Applied Math Seminar

A multi-scale computational frame work to study cell and tissue mechanics

01/22/2018 - 4:15pm
01/22/2018 - 5:15pm
Speaker: 
Ali Nematbakhsh (UC Riverside)
Abstract: 

 How individual cells coordinate tissue-scale processes is still poorly understood topic due to the inherent complexity of emergent tissue level behavior of cells. Recent studies have shown that besides chemical signaling, mechanical interaction between cells also plays a major role in this regard. Testing hypothetical novel biophysical mechanisms across spatial scales require computational models that can span subcellular to tissue levels. However, the task of including detailed descriptions of mechanical interactions between cells including cytoplasm, membrane, cortical stiffness and cell-cell adhesion is challenging due to the prohibitively high computational costs and complexity of intercellular mechanical interaction. In here, we have developed a multi-scale modeling environment called Epi-Scale for simulating cell and tissue mechanics based on the Subcellular Element (SCE) modeling approach. Computational implementation of the model is based on an efficient parallelization algorithm that utilizes Graphical Processing Units (GPUs) for simulating large numbers of cells within a reasonable computational time. As a demonstration of the predictive power of the model, epithelial cells growth and division during development are simulated and polygon class distribution of cells is compared with experimental data. Furthermore, regulation of mechanical properties of cells during mitotic rounding is simulated and contribution of each mechanical property on the expansion and roundness of the cells before division of cells is quantified. It has been shown the mitotic area expansion is largely driven by regulation of cytoplasmic pressure. While, mitotic shape roundness is most sensitive to variation in cell-cell adhesivity and cortical stiffness of cells.

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College

Sparse Additive Modeling

10/30/2017 - 4:15pm
10/30/2017 - 5:15pm
Speaker: 
Prof. Noah Simon (Department of Biostatistics, University of Washington)
Abstract: 

With recent advances in high-throughput technology it is now common to collect enormous quantities of data on a small number of subjects. In particular, in the biomedical field, we often collect extremely high dimensional biomolecular information (eg. gene expression, dna-sequence, and/or epigenetic information). We are often interested in using this information to predict a phenotype: eg. does a person have a given disease? Or is a tumor susceptible to a particular therapy? In these cases we often believe that only a small subset of the biomolecular features are informative for the phenotypic response (though we generally do not know which). Given this, we would like a model-building procedure that selects and uses only a small subset of the available genomic features for predicting phenotype.

The LASSO is one common method that both performs feature selection, and fits a linear model on that selected subset. The LASSO is an attractive method as it is simple, has good theoretical behaviour, is computationally straightforward to fit, and empirically performs well in many applications. However, a linear model may sometimes not be a good approximation to the true underlying relationship between features and response. In this presentation we will discuss Sparse Additive Modeling, an extension to the LASSO that selects features, and fits a more flexible additive model in those features. This, more flexible framework, shares many of the attractive properties of the LASSO (parsimony, computational tractibility, theoretical guarantees, and empirical performance). In addition, in non-linear scenarios it may more adequately model our data.

(hopefully) Very little background will be assumed in this talk: We will begin by introducing and discussing the LASSO, non-parametric regression, and additive modeling. In addition, we will touch on convex optimization and numerical algorithms for high dimensional minimization.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

Aluminum-doped nano-layered metamaterials with hyperbolic dispersion for ultrafast light control on nanoscale

12/04/2017 - 4:15pm
12/04/2017 - 5:15pm
Speaker: 
Prof. Lyuba Kuznetsova (Department of Physics, SDSU)
Abstract: 

A special class of nano-layered hyperbolic metamaterials has received a lot of attention recently due to their unique optical property namely that the dispersion of the dielectric constant for hyperbolic metamaterials exhibits a topological transition in the isofrequency surface from an ellipsoid to a hyperboloid. The unique property of propagating waves in such a metamaterial is that the wavevectors have unbounded magnitudes which allows dramatic increase of the photon density of states. The presence of these additional electromagnetic states allows the modification of the spontaneous emission rate. Exploring these effects with aluminum-doped metamaterials could lead to an efficient integration into current technology for applications in modern communications, super-resolution imaging, and label-free detection of organic and biological systems.

This talk will cover a few computational approaches that are promising for designing aluminum-doped metamaterials with hyperbolic dispersion. In particular, I will introduce our recently developed approach to the analysis of spectroscopic ellipsometry data to extract the optical permittivity for a nano-layered Al:ZnO/ZnO metamaterial. I will discuss intriguing nanocavity devices based on aluminum\dielectric nano-layered metamaterials which allow light confinement beyond diffraction limit. I will also discuss a size-dependent bio-particle sensing technique based on microcavities. I will conclude with our current research on using aluminum-doped metamaterials with hyperbolic dispersion for ultrafast light control on nanoscale.

