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- "no trade theorem" paradox (1)
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Articles 1 - 30 of 54
Full-Text Articles in Physical Sciences and Mathematics
Joule's 19th Century Energy Conservation Meta-Law And The 20th Century Physics (Quantum Mechanics And General Relativity): 21st Century Analysis, Vladik Kreinovich, Olga Kosheleva
Joule's 19th Century Energy Conservation Meta-Law And The 20th Century Physics (Quantum Mechanics And General Relativity): 21st Century Analysis, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
Joule's Energy Conservation Law was the first "meta-law": a general principle that all physical equations must satisfy. It has led to many important and useful physical discoveries. However, a recent analysis seems to indicate that this meta-law is inconsistent with other principles -- such as the existence of free will. We show that this conclusion about inconsistency is based on a seemingly reasonable -- but simplified -- analysis of the situation. We also show that a more detailed mathematical and physical analysis of the situation reveals that not only Joule's principle remains true -- it is actually strengthened: it is …
Deep Learning (Partly) Demystified, Vladik Kreinovich, Olga Kosheleva
Deep Learning (Partly) Demystified, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
Successes of deep learning are partly due to appropriate selection of activation function, pooling functions, etc. Most of these choices have been made based on empirical comparison and heuristic ideas. In this paper, we show that many of these choices -- and the surprising success of deep learning in the first place -- can be explained by reasonably simple and natural mathematics.
How Can We Explain Different Number Systems?, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich
How Can We Explain Different Number Systems?, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
At present, we mostly use decimal (base-10) number system, but in the past, many other systems were used: base-20, base-60 -- which is still reflected in how we divide an hour into minutes and a minute into seconds -- and many others. There is a known explanation for the base-60 system: 60 is the smallest number that can be divided by 2, by 3, by 4, by 5, and by 6. Because of this, e.g., half an hour, one-third of an hour, all the way to one-sixth of an hour all correspond to a whole number of minutes. In this …
How To Reconcile Randomness With Physicists' Belief That Every Theory Is Approximate: Informal Knowledge Is Needed, Ricardo Alvarez, Nick Sims, Christian Servin, Martine Ceberio, Vladik Kreinovich
How To Reconcile Randomness With Physicists' Belief That Every Theory Is Approximate: Informal Knowledge Is Needed, Ricardo Alvarez, Nick Sims, Christian Servin, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we show that physicists' intuition about randomness is not fully consistent with their belief that every theory is only approximate. We also prove that there is no formal way to reconcile these two intuitions, this reconciliation has to be informal. Thus, there are fundamental reasons why informal knowledge is needed for describing the real world.
How User Ratings Change With Time: Theoretical Explanation Of An Empirical Formula, Julio Urenda, Manuel Hernandez, Natalia Villanueva Rosales, Vladik Kreinovich
How User Ratings Change With Time: Theoretical Explanation Of An Empirical Formula, Julio Urenda, Manuel Hernandez, Natalia Villanueva Rosales, Vladik Kreinovich
Departmental Technical Reports (CS)
In many application areas, it is important to predict the user's reaction to new products. In general, this reaction changes with time. Empirical analysis of this dependence has shown that it can be reasonably accurately described by a power law. In this paper, we provide a theoretical explanation for this empirical formula.
How To Assign Grades To Tasks So As To Maximize Student Efforts, Laxman Bokati, Vyacheslav Kalashnikov, Nataliya Kalashnykova, Olga Kosheleva, Vladik Kreinovich
How To Assign Grades To Tasks So As To Maximize Student Efforts, Laxman Bokati, Vyacheslav Kalashnikov, Nataliya Kalashnykova, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In some classes, students want to get a desired passing grade (e.g., C or B) by spending the smallest amount of effort. In such situations, it is reasonable for the instructor to assign the grades for different tasks in such a way that the resulting overall student's effort is the largest possible. In this paper, we show that to achieve this goal, we need to assign, to each task, the number of points proportional to the efforts needed for this task.
