Computer Sciences Commons^™

Facilitating Mathematics And Computer Science Connections: A Cross-Curricular Approach, Kimberly E. Beck, Jessica F. Shumway, Umar Shehzad, Jody Clarke-Midura, Mimi Recker

Publications

In the United States, school curricula are often created and taught with distinct boundaries between disciplines. This division between curricular areas may serve as a hindrance to students' long-term learning and their ability to generalize. In contrast, cross-curricular pedagogy provides a way for students to think beyond the classroom walls and make important connections across disciplines. The purpose of this paper is a theoretical reflection on our use of Expansive Framing in our design of lessons across learning environments within the school. We provide a narrative account of our early work in using this theoretical framework to co-plan and enact …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

An Empirical Study Of Machine Learning Techniques For Accurate Stock Price Forecasting, Daniel Paliulis, Hari Patchigolla

Honors Scholar Theses

This paper presents a comprehensive approach to predicting future stock prices of companies using machine learning and time series analysis. The research problem is centered around addressing the complexity and emotion-driven nature of stock investment decisions. To create an objective determinant in stock decisions, we propose a machine learning model utilizing time series data from major companies, including Amazon, Apple, Google, Nvidia, Meta, Tesla, Salesforce, Intel, and Microsoft. We explore the use of Long Short-Term Memory (LSTM) neural networks, to capture the temporal dynamics of stock prices. These models are designed to process sequential data, maintaining short term and long …

On The Hardness Of The Balanced Connected Subgraph Problem For Families Of Regular Graphs, Harsharaj Pathak

Theory & Applications of Graphs

The Balanced Connected Subgraph problem (BCS) was introduced by Bhore et al. In the BCS problem we are given a vertex-colored graph G = (V, E) where each vertex is colored “red” or “blue”. The goal is to find a maximum cardinality induced connected subgraph H of G such that H contains an equal number of red and blue vertices. This problem is known to be NP-hard for general graphs as well as many special classes of graphs. In this work we explore the time complexity of the BCS problem in case of regular graphs. We prove that the BCS …

The Vulnerabilities To The Rsa Algorithm And Future Alternative Algorithms To Improve Security, James Johnson

Cybersecurity Undergraduate Research Showcase

The RSA encryption algorithm has secured many large systems, including bank systems, data encryption in emails, several online transactions, etc. Benefiting from the use of asymmetric cryptography and properties of number theory, RSA was widely regarded as one of most difficult algorithms to decrypt without a key, especially since by brute force, breaking the algorithm would take thousands of years. However, in recent times, research has shown that RSA is getting closer to being efficiently decrypted classically, using algebraic methods, (fully cracked through limited bits) in which elliptic-curve cryptography has been thought of as the alternative that is stronger than …

Every Relu-Based Neural Network Can Be Described By A System Of Takagi-Sugeno Fuzzy Rules: A Theorem, Barnabas Bede, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

While modern deep-learning neural networks are very successful, sometimes they make mistakes, and since their results are "black boxes" -- no explanation is provided -- it is difficult to determine which recommendations are erroneous. It is therefore desirable to make the resulting computations explainable, i.e., to describe their results by using commonsense rules. In this paper, we use "fuzzy" techniques -- techniques developed by Lotfi Zadeh to deal with commonsense rules formulated by using imprecise ("fuzzy") words from natural language -- to show that such a rule-based representation is always possible. Our result does not yet provide the desired explainability, …

Smooth Non-Additive Integrals And Measures And Their Potential Applications, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we explain why non-additive integrals and measures are needed, how non-additive integrals and measures are related, how to use them in decision making, and how they can help in fundamental physics. These four topics are covered, correspondingly, in Sections 2-5 of this paper.

Why Sigmoid Transformation Helps Incorporate Logic Into Deep Learning: A Theoretical Explanation, Chitta Baral, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional neural networks start from the data, they cannot easily handle prior knowledge -- this is one of the reasons why they often take very long to train. It is desirable to incorporate prior knowledge into deep learning. For the case when this knowledge consists of propositional statements, a successful way to incorporate this knowledge was proposed in a recent paper by van Krieken et al. That paper uses the fact that a neural network does not directly return a truth value, it returns a real value -- in effect, the degree of confidence in the corresponding statement -- from …

If We Add Axiom Of Choice To Constructive Analysis, We Get Classical Arithmetic: An Exercise In Reverse Constructive Mathematics, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A recent paper in Bulletin of Symbolic Logic reminded that the Axiom of Choice is, in general, false in constructive analysis. This result is an immediate consequence of a theorem -- first proved by Tseytin -- that every computable function is continuous. In this paper, we strengthen the result about the Axiom of Choice by proving that this axiom is as non-constructive as possible: namely, that if we add this axiom to constructive analysis, then we get full classical arithmetic.

