Electrostatic forces and the electrostatic properties of molecules in solution are among the most important issues in understanding the structure and function of large biomolecules. The use of implicit-solvent models, such as the Poisson-Boltzmann equation (PBE), have been used with great success as a way of computationally deriving electrostatics properties such molecules. We discuss how to solve an elliptic system of partial differential equations (PDEs) involving the Poisson and the PBEs using path-integral based probabilistic, Feynman-Kac, representations. This leads to a Monte Carlo method for the solution of this system which is specified with a stochastic process, and a score function. We use several techniques to simplify the Monte Carlo method and the stochastic process used in the simulation, such as the walk-on-spheres (WOS) algorithm, and an auxiliary sphere technique to handle internal boundary conditions. We then specify some optimizations using the error (bias) and variance to balance the CPU time. We show that our approach is as accurate as widely used deterministic codes, but has many desirable properties that these methods do not. In addition, the currently optimized codes consume comparable CPU times to the widely used deterministic codes. Thus, we have an very clear example where a Monte Carlo calculation of a low-dimensional PDE is as fast or faster than deterministic techniques at similar accuracy levels.
Michael Mascagni is a professor in the FSU Computer Science Department. He has a special interest in Monte Carlo methods, Random Number Generation, Distributed and Parallel Computing, and Mathematical Biology. He is the author of the SPRNG library, which can generate reliable and statistically sound streams of pseudorandom numbers to be used during a parallel computation. He has many projects that he can suggest to students interested in this area.
A weather report describes the temperature at selected cities across the country, but we know the temperature exists everywhere. If we ask a computer to predict the temperature, it needs to be able to ``fill in'' the territory between the cities, and to estimate how the temperature will vary as we move between the cities. This is an example of the meshing problem. We are asked to consider a country, a building, the wing of a jet plane, which has a shape, and we want to approximate that shape with a finite number of patches of simple shape. This might seem like a simple task if we only need 10 or 15 patches, but the accuracy of the computation might require using a lot of very small patches. In this talk, we discuss some examples of the meshing problem, for 1D, 2D, 2.5D (the surface of a sphere) and 3D. In particular, we introduce some free programs for developing, displaying, and modifying meshes, including trimesh, triangle, distmesh, mesh2d, meshlab and tetgen.
Computer simulation is of critical importance in several engineering and basic science applications. Frequently it is the only way to study complex physics phenomena, design new or improve the existing engineering systems. In this talk, I will review elements of both theory and practice of verification and validation in computational sciences. I will provide examples demonstrating that verification and validation procedures are crucially important for creating successful simulation tools.
Tomasz Plewa is a professor in the FSU Scientific Computing Department. This fall, he is teaching the course "Introduction to Scientific Computing".
Peter Beerli is a professor in the FSU Scientific Computing Department. This fall, he is teaching the course "Inferences in Conservation Genetics". He is in interested in population genetics problems, particularly in how much information we can extract from samples of genetic material.
A wave can travel from San Francisco to Shanghai, but what is actually moving? The water in San Francisco doesn't move to China - instead, it is transmitting a disturbance, a kind of energy. Water waves can be described by a set of complicated mathematical equations - but when the waves are moving a long distance over a relatively shallow basin, these equations can be greatly simplified to what are known as the shallow water equations. In this talk, we will present the 1D shallow water equations, and then show how a version of these equations can be defined for approximation on a computer. The resulting system can be solved as a small MATLAB program. After this talk, you might be interested in looking at the program for the 2D shallow water equations developed by Cleve Moler, founder of MATLAB.
Polymers made in laboratories are not uniform in molecular weight or length. Instead, they contain molecules of different sizes, which can be characterized by the so called "molecular weight distribution" or MWD. This MWD tells us what fraction of the sample is of a given length. I will tell you why rheology - the study of how a material responds to deformation - is an attractive technique for inferring the MWD indirectly. I will describe a common formulation of the problem, and survey three common techniques used to solve it.
Sachin Shanbhag is a professor in the FSU Scientific Computing Department. This fall, he is teaching the course "Algorithms for Science Applications I". His research interests include polymer physics, rheology, complex fluids, and modeling for biological and materials applications.
This seminar will present the basic aspects of coordinate-based, geometric morphometric methods applied to the problem of estimating the shape of the cranial vault (often covered by hair) from visible components of the face represented in 3D surface scans. These results are of considerable interest to those concerned with the optimal design of comfortable, effective helmets for military and civilian use. Similar methods have been used to explore the fit of industrial respirators, and connections between the two areas of inquiry will be discussed.
Dennis Slice is a professor in the FSU Scientific Computing Department.
The rapid increase in the availability of genomic-scale multiple sequence alignments covering diverse sets of taxa (e.g., species) offer new and exciting opportunities for those seeking to understand the processes and patterns of molecular evolution. For example, why are there so many living beetle species and so few living Coelacanths species? Why are Filoviridae infections generally fatal, whereas most Papillomaviridae infections benign? During this introductory lecture I will not answer these specific questions but I will described a variety of phylogenetic methods used by evolutionary biologist to answer these types of questions and more.
