Computer Sciences Commons^™

Sinusoidal Projection For 360° Image Compression And Triangular Discrete Cosine Transform Impact In The Jpeg Pipeline, Iker Vazquez Lopez

Boise State University Theses and Dissertations

The equirectangular projection is commonly used to store and transmit 360' images. However, using the equirectangular projection to store and transmit 360° images is not efficient due to its natural topographic redundancy. To generate the 360° image, captured pixels that form a spherical point cloud in the 3D space are projected onto a 2D plane using the equirectangular projection; generating redundant pixels in the process. These extra pixels in the image add extra memory requirements that have low impact in the final image quality. This dissertation presents results of research into the compression of 360° spherical imagery. It examines and …

Volume 13, Payton Davenport, Audrey Lemons, Jacob Shope, Haley Smith, Cassandra Poole, Rachel Cannon, Rachel Boch, Suzanne Stetson

Incite: The Journal of Undergraduate Scholarship

Introduction Dr. Roger A. Byrne, Dean

From the Editor Dr. Larissa “Kat” Tracy

From the Designers Rachel English, Rachel Hanson

The Effect of Compliment Type on the Estimated Value of the Compliment by Payton Davenport, Audrey Lemons, and Jacob Shope

The Imperial Japanese Military: A New Identity in the Twentieth Century, 1853–1922 by Haley Smith

Longwood University’s campus: Human-cultivated Soil has Higher Microbial Diversity than Soil Collected from Wild Sites by Cassandra Poole

Reminiscent Modernism: Poetry Magazine’s Modernist Nostalgia for the Past by Rachel Cannon

Challenges Faced by Healthcare Workers During the COVID-19 Pandemic: A Preliminary Study of Age and …

Intra-Hour Solar Forecasting Using Cloud Dynamics Features Extracted From Ground-Based Infrared Sky Images, Guillermo Terrén-Serrano

Electrical and Computer Engineering ETDs

Due to the increasing use of photovoltaic systems, power grids are vulnerable to the projection of shadows from moving clouds. An intra-hour solar forecast provides power grids with the capability of automatically controlling the dispatch of energy, reducing the additional cost for a guaranteed, reliable supply of energy (i.e., energy storage). This dissertation introduces a novel sky imager consisting of a long-wave radiometric infrared camera and a visible light camera with a fisheye lens. The imager is mounted on a solar tracker to maintain the Sun in the center of the images throughout the day, reducing the scattering effect produced …

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.

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.

A New Application Of The Central Limit Theorem, Kenneth Winters

Selected Honors Theses

This paper discusses the Central Limit Theorem (CLT) and its applications. The paper gives an introduction to what the CLT is and how it can be applied to real life. Additionally, the paper gives a conceptual understanding of the theorem through various examples and visuals. The paper discusses the applications of the CLT in fields such as computer science, psychology, and political science. The author then suggests a new mathematical theorem as an application of the CLT and provides a proof of the theorem. The new theorem relates to expected value and probabilities of random variables and provides a link …

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, …

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. …

A New Metaphor: How Artificial Intelligence Links Legal Reasoning And Mathematical Thinking, Melissa E. Love Koenig, Colleen Mandell

Marquette Law Review

Artificial intelligence’s (AI’s) impact on the legal community expands exponentially each year. As AI advances, lawyers have more powerful tools to enhance their ability to research and analyze the law, as well as to draft contracts and other legal documents. Lawyers are already using tools powered by AI and are learning to shift their methodologies to take advantage of these enhancements. To continue to grow into their shifting role, lawyers should understand the relationship between AI, mathematics, and legal reasoning.

A Super Fast Algorithm For Estimating Sample Entropy, Weifeng Liu, Ying Jiang, Yuesheng Xu

Mathematics & Statistics Faculty Publications

: Sample entropy, an approximation of the Kolmogorov entropy, was proposed to characterize complexity of a time series, which is essentially defined as − log(B/A), where B denotes the number of matched template pairs with length m and A denotes the number of matched template pairs with m + 1, for a predetermined positive integer m. It has been widely used to analyze physiological signals. As computing sample entropy is time consuming, the box-assisted, bucket-assisted, x-sort, assisted sliding box, and kd-tree-based algorithms were proposed to accelerate its computation. These algorithms require O(N²) or …

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 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 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. …

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 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 …

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.

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 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.

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 …

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 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.

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.

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.

Session 5: Equipment Finance Credit Risk Modeling - A Case Study In Creative Model Development & Nimble Data Engineering, Edward Krueger, Landon Thompson, Josh Moore

SDSU Data Science Symposium

This presentation will focus first on providing an overview of Channel and the Risk Analytics team that performed this case study. Given that context, we’ll then dive into our approach for building the modeling development data set, techniques and tools used to develop and implement the model into a production environment, and some of the challenges faced upon launch. Then, the presentation will pivot to the data engineering pipeline. During this portion, we will explore the application process and what happens to the data we collect. This will include how we extract & store the data along with how it …

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 …

Unexpected Economic Consequence Of Cloud Computing: A Boost To Algorithmic Creativity, Francisco Zapata, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

While theoreticians have been designing more and more efficient algorithms, in the past, practitioners were not very interested in this activity: if a company already owns computers that provide computations in required time, there is nothing to gain by using faster algorithms. We show the situation has drastically changed with the transition to cloud computing: many companies have not yet realized this, but with the transition to cloud computing, any algorithmic speed up leads to immediate financial gain. This also has serious consequences for the whole computing profession: there is a need for professionals better trained in subtle aspects of …