Computer Sciences Commons^™

Numerical Design And Optimization Of Near-Infrared Band- Pass Filter, Hafiza Syeeda Faiza, Ghazi Aman Nowsherwan, Basem A. Abu Izneid, Muhammad Azhar, Saira Riaz, Syed Sajjad Hussain, Saira Ikram, Mohsin Khan, Shahzad Naseem, Mohammad Kanan, Ibrahim M. Mansour

Applied Mathematics & Information Sciences

Band-pass filters functioning in the near-infrared (IR) range are desired for laser technology, multi-photon fluorescence, and IR imaging applications. In this study, we have designed four band-pass filters in the near Infrared spectrum (900-1200 nm) by vertically stacking different high and low-index materials. The band-pass filters are modelled by Essential Macleod software with different thicknesses. The layer’s thicknesses were optimized in such a way to provide the negligible reflectance and maximum transmission on the front side. All the simulated band-pass filters exhibit high transmittance, but TiO2/Al2O3 and Ta2O5/Al2O3 outperforms other modelled structure in terms of performance due to the better …

How To Make Decision Under Interval Uncertainty: Description Of All Reasonable Partial Orders On The Set Of All Intervals, Tiago M. Costa, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we need to make a decision while for each alternative, we only know the corresponding value of the objective function with interval uncertainty. To help a decision maker in this situation, we need to know the (in general, partial) order on the set of all intervals that corresponds to the preferences of the decision maker. For this purpose, in this paper, we provide a description of all such partial orders -- under some reasonable conditions. It turns out that each such order is characterized by two linear inequalities relating the endpoints of the corresponding intervals, and …

Which Fuzzy Implications Operations Are Polynomial? A Theorem Proves That This Can Be Determined By A Finite Set Of Inequalities, Sebastia Massanet, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To adequately represent human reasoning in a computer-based systems, it is desirable to select fuzzy operations that are as close to human reasoning as possible. In general, every real-valued function can be approximated, with any desired accuracy, by polynomials; it is therefore reasonable to use polynomial fuzzy operations as the appropriate approximations. We thus need to select, among all polynomial operations that satisfy corresponding properties -- like associativity -- the ones that best fit the empirical data. The challenge here is that properties like associativity mean satisfying infinitely many constraints (corresponding to infinitely many possible triples of values), while most …

Fuzzy Mathematics Under Non-Minimal "And"-Operations (T-Norms): Equivalence Leads To Metric, Order Leads To Kinematic Metric, Topology Leads To Area Or Volume, Purbita Jana, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Most formulas analyzed in fuzzy mathematics assume -- explicitly or implicitly -- that the corresponding "and"-operation (t-norm) is the simplest minimum operation. In this paper, we analyze what happens if instead, we use other "and"-operations. It turns out that for such operations, a fuzzification of a mathematical theory naturally leads to a more complex mathematical setting: fuzzification of equivalence relation leads to metric, fuzzification of order leads to kinematic metric, and fuzzification of topology leads to area or volume.

Why Deep Learning Is Under-Determined? Why Usual Numerical Methods For Solving Partial Differential Equations Do Not Preserve Energy? The Answers May Be Related To Chevalley-Warning Theorem (And Thus To Fermat Last Theorem), Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we provide a possible explanation to two seemingly unrelated phenomena: (1) that in deep learning, under-determined systems of equations perform much better than the over-determined one -- which are typical in data processing, and that (2) usual numerical methods for solving partial differential equations do not preserve energy. Our explanation is related to the intuition of Fermat behind his Last Theorem and of Euler about more general statements, intuition that led to the proof of Chevalley-Warning Theorem in number theory.

Methodological Lesson Of Pythagorean Triples, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

There are many right triangles in which all three sides a, b, and c have integer lengths. The triples (a,b,c) formed by such lengths are known as Pythagorean triples. Since ancient times, it is known how to generate all Pythagorean triples: we can enumerate primitive Pythagorean triples -- in which the three numbers have no common divisors -- by considering all pairs of natural numbers m>n in which m and n have no common divisors, and taking a =m2 − n2, b = 2mn, and c = m2 + n2. Multiplying all elements of a triple by the same …

Why Resilient Modulus Is Proportional To The Square Root Of Unconfined Compressive Strength (Ucs): A Qualitative Explanation, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

