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Articles 61 - 90 of 114
Full-Text Articles in Applied Mathematics
Avoiding Einstein-Podolsky-Rosen (Epr) Paradox: Towards A More Physically Adequate Description Of A Quantum State, Joseph Bernal, Olga Kosheleva, Vladik Kreinovich
Avoiding Einstein-Podolsky-Rosen (Epr) Paradox: Towards A More Physically Adequate Description Of A Quantum State, Joseph Bernal, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
The famous EPR paradox shows that if we describe quantum particles in the usual way -- by their wave functions -- then we get the following seeming contradiction. If we entangle the states of the two particles, then move them far away from each other, and measure the state of the first particle, then the state of the second particle immediately changes -- which contradicts to special relativity, according to which such immediate-action-at-a-distance is not possible. It is known that, from the physical viewpoint, this is not a real paradox: if we measure any property of the second particle, the …
When Revolutions Succeed? 80/20 Rule And 7 Plus Minus 2 Law Explain The 3.5% Rule, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich
When Revolutions Succeed? 80/20 Rule And 7 Plus Minus 2 Law Explain The 3.5% Rule, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
A statistical analysis of hundreds of successful and unsuccessful revolution attempts led historian to a very unexpected conclusion: that most attempts involving at least 3.5% of the population succeeded, while most attempts that involved a smaller portion of the population failed. In this paper, we show that this unexpected threshold can be explained based on the other two known rules of human behavior: the 80/20 rule (20% of the people drink 80% of the beer) and 7 plus minus 2 law according to which we naturally divide everything into 7 plus minus 2 classes.
How To Make Decisions: Consider Multiple Scenarios, Consult Experts, Play Down Emotions -- Quantitative Explanation Of Commonsense Ideas, Julio Urenda, Francis Biney, Marco Cardiel, Perla De La O, Anthony Desarmier, Noa Dodson, Taylor Dodson, Sebastian Gonzalez, Laura Hinojos, Jorge Huerta, Ryan Jones, Oliver Martinez, Carlos A. Saldaña Matamoros, Manuel Muñoz, Vladik Kreinovich
How To Make Decisions: Consider Multiple Scenarios, Consult Experts, Play Down Emotions -- Quantitative Explanation Of Commonsense Ideas, Julio Urenda, Francis Biney, Marco Cardiel, Perla De La O, Anthony Desarmier, Noa Dodson, Taylor Dodson, Sebastian Gonzalez, Laura Hinojos, Jorge Huerta, Ryan Jones, Oliver Martinez, Carlos A. Saldaña Matamoros, Manuel Muñoz, Vladik Kreinovich
Departmental Technical Reports (CS)
There are a lot of commonsense advices in decision making: e.g., we should consider multiple scenarios, we should consult experts, we should play down emotions. Many of these advices come supported by a surprisingly consistent quantitative evidence. In this paper, on the example of the above advices, we provide a theoretical explanations for these quantitative facts.
Why 7 Plus Minus 2? A Possible Geometric Explanation, Laxman Bokati, Vladik Kreinovich, Jordan Katz
Why 7 Plus Minus 2? A Possible Geometric Explanation, Laxman Bokati, Vladik Kreinovich, Jordan Katz
Departmental Technical Reports (CS)
It is known that, in general, a person keeps in mind between 5 and 9 objects -- this is known as the 7 plus minus 2 law. In this paper, we provide a possible simple geometric explanation for this psychological feature.
