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

Propagation of fluctuations in biochemical systems, I: Linear SSC networks

We investigate the propagation of random fluctuations through biochemical networks in which the number of molecules of each species is large enough so that the concentrations are well modeled by differential equations. We study the effect of network topology on the emergent properties of the reaction system by characterizing the behavior of variance as fluctuations propagate down chains and studying the effect of side chains and feedback loops. We also investigate the asymptotic behavior of the system as one reaction becomes fast relative to the others. © 2007 Springer Science+Business Media, Inc

Small inhibitor of Bcl-2, HA14-1, selectively enhanced the apoptotic effect of cisplatin by modulating Bcl-2 family members in MDA-MB-231 breast cancer cells

Inhibition or downregulation of Bcl-2 represents a new therapeutic approach to by-pass chemoresistance in cancer cells. Therefore, we explored the potential of this approach in breast cancer cells. Cisplatin and paclitaxel induced apoptosis in a dose-dependent manner in MCF-7 (drug-sensitive) and MDA-MB-231 (drug-insensitive) cells. Furthermore, when we transiently silenced Bcl-2, both cisplatin and paclitaxel induced apoptosis more than parental cells. Dose dependent induction of apoptosis by drugs was enhanced by the pre-treatment of these cells with HA14-1, a Bcl-2 inhibitor. Although the effect of cisplatin was significant on both cell lines, the effect of paclitaxel was much less potent only in MDA-MB-231 cells. To further understand the distinct role of drugs in MDA-MB-231 cells pretreated with HA14-1, caspases and Bcl-2 family proteins were studied. The apoptotic effect of cisplatin with or without HA14-1 pre-treatment is shown to be caspase-dependent. Among pro-apoptotic Bcl-2 proteins, Bax and Puma were found to be up-regulated whereas Bcl-2 and Bcl-x(L) were down-regulated when cells were pretreated with HA14-1 followed by paclitaxel or cisplatin. Enforced Bcl-2 expression in MDA-MB-231 cells abrogated the sensitizing effect of HA14-1 in cisplatin induced apoptosis. These results suggest that the potentiating effect of HA14-1 is drug and cell type specific and may not only depend on the inhibition of Bcl-2. Importantly, alteration of other pro-apoptotic or anti-apoptotic Bcl-2 family members may dictate the apoptotic response when HA14-1 is combined with chemotherapeutic drugs

Grassmannian flows and applications to nonlinear partial differential equations

We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary matrix Riccati equations can be generated by projecting linear evolutionary flows on a Stiefel manifold onto a coordinate chart of the underlying Grassmann manifold. Our method relies on extending this idea to the infinite dimensional case. The key is an integral equation analogous to the Marchenko equation in integrable systems, that represents the coodinate chart map. We show explicitly how to generate such solutions to scalar partial differential equations of arbitrary order with nonlocal quadratic nonlinearities using our approach. We provide numerical simulations that demonstrate the generation of solutions to Fisher--Kolmogorov--Petrovskii--Piskunov equations with nonlocal nonlinearities. We also indicate how the method might extend to more general classes of nonlinear partial differential systems.Comment: 26 pages, 2 figure

A meta-analytic review of stand-alone interventions to improve body image

Objective Numerous stand-alone interventions to improve body image have been developed. The present review used meta-analysis to estimate the effectiveness of such interventions, and to identify the specific change techniques that lead to improvement in body image. Methods The inclusion criteria were that (a) the intervention was stand-alone (i.e., solely focused on improving body image), (b) a control group was used, (c) participants were randomly assigned to conditions, and (d) at least one pretest and one posttest measure of body image was taken. Effect sizes were meta-analysed and moderator analyses were conducted. A taxonomy of 48 change techniques used in interventions targeted at body image was developed; all interventions were coded using this taxonomy. Results The literature search identified 62 tests of interventions (N = 3,846). Interventions produced a small-to-medium improvement in body image (d+ = 0.38), a small-to-medium reduction in beauty ideal internalisation (d+ = -0.37), and a large reduction in social comparison tendencies (d+ = -0.72). However, the effect size for body image was inflated by bias both within and across studies, and was reliable but of small magnitude once corrections for bias were applied. Effect sizes for the other outcomes were no longer reliable once corrections for bias were applied. Several features of the sample, intervention, and methodology moderated intervention effects. Twelve change techniques were associated with improvements in body image, and three techniques were contra-indicated. Conclusions The findings show that interventions engender only small improvements in body image, and underline the need for large-scale, high-quality trials in this area. The review identifies effective techniques that could be deployed in future interventions

A cross-sectional study of vascular risk factors in a rural South African population : data from the Southern African Stroke Prevention Initiative (SASPI)

