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Articles 181 - 210 of 667
Full-Text Articles in Mathematics
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.
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.
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 …
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.
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 …
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 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. …
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.
Why Seneca Effect?, Sean R. Aguilar, Vladik Kreinovich
Why Seneca Effect?, Sean R. Aguilar, Vladik Kreinovich
Departmental Technical Reports (CS)
Already ancients noticed that decrease is usually faster than growth -- whether we talk about companies or empires. A modern researcher Ugo Bardi confirmed that this phenomenon is still valid today. He called it Seneca effect, after the ancient philosopher Seneca -- one of those who observed this phenomenon. In this paper, we provide a natural explanation for the Seneca effect.
Why Smaller-Size Objects Affect The Flow Much More Than Larger Ones: A Geometric Explanation With Applications Ranging From Volcanoes And Tornadoes To Blood, Fish, And Building Preservation, Laxman Bokati, Vladik Kreinovich
Why Smaller-Size Objects Affect The Flow Much More Than Larger Ones: A Geometric Explanation With Applications Ranging From Volcanoes And Tornadoes To Blood, Fish, And Building Preservation, Laxman Bokati, Vladik Kreinovich
Departmental Technical Reports (CS)
At first glance, the larger the object, the larger should be its effect on the surroundings -- in particular, the larger should be its effect on the surrounding flow. However, in many practical situations, we observe the opposite effect: smaller-size particles affect the flow much more than larger-size particles. This seemingly counterintuitive phenomena has been observed in many situations: lava flow in the volcanoes, air circulation in tornadoes, blood flow in a body, the effect of fish on water circulation in the ocean, and the effect of added particles on seeping water that damages historic buildings. In this paper, we …
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 …
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.
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 …
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.
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 Exponential Almon Lag Works Well In Econometrics: An Invariance-Based Explanation, Laxman Bokati, Vladik Kreinovich
Why Exponential Almon Lag Works Well In Econometrics: An Invariance-Based Explanation, Laxman Bokati, Vladik Kreinovich
Departmental Technical Reports (CS)
In many econometric situations, we can predict future values of relevant quantities by using an empirical formula known as exponential Almon lag. While this formula is empirically successful, there have been no convincing theoretical explanation for this success. In this paper, we provide such a theoretical explanation based on general invariance ideas.
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 Order And Disorder Affect People's Behavior: An Explanation, Sofia Holguin, Vladik Kreinovich
How Order And Disorder Affect People's Behavior: An Explanation, Sofia Holguin, Vladik Kreinovich
Departmental Technical Reports (CS)
Experimental data shows that people placed in orderly rooms donate more to charity and make healthier food choices that people placed in disorderly rooms. On the other hand, people placed in disorderly rooms show more creativity. In this paper, we provide a possible explanation for these empirical phenomena.
Why Decision Paralysis, Sean Aguilar, Vladik Kreinovich
Why Decision Paralysis, Sean Aguilar, Vladik Kreinovich
Departmental Technical Reports (CS)
If a person has a small number of good alternatives, this person can usually make a good decision, i.e., select one of the given alternatives. However, when we have a large number of good alternatives, people take much longer to make a decision -- sometimes so long that, as a result, no decision is made. How can we explain this seemingly no-optimal behavior? In this paper, we show that this "decision paralysis" can be naturally explained by using the usual decision making ideas.
Why Five Stages Of Solar Activity, Why Five Stages Of Grief, Why Seven Plus Minus Two: A General Geometric Explanation, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich
Why Five Stages Of Solar Activity, Why Five Stages Of Grief, Why Seven Plus Minus Two: A General Geometric Explanation, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
A recent paper showed that the solar activity cycle has five clear stages, and that taking theses stages into account helps to make accurate predictions of future solar activity. Similar 5-stage models have been effective in many other application area, e.g., in psychology, where a 5-stage model provides an effective description of grief. In this paper, we provide a general geometric explanations of why 5-stage models are often effective. This result also explains other empirical facts, e.g., the seven plus minus two law in psychology and the fact that only five space-time dimensions have found direct physical meaning.
Why Micro-Size Objects Affect The Flow Much More Than Larger Ones: A Geometric Explanations With Applications Ranging From Volcanoes And Tornadoes To Blood, Fish, And Building Preservation, Laxman Bokati, Vladik Kreinovich
Why Micro-Size Objects Affect The Flow Much More Than Larger Ones: A Geometric Explanations With Applications Ranging From Volcanoes And Tornadoes To Blood, Fish, And Building Preservation, Laxman Bokati, Vladik Kreinovich
Departmental Technical Reports (CS)
At first glance, the larger the object, the larger should be its effect on the surroundings -- in particular, the larger should be its effect on the surrounding flow. However, in many practical situations, we observe the opposite effect: micro-size particles affect the flow much more than larger-size particles. This seemingly counterintuitive phenomena has been observed in many situations: lava flow in the volcanoes, air circulation in tornadoes, blood flow in a body, the effect of fish on water circulation in the ocean, and the effect of added particles on seeping water that damages historic buildings. In this paper, we …
How To Make Inflation Optimal And Fair, Sean Aguilar, Vladik Kreinovich
How To Make Inflation Optimal And Fair, Sean Aguilar, Vladik Kreinovich
Departmental Technical Reports (CS)
A reasonably small inflation helps economy as a whole -- by encouraging spending, but it also hurts people by decreasing the value of their savings. It is therefore reasonably to come up with an optimal (and fair) level of inflation, that would stimulate economy without hurting people too much. In this paper, we describe how this can be potentially done.
