Roberto Araiza

Towards Combining Probabilistic and Interval Uncertainty in Engineering Calculations: Algorithms for Computing Statistics under Interval Uncertainty, and Their Computational Complexity

In many engineering applications, we have to combine probabilistic and interval uncertainty. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such as mean, variance, autocorrelation, correlation with other measurements. In environmental measurements, we often only measure the values with interval uncertainty. We must therefore modify the existing statistical algorithms to process such interval data.In this paper, we provide a survey of algorithms for computing various statistics under interval uncertainty and their computational complexity. The survey includes both known and new algorithms.

PseudoBase++: an extension of PseudoBase for easy searching, formatting and visualization of pseudoknots.

Pseudoknots have been recognized to be an important type of RNA secondary structures responsible for many biological functions. PseudoBase, a widely used database of pseudoknot secondary structures developed at Leiden University, contains over 250 records of pseudoknots obtained in the past 25 years through crystallography, NMR, mutational experiments and sequence comparisons. To promptly address the growing analysis requests of the researchers on RNA structures and bring together information from multiple sources across the Internet to a single platform, we designed and implemented PseudoBase++, an extension of PseudoBase for easy searching, formatting and visualization of pseudoknots. PseudoBase++ (http://pseudobaseplusplus.utep.edu) maps the PseudoBase dataset into a searchable relational database including additional functionalities such as pseudoknot type. PseudoBase++ links each pseudoknot in PseudoBase to the GenBank record of the corresponding nucleotide sequence and allows scientists to automatically visualize RNA secondary structures with PseudoViewer. It also includes the capabilities of fine-grained reference searching and collecting new pseudoknot information.

Using expert knowledge in solving the seismic inverse problem

In this talk, we analyze how expert knowledge can be used in solving the seismic inverse problem. To determine the geophysical structure of a region, we measure seismic travel times and reconstruct velocities at different depths from this data. There are several algorithms for solving this inverse problem.

Under Interval and Fuzzy Uncertainty, Symmetric Markov Chains Are More Difficult to Predict

Markov chains are an important tool for solving practical problems. In particular, Markov chains have been successfully applied in bioinformatics. Traditional statistical tools for processing Markov chains assume that we know the exact probabilities pij of a transition from the state i to the state j. In reality, we often only know these transition probabilities with interval (or fuzzy) uncertainty. We start the paper with a brief reminder of how the Markov chain formulas can be extended to the cases of such interval and fuzzy uncertainty. In some practical situations, there is another restriction on the Markov chain-that this Markov chain is symmetric in the sense that for every two states i and j, the probability of transitioning from i to j is the same as the probability of transitioning from j to i: pij = pji. In general, symmetry assumptions simplify computations. In this paper, we show that for Markov chains under interval and fuzzy uncertainty, symmetry has the opposite effect: it makes the computational problems more difficult.

Automatic referencing of satellite and radar images

In order to adequately process satellite and radar information, it is necessary to find the exact correspondence between different types of images and between these images and the existing maps. In other words, we need to reference these images. In this paper, we propose new methods for automatic referencing of satellite and radar images.

RNAVLab: A virtual laboratory for studying RNA secondary structures based on grid computing technology

Abstract As ribonucleic acid (RNA) molecules play important roles in many biological processes including gene expression and regulation, their secondary structures have been the focus of many recent studies. Despite the computing power of supercomputers, computationally predicting secondary structures with thermodynamic methods is still not feasible when the RNA molecules have long nucleotide sequences and include complex motifs such as pseudoknots. This paper presents RNAVLab (RNA Virtual Laboratory), a virtual laboratory for studying RNA secondary structures including pseudoknots that allows scientists to address this challenge. Two important case studies show the versatility and functionalities of RNAVLab. The first study quantifies its capability to rebuild longer secondary structures from motifs found in systematically sampled nucleotide segments. The extensive sampling and predictions are made feasible in a short turnaround time because of the grid technology used. The second study shows how RNAVLab allows scientists to study the viral RNA genome replication mechanisms used by members of the virus family Nodaviridae.

Images with Uncertainty: Efficient Algorithms for Shift, Rotation, Scaling, and Registration, and Their Applications to Geosciences

• different images bring different information; so, to get a better understanding, we must fuse the corresponding data; e.g., we must combine a satellite images with a radar image; • comparison of two images – e.g., images made at different moments of time – can also give us information about the changes: e.g., by comparing preand post-earthquake images, we can determine the effect of the earthquake.

Discrete conservation of nonnegativity for elliptic problems solved by the hp-FEM

Most results related to discrete nonnegativity conservation principles (DNCP) for elliptic problems are limited to finite differences and lowest-order finite element methods (FEM). In this paper we show that a straightforward extension to higher-order finite element methods (hp-FEM) in the classical sense is not possible. We formulate a weaker DNCP for the Poisson equation in one spatial dimension and prove it using an interval computing technique. Numerical experiments related to the extension of this result to 2D are presented.

Automatic referencing of multi-spectral images

In order to adequately process satellite and radar information, it is necessary to find the exact correspondence between different types of images and between these images and existing maps. In other words, we need to reference these images. Automatic methods exist for referencing satellite images. These methods are based on using a fast Fourier transform (FFT). They work well because different images of the same area differ mainly by a shift and/or by a rotation. However, these methods do not work well when we attempt to reference radar images or satellite images with a road map because the corresponding images reflect different aspects of the geographic area. We propose new methods for automatic referencing of satellite and radar images to road maps.

Towards a cross-platform microbenchmark suite for evaluating hardware performance counter data

As useful as performance counters are, the meaning of reported aggregate event counts is sometimes questionable. Questions arise due to unanticipated processor behavior, overhead associated with the interface, the granularity of the monitored code, hardware errors, and lack of standards w.r.t. event definitions. To explore these issues, we are conducting a sequence of studies using carefully-crafted microbenchmarks that permit the accurate prediction of event counts and investigation of the differences between hardware-reported and predicted event counts. This paper presents the methodology employed, some of the microbenchmarks developed, and some of the information uncovered to date. The information provided by this work allows application developers to better understand the data provided by hardware performance counters and better utilize it to tune application performance. A goal of this research is to develop a cross-platform microbenchmark suite that can be used by application developers for these purposes. Some of the microbenchmarks in this suite are discussed in the paper.