Epicycles Are Almost As Good As Trigonometric Series: General System-Based Analysis, Griselda Acosta, Eric Smith, Olga Kosheleva, Vladik Kreinovich
Epicycles Are Almost As Good As Trigonometric Series: General System-Based Analysis, Griselda Acosta, Eric Smith, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
To adequately describe the planets' motion, ancient astronomers used epicycles, when a planet makes a circular motion not around the Earth, but around a special auxiliary point which, in turn, performs a circular motion around the Earth -- or around a second auxiliary point which, in turns, rotates around the Earth, etc. Standard textbooks malign this approach by calling it bad science, but in reality, this is, in effect, trigonometric (Fourier) series -- an extremely useful tool in science and engineering. It should be mentioned, however, that the epicycles are almost as good as trigonometric series -- in the sense …
Why Filtering Out Higher Harmonics Makes It Easier To Carry A Tune, Griselda Acosta, Eric Freudenthal, Eric Smith, Vladik Kreinovich
Why Filtering Out Higher Harmonics Makes It Easier To Carry A Tune, Griselda Acosta, Eric Freudenthal, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
A recent patent shows that filtering out higher harmonics helps people sing in-tune. In this paper, we use the general signal processing ideas to explain this empirical phenomenon. We also show that filtering out higher harmonics is the optimal way of increasing the signal-to-noise ratio -- and thus, of making it easier for people to recognize when they are signing out of tune.
If Space-Time Is Discrete, We May Be Able To Solve Np-Hard Problems In Polynomial Time, Ricardo Alvarez, Nick Sims, Christian Servin, Martine Ceberio, Vladik Kreinovich
If Space-Time Is Discrete, We May Be Able To Solve Np-Hard Problems In Polynomial Time, Ricardo Alvarez, Nick Sims, Christian Servin, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
Traditional physics assumes that space and time are continuous. However, this reasonable model leads to some serious problems. One the approaches that physicists follow to solve these problems is to assume that the space-time is actually discrete. In this paper, we analyze possible computational consequences of this discreteness. It turns out that in a discrete space-time, we may be able to solve NP-hard problems in polynomial time.
Geometric Explanation For An Empirical Formula Describing Our Galaxy's Warping, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Geometric Explanation For An Empirical Formula Describing Our Galaxy's Warping, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the first approximation, the shape of our Galaxy -- as well as the shape of many other celestial bodies -- can be naturally explained by geometric symmetries and the corresponding invariances. As a result, we get the familiar shape of a planar spiral. A recent more detailed analysis of our Galaxy's shape has shown that the Galaxy somewhat deviates from this ideal shape: namely, it is not perfectly planar, it is somewhat warped in the third dimension. In this paper, we show that the empirical formula for this warping can also be explained by geometric symmetries and invariance.
Towards A Theoretical Explanation Of How Pavement Condition Index Deteriorates Over Time, Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, Vladik Kreinovich
Towards A Theoretical Explanation Of How Pavement Condition Index Deteriorates Over Time, Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, Vladik Kreinovich
Departmental Technical Reports (CS)
To predict how the Pavement Condition Index will change over time, practitioners use a complex empirical formula derived in the 1980s. In this paper, we provide a possible theoretical explanation for this formula, an explanation based on general ideas of invariance. In general, the existence of a theoretical explanation makes a formula more reliable; thus, we hope that our explanation will make predictions of road quality more reliable.
80/20 Rule Partially Explains 7 Plus Minus 2 Law: General System-Based Analysis, Griselda Acosta, Eric Smith, Vladik Kreinovich
80/20 Rule Partially Explains 7 Plus Minus 2 Law: General System-Based Analysis, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
The 80/20 rule and the 7 plus minus 2 law are examples of difficult to explain empirical facts. According to the 80/20 rule, in each activity, 20% of the people contribute to the 80% of the results. The 7 plus minus 2 law means that we divide objects into 7 plus minus 2 groups -- i.e., into 5 to 9 groups. In this paper, we show that there is a relation between these two facts: namely, we show that, because of the 80/20 rule, the number of classes cannot be smaller than 5. Thus, the 80/20 rule explains the lower …
Why Area Under The Curve In Hypothesis Testing?, Griselda Acosta, Eric Smith, Vladik Kreinovich
Why Area Under The Curve In Hypothesis Testing?, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
To compare two different hypothesis testing techniques, researchers use the following heuristic idea: for each technique, they form a curve describing how the probabilities of type I and type II errors are related for this technique, and then compare areas under the resulting curves. In this paper, we provide a justification for this heuristic idea.
