Stochastic switching in infinite dimensions with applications to random parabolic PDE

© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides

Sensitivity to switching rates in stochastically switched ODEs

We consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices where the individual matrices and the average of the two matrices are all Hurwitz (all eigenvalues have strictly negative real part), but nonetheless the process goes to infinity at large time for certain values of the switching rate. We further construct examples in higher dimensions where again the two individual matrices and their averages are all Hurwitz, but the process has arbitrarily many transitions between going to zero and going to infinity at large time as the switching rate varies. In order to construct these examples, we first prove in general that if each of the individual matrices is Hurwitz, then the process goes to zero at large time for sufficiently slow switching rate and if the average matrix is Hurwitz, then the process goes to zero at large time for sufficiently fast switching rate. We also give simple conditions that ensure the process goes to zero at large time for all switching rates. © 2014 International Press

Keyword-Based Delegable Proofs of Storage

Cloud users (clients) with limited storage capacity at their end can outsource bulk data to the cloud storage server. A client can later access her data by downloading the required data files. However, a large fraction of the data files the client outsources to the server is often archival in nature that the client uses for backup purposes and accesses less frequently. An untrusted server can thus delete some of these archival data files in order to save some space (and allocate the same to other clients) without being detected by the client (data owner). Proofs of storage enable the client to audit her data files uploaded to the server in order to ensure the integrity of those files. In this work, we introduce one type of (selective) proofs of storage that we call keyword-based delegable proofs of storage, where the client wants to audit all her data files containing a specific keyword (e.g., "important"). Moreover, it satisfies the notion of public verifiability where the client can delegate the auditing task to a third-party auditor who audits the set of files corresponding to the keyword on behalf of the client. We formally define the security of a keyword-based delegable proof-of-storage protocol. We construct such a protocol based on an existing proof-of-storage scheme and analyze the security of our protocol. We argue that the techniques we use can be applied atop any existing publicly verifiable proof-of-storage scheme for static data. Finally, we discuss the efficiency of our construction.Comment: A preliminary version of this work has been published in International Conference on Information Security Practice and Experience (ISPEC 2018

On CSP and the Algebraic Theory of Effects

We consider CSP from the point of view of the algebraic theory of effects, which classifies operations as effect constructors or effect deconstructors; it also provides a link with functional programming, being a refinement of Moggi's seminal monadic point of view. There is a natural algebraic theory of the constructors whose free algebra functor is Moggi's monad; we illustrate this by characterising free and initial algebras in terms of two versions of the stable failures model of CSP, one more general than the other. Deconstructors are dealt with as homomorphisms to (possibly non-free) algebras. One can view CSP's action and choice operators as constructors and the rest, such as concealment and concurrency, as deconstructors. Carrying this programme out results in taking deterministic external choice as constructor rather than general external choice. However, binary deconstructors, such as the CSP concurrency operator, provide unresolved difficulties. We conclude by presenting a combination of CSP with Moggi's computational {\lambda}-calculus, in which the operators, including concurrency, are polymorphic. While the paper mainly concerns CSP, it ought to be possible to carry over similar ideas to other process calculi

Diamond Nanowire Transistor with High Current Capability

Carrier confinement in nanowire (NW) structures can offer a host of new material properties compared to bulk electronic devices. Diamond can be considered an ultimate semiconductor given its superlative electronic, physical, and optical properties. However, the development of diamond device technology has been hindered by doping problems in conventional device structures. Here, heavily doped diamond NWs, some 15 nm wide and only 1–2 nm deep overcome these issues and offer a significant advance in NW technology; transistor action can be induced with remote side gates alone, without the need for semiconductor junctions. Quasi-ballistic transport is most-likely responsible for extraordinary current handling capability of the NW transistors fabricated here at some 20 MA cm−2, being around 0.04 G0. This unipolar technology opens up a new paradigm in diamond nanoelectronic device technology