When Is A Single "And"-Condition Enough?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, there are several possible decisions. Any general recommendation means specifying, for each possible decision, conditions under which this decision is recommended. In some cases, a single "and"-condition is sufficient: e.g., a condition under which a patient is recommended to take aspirin is that "the patient has a fever and the patient does not have stomach trouble". In other cases, conditions are more complicated. A natural question is: when is a single "and"-condition enough? In this paper, we provide an answer to this question.

On Dyadic Parity Check Codes And Their Generalizations, Meraiah Martinez

Department of Mathematics: Dissertations, Theses, and Student Research

In order to communicate information over a noisy channel, error-correcting codes can be used to ensure that small errors don’t prevent the transmission of a message. One family of codes that has been found to have good properties is low-density parity check (LDPC) codes. These are represented by sparse bipartite graphs and have low complexity graph-based decoding algorithms. Various graphical properties, such as the girth and stopping sets, influence when these algorithms might fail. Additionally, codes based on algebraically structured parity check matrices are desirable in applications due to their compact representations, practical implementation advantages, and tractable decoder performance analysis. …

Integrating Machine Learning Methods For Medical Diagnosis, Jazmin Quezada

Open Access Theses & Dissertations

Abstract:The rapid advancement of machine learning techniques has revolutionized the field of medical diagnosis by offering powerful tools to analyze complex data sets and make accurate predictions. In this proposed method, we present a novel approach that integrates machine learning and optimization models to enhance the accuracy of medical diagnoses. Our method focuses on fine-tuning and optimizing the parameters of machine learning algorithms commonly used in medical diagnosis, such as logistic regression, support vector machines, and neural networks. By employing optimization techniques, we systematically explore the parameter space of these algorithms to discover the most optimal configurations. Moreover, by representing …

A Bridge Between Graph Neural Networks And Transformers: Positional Encodings As Node Embeddings, Bright Kwaku Manu

Electronic Theses and Dissertations

Graph Neural Networks and Transformers are very powerful frameworks for learning machine learning tasks. While they were evolved separately in diverse fields, current research has revealed some similarities and links between them. This work focuses on bridging the gap between GNNs and Transformers by offering a uniform framework that highlights their similarities and distinctions. We perform positional encodings and identify key properties that make the positional encodings node embeddings. We found that the properties of expressiveness, efficiency and interpretability were achieved in the process. We saw that it is possible to use positional encodings as node embeddings, which can be …

Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury

Master's Theses

A central problem in neuroscience is to understand how memories are formed as a result of the activities of neurons. Valiant’s neuroidal model attempted to address this question by modeling the brain as a random graph and memories as subgraphs within that graph. However the question of memory capacity within that model has not been explored: how many memories can the brain hold? Valiant introduced the concept of interference between memories as the defining factor for capacity; excessive interference signals the model has reached capacity. Since then, exploration of capacity has been limited, but recent investigations have delved into the …

From Type-2 Fuzzy To Type-2 Intervals And Type-2 Probabilities, Vladik Kreinovich, Olga Kosheleva, Luc Longpré

Departmental Technical Reports (CS)

Our knowledge comes from observations, measurements, and expert opinions. Measurements and observations are never 100% accurate, there is always a difference between the measurement result and the actual value of the corresponding quantity. We gauge the resulting uncertainty either by an interval of possible values, or by a probability distribution on the set of possible values, or by a membership function that describes to what extent different values are possible. The information about uncertainty also comes either from measurements or from expert estimates and is, therefore, also uncertain. It is important to take such "type-2" uncertainty into account. This is …

Giant Footprints Of Buddha And Generalized Limits, Julio C. Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

In many places in Asia, there are footprints claimed to be left by Buddha. Many of them are much larger than the usual size of human feet, up to 150 cm and more in length. In this paper, we provide a possible mathematical explanation for such unusual sizes.

