that they are in fact related to the dual cluster variables of cluster algebras. This implies that there is an underlying cluster algebra structure in the quantum Kahler moduli space of manifolds constructed from the corresponding Kahler quotients. We study the S^2 partition function of the gauge theories, showing that it is invariant under dualities/mutations, up to an overall normalization factor whose physical origin and consequences we spell out in detail. We also present similar dualities in N=(2,2)* quiver gauge theories, which are related to dualities of quantum integrable spin chains.

hep-th↗
arXiv2013

Reality problems for the Algebro-Geometric Solutions of Fokas-Lenell hierarchy

In a previous study, we obtained the algebro-geometric solutions and $n$-dark solitons of Forkas-Lenells (FL) hierarchy using algebro-geometric method. In this paper, we construct physically relevant classes of solutions for FL hierarchy by studying the reality conditions for $q=\pm \bar{r}$ based on the idea of Vinikov's homological basis.

nlin.SI↗
arXiv2013

Facile implementation of integrated tempering sampling method to enhance the sampling over a broad range of temperatures

Integrated tempering sampling (ITS) method is an approach to enhance the sampling over a broad range of energies and temperatures in computer simulations. In this paper, a new version of integrated tempering sampling method is proposed. In the new approach presented here, we obtain parameters such as the set of temperatures and the corresponding weighting factors from canonical average of potential energies. These parameters can be easily obtained without estimating partition functions. We apply this new approach to study the Lennard-Jones fluid, the ALA-PRO peptide and the single polymer chain systems to validate and benchmark the method.

physics.comp-ph↗
arXiv2013

Central charges and RG flow of strongly-coupled N=2 theory

We calculate the central charges a, c and k_G of a large class of four-dimensional N=2 superconformal field theories arising from compactifying the six-dimensional N=(2,0) theory on a Riemann surface with regular and irregular punctures. We also study the renormalization group flows between the general Argyres-Douglas theories, which all agree with the a-theorem.

hep-th↗
arXiv2012

The algebro-geometric solutions for Degasperis-Procesi hierarchy

Though completely integrable Camassa-Holm (CH) equation and Degasperis-Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyper-elliptic curves lead to great difficulty in the construction of algebro-geometric solutions of the DP equation. In this paper, we derive the DP hierarchy with the help of Lenard recursion operators. Based on the characteristic polynomial of a Lax matrix for the DP hierarchy, we introduce a third order algebraic curve $\mathcal{K}_{r-2}$ with genus $r-2$, from which the associated Baker-Akhiezer functions, meromorphic function and Dubrovin-type equations are established. Furthermore, the theory of algebraic curve is applied to derive explicit representations of the theta function for the Baker-Akhiezer functions and the meromorphic function. In particular, the algebro-geometric solutions are obtained for all equations in the whole DP hierarchy.

nlin.SI↗
arXiv2012

The Algebro-Geometric Solutions for the Ruijsenaars-Toda Hierarchy

We provide a detailed treatment of Ruijsenaars-Toda (RT) hierarchy with special emphasis on its the theta function representation of all algebro-geometric solutions. The basic tools involve hyperelliptic curve $\mathcal{K}_p$ associated with the Burchnall-Chaundy polynomial, Dubrovin-type equations for auxiliary divisors and associated trace formulas. With the help of a foundamental meromorphic function $ϕ$, Baker-Akhiezer vector $Ψ$ on $\mathcal{K}_p$, the complex-valued algebro-geometric solutions of RT hierarchy are derived.

nlin.SI↗
arXiv2012

The Algebro-Geometric Initial Value Problem for the Relativistic Lotka-Volterra Hierarchy and Quasi-Periodic Solutions

We provide a detailed treatment of relativistic Lotka-Volterra hierarchy and a kind of initial value problem with special emphasis on its the theta function representation of all algebro-geometric solutions. The basic tools involve hyperelliptic curve $\mathcal{K}_n$ associated with the Burchnall-Chaundy polynomial, Dubrovin-type equations for auxiliary divisors and associated trace formulas. With the help of a foundamental meromorphic function $\tildeϕ$ on $\mathcal{K}_p$ and trace formulas, the complex-valued algebro-geometric solutions of of RLV hierarchy are derived.

nlin.SI↗
arXiv2012

A 5d/3d duality from relativistic integrable system

We propose and prove a new exact duality between the F-terms of supersymmetric gauge theories in five and three dimensions with adjoint matter fields. The theories are compactified on a circle and are subject to the Omega deformation. In the limit proposed by Nekrasov and Shatashvili, the supersymmetric vacua become isolated and are identified with the eigenstates of a quantum integrable system. The effective twisted superpotentials are the Yang-Yang functional of the relativistic elliptic Calogero-Moser model. We show that they match on-shell by deriving the Bethe ansatz equation from the saddle point of the five-dimensional partition function. We also show that the Chern-Simons terms match and extend our proposal to the elliptic quiver generalizations.

