Local asymptotics for controlled martingales

We consider controlled martingales with bounded steps where the controller is allowed at each step to choose the distribution of the next step, and where the goal is to hit a fixed ball at the origin at time $n$. We show that the algebraic rate of decay (as $n$ increases to infinity) of the value function in the discrete setup coincides with its continuous counterpart, provided a reachability assumption is satisfied. We also study in some detail the uniformly elliptic case and obtain explicit bounds on the rate of decay. This generalizes and improves upon several recent studies of the one dimensional case, and is a discrete analogue of a stochastic control problem recently investigated in Armstrong and Trokhimtchouck [Calc. Var. Partial Differential Equations 38 (2010) 521-540].Comment: Published at http://dx.doi.org/10.1214/15-AAP1123 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

HardScope: Thwarting DOP with Hardware-assisted Run-time Scope Enforcement

Widespread use of memory unsafe programming languages (e.g., C and C++) leaves many systems vulnerable to memory corruption attacks. A variety of defenses have been proposed to mitigate attacks that exploit memory errors to hijack the control flow of the code at run-time, e.g., (fine-grained) randomization or Control Flow Integrity. However, recent work on data-oriented programming (DOP) demonstrated highly expressive (Turing-complete) attacks, even in the presence of these state-of-the-art defenses. Although multiple real-world DOP attacks have been demonstrated, no efficient defenses are yet available. We propose run-time scope enforcement (RSE), a novel approach designed to efficiently mitigate all currently known DOP attacks by enforcing compile-time memory safety constraints (e.g., variable visibility rules) at run-time. We present HardScope, a proof-of-concept implementation of hardware-assisted RSE for the new RISC-V open instruction set architecture. We discuss our systematic empirical evaluation of HardScope which demonstrates that it can mitigate all currently known DOP attacks, and has a real-world performance overhead of 3.2% in embedded benchmarks

Remarks on a constrained optimization problem for the Ginibre ensemble

We study the limiting distribution of the eigenvalues of the Ginibre ensemble conditioned on the event that a certain proportion lie in a given region of the complex plane. Using an equivalent formulation as an obstacle problem, we describe the optimal distribution and some of its monotonicity properties

LO-FAT: Low-Overhead Control Flow ATtestation in Hardware

Attacks targeting software on embedded systems are becoming increasingly prevalent. Remote attestation is a mechanism that allows establishing trust in embedded devices. However, existing attestation schemes are either static and cannot detect control-flow attacks, or require instrumentation of software incurring high performance overheads. To overcome these limitations, we present LO-FAT, the first practical hardware-based approach to control-flow attestation. By leveraging existing processor hardware features and commonly-used IP blocks, our approach enables efficient control-flow attestation without requiring software instrumentation. We show that our proof-of-concept implementation based on a RISC-V SoC incurs no processor stalls and requires reasonable area overhead.Comment: Authors' pre-print version to appear in DAC 2017 proceeding

Quenched invariance principle for random walks in balanced random environment

We consider random walks in a balanced random environment in $\mathbb{Z}^d$, $d\geq 2$. We first prove an invariance principle (for $d\ge2$) and the transience of the random walks when $d\ge 3$ (recurrence when $d=2$) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments.Comment: Published online in Probab. Theory Relat. Fields, 05 Oct 2010. Typo (in journal version) corrected in (26

What is the correct cost functional for variational data assimilation?

Variational approaches to data assimilation, and weakly constrained four dimensional variation (WC-4DVar) in particular, are important in the geosciences but also in other communities (often under different names). The cost functions and the resulting optimal trajectories may have a probabilistic interpretation, for instance by linking data assimilation with maximum aposteriori (MAP) estimation. This is possible in particular if the unknown trajectory is modelled as the solution of a stochastic differential equation (SDE), as is increasingly the case in weather forecasting and climate modelling. In this situation, the MAP estimator (or “most probable path” of the SDE) is obtained by minimising the Onsager–Machlup functional. Although this fact is well known, there seems to be some confusion in the literature, with the energy (or “least squares”) functional sometimes been claimed to yield the most probable path. The first aim of this paper is to address this confusion and show that the energy functional does not, in general, provide the most probable path. The second aim is to discuss the implications in practice. Although the mentioned results pertain to stochastic models in continuous time, they do have consequences in practice where SDE’s are approximated by discrete time schemes. It turns out that using an approximation to the SDE and calculating its most probable path does not necessarily yield a good approximation to the most probable path of the SDE proper. This suggest that even in discrete time, a version of the Onsager–Machlup functional should be used, rather than the energy functional, at least if the solution is to be interpreted as a MAP estimator

Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher

We consider large deviations for nearest-neighbor random walk in a uniformly elliptic i.i.d. environment. It is easy to see that the quenched and the averaged rate functions are not identically equal. When the dimension is at least four and Sznitman's transience condition (T) is satisfied, we prove that these rate functions are finite and equal on a closed set whose interior contains every nonzero velocity at which the rate functions vanish.Comment: 17 pages. Minor revision. In particular, note the change in the title of the paper. To appear in Probability Theory and Related Fields

Alternative proof for the localization of Sinai's walk

We give an alternative proof of the localization of Sinai's random walk in random environment under weaker hypothesis than the ones used by Sinai. Moreover we give estimates that are stronger than the one of Sinai on the localization neighborhood and on the probability for the random walk to stay inside this neighborhood

One-component plasma on a spherical annulus and a random matrix ensemble

The two-dimensional one-component plasma at the special coupling \beta = 2 is known to be exactly solvable, for its free energy and all of its correlations, on a variety of surfaces and with various boundary conditions. Here we study this system confined to a spherical annulus with soft wall boundary conditions, paying special attention to the resulting asymptotic forms from the viewpoint of expected general properties of the two-dimensional plasma. Our study is motivated by the realization of the Boltzmann factor for the plasma system with \beta = 2, after stereographic projection from the sphere to the complex plane, by a certain random matrix ensemble constructed out of complex Gaussian and Haar distributed unitary matrices.Comment: v2, typos and references corrected, 24 pages, 1 figur

A Mighty Small Heart: The Cardiac Proteome of Adult Drosophila melanogaster

Drosophila melanogaster is emerging as a powerful model system for the study of cardiac disease. Establishing peptide and protein maps of the Drosophila heart is central to implementation of protein network studies that will allow us to assess the hallmarks of Drosophila heart pathogenesis and gauge the degree of conservation with human disease mechanisms on a systems level. Using a gel-LC-MS/MS approach, we identified 1228 protein clusters from 145 dissected adult fly hearts. Contractile, cytostructural and mitochondrial proteins were most abundant consistent with electron micrographs of the Drosophila cardiac tube. Functional/Ontological enrichment analysis further showed that proteins involved in glycolysis, Ca2+-binding, redox, and G-protein signaling, among other processes, are also over-represented. Comparison with a mouse heart proteome revealed conservation at the level of molecular function, biological processes and cellular components. The subsisting peptidome encompassed 5169 distinct heart-associated peptides, of which 1293 (25%) had not been identified in a recent Drosophila peptide compendium. PeptideClassifier analysis was further used to map peptides to specific gene-models. 1872 peptides provide valuable information about protein isoform groups whereas a further 3112 uniquely identify specific protein isoforms and may be used as a heart-associated peptide resource for quantitative proteomic approaches based on multiple-reaction monitoring. In summary, identification of excitation-contraction protein landmarks, orthologues of proteins associated with cardiovascular defects, and conservation of protein ontologies, provides testimony to the heart-like character of the Drosophila cardiac tube and to the utility of proteomics as a complement to the power of genetics in this growing model of human heart disease