How To Efficiently Propagate P-Box Uncertainty, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, to get the desired estimate or prediction, we need to process existing data. This data usually comes from measurements, and measurements are never 100% accurate. Because we only know the input values with uncertainty, the results of processing this data also comes with uncertainty. To make an appropriate decision, we need to know how accurate is the resulting estimate, i.e., how the input uncertainty "propagates" through the data processing algorithm. In the ideal case, when we know the probability distribution of each measurement error, we can, in principle, use Monte-Carlo simulations to describe the uncertainty of …

Uncertainty Quantification For Results Of Ai-Based Data Processing: Towards More Feasible Algorithms, Christoph Q. Lauter, Martine Ceberio, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

AI techniques have been actively and successfully used in data processing. This tendency started with fuzzy techniques, now neural network techniques are actively used. With each new technique comes the need for the corresponding uncertainty quantification (UQ). In principle, for both fuzzy and neural techniques, we can use the usual UQ methods -- however, these techniques often require an unrealistic amount of computation time. In this paper, we show that in both cases, we can use specific features of the corresponding techniques to drastically speed up the corresponding computations.

Usually, Either Left And Right Brains Are Equally Active Or Only One Of Them Is Active: First-Principles Explanation, Julio C. Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that in most practical situations, either both left and right brains are equally active, or only one of them is active. A recent paper showed that this empirical phenomenon can be explained by a realistic model of the brain effectiveness. In this paper, we show that this conclusion can be made without any specific assumptions about the brain, based on first principles.

Which Random-Set Representation Of A Fuzzy Set Is The Simplest?, Vladik Kreinovich, Olga Kosheleva, Hung T. Nguyen

Departmental Technical Reports (CS)

One of the ways to elicit membership degrees is by polling. For example, we ask a group of people how many believe that 30 C is hot. If 8 out of ten say that it is hot, we assign the degree 8/10 to the statement "30 C is hot". In precise mathematical terms, polling can be described via so-called random sets. It is known that every fuzzy set can be obtained this way, i.e., that every fuzzy set can be represented by an appropriate random set. Moreover, it is known that for many fuzzy sets, there are several different random-set …

A Review Of Cyber Attacks On Sensors And Perception Systems In Autonomous Vehicle, Taminul Islam, Md. Alif Sheakh, Anjuman Naher Jui, Omar Sharif, Md Zobaer Hasan

School of Mathematical & Statistical Sciences Faculty Publications

Vehicle automation has been in the works for a long time now. Automatic brakes, cruise control, GPS satellite navigation, etc. are all common features seen in today's automobiles. Automation and artificial intelligence breakthroughs are likely to lead to an increase in the usage of automation technologies in cars. Because of this, mankind will be more reliant on computer-controlled equipment and car systems in our daily lives. All major corporations have begun investing in the development of self-driving cars because of the rapid advancement of advanced driver support technologies. However, the level of safety and trustworthiness is still questionable. Imagine what …

Reducing Uncertainty In Sea-Level Rise Prediction: A Spatial-Variability-Aware Approach, Subhankar Ghosh, Shuai An, Arun Sharma, Jayant Gupta, Shashi Shekhar, Aneesh Subramanian

I-GUIDE Forum

Given multi-model ensemble climate projections, the goal is to accurately and reliably predict future sea-level rise while lowering the uncertainty. This problem is important because sea-level rise affects millions of people in coastal communities and beyond due to climate change's impacts on polar ice sheets and the ocean. This problem is challenging due to spatial variability and unknowns such as possible tipping points (e.g., collapse of Greenland or West Antarctic ice-shelf), climate feedback loops (e.g., clouds, permafrost thawing), future policy decisions, and human actions. Most existing climate modeling approaches use the same set of weights globally, during either regression or …

Why Micro-Funding? Why Small Businesses Are Important? Analysis Based On First Principles, Hein D. Tran, Edwin Tomy George, Vladik Kreinovich

Departmental Technical Reports (CS)

On the one hand, in economics, there is a well-known and well-studied economy of scale: when two smaller companies merge, it lowers their costs and thus, makes them more effective and therefore more competitive. At first glance, this advantage of big size would make economy dominated by big companies -- but in reality, small business remain a significant and important economic sector. Similarly, it is well known and well studied that research collaboration enhances researchers' productivity -- but still a significant portion of important results come from individual efforts. In several applications areas, there are area-specific explanations for this seemingly …

