Computer Sciences Commons^™

Why Physical Power Laws Usually Have Rational Exponents, Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Many physical dependencies are described by power laws y=A*xa, for some exponent a. This makes perfect sense: in many cases, there are no preferred measuring units for the corresponding quantities, so the form of the dependence should not change if we simply replace the original unit with a different one. It is known that such invariance implies a power law. Interestingly, not all exponents are possible in physical dependencies: in most cases, we have power laws with rational exponents. In this paper, we explain the ubiquity of rational exponents by taking into account that in many case, there is also …

Can Physics Attain Its Goals: Extending D'Agostino's Analysis To 21st Century And Beyond, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In his 2000 seminal book, Silvo D'Agostino provided the detailed overview of the history of ideas underlying 19th and 20th century physics. Now that we are two decades into the 21st century, a natural question is: how can we extend his analysis to the 21st century physics -- and, if possible, beyond, to try to predict how physics will change? To perform this analysis, we go beyond an analysis of what happened and focus more on why para-digm changes happened in the history of physics. To better understand these paradigm changes, we analyze now only what were the main ideas …

How To Elicit Complex-Valued Fuzzy Degrees, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the traditional fuzzy logic, an expert's degree of certainty in a statement is described by a single number from the interval [0,1]. However, there are situations when a single number is not sufficient: e.g., a situation when we know nothing and a situation in which we have a lot of arguments for a given statement and an equal number of arguments against it are both described by the same number 0.5. Several techniques have been proposed to distinguish between such situations. The most widely used is interval-valued technique, where we allow the expert to describe his/her degree of certainty …

Towards Optimal Techniques Intermediate Between Interval And Affine, Affine And Taylor, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In data processing, it is important to gauge how input uncertainty affects the results of data processing. Several techniques have been proposed for this gauging, from interval to affine to Taylor techniques. Some of these techniques result in more accurate estimates but require longer computation time, others' results are less accurate but can be obtained faster. Sometimes, we do not have enough time to use more accurate (but more time-consuming) techniques, but we have more time than needed for less accurate ones. In such cases, it is desirable to come up with intermediate techniques that would utilize the available additional …

Discrete Causality Implies Lorenz Group: Case Of 2-D Space-Times, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that for Minkowski space-times of dimension larger than 2, any causality-preserving transformation is linear. It is also known that in a 2-D space-time, there are many nonlinear causality-preserving transformations. In this paper, we show that for 2-D space-times, if we restrict ourselves to discrete space-times, then linearity is retained: only linear transformation preserve causality.

There From The Beginning: The Women Of Los Alamos National Laboratory Supporting National And International Nuclear Security, Olga Martin, Laura Mcclellan, Octavio Ramos, Heather Quinn

International Journal of Nuclear Security

From the beginning of the Manhattan Project in the early 1940s, the women of what would become Los Alamos National Laboratory (LANL) worked in technical positions alongside their male counterparts, played a key role as computers, and worked in administrative jobs as secretaries, phone operators, bookkeepers, and on behalf of the U.S. Army in the Women’s Army Corps.

Throughout the history of the Laboratory, women experts at LANL helped establish and lead important national and international security programs, with careers in science, technology, engineering, and mathematics. Over time, the women of Los Alamos have come together under various Employee Resource …

Don’T Beep At Me: Using Google Maps Apis To Reduce Driving Anxiety, Daniel Chechelnitsky

Mathematics, Statistics, and Computer Science Honors Projects

Stress while driving is a significant issue that causes automobile incidents. Along with the physical injuries, there is often baggage and trauma associated with these accidents. Wearable health monitoring technology, like Smartwatches, has a real possibility to help people further understand the stress inducing processes of driving. Thus to help with this issue, I propose a Google Maps app extension called: "Don't Beep At Me". This project creates a map that is layered by heart rate instead of speed limit and has great potential to be useful for reducing driving anxiety.

