On Probability of Support Recovery for Orthogonal Matching Pursuit Using Mutual Coherence

In this paper we present a new coherence-based performance guarantee for the Orthogonal Matching Pursuit (OMP) algorithm. A lower bound for the probability of correctly identifying the support of a sparse signal with additive white Gaussian noise is derived. Compared to previous work, the new bound takes into account the signal parameters such as dynamic range, noise variance, and sparsity. Numerical simulations show significant improvements over previous work and a closer match to empirically obtained results of the OMP algorithm.Comment: Submitted to IEEE Signal Processing Letters. arXiv admin note: substantial text overlap with arXiv:1608.0038

Well-posedness of Wasserstein Gradient Flow Solutions of Higher Order Evolution Equations

A relaxed notion of displacement convexity is defined and used to establish short time existence and uniqueness of Wasserstein gradient flows for higher order energy functionals. As an application, local and global well-posedness of different higher order non-linear evolution equations are derived. Examples include the thin-film equation and the quantum drift diffusion equation in one spatial variable

Shedding light on new Wess-Zumino couplings with their corrections to all orders in alpha-prime

Motivated by arXiv:1203.5553, we continue to match super string amplitudes with their own effective field theory. We carry out within full details the computations of the complete form of the amplitude of one closed string Ramond-Ramond field and three SYM vertex operators, namely one gauge field and two scalar fields in type IIB(A) super string theories. Making use of the recent two gauge and two scalar couplings to all orders of $\alpha'$, we produce all the infinite gauge poles for $p=n$ case (with $n$ as RR field strength's rank and $p$ as the dimension of a D$_p$-brane). Proceeding with direct and full S-Matrix calculations, we are able to produce even all the infinite gauge poles in u-channel for $p-2=n$ case in field theory as well. New couplings for $p-2=n$ case with their all order $\alpha'$ corrections are discovered. In addition, we explain how to find out all the infinite scalar poles of this amplitude in $s,t$-channels and produce them for $p+2=n$ case. By comparing all of the contact terms of this amplitude, we obtain several new couplings with their higher derivative corrections for $p+2=n,p=n$ cases. These new couplings are neither inside Myers'terms nor within pull-back/Taylor expansions. Finally we comment on some related issues.Comment: 38 pages, No figure, the version that appears in JHEP and a minor correction, CERN-PH-TH/2012-34

More on Ramond-Ramond, SYM, WZ couplings and their corrections in IIA

We obtain the closed form of the correlation function of one current and four spin operators (with different chiralities ) in type IIA superstring theory. The complete form of the S-matrix of one gauge , two fermions (with different chiralities) and one closed string Ramond-Ramond for all order $\alpha'$ type IIA has been explored. Moreover, we make use of a different gauge fixing to be able to find out all the closed forms of correlators. An infinite number of $t,s-$channel fermion poles of this S-matrix in the field theory of IIA is generated. Unlike the the closed form of the correlators of the same amplitude of IIB, for various $p,n$ cases in type IIA we do have different double poles in $t,(t+s+u)$ and in $s,(t+s+u)$ channels and we produced them. We also find new Wess-Zumino couplings of IIA with their third order $\alpha' $ corrections as well as a new form of higher derivative corrections (with different coefficient from its IIB one ) to SYM couplings at third order of $\alpha' $. Using them, we are able to produce a $(t+s+u)$ channel scalar pole of the amplitude for $p+2=n$ case. Finally we make some comments on $\alpha'$ corrections to IIA Superstring theory.Comment: 28 pages, no figure,Latex file and published version in EPJ

On Non-BPS Effective Actions of String Theory

We discuss some physical prospective of the non-BPS effective actions of type IIA and IIB superstring theories. By dealing with the complete all three and four point functions, including a closed string Ramond-Ramond (in terms of both its field strength and its potential), gauge (scalar) fields as well as a real tachyon and under symmetry structures, we find various restricted world volume and bulk Bianchi identities. The complete forms of the non-BPS scattering amplitudes including their Chan-Paton factors are elaborated. All the singularity structures of the non-BPS amplitudes, their all orders $\alpha'$ higher derivative corrections, their contact terms and various modified Bianchi identities are derived. Finally we show that scattering amplitudes computed in different super-ghost pictures are compatible when suitable Bianchi identities are imposed on the Ramond-Ramond fields. Moreover, we argue that the higher derivative expansion in powers of the momenta of the tachyon is universal.Comment: This paper is about D-brane effective actions and is dedicated to the memory of Joe Polchinski, the D-brane master, whom I learnt alot about string theory effective actions. V2 accepted in EPJ

Closed string Ramond-Ramond proposed higher derivative interactions on fermionic amplitudes in IIB

The complete form of the amplitude of one closed string Ramond-Ramond (RR), two fermionic strings and one scalar field in IIB superstring theory has been computed in detail. Deriving $$ by using suitable gauge fixing, we discover some new vertices and their higher derivative corrections. We investigate both infinite gauge and scalar $u-$channel poles of this amplitude. In particular, by using the fact that the kinetic term of fermion fields has no correction, employing Born-Infeld action, the Wess-Zumino terms and their higher derivative corrections, we discover all infinite $t,s-$channel fermion poles. The couplings between one RR and two fermions and all their infinite higher derivative corrections have been explored. In order to look for all infinite $(s+t+u)-$ channel scalar/gauge poles for $p+2=n,p=n$ cases, we obtain the couplings between two fermions-two scalars and two fermions, one scalar and one gauge field as well as all their infinite higher derivative corrections in type IIB. Specifically we make various comments based on arXiv:1205.5079 in favor of universality conjecture for all order higher derivative corrections (with or without low energy expansion) and the relation of open/closed string that is responsible for all superstring scattering amplitudes in IIA,IIB.Comment: 29 pages, figures are removed. Sections 3,4, and 5 are shortened. To appear in NP

Insights from Asteroseismology of Massive Stars: The Need for Additional Angular Momentum Transport Mechanisms

In massive stars, rotation and oscillatory waves can have a tight interplay. In order to assess the importance of additional angular momentum transport mechanisms other than rotation, we compare the asteroseismic properties of a uniformly rotating model and a differentially rotating one. Accordingly, we employ the observed period spacing of 36 dipole g-modes in the Kepler $\sim3.2$ M$_\odot$ target KIC 7760680 to discriminate between these two models. We favor the uniformly rotating model, which fully satisfies all observational constraints. Therefore, efficient angular momentum transport by additional mechanisms such as internal gravity waves, heat-driven modes and magnetic field is needed during early main sequence evolution of massive stars.Comment: Proceedings of "Seismology of the Sun and the Distant Stars 2016". Editors: M\'ario J. P. F. G. Monteiro, Margarida S. Cunha, Jo\~ao Miguel T. Ferreir