Physical Sciences and Mathematics Commons^™

An Approach To Predicting Performance Of Sparse Computations On Nvidia Gpus, Rogelio Long

Open Access Theses & Dissertations

Sparse problems arise from a variety of applications, from scientific simulations to graph analytics. Traditional HPC systems have failed to effectively provide high bandwidth for sparse problems. This limitation is primarily because of the nature of sparse computations and their irregular memory access patterns.We predict the performance of sparse computations given an input matrix and GPU hardware characteristics. This prediction is done by identifying hardware bottlenecks in modern NVIDIA GPUs using roofline trajectory models. Roofline trajectory models give us insight into the performance by simultaneously showing us the effects of strong and weak scaling. We then create regression models for …

Hardware For Quantized Mixed-Precision Deep Neural Networks, Andres Rios

Open Access Theses & Dissertations

Recently, there has been a push to perform deep learning (DL) computations on the edge rather than the cloud due to latency, network connectivity, energy consumption, and privacy issues. However, state-of-the-art deep neural networks (DNNs) require vast amounts of computational power, data, and energyâ??resources that are limited on edge devices. This limitation has brought the need to design domain-specific architectures (DSAs) that implement DL-specific hardware optimizations. Traditionally DNNs have run on 32-bit floating-point numbers; however, a body of research has shown that DNNs are surprisingly robust and do not require all 32 bits. Instead, using quantization, networks can run on …

Study Of Weakly Bound Cluster Anions Using Self Interaction Corrected Density Functional Scheme, Peter Obinna Ufondu

Open Access Theses & Dissertations

The Kohn–Sham formulation of density functional theory (DFT) is a widely used quantum mechanical theory to study chemical and materials properties. The practical application of DFT requires an approximation to the exchange–correlation (XC) functional. These approximations suffer from self-interaction errors due to the incomplete cancellation of the self-Coulomb energy with the approximate self-exchange and correlation energy for one-electron densities. Systems with weakly-bound electrons impose great challenges to semi-local density functional approximations. We use recently developed local scaled self-interaction correction (LSIC) by Zope et al and the Perdew-Zunger SIC method using the Fermi-Löwdin orbitals to calculate the vertical detachment energies (VDEs) …

What Fuzzy And Quantum Computing Can Learn From The Success Of Deep Learning, Shahnaz Shahbazova, Vladik Kreinovich

Departmental Technical Reports (CS)

How can we apply the ideas that made deep neural networks successful to other aspects of computing? For this purpose, we reformulate these ideas in a more general form -- and we show that this generalization also covers fuzzy and quantum computing. This enables us to suggest that similar ideas can be helpful for fuzzy and quantum computing as well. In this suggestion, we are encouraged by the fact that as we show, to some extent, these ideas are already helpful.

Why Quantum Techniques Are A Good First Approximation To Economic Phenomena, And What Next, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

Somewhat surprisingly, several formulas of quantum physics -- the physics of micro-world -- provide a good first approximation to many social phenomena, in particular, to many economic phenomena, phenomena which are very far from micro-physics. In this paper, we provide three possible explanations for this surprising fact. First, we show that several formulas from quantum physics actually provide a good first-approximation description for many phenomena in general, not only to the phenomena of micro-physics. Second, we show that some quantum formulas represent the fastest way to compute nonlinear dependencies and thus, naturally appear when we look for easily computable models; …

What Is The Uncertainty Of The Result Of Data Processing: Fuzzy Analogue Of The Central Limit Theorem, Julio C. Urenda, Olga Kosheleva, Shahnaz Shahbazova, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that, due to the Central Limit Theorem, the probability distribution of the uncertainty of the result of data processing is, in general, close to Gaussian -- or to a distribution from a somewhat more general class known as infinitely divisible. We show that a similar result holds in the fuzzy case: namely, the membership function describing the uncertainty of the result of data processing is, in general, close to Gaussian -- or to a membership function from an explicitly described more general class.