Investigation Of Neutrophil-Like Hl-60 Cell Migration In A 3d Collagen Matrix, Pouye Sedighian

CGU Theses & Dissertations

It is known that cell migration in innate and adaptive immune system plays a fundamental role in human health. Among the immune cells, neutrophils are one of the most essential cells in protecting the body against invading pathogens. In the presence of chemoattractants, these cells are the first responders that start a directed migration toward the injured area. As neutrophils approach the site of infection, they transmigrate to the tissue and follow the chemoattractant concentration gradient to locate and eliminate the invading pathogens. Understanding the patterns and mechanism of neutrophil migration in the presence of chemoattractants could possibly play an …

Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa

Honors Theses

In this paper, we analyze the decoding of cyclic codes. First, we introduce linear and cyclic codes, standard decoding processes, and some standard theorems in coding theory. Then, we will introduce Gr¨obner Bases, and describe their connection to the decoding of cyclic codes. Finally, we go in-depth into how we decode cyclic codes using the key equation, and how a breakthrough by A. Brinton Cooper on decoding BCH codes using Gr¨obner Bases gave rise to the search for a polynomial-time algorithm that could someday decode any cyclic code. We discuss the different approaches taken toward developing such an algorithm and …

Matrix Interpretations And Tools For Investigating Even Functionals, Benjamin Stringer

Theses and Dissertations--Computer Science

Even functionals are a set of polynomials evaluated on the terms of hollow symmetric matrices. Their properties lend themselves to applications such as counting subgraph embeddings in generic (weighted or unweighted) host graphs and computing moments of binary quadratic forms, which occur in combinatorial optimization. This research focuses primarily on counting subgraph embeddings, which is traditionally accomplished with brute-force algorithms or algorithms curated for special types of graphs. Even functionals provide a method for counting subgraphs algebraically in time proportional to matrix multiplication and is not restricted to particular graph types. Counting subgraph embeddings can be accomplished by evaluating a …

Realtime Event Detection In Sports Sensor Data With Machine Learning, Mallory Cashman

Honors Theses and Capstones

Machine learning models can be trained to classify time series based sports motion data, without reliance on assumptions about the capabilities of the users or sensors. This can be applied to predict the count of occurrences of an event in a time period. The experiment for this research uses lacrosse data, collected in partnership with SPAITR - a UNH undergraduate startup developing motion tracking devices for lacrosse. Decision Tree and Support Vector Machine (SVM) models are trained and perform with high success rates. These models improve upon previous work in human motion event detection and can be used a reference …

Rankings Of Mma Fighters, Michael Schaefer

All Graduate Theses, Dissertations, and Other Capstone Projects

Ranking is an essential process that allows sporting authorities to determine the relative performance of athletes. While ranking is straightforward in some sports, it is more complicated in MMA (mixed martial arts), where competition is often fragmented. This paper describes the mathematics behind four existing ranking algorithms: Elo’s System, Massey’s Method, Colley’s Method, and Google’s PageRank, and shows how to adapt them to rank MMA fighters in the UFC (Ultimate Fighting Championship). We also provide a performance analysis for each ranking method.

A Comparison Of Stacking Methods To Estimate Survival Using Residual Lifetime Data From Prevalent Cohort Studies, Zhaoheng Li

Mathematics, Statistics, and Computer Science Honors Projects

Prevalent cohort studies are widely used for their cost-efficiency and convenience. However, in such studies, only the residual lifetime can be observed. Traditionally, researchers rely on self-reported onset times to infer the underlying survival distribution, which may introduce additional bias that confounds downstream analysis. This study compares two stacking procedures and one mixture model approach that uses only residual lifetime data while leveraging the strengths of different estimators. Our simulation results show that the two stacked estimators outperform the nonparametric maximum likelihood estimator (NPMLE) and the mixture model, allowing robust and accurate estimations for underlying survival distributions.

Lasso: Listing All Subset Sums Obediently For Evaluating Unbounded Subset Sums, Christopher N. Burgoyne, Travis J. Wheeler

Graduate Student Theses, Dissertations, & Professional Papers

In this study we present a novel algorithm, LASSO, for solving the unbounded and bounded subset sum problem. The LASSO algorithm was designed to solve the unbounded SSP quickly and to return all subsets summing to a target sum. As speed was the highest priority, we benchmarked the run time performance of LASSO against implementations of some common approaches to the bounded SSP, as well as the only comparable implementation for solving the unbounded SSP that we could find. In solving the bounded SSP, our algorithm had a significantly faster run time than the competing algorithms when the target sum …

Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, Jedidiah Lindborg

College of Graduate Studies: Theses & Dissertations

In reinforcement learning the process of selecting an action during the exploration or exploitation stage is difficult to optimize. The purpose of this thesis is to create an action selection process for an agent by employing a low discrepancy action selection (LDAS) method. This should allow the agent to quickly determine the utility of its actions by prioritizing actions that are dissimilar to ones that it has already picked. In this way the learning process should be faster for the agent and result in more optimal policies.

