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Full-Text Articles in Mathematics
How Viscosity Of An Asphalt Binder Depends On Temperature: Theoretical Explanation Of An Empirical Dependence, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich
How Viscosity Of An Asphalt Binder Depends On Temperature: Theoretical Explanation Of An Empirical Dependence, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich
Departmental Technical Reports (CS)
Pavement must be adequate for all the temperatures, ranging from the winter cold to the summer heat. In particular, this means that for all possible temperatures, the viscosity of the asphalt binder must stay within the desired bounds. To predict how the designed pavement will behave under different temperatures, it is desirable to have a general idea of how viscosity changes with temperature. Pavement engineers have come up with an empirical approximate formula describing this change. However, since this formula is purely empirical, with no theoretical justification, practitioners are often somewhat reluctant to depend on this formula. In this paper, …
Why In Mond -- Alternative Gravitation Theory -- A Specific Formula Works The Best: Complexity-Based Explanation, Olga Kosheleva, Vladik Kreinovich
Why In Mond -- Alternative Gravitation Theory -- A Specific Formula Works The Best: Complexity-Based Explanation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Based on the rotation of the stars around a galaxy center, one can estimate the corresponding gravitational acceleration -- which turns out to be much larger than what Newton's theory predicts based on the masses of all visible objects. The majority of physicists believe that this discrepancy indicates the presence of "dark" matter, but this idea has some unsolved problems. An alternative idea -- known as Modified Newtonian Dynamics (MOND, for short) is that for galaxy-size distances, Newton's gravitation theory needs to be modified. One of the most effective versions of this idea uses so-called simple interpolating function. In this …
Non-Localized Physical Processes Can Help Speed Up Computations, Be It Hidden Variables In Quantum Physics Or Non-Localized Energy In General Relativity, Michael Zakharevich, Olga Kosheleva, Vladik Kreinovich
Non-Localized Physical Processes Can Help Speed Up Computations, Be It Hidden Variables In Quantum Physics Or Non-Localized Energy In General Relativity, Michael Zakharevich, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
While most physical processes are localized -- in the sense that each event can only affect events in its close vicinity -- many physicists believe that some processes are non-local. These beliefs range from more heretic -- such as hidden variables in quantum physics -- to more widely accepted, such as the non-local character of energy in General Relativity. In this paper, we attract attention to the fact that non-local processes bring in the possibility of drastically speeding up computations.
Graph Approach To Uncertainty Quantification, Hector A. Reyes, Cliff Joslyn, Vladik Kreinovich
Graph Approach To Uncertainty Quantification, Hector A. Reyes, Cliff Joslyn, Vladik Kreinovich
Departmental Technical Reports (CS)
Traditional analysis of uncertainty of the result of data processing assumes that all measurement errors are independent. In reality, there may be common factor affecting these errors, so these errors may be dependent. In such cases, the independence assumption may lead to underestimation of uncertainty. In such cases, a guaranteed way to be on the safe side is to make no assumption about independence at all. In practice, however, we may have information that a few pairs of measurement errors are indeed independent -- while we still have no information about all other pairs. Alternatively, we may suspect that for …
Systems Approach Explains Why Low Heart Rate Variability Is Correlated With Depression (And Suicidal Thoughts), Francisco Zapata, Eric Smith, Vladik Kreinovich
Systems Approach Explains Why Low Heart Rate Variability Is Correlated With Depression (And Suicidal Thoughts), Francisco Zapata, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
Depression is a serious medical problem. If diagnosed early, it can usually be cured, but if left undetected, it can lead to suicidal thoughts and behavior. The early stages of depression are difficult to diagnose. Recently, researchers found a promising approach to such diagnosis -- it turns out that depression is correlated with low heart rate variability. In this paper, we show that the general systems approach can explain this empirical relation.