"Negative" Results -- When The Measured Quantity Is Outside The Sensor's Range -- Can Help Data Processing, Jonatan Contreras, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich, Martine Ceberio

Departmental Technical Reports (CS)

In many real-life situations, we know the general form of the dependence y = f(x, c₁, ..., c_m) between physical quantities, but the values need to be determined experimentally, based on the results of measuring x and y. In some cases, we do not get any result of measuring y since the actual value is outside the range of the measuring instrument. Usually, such cases are ignored. In this paper, we show that taking these cases into account can help data processing -- by improving the accuracy of our estimates of c_i and thus, …

So How To Make Group Decisions? Arrow's Impossibility Theorem 70 Years After, Hung T. Nguyen, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In 1951, Kenneth Arrow proved that it is not possible to have a group decision making procedure that satisfies reasonable requirements like fairness. From the theoretical viewpoint, this is a great result -- well-deserving the Nobel Prize that was awarded to Professor Arrow. However, from the practical viewpoint, the question remains -- so how should we make group decisions? A usual way to solve this problem is to provide some reasonable heuristic ideas, but the problem is that different seemingly reasonable idea often lead to different group decision -- this is known, e.g., for different voting schemes. In this paper, …

Invariance-Based Approach: General Methods And Pavement Engineering Case Study, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In many application areas such as pavement engineering, the phenomena are complex, and as a result, we do not have first-principle models describing the corresponding dependencies. Luckily, in many such areas, there is a lot of empirical data and, based on this data, many useful empirical dependencies have been found. The problem is that since many of these dependencies do not have a theoretical explanation, practitioners are often hesitant to use them: there have been many cases when an empirical formula stops being valid when circumstances change. To make the corresponding empirical formulas more reliable, it is therefore desirable to …

How General Is Fuzzy Decision Making?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, users describe their preferences in imprecise (fuzzy) terms. In such situations, fuzzy techniques are a natural way to describe these preferences in precise terms.

Of course, this description is only an approximation to the ideal decision making that a person would perform if we took time to elicit his/her exact preferences. How accurate is this approximation? When can fuzzy decision making -- potentially -- describe the exact decision making, and when there is a limit to the accuracy of fuzzy approximations?

In this paper, we show that decision making can be precisely described in fuzzy terms …

Why Dilated Convolutional Neural Networks: A Proof Of Their Optimality, Jonatan Contreras, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the most effective image processing techniques is the use of convolutional neural networks that use convolutional layers. In each such layer, the value of the output at each point is a combination of input data corresponding to several neighboring points. To improve the accuracy, researchers have developed a version of this technique, in which only data from some of the neighboring points is processed. It turns out that the most efficient case -- called dilated convolution -- is when we select the neighboring points whose differences in both coordinates are divisible by some constant l. In this paper, …

Why Cauchy Membership Functions: Efficiency, Javier Viana, Stephan Ralescu, Kelly Cohen, Anca Ralescu, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy techniques depend heavily on eliciting meaningful membership functions for the fuzzy sets used. Often such functions are obtained from data. Just as often they are obtained from experts knowledgable of the domain and the problem being addressed. However, there are cases when neither is possible, for example because of insufficient data, or unavailable experts. What functions should one choose and what should guide such choice? This paper argues in favor of using Cauchy membership functions, thus named because their expression is similar to that of the Cauchy distributions. The paper provides a theoretical explanation for this choice.

Green Computing: Three Examples Of How Non-Trivial Mathematical Analysis Can Help, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Environment-related problems are extremely important for mankind, the fate of humanity itself depends on our ability to solve these problems. These problems are complex, we cannot solve them without using powerful computers. Thus, in the environmental research, environment-related computing is one of the main computing-related research directions. Another direction is related to the fact that computing itself can be (and currently is) harmful for the environment. How to make computing more environment-friendly, how to move towards green computing -- this is the second important direction. A third direction is motivated by the very complexity of environmental systems: it is difficult …

Why Rectified Linear Neurons: Two Convexity-Related Explanations, Jonatan Contreras, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

At present, the most efficient machine learning technique is deep learning, in which non-linearity is attained by using rectified linear functions s(x)=max(0,x). Empirically, these functions work better than any other nonlinear functions that have been tried. In this paper, we provide a possible theoretical explanation for this empirical fact. This explanation is based on the fact that one of the main applications of neural networks is decision making, when we want to find an optimal solution. We show that the need to adequately deal with situations when the corresponding optimization problem is feasible -- i.e., for which the objective function …

Is It Fair That Advanced Workers Get Paid Disproportionally More: Economic Analysis, Olga Kosheleva, Sean R. Aguilar

Departmental Technical Reports (CS)

On the one hand, everyone agrees that economics should be fair, that workers should get equal pay for equal work. Any instance of unfairness causes a strong disagreement. On the other hand, in many companies, advanced workers -- who produce more than others -- get paid dispropotionally more for their work, and this does not seem to cause any negative feelings. In this paper, we analyze this situation from the economic viewpoint. We show that from this viewpoint, additional payments for advanced workers indeed make economic sense, benefit everyone, and thus -- in contrast to the naive literal interpretation of …

