Physical Sciences and Mathematics Commons^™

Education In The Era Of Google, Wikipedia, And Deep Learning: Are We Humans Still Needed And If Yes For What?, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main purposes of education is to teach skills needed in future life and future jobs. What is important and what is useful changes with time. Before the industrial revolution, routine mechanical work was an important part of human activity – now machines can do it (and do it better). Before printing, copying was an important activity – now copy machines do it. Before computers, humans were needed for computing – now computer do it better. With Wikipedia and Google, there is not much need for scholars being erudite. Even extracting dependencies from data – one of the …

Characterization And Evolution Of The Professor Valley Pennsylvanian Salt Body (Paradox Basin, Ut) Using Gravity And Magnetotellurics, Derek Scott

Open Access Theses & Dissertations

Syndepositional halokinetic movement of the Pennsylvanian Paradox Formation in the Paradox Basin, UT & CO behaved as a control over the development of depositional systems during the Late Paleozoic and early Mesozoic periods (Trudgill, 2011). Understanding the controls on halokinetic evolution in the area serves as an invaluable outcrop analogue for similar subsurface salt bodies in petroleum-bearing basins and provides key insights for hydrocarbon exploration in salt basins world wide. Professor Valley, located 15 miles Northeast of Moab, UT is situated between the Fisher Valley (Onion Creek) and Cache/Salt Valley salt walls. It includes an anomalous, isolated 0.5 km² outcrop …

Evolution Of The Magnetic Properties On Van Der Waals Layered Magnets Via Pressure And Proton Irradiation, Rubyann Olmos

Open Access Theses & Dissertations

Probing the magnetism in quasi two-dimensional materials has the potential in driving their properties towards future use in spin electronic based devices. Studying such layered magnets will enable the scientific community to uncover tunable exotic phases such as superconductivity, quantum paramagnetism, etc. This work examines the influence of two types of external perturbations, namely, the pressure and proton irradiation, on the magnetic properties of several compounds in the van der Waals crystal family.

Pressure has been found to induce structural and magnetic phase transitions in many of these materials. Using hydrostatic pressure as a disorderless approach to manipulate the interlayer …

Integration Of Genetic Isothermal Amplification On Low-Cost Hybrid Paper/Polymer Microfluidic Biochips For High Sensitivity Point-Of-Care Disease Diagnosis, Hamed Tavakoli

Open Access Theses & Dissertations

Infectious diseases and cancer have been two main causes of global death and disability, leading to a significant impact on public health and economies globally. Early diagnosis of these diseases can improve prevention, treatment, and prognosis in clinical practice. However, current laboratory diagnostic approaches require expensive and bulky equipment, well-trained personnel, and time-consuming processes, which puts a great challenge to conventional methods to address, especially in resource-limited settings. Microfluidic lab-on-a-chip presents a unique opportunity for various biomedical applications due to multiple advantages such as low reagent consumption, integration, miniaturization, portability, and automation. Since different microfluidic platform substrates have their advantages …

Fair Bankruptcy Solutions Under Interval Uncertainty, Uyen Pham, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

If the overall amount of the company's assets is smaller than its total debts, then a fair solution is to give, to each creditor, the amount proportional to the corresponding debt, e.g., 10 center for each dollar or 50 cents for each dollar. But what if the debt amounts are not known exactly, and for some creditors, we only know the lower and upper bounds on the actual debt amount? What division will be fair in such a situation? In this paper, we show that the only fair solution is to make payments proportional to an appropriate convex combination of …

Why Some Theoretically Possible Representations Of Natural Numbers Were Historically Used And Some Were Not: An Algorithm-Based Explanation, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Historically, people have used many ways to represent natural numbers: from the original "unary" arithmetic, where each number is represented as a sequence of, e.g., cuts (4 is IIII) to modern decimal and binary systems. However, with all this variety, some seemingly reasonable ways of representing natural numbers were never used. For example, it may seem reasonable to represent numbers as products -- e.g., as products of prime numbers -- such a representation was never used in history. So why some theoretically possible representations of natural numbers were historically used and some were not? In this paper, we propose an …

Why Rectified Linear Unit Is Efficient In Machine Learning: One More Explanation, Barnabas Bede, Vladik Kreinovich, Uyen Pham

Departmental Technical Reports (CS)

In many applications, in particular, in econometric application, deep learning techniques are very effective. In this paper, we provide a new explanation for why rectified linear units -- the main units of deep learning -- are so effective. This explanation is similar to the usual explanation of why Gaussian (normal) distributions are ubiquitous -- namely, it is based on an appropriate limit theorem.

