Finite and infinite soliton and kink-soliton trains of nonlinear Schrödinger equations

International audienceWe will first review known results on multi-solitons of dispersive partial differential equations, which are special solutions behaving like the sum of many weakly-interacting solitary waves. We will then describe our recent joint work with Dong Li on nonlinear Schrödinger equations: Assuming the composing solitons have sufficiently large relative speeds, we prove the existence and uniqueness of a soliton train which is a multi-soliton composed of infinitely many solitons. In the 1D case, we can add to the infinite train an additional half-kink, which is a solution with a non-zero background at minus infinity

Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations

International audienceWe look for solutions to generic nonlinear Schrödinger equations build upon solitons and kinks. Solitons are localized solitary waves and kinks are their non localized counter-parts. We prove the existence of infinite soliton trains, i.e. solutions behaving at large time as the sum of infinitely many solitons. We also show that one can attach a kink at one end of the train. Our proofs proceed by fixed point arguments around the desired profile. We present two approaches leading to different results, one based on a combination of dispersive estimates and Strichartz estimates, the other based only on Strichartz estimates

Fast-moving finite and infinite trains of solitons for nonlinear Schrödinger equations

International audienceWe study *infinite soliton trains* solutions of nonlinear Schrödinger equations (NLS), i.e. solutions behaving at large time as the sum of infinitely many solitary waves. Assuming the composing solitons have sufficiently large relative speeds, we prove the existence and uniqueness of such a soliton train. We also give a new construction of multi-solitons (i.e. finite trains) and prove uniqueness in an exponentially small neighborhood, and we consider the case of solutions composed of several solitons and kinks (i.e. solutions with a non-zero background at infinity)

Stability of periodic waves of 1D cubic nonlinear Schrödinger equations

International audienceWe study the stability of the cnoidal, dnoidal and snoidal elliptic functions as spatially-periodic standing wave solutions of the 1D cubic nonlinear Schrödinger equations. First, we give global variational characterizations of each of these periodic waves, which in particular provide alternate proofs of their orbital stability with respect to same-period perturbations, restricted to certain subspaces. Second, we prove the spectral stability of the cnoidal waves against same-period perturbations (in a certain parameter range), and provide an alternate proof of this (known) fact for the snoidal waves, which does not rely on complete integrability. Third, we give a rigorous version of a formal asymptotic calculation of Rowlands to establish the instability of a class of real-valued periodic waves in 1D, which includes the cnoidal waves of the 1D cubic focusing nonlinear Schrödinger equation, against perturbations with period a large multiple of their fundamental period. Finally, we develop a numerical method to compute the minimizers of the energy with fixed mass and momentum constraints. Numerical experiments support and complete our analytical results

Non-Disclosing Credential On-chaining for Blockchain-based Decentralized Applications

Many service systems rely on verifiable identity-related information of their users. Manipulation and unwanted exposure of this privacy-relevant information, however, must at the same time be prevented and avoided. Peer-to-peer blockchain-based decentralization with a smart contract-based execution model and verifiable off-chain computations leveraging zero-knowledge proofs promise to provide the basis for next-generation, non-disclosing credential management solutions. In this paper, we propose a novel credential on-chaining system that ensures blockchain-based transparency while preserving pseudonymity. We present a general model compliant to the W3C verifiable credential recommendation and demonstrate how it can be applied to solve existing problems that require computational identity-related attribute verification. Our zkSNARKs-based reference implementation and evaluation show that, compared to related approaches based on, e.g., CL-signatures, our approach provides significant performance advantages and more flexible proof mechanisms, underpinning our vision of increasingly decentralized, transparent, and trustworthy service systems

Economics of neuraminidase inhibitor stock piling for pandemic influenza, Singapore.

We compared strategies for stock piling neuraminidase inhibitors to treat and prevent influenza in Singapore. Cost-benefit and cost-effectiveness analyses, with Monte Carlo simulations, were used to determine economic outcomes. A pandemic in a population of 4.2 million would result in an estimated 525-1,775 deaths, 10,700-38,600 hospitalization days, and economic costs of 0.7 dollars to 2.2 billion Singapore dollars. The treatment-only strategy had optimal economic benefits: stock piles of antiviral agents for 40% of the population would save an estimated 418 lives and 414 million dollars, at a cost of 52.6 million dollars per shelf-life cycle of the stock pile. Prophylaxis was economically beneficial in high-risk subpopulations, which account for 78% of deaths, and in pandemics in which the death rate was >0.6%. Prophylaxis for pandemics with a 5% case-fatality rate would save 50,000 lives and 81 billion dollars. These models can help policymakers weigh the options for pandemic planning

10301 Executive Summary and Abstracts Collection -- Service Value Networks

From 25.07.2010 to 30.07.2010, the Perspectives Workshop 10301 ``Perspectives Workshop: Service Value Networks \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available