Many Known Quantum Algorithms Are Optimal: Symmetry-Based Proofs, Vladik Kreinovich, Oscar Galindo, Olga Kosheleva

Departmental Technical Reports (CS)

Many quantum algorithms have been proposed which are drastically more efficient that the best of the non-quantum algorithms for solving the same problems. A natural question is: are these quantum algorithms already optimal -- in some reasonable sense -- or they can be further improved? In this paper, we review recent results showing that many known quantum algorithms are actually optimal. Several of these results are based on appropriate invariances (symmetries).

How To Extend Interval Arithmetic So That Inverse And Division Are Always Defined, Tahea Hossain, Jonathan Rivera, Yash Sharma, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life data processing situations, we only know the values of the inputs with interval uncertainty. In such situations, it is necessary to take this interval uncertainty into account when processing data. Most existing methods for dealing with interval uncertainty are based on interval arithmetic, i.e., on the formulas that describe the range of possible values of the result of an arithmetic operation when the inputs are known with interval uncertainty. For most arithmetic operations, this range is also an interval, but for division, the range is sometimes a disjoint union of two semi-infinite intervals. It is therefore desirable …

Fuzzy Logic Beyond Traditional "And"-Operations, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In the traditional fuzzy logic, we can use "and"-operations (also known as t-norms) to estimate the expert's degree of confidence in a composite statement A&B based on his/her degrees of confidence d(A) and d(B) in the corresponding basic statements A and B. But what if we want to estimate the degree of confidence in A&B&C in situations when, in addition to the degrees of estimate d(A), d(B), and d(C) of the basic statements, we also know the expert's degrees of confidence in the pairs d(A&B), d(A&C), and d(B&C)? Traditional ``and''-operations can provide such an estimate -- but only by ignoring …

Why Kappa Regression?, Julio C. Urenda, Orsolya Csiszár, József Dombi, György Eigner, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A recent book provide examples that a new class of probability distributions and membership functions -- called kappa-regression distributions and membership functions -- leads to better data processing results than using previously known classes. In this paper, we provide a theoretical explanation for this empirical success -- namely, we show that these distributions are the only ones that satisfy reasonable invariance requirements.

Fuzzy Techniques, Laplace Indeterminacy Principle, And Maximum Entropy Approach Explain Lindy Effect And Help Avoid Meaningless Infinities In Physics, Julio C. Urenda, Sean R. Aguilar, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life situations, the only information that we have about some quantity S is a lower bound T ≤ S. In such a situation, what is a reasonable estimate for S? For example, we know that a company has survived for T years, and based on this information, we want to predict for how long it will continue surviving. At first glance, this is a type of a problem to which we can apply the usual fuzzy methodology -- but unfortunately, a straightforward use of this methodology leads to a counter-intuitive infinite estimate for S. There is an empirical …

Godel's Proof Of Existence Of God Revisited, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In his unpublished paper, the famous logician Kurt Godel provided arguments in favor of the existence of God. These arguments are presented in a very formal way, which makes them difficult to understand to many interested readers. In this paper, we describe a simplifying modification of Godel's proof which will hopefully make it easier to understand. We also describe, in clear terms, why Godel's arguments are just that -- arguments -- and not a convincing proof.

What Is Wrong With Micromanagement: Economic View, Sean R. Aguilar, Olga Kosheleva

Departmental Technical Reports (CS)

Purpose: It is well known that micromanagement -- excessive control of employees -- is detrimental to the employees' morale and thus, decreases their productivity. But what if the managers keep people happy -- will there still be negative consequences of micromanagement? This is the problem analyzed in this paper.

Design/methodology/approach: To analyze our problem, we use general -- but simplified -- mathematical models of how productivity depends on the working rate.

Findings: We show that even in the absence of psychological discomfort, micromanagement is still detrimental to productivity. Interestingly, the negative effect of micromanagement increases as the population becomes more …

Why Chomsky Normal Form: A Pedagogical Note, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To simplify the design of compilers, Noam Chomsky proposed to first transform a description of a programming language -- which is usually given in the form of a context-free grammar -- into a simplified "normal" form. A natural question is: why this specific normal form? In this paper, we provide an answer to this question.