An Argument In Favor Of Piecewise-Constant Membership Functions, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
An Argument In Favor Of Piecewise-Constant Membership Functions, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Theoretically, we can have membership functions of arbitrary shape. However, in practice, at any given moment of time, we can only represent finitely many parameters in a computer. As a result, we usually restrict ourselves to finite-parametric families of membership functions. The most widely used families are piecewise linear ones, e.g., triangular and trapezoid membership functions. The problem with these families is that if we know a nonlinear relation y = f(x) between quantities, the corresponding relation between membership functions is only approximate -- since for piecewise linear membership functions for x, the resulting membership function for y is not …
Which Interval-Valued Alternatives Are Possibly Optimal If We Use Hurwicz Criterion, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Vladik Kreinovich
Which Interval-Valued Alternatives Are Possibly Optimal If We Use Hurwicz Criterion, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, for each alternative i, we do not know the corresponding gain xi, we only know the interval [li,ui] of possible gains. In such situations, a reasonable way to select an alternative is to choose some value α from the interval [0,1] and select the alternative i for which the Hurwicz combination α*ui + (1 − α)*li is the largest possible. In situations when we do not know the user's α, a reasonable idea is to select all alternatives that are optimal for some α. In this paper, we describe a feasible algorithm for such a selection.
Standard Interval Computation Algorithm Is Not Inclusion-Monotonic: Examples, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Standard Interval Computation Algorithm Is Not Inclusion-Monotonic: Examples, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
When we usually process data, we, in effect, implicitly assume that we know the exact values of all the inputs. In practice, these values comes from measurements, and measurements are never absolutely accurate. In many cases, the only information about the actual (unknown) values of each input is that this value belongs to an appropriate interval. Under this interval uncertainty, we need to compute the range of all possible results of applying the data processing algorithm when the inputs are in these intervals. In general, the problem of exactly computing this range is NP-hard, which means that in feasible time, …
Epistemic Vs. Aleatory: Case Of Interval Uncertainty, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Vladik Kreinovich
Epistemic Vs. Aleatory: Case Of Interval Uncertainty, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
Interval computations usually deal with the case of epistemic uncertainty, when the only information that we have about a value of a quantity is that this value is contained in a given interval. However, intervals can also represent aleatory uncertainty -- when we know that each value from this interval is actually attained for some object at some moment of time. In this paper, we analyze how to take such aleatory uncertainty into account when processing data. We show that in case when different quantities are independent, we can use the same formulas for dealing with aleatory uncertainty as we …
Will Nanotechnology Bring In The Judgement Day?, Olga Kosheleva, Vladik Kreinovich
Will Nanotechnology Bring In The Judgement Day?, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
There are many current and prospective positive aspects of nanotechnology. However, while we look forward to its future successes, we need to keep our eyes open and be prepared for what will really be a future shock: that quantum computing – an inevitable part of nanotechnology – will enable the future folks to read all our encrypted messages and thus, learn everything that we wanted to keep secret. This will be really the Judgement Day, when all our sins will be open to everyone. How we will react to it? Will this destroy our civilization? Let us hope that the …
Data Processing Under Fuzzy Uncertainty: Towards More Accurate Algorithms, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Data Processing Under Fuzzy Uncertainty: Towards More Accurate Algorithms, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Data that we process comes either from measurements or from experts -- or from the results of previous data processing that were also based on measurements and/or expert estimates. In both cases, the data is imprecise. To gauge the accuracy of the results of data processing, we need to take the corresponding data uncertainty into account. In this paper, we describe a new algorithm for taking fuzzy uncertainty into account, an algorithm that, for small number of inputs, leads to the same or even better accuracy than the previously proposed methods.
