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Articles 1 - 30 of 143
Full-Text Articles in Theory and Algorithms
Parameter Estimation And Inference Of Spatial Autoregressive Model By Stochastic Gradient Descent, Gan Luan
Parameter Estimation And Inference Of Spatial Autoregressive Model By Stochastic Gradient Descent, Gan Luan
Dissertations
Stochastic gradient descent (SGD) is a popular iterative method for model parameter estimation in large-scale data and online learning settings since it goes through the data in only one pass. While SGD has been well studied for independent data, its application to spatially-correlated data largely remains unexplored. This dissertation develops SGD-based parameter estimation and statistical inference algorithms for the spatial autoregressive (SAR) model, a common model for spatial lattice data.
This research contains three parts. (I) The first part concerns SGD estimation and inference for the SAR mean regression model. A new SGD algorithm based on maximum likelihood estimator (MLE) …
Implementation Of Switching Algorithm For Svpwm Inverter In Induction Motor Drive System On Electric Vehicle Applications, Bayu Praharsena, Mohammad Jauhari, Era Purwanto, Mentari Putri Jati, Angga Wahyu Aditya, Aries Alfian Prasetyo
Implementation Of Switching Algorithm For Svpwm Inverter In Induction Motor Drive System On Electric Vehicle Applications, Bayu Praharsena, Mohammad Jauhari, Era Purwanto, Mentari Putri Jati, Angga Wahyu Aditya, Aries Alfian Prasetyo
Elinvo (Electronics, Informatics, and Vocational Education)
Electric cars are the way to reduce global warming and fuel shortages. Performance variable speed drive is needed for various drive electric vehicle applications. Unfortunately, high performance is still being investigated with a variety of drive systems. This paper presents a design, analysis, and implementation of the SV-PWM inverter motor drive system. The SV-PWM algorithm in design using Matlab, to analyze the system include signal response, THD-V, THD-I. All algorithms are embedded in STM32F4, as the main controller. The hardware uses a 3-phase motor control Steval power module. Response speed and output signal inverters are shown in chart form for …
Computer Program Simulation Of A Quantum Turing Machine With Circuit Model, Shixin Wu
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.
Human Behavior In Domestic Environments: Prediction And Applications, Sharare Zehtabian
Human Behavior In Domestic Environments: Prediction And Applications, Sharare Zehtabian
Electronic Theses and Dissertations, 2020-2023
A longstanding goal of human behavior science is to model and predict how humans interact with each other or with other systems. Such models are beneficial and have many applications, including designing and implementing assistive technologies, improving users' experiences and quality of life and making better decisions to create public policies. Behavior is highly complex due to uncertainties and a lack of scientific tools to measure it. Hence prediction of human behavior cannot be 100% accurate. However, prediction is also not hopeless because the biological needs, as well as cultural conventions (for instance, regarding meal times) set the general patterns …
Component Damage Source Identification For Critical Infrastructure Systems, Nathan Davis
Component Damage Source Identification For Critical Infrastructure Systems, Nathan Davis
Graduate Theses and Dissertations
Cyber-Physical Systems (CPS) are becoming increasingly prevalent for both Critical Infrastructure and the Industry 4.0 initiative. Bad values within components of the software portion of CPS, or the computer systems, have the potential to cause major damage if left unchecked, and so detection and locating of where these occur is vital. We further define features of these computer systems and create a use-based system topology. We then introduce a function to monitor system integrity and the presence of bad values as well as an algorithm to locate them. We then show an improved version, taking advantage of several system properties …
Towards Understanding Why Lookahead Generalizes Better Than Sgd And Beyond, Pan Zhou, Hanshu Yan, Xiaotong Yuan, Jiashi Feng, Shuicheng Yan
Towards Understanding Why Lookahead Generalizes Better Than Sgd And Beyond, Pan Zhou, Hanshu Yan, Xiaotong Yuan, Jiashi Feng, Shuicheng Yan
Research Collection School Of Computing and Information Systems
To train networks, lookahead algorithm [1] updates its fast weights k times via an inner-loop optimizer before updating its slow weights once by using the latest fast weights. Any optimizer, e.g. SGD, can serve as the inner-loop optimizer, and the derived lookahead generally enjoys remarkable test performance improvement over the vanilla optimizer. But theoretical understandings on the test performance improvement of lookahead remain absent yet. To solve this issue, we theoretically justify the advantages of lookahead in terms of the excess risk error which measures the test performance. Specifically, we prove that lookahead using SGD as its inner-loop optimizer can …
Beyond Smoothness : Incorporating Low-Rank Analysis Into Nonparametric Density Estimation, Rob Vandermeulen, Antoine Ledent
Beyond Smoothness : Incorporating Low-Rank Analysis Into Nonparametric Density Estimation, Rob Vandermeulen, Antoine Ledent
Research Collection School Of Computing and Information Systems
The construction and theoretical analysis of the most popular universally consistent nonparametric density estimators hinge on one functional property: smoothness. In this paper we investigate the theoretical implications of incorporating a multi-view latent variable model, a type of low-rank model, into nonparametric density estimation. To do this we perform extensive analysis on histogram-style estimators that integrate a multi-view model. Our analysis culminates in showing that there exists a universally consistent histogram-style estimator that converges to any multi-view model with a finite number of Lipschitz continuous components at a rate of ˜O(1/3√n) in L1 error. In contrast, the standard histogram estimator …
Context-Aware Graph Convolutional Network For Dynamic Origin-Destination Prediction, Juan Nathaniel, Baihua Zheng
Context-Aware Graph Convolutional Network For Dynamic Origin-Destination Prediction, Juan Nathaniel, Baihua Zheng
Research Collection School Of Computing and Information Systems
A robust Origin-Destination (OD) prediction is key to urban mobility. A good forecasting model can reduce operational risks and improve service availability, among many other upsides. Here, we examine the use of Graph Convolutional Net-work (GCN) and its hybrid Markov-Chain (GCN-MC) variant to perform a context-aware OD prediction based on a large-scale public transportation dataset in Singapore. Compared with the baseline Markov-Chain algorithm and GCN, the proposed hybrid GCN-MC model improves the prediction accuracy by 37% and 12% respectively. Lastly, the addition of temporal and historical contextual information further improves the performance of the proposed hybrid model by 4 –12%.
