On the variational structure of breather solutions

In this paper we give a systematic and simple account that put in evidence that many breather solutions of integrable equations satisfy suitable variational elliptic equations, which also implies that the stability problem reduces in some sense to $(i)$ the study of the spectrum of explicit linear systems (\emph{spectral stability}), and $(ii)$ the understanding of how bad directions (if any) can be controlled using low regularity conservation laws. We exemplify this idea in the case of the modified Korteweg-de Vries (mKdV), Gardner, and sine-Gordon (SG) equations. Then we perform numerical simulations that confirm, at the level of the spectral problem, our previous rigorous results, where we showed that mKdV breathers are $H^2$ and $H^1$ stable, respectively. In a second step, we also discuss the Gardner and the Sine-Gordon cases, where the spectral study of a fourth-order linear matrix system is the key element to show stability. Using numerical methods, we confirm that all spectral assumptions leading to the $H^2\times H^1$ stability of SG breathers are numerically satisfied, even in the ultra-relativistic, singular regime. In a second part, we study the periodic mKdV case, where a periodic breather is known from the work of Kevrekidis et al. We rigorously show that these breathers satisfy a suitable elliptic equation, and we also show numerical spectral stability. However, we also identify the source of nonlinear instability in the case described in Kevrekidis et al. Finally, we present a new class of breather solution for mKdV, believed to exist from geometric considerations, and which is periodic in time and space, but has nonzero mean, unlike standard breathers.Comment: 55 pages; This paper is an improved version of our previous paper 1309.0625 and hence we replace i

On the nonlinear stability of mKdV breathers

A mathematical proof for the stability of mKdV breathers is announced. This proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.Comment: 7 p

Bound non-locality and activation

We investigate non-locality distillation using measures of non-locality based on the Elitzur-Popescu-Rohrlich decomposition. For a certain number of copies of a given non-local correlation, we define two quantities of interest: (i) the non-local cost, and (ii) the distillable non-locality. We find that there exist correlations whose distillable non-locality is strictly smaller than their non-local cost. Thus non-locality displays a form of irreversibility which we term bound non-locality. Finally we show that non-local distillability can be activated.Comment: 4 pages, 1 figur

Bell inequalities from multilinear contractions

We provide a framework for Bell inequalities which is based on multilinear contractions. The derivation of the inequalities allows for an intuitive geometric depiction and their violation within quantum mechanics can be seen as a direct consequence of non-vanishing commutators. The approach is motivated by generalizing recent work on non-linear inequalities which was based on the moduli of complex numbers, quaternions and octonions. We extend results on Peres conjecture about the validity of Bell inequalities for quantum states with positive partial transposes. Moreover, we show the possibility of obtaining unbounded quantum violations albeit we also prove that quantum mechanics can only violate the derived inequalities if three or more parties are involved.Comment: Published versio

Collective Coordinates Theory for Discrete Soliton Ratchets in the sine-Gordon Model

A collective coordinate theory is develop for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as an approximated solution of the discrete non-linear equation. The evolution of these two collective coordinates, obtained by means of the Generalized Travelling Wave Method, explains the mechanism underlying the soliton ratchet and captures qualitatively all the main features of this phenomenon. The theory accounts for the existence of a non-zero depinning threshold, the non-sinusoidal behaviour of the average velocity as a function of the difference phase between the harmonics of the driver, the non-monotonic dependence of the average velocity on the damping and the existence of non-transporting regimes beyond the depinning threshold. In particular it provides a good description of the intriguing and complex pattern of subspaces corresponding to different dynamical regimes in parameter space

Comparative biochemical and functional analysis of viral and human secreted tumor necrosis factor (TNF) decoy receptors