Shall We Ignore All Intermediate Grades?, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In most European universities, the overall student's grade for a course is determined exclusively by this student's performance on the final exam. All intermediate grades -- on homework, quizzes, and previous texts -- are, in effect, ignored. This arrangement helps gauge the student's performance by the knowledge that the student shows at the end of the course. The main drawback of this approach is that some students do not start studying until later, thinking that they can catch up and even get an excellent grade -- and this hurts their performance. To motivate students to study hard throughout the semester, …

Why Too Much Interaction Between Different Parts Of The Brain Leads To Unhappiness, Ricardo Alvarez, Yamel Hernandez, Vladik Kreinovich

Departmental Technical Reports (CS)

Reasonably recent experiments show that unhappiness is strongly correlated with the excessive interaction between two parts of the brain -- amygdala and hippocampus. At first glance, in situations when outside signals are positive, additional interaction between two parts of the brain that get signals from different sensors should only reinforce the positive feeling. In this paper, we provide a simple explanation of why, instead of the expected reinforcement, we observe unhappiness.

How To Teach Advanced Highly Motivated Students: Teaching Strategy Of Iosif Yakovlevich Verebeichik, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The paper describes and explains the teaching strategy of Iosif Yakovlevich Verebeichik, a successful mathematics teacher at special mathematical high schools -- schools for students interested in and skilled in mathematics. The resulting strategy seems counterintuitive and contrary to all the pedagogical advice. Our explanation is not complete: it worked well for this teacher, but others who tried to follow seemingly the same strategy did not succeed. How he made it work, how can others make it work -- this is still not clear. In the words of Verebeichik himself, while mathematics itself is a science, teaching mathematics is an …

Extension To Multidimensional Problems Of A Fuzzy-Based Explainable & Noise-Resilient Algorithm, Javier Viana, Stephan Ralescu, Kelly Cohen, Anca Ralescu, Vladik Kreinovich

Departmental Technical Reports (CS)

While Deep Neural Networks (DNNs) have shown incredible performance in a variety of data, they are brittle and opaque: easily fooled by the presence of noise, and difficult to understand the underlying reasoning for their predictions or choices. This focus on accuracy at the expense of interpretability and robustness caused little concern since, until recently, DNNs were employed primarily for scientific and limited commercial work. An increasing, widespread use of artificial intelligence and growing emphasis on user data protections, however, motivates the need for robust solutions with explainable methods and results. In this work, we extend a novel fuzzy based …

Discrepancy-Based Analysis Of Measurement Sampling Points In Compressive Sensing, Felipe Batista Da Silva

Open Access Theses & Dissertations

Compressive sensing (CS) is a technique in signal processing that under certain conditions allows someone to reconstruct sparse signals from fewer linear measurements. A problem in CS is modeled in terms of an underdetermined linear system, whose associated matrix is previously designed. Then, it is of interest in CS to know what a good sampling defined by the sensing matrix is and how to measure it. In this work, we provided analytical proofs of properties of the metric discrepancy that allow us to propose a fast algorithm for discrepancy calculation. Such metric measures the quality of the sampling measurement points …

The Hybridizing Ions Treatment (Hit) Method Development And Computational Study On Sars-Cov-2 E Protein., Shengjie Sun

Open Access Theses & Dissertations

Fast and accurate calculations of the electrostatic features for highly charged biomolecules such as DNA, RNA, highly charged proteins, are crucial but challenging tasks. Traditional implicit solvent methods calculate the electrostatic features fast, but they are not able to balance the high net charges in the biomolecules effectively. Explicit solvent methods add unbalanced ions to neutralize the highly charged biomolecules in molecular dynamic simulations, which require more expensive computing resources. Here we developed a novel method, the Hybridizing Ions Treatment (HIT) method, which hybridizes the implicit solvent method with the explicit method to realistically calculate the electrostatic potential for highly …

Order Relations Are Ubiquitously Fundamental: Alexandrov(-Zeeman) Theorem Extended From Space-Time Physics To Logical Reasoning And Decision Making, Vladik Kreinovich, Olga Kosheleva, Laxman Bokati, Laura Berrout

Departmental Technical Reports (CS)

In all areas of human activity, there are natural ordering relations: causality in space-time physics, preference in decision making, and logical inference in reasoning. In space-time physics, a 1950 theorem by A. D. Alexandrov proved that causality relation is fundamental: many other features, including numerical characteristics of time and space, can be reconstructed from this relation. In this paper, we provide simple proofs that, similarly, the corresponding ordering relations are fundamental in decision making and in logical reasoning.