Computer Sciences Commons^™

What Is The True Formula For Soil Permeability? Not Clear, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

To design and maintain pavements, it is important to know how fast water will penetrate the underlying soil. The speed of this penetration is determined by a quantity called permeability. There are several seemingly very different empirical and semi-empirical formulas that predict permeability. A recent attempt to select the formula that best fits the experimental data ended up in an unexpected conclusion that all three formula provide a good fit for the data. But these formulas are very different, how come that all three of them fit the same data? In this paper, we explain this somewhat paradoxical result.

How To Best Write Research Papers: Basic English? Sophisticated English?, Martine Ceberio, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Instructors from English department praise our students when they use the most sophisticated grammatical constructions and the most appropriate (often rarely used) words -- as long as this helps better convey all the subtleties of the meaning. On the other hand, we usually teach the students to use the most primitive Basic English when writing our papers -- this way, the resulting paper will be most accessible to the international audience. Who is right? In this paper, we analyze this question by using a natural model -- inspired by Zipf's law -- and we conclude that to achieve the largest …

Low-Complexity Zonotopes Can Enhance Uncertainty Quantification (Uq), Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, the only information that we know about the measurement error is the upper bound D on its absolute value. In this case, once we know the measurement result X, the only information that we have about the actual value x of the corresponding quantity is that this value belongs to the interval [X − D, X + D]. How can we estimate the accuracy of the result of data processing under this interval uncertainty? In general, computing this accuracy is NP-hard, but in the usual case when measurement errors are relatively small, we can linearize the …

Why Romans Sometimes Wrote 8 As Viii, And Sometimes As Iix: A Possible Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Most of us are familiar with Roman numerals and with the standard way of describing numbers in the form of these numerals. What many people do not realize is that the actual ancient Romans often deviated from these rules. For example, instead of always writing the number 8 as VIII, i.e., 5 + 3, they sometimes wrote it as IIX, i.e., as 10 − 2. Some of such differences can be explained: e.g., the unusual way of writing 98 as IIC, i.e., as 100 − 2, can be explained by the fact that the Latin word for 98 literally means …

Why Do We Need Two Doses Of Covid-19 Vaccine: A Qualitative Explanation, Laxman Bokati, Julio Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that the most effective protection from Covid-19 comes if the vaccination is done in two doses separated by several weeks. In this paper, we provide a qualitative explanation for this empirical fact.

Why T-Duality: A Simple Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many physical theories, there is a -- somewhat surprising -- similarity between events corresponding to large distances R and events corresponding to very small distances 1/R. Such similarity is known as T-duality. At present, the only available explanation for T-duality comes from a complex mathematical analysis of the corresponding formulas. In this paper, we provide an alternative explanation based on the fundamental notion of causality.

What Is The Logic Behind Cistercian Numbers?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the 13-15 centuries, many European monasteries used an unusual number system developed originally by the Cistercian monks; later on, this system was used by winemakers. In this paper, we provide a possible explanation of why these particular symbols were used.

Zadeh's Vision, Modern Physics, And The Future Of Computing, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

At first glance, Zadeh's ideas that everything is a matter of degree seem to be more appropriate for situations when we do not know the exact equations, when we only have expert rules for control and/or decision making. From this viewpoint, it may seem that in physics, where equations are ubiquitous and all the terms seem precise, there is not much place for fuzziness. But, as we show, in reality, fuzzy ideas can help -- and help dramatically -- in physics as well: in spite of the first impression, as physicists know well, many arguments in physics rely heavily on …

The Utep Corpus Of Dissatisfaction In Spoken Dialog, Jonathan E. Avila, Nigel Ward, Aaron Alarcon

Departmental Technical Reports (CS)

We present a corpus of spoken dialogs collected to support research in the automatic detection of times of dissatisfaction. We collected 191 mock customer-merchant dialogs in two conditions: one where the scripts guided the participants to a satisfactory, mutually agreeable outcome, and one where agreement was precluded. Most dialogs were 1 to 5 minutes in length. The corpus and metadata are freely available for research purposes.

How To Guarantee Fairness Of Grading Without Sacrificing Privacy?, Vladik Kreinovich, Olga Kosheleva, Christian Servin

Departmental Technical Reports (CS)

Everyone -– instructors and students –- want to make sure that grading of each test is fair, that the only thing that determines the students’ grade is their level of knowledge, that different students get the same penalty for the same mistake, irrespective of their gender, of their past grades, of their behavior in the class, of how many classes they missed, etc. How to help instructors achieve this goal? How to make sure that students are convinced that grading was indeed fair? In this paper, we describe possible measures: anonymous submissions, forming (and posting for all the student to …

How To Estimate Time Needed For Software Migration, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we need to migrate the existing software package to a new programming language and/or a new operating system. In such a migration, it is important to be able to accurately estimate time needed for this migration: if we underestimate this time, we will lose money and may go bankrupt; if we overestimate this time, other companies who estimate more accuracy will outbid us, and we will lose the contract. The formulas currently used for estimating migration time often lead to underestimation. In this paper, we start with the main ideas behind the existing formulas, and show …

