Computer Sciences Commons^™

How To Detect Crisp Sets Based On Subsethood Ordering Of Normalized Fuzzy Sets? How To Detect Type-1 Sets Based On Subsethood Ordering Of Normalized Interval-Valued Fuzzy Sets?, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

If all we know about normalized fuzzy sets is which set is a subset of which, will we be able to detect crisp sets? It is known that we can do it if we allow all possible fuzzy sets, including non-normalized ones. In this paper, we show that a similar detection is possible if we only allow normalized fuzzy sets. We also show that we can detect type-1 fuzzy sets based on the subsethood ordering of normalized interval-valued fuzzy sets.

Towards Foundations Of Fuzzy Utility: Taking Fuzziness Into Account Naturally Leads To Intuitionistic Fuzzy Degrees, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

The traditional utility-based decision making theory assumes that for every two alternatives, the user is either absolutely sure that the first alternative is better, or that the second alternative is better, or that the two alternatives are absolutely equivalent. In practice, when faced with alternatives of similar value, people are often not fully sure which of these alternatives is better. To describe different possible degrees of confidence, it is reasonable to use fuzzy logic techniques. In this paper, we show that, somewhat surprisingly, a reasonable fuzzy modification of the traditional utility elicitation procedure naturally leads to intuitionistic fuzzy degrees.

How Many Monte-Carlo Simulations Are Needed To Adequately Process Interval Uncertainty: An Explanation Of The Smart Electric Grid-Related Simulation Results, Afshin Gholamy, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the possible ways of dealing with interval uncertainty is to use Monte-Carlo simulations. A recent study of using this technique for the analysis of different smart electric grid-related algorithms shows that we need approximately 500 simulations to compute the corresponding interval range with 5% accuracy. In this paper, we provide a theoretical explanation for these empirical results.

Measures Of Specificity Used In The Principle Of Justifiable Granularity: A Theoretical Explanation Of Empirically Optimal Selections, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To process huge amounts of data, one possibility is to combine some data points into granules, and then process the resulting granules. For each group of data points, if we try to include all data points into a granule, the resulting granule often becomes too wide and thus rather useless; on the other case, if the granule is too narrow, it includes only a few of the corresponding point -- and is, thus, also rather useless. The need for the trade-off between coverage and specificity is formalized as the principle of justified granularity. The specific form of this principle …

Parallelization And Scalability Analysis Of The \\[1pc] 3d Spatially Variant Lattice Algorithm, Henry Roger Moncada Lopez

Open Access Theses & Dissertations

The purpose of this research is to design a faster implementation of an algorithm to generate 3D spatially variant lattices (SVL) and improve its performance when it is running on a parallel computer system. The algorithm is used to synthesize a SVL for a periodic structure. The algorithm has the ability to spatially vary the unit cell, the orientation of the unit cells, lattice spacing, fill fraction, material composition, and lattice symmetry. The algorithm produces a lattice that is smooth, continuous and free of defects. The lattice spacing remains strikingly uniform even when the lattice is spatially varied. This is …

Deep Learning Models For Scoring Protein-Ligand Interaction Energies, Md Mahmudulla Hassan

Open Access Theses & Dissertations

In recent years, the cheminformatics community has seen an increased success with machine learning-based scoring functions for estimating binding affinities. The prediction of protein-ligand binding affinities is crucial for drug discovery research. Many physics-based scoring functions have been developed over the years. Lately, machine learning approaches are proven to boost the performance of traditional scoring functions. In this study, two scoring functions were developed; one is based on the Convolutional Neural Networks and the other one, called DLSCORE, is based on an ensemble of fully connected neural networks. Both the models were trained on the refined PDBbind (v.2016) dataset using …

Analysis Of High Performance Scientific Programming Workflows, Withana Kankanamalage Umayanganie Klaassen

Open Access Theses & Dissertations

Substantial time is spent on building, optimizing and maintaining large-scale software that is run on supercomputers. However, little has been done to utilize overall resources efficiently when it comes to including expensive human resources. The community is beginning to acknowledge that optimizing the hardware performance such as speed and memory bottlenecks contributes less to the overall productivity than does the development lifecycle of high-performance scientific applications. Researchers are beginning to look at overall scientific workflows for high performance computing. Scientific programming productivity is measured by time and effort required to develop, configure, and maintain a simulation experiment and its constituent …

Decision Making For Dynamic Systems Under Uncertainty: Predictions And Parameter Recomputations, Leobardo Valera

Open Access Theses & Dissertations

In this Thesis, we are interested in making decision over a model of a dynamic system. We want to know, on one hand, how the corresponding dynamic phenomenon unfolds under different input parameters (simulations). These simulations might help researchers to design devices with a better performance than the actual ones. On the other hand, we are also interested in predicting the behavior of the dynamic system based on knowledge of the phenomenon in order to prevent undesired outcomes. Finally, this Thesis is concerned with the identification of parameters of dynamic systems that ensure a specific performance or behavior.