Jim Wilgenbusch is a Research Associate in the FSU Scientific Computing Department, and manager of the Technical Support Group (TSG). He is interested in a mix of theoretical and empirical problems, including work on assessment of Markov Chain Monte Carlo (MCMC) convergence as well as analysis of lizard phylogeny. He coordinates the development and user support of PAUP* and provides leadership in the deployment of tools for distributed computing at the Scientific Computing Department. He is also the director of FSU's High Performance Computing (HPC) center.
Multicore computers are now widely available. Theoretically, a computer with 10 cores can run a program 10 times as fast - but only if the user knows how to get the cores to cooperate on a common problem. MATLAB's Parallel Computing Toolbox offers three different approaches to this problem, including the simple parfor command that makes a for loop execute in parallel, the spmd system for other calculations that must be carried out simultaneously, and a task command for running many related computations independently and collecting the results at the end.
One of the beauties of mathematics is that it can often identify similarities and connections between seemingly unrelated objects. Similarly, in computational science, it often happens that a method developed to handle a very specific problem turns out to be helpful in understanding a variety of other problems that weren't under consideration. In this talk, we will discuss one such method, the centroidal Voronoi tessellation. We will show how this method is used to solve a simply-stated geometric problem, and show how this idea can help to answer questions in several entirely separate areas.
Max Gunzburger is a professor in the FSU Scientific Computing Department.
Being healthy is one of the big concerns of each individual, but that has been influenced not only by individual health and life style but also by population health. The spreading and dynamics of a disease within a population is the subject of many studies. A standard model in epidemiology is the SIR model, in which individuals are classified in three components (Susceptible, Infected, Recovered). Commonly, the contact among individuals and the disease transmission rate is considered the same during the epidemic. Contact network and disease transmission play an important role to model the system in order to estimate the disease outbreak, basic reproductive ratio known as R0, etc. These two concepts are important for applying preventive care such as vaccination, and closing schools. What preventive methods do is changing the connectivity or transmission rates over time. To model and study the dynamics of this system, I have combined the SIR model which can be represented as a set of ordinary differential equations with a Markov chain-based model, which represents the contact network as a large transition matrix among individuals. The new model is presented for several network structures. Some of the preventive methods are applied and been tested as well.
Haleh Askhi is a graduate student in the FSU Scientific Computing Department. She works with Professor Peter Beerli.
How many fish in the sea? At what rate is bird flu being transmitted? How many whales were in the sea before whaling? These are just some of the questions that can be answered using present population genetics methods. In order to answer these questions, we use Bayesian statistical methods and models of evolution. Our primary model is called the coalescent; it is a framework that allows us to take any two distinct genes, and determine how far in the past we must go until it is likely that the genes meet in a common ancestor. The method has been extended to the structured coalescent, which can also model the rate of gene flow between different geographical locations. Current inference programs take a long time and produce inaccurate results when the rate of gene flow is high. What I have done is create a continuous model of gene flow, which can handle high rates with ease. I will demonstrate this new method works, and its performance in a statistical inference program.
Michal Palczewski is a graduate student in the FSU Scientific Computing Department. He works with Professor Peter Beerli.
OpenMP and MPI are two systems that make it possible for C and FORTRAN programs to take advantage of parallel programming techniques. A person interested in parallel programming should begin with OpenMP - it allows a user to take a step-by-step approach. You can experiment with making a single loop parallel, and if that goes well, trying another one. In this talk, we will present some examples of computations that can be run in parallel, and show the OpenMP instructions that are necessary.
Over the last four decades, numerical modeling has become a vital tool to help understand and predict complex physical, chemical, and biological processes of subsurface environmental systems. Due to lack of data and knowledge to describe the processes and their interactions, model predictions are inherently uncertain. Quantification of predictive uncertainty is critical to science-based decision-making. It can improve defensibility of model results and reduce cost of water resource management and environmental protection. This presentation will introduce several case studies of numerical simulation of subsurface flow and solute transport in saturated and unsaturated porous and fractured media. The numerical modeling is used to assess two hierarchical types of uncertainty, parametric and conceptual model uncertainties, due to non-unique description of model parameter and model structure. Assessing parametric uncertainty is to quantify predictive uncertainty of a single model, whereas assessing conceptual model uncertainty is to evaluate variability in model predictions, at a higher level, arising from multiple acceptable models. This presentation will introduce a Bayesian method to jointly assess conceptual model and parametric uncertainties.
Ming Ye is a professor in the FSU Scientific Computing Department. This fall, he is teaching the course "Symbolic and Numerical Computations". He is interested in stochastic methods to describe flow and transport in randomly heterogeneous media, geostatistical methods for the spatial analysis of hydrologic data, efficient inverse methods under parameter and conceptual model uncertainty, integrated analysis of groundwater parameter, conceptual model, and scenario uncertainty, high performance computing, computational investigation of flow and transport in unsaturated fractured systems, identification of geologic structure of unsaturated porous media and estimation of equivalent hydraulic parameters.