Exo-Sir: An Epidemiological Model To Analyze The Impact Of Exogenous Spread Of Infection, Nirmal Kumar Sivaraman, Manas Gaur, Shivansh Baijal, Sakthi Balan Muthiah, Amit Sheth

Publications

Epidemics like Covid-19 and Ebola have impacted people's lives significantly. The impact of mobility of people across the countries or states in the spread of epidemics has been significant. The spread of disease due to factors local to the population under consideration is termed the endogenous spread. The spread due to external factors like migration, mobility, etc. is called the exogenous spread. In this paper, we introduce the Exo-SIR model, an extension of the popular SIR model and a few variants of the model. The novelty in our model is that it captures both the exogenous and endogenous spread of …

Stroke Clustering And Fitting In Vector Art, Khandokar Shakib

Senior Independent Study Theses

Vectorization of art involves turning free-hand drawings into vector graphics that can be further scaled and manipulated. In this paper, we explore the concept of vectorization of line drawings and study multiple approaches that attempt to achieve this in the most accurate way possible. We utilize a software called StrokeStrip to discuss the different mathematics behind the parameterization and fitting involved in the drawings.

Highlights Generation For Tennis Matches Using Computer Vision, Natural Language Processing And Audio Analysis, Alon Liberman

Senior Independent Study Theses

This project uses computer vision, natural language processing and audio analysis to automatize the highlights generation task for tennis matches. Computer vision techniques such as camera shot detection, hough transform and neural networks are used to extract the time intervals of the points. To detect the best points, three approaches are used. Point length suggests which points correspond to rallies and aces. The audio waves are analyzed to search for the highest audio peaks, which indicate the moments where the crowd cheers the most. Sentiment analysis, a natural language processing technique, is used to look for points where the commentators …

Sufficient Condition For The Possibility Of Completing The Pursuit, Nodirbek Umrzaqov

Scientific Bulletin. Physical and Mathematical Research

In this paper, the problem of chase is represented by a system of linear differential equations of motion dynamics. In this case, there is an integral limit to the control parameter of the evader, and a geometric limit to the control parameter of the pursuer. The pursuer is allowed to use the control that the fugitive has used so far to build his control. There are enough conditions for the game to end even if it starts from any starting point. An algorithm for constructing the control function of the pursuer is defined. It should also be noted that the …

Computer Program Simulation Of A Quantum Turing Machine With Circuit Model, Shixin Wu

Mathematical Sciences Technical Reports (MSTR)

Molina and Watrous present a variation of the method to simulate a quantum Turing machine employed in Yao’s 1995 publication “Quantum Circuit Complexity”. We use a computer program to implement their method with linear algebra and an additional unitary operator defined to complete the details. Their method is verified to be correct on a quantum Turing machine.

Negations Of Probability Distributions: A Survey, Ildar Z. Baryrshin, Nailya I. Kubysheva, Venera R. Bayrasheva, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In recent years many papers have been devoted to the analysis and applications of negations of finite probability distributions (PD), first considered by Ronald Yager. This paper gives a brief overview of some formal results on the definition and properties of negations of PD. Negations of PD are generated by negators of probability values transforming element-by-element PD into a negation of PD. Negators are non-increasing functions of probability values. There are two types of negators: PD-independent and PD-dependent negators. Yager's negator is fundamental in the characterization of linear PD-independent negators as a convex combination of Yager's negator and uniform negator. …

How To Select Typical Objects, Mariana Benitez, Jeffrey Weidner, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we have a large number of objects, too many to be able to thoroughly analyze each of them. To get a general understanding, we need to select a representative sample. For us, this problem was motivated to analyze the possible effect of an earthquake on buildings in El Paso, Texas. In this paper, we provide a reasonable formalization of this problem, and provide a feasible algorithm for solving thus formalized problem.