Understanding the …

Estimating The Optimal Cutoff Point For Logistic Regression, Zheng Zhang

Open Access Theses & Dissertations

Binary classification is one of the main themes of supervised learning. This research is concerned about determining the optimal cutoff point for the continuous-scaled outcomes (e.g., predicted probabilities) resulting from a classifier such as logistic regression. We make note of the fact that the cutoff point obtained from various methods is a statistic, which can be unstable with substantial variation. Nevertheless, due partly to complexity involved in estimating the cutpoint, there has been no formal study on the variance or standard error of the estimated cutoff point.

In this Thesis, a bootstrap aggregation method is put forward to estimate the …

Forecasting Space Weather Using Deep Learning Techniques, Sumi None Dey

Open Access Theses & Dissertations

Solar activity gives rise to various kinds of space weather among which solar flares have serious detrimental eects on both near-Earth space and our upper atmosphere that will have consequent influence in our lives. For example, solar flares can damage satellite infrastructure, hinder power grids, disrupt Global Positioning Systems (GPS) and disrupt long-distance communication. Airplane pilots, cabin crew and astronauts can be aected by the harmful radiation released from the Sun. As a result, there is a need of a methodology to forecast space weather accurately. In this work, we have developed a deep learning architecture to do the short-range …

A Framework To Audit Scheduling Events In The Linux Operating System, Edward G. Hudgins

Open Access Theses & Dissertations

Soft real-time systems have responsiveness requirements that are desirable but not critical for operational effectiveness. This Thesis describes a new scheduler logging framework named "Integrated Process Scheduler Archiver" (IPSA) intended to assist with this analysis. Due to human sensitivity to interface delays on gesture-driven devices, mobile devices are a common case of soft-real time systems. Mobile systems generally do not incorporate real-time schedulers, but instead utilize over-provisioning and a variety of scheduling heuristics to generally provide acceptable responsiveness. These devices are highly multi-programmed Energy limitations on mobile limit the extent of overprovisioning, thereby increasing the sensitivity of system behavior to …

Tracking Topical Evolution In Large Document Collections, Sheikh Motahar Naim

Open Access Theses & Dissertations

A large document collection that builds up over time usually contains a number of different themes. All of these themes or topics are not equally important at the same time. One topic might have high probabilities in some years due to some relevant events, and low probabilities in other years. Analyzing the evolution of such topics has useful applications in a variety of domains, for example, helping researchers to quickly see the changes of research topics in an area, assisting intelligence agents in tracking the activities of a terrorist group, or monitoring damages caused by a natural disaster. In this …

Extraction Of Fiber Morphology From Sem Images For Quality Control Of Fiber Reinforced Composites Manufacturing, Md Fashiar Rahman

Open Access Theses & Dissertations

The morphology of fibers (e.g. spatial uniformity, orientation, and length) plays a decisive role in determining the material properties or fabrication quality of fiber-reinforced nanocomposites. Hence, determining the morphology becomes a very critical issue in the field of nanocomposite quality control. The conventional way of quality inspection is to take the scanning electron microscopic (SEM) images of the cross-section of composite material and do the visual checking of these SEM images to evaluate the nanofiber alignment and length distribution. But this type of inspection is often subjective, inaccurate and time consuming. Moreover, the extremely small size of nanofibers makes the …

Why Rectified Linear Neurons Are Efficient: Symmetry-Based, Complexity-Based, And Fuzzy-Based Explanations, Olac Fuentes, Justin Parra, Elizabeth Y. Anthony, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditionally, neural networks used a sigmoid activation function. Recently, it turned out that piecewise linear activation functions are much more efficient -- especially in deep learning applications. However, so far, there have been no convincing theoretical explanation for this empirical efficiency. In this paper, we show that, by using different uncertainty techniques, we can come up with several explanations for the efficiency of piecewise linear neural networks. The existence of several different explanations makes us even more confident in our results -- and thus, in the efficiency of piecewise linear activation functions.

