Physical Sciences and Mathematics Commons^™

From Gig Economy To Gig Education, Olga Kosheleva, Julian Viera Jr., Vladik Kreinovich

Departmental Technical Reports (CS)

Modern economy has benefited from gig economy idea, where, instead of hiring permanent employees, a company assigns each task to the person who is the most efficient in performing this task. This way, each task is performed in the best possible way -- by a person who is the most suited for this job. Why not extend this idea to education? Every student deserves the best possible teacher in every topic. So why not have a teacher who is the best in town in explaining quadratic equations teach quadratic equations to all the students from the town? In this paper, …

Should School Feel Like A Family: Lessons From Business Controversy As Interpreted By Decision Making Theory, Olga Kosheleva, Julian Viera Jr., Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional business theory promoted the ideal of business as a family: everyone should feel good about each other, all employees should feel good working together towards a joint goal. Recently, however, researchers claim that the well-promoted ideal is unattainable, it is a ruse causing everyone to overwork. Instead, these researchers propose a non-emotional collaboration of adults working temporarily on a joint project. In this paper, we show that this new trend is not just based on anecdotal evidence, it actually has a solid foundation in decision theory. So maybe we should apply this new trend to teaching too - and …

Towards Optimal Implementation Of Decentralized Currencies: How To Best Select Probabilities In An Ethereum-Type Proof-Of-Stake Protocol, Thach N. Nguyen, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

Nowadays, most financial transactions are based on a centralized system, when all the transaction records are stored in a central location. This centralization makes the financial system vulnerable to cyber-attacks. A natural way to make the financial system more robust and less vulnerable is to switch to decentralized currencies. Such a transition will also make financial system more transparent. Historically first currency of this type -- bitcoin -- use a large amount of electric energy to mine new coins and is, thus, not scalable to the level of financial system as a whole. A more realistic and less energy-consuming scheme …

Why Early Galaxies Were Pickle-Shaped: A Geometric Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The vast majority of currently observed geometric shapes of celestial bodies can be explained by a simple symmetry idea: the initial distribution of matter is invariant with respect to shifts, rotations, and scaling, but this distribution is unstable, so we have spontaneous symmetry breaking. According to statistical physics, among all possible transitions, the most probable are the ones that retain the largest number of symmetries. This explains the currently observed shapes and -- on the qualitative level -- their relative frequency. According to this idea, the most probable first transition is into a planar (pancake) shape, then into …

Translating Discrete Estimates Into A Less Detailed Scale: An Optimal Approach, Thongchai Dumrongpokaphan, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we use estimates that experts make on a 0-to-n scale. For example, to estimate the quality of a lecturer, we ask each student to evaluate this quality by selecting an integer from 0 to n. Each such estimate may be subjective; so, to increase the estimates' reliability, it is desirable to combine several estimates of the corresponding quality. Sometimes, different estimators use slightly different scales: e.g., one estimator uses a scale from 0 to n+1, and another estimator uses a scale from 0 to n. In such situations, it is desirable to translate these estimates to …

Relativistic Effects Can Be Used To Achieve A Universal Square-Root (Or Even Faster) Computation Speedup, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we show that special relativity phenomenon can be used to reduce computation time of any algorithm from T to square root of T. For this purpose, we keep computers where they are, but the whole civilization starts moving around the computer -- at an increasing speed, reaching speeds close to the speed of light. A similar square-root speedup can be achieved if we place ourselves near a growing black hole. Combining the two schemes can lead to an even faster speedup: from time T to the 4-th order root of T.

Secure Multi-Agent Quantum Communication: Towards The Most Efficient Scheme (A Pedagogical Remark), Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many economic and financial applications, it is important to have secure communications. At present, communication security is provided mostly by RSA coding, but the emergent quantum computing can break this encoding, thus making it not secure. One way to make communications absolutely secure is to use quantum encryption. The existing schemes for quantum encryption are aimed at agent-to-agent communications; however, in practice, we often need secure multi-agent communications, where each of the agents has the ability to securely send messages to everyone else. In principle, we can repeat the agent-to-agent scheme for each pair of agents, but this requires …

Computing With Words -- When Results Do Not Depend On The Selection Of The Membership Function, Christopher W. Tovar, Carlos Cervantes, Mario Delgado, Stephanie Figueroa, Caleb Gillis, Daniel Gomez, Andres Llausas, Julio C. Lopez Molinar, Mariana Rogriguez, Alexander Wieczkowski, Francisco Zapata, Vladik Kreinovich

Departmental Technical Reports (CS)

Often, we need to transform natural-language expert knowledge into computer-understandable numerical form. One of the most successful ways to do it is to use fuzzy logic and membership functions. The problem is that membership functions are subjective. It is therefore desirable to look for cases when the results do not depend on this subjective choice. In this paper, after describing a known example of such a situation, we list several other examples where the results do not depend on the subjective choice of a membership function.

