Why Menzerath's Law?,
2022
The University of Texas at El Paso
Why Menzerath's Law?, Julio Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
In linguistics, there is a dependence between the length of the sentence and the average length of the word: the longer the sentence, the shorter the words. The corresponding empirical formula is known as the Menzerath's Law. A similar dependence can be observed in many other application areas, e.g., in the analysis of genomes. The fact that the same dependence is observed in many different application domains seems to indicate there should be a general domain-independent explanation for this law. In this paper, we show that indeed, this law can be derived from natural invariance requirements.
How To Select A Representative Sample For A Family Of Functions?,
2022
The University of Texas at El Paso
How To Select A Representative Sample For A Family Of Functions?, Leobardo Valera, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
Predictions are rarely absolutely accurate. Often, the future values of quantities of interest depend on some parameters that we only know with some uncertainty. To make sure that all possible solutions satisfy desired constraints, it is necessary to generate a representative finite sample, so that if the constraints are satisfied for all the functions from this sample, then we can be sure that these constraints will be satisfied for the actual future behavior as well. At present, such a sample is selected based by Monte-Carlo simulations, but, as we show, such selection may underestimate the danger of violating the constraints. …
Why Hate: Analysis Based On Decision Theory,
2022
The University of Texas at El Paso
Why Hate: Analysis Based On Decision Theory, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
At first glance, from the general decision-theory viewpoint, hate (and other negative feelings towards each other) makes no sense, since they decrease the utility (i.e., crudely speaking, level of happiness) of the person who experiences these feelings. Our detailed analysis shows that there are situations when such negative feelings make perfect sense: namely, when you have a large group of people almost all of whom are objectively unhappy. In such situations -- e.g., on the battlefield -- negative feelings help keep their spirits high in spite of the harsh situation. This explanation leads to recommendations on how to decrease the …
How To Solve The Apportionment Paradox,
2022
The University of Texas at El Paso
How To Solve The Apportionment Paradox, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that often, after it is proven that a new statement is equivalent to the original definition, this new statement becomes the accepted new definition of the same notion. In this paper, we provide a natural explanation for this empirical phenomenon.
How To Solve The Apportionment Paradox,
2022
The University of Texas at El Paso
How To Solve The Apportionment Paradox, Christopher Reyes, Vladik Kreinovich
Departmental Technical Reports (CS)
In the ideal world, the number of seats that each region or each community gets in a representative body should be exactly proportional to the population of this region or community. However, since the number of seats allocated to each region or community is whole, we cannot maintain the exact proportionality. Not only this leads to a somewhat unfair situation, when residents of one region get more votes per person than residents of another one, it also leads to paradoxes -- e.g., sometimes a region that gained the largest number of people loses a number of seats. To avoid this …
A Possible Common Mechanism Behind Skew Normal Distributions In Economics And Hydraulic Fracturing-Induced Seismicity,
2022
The University of Texas at El Paso
A Possible Common Mechanism Behind Skew Normal Distributions In Economics And Hydraulic Fracturing-Induced Seismicity, Laxman Bokati, Aaron Velasco, Vladik Kreinovich, Kittawit Autchariyapanitkul
Departmental Technical Reports (CS)
Many economic situations -- and many situations in other application areas -- are well-described by a special asymmetric generalization of normal distributions -- known as skew-normal. However, there is no convincing theoretical explanation for this empirical phenomenon. To be more precise, there are convincing explanations for the ubiquity of normal distributions, but not for the transformation that turns normal into skew-normal. In this paper, we use the analysis of hydraulic fracturing-induced seismicity to show explain the ubiquity of such a transformation.