Ranking-Based Voting Revisited: Maximum Entropy Approach Leads To Borda Count (And Its Versions), Olga Kosheleva, Vladik Kreinovich, Guo Wei
Ranking-Based Voting Revisited: Maximum Entropy Approach Leads To Borda Count (And Its Versions), Olga Kosheleva, Vladik Kreinovich, Guo Wei
Departmental Technical Reports (CS)
In many practical situations, we need to make a group decision that takes into account preferences of all the participants. Ideally, we should elicit, from each participant, a full information about his/her preferences, but such elicitation is usually too time-consuming to be practical. Instead, we only elicit, from each participant, his/her ranking of different alternatives. One of the semi-heuristic methods for decision making under such information is Borda count, when for each alternative and each participant, we count how many alternatives are worse, and then select the alternatives for which the sum of these numbers is the largest. In this …
Why Matrix Factorization Works Well In Recommender Systems: A Systems-Based Explanation, Griselda Acosta, Manuel Hernandez, Natalia Villanueva-Rosales, Eric Smith, Vladik Kreinovich
Why Matrix Factorization Works Well In Recommender Systems: A Systems-Based Explanation, Griselda Acosta, Manuel Hernandez, Natalia Villanueva-Rosales, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
Many computer-based services use recommender systems that predict our preferences based on our degree of satisfaction with the past selections. One of the most efficient techniques making recommender systems successful is matrix factorization. While this technique works well, until now, there was no general explanation of why it works. In this paper, we provide such an explanation.
Dynamic Triggering Of Earthquakes: Symmetry-Based Geometric Analysis, Laxman Bokati, Richard Alfaro, Aaron A. Velasco, Vladik Kreinovich
Dynamic Triggering Of Earthquakes: Symmetry-Based Geometric Analysis, Laxman Bokati, Richard Alfaro, Aaron A. Velasco, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that seismic waves from a remote earthquake can trigger a small local earthquake. Recent analysis has shown that this triggering occurs mostly when the direction of the incoming wave is orthogonal to the direction of the local fault, some triggerings occur when these directions are parallel, and very few triggerings occur when the angle between these two directions is different from 0 and 90 degrees. In this paper, we propose a symmetry-based geometric explanation for this unexpected observation.
How We Can Explain Simple Empirical Memory Rules, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
How We Can Explain Simple Empirical Memory Rules, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Researchers have found out that normally, we remember about 30% of the information; however, if immediately after reading, we get a test, the rate increases to 45%. In this paper, we show that Zipf law can explain this empirical dependence.
Why Pink Noise Is Best For Enhancing Sleep And Memory: System-Based Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich
Why Pink Noise Is Best For Enhancing Sleep And Memory: System-Based Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
Several researchers found out that acoustic stimulation during sleep enhances sleep and enhances memory. An interesting -- and somewhat mysterious -- part of this phenomenon is that out of all possible types of noise, the pink noise leads to the most efficient stimulation. In this paper, we use general system-based ideas to explain why in this phenomenon, pink noise works best.
Why Iq Test Scores Are Slightly Decreasing: Possible System-Based Explanation For The Reversed Flynn Effect, Griselda Acosta, Eric Smith, Vladik Kreinovich
Why Iq Test Scores Are Slightly Decreasing: Possible System-Based Explanation For The Reversed Flynn Effect, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
Researchers who monitor the average intelligence of human population have reasonably recently made an unexpected observation: that after many decades in which this level was constantly growing (this is known as the Flynn effect), at present, this level has started decreasing again. In this paper, we show that this reversed Flynn effect can be, in principle, explained in general system-based terms: namely, it is similar to the fact that a control system usually overshoots before stabilizing at the desired level. A similar idea may explain another unexpected observation -- that the Universe's expansion rate, which was supposed to be decreasing, …
In Alsina Et Al. Derivation Of Min-Max Fuzzy Logic From Distributivity, All Conditions Are Necessary: A Proof, Vladik Kreinovich, Ildar Batyrshin, Nailya Kubysheva
In Alsina Et Al. Derivation Of Min-Max Fuzzy Logic From Distributivity, All Conditions Are Necessary: A Proof, Vladik Kreinovich, Ildar Batyrshin, Nailya Kubysheva
Departmental Technical Reports (CS)
In their 1983 paper, C. Alsina, E. Trillas, and L. Valverde proved that distributivity, monotonicity, and boundary conditions imply that the "and"-operation is min and the "or"-operation is max. In this paper, we show that all these conditions are necessary for Alsina et al. result to be true.
