Physical Sciences and Mathematics Commons^™

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 …

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 …

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.

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. …

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.

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 …

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 …

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 …

Coding Overhead Of Mobile Apps, Yoonsik Cheon

Departmental Technical Reports (CS)

A mobile app runs on small devices such as smartphones and tablets. Perhaps, because of this, there is a common misconception that writing a mobile app is simpler than a desktop application. In this paper, we show that this is indeed a misconception, and it's the other way around. We perform a small experiment to measure the source code sizes of a desktop application and an equivalent mobile app written in the same language. We found that the mobile version is 19% bigger than the desktop version in terms of the source lines of code, and the mobile code is …

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 …

Need For Diversity In Elected Decision-Making Bodies: Economics-Related Analysis, Nguyen Ngoc Thach, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

On a qualitative level, everyone understands the need to have diversity in elected decision-making bodies, so that the viewpoint of each group be properly taken into account. However, when only the usual economic criteria are used in this election -- e.g., in the election of company's board -- the resulting bodies often under-represent some groups (e.g., women). A frequent way to remedy this situation is to artificially enforce diversity instead of strictly following purely economic criteria. In this paper, we show the current seeming contradiction between economics and diversity is caused by the imperfection of the use economic models: in …

Why Majority Rule Does Not Work In Quantum Computing: A Pedagogical Explanation, Oscar Galindo, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To increase the reliability of computations result, a natural idea is to use duplication: we let several computers independently perform the same computations, and then, if their results differ, we select the majority's result. Reliability is an important issue for quantum computing as well, since in quantum physics, all the processes are probabilistic, so there is always a probability that the result will be wrong. It thus seems natural to use the same majority rule for quantum computing as well. However, it is known that for general quantum computing, this scheme does not work. In this paper, we provide a …

Let Us Use Negative Examples In Regression-Type Problems Too, Jonatan Contreras, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich, Martine Ceberio

Departmental Technical Reports (CS)

In many practical situations, we need to reconstruct the dependence between quantities x and y based on several situations in which we know both x and y values. Such problems are known as regression problems. Usually, this reconstruction is based on positive examples, when we know y -- at least, with some accuracy. However, in addition, we often also know some examples in which we have negative information about y -- e.g., we know that y does not belong to a certain interval. In this paper, we show how such negative examples can be used to make the solution …

Adversarial Teaching Approach To Cybersecurity: A Mathematical Model Explains Why It Works Well, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Teaching cybersecurity means teaching all possible ways how software can be attacked -- and how to fight such attacks. From the usual pedagogical viewpoint, a natural idea seems to be to teach all these ways one by one. Surprisingly, a completely different approach works even better: when the class is divided into sparring mini-teams that try their best to attack each other and defend from each other. In spite of the lack of thoroughness, this approach generates good specialists -- but why? In this paper, by analyzing a simple mathematical model of this situation, we explain why this approach work …

How To Make Sure That Robot's Behavior Is Human-Like, Vladik Kreinovich, Olga Kosheleva, Laxman Bokati

Departmental Technical Reports (CS)

In many applications -- e.g., in health care -- it is desirable to make robots behave human-like. This means, in particular, that robotic control should not be optimal, it should be similar to human (suboptimal) behavior. People's decisions are based on bounded rationality: since we cannot compute an optimal solution for all possible situations, we divide situations into groups and come up with a solution appropriate for each group. What is optimal here is the division into groups. It is therefore desirable to implement a similar algorithm for robots. To help with such algorithms, we provide techniques that help optimally …

Grading Homeworks, Verifying Code: How Thorough Should The Feedback Be?, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the ideal world, we should assign many homeworks and give a thorough feedback for each homework. However, in reality, the instructor's time is limited, so we can either assign few homeworks and give a detailed feed back for all of them, or we can assign many homeworks, but give a less thorough feedback. What is the optimal thoroughness? A similar question can be raised for code verification: what is the optimal amount of feedback that should be provided to each programmer? In this paper, we provide answers to these questions.

How Mathematics And Computing Can Help Fight The Pandemic: Two Pedagogical Examples, Julio Urenda, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

With the 2020 pandemic came unexpected mathematical and computational problems. In this paper, we provide two examples of such problems -- examples that we present in simplified pedagogical form. The problems are related to the need for social distancing and to the need for fast testing. We hope that these examples will help students better understand the importance of mathematical models.