Bhutan Landscape Anomaly: Possible Effect On Himalayan Economy (In View Of Optimal Description Of Elevation Profiles), Thach N. Nguyen, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

Economies of countries located in seismic zones are strongly effected by this seismicity. If we underestimate the seismic activity, then a reasonably routine earthquake can severely damage the existing structures and thus, lead to huge economic losses. On the other hand, if we overestimate the seismic activity, we waste a lot of resources on unnecessarily fortifying all the buildings -- and this too harms the economies. From this viewpoint, it is desirable to have estimations of regional seismic activities which are as accurate as possible. Current predictions are mostly based on the standard geophysical understanding of earthquakes as being largely …

Symmetries Are Important, Vladik Kreinovich

Departmental Technical Reports (CS)

This short article explains why symmetries are important, and how they influenced many research projects in which I participated.

Comparing Us And Russian Grading Scales, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the US, grades are usually based on comprehensive written exams: the larger the proportion of topic in which the student shows knowledge, the higher the student's grade. In contrast, in Russia, the grades are based on oral exams, and the bulk of the grade comes from a student answering questions of a few (usually, three) randomly selected topics. A natural question is: what is the relation between the two grading scales? It turns out that "excellent" and "good" grades means the same in both scales, while the US "satisfactory" level is higher than a similar Russian level.

Preferences (Partial Pre-Orders) On Complex Numbers -- In View Of Possible Use In Quantum Econometrics, Songsak Sriboonchitta, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In economic application, it is desirable to find an optimal solution -- i.e., a solution which is preferable to any other possible solution. Traditionally, the state of an economic system has been described by real-valued quantities such as profit, unemployment level, etc. For such quantities, preferences correspond to natural order between real numbers: all things being equal, the more profit the better, and the smaller unemployment, the better. Lately, it turned out that to adequately describe economic phenomena, it is often convenient to use complex numbers. From this viewpoint, a natural question is: what are possible orders on complex numbers? …

All Maximally Complex Problems Allow Simplifying Divide-And-Conquer Approach: Intuitive Explanation Of A Somewhat Counterintuitive Ladner's Result, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Ladner's 1975 result says that any NP-complete problem -- i.e., in effect, any maximally complex problem -- can be reduced to solving two easier problems. This result sounds counter-intuitive: if a problem is maximally complex, how can it be reduced to simpler ones? In this paper, we provide an intuitive explanation for this result. Our main argument is that since complexity and easiness-to-divide are not perfectly correlated, it is natural to expect that maximally complex problem is not maximally difficult to divide. Our related argument is that -- as this result shows -- NP-completeness is a sufficient but not a …

Experimental Determination Of Mechanical Properties Is, In General, Np-Hard -- Unless We Measure Everything, Yan Wang, Oscar Galindo, Michael Baca, Jake Lasley, Vladik Kreinovich

Departmental Technical Reports (CS)

When forces are applied to different parts of a construction, they cause displacements. In practice, displacements are usually reasonably small. In this case, we can safely ignore quadratic and higher order terms in the corresponding dependence and assume that the forces linear depend on displacements. The coefficients of this linear dependence determine the mechanical properties of the construction and thus, need to be experimentally determined. In the ideal case, when we measure the forces and displacements at all possible locations, it is easy to find the corresponding coefficients: it is sufficient to solve the corresponding system of linear equations. In …

How To Describe Correlation In The Interval Case?, Carlos Jimenez, Francisco Zapata, Vladik Kreinovich

Departmental Technical Reports (CS)

In many areas of science and engineering, we want to change a difficult-to-directly-change quantity -- e.g., the economy's growth rate. Since we cannot directly change the desired quantity, we need to find easier-to-change auxiliary quantities that are correlated with the desired quantity -- in the sense that a change in the auxiliary quantity will cause the change in the desired quantity as well. How can we describe this intuitive notion of correlation in precise terms? The traditional notion of correlation comes from situations in which there are many independent factors causing the predictive model to differ from the actual values …

