Theory and Algorithms Commons^™

Combinatorics Syllabus, Tugce Ozdemir

Open Educational Resources

No abstract provided.

Artificial Intelligence And The Situational Rationality Of Diagnosis: Human Problem-Solving And The Artifacts Of Health And Medicine, Michael W. Raphael

Publications and Research

What is the problem-solving capacity of artificial intelligence (AI) for health and medicine? This paper draws out the cognitive sociological context of diagnostic problem-solving for medical sociology regarding the limits of automation for decision-based medical tasks. Specifically, it presents a practical way of evaluating the artificiality of symptoms and signs in medical encounters, with an emphasis on the visualization of the problem-solving process in doctor-patient relationships. In doing so, the paper details the logical differences underlying diagnostic task performance between man and machine problem-solving: its principle of rationality, the priorities of its means of adaptation to abstraction, and the effects …

An Analysis Of The Friendship Paradox And Derived Sampling Methods, Yitzchak Novick

Dissertations, Theses, and Capstone Projects

The friendship paradox (FP) is the famous sampling-bias phenomenon that leads to the seemingly paradoxical truth that, on average, people’s friends have more friends than they do. Among the many far-reaching research findings the FP inspired is a sampling method that samples neighbors of vertices in a graph in order to acquire random vertices that are of higher expected degree than average.

Our research examines the friendship paradox on a local level. We seek to quantify the impact of the FP on an individual vertex by defining the vertex’s “friendship index”, a measure of the extent to which the phenomenon …

On The Cryptographic Deniability Of The Signal Protocol, Nihal Vatandas

Dissertations, Theses, and Capstone Projects

Offline deniability is the ability to a posteriori deny having participated in a particular communication session. This property has been widely assumed for the Signal messaging application, yet no formal proof has appeared in the literature. In this work, we present the first formal study of the offline deniability of the Signal protocol. Our analysis shows that building a deniability proof for Signal is non-trivial and requires strong assumptions on the underlying mathematical groups where the protocol is run.

To do so, we study various implicitly authenticated key exchange protocols, including MQV, HMQV, and 3DH/X3DH, the latter being the core …

Coded Distributed Function Computation, Pedro J. Soto

Dissertations, Theses, and Capstone Projects

A ubiquitous problem in computer science research is the optimization of computation on large data sets. Such computations are usually too large to be performed on one machine and therefore the task needs to be distributed amongst a network of machines. However, a common problem within distributed computing is the mitigation of delays caused by faulty machines. This can be performed by the use of coding theory to optimize the amount of redundancy needed to handle such faults. This problem differs from classical coding theory since it is concerned with the dynamic coded computation on data rather than just statically …

The Significance Of Sonic Branding To Strategically Stimulate Consumer Behavior: Content Analysis Of Four Interviews From Jeanna Isham’S “Sound In Marketing” Podcast, Ina Beilina

Student Theses and Dissertations

Purpose:
Sonic branding is not just about composing jingles like McDonald’s “I’m Lovin’ It.” Sonic branding is an industry that strategically designs a cohesive auditory component of a brand’s corporate identity. This paper examines the psychological impact of music and sound on consumer behavior reviewing studies from the past 40 years and investigates the significance of stimulating auditory perception by infusing sound in consumer experience in the modern 2020s.

Design/methodology/approach:
Qualitative content analysis of audio media was used to test two hypotheses. Four archival oral interview recordings from Jeanna Isham’s podcast “Sound in Marketing” featuring the sonic branding experts …

Introduction To Discrete Mathematics: An Oer For Ma-471, Mathieu Sassolas

Open Educational Resources

The first objective of this book is to define and discuss the meaning of truth in mathematics. We explore logics, both propositional and first-order , and the construction of proofs, both formally and human-targeted. Using the proof tools, this book then explores some very fundamental definitions of mathematics through set theory. This theory is then put in practice in several applications. The particular (but quite widespread) case of equivalence and order relations is studied with detail. Then we introduces sequences and proofs by induction, followed by number theory. Finally, a small introduction to combinatorics is …

Solving Multiple Inference In Graphical Models, Cong Chen

Dissertations, Theses, and Capstone Projects

For inference problems in graphical models, much effort has been directed at algorithms for obtaining one single optimal prediction. In practice, the data is often noisy or incomplete, which makes one single optimal solution unreliable. To address this problem, multiple Inference is proposed to find several best solutions, M-Best, where multiple hypotheses are preferred for advanced reasoning. People use oracle accuracy as an evaluation criterion expecting one of the solutions has high accuracy with the ground truth. It has been shown that it is beneficial for the top solutions to be diverse. Approaches for solving diverse multiple inference are proposed …

Teaching Machine Learning For The Physical Sciences: A Summary Of Lessons Learned And Challenges, Viviana Acquaviva

Publications and Research

This paper summarizes some challenges encountered and best practices established in several years of teaching Machine Learning for the Physical Sciences at the undergraduate and graduate level. I discuss motivations for teaching ML to physicists, desirable properties of pedagogical materials, such as accessibility, relevance, and likeness to real-world research problems, and give examples of components of teaching units.