hep-th↗
arXiv2012

The algebro-geometric solutions for Hunter-Saxton hierarchy

This paper is dedicated to provide theta function representation of algebro-geometric solutions and related crucial quantities for the Hunter-Saxton (HS) hierarchy through studying a algebro-geometric initial value problem. Our main tools include the polynomial recursive formalism to derive the HS hierarchy, the hyperelliptic curve with finite number of genus, the Baker-Akhiezer functions, the meromorphic function, the Dubrovin-type equations for auxiliary divisors, and the associated trace formulas. With the help of these tools, the explicit representations of the Baker-Ahhiezer functions, the meromorphic function, and the algebro-geometric solutions are obtained for the entire HS hierarchy.

nlin.SI↗
arXiv2011

Scattering of Giant Holes

We study scalar excitations of high spin operators in N=4 super Yang-Mills theory, which are dual to solitons propagating on a long folded string in AdS_3 x S^1. In the spin chain description of the gauge theory, these are associated to holes in the magnon distribution in the sl(2,R) sector. We compute the all-loop hole S-matrix from the asymptotic Bethe ansatz, and expand in leading orders at weak and strong coupling. The worldsheet S-matrix of solitonic excitations on the GKP string is calculated using semiclassical quantization. We find an exact agreement between the gauge theory and string theory results.

hep-th↗
arXiv2010

Active microcantilevers based on piezoresistive ferromagnetic thin films

We report the piezoresisitivity in magnetic thin films of FeGa and their use for fabricating self transducing microcantilevers. The actuation occurs as a consequence of both the ferromagnetic and magnetostrictive property of FeGa thin films, while the deflection readout is achieved by exploiting the piezoresisitivity of these films. This self-sensing, self-actuating micromechanical system involves a very simple bilayer structure, which eliminates the need for the more complex piezoelectric stack that is commonly used in active cantilevers. Thus, it potentially opens opportunities for remotely actuated, cantilever-based sensors.

cond-mat.mes-hall↗
arXiv2009

The composite absolute penalties family for grouped and hierarchical variable selection

Extracting useful information from high-dimensional data is an important focus of today's statistical research and practice. Penalized loss function minimization has been shown to be effective for this task both theoretically and empirically. With the virtues of both regularization and sparsity, the $L_1$-penalized squared error minimization method Lasso has been popular in regression models and beyond. In this paper, we combine different norms including $L_1$ to form an intelligent penalty in order to add side information to the fitting of a regression or classification model to obtain reasonable estimates. Specifically, we introduce the Composite Absolute Penalties (CAP) family, which allows given grouping and hierarchical relationships between the predictors to be expressed. CAP penalties are built by defining groups and combining the properties of norm penalties at the across-group and within-group levels. Grouped selection occurs for nonoverlapping groups. Hierarchical variable selection is reached by defining groups with particular overlapping patterns. We propose using the BLASSO and cross-validation to compute CAP estimates in general. For a subfamily of CAP estimates involving only the $L_1$ and $L_{\infty}$ norms, we introduce the iCAP algorithm to trace the entire regularization path for the grouped selection problem. Within this subfamily, unbiased estimates of the degrees of freedom (df) are derived so that the regularization parameter is selected without cross-validation. CAP is shown to improve on the predictive performance of the LASSO in a series of simulated experiments, including cases with $p\gg n$ and possibly mis-specified groupings. When the complexity of a model is properly calculated, iCAP is seen to be parsimonious in the experiments.

math.ST↗
arXiv2008

A path following algorithm for Sparse Pseudo-Likelihood Inverse Covariance Estimation (SPLICE)

Given n observations of a p-dimensional random vector, the covariance matrix and its inverse (precision matrix) are needed in a wide range of applications. Sample covariance (e.g. its eigenstructure) can misbehave when p is comparable to the sample size n. Regularization is often used to mitigate the problem. In this paper, we proposed an l1-norm penalized pseudo-likelihood estimate for the inverse covariance matrix. This estimate is sparse due to the l1-norm penalty, and we term this method SPLICE. Its regularization path can be computed via an algorithm based on the homotopy/LARS-Lasso algorithm. Simulation studies are carried out for various inverse covariance structures for p=15 and n=20, 1000. We compare SPLICE with the l1-norm penalized likelihood estimate and a l1-norm penalized Cholesky decomposition based method. SPLICE gives the best overall performance in terms of three metrics on the precision matrix and ROC curve for model selection. Moreover, our simulation results demonstrate that the SPLICE estimates are positive-definite for most of the regularization path even though the restriction is not enforced.

stat.ME↗