How To Get The Most Accurate Measurement-Based Estimates, Salvador Robles, Martine Ceberio, Vladik Kreinovich
How To Get The Most Accurate Measurement-Based Estimates, Salvador Robles, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we want to estimate a quantity y that is difficult -- or even impossible -- to measure directly. In such cases, often, there are easier-to-measure quantities x1, ..., xn that are related to y by a known dependence y = f(x1,...,xn). So, to estimate y, we can measure these quantities xi and use the measurement results to estimate y. The two natural questions are: (1) within limited resources, what is the best accuracy with which we can estimate y, and (2) to reach a given accuracy, what amount …
Anomaly Detection In Crowdsourcing: Why Midpoints In Interval-Valued Approach, Alejandra De La Pena, Damian L. Gallegos Espinoza, Vladik Kreinovich
Anomaly Detection In Crowdsourcing: Why Midpoints In Interval-Valued Approach, Alejandra De La Pena, Damian L. Gallegos Espinoza, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations -- e.g., when preparing examples for a machine learning algorithm -- we need to label a large number of images or speech recordings. One way to do it is to pay people around the world to perform this labeling; this is known as crowdsourcing. In many cases, crowd-workers generate not only answers, but also their degrees of confidence that the answer is correct. Some crowd-workers cheat: they produce almost random answers without bothering to spend time analyzing the corresponding image. Algorithms have been developed to detect such cheaters. The problem is that many crowd-workers cannot describe …
Aquatic Ecotoxicology: Theoretical Explanation Of Empirical Formulas, Demetrius R. Hernandez, George M. Molina Holguin, Francisco Parra, Vivian Sanchez, Vladik Kreinovich
Aquatic Ecotoxicology: Theoretical Explanation Of Empirical Formulas, Demetrius R. Hernandez, George M. Molina Holguin, Francisco Parra, Vivian Sanchez, Vladik Kreinovich
Departmental Technical Reports (CS)
To analyze the effect of pollution on marine life, it is important to know how exactly the concentration of toxic substances decreases with time. There are several semi-empirical formulas that describe this decrease. In this paper, we provide a theoretical explanation for these empirical formulas.
Word Representation: Theoretical Explanation Of An Empirical Fact, Leonel Escapita, Diana Licon, Madison Anderson, Diego Pedraza, Vladik Kreinovich
Word Representation: Theoretical Explanation Of An Empirical Fact, Leonel Escapita, Diana Licon, Madison Anderson, Diego Pedraza, Vladik Kreinovich
Departmental Technical Reports (CS)
There is a reasonably accurate empirical formula that predicts, for two words i and j, the number Xij of times when the word i will appear in the vicinity of the word j. The parameters of this formula are determined by using the weighted least square approach. Empirically, the predictions are the most accurate if we use the weights proportional to a power of Xij. In this paper, we provide a theoretical explanation for this empirical fact.
Resource Allocation For Multi-Tasking Optimization: Explanation Of An Empirical Formula, Alan Gamez, Antonio Aguirre, Christian Cordova, Alberto Miranda, Vladik Kreinovich
Resource Allocation For Multi-Tasking Optimization: Explanation Of An Empirical Formula, Alan Gamez, Antonio Aguirre, Christian Cordova, Alberto Miranda, Vladik Kreinovich
Departmental Technical Reports (CS)
For multi-tasking optimization problems, it has been empirically shown that the most effective resource allocation is attained when we assume that the gain of each task logarithmically depends on the computation time allocated to this task. In this paper, we provide a theoretical explanation for this empirical fact.
