Diffusion multi-rate LMS algorithm for acoustic sensor networks

In this paper, we present a diffusion multi-rate least-mean-square (LMS) algorithm, named DMLMS, which is an effective solution for distributed estimation when two or more observation sequences are available with different sampling rates. Then, we focus on a more practical application in the wireless acoustic sensor networks (ASN). The filtered-x LMS (FxLMS) algorithm is extended to the distributed multi-rate system and it introduces collaboration between nodes following a diffusion strategy. Simulation results show that the effectiveness of the proposed algorithms

Frozen Gaussian approximation for general linear strictly hyperbolic system: formulation and Eulerian methods

The frozen Gaussian approximation, proposed in [Lu and Yang, [15]], is an efficient computational tool for high frequency wave propagation. We continue in this paper the development of frozen Gaussian approximation. The frozen Gaussian approximation is extended to general linear strictly hyperbolic systems. Eulerian methods based on frozen Gaussian approximation are developed to overcome the divergence problem of Lagrangian methods. The proposed Eulerian methods can also be used for the Herman-Kluk propagator in quantum mechanics. Numerical examples verify the performance of the proposed methods

Hardy-Sobolev-Maz'ya inequalities for higher order derivatives on half spaces

By using, among other things, the Fourier analysis techniques on hyperbolic and symmetric spaces, we establish the Hardy-Sobolev-Maz'ya inequalities for higher order derivatives on half spaces. The proof relies on a Hardy-Littlewood-Sobolev inequality on hyperbolic spaces which is of its independent interest. We also give an alternative proof of Benguria, Frank and Loss' work concerning the sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half space. Finally, we show the sharp constant in the Hardy-Sobolev-Maz'ya inequality for bi-Laplacian in the upper half space of dimension five coincides with the Sobolev constant.Comment: 32 page

The electromagnetic form factors of Λ\Lambda hyperon in e+e−→ΛˉΛe^+e^-\rightarrow \bar\Lambda\Lambda

We study the electromagnetic form factors of $\Lambda$ hyperon in the timelike region using the recent experimental data in the exclusive production of $\bar{\Lambda} \Lambda$ pair in electron-position annihilation. We present a pQCD inspired parametrization of $G_E(s)$ and $G_M(s)$ with only two parameters, and we consider a suppression mechanism of the electric form factor $G_E(s)$ compared to the magnetic form factor $G_M(s)$. The parameters are determined through fitting our parametrization to the effective form factor data in the reaction $e^+e^-\rightarrow \bar\Lambda\Lambda$. Except the threshold region, our parametrization can reproduce satisfactorily the known behavior of the existing data from the BarBar, DM2 and BESIII Collaborations. We also predict the double spin polarization observables $A_{xx}$, $A_{yy}$ and $A_{zz}$ in $e^+e^-\rightarrow \bar\Lambda\Lambda$.Comment: 5 pages, 3 figure

Phase Space Sketching for Crystal Image Analysis based on Synchrosqueezed Transforms

Recent developments of imaging techniques enable researchers to visualize materials at the atomic resolution to better understand the microscopic structures of materials. This paper aims at automatic and quantitative characterization of potentially complicated microscopic crystal images, providing feedback to tweak theories and improve synthesis in materials science. As such, an efficient phase-space sketching method is proposed to encode microscopic crystal images in a translation, rotation, illumination, and scale invariant representation, which is also stable with respect to small deformations. Based on the phase-space sketching, we generalize our previous analysis framework for crystal images with simple structures to those with complicated geometry

Analytic Constructions of General n-Qubit Controlled Gates

In this Letter, we present two analytic expressions that most generally simulate $n$-qubit controlled-$U$ gates with standard one-qubit gates and CNOT gates using exponential and polynomial complexity respectively. Explicit circuits and general expressions of decomposition are derived. The exact numbers of basic operations in these two schemes are given using gate counting technique.Comment: 4 pages 7 figure

SL(n,R)-Toda Black Holes

We consider D-dimensional Einstein gravity coupled to (n-1) U(1) vector fields and (n-2) dilatonic scalars. We find that for some appropriate exponential dilaton couplings of the field strengths, the equations of motion for the static charged ansatz can be reduced to a set of one-dimensional SL(n,R) Toda equations. This allows us to obtain a general class of explicit black holes with mass and (n-1) independent charges. The near-horizon geometry in the extremal limit is AdS_2 x S^{D-2}. The n=2 case gives the Reissner-Nordstrom solution, and the n=3 example includes the Kaluza-Klein dyon. We study the global structure and the black hole thermodynamics and obtain the universal entropy product formula. We also discuss the characteristics of extremal multi-charge black holes that have positive, zero or negative binding energies.Comment: Latex, 20 page