Background: Rural sub-Saharan Africa is at an early stage of economic and health transition. It is predicted that the 21st century will see a serious added economic burden from non-communicable disease including vascular disease in low-income countries as they progress through the transition. The stage of vascular disease in a population is thought to result from the prevalence of vascular risk factors. Already hypertension and stroke are common in adults in sub-Saharan Africa. Using a multidisciplinary approach we aimed to assess the prevalence of several vascular risk factors in Agincourt, a rural demographic surveillance site in South Africa. Methods: We performed a cross sectional random sample survey of adults aged over 35 in Agincourt (population ≈ 70 000). Participants were visited at home by a trained nurse who administered a questionnaire, carried out clinical measurements and took a blood sample. From this we assessed participants' history of vascular risk, blood pressure using an OMRON 705 CP monitor, waist circumference, body mass index (BMI), ankle brachial index (ABI), and total and HDL cholesterol. Results: 402 people (24% men) participated. There was a high prevalence of smoking in men, but the number of cigarettes smoked was small. There was a striking difference in mean BMI between men and women (22.8 kg/m2 versus 27.2 kg/m2), but levels of blood pressure were very similar. 43% of participants had a blood pressure greater than 140/90 or were on anti-hypertensive treatment and 37% of participants identified with measured high blood pressure were on pharmacological treatment. 12% of participants had an ABI of < 0.9, sugesting the presence of sub-clinical atheroma. 25.6% of participants had a total cholesterol level > 5 mmol/l. Conclusion: We found a high prevalence of hypertension, obesity in women, and a suggestion of subclinical atheroma despite relatively favourable cholesterol levels in a rural South African population. South Africa is facing the challenge of an emerging epidemic of vascular disease. Research to establish the social determinates of these risk factors and interventions to reduce both individual and population risk are required

A four-helix bundle stores copper for methane oxidation

Methane-oxidising bacteria (methanotrophs) require large quantities of copper for the membrane-bound (particulate) methane monooxygenase (pMMO). Certain methanotrophs are also able to switch to using the iron-containing soluble MMO (sMMO) to catalyse methane oxidation, with this switchover regulated by copper. MMOs are Nature’s primary biological mechanism for suppressing atmospheric levels of methane, a potent greenhouse gas. Furthermore, methanotrophs and MMOs have enormous potential in bioremediation and for biotransformations producing bulk and fine chemicals, and in bioenergy, particularly considering increased methane availability from renewable sources and hydraulic fracturing of shale rock. We have discovered and characterised a novel copper storage protein (Csp1) from the methanotroph Methylosinus trichosporium OB3b that is exported from the cytosol, and stores copper for pMMO. Csp1 is a tetramer of 4-helix bundles with each monomer binding up to 13 Cu(I) ions in a previously unseen manner via mainly Cys residues that point into the core of the bundle. Csp1 is the first example of a protein that stores a metal within an established protein-folding motif. This work provides a detailed insight into how methanotrophs accumulate copper for the oxidation of methane. Understanding this process is essential if the wide-ranging biotechnological applications of methanotrophs are to be realised. Cytosolic homologues of Csp1 are present in diverse bacteria thus challenging the dogma that such organisms do not use copper in this location

A relocatable ocean model in support of environmental emergencies

During the Costa Concordia emergency case, regional, subregional, and relocatable ocean models have been used together with the oil spill model, MEDSLIK-II, to provide ocean currents forecasts, possible oil spill scenarios, and drifters trajectories simulations. The models results together with the evaluation of their performances are presented in this paper. In particular, we focused this work on the implementation of the Interactive Relocatable Nested Ocean Model (IRENOM), based on the Harvard Ocean Prediction System (HOPS), for the Costa Concordia emergency and on its validation using drifters released in the area of the accident. It is shown that thanks to the capability of improving easily and quickly its configuration, the IRENOM results are of greater accuracy than the results achieved using regional or subregional model products. The model topography, and to the initialization procedures, and the horizontal resolution are the key model settings to be configured. Furthermore, the IRENOM currents and the MEDSLIK-II simulated trajectories showed to be sensitive to the spatial resolution of the meteorological fields used, providing higher prediction skills with higher resolution wind forcing.MEDESS4MS Project; TESSA Project; MyOcean2 Projectinfo:eu-repo/semantics/publishedVersio

Formation of Supermassive Black Holes

Evidence shows that massive black holes reside in most local galaxies. Studies have also established a number of relations between the MBH mass and properties of the host galaxy such as bulge mass and velocity dispersion. These results suggest that central MBHs, while much less massive than the host (~ 0.1%), are linked to the evolution of galactic structure. In hierarchical cosmologies, a single big galaxy today can be traced back to the stage when it was split up in hundreds of smaller components. Did MBH seeds form with the same efficiency in small proto-galaxies, or did their formation had to await the buildup of substantial galaxies with deeper potential wells? I briefly review here some of the physical processes that are conducive to the evolution of the massive black hole population. I will discuss black hole formation processes for `seed' black holes that are likely to place at early cosmic epochs, and possible observational tests of these scenarios.Comment: To appear in The Astronomy and Astrophysics Review. The final publication is available at http://www.springerlink.co