Lefschetz Center for Dynamical Systems Seminar
Abstract: We consider two special reducible cases for the Volterra and the Levin-Nohel retarded equations with infinite delay. We address global questions like the existence of Liapunov functions and, consequently, of attractors for the nonlinear systems generated by these equations as well as the attractors for the reduced systems. Some Morse-Smale structures of these two reducible equations are also identified.
Brown University
Center for Statistical Sciences
2007 Lectureship Series
Biostatistics in the Post-genomic Era:
Statistical Methodology & Applications in Bioinformatics
Department of Biostatistics, Harvard School of Public Health, Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute | |
Refreshments beginning at 3:15 p.m. |
Abstract: Loss of heterozygosity (LOH) and copy number changes of chromosomal regions bearing tumor suppressor genes or oncogenes are key events in the evolution of cancer cells. Identification of such regions in each sample accurately, and summarizing across multiple samples can suggest cancer-related genes for further experiments. Oligonucleotide SNP microarrays now have up to 500,000 SNP markers that can provide genotypes and signal values simultaneously. I will describe analysis methods for using such arrays for the identification of LOH events without comparison to normal controls. I will also discuss allelic-imbalance analysis as an extension of LOH analysis.
Sponsored by: The Charles K. Colver Lectureship and Publication Fund
Center for Fluid Mechanics
And
The Fluids, Thermal, And Chemical Processes Group
Of
The Division Of Engineering
Seminar Series
Department of Mechanical Engineering, University of Delaware, Newark DE 19716 | |
Multiphase Flows in Medicine and Biology | |
Abstract: In this talk we will report our recent investigation of two biomedical particulate flows. The first one concerns micron-size gas bubbles that are intravenously injected into patients' body to improve the contrast of ultrasound blood flow images. These bubbles are encapsulated by a thin layer (~4-10nm) of protein, lipids and other surface active materials to prevent their premature dissolution in the blood. Destruction of microbubble agents by strong ultrasound pulses are being used in real time blood flow velocity measurement, stimulating arteriogenesis (generation of new arteries) and targeted drug delivery. The encapsulation critically affects the performance of these agents in all applications. We have developed an interface model of the encapsulation that has an intrinsic surface rheology with surface viscosity and elasticity. In this talk, I will describe our approach that includes determination of rheological properties using one set of in vitro experiment, and then model validation using another set. Data on several contrast agents such as Sonazoid (Amersham Health, Oslo, Norway), Optison (GE Health Care, Princeton, NJ), Definity (Bristol Myers Squibb, N. Billerica, MA) will be presented. I will also present a model for the dissolution of microbubbles that accounts for the effects of encapsulation: the encapsulation hinders the permeability of the gas-liquid surface and its elasticity balances the surface tension induced stress.
In the second part of the talk, I will discuss our computational approach to modeling deformation, motion and adhesion of drops, cells or capsules. The adhesion of cells to substrates is a critical step in many biological events. Previous studies idealized leukocytes as a microvilli-coated hard sphere covered with adhesion receptors, and therefore did not consider the effects due to cell deformability and flow inside the cell. A lift force of purely hydrodynamic origin would act on adhered cells as on any other deformable particles in shear near a wall. In contrast to a rigid sphere in a wall bounded shear (Stokes flow limit), a deforming drop experiences lateral lift away from the wall. We couple our front-tracking algorithm with models for membrane elasticity and stochastic receptor-ligand binding. The cell membrane is modeled by a Neo-Hookean constitutive relation. The bonds are modeled as a Hookean spring. The result shows the lift force on the cell pushes it away from the substrate while the shear-induced torque acts to pull it towards the substrate. The effect of cell deformation on a state diagram for cell adhesion/detachment is examined by varying the membrane elasticity parameter. If time permits, I will briefly discuss deformation of a viscoelastic (Oldroyd B) drop in a simple shear flow: drop deformation overshoots due to the finite time it takes to develop the viscoelastic stress. This stress is inhibitive and leads to a decreased steady value of deformation. We provide an ordinary differential equation model for observed scalings.
Brown Analysis Seminar
Brown University
Division of Applied Mathematics
TRANSATLANTIC SEMINAR
Abstract: We consider the global attractor generated by a scalar semilinear parabolic equation of the form $u_t = u_{xx} + f(u,u_x)$, defined on the circle $S^1=\R/2\pi\Z$, with a dissipative nonlinearity $f$. We discuss the realization of these attractors by nonlinearities of the form $f=f(u)$
Brown University
Center for Statistical Sciences
2007 Lectureship Series
Biostatistics in the Post-genomic Era:
Statistical Methodology & Applications in Bioinformatics
The Process, Data Analysis and Quality Control | |
Abstract: High throughput screening (HTS) has become one of the main methods for generating leads for drug discovery. HTS has been a fast growing field in the pharmaceutical industry in the last decade, as well as in academic institutes in recent years. The first part of this presentation will introduce the current status of HTS, including assay development and HTS processes. The second half will focus on HTS quality control and the data analysis process.
Sponsored by: The Charles K. Colver Lectureship and Publication Fund
PDE Seminar
Department of Mathematics Colloquium
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