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Articles 1 - 30 of 110
Full-Text Articles in Physical Sciences and Mathematics
Why Was Nicholson's Theory So Successful: An Explanation Of A Mysterious Episode In 20 Century Atomic Physics, Olga Kosheleva, Vladik Kreinovich
Why Was Nicholson's Theory So Successful: An Explanation Of A Mysterious Episode In 20 Century Atomic Physics, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the early 1910s, John Nicholson suggested that all atoms are formed by four basic elementary particles. This theory had a spectacular match with observations: it explained, with an unbelievable accuracy of 0.1, the atomic weights of all 92 elements known at that time. Specifically, it was shown that every atomic weight can be represented, with this accuracy, as an integer combination of four basic atomic weights. However, in a few years, this theory turned out to be completely wrong: atoms consist of protons, neutrons, and electrons, not of Nicholson's particles. This mysterious episode seems to contradict the usual development …
Need For Shift-Invariant Fractional Differentiation Explains The Appearance Of Complex Numbers In Physics, Olga Kosheleva, Vladik Kreinovich
Need For Shift-Invariant Fractional Differentiation Explains The Appearance Of Complex Numbers In Physics, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Complex numbers are ubiquitous in physics, they lead to a natural description of different physical processes and to efficient algorithms for solving the corresponding problems. But why this seemingly counterintuitive mathematical construction is so natural here? In this paper, we provide a possible explanation of this phenomenon: namely, we show that complex numbers appear if take into account that some physical system are described by derivatives of fractional order and that a physically meaningful analysis of such derivatives naturally leads to complex numbers.
Why Physical Processes Are Smooth Or Almost Smooth: A Possible Physical Explanation Based On Intuitive Ideas Behind Energy Conservation, Olga Kosheleva, Vladik Kreinovich
Why Physical Processes Are Smooth Or Almost Smooth: A Possible Physical Explanation Based On Intuitive Ideas Behind Energy Conservation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
While there are some non-smooth (and even discontinuous) processes in nature, most processes are smooth or almost smooth. This smoothness help estimate physical quantities, but a natural question is: why are physical processes smooth or almost smooth? Are there any fundamental reasons for this ubiquitous smoothness? In this paper, we provide a possible physical explanation for emirical smoothness: namely, we show that smoothness naturally follows from intuitive ideas behind energy conservation.
Building Postsecondary Pathways For Latinx Students In Computing: Lessons From Hispanic-Serving Institutions, Anne-Marie Núñez, David S. Knight, Sanga Kim
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 …
So How Were The Tents Of Israel Placed? A Bible-Inspired Geometric Problem, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
So How Were The Tents Of Israel Placed? A Bible-Inspired Geometric Problem, Julio 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? A traditional Rabbinical interpretation is that the placement of the tents provided full privacy: from each entrance, one could not see what is happening at any other entrance. This motivates a natural geometric question: how exactly were these tents placed? In this paper, we provide an answer to this question.
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
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 Ancient Egyptians Preferred Some Sum-Of-Inverses Representations Of Fractions?, Olga Kosheleva, Vladik Kreinovich
Why Ancient Egyptians Preferred Some Sum-Of-Inverses Representations Of Fractions?, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Ancient Egyptians represented a fraction as a sum of inverses of natural numbers, with the smallest possible number of terms. In our previous paper, we explained that this representation makes sense since it leads to the optimal way of solving a problem frequently mentioned in the Egyptian papyri: dividing bread between workers. However, this does not explain why ancient Egyptians preferred some representations with the same number of terms but not others. For example, to represent 2/3, they used the sum 1/2 + 1/6 but not the sum 1/3 + 1/3 with the same number of terms. In this paper, …
What If You Are Late On Several (Relatively Small) Tasks?, Olga Kosheleva, Vladik Kreinovich
What If You Are Late On Several (Relatively Small) Tasks?, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In practice, we sometimes end up in a situation when we are late on several relatively small tasks. We cannot finish them all, so which ones should we do first? We show that in general, this is an NP-complete problem. In the typical situation when all the tasks are of approximately the same importance and requires approximately the same time to finish, we can have an explicit solution to this problem. In a nutshell, the resulting (somewhat counterintuitive) recommendation is to start with things which are not yet late or only a few days late. Actually, this recommendation makes sense: …
A Possible (Qualitative) Explanation Of The Hierarchy Problem In Theoretical Physics, Olga Kosheleva, Vladik Kreinovich
A Possible (Qualitative) Explanation Of The Hierarchy Problem In Theoretical Physics, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the important open problem in theoretical physics is the hierarchy problem: how to explain that some physical constant are many orders of magnitude larger than others. In this paper, we provide a possible qualitative explanation for this phenomenon.