The strength of the pavement is determine by its resilient modulus, i.e., by its ability to withstand (practically) instantaneous stresses caused by the passing traffic. However, the resilient modulus is not easy to measure: its measurement requires a special expensive equipment that many labs do not have. So, instead of measuring it, practitioners often measure easier-to-measure Unconfined Compressive Strength (UCS) -- that describes the effect of a continuously applied force -- and estimate the resilient modulus based on the result of this measurement. An empirical formula shows that the resilient modulus is proportional to the square root of the Unconfined …

How To Estimate Unknown Unknowns: From Cosmic Light To Election Polls, Talha Azfar, Vignesh Ponraj, Vladik Kreinovich, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

In two different areas of research -- in the study of space light and in the study of voting -- the observed value of the quantity of interest is twice larger than what we would expect. That the observed value is larger makes perfect sense: there are phenomena that we do not take into account in our estimations. However, the fact that the observed value is exactly twice larger deserves explanation. In this paper, we show that Laplace Indeterminacy Principle leads to such an explanation.

How To Combine Probabilistic And Fuzzy Uncertainty: Theoretical Explanation Of Clustering-Related Empirical Result, Lázló Szilágyi, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In contrast to crisp clustering techniques that assign each object to a class, fuzzy clustering algorithms assign, to each object and to each class, a degree to which this object belongs to this class. In the most widely used fuzzy clustering algorithm -- fuzzy c-means -- for each object, degrees corresponding to different classes add up to 1. From this viewpoint, these degrees act as probabilities. There exist alternative fuzzy-based clustering techniques in which, in line with the general idea of the fuzzy set, the largest of the degrees is equal to 1. In some practical situations, the probability-type fuzzy …

Fuzzy Techniques Explain The Effectiveness Of Relu Activation Function In Deep Learning, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the last decades, deep learning has led to spectacular successes. One of the reasons for these successes was the fact that deep neural networks use a special Rectified Linear Unit (ReLU) activation function s(x) = max(0,x). Why this activation function is so successful is largely a mystery. In this paper, we show that common sense ideas -- as formalized by fuzzy logic -- can explain this mysterious effectiveness.

Why 6-Labels Uncertainty Scale In Geosciences: Probability-Based Explanation, Aaron Velasco, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To describe uncertainty in geosciences, several researchers have recently proposed a 6-labels uncertainty scale, in which one the labels corresponds to full certainty, one label to the absence of any knowledge, and the remaining four labels correspond to the degrees of confidence from the intervals [0,0.25], [0.25,0.5], [0.5,0.75], and [0.75,1]. Tests of this 6-labels scale indicate that it indeed conveys uncertainty information to geoscientists much more effectively than previously proposed uncertainty schemes. In this paper, we use probability-related techniques to explain this effectiveness.

Complex Numbers Explain Why In Chinese Tradition, 4 Is Bad But 8 Is Good, Luc Longpre, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the traditional Chinese culture, 4 is considered to be an unlucky number, while the number 8 is considered to be very lucky. In this paper, we show that both "badness" and "goodness" can be explained if we take into account the role of complex numbers in the analysis of general dynamical systems.

Why Bump Reward Function Works Well In Training Insulin Delivery Systems, Lehel Dénes-Fazakas, Lásló Szilágyi, Gyorgy Eigner, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

Diabetes is a disease when the body can no longer properly regulate blood glucose level, which can lead to life-threatening situations. To avoid such situations and regulate blood glucose level, patients with severe form of diabetes need insulin injections. Ideally, the system should automatically decide when best to inject insulin and how much to inject. To find the optimal control, researchers applied machine learning with different reward functions. It turns out that the most effective learning occurred when they used the so-called bump function. In this paper, we provide a possible explanation for this empirical result.

We Can Always Reduce A Non-Linear Dynamical System To Linear -- At Least Locally -- But Does It Help?, Orsolya Csiszar, Gábor Csiszar, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

Many real-life phenomena are described by dynamical systems. Sometimes, these dynamical systems are linear. For such systems, solutions are well known. In some cases, it is possible to transform a nonlinear system into a linear one by appropriately transforming its variables, and this helps to solve the original nonlinear system. For other nonlinear systems -- even for the simplest ones -- such transformation is not known. A natural question is: which nonlinear systems allow such transformations? In this paper, we show that we can always reduce a nonlinear system to a linear one -- but, in general, it does not …