Beyond P-Boxes And Interval-Valued Moments: Natural Next Approximations To General Imprecise Probabilities, Olga Kosheleva, Vladik Kreinovich
Beyond P-Boxes And Interval-Valued Moments: Natural Next Approximations To General Imprecise Probabilities, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
To make an adequate decision, we need to know the probabilities of different consequences of different actions. In practice, we only have partial information about these probabilities -- this situation is known as imprecise probabilities. A general description of all possible imprecise probabilities requires using infinitely many parameters. In practice, the two most widely used few-parametric approximate descriptions are p-boxes (bounds on the values of the cumulative distribution function) and interval-valued moments (i.e., bounds on moments). In some situations, these approximations are not sufficiently accurate. So, we need more accurate more-parametric approximations. In this paper, we explain what are the …
Why Beta Priors: Invariance-Based Explanation, Olga Kosheleva, Vladik Kreinovich, Kittawit Autchariyapanitkul
Why Beta Priors: Invariance-Based Explanation, Olga Kosheleva, Vladik Kreinovich, Kittawit Autchariyapanitkul
Departmental Technical Reports (CS)
In the Bayesian approach, to describe a prior distribution on the set [0,1] of all possible probability values, typically, a Beta distribution is used. The fact that there have been many successful applications of this idea seems to indicate that there must be a fundamental reason for selecting this particular family of distributions. In this paper, we show that the selection of this family can indeed be explained if we make reasonable invariance requirements.
How To Gauge A Combination Of Uncertainties Of Different Type: General Foundations, Ingo Neumann, Vladik Kreinovich, Thach N. Nguyen
How To Gauge A Combination Of Uncertainties Of Different Type: General Foundations, Ingo Neumann, Vladik Kreinovich, Thach N. Nguyen
Departmental Technical Reports (CS)
In many practical situations, for some components of the uncertainty (e.g., of the measurement error) we know the corresponding probability distribution, while for other components, we know only upper bound on the corresponding values. To decide which of the algorithms or techniques leads to less uncertainty, we need to be able to gauge the combined uncertainty by a single numerical value -- so that we can select the algorithm for which this values is the best. There exist several techniques for gauging the combination of interval and probabilistic uncertainty. In this paper, we consider the problem of gauging the combination …
How To Make A Decision Based On The Minimum Bayes Factor (Mbf): Explanation Of The Jeffreys Scale, Vladik Kreinovich, Olga Kosheleva, Nguyen Duc Trung
How To Make A Decision Based On The Minimum Bayes Factor (Mbf): Explanation Of The Jeffreys Scale, Vladik Kreinovich, Olga Kosheleva, Nguyen Duc Trung
Departmental Technical Reports (CS)
In many practical situations, we need to select a model based on the data. It is, at present, practically a consensus that the traditional p-value-based techniques for such selection often do not lead to adequate results. One of the most widely used alternative model selection techniques is the Minimum Bayes Factor (MBF) approach, in which a model is preferred if the corresponding Bayes factor -- the ratio of likelihoods corresponding to this model and to the competing model -- is sufficiently large for all possible prior distributions. Based on the MBF values, we can decide how strong is the evidence …
Why Derivative: Invariance-Based Explanation, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Why Derivative: Invariance-Based Explanation, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
To many students, the notion of a derivative seems unrelated to any previous mathematics -- and is, thus, difficult to study and to understand. In this paper, we show that this notion can be naturally derived from a more intuitive notion of invariance.
How To Reconcile Maximum Entropy Approach With Intuition: E.G., Should Interval Uncertainty Be Represented By A Uniform Distribution, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta
How To Reconcile Maximum Entropy Approach With Intuition: E.G., Should Interval Uncertainty Be Represented By A Uniform Distribution, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta
Departmental Technical Reports (CS)
In many practical situations, we only have partial information about the probabilities; this means that there are several different probability distributions which are consistent with our knowledge. In such cases, if we want to select one of these distributions, it makes sense not to pretend that we have a small amount of uncertainty -- and thus, it makes sense to select a distribution with the largest possible value of uncertainty. A natural measure of uncertainty of a probability distribution is its entropy. So, this means that out of all probability distributions consistent with our knowledge, we select the one whose …
Why The Obvious Necessary Condition Is (Often) Also Sufficient (Toncas): An Explanation Of The Phenomenon, Julio C. Urenda, Vladik Kreinovich
Why The Obvious Necessary Condition Is (Often) Also Sufficient (Toncas): An Explanation Of The Phenomenon, Julio C. Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
In many graph-related problems, an obvious necessary condition is often also sufficient. This phenomenon is so ubiquitous that it was even named TONCAS, after the first letters of the phrase describing this phenomenon. In this paper, we provide a possible explanation for this phenomenon.