When Is Deep Learning Better And When Is Shallow Learning Better: Qualitative Analysis, Salvador Robles Herrera, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, deep neural networks work better than the traditional "shallow" ones, however, in some cases, the shallow neural networks lead to better results. At present, deciding which type of neural networks will work better is mostly done by trial and error. It is therefore desirable to come up with some criterion of when deep learning is better and when shallow is better. In this paper, we argue that this depends on whether the corresponding situation has natural symmetries: if it does, we expect deep learning to work better, otherwise we expect shallow learning to be more effective. …

Why Constraint Interval Arithmetic Works Well: A Theorem Explains Empirical Success, Barnabas Bede, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

Often, we are interested in a quantity that is difficult or impossible to measure directly, e.g., tomorrow's temperature. To estimate this quantity, we measure auxiliary easier-to-measure quantities that are related to the desired ones by a known dependence, and use the known relation to estimate the desired quantity. Measurements are never absolutely accurate, there is always a measurement error, i.e., a non-zero difference between the measurement result and the actual (unknown) value of the corresponding quantity. In many practical situations, the only information that we have about each measurement error is the bound on its absolute value. In such situations, …

Game-Theoretic Approach Explains -- On The Qualitative Level -- The Antigenic Map Of Covid-19 Variants, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

To effectively defend the population against future variants of Covid-19, it is important to be able to predict how it will evolve. For this purpose, it is necessary to understand the logic behind its evolution so far. At first glance, this evolution looks random and thus, difficult to predict. However, we show that already a simple game-theoretic model can actually explain -- on the qualitative level -- how this virus mutated so far.

Why Menzerath's Law?, Julio Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

In linguistics, there is a dependence between the length of the sentence and the average length of the word: the longer the sentence, the shorter the words. The corresponding empirical formula is known as the Menzerath's Law. A similar dependence can be observed in many other application areas, e.g., in the analysis of genomes. The fact that the same dependence is observed in many different application domains seems to indicate there should be a general domain-independent explanation for this law. In this paper, we show that indeed, this law can be derived from natural invariance requirements.

How To Solve The Apportionment Paradox, Christopher Reyes, Vladik Kreinovich

Departmental Technical Reports (CS)

In the ideal world, the number of seats that each region or each community gets in a representative body should be exactly proportional to the population of this region or community. However, since the number of seats allocated to each region or community is whole, we cannot maintain the exact proportionality. Not only this leads to a somewhat unfair situation, when residents of one region get more votes per person than residents of another one, it also leads to paradoxes -- e.g., sometimes a region that gained the largest number of people loses a number of seats. To avoid this …

Why Hate: Analysis Based On Decision Theory, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

At first glance, from the general decision-theory viewpoint, hate (and other negative feelings towards each other) makes no sense, since they decrease the utility (i.e., crudely speaking, level of happiness) of the person who experiences these feelings. Our detailed analysis shows that there are situations when such negative feelings make perfect sense: namely, when you have a large group of people almost all of whom are objectively unhappy. In such situations -- e.g., on the battlefield -- negative feelings help keep their spirits high in spite of the harsh situation. This explanation leads to recommendations on how to decrease the …

How To Solve The Apportionment Paradox, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that often, after it is proven that a new statement is equivalent to the original definition, this new statement becomes the accepted new definition of the same notion. In this paper, we provide a natural explanation for this empirical phenomenon.

