On existence of proper solutions of quasilinear second order differential equations

In the paper, the nonlinear differential equation $(a(t)|y^{\prime}|^{p-1}y^{\prime})^{\prime}+b(t)g(y^{\prime})+r(t)f(y)=e(t)$ is studied. Sufficient conditions for the nonexistence of singular solutions of the first and second kind are given. Hence, sufficient conditions for all nontrivial solutions to be proper are derived. Sufficient conditions for the nonexistence of weakly oscillatory solutions are given

On Stochastic Approximations Driven by Sample Averages: Convergence Results via the ODE Method

We consider a class of projected stochastic approximation algorithms drive by sample averages. These algorithms arise naturally in problems of on-line parametric optimization for discrete event dynamical systems., e.g., queueing systems and Petri net models. We develop a general framework for investigating the a.s. convergence of the iterate sequence, and show how such convergence results can be obtained by means of the ordinary differential equation (ODE) method under a condition of exponential convergence. We relate this condition of exponential convergence to certain Large Deviations upper bounds which are uniform in both the parameter q and the initial condition x. To demonstrate the applicability of the results, we specialize them to two specific classes of state processes, namely sequences of i.i.d. random variables and finite state time-homogeneous Markov chains. In both cases, we identify simple (and checkable) conditions that ensure the validity of a uniform Large Deviations upper bound

NASA's Solar Dynamics Observatory (SDO): A Systems Approach to a Complex Mission

The Solar Dynamics Observatory (SDO) includes three advanced instruments, massive science data volume, stringent science data completeness requirements, and a custom ground station to meet mission demands. The strict instrument science requirements imposed a number of challenging drivers on the overall mission system design, leading the SDO team to adopt an integrated systems engineering presence across all aspects of the mission to ensure that mission science requirements would be met. Key strategies were devised to address these system level drivers and mitigate identified threats to mission success. The global systems engineering team approach ensured that key drivers and risk areas were rigorously addressed through all phases of the mission, leading to the successful SDO launch and on-orbit operation. Since launch, SDO's on-orbit performance has met all mission science requirements and enabled groundbreaking science observations, expanding our understanding of the Sun and its dynamic processes

Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Report

This report describes the 2014 study by the Science Definition Team (SDT) of the Wide-Field Infrared Survey Telescope (WFIRST) mission. It is a space observatory that will address the most compelling scientific problems in dark energy, exoplanets and general astrophysics using a 2.4-m telescope with a wide-field infrared instrument and an optical coronagraph. The Astro2010 Decadal Survey recommended a Wide Field Infrared Survey Telescope as its top priority for a new large space mission. As conceived by the decadal survey, WFIRST would carry out a dark energy science program, a microlensing program to determine the demographics of exoplanets, and a general observing program utilizing its ultra wide field. In October 2012, NASA chartered a Science Definition Team (SDT) to produce, in collaboration with the WFIRST Study Office at GSFC and the Program Office at JPL, a Design Reference Mission (DRM) for an implementation of WFIRST using one of the 2.4-m, Hubble-quality telescope assemblies recently made available to NASA. This DRM builds on the work of the earlier WFIRST SDT, reported by Green et al. (2012) and the previous WFIRST-2.4 DRM, reported by Spergel et. (2013). The 2.4-m primary mirror enables a mission with greater sensitivity and higher angular resolution than the 1.3-m and 1.1-m designs considered previously, increasing both the science return of the primary surveys and the capabilities of WFIRST as a Guest Observer facility. The addition of an on-axis coronagraphic instrument to the baseline design enables imaging and spectroscopic studies of planets around nearby stars.Comment: This report describes the 2014 study by the Science Definition Team of the Wide-Field Infrared Survey Telescope mission. 319 pages; corrected a misspelled name in the authors list and a typo in the abstrac

Wide Field Infrared Survey Telescope (WFIRST) Observatory Overview

NASA's Wide Field Infrared Survey Telescope (WFIRST) is being designed to deliver unprecedented capability in dark energy and exoplanet science, and to host a technology demonstration coronagraph for exoplanet imaging and spectroscopy. The observatory design has matured since 2013; we present a comprehensive description of the observatory configuration as refined during the WFIRST Phase-A study. The observatory is based on an existing, repurposed 2.4 meter space telescope coupled with a 288 megapixel near-infrared (0.6 to 2 microns) HgCdTe focal plane array with multiple imaging and spectrographic modes. Together they deliver a 0.28 square degree field of view, which is approximately 100 times larger than the Hubble Space Telescope, and a sensitivity that enables rapid science surveys. In addition, the coronagraph technology demonstration will prove the feasibility of new techniques for exoplanet discovery, imaging, and spectral analysis. A composite truss structure meters both instruments to the telescope assembly, and the instruments and the spacecraft are flight serviceable. We present configuration changes since 2013 that improved interfaces, improved testability, and reduced technical risk. We provide an overview of our Integrated Modeling results, performed at an unprecedented level for a phase-A study, to illustrate performance margins with respect to static wavefront error, jitter, and thermal drift