Reduced body weight is a common effect of gene knockout in mice

<p>Abstract</p> <p>Background</p> <p>During a search for obesity candidate genes in a small region of the mouse genome, we noticed that many genes when knocked out influence body weight. To determine whether this was a general feature of gene knockout or a chance occurrence, we surveyed the Jackson Laboratory Mouse Genome Database for knockout mouse strains and their phenotypes. Body weights were not available for all strains so we also obtained body weight information by contacting a random sample of investigators responsible for a knockout strain.</p> <p>Results</p> <p>We classified each knockout mouse strain as (1) lighter and smaller, (2) larger and heavier, or (3) the same weight, relative to control mice. We excluded knockout strains that died early in life, even though this type of lethality is often associated with a small embryo or reduced body size. Based on a dataset of 1,977 knockout strains, we found that that 31% of viable knockout mouse strains weighed less and an additional 3% weighed more than did controls.</p> <p>Conclusion</p> <p>Body weight is potentially a latent variable in about a third of experiments that use knockout mice and should be considered in interpreting experimental outcomes, e.g., in studies of hypertension, drug and hormone metabolism, organ development, cell proliferation and apoptosis, digestion, heart rate, or atherosclerosis. If we assume that the knockout genes we surveyed are representative then upward of 6,000 genes are predicted to influence the size of a mouse. Body weight is highly heritable, and numerous quantitative trait loci have been mapped in mice, but "multigenic" is an insufficient term for the thousands of loci that could contribute to this complex trait.</p

Heart Rhythm Monitoring Strategies for Cryptogenic Stroke: 2015 Diagnostics and Monitoring Stroke Focus Group Report.

No abstract available

Defining care products to finance health care in the Netherlands

A case-mix project started in the Netherlands with the primary goal to define a complete set of health care products for hospitals. The definition of the product structure was completed 4 years later. The results are currently being used for billing purposes. This paper focuses on the methodology and techniques that were developed and applied in order to define the casemix product structure. The central research question was how to develop a manageable product structure, i.e., a limited set of hospital products, with acceptable cost homogeneity. For this purpose, a data warehouse with approximately 1.5 million patient records from 27 hospitals was build up over a period of 3 years. The data associated with each patient consist of a large number of a priori independent parameters describing the resource utilization in different stages of the treatment process, e.g., activities in the operating theatre, the lab and the radiology department. Because of the complexity of the database, it was necessary to apply advanced data analysis techniques. The full analyses process that starts from the database and ends up with a product definition consists of four basic analyses steps. Each of these steps has revealed interesting insights. This paper describes each step in some detail and presents the major results of each step. The result consists of 687 product groups for 24 medical specialties used for billing purposes

Stability of Strong Species Interactions Resist the Synergistic Effects of Local and Global Pollution in Kelp Forests

Foundation species, such as kelp, exert disproportionately strong community effects and persist, in part, by dominating taxa that inhibit their regeneration. Human activities which benefit their competitors, however, may reduce stability of communities, increasing the probability of phase-shifts. We tested whether a foundation species (kelp) would continue to inhibit a key competitor (turf-forming algae) under moderately increased local (nutrient) and near-future forecasted global pollution (CO2). Our results reveal that in the absence of kelp, local and global pollutants combined to cause the greatest cover and mass of turfs, a synergistic response whereby turfs increased more than would be predicted by adding the independent effects of treatments (kelp absence, elevated nutrients, forecasted CO2). The positive effects of nutrient and CO2 enrichment on turfs were, however, inhibited by the presence of kelp, indicating the competitive effect of kelp was stronger than synergistic effects of moderate enrichment of local and global pollutants. Quantification of physicochemical parameters within experimental mesocosms suggests turf inhibition was likely due to an effect of kelp on physical (i.e. shading) rather than chemical conditions. Such results indicate that while forecasted climates may increase the probability of phase-shifts, maintenance of intact populations of foundation species could enable the continued strength of interactions and persistence of communities