Why Lasso, En, And Clot: Invariance-Based Explanation, Hamza Alkhatib, Ingo Neumann, Vladik Kreinovich, Chon Van Le
Why Lasso, En, And Clot: Invariance-Based Explanation, Hamza Alkhatib, Ingo Neumann, Vladik Kreinovich, Chon Van Le
Departmental Technical Reports (CS)
In many practical situations, observations and measurement results are consistent with many different models -- i.e., the corresponding problem is ill-posed. In such situations, a reasonable idea is to take into account that the values of the corresponding parameters should not be too large; this idea is known as regularization. Several different regularization techniques have been proposed; empirically the most successful are LASSO method, when we bound the sum of absolute values of the parameters, and EN and CLOT methods in which this sum is combined with the sum of the squares. In this paper, we explain the empirical success …
Neutron Lifetime Puzzle And Nuclear Stability: A Possible Relation, Olga Kosheleva, Vladik Kreinovich
Neutron Lifetime Puzzle And Nuclear Stability: A Possible Relation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that a free neutron decays into a proton, an electron, and an anti-neutrino. Interesting, recent attempts to measure the neutron's lifetime has led to two slightly different estimates: namely, the number of decaying neutrons is somewhat larger than the number of newly created protons. This difference is known as the neutron lifetime puzzle. A natural explanation for this difference is that in some cases, a neutron decays not into a proton, but into some other particle. If this explanation is true, this implies that nuclei with a sufficiently large number of neutrons will be unstable. Based on …
Why Experts Sometimes Do Not Perform Well In Unusual Situations, Julio C. Urenda, Vladik Kreinovich
Why Experts Sometimes Do Not Perform Well In Unusual Situations, Julio C. Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
We expect that the quality of experts' decisions increases with their experience. This is indeed true for reasonably routine situations. However, surprisingly, empirical data shows that in unusual situations, novice experts make much better decisions than more experience ones. This phenomenon is especially unexpected for medical emergency situations: it turns out that the mortality rate of patients treated by novice doctors is a third lower than for patients treated by experience doctors. In this paper, we provide a possible explanation for this seemingly counterintuitive phenomenon.
Unexpected Empirical Dependence Of Calf Gender On Insemination Time: System-Based Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich
Unexpected Empirical Dependence Of Calf Gender On Insemination Time: System-Based Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
To improve the efficiency of artificial insemination, farmers equip cows with sensors, based on which a computer system determines the cow's insemination window. Analysis of the resulting calves showed an unexpected dependence of the calf's gender on the insemination time: cows inseminated earlier in their window mostly gave birth to female calves, while cows inseminated later in their window mostly gave birth to males. In this paper, we provide a general system-based explanation for this phenomenon.
Dunning-Kruger Effect: A Simple System-Based Explanation, Griselda Acosta, Eric Smith
Dunning-Kruger Effect: A Simple System-Based Explanation, Griselda Acosta, Eric Smith
Departmental Technical Reports (CS)
In their 1999 paper, psychologists David Dunning and Justin Kruger showed that, in general, experts not only provide better estimates of different situations, but they also provide a better estimates of the accuracy of their estimates. Which this phenomenon has been confirmed by many follow-up experiments, it remains largely unexplained. In this paper, we provide a simple system-based qualitative explanation for the Dunning-Kruger effect.
In The Absence Of Information, 1/N Investment Makes Perfect Sense, Julio Urenda, Vladik Kreinovich
In The Absence Of Information, 1/N Investment Makes Perfect Sense, Julio Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
When people have several possible investment instruments, people often invest equally into these instruments: in the case of n instruments, they invest 1/n of their money into each of these instruments. Of course, if additional information about each instrument is available, this 1/n investment strategy is not optimal. We show, however, that in the absence of reliable information, 1/n investment is indeed the best strategy.