How To Detect The Fundamental Frequency: Approach Motivated By Soft Computing And Computational Complexity, Eric Freudenthal, Olga Kosheleva, Vladik Kreinovich
How To Detect The Fundamental Frequency: Approach Motivated By Soft Computing And Computational Complexity, Eric Freudenthal, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Psychologists have shown that most information about the mood and attitude of a speaker is carried by the lowest (fundamental) frequency. Because of this frequency's importance, even when the corresponding Fourier component is weak, the human brain reconstruct this frequency based on higher harmonics. The problems is that many people lack this ability. To help them better understand moods and attitudes in social interaction, it is therefore desirable to come up with devices and algorithms that would reconstruct the fundamental frequency. In this paper, we show that ideas from soft computing and computational complexity can be used for this purpose.
Why Time Seems To Pass Slowly For Unpleasant Experiences And Quickly For Pleasant Experiences: An Explanation Based On Decision Theory, Laxman Bokati, Vladik Kreinovich
Why Time Seems To Pass Slowly For Unpleasant Experiences And Quickly For Pleasant Experiences: An Explanation Based On Decision Theory, Laxman Bokati, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that our perception of time depends on our level of happiness: time seems to pass slower when we have unpleasant experiences and faster if our experiences are pleasant. Several explanations have been proposed for this effect. However, these explanations are based on specific features of human memory and/or human perception, features that, in turn, need explaining. In this paper, we show that this effect can be explained on a much more basic level of decision theory, without utilizing any specific features of human memory or perception.
Monotonic Bit-Invariant Permutation-Invariant Metrics On The Set Of All Infinite Binary Sequences, Irina Padilla, Vladik Kreinovich
Monotonic Bit-Invariant Permutation-Invariant Metrics On The Set Of All Infinite Binary Sequences, Irina Padilla, Vladik Kreinovich
Departmental Technical Reports (CS)
In a computer, all the information about an object is described by a sequence of 0s and 1s. At any given moment of time, we only have partial information, but as we perform more measurements and observations, we get longer and longer sequence that provides a more and more accurate description of the object. In the limit, we get a perfect description by an infinite binary sequence. If the objects are similar, measurement results are similar, so the resulting binary sequences are similar. Thus, to gauge similarity of two objects, a reasonable idea is to define an appropriate metric on …
Physical Trajectories Are Smooth, With Velocities At Least As Continuous As Brownian Motion, Olga Kosheleva, Vladik Kreinovich
Physical Trajectories Are Smooth, With Velocities At Least As Continuous As Brownian Motion, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
The fact that the kinetic energy of a particle cannot exceed its overall energy implies that the velocity -- i.e. the derivative of the trajectory -- should be bounded. This means, in effect, that all the trajectories are differentiable (smooth). However, at first glance, there seems to be no direct requirement that the velocities continuously depend on time. In this paper, we show that the properties of electromagnetic field necessitate that the velocities are continuous functions of time -- moreover, that they are at least as continuous as the Brownian motion.
Why Would Anyone Invest In A High-Risk Low-Profit Enterprise?, Olga Kosheleva, Vladik Kreinovich
Why Would Anyone Invest In A High-Risk Low-Profit Enterprise?, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Strangely enough, investors invest in high-risk low-profit enterprises as well. At first glance, this seems to contradict common sense and financial basics. However, we show that such investments make perfect sense as long as the related risks are independent from the risks of other investments. Moreover, we show that an optimal investment portfolio should allocate some investment to this enterprise.
Why Rectified Power (Repu) Activation Functions Are Efficient In Deep Learning: A Theoretical Explanation, Laxman Bokati, Vladik Kreinovich, Joseph Baca, Natasha Rovelli
Why Rectified Power (Repu) Activation Functions Are Efficient In Deep Learning: A Theoretical Explanation, Laxman Bokati, Vladik Kreinovich, Joseph Baca, Natasha Rovelli
Departmental Technical Reports (CS)
At present, the most efficient machine learning techniques is deep learning, with neurons using Rectified Linear (ReLU) activation function s(z) = max(0,z), in many cases, the use of Rectified Power (RePU) activation functions (s(z))^p -- for some p -- leads to better results. In this paper, we explain these results by proving that RePU functions (or their "leaky" versions) are optimal with respect that all reasonable optimality criteria.
Over-Measurement Paradox: Suspension Of Thermonuclear Research Center And Need To Update Standards, Hector Reyes, Saeid Tizpaz-Niari, Vladik Kreinovich
Over-Measurement Paradox: Suspension Of Thermonuclear Research Center And Need To Update Standards, Hector Reyes, Saeid Tizpaz-Niari, Vladik Kreinovich
Departmental Technical Reports (CS)
In general, the more measurements we perform, the more information we gain about the system and thus, the more adequate decisions we will be able to make. However, in situations when we perform measurements to check for safety, the situation is sometimes opposite: the more additional measurements we perform beyond what is required, the worse the decisions will be: namely, the higher the chance that a perfectly safe system will be erroneously classified as unsafe and therefore, unnecessary additional features will be added to the system design. This is not just a theoretical possibility: exactly this phenomenon is one of …
Everyone Is Above Average: Is It Possible? Is It Good?, Vladik Kreinovich, Olga Kosheleva
Everyone Is Above Average: Is It Possible? Is It Good?, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
Starting with the 1980s, a popular US satirical radio show described a fictitious town Lake Wobegon where ``all children are above average'' -- parodying the way parents like to talk about their children. This everyone-above-average situation was part of the fiction since, if we interpret the average in the precise mathematical sense, as average over all the town's children, then such a situation is clearly impossible. However, usually, when parents make this claim, they do not mean town-wise average, they mean average over all the kids with whom their child directly interacts. Somewhat surprisingly, it turns out that if we …