2nd Joint UTEP/NMSU Workshop on Mathematics and

Computer Science

El Paso, Texas

Saturday, November 17, 2007

Sarala Arunagiri, Seetharami Seelam, Ron A. Oldfield, Maria Ruiz Varela, Patricia J. Teller, and Rolf Riesen

(Department of Computer Science, UTEP)

IMPACT OF CHECKPOINT LATENCY ON THE OPTIMAL CHECKPOINT INTERVAL AND EXECUTION TIME

The massive scale of current and next-generation massively parallel processing (MPP) systems presents significant challenges related to fault tolerance. In particular, the standard approach to fault tolerance, application-directed checkpointing, puts an incredible strain on the storage system and the interconnection network. This results in overheads on the application that severely impact performance and scalability. The checkpoint overhead can be reduced by decreasing the checkpoint latency, which is the time to write a checkpoint file, or by increasing the checkpoint interval, which is the compute time between writing checkpoint files. However, increasing the checkpoint interval may increase execution time in the presence of failures. The relationship among the mean time to interruption (MTTI), the checkpoint parameters, and the expected application execution time can be explored using a model, e.g., the model developed by researchers at Los Alamos National Laboratory (LANL). Such models may be used to calculate the optimal periodic checkpoint interval. In this paper, we use the LANL model of checkpointing and thorough mathematical analysis we show the impact of a change in the checkpoint latency on the optimal checkpoint interval and the overall execution time of the application.

For checkpoint latencies, d1 and d2, and the corresponding optimal checkpoint intervals, t1 and t2, our analysis shows the following results: (1) For a given MTTI, if d1 is greater than d2, t1 is greater than or equal to t2. (2) When the checkpoint interval is fixed, a decrease in checkpoint latency results in a decrease in application execution time. (3) A reduction in checkpoint latency, from d1 to d2, and a corresponding change of the checkpoint interval from the optimal checkpoint interval associated with d1, t1, to that associated with d2, t2, translates to reduced application execution time when the difference between t1 and t2 exceeds a certain threshold value, which can be as large as 12% of t_opt.

In terms of application execution times, the approximation error of the optimal checkpoint interval is not significant. However, when we consider other performance metrics of the application, such as network bandwidth consumption and I/O bandwidth consumption, we conjecture that the information obtained by the analysis presented in this report could be of value in reducing resource consumption.

The full paper is available in pdf

Tunna Baruah

(Department of Physics, UTEP)

UNDERSTANDING MOLECULAR PROPERTIES FROM DENSITY FUNCTIONAL THEORY

Molecules and low-dimensional systems such as atomic clusters, quantum dots, nanotubes show interesting novel properties that are quite different from bulk materials. Computational studies play an important role in understanding fundamental properties of these systems, which in turn is useful in manipulating these systems for possible technological application. In this talk, I will present an overview of first principle based density functional calculations on molecular systems. In particular I will present our calculations on various novel systems such as light harvesting molecular solar cell, molecules with large magnetization reversal energy, inorganic cage molecules and clusters of metal atoms.

Jakub Cerveny and Pavel Solin

(Department of Mathematical Sciences, UTEP)

ON MULTI-MESH HP-FEM FOR COUPLED PROBLEMS

While numerical methods for single-field problems have reached a high degree of maturity already, computational methods for coupled problems have been far less developed. The reason is that the solution of a coupled problem is much more difficult compared to the solution of any single-field problem involved. This is due to the fact that

- various physical fields such as, e.g., the temperature, velocity, pressure, electric field, or magnetic field exhibit important qualitative differences which make a uniform computational approach very difficult or impossible,
- physical fields generally belong to different spaces of functions where different types of finite elements are needed.

References

P. Monk, Finite Element Methods for Maxwell's Equations, Clarendon Press, Oxford, 2002.

P. Solin, J. Cerveny, and I. Dolezel, Arbitrary-Level Hanging Nodes and Automatic Adaptivity in the hp-FEM, accepted to Math. Comp. Sim., 2006.

P. Solin, J. Cerveny, and L. Dubcova, Adaptive Multi-Mesh hp-FEM for Linear Termoelasticity, CMAME, submitted, November 2007.

P. Solin, K. Segeth, and I. Dolezel, Higher-Order Finite Element Methods, Chapman & Hall/CRC Press, 2003.

Russell R. Chianelli

(Materials Research and Technology Institute, UTEP)

SIMULATION AND SYNCHROTRON TECHNIQUES APPLIED TO PROBLEMS IN MATERIALS SCIENCE: CATALYSTS AND AZUL MAYA PIGMENTS

Combining simulations with advanced synchrotron techniques accelerates understanding of structure in disordered, amorphous and surface materials. The acceleration of this understanding has allowed rapid development of structure/function co-relations that advance commercial application of novel materials. In this presentation we review the application of simulations using CERIUS2 (ACCELRYS CORP.) programs and multiple synchrotron characterization techniques to two classes of materials defined as "surface compounds." One class of surface compounds is materials like MoS(2-x)C(x) that are widely used petroleum catalysts that improve the environmental properties of transportation fuels. These compounds may be viewed as "sulfide supported carbides" in their catalytically active states. The second class of "surface compounds" is the "Maya Blue" pigments that are based on technology created by the ancient Maya. These compounds are organic/inorganic "surface complexes" consisting of the dye indigo and palygorskite, a common clay. Both of these materials are currently being commercialized based on the results obtained through the combination of simulation and synchrotron studies.