An Adaptive Cryptosystem On A Finite Field, Awnon Bhowmik, Unnikrishnan Menon

Publications and Research

Owing to mathematical theory and computational power evolution, modern cryptosystems demand ingenious trapdoor functions as their foundation to extend the gap between an enthusiastic interceptor and sensitive information. This paper introduces an adaptive block encryption scheme. This system is based on product, exponent, and modulo operation on a finite field. At the heart of this algorithm lies an innovative and robust trapdoor function that operates in the Galois Field and is responsible for the superior speed and security offered by it. Prime number theorem plays a fundamental role in this system, to keep unwelcome adversaries at bay. This is a …

On Communication For Distributed Babai Point Computation, Maiara F. Bollauf, Vinay A. Vaishampayan, Sueli I.R. Costa

Publications and Research

We present a communication-efficient distributed protocol for computing the Babai point, an approximate nearest point for a random vector X∈Rn in a given lattice. We show that the protocol is optimal in the sense that it minimizes the sum rate when the components of X are mutually independent. We then investigate the error probability, i.e. the probability that the Babai point does not coincide with the nearest lattice point, motivated by the fact that for some cases, a distributed algorithm for finding the Babai point is sufficient for finding the nearest lattice point itself. Two different probability models for X …

Decoding Clinical Biomarker Space Of Covid-19: Exploring Matrix Factorization-Based Feature Selection Methods, Farshad Saberi-Movahed, Mahyar Mohammadifard, Adel Mehrpooya, Mohammad Rezaei-Ravari, Kamal Berahmand, Mehrdad Rostami, Saeed Karami, Mohammad Najafzadeh, Davood Hajinezhad, Mina Jamshidi, Farshid Abedi, Mahtab Mohammadifard, Elnaz Farbod, Farinaz Safavi, Mohammadreza Dorvash, Shahrzad Vahedi, Mahdi Eftekhari, Farid Saberi-Movahed, Iman Tavassoly

Publications and Research

One of the most critical challenges in managing complex diseases like COVID-19 is to establish an intelligent triage system that can optimize the clinical decision-making at the time of a global pandemic. The clinical presentation and patients’ characteristics are usually utilized to identify those patients who need more critical care. However, the clinical evidence shows an unmet need to determine more accurate and optimal clinical biomarkers to triage patients under a condition like the COVID-19 crisis. Here we have presented a machine learning approach to find a group of clinical indicators from the blood tests of a set of COVID-19 …

The “Knapsack Problem” Workbook: An Exploration Of Topics In Computer Science, Steven Cosares

Open Educational Resources

This workbook provides discussions, programming assignments, projects, and class exercises revolving around the “Knapsack Problem” (KP), which is widely a recognized model that is taught within a typical Computer Science curriculum. Throughout these discussions, we use KP to introduce or review topics found in courses covering topics in Discrete Mathematics, Mathematical Programming, Data Structures, Algorithms, Computational Complexity, etc. Because of the broad range of subjects discussed, this workbook and the accompanying spreadsheet files might be used as part of some CS capstone experience. Otherwise, we recommend that individual sections be used, as needed, for exercises relevant to a course in …

Modeling And Analysis Of Affiliation Networks With Subsumption, Alexey Nikolaev

Dissertations, Theses, and Capstone Projects

An affiliation (or two-mode) network is an abstraction commonly used for representing systems with group interactions. It consists of a set of nodes and a set of their groupings called affiliations. We introduce the notion of affiliation network with subsumption, in which no affiliation can be a subset of another. A network with this property can be modeled by an abstract simplicial complex whose facets are the affiliations of the network.

We introduce a new model for generating affiliation networks with and without subsumption (represented as simplicial complexes and hypergraphs, respectively). In this model, at each iteration, a constant number …

Extending Import Detection Algorithms For Concept Import From Two To Three Biomedical Terminologies, Vipina K. Keloth, James Geller, Yan Chen, Julia Xu

Publications and Research

Background: While enrichment of terminologies can be achieved in different ways, filling gaps in the IS-A hierarchy backbone of a terminology appears especially promising. To avoid difficult manual inspection, we started a research program in 2014, investigating terminology densities, where the comparison of terminologies leads to the algorithmic discovery of potentially missing concepts in a target terminology. While candidate concepts have to be approved for import by an expert, the human effort is greatly reduced by algorithmic generation of candidates. In previous studies, a single source terminology was used with one target terminology.