How To Explain That Changes In Elderlies Depression Level Are Uniformly Distributed, Griselda Acosta, Eric Smith, Vladik Kreinovich
How To Explain That Changes In Elderlies Depression Level Are Uniformly Distributed, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
Changes in the elderlies depression level result from a large number of small independent factors. Such situations are ubiquitous in applications. In most such cases, due to the Central Limit Theorem, the corresponding distribution is close to Gaussian. For the changes in the elderlies depression level, however, the empirical distribution is far from Gaussian: it is uniform. In this paper, we provide a possible explanation for the emergence of the uniform distribution.
Status Quo Bias Actually Helps Decision Makers To Take Nonlinearity Into Account: An Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich
Status Quo Bias Actually Helps Decision Makers To Take Nonlinearity Into Account: An Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the main motivations for designing computer models of complex systems is to come up with recommendations on how to best control these systems. Many complex real-life systems are so complicated that it is not computationally possible to use realistic nonlinear models to find the corresponding optimal control. Instead, researchers make recommendations based on simplified -- e.g., linearized -- models. The recommendations based on these simplified models are often not realistic but, interestingly, they can be made more realistic if we "tone them down" -- i.e., consider predictions and recommendations which are close to the current status quo state. …
Smaller Standard Deviation For Initial Weights Improves Performance Of Classifying Neural Networks: A Theoretical Explanation Of Unexpected Simulation Results, Diego Aguirre, Philip Hassoun, Rafael Lopez, Crystal Serrano, Marcoantonio R. Soto, Andrea Torres, Vladik Kreinovich
Smaller Standard Deviation For Initial Weights Improves Performance Of Classifying Neural Networks: A Theoretical Explanation Of Unexpected Simulation Results, Diego Aguirre, Philip Hassoun, Rafael Lopez, Crystal Serrano, Marcoantonio R. Soto, Andrea Torres, Vladik Kreinovich
Departmental Technical Reports (CS)
Numerical experiments show that for classifying neural networks, it is beneficial to select a smaller deviation for initial weights that what is usually recommended. In this paper, we provide a theoretical explanation for these unexpected simulation results.
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.
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 …
A Natural Explanation For The Minimum Entropy Production Principle, Griselda Acosta, Eric Smith, Vladik Kreinovich
A Natural Explanation For The Minimum Entropy Production Principle, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
It is well known that, according to the second law of thermodynamics, the entropy of a closed system increases (or at least stays the same). In many situations, this increase is the smallest possible. The corresponding minimum entropy production principle was first formulated and explained by a future Nobelist Ilya Prigogine. Since then, many possible explanations of this principle appeared, but all of them are very technical, based on complex analysis of differential equations describing the system's dynamics. Since this phenomenon is ubiquitous for many systems, it is desirable to look for a general system-based explanation, explanation that would not …
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.
Common Sense Addition Explained By Hurwicz Optimism-Pessimism Criterion, Bibek Aryal, Laxman Bokati, Karla Godinez, Shammir Ibarra, Heyi Liu, Bofei Wang, Vladik Kreinovich
Common Sense Addition Explained By Hurwicz Optimism-Pessimism Criterion, Bibek Aryal, Laxman Bokati, Karla Godinez, Shammir Ibarra, Heyi Liu, Bofei Wang, Vladik Kreinovich
Departmental Technical Reports (CS)
If we place a can of coke that weigh 0.35 kg into a car that weighs 1 ton = 1000 kg, what will be the resulting weight of the car? Mathematics says 1000.35 kg, but common sense says 1 ton. In this paper, we show that this common sense answer can be explained by the Hurwicz optimism-pessimism criterion of decision making under interval uncertainty.
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, …
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.
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.
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 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.
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.
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.
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 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 …