Possibility To Algorithmically Check: Yet Another Reason Why Current Definitions Have Been Selected In Elementary Mathematics, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Possibility To Algorithmically Check: Yet Another Reason Why Current Definitions Have Been Selected In Elementary Mathematics, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
At first glance, many definitions in mathematics -- especially in elementary mathematics -- seem arbitrary. Why is 1 not considered a prime number? Why is a square considered to be a particular case of a parallelogram -- in some old textbooks, a parallelogram was defined in such a way as to exclude the square. In his 2018 article, Art Duval explained many such definitions by a natural requirement to make the corresponding results (theorems) as simple as possible. However, elementary mathematics is not just about theorems and proofs, it is also about computations. In this paper, we show that from …
Why Strings, Why Quark Confinement: A Simple Qualitative Explanation, Olga Kosheleva, Vladik Kreinovich
Why Strings, Why Quark Confinement: A Simple Qualitative Explanation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In this pedagogical article, we recall the infinities problem of modern physics, and we show that the natural way to overcome this problem naturally leads to strings and to quark confinement.
Why Quantiles Are A Good Description Of Volatility In Economics: A Pedagogical Explanation, Sean R. Aguilar, Vladik Kreinovich, Uyen Pham
Why Quantiles Are A Good Description Of Volatility In Economics: A Pedagogical Explanation, Sean R. Aguilar, Vladik Kreinovich, Uyen Pham
Departmental Technical Reports (CS)
To make investment decisions, we need to know, for each financial instrument, not only its expected return -- but also how the actual return may deviate from its expected value. A numerical measure of such deviations is known as volatility. Originally, volatility was measured by the srabdard deviation from the expected price, but it turned out that this measure does not always adequately describe our perception of volatility. Empirically, it turned out that quantiles are a more adequate description of volatility. In this paper, we provide an explanation of this empirical phenomenon.
Should Fighting Corruption Always Be One Of The Main Pre-Requisites For Economic Help?, Sean R. Aguilar, Vladik Kreinovich
Should Fighting Corruption Always Be One Of The Main Pre-Requisites For Economic Help?, Sean R. Aguilar, Vladik Kreinovich
Departmental Technical Reports (CS)
In general, corruption is bad. In many cases, it makes sense to make fighting corruption one of the main pre-requisites for getting financial help: we do not want this money to line the pockets of corrupted officials, we want to help the people. In this paper, we argue, however, that in some cases -- of over-regulated and/or oppressive regimes -- too much emphasis on fighting corruption may be counter-productive: instead of helping people, it may hurt them.
Being Active In Research Makes A Person A Better Teacher And Even Helps When Working For A Company, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
Being Active In Research Makes A Person A Better Teacher And Even Helps When Working For A Company, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
At first glance, it looks like being active in research is not necessarily related to a person's success in being a teacher or being a productive company employee -- moreover, it looks like research distracts from other tasks. Somewhat surprisingly, however, in practice, the best teachers and the best employees are actually the ones who are active in research. In this paper, we provide an explanation for this seemingly counter-intuitive phenomenon.