How To Reach A Joint Decision With The Smallest Need For Compromise, Sofia Holguin, Olga Kosheleva
How To Reach A Joint Decision With The Smallest Need For Compromise, Sofia Holguin, Olga Kosheleva
Departmental Technical Reports (CS)
Usually, people's interests do not match perfectly. So when several people need to make a joint decision, they need to compromise. The more people one has to coordinate the decision with, the fewer chances that each person's preferences will be properly taken into account. Therefore, when a large group of people need to make a decision, it is desirable to make sure that this decision can be reached by dividing all the people into small-size groups so that this decision can reach a compromise between the members of each group. In this paper, we use a recent mathematical result to …
Need For Optimal Distributed Measurement Of Cumulative Quantities Explains The Ubiquity Of Absolute And Relative Error Components, Hector A. Reyes, Aaron D. Brown, Jeffrey Escamilla, Ethan D. Kish, Vladik Kreinovich
Need For Optimal Distributed Measurement Of Cumulative Quantities Explains The Ubiquity Of Absolute And Relative Error Components, Hector A. Reyes, Aaron D. Brown, Jeffrey Escamilla, Ethan D. Kish, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we need to measure the value of a cumulative quantity, i.e., a quantity that is obtained by adding measurement results corresponding to different spatial locations. How can we select the measuring instruments so that the resulting cumulative quantity can be determined with known accuracy -- and, to avoid unnecessary expenses, not more accurately than needed? It turns out that the only case where such an optimal arrangement is possible is when the required accuracy means selecting the upper bounds on absolute and relative error components. This results provides a possible explanation for the ubiquity of such …
Dielectric Barrier Discharge (Dbd) Thrusters -- Aerospace Engines Of The Future: Invariance-Based Analysis, Alexis Lupo, Vladik Kreinovich
Dielectric Barrier Discharge (Dbd) Thrusters -- Aerospace Engines Of The Future: Invariance-Based Analysis, Alexis Lupo, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the most prospective aerospace engines is a Dielectric Barrier Discharge (DBD) thruster -- an effective electric engine without moving parts. Originally designed by NASA for flights over other planets, it has been shown to be very promising for Earth-based flights as well. The efficiency of this engine depends on the proper selection of the corresponding electric field. To make this selection, we need to know, in particular, how its thrust depends on the atmospheric pressure. At present, for this dependence, we only know an approximate semi-empirical formula. In this paper, we use natural invariance requirements to come up …
Why Color Optical Computing, Victor L. Timchenko, Yury P. Kondratenko, Vladik Kreinovich
Why Color Optical Computing, Victor L. Timchenko, Yury P. Kondratenko, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we show that requirements that computations be fast and noise-resistant naturally lead to what we call color-based optical computing.
Hunting Habits Of Predatory Birds: Theoretical Explanation Of An Empirical Formula, Adilene Alaniz, Jiovani Hernandez, Andres D. Munoz, Vladik Kreinovich
Hunting Habits Of Predatory Birds: Theoretical Explanation Of An Empirical Formula, Adilene Alaniz, Jiovani Hernandez, Andres D. Munoz, Vladik Kreinovich
Departmental Technical Reports (CS)
Predatory birds play an important role in an ecosystem. It is therefore important to study their hunting behavior, in particular, the distribution of their waiting time. A recent empirical study showed that the waiting time is distributed according to the power law. In this paper, we use natural invariance ideas to come up with a theoretical explanation for this empirical dependence.
How To Describe Variety Of A Probability Distribution: A Possible Answer To Yager's Question, Vladik Kreinovich
How To Describe Variety Of A Probability Distribution: A Possible Answer To Yager's Question, Vladik Kreinovich
Departmental Technical Reports (CS)
Entropy is a natural measure of randomness. It progresses from its smallest possible value 0 -- when we have a deterministic case in which one alternative i occurs with probability 1 (pi = 1), to the largest possible value which is attained at a uniform distribution p1 = ... = pn = 1/n. Intuitively, both in the deterministic case and in the uniform distribution case, there is not much variety in the distribution, while in the intermediate cases, when we have several different values pi, there is a strong variety. Entropy does not seem to capture this notion of variety. …
Why 1/(1+D) Is An Effective Distance-Based Similarity Measure: Two Explanations, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich
Why 1/(1+D) Is An Effective Distance-Based Similarity Measure: Two Explanations, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Most of our decisions are based on the notion of similarity: we use a decision that helped in similar situations. From this viewpoint, it is important to have, for each pair of situations or objects, a numerical value describing similarity between them. This is called a similarity measure. In some cases, the only information that we can use to estimate the similarity value is some natural distance measure d(a,b). In many such situations, empirical data shows that the similarity measure 1/(1+d) is very effective. In this paper, we provide two explanations for this effectiveness.