In The Discrete Case, Averaging Cannot Be Consistent, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When we have two estimates of the same quantity, it is desirable to combine them into a single more accurate estimate. In the usual case of continuous quantities, a natural idea is to take the arithmetic average of the two estimates. If we have four estimates, then we can divide them into two pairs, average each pair, and then average the resulting averages. Arithmetic average is consistent in the sense that the result does not depend on how we divide the original four estimates into two pairs. For discrete quantities -- e.g., quantities described by integers -- the arithmetic average …

Probability-Based Approach Explains (And Even Improves) Heuristic Formulas Of Defuzzification, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy techniques have been successfully used in many applications. However, often, formulas for processing fuzzy information are often heuristic: they lack a convincing justification, and thus, users are sometimes reluctant to use them. In this paper, we show that we can justify (and sometimes even improve) these methods if we use a probability-based approach.

Psychological Behavior Of English Learners Utilizing A Cognitive Tutor In An Online Pre-Calculus, Julian Viera Jr., Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The educational landscape is becoming a digital learning environment. Students in today's digital world draw from multiple sources of information; from hypertext, videos, social media, to video games and internet searches. English Learners, individuals learning two languages at once, who use software written in English have a passive relationship with the computer when software is not in their native language. They feel that this educational software belongs to another culture. This paper will present findings from a study with English Learners' engagement in a fully online pre-calculus course. The authors utilized Cultural-Historical Activity Theory to describe how English Learners' created …

Measurement-Type "Calibration" Of Expert Estimates Improves Their Accuracy And Their Usability: Pavement Engineering Case Study, Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, Vladik Kreinovich

Departmental Technical Reports (CS)

In many applications areas, including pavement engineering, experts are used to estimate the values of the corresponding quantities. Expert estimates are often imprecise. As a result, it is difficult to find experts whose estimates will be sufficiently accurate, and for the selected experts, the accuracy is often barely within the desired accuracy. A similar situations sometimes happens with measuring instruments, but usually, if a measuring instrument stops being accurate, we do not dismiss it right away, we first try to re-calibrate it -- and this re-calibration often makes it more accurate. We propose to do the same for experts -- …

Current Quantum Cryptography Algorithm Is Optimal: A Proof, Oscar Galindo, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

One of the main reasons for the current interest in quantum computing is that, in principle, quantum algorithms can break the RSA encoding, the encoding that is used for the majority secure communications -- in particular, the majority of e-commerce transactions are based on this encoding. This does not mean, of course, that with the emergence of quantum computers, there will no more ways to secretly communicate: while the existing non-quantum schemes will be compromised, there exist a quantum cryptographic scheme that will enables us to secretly exchange information. In this scheme, however, there is a certain probability that an …

A Symmetry-Based Explanation Of The Main Idea Behind Chubanov's Linear Programming Algorithm, Olga Kosheleva, Vladik Kreinovich, Thongchai Dumrongpokaphan

Departmental Technical Reports (CS)

Many important real-life optimization problems can be described as optimizing a linear objective function under linear constraints -- i.e., as a linear programming problem. This problem is known to be not easy to solve. Reasonably natural algorithms -- such as iterative constraint satisfaction or simplex method -- often require exponential time. There exist efficient polynomial-time algorithms, but these algorithms are complicated and not very intuitive. Also, in contrast to many practical problems which can be computed faster by using parallel computers, linear programming has been proven to be the most difficult to parallelize. Recently, Sergei Chubanov proposed a modification of …

Why Max And Average Poolings Are Optimal In Convolutional Neural Networks, Ahnaf Farhan, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we do not know the exact relation between different quantities; this relation needs to be determined based on the empirical data. This determination is not easy -- especially in the presence of different types of uncertainty. When the data comes in the form of time series and images, many efficient techniques for such determination use algorithms for training convolutional neural network. As part of this training, such networks "pool" several values corresponding to nearby temporal or spatial points into a single value. Empirically, the most efficient pooling algorithm consists of taking the maximum of the pooled …

Towards Parallel Quantum Computing: Standard Quantum Teleportation Algorithm Is, In Some Reasonable Sense, Unique, Oscar Galindo, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical problems, the computation speed of modern computers is not sufficient. Due to the fact that all speeds are bounded by the speed of light, the only way to speed up computations is to further decrease the size of the memory and processing cells that form a computational device. At the resulting size level, each cell will consist of a few atoms -- thus, we need to take quantum effects into account. For traditional computational devices, quantum effects are largely a distracting noise, but new quantum computing algorithms have been developed that use quantum effects to speed up …

