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.

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.

A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.

Systematic review and metasummary of attitudes toward research in emergency medical conditions

Emergency departments are challenging research settings, where truly informed consent can be difficult to obtain. A deeper understanding of emergency medical patients' opinions about research is needed. We conducted a systematic review and meta-summary of quantitative and qualitative studies on which values, attitudes, or beliefs of emergent medical research participants influence research participation. We included studies of adults that investigated opinions toward emergency medicine research participation. We excluded studies focused on the association between demographics or consent document features and participation and those focused on non-emergency research. In August 2011, we searched the following databases: MEDLINE, EMBASE, Google Scholar, Scirus, PsycINFO, AgeLine and Global Health. Titles, abstracts and then full manuscripts were independently evaluated by two reviewers. Disagreements were resolved by consensus and adjudicated by a third author. Studies were evaluated for bias using standardised scores. We report themes associated with participation or refusal. Our initial search produced over 1800 articles. A total of 44 articles were extracted for full-manuscript analysis, and 14 were retained based on our eligibility criteria. Among factors favouring participation, altruism and personal health benefit had the highest frequency. Mistrust of researchers, feeling like a 'guinea pig' and risk were leading factors favouring refusal. Many studies noted limitations of informed consent processes in emergent conditions. We conclude that highlighting the benefits to the participant and society, mitigating risk and increasing public trust may increase research participation in emergency medical research. New methods for conducting informed consent in such studies are needed.

Selected Gamma Aminobutyric Acid (GABA) Esters may Provide Analgesia for Some Central Pain Conditions.

Central pain is an enigmatic, intractable condition, related to destruction of thalamic areas, resulting in likely loss of inhibitory synaptic transmission mediated by GABA. It is proposed that treatment of central pain, a localized process, may be treated by GABA supplementation, like Parkinson's disease and depression. At physiologic pH, GABA exists as a zwitterion that is poorly permeable to the blood brain barrier (BBB). Because the pH of the cerebral spinal fluid (CSF) is acidic relative to the plasma, ion trapping may allow a GABA ester prodrug to accumulate and be hydrolyzed within the CSF. Previous investigations with ester local anesthetics may be applicable to some GABA esters since they are weak bases, hydrolyzed by esterases and cross the BBB. Potential non-toxic GABA esters are discussed. Many GABA esters were investigated in the 1980s and it is hoped that this paper may spark renewed interest in their development.

Long-duration animal tracking in difficult lighting conditions.

High-throughput analysis of animal behavior requires software to analyze videos. Such software typically depends on the experiments' being performed in good lighting conditions, but this ideal is difficult or impossible to achieve for certain classes of experiments. Here, we describe techniques that allow long-duration positional tracking in difficult lighting conditions with strong shadows or recurring "on"/"off" changes in lighting. The latter condition will likely become increasingly common, e.g., for Drosophila due to the advent of red-shifted channel rhodopsins. The techniques enabled tracking with good accuracy in three types of experiments with difficult lighting conditions in our lab. Our technique handling shadows relies on single-animal tracking and on shadows' and flies' being accurately distinguishable by distance to the center of the arena (or a similar geometric rule); the other techniques should be broadly applicable. We implemented the techniques as extensions of the widely-used tracking software Ctrax; however, they are relatively simple, not specific to Drosophila, and could be added to other trackers as well.

Differences in onset and abuse/dependence episodes between prescription opioids and heroin: results from the National Epidemiologic Survey on Alcohol and Related Conditions.

OBJECTIVES: To examine patterns of onset and abuse/dependence episodes of prescription opioid (PO) and heroin use disorders in a national sample of adults, and to explore differences by gender and substance abuse treatment status. METHODS: Analyses of data from the 2001-2002 National Epidemiologic Survey on Alcohol and Related Conditions (N = 43,093). RESULTS: Of all respondents, 5% (n = 1815) reported a history of nonmedical PO use (NMPOU) and 0.3% (n = 150) a history of heroin use. Abuse was more prevalent than dependence among NMPOUs (PO abuse, 29%; dependence, 7%) and heroin users (heroin abuse, 63%; dependence, 28%). Heroin users reported a short mean interval from first use to onset of abuse (1.5 years) or dependence (2.0 years), and a lengthy mean duration for the longest episode of abuse (66 months) or dependence (59 months); the corresponding mean estimates for PO abuse and dependence among NMPOUs were 2.6 and 2.9 years, respectively, and 31 and 49 months, respectively. The mean number of years from first use to remission from the most recent episode was 6.9 years for PO abuse and 8.1 years for dependence; the mean number of years from first heroin use to remission from the most recent episode was 8.5 years for heroin abuse and 9.7 years for dependence. Most individuals with PO or heroin use disorders were remitted from the most recent episode. Treated individuals, whether their problem was heroin or POs, tended to have a longer mean duration of an episode than untreated individuals. CONCLUSION: Periodic remissions from opioid or heroin abuse or dependence episodes occur commonly but take a long time. Timely and effective use of treatment services are needed to mitigate the many adverse consequences from opioid/heroin abuse and dependence.