Shall We Use Logical Approach Or More Traditional Mamdani Approach In Fuzzy Control: Pragmatic Analysis,
2022
The University of Texas at El Paso
Shall We Use Logical Approach Or More Traditional Mamdani Approach In Fuzzy Control: Pragmatic Analysis, R. Noah Padilla, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Fuzzy control methodology transforms the experts' if-then rules into a precise control strategy. From the logical viewpoint, an if-then rule means implication, so it seems reasonable to use fuzzy implication in this transformation. However, this logical approach is not what the first fuzzy controllers used. The traditional fuzzy control approach -- first proposed by Mamdani -- transforms the if-then rules into a statement that only contains and's and or's, and does not use fuzzy implication at all. So, a natural question arises: shall we use logical approach or the traditional approach? In this paper, we analyze this question on the …
Why Optimization Is Faster Than Solving Systems Of Equations: A Qualitative Explanation,
2022
The University of Texas at El Paso
Why Optimization Is Faster Than Solving Systems Of Equations: A Qualitative Explanation, Siyu Deng, Bimal K. C, Vladik Kreinovich
Departmental Technical Reports (CS)
Most practical problems lead either to solving a system of equation or to optimization. From the computational viewpoint, both classes of problems can be reduced to each other: optimization can be reduced to finding points at which all partial derivatives are zeros, and solving systems of equations can be reduced to minimizing sums of squares. It is therefore natural to expect that, on average, both classes of problems have the same computational complexity -- i.e., require about the same computation time. However, empirically, optimization problems are much faster to solve. In this paper, we provide a possible explanation for this …
Spiral Arms Around A Star: Geometric Explanation,
2022
The University of Texas at El Paso
Spiral Arms Around A Star: Geometric Explanation, Juan L. Puebla, Vladik Kreinovich
Departmental Technical Reports (CS)
Recently, astronomers discovered spiral arms around a star. While their shape is similar to the shape of the spiral arms in the galaxies, however, because of the different scale, galaxy-related physical explanations of galactic spirals cannot be directly applied to explaining star-size spiral arms. In this paper, we show that, in contrast to more specific physical explanation, more general symmetry-based geometric explanations of galactic spiral can explain spiral arms around a star.
Why Self-Esteem Helps To Solve Problems: An Algorithmic Explanation,
2022
The University of Texas at El Paso
Why Self-Esteem Helps To Solve Problems: An Algorithmic Explanation, Oscar Ortiz, Henry Salgado, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that self-esteem helps solve problems. From the algorithmic viewpoint, this seems like a mystery: a boost in self-esteem does not provide us with new algorithms, does not provide us with ability to compute faster -- but somehow, with the same algorithmic tools and the same ability to perform the corresponding computations, students become better problem solvers. In this paper, we provide an algorithmic explanation for this surprising empirical phenomenon.
How To Describe Hypothetic Truly Rare Events (With Probability 0),
2022
The University of Texas at El Paso
How To Describe Hypothetic Truly Rare Events (With Probability 0), Luc Longpre, Vladik Kreinovich
Departmental Technical Reports (CS)
In probability theory, rare events are usually described as events with low probability p, i.e., events for which in N observations, the event happens n(N) ~ p*N times. Physicists and philosophers suggested that there may be events which are even rarer, in which n(N) grows slower than N. However, this idea has not been developed, since it was not clear how to describe it in precise terms. In this paper, we propose a possible precise description of this idea, and we use this description to answer a natural question: when two different functions n(N) lead to the same class of …
One More Physics-Based Explanation For Rectified Linear Neurons,
2022
The University of Texas at El Paso
One More Physics-Based Explanation For Rectified Linear Neurons, Jonatan Contreras, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
The main idea behind artificial neural networks is to simulate how data is processed in the data processing devoice that has been optimized by million-years natural selection -- our brain. Such networks are indeed very successful, but interestingly, the most recent successes came when researchers replaces the original biology-motivated sigmoid activation function with a completely different one -- known as rectified linear function. In this paper, we explain that this somewhat unexpected function actually naturally appears in physics-based data processing.
How To Make Quantum Ideas Less Counter-Intuitive: A Simple Analysis Of Measurement Uncertainty Can Help,
2022
The University of Texas at El Paso
How To Make Quantum Ideas Less Counter-Intuitive: A Simple Analysis Of Measurement Uncertainty Can Help, Olga Kosheleva, Vladik Kreinovich, Louis Ray Lopez
Departmental Technical Reports (CS)
Our intuition about physics is based on macro-scale phenomena, phenomena which are well described by non-quantum physics. As a result, many quantum ideas sound counter-intuitive -- and this slows down students' learning of quantum physics. In this paper, we show that a simple analysis of measurement uncertainty can make many of the quantum ideas much less counter-intuitive and thus, much easier to accept and understand.