How To Simulate If We Only Have Partial Information But We Want Reliable Results?, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

The main objective of a smart energy system is to make control decisions that would make energy systems more efficient and more reliable. To select such decisions, the system must know the consequences of different possible decisions. Energy systems are very complex, they cannot be described by a simple formula, the only way to reasonably accurately find such consequences is to test each decision on a simulated system. The problem is that the parameters describing the system and its environment are usually known with uncertainty, and we need to produce reliable results -- i.e., results that will be true for …

Acceleration Skinning: Kinematics-Driven Cartoon Effects For Articulated Characters, Niranjan Kalyanasundaram

All Theses

Secondary effects are key to adding fluidity and style to animation. This thesis introduces the idea of “Acceleration Skinning” following a recent well-received technique, Velocity Skinning, to automatically create secondary motion in character animation by modifying the standard pipeline for skeletal rig skinning. These effects, which animators may refer to as squash and stretch or drag, attempt to create an illusion of inertia. In this thesis, I extend the Velocity Skinning technique to include acceleration for creating a wider gamut of cartoon effects. I explore three new deformers that make use of this Acceleration Skinning framework: followthrough, centripetal stretch, and …

Linear Algebra For Computer Science, M. Thulasidas

Research Collection School Of Computing and Information Systems

This textbook introduces the essential concepts and practice of Linear Algebra to the undergraduate student of computer science. The focus of this book is on the elegance and beauty of the numerical techniques and algorithms originating from Linear Algebra. As a practical handbook for computer and data scientists, LA4CS restricts itself mostly to real fields and tractable discourses, rather than deep and theoretical mathematics.

Why Moments (And Generalized Moments) Are Used In Statistics And Why Expected Utility Is Used In Decision Making: A Possible Explanation, R. Noah Padilla, Vladik Kreinovich

Departmental Technical Reports (CS)

Among the most efficient characteristics of a probability distribution are its moments and, more generally, generalized moments. One of the most adequate numerical characteristics describing human behavior is expected utility. In both cases, the corresponding characteristic is the sum of results of applying appropriate nonlinear functions applied to individual inputs. In this paper, we provide a possible theoretical explanation of why such functions are efficient.

How Multi-View Techniques Can Help In Processing Uncertainty, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Multi-view techniques help us reconstruct a 3-D object and its properties from its 2-D (or even 1-D) projections. It turns out that similar techniques can be used in processing uncertainty -- where many problems can reduced to a similar task of reconstructing properties of a multi-D object from its 1-D projections. In this chapter, we provide an overview of these techniques.

Why Do People Become Addicted: Towards A Theoretical Explanation For Eyal's Experiment-Based Hook Model, Christopher Reyes, Vladik Kreinovich

Departmental Technical Reports (CS)

Why do people become addicted, e.g., to gambling? Experiments have shown that simple lotteries, in which we can win a small prize with a certain probability, and not addictive. However, if we add a second possibility -- of having a large prize with a small probability -- the lottery becomes highly addictive to many participants. In this paper, we provide a possible theoretical explanation for this empirical phenomenon.

Why Ovals In Eliciting Intervals?, Joshua Zamora, Vladik Kreinovich

Departmental Technical Reports (CS)

To elicit people's opinions, we usually ask them to mark their degree of satisfaction on a scale -- e.g., from 0 to 5 or from 0 to 10. Often, people are unsure about the exact degree: 7 or 8? To cover such situations, it is desirable to elicit not a single value but an interval of possible values. However, it turns out that most people are not comfortable with marking an interval. Empirically, it turned out that the best way to elicit an interval is to ask them to draw an oval whose intersection with the 0-to-10 line is the …

Decision Making Under Uncertainty: Cases When We Only Know An Upper Bound Or A Lower Bound, Toshiki Kamio, Gavin Baechle, Vladik Kreinovich

Departmental Technical Reports (CS)

In situations when we have a perfect knowledge about the outcomes of several situations, a natural idea is to select the best of these situations. For example, among different investments, we should select the one with the largest gain. In practice, however, we rarely know the exact consequences of each action. In some cases, we know the lower and upper bounds on the corresponding gain. It has been proven that in such cases, an appropriate decision is to use Hurwicz optimism-pessimism criterion. In this paper, we extend the corresponding results to the cases when we only know an upper bound …