How To Describe Hypothetic Truly Rare Events (With Probability 0), Luc Longpre, Vladik Kreinovich

Departmental Technical Reports (CS)

In probability theory, rare events are usually described as events with low probability p, i.e., events for which in N observations, the event happens n(N) ~ p*N times. Physicists and philosophers suggested that there may be events which are even rarer, in which n(N) grows slower than N. However, this idea has not been developed, since it was not clear how to describe it in precise terms. In this paper, we propose a possible precise description of this idea, and we use this description to answer a natural question: when two different functions n(N) lead to the same class of …

How To Make Quantum Ideas Less Counter-Intuitive: A Simple Analysis Of Measurement Uncertainty Can Help, Olga Kosheleva, Vladik Kreinovich, Louis Ray Lopez

Departmental Technical Reports (CS)

Our intuition about physics is based on macro-scale phenomena, phenomena which are well described by non-quantum physics. As a result, many quantum ideas sound counter-intuitive -- and this slows down students' learning of quantum physics. In this paper, we show that a simple analysis of measurement uncertainty can make many of the quantum ideas much less counter-intuitive and thus, much easier to accept and understand.

Shall We Use Logical Approach Or More Traditional Mamdani Approach In Fuzzy Control: Pragmatic Analysis, R. Noah Padilla, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy control methodology transforms the experts' if-then rules into a precise control strategy. From the logical viewpoint, an if-then rule means implication, so it seems reasonable to use fuzzy implication in this transformation. However, this logical approach is not what the first fuzzy controllers used. The traditional fuzzy control approach -- first proposed by Mamdani -- transforms the if-then rules into a statement that only contains and's and or's, and does not use fuzzy implication at all. So, a natural question arises: shall we use logical approach or the traditional approach? In this paper, we analyze this question on the …

Why Deep Neural Networks: Yet Another Explanation, Ricardo Lozano, Ivan Montoya Sanchez, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main motivations for using artificial neural networks was to speed up computations. From this viewpoint, the ideal configuration is when we have a single nonlinear layer: this configuration is computationally the fastest, and it already has the desired universal approximation property. However, the last decades have shown that for many problems, deep neural networks, with several nonlinear layers, are much more effective. How can we explain this puzzling fact? In this paper, we provide a possible explanation for this phenomena: that the universal approximation property is only true in the idealized setting, when we assume that all …

Why Optimization Is Faster Than Solving Systems Of Equations: A Qualitative Explanation, Siyu Deng, Bimal K. C, Vladik Kreinovich

Departmental Technical Reports (CS)

Most practical problems lead either to solving a system of equation or to optimization. From the computational viewpoint, both classes of problems can be reduced to each other: optimization can be reduced to finding points at which all partial derivatives are zeros, and solving systems of equations can be reduced to minimizing sums of squares. It is therefore natural to expect that, on average, both classes of problems have the same computational complexity -- i.e., require about the same computation time. However, empirically, optimization problems are much faster to solve. In this paper, we provide a possible explanation for this …

Spiral Arms Around A Star: Geometric Explanation, Juan L. Puebla, Vladik Kreinovich

Departmental Technical Reports (CS)

Recently, astronomers discovered spiral arms around a star. While their shape is similar to the shape of the spiral arms in the galaxies, however, because of the different scale, galaxy-related physical explanations of galactic spirals cannot be directly applied to explaining star-size spiral arms. In this paper, we show that, in contrast to more specific physical explanation, more general symmetry-based geometric explanations of galactic spiral can explain spiral arms around a star.

Why Self-Esteem Helps To Solve Problems: An Algorithmic Explanation, Oscar Ortiz, Henry Salgado, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that self-esteem helps solve problems. From the algorithmic viewpoint, this seems like a mystery: a boost in self-esteem does not provide us with new algorithms, does not provide us with ability to compute faster -- but somehow, with the same algorithmic tools and the same ability to perform the corresponding computations, students become better problem solvers. In this paper, we provide an algorithmic explanation for this surprising empirical phenomenon.

Why Immunodepressive Drugs Often Make People Happier, Joshua Ramos, Dario Vasquez, Ruth Trejo, Vladik Kreinovich

Departmental Technical Reports (CS)

Many immunodepressive drugs have an unusual side effect on the patient's mood: they often make the patient happier. This side hae been observed for many different immunodepressive drugs, with different chemical composition. Thus, it is natural to conclude that there must be some general reason for this empirical phenomenon, a reason not related to the chemical composition of any specific drug -- but rather with their general functionality. In this paper, we provide such an explanation.

Explaining An Empirical Formula For Bioreaction To Similar Stimuli (Covid-19 And Beyond), Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

A recent comparative analysis of biological reaction to unchanging vs. rapidly changing stimuli -- such as Covid-19 or flu viruses -- uses an empirical formula describing how the reaction to a similar stimulus depends on the distance between the new and original stimuli. In this paper, we provide a from-first-principles explanation for this empirical formula.