Local-Global Support For Earth Sciences: Economic Analysis, Uyen Hoang Pham, Aaron Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

Most funding for science comes from taxpayers. So, it is very important to be able to convince taxpayers that this funding is potentially beneficial for them. This task is easier in Earth sciences, e.g., in meteorology, where there are clear local benefits. The problem is that while many people support local studies focused on their region, they do not always have a good understanding of the fact that effective local benefits require also studying surrounding areas -- and what should be the optimal balance between local and (more) global studies. In this paper, on a (somewhat) simplified model of the …

Approximate Stochastic Dominance Revisited, Chon Van Le, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

According to decision theory, in general, to recommend the best of possible actions, we need to know, for each possible action, the probabilities of different outcomes, and we also need to know the decision maker's utility function -- that describes his/her preferences. For some pairs of probability distributions, however, we can make such a recommendation without knowing the exact form of the utility function -- e.g., in financial applications, we only need to know that a larger amount is preferable to a smaller one. Such situations, when we can make decisions based only on the information about probabilities, are known …

Just-In-Accuracy: Mobile Approach To Uncertainty, Martine Ceberio, Christoph Q. Lauter, Vladik Kreinovich

Departmental Technical Reports (CS)

To make a mobile device last longer, we need to limit computations to a bare minimum. One way to do that, in complex control and decision making problems, is to limit precision with which we do computations, i.e., limit the number of bits in the numbers' representation. A problem is that often, we do not know with what precision should we do computations to get the desired accuracy of the result. What we propose is to first do computations with very low precision, then, based on these computations, estimate what precision is needed to achieve the given accuracy, and then …

How To Deal With Inconsistent Intervals: Utility-Based Approach Can Overcome The Limitations Of The Purely Probability-Based Approach, Kittawit Autchariyapanitkul, Tomoe Entani, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many application areas, we rely on experts to estimate the numerical values of some quantities. Experts can provide not only the estimates themselves, they can also estimate the accuracies of their estimates -- i.e., in effect, they provide an interval of possible values of the quantity of interest. To get a more accurate estimate, it is reasonable to ask several experts -- and to take the intersection of the resulting intervals. In some cases, however, experts overestimate the accuracy of their estimates, their intervals are too narrow -- so narrow that they are inconsistent: their intersection is empty. In …

How To Make Machine Learning Financial Recommendations More Fair: Theoretical Explanation, Tho M. Nguyen, Saeid Tizpaz-Niari, Vladik Kreinovich

Departmental Technical Reports (CS)

Machine learning has been actively and successfully used to make financial decisions. In general, these systems work reasonably well. However, in some cases, these systems show unexpected bias towards minority groups -- the bias that is sometime much larger than the bias in the data on which they were trained. A recent paper analyzed whether a proper selection of hyperparameters can decrease this bias. It turned out that while the selection of hyperparameters indeed affect the system's fairness, only a few of the hyperparameters lead to consistent improvement of fairness: the number of features used for training and the number …

Utilizing Graph Thickness Heuristics On The Earth-Moon Problem, Robert C. Weaver

Rose-Hulman Undergraduate Mathematics Journal

This paper utilizes heuristic algorithms for determining graph thickness in order to attempt to find a 10-chromatic thickness-2 graph. Doing so would eliminate 9 colors as a potential solution to the Earth-moon Problem. An empirical analysis of the algorithms made by the author are provided. Additionally, the paper lists various graphs that may or nearly have a thickness of 2, which may be solutions if one can find two planar subgraphs that partition all of the graph’s edges.

Machine Learning And Causality For Interpretable And Automated Decision Making, Maria Lentini

Theses and Dissertations

This abstract explores two key areas in decision science: automated and interpretable decision making. In the first part, we address challenges related to sparse user interaction data and high item turnover rates in recommender systems. We introduce a novel algorithm called Multi-View Interactive Collaborative Filtering (MV-ICTR) that integrates user-item ratings and contextual information, improving performance, particularly for cold-start scenarios. In the second part, we focus on Student Prescription Trees (SPTs), which are interpretable decision trees. These trees use a black box "teacher" model to predict counterfactuals based on observed covariates. We experiment with a Bayesian hierarchical binomial regression model as …