How To Make A Proof Of Halting Problem More Convincing: A Pedagogical Remark, Benjamin W. Robertson, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

As an example of an algorithmically undecidable problem, most textbooks list the impossibility to check whether a given program halts on given data. A usual proof of this result is based on the assumption that the hypothetical halt-checker works for all programs. To show that a halt-checker is impossible, we design an auxiliary program for which the existence of such a halt-checker leads to a contradiction. However, this auxiliary program is usually very artificial. So, a natural question arises: what if we only require that the halt-checker work for reasonable programs? In this paper, we show that even with such …

Why Triangular Membership Functions Are Often Efficient In F-Transform Applications: Relation To Interval Uncertainty\\ And Haar Wavelets, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy techniques describe expert opinions. At first glance, we would therefore expect that the more accurately the corresponding membership functions describe the expert's opinions, the better the corresponding results. In practice, however, contrary to these expectations, the simplest -- and not very accurate -- triangular membership functions often work the best. In this paper, on the example of the use of membership functions in F-transform techniques, we provide a possible theoretical explanation for this surprising empirical phenomenon.

How To Store Tensors In Computer Memory: An Observation, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, after explaining the need to use tensors in computing, we analyze the question of how to best store tensors in computer memory. Somewhat surprisingly, with respect to a natural optimality criterion, the standard way of storing tensors turns out to be one of the optimal ones.

Beyond Integration: A Symmetry-Based Approach To Reaching Stationarity In Economic Time Series, Songsak Sriboonchitta, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Many efficient data processing techniques assume that the corresponding process is stationary. However, in areas like economics, most processes are not stationery: with the exception of stagnation periods, economies usually grow. A known way to apply stationarity-based methods to such processes -- integration -- is based on the fact that often, while the process itself is not stationary, its first or second differences are stationary. This idea works when the trend polynomially depends on time. In practice, the trend is usually non-polynomial: it is often exponentially growing, with cycles added. In this paper, we shod how integration techniques can be …

Why Sparse?, Thongchai Dumrongpokaphan, Olga Kosheleva, Vladik Kreinovich, Aleksandra Belina

Departmental Technical Reports (CS)

In many situations, a solution to a practical problem is sparse, i.e., corresponds to the case when most of the parameters describing the solution are zeros, and only a few attain non-zero values. This surprising empirical phenomenon helps solve the corresponding problems -- but it remains unclear why this phenomenon happens. In this paper, we provide a possible theoretical explanation for this mysterious phenomenon.

Z-Numbers: How They Describe Student Confidence And How They Can Explain (And Improve) Laplacian And Schroedinger Eigenmap Dimension Reduction In Data Analysis, Vladik Kreinovich, Olga Kosheleva, Michael Zakharevich

Departmental Technical Reports (CS)

Experts have different degrees of confidence in their statements. To describe these different degrees of confidence, Lotfi A. Zadeh proposed the notion of a Z-number: a fuzzy set (or other type of uncertainty) supplemented by a degree of confidence in the statement corresponding to fuzzy sets. In this chapter, we show that Z-numbers provide a natural formalization of the competence-vs-confidence dichotomy, which is especially important for educating low-income students. We also show that Z-numbers provide a natural theoretical explanation for several empirically heuristic techniques of dimension reduction in data analysis, such as Laplacian and Schroedinger eigenmaps, and, moreover, show how …

Why Taylor Models And Modified Taylor Models Are Empirically Successful: A Symmetry-Based Explanation, Mioara Joldes, Christoph Lauter, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we show that symmetry-based ideas can explain the empirical success of Taylor models and modified Taylor models in representing uncertainty.

How To Best Apply Neural Networks In Geosciences: Towards Optimal "Averaging" In Dropout Training, Afshin Gholamy, Justin Parra, Vladik Kreinovich, Olac Fuentes, Elizabeth Y. Anthony

Departmental Technical Reports (CS)

The main objectives of geosciences is to find the current state of the Earth -- i.e., solve the corresponding inverse problems -- and to use this knowledge for predicting the future events, such as earthquakes and volcanic eruptions. In both inverse and prediction problems, often, machine learning techniques are very efficient, and at present, the most efficient machine learning technique is deep neural training. To speed up this training, the current learning algorithms use dropout techniques: they train several sub-networks on different portions of data, and then "average" the results. A natural idea is to use arithmetic mean for this …