One More Physics-Based Explanation For Rectified Linear Neurons, Jonatan Contreras, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

The main idea behind artificial neural networks is to simulate how data is processed in the data processing devoice that has been optimized by million-years natural selection -- our brain. Such networks are indeed very successful, but interestingly, the most recent successes came when researchers replaces the original biology-motivated sigmoid activation function with a completely different one -- known as rectified linear function. In this paper, we explain that this somewhat unexpected function actually naturally appears in physics-based data processing.

How To Select A Representative Sample For A Family Of Functions?, Leobardo Valera, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

Predictions are rarely absolutely accurate. Often, the future values of quantities of interest depend on some parameters that we only know with some uncertainty. To make sure that all possible solutions satisfy desired constraints, it is necessary to generate a representative finite sample, so that if the constraints are satisfied for all the functions from this sample, then we can be sure that these constraints will be satisfied for the actual future behavior as well. At present, such a sample is selected based by Monte-Carlo simulations, but, as we show, such selection may underestimate the danger of violating the constraints. …

A Possible Common Mechanism Behind Skew Normal Distributions In Economics And Hydraulic Fracturing-Induced Seismicity, Laxman Bokati, Aaron Velasco, Vladik Kreinovich, Kittawit Autchariyapanitkul

Departmental Technical Reports (CS)

Many economic situations -- and many situations in other application areas -- are well-described by a special asymmetric generalization of normal distributions -- known as skew-normal. However, there is no convincing theoretical explanation for this empirical phenomenon. To be more precise, there are convincing explanations for the ubiquity of normal distributions, but not for the transformation that turns normal into skew-normal. In this paper, we use the analysis of hydraulic fracturing-induced seismicity to show explain the ubiquity of such a transformation.

Physical Meaning Often Leads To Natural Derivations In Elementary Mathematics: On The Examples Of Solving Quadratic And Cubic Equations, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Usual derivation of many formulas of elementary mathematics -- such as the formulas for solving quadratic equation -- often leave un unfortunate impression that mathematics is a collection of unrelated unnatural trick. In this paper, on the example of formulas for solving quadratic and cubic equations, we show that these derivations can be made much more natural if we take physical meaning into account.

Ordered Weighted Averaging (Owa), Decision Making Under Uncertainty, And Deep Learning: How Is This All Related?, Vladik Kreinovich

Departmental Technical Reports (CS)

Among many research areas to which Ron Yager contributed are decision making under uncertainty (in particular, under interval and fuzzy uncertainty) and aggregation -- where he proposed, analyzed, and utilized ordered weighted averaging (OWA). The OWA algorithm itself provides only a specific type of data aggregation. However, it turns out that if we allow several OWA stages, one after another, we obtain a scheme with a universal approximation property -- moreover, a scheme which is perfectly equivalent to modern ReLU-based deep neural networks. In this sense, Ron Yager can be viewed as a (grand)father of ReLU-based deep learning. We also …

Need For Techniques Intermediate Between Interval And Probabilistic Ones, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In high performance computing, when we process a large amount of data, we do not have much information about the dependence between measurement errors corresponding to different inputs. To gauge the uncertainty of the result of data processing, the two usual approaches are: the interval approach, when we consider the worst-case scenario in which all measurement errors are strongly correlated, and the probabilistic approach, when we assume that all these errors are independent. The problem is that usually, the interval approach leads to too pessimistic, too large uncertainty estimates, while the probabilistic approach often underestimates the resulting uncertainty. To get …

Fuzzy Or Neural, Type-1 Or Type-2 -- When Each Is Better: First-Approximation Analysis, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In many practical situations, we need to determine the dependence between different quantities based on the empirical data. Several methods exist for solving this problem, including neural techniques and different versions of fuzzy techniques: type-1, type-2, etc. In some cases, some of these techniques work better, in other cases, other methods work better. Usually, practitioners try several techniques and select the one that works best for their problem. This trying often requires a lot of efforts. It would be more efficient if we could have a priori recommendations about which technique is better. In this paper, we use the first-approximation …