Computer Sciences Commons^™

Five Revolutionary Ideas In The 1950s-70s Science: 90th Birthday Of Revolt Pimenov, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

This year, Revolt Pimenov, a philosophical thinker whose main ideas were in geometry of space-time, would have turned 90. In this essay, we explain how in the 1950s-70s, when he was most productive, his were two of the five natural and important revolutionary scientific ideas -- along with fuzzy logic, constructive mathematics, and scalar-tensor theory of gravitation, ideas that, in our opinions, still have potential to change the world.

How To Teach Advanced Highly Motivated Students: Teaching Strategy Of Iosif Yakovlevich Verebeichik, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The paper describes and explains the teaching strategy of Iosif Yakovlevich Verebeichik, a successful mathematics teacher at special mathematical high schools -- schools for students interested in and skilled in mathematics. The resulting strategy seems counterintuitive and contrary to all the pedagogical advice. Our explanation is not complete: it worked well for this teacher, but others who tried to follow seemingly the same strategy did not succeed. How he made it work, how can others make it work -- this is still not clear. In the words of Verebeichik himself, while mathematics itself is a science, teaching mathematics is an …

Digital Twin Technology Applications For Transportation Infrastructure - A Survey-Based Study, Hector Cruz

Open Access Theses & Dissertations

In the past couple of decades, various industries have taken advantage of emerging advanced technologies, such as digital twin (DT), to find more effective solutions in their respective areas. In the transportation infrastructure sector, the concept and implementation of DT technologies are slowly gaining traction but lagging behind other major industries. To better understand the limitations, opportunities and challenges for the adoption of DT in this sector, a survey questionnaire was distributed to collect information from industry professionals involved in transportation infrastructure projects. The purpose of this study is to understand how DT technology is being perceived by the industry. …

On Using Demographic Data With Deprivation Index For Predicting Chronic Diseases, Olugbenga Temitope Iyiola

Open Access Theses & Dissertations

Researchers have worked on modeling and predicting the likelihood of developingchronic diseases, such as diabetes and high blood pressure, using medical data (e.g., heart-rate, blood sugar). However, many of these diseases demonstrate strong links with demographics and socio-economic status (e.g., race, gender, income). It is also less time-consuming to retrieve demographic and socio-economic data, some of which are publicly available through US Census Bureau, than to carry out medical tests. Hence, demographic data can give a quicker estimate of the susceptibility of a person to a chronic disease.

In this work, we study the effect of using medical vs. demographics …

Addressing Challenges In Aggregating And Analyzing Agroecological Data, Sarah E. Mccord

Open Access Theses & Dissertations

Agroecosystems face multiple threats including land degradation and climate change, changing and competing land uses, invasive species and disease spread, and biodiversity loss. While scientists seek to understand rapidly changing ecosystems, land managers are struggling to maintain ecosystem services amid transitions to novel ecosystem states. Understanding agroecosystem drivers and ensuing responses requires quality information about ecosystems that span biomes, trophic scales, ecological processes, spatiotemporal scales, land use, and land ownership. Yet, using multi-scale agroecosystem information can be frustrating for both scientific researchers and land managers as it is difficult to locate data that are trustworthy, easily accessible, standardized, and connected …

Making Valid Inferences With Decision Tree, George Ekow Quaye

Open Access Theses & Dissertations

HypoThesis testing and Confidence Interval (CI) estimates are key statistics in predicting future values in data analysis. Most often, CI estimates are directly obtained from the summary statistics of a particular statistical methodology output. However, when it comes to the summary of decision tree outputs, these CI estimates are not directly obtained. So a na\"{i}ve way of making node-level inference is to construct a $(1-\alpha) \times 100\%$ confidence interval for a node mean $\bar{y}_t$ using the relation: $\bar{y}_t \, \pm \, z_{1-\alpha/2} \, \frac{s_t}{\sqrt{n_t}}$, where $\bar{y}_t$ is the node mean and $s_t$ is the standard deviation estimates from the decision …

How Does Land Cover Classification In Google Earth Engine Compare With Traditional Methods Of Land Cover Classification? What Are The Tradeoffs?, Carlos Sebastian Reyes