Distributed economic control of dynamically coupled networks

This paper investigates the synthesis of distributed economic control algorithms under which dynamically coupled physical systems are regulated to a variational equilibrium of a constrained convex game. We study two complementary cases: (i) each subsystem is linear and controllable; and (ii) each subsystem is nonlinear and in the strict-feedback form. The convergence of the proposed algorithms is guaranteed using Lyapunov analysis. Their performance is verified by two case studies on a multi-zone building temperature regulation problem and an optimal power flow problem, respectively.Comment: 14 pages, 4 figures, journa

A sharp Trudinger-Moser inequality on any bounded and convex planar domain

Wang and Ye conjectured in [22]: Let $\Omega$ be a regular, bounded and convex domain in $\mathbb{R}^{2}$. There exists a finite constant $C({\Omega})>0$ such that $$\int_{\Omega}e^{\frac{4\pi u^{2}}{H_{d}(u)}}dxdy\le C(\Omega),\;\;\forall u\in C^{\infty}_{0}(\Omega),$$ where $H_{d}=\int_{\Omega}|\nabla u|^{2}dxdy-\frac{1}{4}\int_{\Omega}\frac{u^{2}}{d(z,\partial\Omega)^{2}}dxdy$ and $d(z,\partial\Omega)=\min\limits_{z_{1}\in\partial\Omega}|z-z_{1}|$.} The main purpose of this paper is to confirm that this conjecture indeed holds for any bounded and convex domain in $\mathbb{R}^{2}$ via the Riemann mapping theorem (the smoothness of the boundary of the domain is thus irrelevant). We also give a rearrangement-free argument for the following Trudinger-Moser inequality on the hyperbolic space $\mathbb{B}=\{z=x+iy:|z|=\sqrt{x^{2}+y^{2}}<1\}$: $$\sup_{\|u\|_{\mathcal{H}}\leq 1} \int_{\mathbb{B}}(e^{4\pi u^{2}}-1-4\pi u^{2})dV=\sup_{\|u\|_{\mathcal{H}}\leq 1}\int_{\mathbb{B}}\frac{(e^{4\pi u^{2}}-1-4\pi u^{2})}{(1-|z|^{2})^{2}}dxdy< \infty,$$ by using the method employed earlier by Lam and the first author [9, 10], where $\mathcal{H}$ denotes the closure of $C^{\infty}_{0}(\mathbb{B})$ with respect to the norm $$\|u\|_{\mathcal{H}}=\int_{\mathbb{B}}|\nabla u|^{2}dxdy-\int_{\mathbb{B}}\frac{u^{2}}{(1-|z|^{2})^{2}}dxdy.$$ Using this strengthened Trudinger-Moser inequality, we also give a simpler proof of the Hardy-Moser-Trudinger inequality obtained by Wang and Ye [22]

Green's functions of Paneitz and GJMS operators on hyperbolic spaces and sharp Hardy-Sobolev-Maz'ya inequalities on half spaces

Using the Fourier analysis techniques on hyperbolic spaces and Green's function estimates, we confirm in this paper the conjecture given by the same authors in [43]. Namely, we prove that the sharp constant in the $\frac{n-1}{2}$-th order Hardy-Sobolev-Maz'ya inequality in the upper half space of dimension $n$ coincides with the best $\frac{n-1}{2}$-th order Sobolev constant when $n$ is odd and $n\geq9$ (See Theorem 1.6). We will also establish a lower bound of the coefficient of the Hardy term for the $k-$th order Hardy-Sobolev-Maz'ya inequality in upper half space in the remaining cases of dimension $n$ and $k$-th order derivatives (see Theorem 1.7). Precise expressions and optimal bounds for Green's functions of the operator $-\Delta_{\mathbb{H}}-\frac{(n-1)^{2}}{4}$ on the hyperbolic space $\mathbb{B}^n$ and operators of the product form are given, where $\frac{(n-1)^{2}}{4}$ is the spectral gap for the Laplacian $-\Delta_{\mathbb{H}}$ on $\mathbb{B}^n$. Finally, we give the precise expression and optimal pointwise bound of Green's function of the Paneitz and GJMS operators on hyperbolic space, which are of their independent interest (see Theorem 1.10).Comment: 33 page