Approximate Version Of Interval Computation Is Still Np-Hard, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

It is known that, in general, the problem of computing the range of a given polynomial on given intervals is NP-hard. For some NP-hard optimization problems, the approximate version -- e.g., if we want to find the value differing from the maximum by no more than a factor of 2 -- becomes feasible. Thus, a natural question is: what if instead of computing the exact range, we want to compute the enclosure which is, e.g., no more than twice wider than the actual range? In this paper, we show that this approximate version is still NP-hard, whether we want it …

Are There Traces Of Megacomputing In Our Universe, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The recent successes of quantum computing encouraged many researchers to search for other unconventional physical phenomena that could potentially speed up computations. Several promising schemes have been proposed that will -- hopefully -- lead to faster computations in the future. Some of these schemes -- similarly to quantum computing -- involve using events from the micro-world, others involve using large-scale phenomena. If some civilization used micro-world for computations, this will be difficult for us to notice, but if they use mega-scale effects, maybe we can notice these phenomena? In this paper, we analyze what possible traces such megacomputing can leave …

Natural Invariance Explains Empirical Success Of Specific Membership Functions, Hedge Operations, And Negation Operations, Julio Urenda, Orsoly Csiszár, Gábor Csiszár, József Dombi, György Eigner, Vladik Kreinovich

Departmental Technical Reports (CS)

Empirical studies have shown that in many practical problems, out of all symmetric membership functions, special distending functions work best, and out of all hedge operations and negation operations, fractional linear ones work the best. In this paper, we show that these empirical successes can be explained by natural invariance requirements.

What If Not All Interval-Valued Fuzzy Degrees Are Possible?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the applications of intervals is in describing experts' degrees of certainty in their statements. In this application, not all intervals are realistically possible. To describe all realistically possible degrees, we end up with a mathematical question of describing all topologically closed classes of intervals which are closed under the appropriate minimum and maximum operations. In this paper, we provide a full description of all such classes.

Reward For Good Performance Works Better Than Punishment For Mistakes: Economic Explanation, Olga Kosheleva, Julio Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

How should we stimulate people to make them perform better? How should we stimulate students to make them study better? Many experiments have shown that reward for good performance works better than punishment for mistakes. In this paper, we provide a possible theoretical explanation for this empirical fact.

How To Efficiently Store Intermediate Results In Quantum Computing: Theoretical Explanation Of The Current Algorithm, Oscar Galindo, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In complex time-consuming computations, we rarely have uninterrupted access to a high performance computer: usually, in the process of computation, some interruptions happen, so we need to store intermediate results until computations resume. To decrease the probability of a mistake, it is often necessary to run several identical computations in parallel, in which case several identical intermediate results need to be stored. In particular, for quantum computing, we need to store several independent identical copies of the corresponding qubits -- quantum versions of bits. Storing qubit states is not easy, but it is possible to compress the corresponding multi-qubit states: …

Optimization Under Fuzzy Constraints: Need To Go Beyond Bellman-Zadeh Approach And How It Is Related To Skewed Distributions, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

In many practical situations, we need to optimize the objective function under fuzzy constraints. Formulas for such optimization are known since the 1970s paper by Richard Bellman and Lotfi Zadeh, but these formulas have a limitation: small changes in the corresponding degrees can lead to a drastic change in the resulting selection. In this paper, we propose a natural modification of this formula, a modification that no longer has this limitation. Interestingly, this formula turns out to be related for formulas for skewed (asymmetric) generalizations of the normal distribution.

Why It Is Sufficient To Have Real-Valued Amplitudes In Quantum Computing, Isaac Bautista, Vladik Kreinovich, Olga Kosheleva, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

In the last decades, a lot of attention has been placed on quantum algorithms -- algorithms that will run on future quantum computers. In principle, quantum systems can use any complex-valued amplitudes. However, in practice, quantum algorithms only use real-valued amplitudes. In this paper, we provide a simple explanation for this empirical fact.

Formal Concept Analysis Techniques Can Help In Intelligent Control, Deep Learning, Etc., Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we show that formal concept analysis is a particular case of a more general problem that includes deriving rules for intelligent control, finding appropriate properties for deep learning algorithms, etc. Because of this, we believe that formal concept analysis techniques can be (and need to be) extended to these application areas as well. To show that such an extension is possible, we explain how these techniques can be applied to intelligent control.

How Expert Knowledge Can Help Measurements: Three Case Studies, Vladik Kreinovich

Departmental Technical Reports (CS)

In addition to measurement results, we often have expert estimates. These estimates provides an additional information about the corresponding quantities. However, it is not clear how to incorporate these estimates into a metrological analysis: metrological analysis is usually based on justified statistical estimates, but expert estimates are usually not similarly justified. One way to solve this problem is to calibrate an expert the same way we calibrate measuring instruments. In the first two case studies, we show that such a calibration indeed leads to useful result. The third case study provides an example of another use of expert knowledge in …

Neural Networks, Vladik Kreinovich

Departmental Technical Reports (CS)

A neural network is a general term for machine learning tools that emulate how neurons work in our brains.

Ideally, these tools do what we scientists are supposed to do: we feed them examples of the observed system's behavior, and hopefully, based on these examples, the tool will predict the future behavior of similar systems. Sometimes they do predict -- but in many other cases, the situation is not so simple.

The goal of this entry is to explain what these tools can and cannot do -- without going into too many technical details.

Absence Of Remotely Triggered Large Earthquakes: A Geometric Explanation, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that seismic waves from a large earthquake can trigger earthquakes in distant locations. Some of the triggered earthquakes are strong themselves. Interestingly, strong triggered earthquakes only happen within a reasonably small distance (less than 1000 km) from the original earthquake. Even catastrophic earthquakes do not trigger any strong earthquakes beyond this distance. In this paper, we provide a possible geometric explanation for this phenomenon.