Physical Meaning Often Leads To Natural Derivations In Elementary Mathematics: On The Examples Of Solving Quadratic And Cubic Equations,
2022
El Paso Community College
Physical Meaning Often Leads To Natural Derivations In Elementary Mathematics: On The Examples Of Solving Quadratic And Cubic Equations, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Usual derivation of many formulas of elementary mathematics -- such as the formulas for solving quadratic equation -- often leave un unfortunate impression that mathematics is a collection of unrelated unnatural trick. In this paper, on the example of formulas for solving quadratic and cubic equations, we show that these derivations can be made much more natural if we take physical meaning into account.
Why Immunodepressive Drugs Often Make People Happier,
2022
The University of Texas at El Paso
Why Immunodepressive Drugs Often Make People Happier, Joshua Ramos, Dario Vasquez, Ruth Trejo, Vladik Kreinovich
Departmental Technical Reports (CS)
Many immunodepressive drugs have an unusual side effect on the patient's mood: they often make the patient happier. This side hae been observed for many different immunodepressive drugs, with different chemical composition. Thus, it is natural to conclude that there must be some general reason for this empirical phenomenon, a reason not related to the chemical composition of any specific drug -- but rather with their general functionality. In this paper, we provide such an explanation.
Explaining An Empirical Formula For Bioreaction To Similar Stimuli (Covid-19 And Beyond),
2022
The University of Texas at El Paso
Explaining An Empirical Formula For Bioreaction To Similar Stimuli (Covid-19 And Beyond), Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Departmental Technical Reports (CS)
A recent comparative analysis of biological reaction to unchanging vs. rapidly changing stimuli -- such as Covid-19 or flu viruses -- uses an empirical formula describing how the reaction to a similar stimulus depends on the distance between the new and original stimuli. In this paper, we provide a from-first-principles explanation for this empirical formula.
Number Of Bounded Distance Equivalence Classes In Hulls Of Repetitive Delone Sets,
2022
The University of Texas Rio Grande Valley
Number Of Bounded Distance Equivalence Classes In Hulls Of Repetitive Delone Sets, Dirk Frettlöh, Alexey Garber, Lorenzo Sadun
School of Mathematical & Statistical Sciences Faculty Publications
Two Delone sets are bounded distance equivalent to each other if there is a bijection between them such that the distance of corresponding points is uniformly bounded. Bounded distance equivalence is an equivalence relation. We show that the hull of a repetitive Delone set with finite local complexity has either one equivalence class or uncountably many.
Optimal Quantization For Mixed Distributions Generated By Two Uniform Distributions,
2022
The University of Texas Rio Grande Valley
Optimal Quantization For Mixed Distributions Generated By Two Uniform Distributions, Ashley Gomez, Olga Lopez, Mrinal Kanti Roychowdhury
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, for mixed distributions generated by two uniform distributions we investigate the optimal sets of n-means and the nth quantization errors for all positive integers n. Some conjectures and open problems are also given.
Integrable Semi-Discretization Of A Modified Short Wave Equation,
2022
The University of Texas Rio Grande Valley
Integrable Semi-Discretization Of A Modified Short Wave Equation, Yujuan Zhang, Ruyun Ma, Na Xiong, Bao-Feng Feng
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we are concerned with one of the integrable equations proposed by Hone et al. (2018). We firstly show that it can be derived from the Tzitzeica equation through hodograph or reciprocal transformations and it is linked to the short wave limits of the DP and Novikov equations, respectively, through Miura transformations. Based on the semi-discrete analogue of CKP-Toda hierarchy, we construct the integrable semi-discretization of what we call the modified short wave equation and provide its multi-soliton solution.
Spectra Of Variants Of Distance Matrices Of Graphs And Digraphs: A Survey,
2022
Swarthmore College
Spectra Of Variants Of Distance Matrices Of Graphs And Digraphs: A Survey, L. Hogben, Carolyn Reinhart
Mathematics & Statistics Faculty Works
Distance matrices of graphs were introduced by Graham and Pollack in 1971 to study a problem in communications. Since then, there has been extensive research on the distance matrices of graphs—a 2014 survey by Aouchiche and Hansen on spectra of distance matrices of graphs lists more than 150 references. In the last 10 years, variants such as the distance Laplacian, the distance signless Laplacian, and the normalized distance Laplacian matrix of a graph have been studied. After a brief description of the early history of the distance matrix and its motivating problem, this survey focuses on comparing and contrasting techniques …
