Brown University Center for Statistical Sciences,
Statistics Seminar
University of Florida | |
1st Floor Conference Room 106 |
Abstract: We model (sparse) functional data from many subjects with a regression spline linear mixed model. In this model, the expected values for any subject (conditional on the random effects) can be written as the sum of a population curve and a subject specific deviate from this population curve. The population curve and the subject specific deviates are both modeled as b-splines with k and k0 knots located at tk and tk0, respectively. We sample from the posterior p (k, tk, k0, tk0 |y), where y is the observed data, using reversible jump MCMC methods. Sampling from this posterior distribution is complicated by the fact that no analytical form for p (y|k, tk, k0, tk0) exists. We explore two approximations to this likelihood and study how each approximation penalizes linear mixed models with too many knots. We illustrate the methodology on data from a study examining the relation between depression and the frequency at which luteinising hormone is released into the bloodstream.
This is joint work with Carsten Botts at Williams College.
Brown University
Joint Materials/Solid Mechanics Seminar Series
Mechanical Engineering Department, University of California, Santa Barbara | |
Reversible Adhesives, and Mass/Chemical Sensors | |
Abstract: Many insects and lizards display the amazing ability to climb and stick to just about any surface. Recent research has honed in on these systems to better understand how they work, particularly on how fine sub-micron hairs enhance van der Waals, or other interactions, creating significant amounts of adhesion. To achieve this, nature has created a hierarchal structure to conform over a range of size scale. In this work, we discuss microfabrication techniques used to create a synthetic dry adhesive modeled after the fine hair adhesive motif found in nature. In addition, a new testing technique developed using a nanoindenter to measure adhesion between the structures and a 5 mm aluminum flat punch will be discussed. Preliminary results on the actuation of these multi-scaled structures show significant promise towards chip-compatible biomimetic adhesives.
By understanding thoroughly the dynamics of resonant MEMS, we can not only predict device behavior to eliminate unwanted effects, but also use nonlinear effects to design better sensors and systems. The second half of the talk will center on examples of utilizing and exploiting nonlinear effects to design micro and nano-scale resonant sensors. The design of a nonlinear, parametrically resonant mass/chemical sensor will be discussed in detail and preliminary sensor data and noise analysis will also be discussed.
Cognitive & Linguistic Sciences Colloquium
Center for Fluid Mechanics
And
The Fluids, Thermal And Chemical Processes Group
Of
The Division of Engineering
Seminar Series
Imperial College, London | |
Indicator Of "High" Reynolds Number | |
Abstract: Self-similarity and scale separation, specifically in the form of an overlap region in the mean velocity (e.g. Millikan, 1938) and an inertial subrange (or at least self-similar scaling of the velocity spectra in that wavenumber region) are widely-accepted hypotheses in the study of turbulent flows. In this work we seek to improve the definition of "high Reynolds number", important for extrapolation of scaling results from laboratory conditions, by demonstrating the link between the two in wall-bounded flows: the oft-quoted equivalence of the mean velocity overlap in physical space, or ``inertial sublayer", with the inertial subrange in wavenumber space.
The importance of both the mixing transition, or separation of viscous and turbulent energy-bearing scales (Dimotakis, 2000), and development of self-similar spectral scaling to similarity in physical space is demonstrated using high Reynolds number pipe flow data from the Princeton/ONR Superpipe.
Special PDE Seminar
Brown University
Joint Materials/Solid Mechanics Seminar Series
Abstract: Following the evolutionary arrival of collagen nearly 800 million years ago, fossil evidence demonstrates the rapid proliferation of metazoans. These data imply that something about the physicochemical nature of fibrillar collagen qualifies it as a superlative,adaptable, biocompatible "glue". The primary functional role of fibrillar collagens is to transmit tensile mechanical load. Even in cartilage, which resists compressive load, the type II collagen network constrains the swelling pressure of the resident negatively charged glycosaminoglycans and is thus in constant tension. Fibrillar collagen monomers are secreted by fibroblastic cells and assemble to form fibrils which are incorporated into adaptable, higher-order, load-bearing structures (ligament, tendon, cornea). The adaptability of fibrillar collagen is generally attributed to the fact that it can be polymerized into fibrils which may add collagen monomer both laterally and longitudinally. In addition, collagen monomers may also be removed via cleavage through the action of enzymes (collagenase). Recent investigations into connective tissue adaptation demonstrate that fibroblastic cells respond to mechanical load (mechanotransduction) by paradoxically upregulating both catabolic and anabolic molecule expression. It is proposed here that the cellular response to load is necessary, but not sufficient to produce an organized, load-adapted matrix. In addition to stimulating the cellular response, we propose that mechanical loads must also stabilize collagen that is loaded (or in use) against enzymatic degradation. In support of this hypothesis, we demonstrate the ability to "sculpt" native corneal stroma by mere application of collagenase to a strip of devitalized stroma subjected to a uniaxial load (which puts some fibrils in greater tension than others). Results show the preferential degradation of fibrils which were under lower tension. The implications of this are far reaching and include practical methods to accelerate tissue engineering of load bearing collagenous matrices including the cornea. The implications for our understanding of collagenous matrix embryogenesis, homeostasis, remodeling, repair and pathology are not lost on the author.
Thanksgiving Talk
Applied Mathematics Colloquium
Brown University, Division of Applied Mathematics | |
Look at Each Other | |
ALL WELCOME |
Abstract: Mathematicians complain that media treatments of their subject are scanty. The media complain that mathematicians give them nothing that is comprehensible or arouses interest. My complaint is that media treatments (from papers to novels to movies and plays) go for the sensational and avoid the mathematizations that characterize contemporary life. In any case, to what extent do the media treatments affect the public's conception of mathematics?
PDE Seminar
Department of Mathematics Colloquium
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