Where: 
Mondays 4:15-5:15 pm Emmy Noether Rm Millikan 1021 Pomona College

Machine Learning in the Web World

09/21/2017 - 4:15pm
09/21/2017 - 5:15pm
Speaker: 
Alpan Raval (CGU, Keck Graduate Institute)
Abstract: 

In this talk I will present a very high-level (equation-free) overview of some Machine Learning (ML) projects at LinkedIn and the data used to drive them. I will describe the problems and discuss the challenges in implementing ML solutions to these problems. Many of these challenges are common to large internet companies — examples include: high volumes of dynamic data, noisy ground truth, and time-to-inference requirements — while a few are specific to the LinkedIn platform.

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College

Chaos expansion and SPDEs.

11/27/2017 - 5:30pm
11/27/2017 - 6:30pm
Speaker: 
Sergey Vladimir Lototsky (USC)
Abstract: 

Chaos expansion is separation of random and deterministic components of the model and can be considered an analog of the classical Fourier method. For stochastic partial differential equations, chaos expansion leads to new analytical tools to study the equations and new algorithms to solve the equations numerical. Specific examples include construction of a solution for equations that do not satisfy classical parabolicity condition and mean-preserving renormalization of nonlinear equations.

Where: 
Emmy Noether Rm, Millikan 1021, Pomona

Numerical Methods for Reaction-Diffusion Equations and the Application in Computational Biology

10/23/2017 - 4:15pm
10/23/2017 - 5:15pm
Speaker: 
Weitao Chen (UCR)
Abstract: 

Reaction-diffusion equations have wide applications in natural and engineering sciences. The efficiency of numerical methods for these equations is often limited by the severe stability conditions due to diffusion and stiff reactions, as well as the curse of dimensionality for equations in high-dimensional spaces. We developed a numerical method to improve the efficiency by relaxing stability constraints, coupled with sparse grid technique, for solving reaction-diffusion equations in high dimensions. We also extend this method to more general systems with nonhomogeneous boundary conditions or explicitly time-dependent reactions. In addition, I will introduce its application in modeling a complex biological system, the macropatterning in mouse tongue, to understand the robustness strategies in pattern formation on a growing tissue.

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College

Streaming t-SNE

10/09/2017 - 4:15pm
10/09/2017 - 5:15pm
Speaker: 
Mariam Salloum (CMC)
Abstract: 

Data sets involving many dimensions are commonplace in scientific computing and machine learning, however, the human visual system is limited to interpreting data in only two or three dimensions. An award-wining technique called Student-T Stochastic Neighbor Embedding (t-SNE) has been presented to embed data of high dimension into a 2-D or 3-D space, while preserving local relationships in the original data. This has yielded marked improvements in the quality of the embedding, especially with regard to its ability to preserve clustering and structure. However, the original t-SNE can only be used in batch mode, i.e. all data must be available prior to the start of the algorithm. It is therefore compelling to have a version of t-SNE which can accommodate a streaming operational mode, i.e. to incorporate new information into the embedded representation as it arrives. Such a system would allow an operator to observe changes in complex, high dimensional data in near real-time. In this work, we present a streaming t-SNE variation and provide visualizations with streaming data.

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College

organizational discussion

09/04/2017 - 4:15pm
09/04/2017 - 5:15pm
Speaker: 
TBA
Abstract: 

 TBA

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College

The Fast Radial Basis Functions Orthogonal Gradients (RBF-OGr) method for solving PDEs on arbitrary surfaces

11/13/2017 - 4:15pm
11/13/2017 - 5:15pm
Speaker: 
Cecile Piret (Michigan Tech University)
Abstract: 

The RBF-OGr method was introduced in [Piret, 2012] to discretize differential operators defined on arbitrary manifolds defined exclusively by a point cloud. The method was designed to take advantage of the meshfree character of RBFs, which offers the flexibility to represent complex geometries in any spatial dimension while providing a high order of accuracy. A large limitation of the original RBF-OGr method was its large computational complexity, which greatly restricted the size of the point cloud. In this talk, a fast version of the RBF-OGr method will be introduced. This latest algorithm makes use of the RBF-Finite Difference (RBF-FD) technique for building sparse differentiation matrices discretizing continuous differential operators such as the Laplace-Beltrami or the surface biharmonic operators.

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College

RNA Interactions - a PDE Story

09/18/2017 - 4:15pm
09/18/2017 - 5:15pm
Speaker: 
Maryann Hohn (UCSD)
Abstract: 

Small non-coding RNAs regulate developmental events through certain interactions with messenger RNA (mRNA). By binding to specific sites on a strand of mRNA, small RNAs may cause a gene to be activated or suppressed, turning a gene "on" or "off". To better understand these interactions, we developed a mathematical model that consists of a system of coupled partial differential equations describing mRNA and small RNA interactions across cells and tissue. In this talk, we will discuss the mathematical models created and numerical simulations using these equations.

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College
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