Une classification des hypothèses calculatoire dans le modèle du groupe algébrique

International audiencea We give a taxonomy of computational assumptions in the algebraic group model (AGM). We first analyze Boyen's Uber assumption family for bilinear groups and then extend it in several ways to cover assumptions as diverse as Gap Diffie-Hellman and LRSW. We show that in the AGM every member of these families is implied by the q-discrete logarithm (DL) assumption, for some q that depends on the degrees of the polynomials defining the Uber assumption. Using the meta-reduction technique, we then separate (q + 1)-DL from q-DL, which yields a classification of all members of the extended Uber-assumption families. We finally show that there are strong assumptions, such as one-more DL, that provably fall outside our classification, by proving that they cannot be reduced from q-DL even in the AGM

A Non-Interactive Shuffle Argument With Low Trust Assumptions

A shuffle argument is a cryptographic primitive for proving correct behaviour of mix-networks without leaking any private information. Several recent constructions of non-interactive shuffle arguments avoid the random oracle model but require the public key to be trusted. We augment the most efficient argument by Fauzi et al. [Asiacrypt 2017] with a distributed key generation protocol that assures soundness of the argument if at least one party in the protocol is honest and additionally provide a key verification algorithm which guarantees zero-knowledge even if all the parties are malicious. Furthermore, we simplify their construction and improve security by using weaker assumptions while retaining roughly the same level of efficiency. We also provide an implementation to the distributed key generation protocol and the shuffle argument

The Multi-Base Discrete Logarithm Problem: Tight Reductions and Non-Rewinding Proofs for Schnorr Identification and Signatures

We introduce the Multi-Base Discrete Logarithm (MBDL) problem. We use this to give reductions, for Schnorr and Okamoto identification and signatures, that are non-rewinding and, by avoiding the notorious square-root loss, tighter than the classical ones from the Discrete Logarithm (DL) problem. This fills a well-known theoretical and practical gap regarding the security of these schemes. We show that not only is the MBDL problem hard in the generic group model, but with a bound that matches that for DL, so that our new reductions justify the security of these primitives for group sizes in actual use

Matrix PRFs: Constructions, Attacks, and Applications to Obfuscation

We initiate a systematic study of pseudorandom functions (PRFs) that are computable by simple matrix branching programs; we refer to these objects as “matrix PRFs”. Matrix PRFs are attractive due to their simplicity, strong connections to complexity theory and group theory, and recent applications in program obfuscation. Our main results are: * We present constructions of matrix PRFs based on the conjectured hardness of some simple computational problems pertaining to matrix products. * We show that any matrix PRF that is computable by a read-c, width w branching program can be broken in time poly(w^c); this means that any matrix PRF based on constant-width matrices must read each input bit omega(log lambda) times. Along the way, we simplify the “tensor switching lemmas” introduced in previous IO attacks. * We show that a subclass of the candidate local-PRG proposed by Barak et al. [Eurocrypt 2018] can be broken using simple matrix algebra. * We show that augmenting the CVW18 IO candidate with a matrix PRF provably immunizes the candidate against all known algebraic and statistical zeroizing attacks, as captured by a new and simple adversarial model

New Techniques for Obfuscating Conjunctions

A conjunction is a function $f(x_1,\dots,x_n) = \bigwedge_{i \in S} l_i$ where $S \subseteq [n]$ and each $l_i$ is $x_i$ or $\neg x_i$. Bishop et al. (CRYPTO 2018) recently proposed obfuscating conjunctions by embedding them in the error positions of a noisy Reed-Solomon codeword and encoding the codeword in a group exponent. They prove distributional virtual black box (VBB) security in the generic group model for random conjunctions where $|S| \geq 0.226n$. While conjunction obfuscation was known from LWE due to Wichs and Zirdelis (FOCS 2017) and Goyal et al. (FOCS 2017), these constructions rely on substantial technical machinery. In this work, we conduct an extensive study of simple conjunction obfuscation techniques. - We abstract the Bishop et al. scheme to obtain an equivalent yet more efficient dual\u27\u27 scheme that can handle conjunctions over exponential size alphabets. This scheme admits a straightforward proof of generic group security, which we combine with a novel combinatorial argument to obtain distributional VBB security for $|S|$ of any size. - If we replace the Reed-Solomon code with a random binary linear code, we can prove security from standard LPN and avoid encoding in a group. This addresses an open problem posed by Bishop et al. to prove security of this simple approach in the standard model. - We give a new construction that achieves information theoretic distributional VBB security and weak functionality preservation for $|S| \geq n - n^\delta$ and $\delta < 1$. Assuming discrete log and $\delta < 1/2$, we satisfy a stronger notion of functionality preservation for computationally bounded adversaries while still achieving information theoretic security