© 2015 by The American Society for Biochemistry and Molecular Biology, Inc. The blockade of tumor necrosis factor (TNF) by etanercept, a soluble version of the human TNF receptor 2 (hTNFR2), is a well established strategy to inhibit adverse TNF-mediated inflammatory responses in the clinic. A similar strategy is employed by poxviruses, encoding four viral TNF decoy receptor homologues (vTNFRs) named cytokine response modifier B (CrmB), CrmC, CrmD, and CrmE. These vTNFRs are differentially expressed by poxviral species, suggesting distinct immunomodulatory properties. Whereas the human variola virus and mouse ectromelia virus encode one vTNFR, the broad host range cowpox virus encodes all vTNFRs. We report the first comprehensive study of the functional and binding properties of these four vTNFRs, providing an explanation for their expression profile among different poxviruses. In addition, the vTNFRs activities were compared with the hTNFR2 used in the clinic. Interestingly, CrmB from variola virus, the causative agent of smallpox, is the most potent TNFR of those tested here including hTNFR2. Furthermore, we demonstrate a new immunomodulatory activity of vTNFRs, showing that CrmB and CrmD also inhibit the activity of lymphotoxin β. Similarly, we report for the first time that the hTNFR2 blocks the biological activity of lymphotoxin β. The characterization of vTNFRs optimized during virus-host evolution to modulate the host immune response provides relevant information about their potential role in pathogenesis and may be used to improve anti-inflammatory therapies based on soluble decoy TNFRs.Ministry of Economy and Competitiveness Grants SAF2009-07857 and SAF2012-38957Peer Reviewe

Poxvirus-encoded TNF decoy receptors inhibit the biological activity of transmembrane TNF

© 2015 The Authors. Poxviruses encode up to four different soluble TNF receptors, named cytokine response modifier B (CrmB), CrmC, CrmD and CrmE. These proteins mimic the extracellular domain of the cellular TNF receptors to bind and inhibit the activity of TNF and, in some cases, other TNF superfamily ligands. Most of these ligands are released after the enzymic cleavage of a membrane precursor. However, transmembrane TNF (tmTNF) is not only a precursor of soluble TNF but also exerts specific pro-inflammatory and immunological activities. Here, we report that viral TNF receptors bound and inhibited tmTNF and describe some interesting differences in their activity against the soluble cytokine. Thus, CrmE, which does not inhibit mouse soluble TNF, could block murine tmTNF-induced cytotoxicity. We propose that this anti-tmTNF effect should be taken into consideration when assessing the role of viral TNF decoy receptors in the pathogenesis of poxvirus.Ministry of Economy and Competitiveness Grants SAF2009-07857 and SAF2012-38957.S. M. P. was recipient of a JAE PhD Studentship from Consejo Superior de Investigaciones Científicas and a studentship from Fundación Severo OchoaPeer Reviewe

Review on the Stability of the Peregrine and Related Breathers

In this note, we review stability properties in energy spaces of three important nonlinear Schrödinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev. More precisely, we show that these breathers are unstable according to a standard definition of stability. Suitable Lyapunov functionals are described, as well as their underlying spectral properties. As an immediate consequence of the first variation of these functionals, we also present the corresponding nonlinear ODEs fulfilled by these nonlinear Schrödinger breathers. The notion of global stability for each breather mentioned above is finally discussed. Some open questions are also briefly mentioned

The Akhmediev breather is unstable

In this note, we give a rigorous proof that the NLS periodic Akhmediev breather is unstable. The proof follows the ideas in Muñoz (Proyecciones (Antofagasta) 36(4):653–683, 2017), in the sense that a suitable modification of the Stokes wave is the global attractor of the local Akhmediev dynamics for sufficiently large time, and therefore the latter cannot be stable in any suitable finite energy periodic Sobolev space

Scalability of GHZ and random-state entanglement in the presence of decoherence

We derive analytical upper bounds for the entanglement of generalized Greenberger-Horne-Zeilinger states coupled to locally depolarizing and dephasing environments, and for local thermal baths of arbitrary temperature. These bounds apply for any convex quantifier of entanglement, and exponential entanglement decay with the number of constituent particles is found. The bounds are tight for depolarizing and dephasing channels. We also show that randomly generated initial states tend to violate these bounds, and that this discrepancy grows with the number of particles.Comment: 9 pages, 3 figure