What Was More Frequently Used -- "And" Or "Or": Based On Analysis Of European Languages, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional logic has two main connectives: "and" and "or". A natural question is: which of the two is more frequently used? This question is easy to answer for the current usage of these connectives -- we can simply analyze all the texts, but what can we say about the past usage? To answer this question, we use the known linguistics fact that, in general, notions that are more frequently used are described by shorter words. It turns out that in most European languages, the word for "and" is shorter -- or of the same length -- as the word for …

How To Propagate Interval (And Fuzzy) Uncertainty: Optimism-Pessimism Approach, Vinícius F. Wasques, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, inputs to a data processing algorithm are known with interval uncertainty, and we need to propagate this uncertainty through the algorithm, i.e., estimate the uncertainty of the result of data processing. Traditional interval computation techniques provide guaranteed estimates, but from the practical viewpoint, these bounds are too pessimistic: they take into account highly improbable worst-case situations when all the measurement and estimation errors happen to be strongly correlated. In this paper, we show that a natural idea of having more realistic estimates leads to the use of so-called interactive addition of intervals, techniques that has already …

Numerical Simulation Of The Korteweg–De Vries Equation With Machine Learning, Kristina O. F. Williams, Benjamin F. Akers

Faculty Publications

A machine learning procedure is proposed to create numerical schemes for solutions of nonlinear wave equations on coarse grids. This method trains stencil weights of a discretization of the equation, with the truncation error of the scheme as the objective function for training. The method uses centered finite differences to initialize the optimization routine and a second-order implicit-explicit time solver as a framework. Symmetry conditions are enforced on the learned operator to ensure a stable method. The procedure is applied to the Korteweg–de Vries equation. It is observed to be more accurate than finite difference or spectral methods on coarse …

Computation Offloading Design For Deep Neural Network Inference On Iot Devices, Asmika Boosarapu

Theses and Dissertations

In recent times, advances in the technologies of Internet-of-Things (IoT) and Deep Neural Networks (DNN) have significantly increased the accuracy and speed of a variety of smart applications. However, one of the barriers to deploying DNN to IoT is the computational limitations of IoT devices as compared with the computationally expensive task of DNN inference. Computation offloading is an approach that addresses this problem by offloading DNN computation tasks to cloud servers. In this thesis we propose a collaborative computation offloading solution, in which some of the work is done on the IoT device, and the remainder of the work …

Which Activation Function Works Best For Training Artificial Pancreas: Empirical Fact And Its Theoretical Explanation, Lehel Dénes-Fazakas, Lásló Szilágyi, György Eigner, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the most effective ways to help patients at the dangerous levels of diabetes is an artificial pancreas, a device that constantly monitors the patient's blood sugar level and injects insulin based on this level. Patient's reaction to insulin is highly individualized, so the artificial pancreas needs to be trained on each patient. It turns out that the best training results are attained when instead of the usual ReLU neurons, we use their minor modification known as Exponential Linear Units (ELU). In this paper, we provide a theoretical explanation for the empirically observed effectiveness of ELUs.

Dialogs Re-Enacted Across Languages, Version 2, Nigel G. Ward, Jonathan E. Avila, Emilia Rivas, Divette Marco

Departmental Technical Reports (CS)

To support machine learning of cross-language prosodic mappings and other ways to improve speech-to-speech translation, we present a protocol for collecting closely matched pairs of utterances across languages, a description of the resulting data collection and its public release, and some observations and musings. This report is intended for:

• people using this corpus
• people extending this corpus
• people designing similar collections of bilingual dialog data.

Change Notes. This version supersedes UTEP-CS-22-108. There is some new information and numerous clarifications, mostly arising from our experiences diversifying our corpus and helping a vendor to use this protocol.

Natural Color Interpretation Of Interval-Valued Fuzzy Degrees, Victor L. Timchenko, Yury P. Kondratenko, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

Intuitively, interval-values fuzzy degrees are more adequate for representing expert uncertainty than the traditional [0,1]-based ones. Indeed, the very need for fuzzy degrees comes from the fact that experts often cannot describe their opinion not in terms of precise numbers, but by using imprecise ("fuzzy") words from natural language like "small". In such situations, it is strange to expect the same expert to be able to provide an exact number describing his/her degree of certainty; it is more natural to ask this expert to mark the whole interval (or even, more generally, a fuzzy set of possible degrees). In spite …

Logical Inference Inevitably Appears: Fuzzy-Based Explanation, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich, Orsolya Csiszar

Departmental Technical Reports (CS)

Many thousands years ago, our primitive ancestors did not have the ability to reason logically and to perform logical inference. This ability appeared later. A natural question is: was this appearance inevitable -- or was this a lucky incident that could have been missed? In this paper, we use fuzzy techniques to provide a possible answer to this question. Our answer is: yes, the appearance of logical inference in inevitable.