Why Deep Learning Methods Use Kl Divergence Instead Of Least Squares: A Possible Pedagogical Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In most applications of data processing, we select the parameters that minimize the mean square approximation error. The same Least Squares approach has been used in the traditional neural networks. However, for deep learning, it turns out that an alternative idea works better -- namely, minimizing the Kullback-Leibler (KL) divergence. The use of KL divergence is justified if we predict probabilities, but the use of this divergence has been successful in other situations as well. In this paper, we provide a possible explanation for this empirical success. Namely, the Least Square approach is optimal when the approximation error is normally …

Sudoku App: Model-Driven Development Of Android Apps Using Ocl?, Yoonsik Cheon, Aditi Barua

Departmental Technical Reports (CS)

Model driven development (MDD) shifts the focus of software development from writing code to building models by developing an application as a series of transformations on models including eventual code generation. Can the key ideas of MDD be applied to the development of Android apps, one of the most popular mobile platforms of today? To answer this question, we perform a small case study of developing an Android app for playing Sudoku puzzles. We use the Object Constraint Language (OCL) as the notation for creating precise models and translate OCL constraints to Android Java code. Our findings are mixed in …

Propagation Of Probabilistic Uncertainty: The Simplest Case (A Brief Pedagogical Introduction), Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The main objective of this text is to provide a brief introduction to formulas describing the simplest case of propagation of probabilistic uncertainty -- for students who have not yet taken a probability course.

Impacts Of Java Language Features On The Memory Performances Of Android Apps, Yoonsik Cheon, Adriana Escobar De La Torre

Departmental Technical Reports (CS)

Android apps are written in Java, but unlike Java applications they are resource-constrained in storage capacity and battery lifetime. In this document, we perform an experiment to measure quantitatively the impact of Java language and standard API features on the memory efficiency of Android apps. We focus on garbage collection because it is a critical process for performance affecting user experience. We learned that even Java language constructs and standard application programming interfaces (APIs) may be a source of a performance problem causing a significant memory overhead for Android apps. Any critical section of code needs to be scrutinized on …

Need For A Large-N Array (And Wavelets And Differences) To Determine The Assumption-Free 3-D Earth Model, Solymar Ayala Cortez, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main objectives of geophysical seismic analysis is to determine the Earth's structure. Usually, to determine this structure, geophysicists supplement the measurement results with additional geophysical assumptions. An important question is: when is it possible to reconstruct the Earth's structure uniquely based on the measurement results only, without the need to use any additional assumptions? In this paper, we show that for this, one needs to use large-N arrays -- 2-D arrays of seismic sensors. To actually perform this reconstruction, we need to use differences between measurements by neighboring sensor and we need to apply wavelet analysis to …

Efficient Parameter-Estimating Algorithms For Symmetry-Motivated Models: Econometrics And Beyond, Vladik Kreinovich, Anh H. Ly, Olga Kosheleva, Songsak Sriboonchitta

Departmental Technical Reports (CS)

It is known that symmetry ideas can explain the empirical success of many non-linear models. This explanation makes these models theoretically justified and thus, more reliable. However, the models remain non-linear and thus, identification or the model's parameters based on the observations remains a computationally expensive nonlinear optimization problem. In this paper, we show that symmetry ideas can not only help to select and justify a nonlinear model, they can also help us design computationally efficient almost-linear algorithms for identifying the model's parameters.

How To Use Absolute-Error-Minimizing Software To Minimize Relative Error: Practitioner's Guide, Afshin Gholamy, Vladik Kreinovich

Departmental Technical Reports (CS)

In many engineering and scientific problems, there is a need to find the parameters of a dependence from the experimental data. There exist several software packages that find the values for these parameters -- values for which the mean square value of the absolute approximation error is the smallest. In practice, however, we are often interested in minimizing the mean square value of the relative approximation error. In this paper, we show how we can use the absolute-error-minimizing software to minimize the relative error.

Practical Need For Algebraic (Equality-Type) Solutions Of Interval Equations And For Extended-Zero Solutions, Ludmila Dymova, Pavel Sevastjanov, Andrzej Pownuk, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main problems in interval computations is solving systems of equations under interval uncertainty. Usually, interval computation packages consider united, tolerance, and control solutions. In this paper, we explain the practical need for algebraic (equality-type) solutions, when we look for solutions for which both sides are equal. In situations when such a solution is not possible, we provide a justification for extended-zero solutions, in which we ignore intervals of the type [−a, a].