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.

Towards a field-compatible optical spectroscopic device for cervical cancer screening in resource-limited settings: effects of calibration and pressure.

Quantitative optical spectroscopy has the potential to provide an effective low cost, and portable solution for cervical pre-cancer screening in resource-limited communities. However, clinical studies to validate the use of this technology in resource-limited settings require low power consumption and good quality control that is minimally influenced by the operator or variable environmental conditions in the field. The goal of this study was to evaluate the effects of two sources of potential error: calibration and pressure on the extraction of absorption and scattering properties of normal cervical tissues in a resource-limited setting in Leogane, Haiti. Our results show that self-calibrated measurements improved scattering measurements through real-time correction of system drift, in addition to minimizing the time required for post-calibration. Variations in pressure (tested without the potential confounding effects of calibration error) caused local changes in vasculature and scatterer density that significantly impacted the tissue absorption and scattering properties Future spectroscopic systems intended for clinical use, particularly where operator training is not viable and environmental conditions unpredictable, should incorporate a real-time self-calibration channel and collect diffuse reflectance spectra at a consistent pressure to maximize data integrity.

Evolution of networks and sequences in eukaryotic cell cycle control.

The molecular networks regulating the G1-S transition in budding yeast and mammals are strikingly similar in network structure. However, many of the individual proteins performing similar network roles appear to have unrelated amino acid sequences, suggesting either extremely rapid sequence evolution, or true polyphyly of proteins carrying out identical network roles. A yeast/mammal comparison suggests that network topology, and its associated dynamic properties, rather than regulatory proteins themselves may be the most important elements conserved through evolution. However, recent deep phylogenetic studies show that fungal and animal lineages are relatively closely related in the opisthokont branch of eukaryotes. The presence in plants of cell cycle regulators such as Rb, E2F and cyclins A and D, that appear lost in yeast, suggests cell cycle control in the last common ancestor of the eukaryotes was implemented with this set of regulatory proteins. Forward genetics in non-opisthokonts, such as plants or their green algal relatives, will provide direct information on cell cycle control in these organisms, and may elucidate the potentially more complex cell cycle control network of the last common eukaryotic ancestor.

Memory in posttraumatic stress disorder: properties of voluntary and involuntary, traumatic and nontraumatic autobiographical memories in people with and without posttraumatic stress disorder symptoms.

One hundred fifteen undergraduates rated 15 word-cued memories and their 3 most negatively stressful, 3 most positive, and 7 most important events and completed tests of personality and depression. Eighty-nine also recorded involuntary memories online for 1 week. In the first 3-way comparisons needed to test existing theories, comparisons were made of memories of stressful events versus control events and involuntary versus voluntary memories in people high versus low in posttraumatic stress disorder (PTSD) symptom severity. For all participants, stressful memories had more emotional intensity, more frequent voluntary and involuntary retrieval, but not more fragmentation. For all memories, participants with greater PTSD symptom severity showed the same differences. Involuntary memories had more emotional intensity and less centrality to the life story than voluntary memories. Meeting the diagnostic criteria for traumatic events had no effect, but the emotional responses to events did. In 533 undergraduates, correlations among measures were replicated and the Negative Intensity factor of the Affect Intensity Measure correlated with PTSD symptom severity. No special trauma mechanisms were needed to account for the results, which are summarized by the autobiographical memory theory of PTSD.