Open Access Theses & Dissertations

The project focuses on comparing land cover classification of traditional methods such as ArcGIS with newer ones such as Google Earth Engine (GEE) as well as discussing any potential tradeoffs. Two studies were performed in both platforms, the first involved analyzing land cover change in the Middle Rio Grande (MRG) region of southern New Mexico, far west Texas, and northern Chihuahua, Mexico. The MRG study focused on urban and agricultural change in the region using two different classification methods. The second study focused on creating a post-hurricane damage assessment (PDA) with the goal of developing an automated method of estimating …

Why Decimal System? Why Communities With More Than 150 Folks Tend To Split? New Consequences Of The Seven Plus Minus Two Law, Leobardo Orea Amador, Vladik Kreinovich

Departmental Technical Reports (CS)

Why are we using the decimal system to describe numbers? Why all over the world, communities with more than 150 folks tend to split? In this paper, we show that both phenomena -- as well as some other phenomena -- can be explained if we take into account the seven plus minus two law, according to which a person can keep in immediate memory from 5 to 9 items.

Why, In Deep Learning, Non-Smooth Activation Function Works Better Than Smooth Ones, Daniel Cruz, Richard Godoy, Vladik Kreinovich

Departmental Technical Reports (CS)

Since in the physical world, most dependencies are smooth (differentiable), traditionally, smooth functions were used to approximate these dependencies. In particular, neural networks used smooth activation functions such as the sigmoid function. However, the successes of deep learning showed that in many cases, non-smooth activation functions like max(0,z) work much better. In this paper, we explain why in many cases, non-smooth approximating functions often work better -- even when the approximated dependence is smooth.

Why Semi-Supervised Learning Makes Sense: A Pedagogical Note, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The main idea behind semi-supervised learning is that when we do not enough human-generated labels, we train a machine learning system based on what we have, and we add the resulting labels (called pseudo-labels) to the training sample. Interesting, this idea works well, but why is somewhat a mystery: we did not add any new information so why is this working? There exist explanations for this empirical phenomenon, but most these explanations are based on complicated math. In this paper, we provide a simple intuitive explanation.

Why ∞ Is A Reasonable Symbol For Infinity, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The fact that ∞ is actively used as a symbol for infinity shows that this symbol is probably reasonable in this role, but why? In this paper, we provide a possible explanation for why this is indeed a reasonable symbol for infinity.

Lev Landau's Marital Advice Explained, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Nobelist physicist Lev Landau was known for applying mathematical and physical reasoning to human relations. His advices may have been somewhat controversial, but they were usually well motivated. However, there was one advice for which no explanation remains -- that a person should not marry his/her first and second true loves, and only start thinking about marriage starting with the third true love. In this paper, we provide a possible Landau-style motivation for this advice.

Limit Theorems As Blessing Of Dimensionality: Neural-Oriented Overview, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

As a system becomes more complex, at first, its description and analysis becomes more complicated. However, a further increase in the system's complexity often makes this analysis simpler. A classical example is Central Limit Theorem: when we have a few independent sources of uncertainty, the resulting uncertainty is very difficult to describe, but as the number of such sources increases, the resulting distribution get close to an easy-to-analyze normal one -- and indeed, normal distributions are ubiquitous. We show that such limit theorems often make analysis of complex systems easier -- i.e., lead to blessing of dimensionality phenomenon -- for …

What Is 1/0 From The Practical Viewpoint: A Pedagogical Note, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

What is 1/0? Students are first taught -- in elementary school -- that it is undefined, then -- in calculus -- then it is infinity. In both cases, the answer is usually provided based on abstract reasoning. But what about the practical meaning? In this paper, we show that, depending on the specific practical problem, we can have different answers to this question: in some practical problems, the correct answer is that 1/0 is undefined, in others, the correct answer is that 1/0 =0 -- and there are probably other practical problems where we can have different answers. Bottom line: …

Selfish Gene Theory Explains Oedipus Complex, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Sigmund Freud famously placed what he called Oedipus complex at the center of his explanation of psychological and psychiatric problems. Freund's analysis was based on anecdotal evidence and intuition, not on solid experiments -- as a result, for a long time, many psychologists dismissed the universality of Freud's findings. However, lately, experiments seem to confirm that indeed men, on average, select wives who resemble their mothers, and women select husbands who resemble their mothers. In this paper, we provide a possible biological explanation for this observational phenomenon.