Methods: In this paper, we are extending …

Unclonable Secret Keys, Marios Georgiou

Dissertations, Theses, and Capstone Projects

We propose a novel concept of securing cryptographic keys which we call “Unclonable Secret Keys,” where any cryptographic object is modified so that its secret key is an unclonable quantum bit-string whereas all other parameters such as messages, public keys, ciphertexts, signatures, etc., remain classical. We study this model in the authentication and encryption setting giving a plethora of definitions and positive results as well as several applications that are impossible in a purely classical setting.

In the authentication setting, we define the notion of one-shot signatures, a fundamental element in building unclonable keys, where the signing key not only …

Set Operators, Xiaojin Ye

Dissertations, Theses, and Capstone Projects

My research is centered on set operators. These are universally applicable regardless of the internal structure (numeric or non-numeric) of each individual observed datum. In our research, we have developed the theory of set operators to fill holes and gaps in observed data and eliminate paper shred garbage, thereby changing the observed symbolic data set into one whose pattern is closer to the pattern in the underlying population from which the observed data set was sampled with perturbations.

We describe different set operators including increasing operators, decreasing operators, ex- pansive operators, contractive operators, union preserving operators, intersection preserving op- erators, …

Novel Fast Algorithms For Low Rank Matrix Approximation, John T. Svadlenka

Dissertations, Theses, and Capstone Projects

Recent advances in matrix approximation have seen an emphasis on randomization techniques in which the goal was to create a sketch of an input matrix. This sketch, a random submatrix of an input matrix, having much fewer rows or columns, still preserves its relevant features. In one of such techniques random projections approximate the range of an input matrix. Dimension reduction transforms are obtained by means of multiplication of an input matrix by one or more matrices which can be orthogonal, random, and allowing fast multiplication by a vector. The Subsampled Randomized Hadamard Transform (SRHT) is the most popular among …

Philosophical Perspectives, Jochen Albrecht

Publications and Research

This entry follows in the footsteps of Anselin’s famous 1989 NCGIA working paper entitled “What is special about spatial?” (a report that is very timely again in an age when non-spatial data scientists are ignorant of the special characteristics of spatial data), where he outlines three unrelated but fundamental characteristics of spatial data. In a similar vein, I am going to discuss some philosophical perspectives that are internally unrelated to each other and could warrant individual entries in this Body of Knowledge. The first one is the notions of space and time and how they have evolved in …

Multimodal Data Integration For Real-Time Indoor Navigation Using A Smartphone, Yaohua Chang

Dissertations and Theses

We propose an integrated solution of indoor navigation using a smartphone, especially for assisting people with special needs, such as the blind and visually impaired (BVI) individuals. The system consists of three components: hybrid modeling, real-time navigation, and client-server architecture. In the hybrid modeling component, the hybrid model of a building is created region by region and is organized in a graph structure with nodes as destinations and landmarks, and edges as traversal paths between nodes. A Wi-Fi/cellular-data connectivity map, a beacon signal strength map, a 3D visual model (with destinations and landmarks annotated) are collected while a modeler walks …

V-Slam And Sensor Fusion For Ground Robots, Ejup Hoxha

Dissertations and Theses

In underground, underwater and indoor environments, a robot has to rely solely on its on-board sensors to sense and understand its surroundings. This is the main reason why SLAM gained the popularity it has today. In recent years, we have seen excellent improvement on accuracy of localization using cameras and combinations of different sensors, especially camera-IMU (VIO) fusion. Incorporating more sensors leads to improvement of accuracy,but also robustness of SLAM. However, while testing SLAM in our ground robots, we have seen a decrease in performance quality when using the same algorithms on flying vehicles.We have an additional sensor for ground …

An Optimized Encoding Algorithm For Systematic Polar Codes, Xiumin Wang, Zhihong Zhang, Jun Li, Yu Wang, Haiyan Cao, Zhengquan Li, Liang Shan

Publications and Research

Many different encoding algorithms for systematic polar codes (SPC) have been introduced since SPC was proposed in 2011. However, the number of the computing units of exclusive OR (XOR) has not been optimized yet. According to an iterative property of the generator matrix and particular lower triangular structure of the matrix, we propose an optimized encoding algorithm (OEA) of SPC that can reduce the number of XOR computing units compared with existing non-recursive algorithms. We also prove that this property of the generator matrix could extend to different code lengths and rates of the polar codes. Through the matrix segmentation …

List, Sample, And Count, Ali Assarpour

Dissertations, Theses, and Capstone Projects

Counting plays a fundamental role in many scientific fields including chemistry, physics, mathematics, and computer science. There are two approaches for counting, the first relies on analytical tools to drive closed form expression, while the second takes advantage of the combinatorial nature of the problem to construct an algorithm whose output is the number of structures. There are many algorithmic techniques for counting, they cover the explicit approach of counting by listing to the approximate approach of counting by sampling.