Distributions On An Interval As A Scale-Invariant Combination Of Scale-Invariant Functions: Theoretical Explanation Of Empirical Marchenko-Pastur-Type Distributions, Vladik Kreinovich, Kevin Alvarez, Chon Van Le

Departmental Technical Reports (CS)

In many practical situations, we know the lower and upper bounds L and U on possible values of a quantity x. In such situations, the probability distribution of this quantity is also located on the corresponding interval [L, U]. In many such cases, the empirical probability distribution has the form d(x) = const * (x − L)α− * (U − x)α+ * xα. In the particular case α− = α+ = 0.5 and α = −1, we get the Marchenko-Pastur distribution that describes the distribution of the eigenvalues of a random matrix. However, in some cases, the empirical distribution corresponds …

When To Stop Computing And Start Investing, Sean R. Aguilar, Olga Kosheleva

Departmental Technical Reports (CS)

Purpose: The purpose of the study is to analyze when -- while predicting the future price of a financial instrument -- we should stop computations and start using this information for the actual investment.

Design/methodology/approach: We derive the explicit formulas explaining how the resulting gain depends on the duration of computations.

Findings: We provide an algorithm that enables us to decide the computation time that leads to the largest possible gain.

Originality/value: To the best of our knowledge, this is the first solution to the problem. Following our recommendations will allow investors to select the computation time for which the …

Tents Of Israel Revisited: Audio Privacy, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In one of the Biblical stories, prophet Balaam blesses the tents of Israel for being good. But what can be so good about the tents? The traditional Rabbinical interpretation is that the placement of the tents provided full privacy. In our previous paper, we considered the consequences of visual privacy: from each entrance, one cannot see what is happening at any other entrance. In this paper, we analyze the possible consequences of audio privacy: from each tent, you cannot hear what is going on in other tents.

How To Gauge Reliability Of A Binary Classification Result: A Simple Case, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we need to make a binary decision based on the available data: whether an incoming email is a spam or not, whether to give a bank loan to a company, etc. In many such situations, we can (and do) use machine learning to come up with such a decision. The problem is that while the results of a machine learning model are not 100% reliable, the existing machine learning algorithms do not allow us to decide how reliable is each result. In this paper, for simple examples, we provide a technique for gauging this reliability.

Why Homogeneous Membranes Lead To Optimal Water Desalination: A Possible Explanation, Julio Urenda, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A recent experiment has shown that out of all possible biological membranes, homogeneous ones proved the most efficient water desalination. In this paper, we show that natural symmetry ideas lead to a theoretical explanation for this empirical fact.

Why Gradient Descent -- Not The Best Optimization Technique -- Works Best In Neural Networks: Qualitative Explanation, Jonatan Contreras, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In a usual Numerical Methods class, students learn that gradient descent is not an efficient optimization algorithm, and that more efficient algorithms exist, algorithms which are actually used in state-of-the-art numerical optimization packages. On the other hand, in solving optimization problems related to machine learning -- and, in particular, in currently most efficient deep learning -- gradient descent (in the form of backpropagation) is much more efficient than any of the alternatives that have been tried. How can we reconcile these two statements? In this paper, we explain that, in reality, there is no contradiction here. Namely, in usual applications …

Why Question-Based Reasoning Leads To Constructive Approach To Knowledge, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Once we have partial knowledge, what next question do we usually pursue? Empirical study shows, e.g., that if we know that A \/ B is true, but we do not know whether A is true or B is true, then the usual next step is to ask whether A is true or B is true. This selection of the next step is in line with the constructive approach to knowledge, in which when A \/ B is true, this means that we either know that A is true, or we know that B is true. In this paper, we provide …

Can Ideas Behind Ancient Egyptian Fractions Speed Up Modern Computers?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To divide two numbers a and b, modern computers use an algorithm which is more efficient that what we humans normally do: they compute a*(1/b), where for all sufficiently small integers b, the inverse 1/b is pre-computed. For fractions, when both a and b are integers, this algorithm requires only one multiplication. Can we make the procedure even faster by not using multiplication at all? To do this, we need to represent each fraction as the sum of inverses -- which, interestingly, is how ancient Egyptians represented fractions.

Building Postsecondary Pathways For Latinx Students In Computing: Lessons From Hispanic-Serving Institutions, Anne-Marie Núñez, David S. Knight, Sanga Kim

Departmental Technical Reports (CS)

While the COVID-19 pandemic has transformed the use of technology in education and the workforce, a shortage of computer scientists continues, and computing remains one of the least diverse STEM disciplines. Efforts to diversify the computing industry often focus on the most selective postsecondary institutions, which are predominantly White. We highlight the role of Hispanic-Serving Institutions (HSI) in gradating large numbers of STEM graduates of color, particularly Latinx students. HSIs are uniquely positioned to leverage asset-based approaches that value students’ cultural background. We describe the practices educators use in the Computing Alliance for Hispanic-Serving Institutions, a network of 40 HSIs …

A Natural Formalization Of Changing-One's-Mind Leads To Square Root Of "Not" And To Complex-Valued Fuzzy Logic, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

We show that a natural formalization of the process of changing one's mind leads to such seemingly non-intuitive ideas as square root of "not" and complex-valued fuzzy degrees.