Is Fully Explainable Ai Even Possible: Fuzzy-Based Analysis, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main limitations of many current AI-based decision-making systems is that they do not provide any understandable explanations of how they came up with the produced decision. Taking into account that these systems are not perfect, that their decisions are sometimes far from good, the absence of an explanation makes it difficult to separate good decisions from suspicious ones. Because of this, many researchers are working on making AI explainable. In some applications areas -- e.g., in chess -- practitioners get an impression that there is a limit to understandability, that some decisions remain inhuman -- not explainable. …

Why Fuzzy Control Is Often More Robust (And Smoother): A Theoretical Explanation, Orsolya Csiszar, Gábor Csiszar, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, practitioners use easier-to-compute fuzzy control to approximate the more-difficult-co-compute optimal control. As expected, for many characteristics, this approximate control is slightly worse than the optimal control it approximates, However, with respect to robustness or smoothness, the approximating fuzzy control is often better than the original one. In this paper, we provide a theoretical explanation for this somewhat mysterious empirical phenomenon.

Why Softmax? Because It Is The Only Consistent Approach To Probability-Based Classification, Anatole Lokshin, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical problems, the most effective classification techniques are based on deep learning. In this approach, once the neural network generates values corresponding to different classes, these values are transformed into probabilities by using the softmax formula. Researchers tried other transformation, but they did not work as well as softmax. A natural question is: why is softmax so effective? In this paper, we provide a possible explanation for this effectiveness: namely, we prove that softmax is the only consistent approach to probability-based classification. In precise terms, it is the only approach for which two reasonable probability-based ideas -- Least …

Selecting The Most Adequate Fuzzy Operation For Explainable Ai: Empirical Fact And Its Possible Theoretical Explanation, Orsolya Csiszar, Gábor Csiszar, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

A reasonable way to make AI results explainable is to approximate the corresponding deep-learning-generated function by a simple expression formed by fuzzy operations. Experiments on real data show that out of all easy-to-compute fuzzy operations, the best approximation is attained if we use an operation a + b − 0.5 ( limited to the interval [0,1]$. In this paper, we provide a possible theoretical explanation for this empirical result.

(R2051) Analysis Of Map/Ph1, Ph2/2 Queueing Model With Working Breakdown, Repairs, Optional Service, And Balking, G. Ayyappan, G. Archana

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a classical queueing system with two types of heterogeneous servers has been considered. The Markovian Arrival Process (MAP) is used for the customer arrival, while phase type distribution (PH) is applicable for the offering of service to customers as well as the repair time of servers. Optional service are provided by the servers to the unsatisfied customers. The server-2 may get breakdown during the busy period of any type of service. Though the server- 2 got breakdown, server-2 has a capacity to provide the service at a slower rate to the current customer who is receiving service …

Deep Learning Recommendations For The Acl2 Interactive Theorem Prover, Robert K. Thompson, Robert K. Thompson

Master's Theses

Due to the difficulty of obtaining formal proofs, there is increasing interest in partially or completely automating proof search in interactive theorem provers. Despite being a theorem prover with an active community and plentiful corpus of 170,000+ theorems, no deep learning system currently exists to help automate theorem proving in ACL2. We have developed a machine learning system that generates recommendations to automatically complete proofs. We show that our system benefits from the copy mechanism introduced in the context of program repair. We make our system directly accessible from within ACL2 and use this interface to evaluate our system in …

A Survey On Online Matching And Ad Allocation, Ryan Lee

Theses

One of the classical problems in graph theory is matching. Given an undirected graph, find a matching which is a set of edges without common vertices. In 1990s, Richard Karp, Umesh Vazirani, and Vijay Vazirani would be the first computer scientists to use matchings for online algorithms [8]. In our domain, an online algorithm operates in the online setting where a bipartite graph is given. On one side of the graph there is a set of advertisers and on the other side we have a set of impressions. During the online phase, multiple impressions will arrive and the objective of …

Using Deep Neural Networks To Classify Astronomical Images, Andrew D. Macpherson

Honors Projects

As the quantity of astronomical data available continues to exceed the resources available for analysis, recent advances in artificial intelligence encourage the development of automated classification tools. This paper lays out a framework for constructing a deep neural network capable of classifying individual astronomical images by describing techniques to extract and label these objects from large images.