This thesis looks at counting three sets of objects. First, we consider a subclass of boolean functions that are monotone. …

Rationality And Efficient Verifiable Computation, Matteo Campanelli

Dissertations, Theses, and Capstone Projects

In this thesis, we study protocols for delegating computation in a model where one of the parties is rational. In our model, a delegator outsources the computation of a function f on input x to a worker, who receives a (possibly monetary) reward. Our goal is to design very efficient delegation schemes where a worker is economically incentivized to provide the correct result f(x). In this work we strive for not relying on cryptographic assumptions, in particular our results do not require the existence of one-way functions.

We provide several results within the framework of rational proofs introduced by Azar …

Multiple Sclerosis Identification Based On Fractional Fourier Entropy And A Modified Jaya Algorithm, Shui-Hua Wang, Hong Cheng, Preetha Phillips, Yu-Dong Zhang

Publications and Research

Aim: Currently, identifying multiple sclerosis (MS) by human experts may come across the problem of “normal-appearing white matter”, which causes a low sensitivity. Methods: In this study, we presented a computer vision based approached to identify MS in an automatic way. This proposed method first extracted the fractional Fourier entropy map from a specified brain image. Afterwards, it sent the features to a multilayer perceptron trained by a proposed improved parameter-free Jaya algorithm. We used cost-sensitivity learning to handle the imbalanced data problem. Results: The 10 × 10-fold cross validation showed our method yielded a sensitivity of 97.40 ± 0.60%, …

Cryptosystems Using Subgroup Distortion, Indira Chatterji, Delaram Kahrobaei, Ni Yen Lu

Publications and Research

In this paper we propose cryptosystems based on subgroup distortion in hyperbolic groups. We also include concrete examples of hyperbolic groups as possible platforms.

Relating Justification Logic Modality And Type Theory In Curry–Howard Fashion, Konstantinos Pouliasis

Dissertations, Theses, and Capstone Projects

This dissertation is a work in the intersection of Justification Logic and Curry--Howard Isomorphism. Justification logic is an umbrella of modal logics of knowledge with explicit evidence. Justification logics have been used to tackle traditional problems in proof theory (in relation to Godel's provability) and philosophy (Gettier examples, Russel's barn paradox). The Curry--Howard Isomorphism or proofs-as-programs is an understanding of logic that places logical studies in conjunction with type theory and -- in current developments -- category theory. The point being that understanding a system as a logic, a typed calculus and, a language of a class of categories constitutes …

Gradient Estimation For Attractor Networks, Thomas Flynn

Dissertations, Theses, and Capstone Projects

It has been hypothesized that neural network models with cyclic connectivity may be more powerful than their feed-forward counterparts. This thesis investigates this hypothesis in several ways. We study the gradient estimation and optimization procedures for several variants of these networks. We show how the convergence of the gradient estimation procedures are related to the properties of the networks. Then we consider how to tune the relative rates of gradient estimation and parameter adaptation to ensure successful optimization in these models. We also derive new gradient estimators for stochastic models. First, we port the forward sensitivity analysis method to the …

Ethics And Bias In Machine Learning: A Technical Study Of What Makes Us “Good”, Ashley Nicole Shadowen

Student Theses

The topic of machine ethics is growing in recognition and energy, but bias in machine learning algorithms outpaces it to date. Bias is a complicated term with good and bad connotations in the field of algorithmic prediction making. Especially in circumstances with legal and ethical consequences, we must study the results of these machines to ensure fairness. This paper attempts to address ethics at the algorithmic level of autonomous machines. There is no one solution to solving machine bias, it depends on the context of the given system and the most reasonable way to avoid biased decisions while maintaining the …

Approximation Algorithms For Effective Team Formation, George Rabanca

Dissertations, Theses, and Capstone Projects

This dissertation investigates the problem of creating multiple disjoint teams of maximum efficacy from a fixed set of workers. We identify three parameters which directly correlate to the team effectiveness — team expertise, team cohesion and team size — and propose efficient algorithms for optimizing each in various settings. We show that under standard assumptions the problems we explore are not optimally solvable in polynomial time, and thus we focus on developing efficient algorithms with guaranteed worst case approximation bounds. First, we investigate maximizing team expertise in a setting where each worker has different expertise for each job and each …