Lenka Dubcova and Pavel Solin

(Department of Mathematical Sciences, UTEP)

COMPUTER MODELING OF AN ELECTROMAGNETIC-THERMAL COUPLED PROBLEM

In electromagnetic-thermal coupled problems such as microwave-heating, the electric field deposits energy into the heated material which causes its temperature to rise. On the other hand, the rising temperature changes certain dielectric properties of the material which has an effect on the original electromagnetic field. In this way, the processes are coupled both ways. Time-harmonic Maxwell's equations are used to model the electromagnetic field and the thermal part of the process is modeled using the heat-transfer equation. We present a monolithically coupled model where the Maxwell's equations are discretized using higher-order edge elements, and standard continuous elements are used for the temperature. As an introduction, we say a few words about the hp-FEM and automatic adaptivity. Numerical examples of microwave heating are presented.

References

P. Monk, Finite Element Methods for Maxwell's Equations, Clarendon Press, Oxford, 2002.

P. Solin, J. Cerveny, and I. Dolezel, Arbitrary-Level Hanging Nodes and Automatic Adaptivity in the hp-FEM, accepted to Math. Comp. Sim., 2006.

P. Solin, K. Segeth, and I. Dolezel, Higher-Order Finite Element Methods, Chapman & Hall/CRC Press, 2003.

Eric Freudenthal

(Department of Computer Science, UTEP)

CONSISTENT HASHING: AN EFFICIENT APPROACH FOR DISTRIBUTED INDEXING

Consistent Hashing is a relatively new approach to constructing an index among a set of distributed systems called a Distributed Hash Table (DHT). The set of systems is partitioned through the assignment of random node identifiers, and key-value mappings are stored in hosts host whose identifiers are "nearest" to the hash of the mapping's key.

When the number of participating hosts is large and changes over time, it becomes impractical to consistently disseminate the current set of participants and their identifiers, but nonetheless, it is desirable to permit efficient indexing despite this lack of global knowledge. Techniques have been developed to permit participants to efficiently construct and maintain routing infrastructures that permit hosts to cooperatively discover others near to any particular identifier through a process of O(log(N)) communications, where N is the number of participating systems.

This talk will present an introduction of consistent hashing, distributed hash tables, and open research challenges related to them.

Bio: Eric Freudenthal is an Assistant Professor in the Computer Science department at UTEP. He is one of the originators of Coral/CDN, a self-organizing content distribution network that runs upon Planetlab and serves tens-of-millions of web pages daily. Coral's indexing mechanism is a novel "sloppy" DHT that provides bandwidth that scales linearly with offered load.

Eric Freudenthal and Luc Longpre

(Department of Computer Science, UTEP)

FERN: A MUTABLE AUTHENTICATED DICTIONARY FOR PEER-TO-PEER SYSTEMS

While peer-to-peer systems are notorious for their ability to exploit available resources to efficiently disseminate information, these systems provide no guarantees of data integrity. Self-validating authenticated dictionaries built upon (merkle-) hash-trees can be incrementally distributed upon a peer-to-peer framework and thus can disseminate key:value mappings with strong integrity guarantees.

It is desirable to permit the publisher of an authenticated dictionary to efficiently disseminate updates with equivalent integrity properties. Several approaches have been proposed. Fern's data structure and algorithm are significantly simpler than others' approaches, and Fern's performance is competitive or superior. We present the structure of Fern and an informal analysis of the number of vertices of a Fern-trie that must be transferred to systems that monitoring a set of key:value mappings stored within Fern.

Vladik Kreinovich

(Department of Computer Science, UTEP)

APPLICATION-MOTIVATED COMBINATIONS OF INTERVAL, AND PROBABILITY APPROACHES, WITH APPLICATION TO GEOINFORMATICS, BIOINFORMATICS, AND ENGINEERING

Since the 1960s, many algorithms have been designed to deal with interval uncertainty. In the last decade, there has been a lot of progress in extending these algorithms to the case when we have a combination of interval and probabilistic uncertainty. We provide an overview of related algorithms, results, and remaining open problems.

Luc Longpre

(Department of Computer Science, UTEP)

Pierre McKenzie

(U. de Montreal)

SOLITAIRE

Klondike is the well-known 52-card Solitaire game available on almost every computer. We have investigated the complexity of determining whether an n-card Klondike initial configuration can lead to a win. To talk about complexity, we need to generalize the game with an arbitrary number of cards. We have shown that the problem NP-complete. A proof of this can be presented to a mathematically oriented general audience. The problem remains NP-complete when only three suits are allowed instead of the usual four. When only two suits of opposite color are available, the problem is NLog-space-hard. When the only two suits have the same color, two restrictions are shown in AC0 and in NL respectively. When a single suit is allowed, the problem drops in complexity down to AC0[3], that is, the problem is solvable by a family of constant depth unbounded fan-in {and, or, mod3}-circuits. Other cases are studied: for example, “no King” variant with an arbitrary number of suits of the same color and with an empty “pile” is NLog-space-complete.