Fair And Diverse Group Formation Based On Multidimensional Features, Mohammed Saad A Alqahtani
Fair And Diverse Group Formation Based On Multidimensional Features, Mohammed Saad A Alqahtani
Graduate Theses and Dissertations
The goal of group formation is to build a team to accomplish a specific task. Algorithms are being developed to improve the team's effectiveness so formed and the efficiency of the group selection process. However, there is concern that team formation algorithms could be biased against minorities due to the algorithms themselves or the data on which they are trained. Hence, it is essential to build fair team formation systems that incorporate demographic information into the process of building the group. Although there has been extensive work on modeling individuals’ expertise for expert recommendation and/or team formation, there has been …
Local Feature Selection For Multiple Instance Learning With Applications., Aliasghar Shahrjooihaghighi
Local Feature Selection For Multiple Instance Learning With Applications., Aliasghar Shahrjooihaghighi
Electronic Theses and Dissertations
Feature selection is a data processing approach that has been successfully and effectively used in developing machine learning algorithms for various applications. It has been proven to effectively reduce the dimensionality of the data and increase the accuracy and interpretability of machine learning algorithms. Conventional feature selection algorithms assume that there is an optimal global subset of features for the whole sample space. Thus, only one global subset of relevant features is learned. An alternative approach is based on the concept of Local Feature Selection (LFS), where each training sample can have its own subset of relevant features. Multiple Instance …
Russian Logics And The Culture Of Impossible: Part 1. Recovering Intelligentsia Logics, Ksenia Tatarchenko, Anya Yermakova, Liesbeth De Mol
Russian Logics And The Culture Of Impossible: Part 1. Recovering Intelligentsia Logics, Ksenia Tatarchenko, Anya Yermakova, Liesbeth De Mol
Research Collection College of Integrative Studies
This article reinterprets algorithmic rationality by looking at the interaction between mathematical logic, mechanized reasoning, and, later, computing in the Russian Imperial and Soviet contexts to offer a history of the algorithm as a mathematical object bridging the inner and outer worlds, a humanistic vision that we, following logician Vladimir Uspensky, call the “culture of the impossible.” We unfold the deep roots of this vision as embodied in scientific intelligentsia. In Part I, we examine continuities between the turn-of-the-twentieth-century discussions of poznaniye—an epistemic orientation towards the process of knowledge acquisition—and the postwar rise of the Soviet school of mathematical logic. …
Rmix: Learning Risk-Sensitive Policies For Cooperative Reinforcement Learning Agents, Wei Qiu, Xinrun Wang, Runsheng Yu, Xu He, Rundong Wang, Bo An, Svetlana Obraztsova, Zinovi Rabinovich
Rmix: Learning Risk-Sensitive Policies For Cooperative Reinforcement Learning Agents, Wei Qiu, Xinrun Wang, Runsheng Yu, Xu He, Rundong Wang, Bo An, Svetlana Obraztsova, Zinovi Rabinovich
Research Collection School Of Computing and Information Systems
Current value-based multi-agent reinforcement learning methods optimize individual Q values to guide individuals' behaviours via centralized training with decentralized execution (CTDE). However, such expected, i.e., risk-neutral, Q value is not sufficient even with CTDE due to the randomness of rewards and the uncertainty in environments, which causes the failure of these methods to train coordinating agents in complex environments. To address these issues, we propose RMIX, a novel cooperative MARL method with the Conditional Value at Risk (CVaR) measure over the learned distributions of individuals' Q values. Specifically, we first learn the return distributions of individuals to analytically calculate CVaR …
Ggnb: Graph-Based Gaussian Naive Bayes Intrusion Detection System For Can Bus, Riadul Islam, Maloy K. Devnath, Manar D. Samad, Syed Md Jaffrey Al Kadry
Ggnb: Graph-Based Gaussian Naive Bayes Intrusion Detection System For Can Bus, Riadul Islam, Maloy K. Devnath, Manar D. Samad, Syed Md Jaffrey Al Kadry
Computer Science Faculty Research
The national highway traffic safety administration (NHTSA) identified cybersecurity of the automobile systems are more critical than the security of other information systems. Researchers already demonstrated remote attacks on critical vehicular electronic control units (ECUs) using controller area network (CAN). Besides, existing intrusion detection systems (IDSs) often propose to tackle a specific type of attack, which may leave a system vulnerable to numerous other types of attacks. A generalizable IDS that can identify a wide range of attacks within the shortest possible time has more practical value than attack-specific IDSs, which is not a trivial task to accomplish. In this …