How The Pavement Strength Changes With Time: Ai Ideas Help To Explain Semi-Empirical Formulas, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich
How The Pavement Strength Changes With Time: Ai Ideas Help To Explain Semi-Empirical Formulas, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we use AI ideas to provide a theoretical explanation for semi-empirical formulas that describe how the pavement strength changes with time, and how we can predict the pavement lifetime.
A General Commonsense Explanation Of Several Medical Results, Olga Kosheleva, Vladik Kreinovich
A General Commonsense Explanation Of Several Medical Results, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we show that many recent experimental medical results about the effect of different factors on our health can be explained by common sense ideas.
Invariance Explains Empirical Success Of Many Intelligent Techniques, Olga Kosheleva, Vladik Kreinovich
Invariance Explains Empirical Success Of Many Intelligent Techniques, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many applications of intelligent computing, we need to choose an appropriate function -- e.g., an appropriate re-scaling function, or an appropriate aggregation function. In applications of intelligent techniques, the problem of selecting an optimal function is usually too complex or too imprecise to be solved analytically, so the best functions are found empirically, by trying a large number of alternatives. In this paper, we show that in many such cases, the resulting empirical choice can be explained by natural invariance ideas. Example range from applications to building blocks of intelligent techniques -- such as aggregation (including hierarchical aggregation) and …
Why Best-Worst Method Works Well, Sean Aguilar, Vladik Kreinovich
Why Best-Worst Method Works Well, Sean Aguilar, Vladik Kreinovich
Departmental Technical Reports (CS)
In many cases, experts are much more accurate when they estimate the ratio of two quantities than when they estimate the actual values. For example, if it difficult to accurately estimate the height of a person on a photo, but if we have two people standing side by side, we can easily estimate to what extent one of them is taller than the other one. To get accurate estimates, it is therefore desirable to use such ratio estimates. Empirical analysis shows that to obtain the most accurate results, we need to compare all the objects with either the "best" object …
Seemingly Counter-Intuitive Features Of Good-To-Great Companies Actually Make Perfect Sense: Possible Algorithmics-Based Explanations, Francisco Zapata, Eric Smith, Olga Kosheleva, Vladik Kreinovich
Seemingly Counter-Intuitive Features Of Good-To-Great Companies Actually Make Perfect Sense: Possible Algorithmics-Based Explanations, Francisco Zapata, Eric Smith, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the late 1990s, researchers analyzed what distinguishes great companies from simply good ones. They found several features that are typical for great companies. Interestingly, most of these features seem counter-intuitive. In this paper, we show that from the algorithmic viewpoint, many of these features make perfect sense. Some of the resulting explanations are simple and straightforward, other explanations rely on complex not-well-publicized results from theoretical computer science.
How Hot Is Too Hot, Sofia Holguin, Vladik Kreinovich
How Hot Is Too Hot, Sofia Holguin, Vladik Kreinovich
Departmental Technical Reports (CS)
A recent study has shown that the temperature threshold -- after which even young healthy individuals start feeling the effect of heat on their productivity -- is 30.5 ± 1 C. In this paper, we use decision theory ideas to provide a theoretical explanation for this empirical finding.
What Is The Most Adequate Fuzzy Methodology?, Noah Velasco, Olga Kosheleva, Vladik Kreinovich
What Is The Most Adequate Fuzzy Methodology?, Noah Velasco, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In practice, there is often a need to describe the relation y = f(x) between two quantities in algorithmic form: e.g., we want to describe the control value y corresponding to the given input x, or we want to predict the future value y based on the current value x. In many such cases, we have expert knowledge about the desired dependence, but experts can only describe their knowledge by using imprecise ("fuzzy") words from a natural language. Methodologies for transforming such knowledge into an algorithm y = f(x) are known as fuzzy methodologies. There exist several fuzzy methodologies, a …