Yet Another Possible Explanation Of Egyptian Fractions: Motivated By Fairness, Olga Kosheleva, Vladik Kreinovich
Yet Another Possible Explanation Of Egyptian Fractions: Motivated By Fairness, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Ancient Egyptians represented fractions as sums of inverses of natural numbers, and they made sure that all these natural numbers are different. The representation as a sum of inverses makes some sense: it is known to lead to an optimal solution to the problem of dividing bread between workers, a problem often described in the Egyptian papyri. However, this does not explain why the corresponding natural numbers should be all different: some representations with the same natural number repeated several times lead to the same smallest number of cuts as the representations that the ancient Egyptians actually used. In this …
Why Min, Max, Opening, And Closing Stock Prices Are Empirically Most Appropriate For Predictions, And Why Their Linear Combination Provides The Best Estimate For Beta, Somsak Chanaim, Olga Kosheleva, Vladik Kreinovich
Why Min, Max, Opening, And Closing Stock Prices Are Empirically Most Appropriate For Predictions, And Why Their Linear Combination Provides The Best Estimate For Beta, Somsak Chanaim, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
While we have moment-by-moment prices of each stock, we cannot use all this information to predict the future stock prices, we need to combine them into a few characteristics of the daily stock price. Empirically, it turns out that the best characteristics are the lowest daily price, the highest daily price, the opening price, and the closing price. In the paper, we provide a theoretical explanation for this empirical phenomenon. We also explain why empirically, it turns out that the best way to find the stock's beta coefficient is to consider a convex combination of the about four characteristics.
A Natural Formalization Of Changing-One's-Mind Leads To Square Root Of "Not" And To Complex-Valued Fuzzy Logic, Olga Kosheleva, Vladik Kreinovich
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
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
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.
How To Explain The Relation Between Different Empirical Covid-19 Self-Isolation Periods, Christian Servin, Olga Kosheleva, Vladik Kreinovich
How To Explain The Relation Between Different Empirical Covid-19 Self-Isolation Periods, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Empirical data implies that, to avoid infecting others, an asymptomatic career of Covid-19 should self-isolate for a period of 10 days, a patient who experiences symptoms for 20 days, and a person who was in contact with a Covid-19 patient should self-isolate for 14 days. In this paper, we use Laplace's Principle of Insufficient Reason to provide a simple explanation for the relation between these three self-isolation periods.
What If We Use Almost-Linear Functions Instead Of Linear Ones As A First Approximation In Interval Computations, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
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
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
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 …
Egyptian Fractions As Approximators, Olga Kosheleva, Vladik Kreinovich
Egyptian Fractions As Approximators, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In ancient Egypt, fractions were represented as the sum of inverses to natural numbers. Processing fractions in this representation is computationally complicated. Because of this complexity, traditionally, Egyptian fractions used to be considered an early inefficient approach. In our previous papers, we showed, however, that the Egyptian fractions actually provide an optimal solution to problems important for ancient Egypt -- such as the more efficient distribution of food between workers. In these papers, we assumed, for simplicity, that we know the exact amount of food needed for each worker -- and that this value must be maintained with absolute accuracy. …
Coding Overhead Of Mobile Apps, Yoonsik Cheon
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
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
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 …
Does Transition To Democracy Lead To Chaos: A Theorem, Olga Kosheleva, Vladik Kreinovich
Does Transition To Democracy Lead To Chaos: A Theorem, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
When a country transitions to democracy, at first, many political parties appear. A natural question is whether the number of such parties feasible and reasonable -- or whether this is a complete chaos. In this paper, we formulate a simplified version of this question in precise terms and show that the number of parties will be feasible -- i.e., that transition to democracy does not lead to chaos.
Rosenzweig, Equality, And Assignment, Olga Kosheleva, Vladik Kreinovich
Rosenzweig, Equality, And Assignment, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In his seminal book "The Star of Redemption", the renowned philosopher Franz Rosenzweig illustrated his ideas by the intuitive difference between mathematical statements A=B and B=A. Of course, from the purely mathematical viewpoint, these two statements are always equivalent, so to a person trained in mathematics -- even in simple school mathematics -- this illustration is puzzling. What we show is that from the viewpoint of common folks, there is indeed a subtle difference between how people understand these two equalities. To us, the understanding of this difference helped us better understand Rosenzweig's ideas. But we believe that this difference …
Need For Diversity In Elected Decision-Making Bodies: Economics-Related Analysis, Nguyen Ngoc Thach, Olga Kosheleva, Vladik Kreinovich
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 …