How To Find The Dependence Based On Measurements With Unknown Accuracy: Towards A Theoretical Justification For Midpoint And Convex-Combination Interval Techniques And Their Generalizations, Somsak Chanaim, Vladik Kreinovich

Departmental Technical Reports (CS)

In practice, we often need to find regression parameters in situations when for some of the values, we have several results of measuring this same value. If we know the accuracy of each of these measurements, then we can use the usual statistical techniques to combine the measurement results into a single estimate for the corresponding value. In some cases, however, we do not know these accuracies, so what can we do? In this paper, we describe two natural approaches to solving this problem. In addition to describing general techniques, our results also provide a theoretical explanation for several semi-heuristic …

Why Significant Wave Height And Rogue Waves Are So Defined: A Possible Explanation, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Data analysis has shown that if we want to describe the wave pattern by a single characteristic, the best characteristic is the average height of the highest one third of the waves; this characteristic is called significant wave height. Once we know the value of this characteristic, a natural next question is: what is the highest wave that we should normally observe -- so that waves higher than this amount would be rare ("rogue"). Empirically, it has been shown that rogue waves are best defined as the ones which are at least twice higher than the significant wave height. In …

How To Describe Measurement Errors: A Natural Generalization Of The Central Limit Theorem Beyond Normal (And Other Infinitely Divisible) Distributions, Julio Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When precise measurement instruments are designed, designers try their best to decrease the effect of the main factors leading to measurement errors. As a result of this decrease, the remaining measurement error is the joint result of a large number of relatively small independent error components. According to the Central Limit Theorem, under reasonable conditions, when the number of components increases, the resulting distribution tends to Gaussian (normal). Thus, in practice, when the number of components is large, the distribution is close to normal -- and normal distributions are indeed ubiquitous in measurements. However, in some practical situations, the distribution …

Data Analytics Beyond Traditional Probabilistic Approach To Uncertainty, Vladik Kreinovich

Departmental Technical Reports (CS)

Data for processing mostly comes from measurements, and measurements are never absolutely accurate: there is always the "measurement error" -- the difference between the measurement result and the actual (unknown) value of the measured quantity. In many applications, it is important to find out how these measurement errors affect the accuracy of the result of data processing. Traditional data processing techniques implicitly assume that we know the probability distributions. In many practical situations, however, we only have partial information about these distributions. In some cases, all we know is the upper bound on the absolute value of the measurement error. …

White- And Black-Box Computing And Measurements Under Limited Resources: Cloud, High Performance, And Quantum Computing, And Two Case Studies -- Robotic Boat And Hierarchical Covid Testing, Vladik Kreinovich, Martine Ceberio, Olga Kosheleva

Departmental Technical Reports (CS)

In many practical problems, it is important to take into account that our computational and measuring resources are limited. In this paper, we overview main resource limitations for different types of computers, and we provide two case studies explaining how to best take this resource limitation into account.

How To Separate Absolute And Relative Error Components: Interval Case, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Usually, measurement errors contain both absolute and relative components. To correctly gauge the amount of measurement error for all possible values of the measured quantity, it is important to separate these two error components. For probabilistic uncertainty, this separation can be obtained by using traditional probabilistic techniques. The problem is that in many practical situations, we do not know the probability distribution, we only know the upper bound on the measurement error. In such situations of interval uncertainty, separation of absolute and relative error components is not easy. In this paper, we propose a technique for such a separation based …

What If We Use Almost-Linear Functions Instead Of Linear Ones As A First Approximation In Interval Computations, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, the only information that we have about measurement errors is the upper bound on their absolute values. In such situations, the only information that we have after the measurement about the actual (unknown) value of the corresponding quantity is that this value belongs to the corresponding interval: e.g., if the measurement result is 1.0, and the upper bound is 0.1, then this interval is [1.0−0.1,1.0+0.1] = [0.9,1.1]. An important practical question is what is the resulting interval uncertainty of indirect measurements, i.e., in other words, how interval uncertainty propagates through data processing. There exist feasible algorithms …

Why Number Of Color Difference Works Better In Detecting Melanoma Than Number Of Colors: A Possible Fractal-Based Explanation, Julio Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

At present, the best way to detect melanoma based on an image of a skin spot is to count the number of different colors in this image. A recent paper has shown that the detection can improve if instead of the number of colors, we use the difference between numbers of colors computed by using different thresholds. In this paper, we provide a possible fractal-based explanation for this empirical fact.