Need To Combine Interval And Probabilistic Uncertainty: What Needs To Be Computed, What Can Be Computed, What Can Be Feasibly Computed, And How Physics Can Help, Songsak Sriboonchitta, Thach N. Nguyen, Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

In many practical situations, the quantity of interest is difficult to measure directly. In such situations, to estimate this quantity, we measure easier-to-measure quantities which are related to the desired one by a known relation, and we use the results of these measurement to estimate the desired quantity. How accurate is this estimate?

Traditional engineering approach assumes that we know the probability distributions of measurement errors; however, in practice, we often only have partial information about these distributions. In some cases, we only know the upper bounds on the measurement errors; in such cases, the only thing we know about …

Which Fuzzy Logic Operations Are Most Appropriate For Ontological Semantics: Theoretical Explanation Of Empirical Observations, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In several of their papers, Victor Raskin and coauthors proposed to use fuzzy techniques to make ontological semantics techniques more adequate in dealing with natural language. Specifically, they showed that the most adequate results appear when we use min as an "and"-operation and max as an "or"-operation. It is interesting that in other applications of fuzzy techniques, such as intelligent control, other versions of fuzzy techniques are the most adequate. In this chapter, we explain why the above techniques are empirically the best in the semantics case.

Why Bohmian Approach To Quantum Econometrics: An Algebraic Explanation, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Many equations in economics and finance are very complex. As a result, existing methods of solving these equations are very complicated and time-consuming. In many practical situations, more efficient algorithms for solving new complex equations appear when it turns out that these equations can be reduced to equations from other application areas -- equations for which more efficient algorithms are already known. It turns out that some equations in economics and finance can be reduced to equations from physics -- namely, from quantum physics. The resulting approach for solving economic equations is known as quantum econometrics. In quantum physics, …

How To Select The Best Paper: Towards Justification (And Possible Enhancement) Of Current Semi-Heuristic Procedures, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To select the best paper at a conference or in a journal, people use reasonably standard semi-heuristic procedures like averaging scores. These procedures usually work well, but sometimes, new situations appear for which the existing procedures are not automatically applicable. Since the existing procedures are heuristic, it is often not clear how to extend them to new situations. In this paper, we provide a possible explanation for the existing procedures. This explanations enables us to naturally generalize these procedures to possible new situations.

Decision Making Under Interval Uncertainty: Beyond Hurwicz Pessimism-Optimism Criterion, Tran Anh Tuan, Vladik Kreinovich, Thach N. Nguyen

Departmental Technical Reports (CS)

In many practical situations, we do not know the exact value of the quantities characterizing the consequences of different possible actions. Instead, we often only known lower and upper bounds on these values, i.e., we only know intervals containing these values. To make decisions under such interval uncertainty, the Nobelist Leo Hurwicz proposed his optimism-pessimism criterion. It is known, however, that this criterion is not perfect: there are examples of actions which this criterion considers to be equivalent but which for which common sense indicates that one of them is preferable. These examples mean that Hurwicz criterion must be extended, …

Why Triangular And Trapezoid Membership Functions: A Simple Explanation, Vladik Kreinovich, Olga Kosheleva, Shahnaz Shahbazova

Departmental Technical Reports (CS)

In principle, in applications of fuzzy techniques, we can have different complex membership functions. In many practical applications, however, it turns out that to get a good quality result -- e.g., a good quality control -- it is sufficient to consider simple triangular and trapezoid membership functions. There exist explanations for this empirical phenomenon, but the existing explanations are rather mathematically sophisticated and are, thus, not very intuitively clear. In this paper, we provide a simple -- and thus, more intuitive -- explanation for the ubiquity of triangular and trapezoid membership functions.

Optimization Under Fuzzy Constraints: From A Heuristic Algorithm To An Algorithm That Always Converges, Vladik Kreinovich, Juan Carlos Figueroa-Garcia

Departmental Technical Reports (CS)

An efficient iterative heuristic algorithm has been used to implement Bellman-Zadeh solution to the problem of optimization under fuzzy constraints. In this paper, we analyze this algorithm, explain why it works, show that there are cases when this algorithm does not converge, and propose a modification that always converges.