Mexican Folk Arithmetic Algorithm Makes Perfect Sense, Julio C. Urenda, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional algorithms for addition and multiplication -- that we all study at school -- start with the lowest possible digits. Interestingly, many people in Mexico use a different algorithm, in which operations start with the highest digits. We show that in many situations, this alternative algorithm is indeed more efficient -- especially in typical practical situations when we know the values -- that we need to add or subtract -- only with uncertainty.

Baudelaire's Ideas Of Vagueness And Uniqueness In Art: Algorithm-Based Explanations, Luc Longpre, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

According to the analysis by the French philosopher Jean-Paul Sartre, the famous French poet and essayist Charles Baudelaire described (and followed) two main -- somewhat unusual -- ideas about art: that art should be vague, and that to create an object of art, one needs to aim for uniqueness. In this paper, we provide an algorithm-based explanation for these seemingly counter-intuitive ideas, explanation related to Kolmogorov complexity-based formalization of Garrett Birkhoff's theory of beauty.

How Much For A Set: General Case Of Decision Making Under Set-Valued Uncertainty, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In real life, we often need to make a decision, i.e., we need to select one of the possible alternatives. In many practical situations, our objective is financial: we need to select an alternative that will bring us the largest financial gain. The problem is that usually, we only know the gain corresponding to each alternative with some uncertainty: instead of the exact numerical value of this gain, there is a whole set of possible values of this gain. How can we make decisions under such interval-valued uncertainty? An answer to this question is known for the case when these …

Why Fuzzy Techniques In Explainable Ai? Which Fuzzy Techniques In Explainable Ai?, Kelly Cohen, Laxman Bokati, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of big challenges of many state-of-the-art AI techniques such as deep learning is that their results do not come with any explanations -- and, taking into account that some of the resulting conclusions and recommendations are far from optimal, it is difficult to distinguish good advice from bad one. It is therefore desirable to come up with explainable AI. In this paper, we argue that fuzzy techniques are a proper way to this explainability, and we also analyze which fuzzy techniques are most appropriate for this purpose. Interestingly, it turns out that the answer depends on what problem we …

How Void Ratio Depends On Grain Size In Soil Mechanics: Theoretical Explanation, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

When designing a road, it is important to know how many voids are in the underlying soil -- since these voids will affect the road stiffness. It is difficult to measure the voids ratio directly, so instead, we need to estimate it based on easier-to-measure characteristics such as grain size. There are empirical formulas for such estimation. In this paper, we provide a possible theoretical explanation for these empirical formulas.

Why Base-20, Base-40, And Base-60 Number Systems?, Sean R. Aguilar, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Historically, to describe numbers, some cultures used bases much larger than our usual base 10, namely, bases 20, 40, and 60. There are explanations for base 60, there is some explanation for base 20, but base 40 -- used in medieval Russia -- remains largely a mystery. In this paper, we provide a possible explanation for all these three bases, an explanation based on the natural need to manage large groups of people. We also speculate why different cultures used different bases.

Dimension Compactification Naturally Follows From First Principles, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

According to modern physics, space-time originally was of dimension 11 or higher, but then additional dimensions became compactified, i.e., size in these directions remains small and thus, not observable. As a result, at present, we only observed 4 dimensions of space-time. There are mechanisms that explain how compactification may have occurred, but the remaining question is why it occurred. In this paper, we provide two first-principles-based explanations for space-time compactification: based on Second Law of Thermodynamics and based on geometry and symmetries.

Additional Spatial Dimensions Can Help Speed Up Computations, Luc Longpre, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

While we currently only observe 3 spatial dimensions, according to modern physics, our space is actually at least 10-dimensional. In this paper, on different versions of the multi-D spatial models, we analyze how the existence of the additional spatial dimensions can help computations. It turns out that in all the versions, there is some speed up -- moderate when the extra dimensions are actually compactified, and drastic if extra dimensions are separated by a potential barrier.

