Berry-Esseen Bounds of Normal and Non-normal Approximation for Unbounded Exchangeable Pairs

An exchangeable pair approach is commonly taken in the normal and non-normal approximation using Stein's method. It has been successfully used to identify the limiting distribution and provide an error of approximation. However, when the difference of the exchangeable pair is not bounded by a small deterministic constant, the error bound is often not optimal. In this paper, using the exchangeable pair approach of Stein's method, a new Berry-Esseen bound for an arbitrary random variable is established without a bound on the difference of the exchangeable pair. An optimal convergence rate for normal and non-normal approximation is achieved when the result is applied to various examples including the quadratic forms, general Curie-Weiss model, mean field Heisenberg model and colored graph model.Comment: 51 page

Controlling decoherence speed limit of a single impurity atom in a Bose-Einstein-condensate reservoir

We study the decoherence speed limit (DSL) of a single impurity atom immersed in a Bose-Einsteincondensed (BEC) reservoir when the impurity atom is in a double-well potential. We demonstrate how the DSL of the impurity atom can be manipulated by engineering the BEC reservoir and the impurity potential within experimentally realistic limits. We show that the DSL can be controlled by changing key parameters such as the condensate scattering length, the effective dimension of the BEC reservoir, and the spatial configuration of the double-well potential imposed on the impurity. We uncover the physical mechanisms of controlling the DSL at root of the spectral density of the BEC reservoir.Comment: 8 pages, 8 figure

Adversarial Discriminative Heterogeneous Face Recognition

The gap between sensing patterns of different face modalities remains a challenging problem in heterogeneous face recognition (HFR). This paper proposes an adversarial discriminative feature learning framework to close the sensing gap via adversarial learning on both raw-pixel space and compact feature space. This framework integrates cross-spectral face hallucination and discriminative feature learning into an end-to-end adversarial network. In the pixel space, we make use of generative adversarial networks to perform cross-spectral face hallucination. An elaborate two-path model is introduced to alleviate the lack of paired images, which gives consideration to both global structures and local textures. In the feature space, an adversarial loss and a high-order variance discrepancy loss are employed to measure the global and local discrepancy between two heterogeneous distributions respectively. These two losses enhance domain-invariant feature learning and modality independent noise removing. Experimental results on three NIR-VIS databases show that our proposed approach outperforms state-of-the-art HFR methods, without requiring of complex network or large-scale training dataset

Classical Equation of Electromagnetic Field in the Higgs Boson Field and Estimation on the Static Electrical Polarizability of Leptons

In our paper we derived the classical motion equation of electromagnetic field in space with Higgs field and by means of it discussed the distributions of charge and current formed when the static electrical and magnetic fields are interacting with the spherically symmetrical Higgs field, and predicted the electrical polarizability of electron

Path Integral by Space-time Slicing Approximation In Open Bosonic String Field

In our paper, we considered how to apply the traditional Feynman path integral to string field. By constructing the complete set in Fock space of non-relativistic and relativistic open bosonic string fields, we extended Feynman path integral to path integral on functional field and use it to quantize open bosonic string field

Impurity-induced Dicke quantum phase transition in an impurity-doped cavity-Bose-Einstein condensate

We present a new generalized Dicke model, an impurity-doped Dicke model (IDDM), by the use of an impurity-doped cavity-Bose-Einstein condensate. It is shown that the impurity atom can induce Dicke quantum phase transition (QPT) from the normal phase to superradiant phase at a critic value of the impurity population. It is found that the IDDM exhibits continuous Dicke QPT with an infinite number of critical points, which is significantly different from that observed in the standard Dicke model with only one critical point. It is revealed that the impurity-induced Dicke QPT can happen in an arbitrary coupling regime of the cavity field and atoms while the Dicke QPT in the standard Dicke model occurs only in the strong coupling regime of the cavity field and atoms. This opens a way to observe the Dicke QPT in the intermediate and even weak coupling regime of the cavity field and atoms.Comment: 7 pages, 3 figure

Limit theorems with rate of convergence under sublinear expectations

Under the sublinear expectation $\mathbb{E}[\cdot]:=\sup_{\theta\in \Theta} E_\theta[\cdot]$ for a given set of linear expectations $\{E_\theta: \theta\in \Theta\}$, we establish a new law of large numbers and a new central limit theorem with rate of convergence. We present some interesting special cases and discuss a related statistical inference problem. We also give an approximation and a representation of the $G$-normal distribution, which was used as the limit in Peng (2007)'s central limit theorem, in a probability space.Comment: 34 page

Finite element computations on quadtree meshes: strain smoothing and semi-analytical formulation

This short communication discusses two alternate techniques to treat hanging nodes in a quadtree mesh. Both the techniques share similarities, in that, they require only boundary information. Moreover, they do not require an explicit form of the shape functions, unlike the conventional approaches, for example, as in the work of Gupta \cite{gupta1978} or Tabarraei and Sukumar \cite{tabarraeisukumar2005}. Hence, no special numerical integration technique is required. One of the techniques relies on the strain projection procedure, whilst the other is based on the scaled boundary finite element method. Numerical examples are presented to demonstrate the accuracy and the convergence properties of the two techniques

Quantum speed-up of multiqubit open system via dynamical decoupling pulses

We present a method to accelerate the dynamical evolution of multiqubit open system by employing dynamical decoupling pulses (DDPs) when the qubits are initially in W-type states. It is found that this speed-up evolution can be achieved in both of the weak-coupling regime and the strong-coupling regime. The physical mechanism behind the acceleration evolution is explained as the result of the joint action of the non-Markovianity of reservoirs and the excited-state population of qubits. It is shown that both of the non-Markovianity and the excited-state population can be controlled by DDPs to realize the quantum speed-up.Comment: 8 pages, 5 figure

Free vibration and mechanical buckling of plates with in-plane material inhomogeneity - a three dimensional consistent approach

In this article, we study the free vibration and the mechanical buckling of plates using a three dimensional consistent approach based on the scaled boundary finite element method. The in-plane dimensions of the plate are modeled by two-dimensional higher order spectral element. The solution through the thickness is expressed analytically with Pade expansion. The stiffness matrix is derived directly from the three dimensional solutions and by employing the spectral element, a diagonal mass matrix is obtained. The formulation does not require ad hoc shear correction factors and no numerical locking arises. The material properties are assumed to be temperature independent and graded only in the in-plane direction by a simple power law. The effective material properties are estimated using the rule of mixtures. The influence of the material gradient index, the boundary conditions and the geometry of the plate on the fundamental frequencies and critical buckling load are numerically investigated