Joel Lucero-Bryan

(Department of Mathematical Sciences, NMSU)

A RESULT CONCERNING THE RATIONAL NUMBERS

Topological spaces are fundamental objects of study in Mathematics. In a given topological space, one can define operations known as the closure and limit point operators. These different, but related, operators each naturally give rise to a Boolean algebra with additional operations (BAO for short). In the 1940’s, McKinsey and Tarski axiomatized the BAO arising from the closure operator of a dense-in-itself metrizable space. As a corollary, the BAO’s coming from the closure operator of the real numbers, the rational numbers, and the Cantor space each have the same axiomatization. In the spirit of McKinsey and Tarski’s work, during the 1990’s Shehtman axiomatized the BAO arising from the limit point operator of a 0-dimensional dense-in-itself metrizable space. From Shehtman’s work it follows that the BAO coming from the limit point operator of the rational numbers has the same axiomatization as the BAO coming from the limit point operator of the Cantor space. In this talk we present a new and simplified proof of this axiomatization, which takes advantage of new techniques in modal logic introduced in the past decade.

Hung T. Nguyen and Hien Tran

(Department of Mathematical Sciences, NMSU)

ON FOUNDATIONS OF STOCHASTIC DOMINANCE IN MATHEMATICAL FINANCE

In order to investigate the stochastic dominance approach to decision-making under risk and uncertainty in mathematical finance, in a more realistic setting, we re-examine the current practice of SD. Several improvements and extensions have been found, including procedures on approximations of utility functions, elimination of the assumption of differentiability of utility functions, as well as necessary and sufficient conditions for SD rules.

Enrico Pontelli and Son Tran

(Department of Computer Science, NMSU)

LOGIC PROGRAMMING WITH ABSTRACT CONSTRAINT ATOMS

We provide new perspectives on the semantics of logic programs with abstract constraints. Abstract constraints are formal entities that have been introduced to enable the analysis of various classes of extensions of logic programming, including aspects like collections and aggregates. To this end we introduce several notions of computation and propose to use the results of computations as answer sets of programs with constraints.

We discuss the rationale behind different classes of computations and study the relationships among them and among the corresponding concepts of answer sets. The proposed semantics generalize the answer set semantics for programs with monotone, convex and/or arbitrary constraints described in the literature.

Andrzej Pownuk

(Department of Mathematical Sciences, UTEP)

GENERAL INTERVAL FEM PROGRAM BASED ON SENSITIVITY ANALYSIS METHOD

Today there are many methods for solution of equation with interval parameters. Unfortunately there are very few efficient methods which can be directly applied for solution of complex engineering problems. Sensitivity analysis method gives very good inner approximation of the exact solution set. This method was implemented in C++ language by the author and the program can be recompiled on Windows, Linux and Solaris operating systems. The program is able to solve 1D, 2D and 3D linear problems of electrostatics with interval parameters. In order to describe structure with uncertain parameters special scripting language was applied. The program is able to solve problems using endpoint combination method and Taylor expansion method. Additionally it is possible to solve problems with uncertain functional parameters. In order to do that it is necessary special finite elements. The program is very universal and can be applied to the solution of complex engineering problem. The program is a part web application, which is written in php language and can be run on the authors web page http://andrzej.pownuk.com. The program is object oriented and can be very easily extended to the solution of more complicated problems like for example nonlinear problems of computational mechanics.

Granville Sewell

(Department of Mathematical Sciences, UTEP)

THE PDE2D COLLOCATION FINITE ELEMENT METHOD

PDE2D (www.pde2d.com, sold through Visual Numerics' e-commerce site) is a finite element program which solves very general PDE systems in 1D intervals, arbitrary 2D regions and a wide range of simple 3D regions. Both Galerkin and collocation options are available for 1D and 2D problems, only collocation for 3D problems. The collocation algorithms have some novel features, particularly relating to how non-rectangular regions are handled. Some advantages and disadvantages of these collocation algorithms are discussed, relative to the more standard Galerkin methods.

Karen Villaverde

(Department of Computer Science, NMSU)

ESTIMATING VARIANCE UNDER INTERVAL UNCERTAINTY: PARALLEL ALGORITHMS

Traditional data processing in science and engineering starts with computing the basic statistical characteristics such as the population mean E and population variance V. In computing these characteristics, it is usually assumed that the corresponding data values x1,...,xn are known exactly. In many practical situations, we only know intervals [xi] that contain the actual (unknown) values of xi. In this case, different possible values of xi lead, in general, to different values of E and V. In such situations, we are interested in producing the intervals of possible values of E and V. There exist algorithms for producing such interval and fuzzy estimates. However, these algorithms are more complex than the typical data processing formulas and thus, require a larger amount of computation time. If we have several processors, then, it is desirable to perform these algorithms in parallel on several processors, and thus, to speed up computations. In this paper, we show how the algorithms for estimating variance under interval and fuzzy uncertainty can be parallelized.