Each Realistic Continuous Functional Dependence Implies A Relation Between Some Variables: A Theoretical Explanation Of A Fuzzy-Related Empirical Phenomenon, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In principle, one can have a continuous functional dependence y=f(x1,...,x_n) for which, for each proper subset of n+1 variable x1,...,x_n,y, there is no relation: i.e., for each selection of n variables out of these n+1, all combinations of these n values are possible. However, for fuzzy operations, there is always some non-trivial relation between y and one of the inputs xi; for example, for "and"-operations (t-norms) y=f(x1,x2), we have y ≤ x1; for "or"-operations (t-conorms) y=f(x1,x2) we have x1 ≤ y, etc. In this paper, we prove a general mathematical explanation for this empirical fact.

Fuzzy Logic Leads To A More Adequate Way Of Processing Likert-Scale Values: Case Study Of Burnout, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Many phenomena like burnout are gauged by computing a linear combination of user-provided Likert-scale values. The problem with this traditional approach is that, while it makes sense to have linear combination of weights or other physical characteristics, a linear combination of Likert-scale values like "good" and "satisfactory" does not make sense. The only reason why linear combinations are used in practice is that the corresponding data processing tools are readily available. A more adequate approach would be to use fuzzy logic -- a technique specifically designed to deal with Likert-scale values. We show that fuzzy logic actually leads to a …

What Teachers Can Learn From Machine Learning, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Decades ago, machine learning was not as good as human learning, so many machine learning techniques were borrowed from how we humans learn -- be it on the level of concepts or on the level of biological neurons, cells responsible for mental activities such as learning. Lately, however, machine learning techniques such as deep learning have started outperforming humans. It is therefore time to start borrowing the other way around, i.e., using machine learning experience to improve our human teaching and learning. In this paper, we describe several relevant ideas -- and explain how some of these ideas are related …

What Is The True Formula For Soil Permeability? Not Clear, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

To design and maintain pavements, it is important to know how fast water will penetrate the underlying soil. The speed of this penetration is determined by a quantity called permeability. There are several seemingly very different empirical and semi-empirical formulas that predict permeability. A recent attempt to select the formula that best fits the experimental data ended up in an unexpected conclusion that all three formula provide a good fit for the data. But these formulas are very different, how come that all three of them fit the same data? In this paper, we explain this somewhat paradoxical result.

How To Best Write Research Papers: Basic English? Sophisticated English?, Martine Ceberio, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Instructors from English department praise our students when they use the most sophisticated grammatical constructions and the most appropriate (often rarely used) words -- as long as this helps better convey all the subtleties of the meaning. On the other hand, we usually teach the students to use the most primitive Basic English when writing our papers -- this way, the resulting paper will be most accessible to the international audience. Who is right? In this paper, we analyze this question by using a natural model -- inspired by Zipf's law -- and we conclude that to achieve the largest …

Low-Complexity Zonotopes Can Enhance Uncertainty Quantification (Uq), Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, the only information that we know about the measurement error is the upper bound D on its absolute value. In this case, once we know the measurement result X, the only information that we have about the actual value x of the corresponding quantity is that this value belongs to the interval [X − D, X + D]. How can we estimate the accuracy of the result of data processing under this interval uncertainty? In general, computing this accuracy is NP-hard, but in the usual case when measurement errors are relatively small, we can linearize the …

Why Romans Sometimes Wrote 8 As Viii, And Sometimes As Iix: A Possible Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Most of us are familiar with Roman numerals and with the standard way of describing numbers in the form of these numerals. What many people do not realize is that the actual ancient Romans often deviated from these rules. For example, instead of always writing the number 8 as VIII, i.e., 5 + 3, they sometimes wrote it as IIX, i.e., as 10 − 2. Some of such differences can be explained: e.g., the unusual way of writing 98 as IIC, i.e., as 100 − 2, can be explained by the fact that the Latin word for 98 literally means …