Maximum Entropy Approach To Portfolio Optimization: Economic Justification Of An Intuitive Diversity Idea, Laxman Bokati, Vladik Kreinovich
Maximum Entropy Approach To Portfolio Optimization: Economic Justification Of An Intuitive Diversity Idea, Laxman Bokati, Vladik Kreinovich
Departmental Technical Reports (CS)
The traditional Markowitz approach to portfolio optimization assumes that we know the means, variances, and covariances of the return rates of all the financial instruments. In some practical situations, however, we do not have enough information to determine the variances and covariances, we only know the means. To provide a reasonable portfolio allocation for such cases, researchers proposed a heuristic maximum entropy approach. In this paper, we provide an economic justification for this heuristic idea.
Nonlinear Mechanical Properties Of Road Pavements: Geometric Symmetries Explain The Empirical Difference Between Roads Built On Clay Vs. Granular Soils, Afshin Gholamy, Vladik Kreinovich
Nonlinear Mechanical Properties Of Road Pavements: Geometric Symmetries Explain The Empirical Difference Between Roads Built On Clay Vs. Granular Soils, Afshin Gholamy, Vladik Kreinovich
Departmental Technical Reports (CS)
It is empirically known that roads built on clay soils have different nonlinear mechanical properties than roads built on granular soils (such as gravel or sand). In this paper, we show that this difficult-to-explain empirical fact can be naturally explained if we analyze the corresponding geometric symmetries.
Why Top Experts Are Paid So Much: Economics-Based Explanation, Julio C. Urenda, Vladik Kreinovich
Why Top Experts Are Paid So Much: Economics-Based Explanation, Julio C. Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
At first glance, it seems that people should be paid in proportion to their contribution, so if one person produces a little more than the other one, he/she should be paid a little more. In reality, however, top performers are paid dis-proportionally more than those whose performance is slightly worse. How can we explain this from an economic viewpoint? We show that actually there is no paradox here: a simple economic analysis shows that in many area, it makes perfect economic sense to pay much more to top performers.
Intuitive Idea Of Implication Vs. Formal Definition: How To Define The Corresponding Degree, Olga Kosheleva, Vladik Kreinovich
Intuitive Idea Of Implication Vs. Formal Definition: How To Define The Corresponding Degree, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Formal implication does not capture the intuitive idea of "if A then B", since in formal implication, every two true statements -- even completely unrelated ones -- imply each other. A more adequate description of intuitive implication happens if we consider how much the use of A can shorten a derivation of B. At first glance, it may seem that the number of bits by which we shorten this derivation is a reasonable degree of implication, but we show that this number is not in good accordance with our intuition, and that a natural formalization of this intuition leads to …
Why Some Non-Classical Logics Are More Studied?, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Why Some Non-Classical Logics Are More Studied?, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Departmental Technical Reports (CS)
It is well known that the traditional 2-valued logic is only an approximation to how we actually reason. To provide a more adequate description of how we actually reason, researchers proposed and studied many generalizations and modifications of the traditional logic, generalizations and modifications in which some rules of the traditional logic are no longer valid. Interestingly, for some of such rules (e.g., for law of excluded middle), we have a century of research in logics that violate this rule, while for others (e.g., commutativity of ``and''), practically no research has been done. In this paper, we show that fuzzy …
Scale-Invariance-Based Pre-Processing Drastically Improves Neural Network Learning: Case Study Of Diagnosing Lung Dysfunction In Children, Nancy Avila, Julio Urenda, Nelly Gordillo, Vladik Kreinovich
Scale-Invariance-Based Pre-Processing Drastically Improves Neural Network Learning: Case Study Of Diagnosing Lung Dysfunction In Children, Nancy Avila, Julio Urenda, Nelly Gordillo, Vladik Kreinovich
Departmental Technical Reports (CS)
To adequately treat different types of lung dysfunctions in children, it is important to properly diagnose the corresponding dysfunction, and this is not an easy task. Neural networks have been trained to perform this diagnosis, but they are not perfect in diagnostics: their success rate is 60%. In this paper, we show that by selecting an appropriate invariance-based pre-processing, we can drastically improve the diagnostic success, to 100% for diagnosing the presence of a lung dysfunction.