Three-Dimensional Graph Matching To Identify Secondary Structure Correspondence Of Medium-Resolution Cryo-Em Density Maps, Bahareh Behkamal, Mahmoud Naghibzadeh, Mohammad Reza Saberi, Zeinab Amiri Tehranizadeh, Andrea Pagnani, Kamal Al Nasr
Three-Dimensional Graph Matching To Identify Secondary Structure Correspondence Of Medium-Resolution Cryo-Em Density Maps, Bahareh Behkamal, Mahmoud Naghibzadeh, Mohammad Reza Saberi, Zeinab Amiri Tehranizadeh, Andrea Pagnani, Kamal Al Nasr
Computer Science Faculty Research
Cryo-electron microscopy (cryo-EM) is a structural technique that has played a significant role in protein structure determination in recent years. Compared to the traditional methods of X-ray crystallography and NMR spectroscopy, cryo-EM is capable of producing images of much larger protein complexes. However, cryo-EM reconstructions are limited to medium-resolution (~4–10 Å) for some cases. At this resolution range, a cryo-EM density map can hardly be used to directly determine the structure of proteins at atomic level resolutions, or even at their amino acid residue backbones. At such a resolution, only the position and orientation of secondary structure elements (SSEs) such …
Comparison Of Multiple Imputation Algorithms And Verification Using Whole-Genome Sequencing In The Cmuh Genetic Biobank, Ting-Yuan Liu, Chih-Fan Lin, Hsing-Tsung Wu, Ya-Lun Wu, Yu-Chia Chen, Chi-Chou Liao, Yu-Pao Chou, Dysan Chao, Hsing-Fang Lu, Ya-Sian Chang, Jan-Gowth Chang, Kai-Cheng Hsu, Fuu‑Jen Tsai
Comparison Of Multiple Imputation Algorithms And Verification Using Whole-Genome Sequencing In The Cmuh Genetic Biobank, Ting-Yuan Liu, Chih-Fan Lin, Hsing-Tsung Wu, Ya-Lun Wu, Yu-Chia Chen, Chi-Chou Liao, Yu-Pao Chou, Dysan Chao, Hsing-Fang Lu, Ya-Sian Chang, Jan-Gowth Chang, Kai-Cheng Hsu, Fuu‑Jen Tsai
BioMedicine
A genome-wide association study (GWAS) can be conducted to systematically analyze the contributions of genetic factors to a wide variety of complex diseases. Nevertheless, existing GWASs have provided highly ethnic specific data. Accordingly, to provide data specific to Taiwan, we established a large-scale genetic database in a single medical institution at the China Medical University Hospital. With current technological limitations, microarray analysis can detect only a limited number of single-nucleotide polymorphisms (SNPs) with a minor allele frequency of >1%. Nevertheless, imputation represents a useful alternative means of expanding data. In this study, we compared four imputation algorithms in terms of …
Information Extraction And Classification On Journal Papers, Lei Yu
Information Extraction And Classification On Journal Papers, Lei Yu
School of Computing: Dissertations, Theses, and Student Research
The importance of journals for diffusing the results of scientific research has increased considerably. In the digital era, Portable Document Format (PDF) became the established format of electronic journal articles. This structured form, combined with a regular and wide dissemination, spread scientific advancements easily and quickly. However, the rapidly increasing numbers of published scientific articles requires more time and effort on systematic literature reviews, searches and screens. The comprehension and extraction of useful information from the digital documents is also a challenging task, due to the complex structure of PDF.
To help a soil science team from the United States …
Analytical Models For Traffic Congestion And Accident Analysis, Hongrui Liu, Rahul Ramachandra Shetty
Analytical Models For Traffic Congestion And Accident Analysis, Hongrui Liu, Rahul Ramachandra Shetty
Mineta Transportation Institute
In the US, over 38,000 people die in road crashes each year, and 2.35 million are injured or disabled, according to the statistics report from the Association for Safe International Road Travel (ASIRT) in 2020. In addition, traffic congestion keeping Americans stuck on the road wastes millions of hours and billions of dollars each year. Using statistical techniques and machine learning algorithms, this research developed accurate predictive models for traffic congestion and road accidents to increase understanding of the complex causes of these challenging issues. The research used US Accidents data consisting of 49 variables describing 4.2 million accident records …
Transfer-Learned Pruned Deep Convolutional Neural Networks For Efficient Plant Classification In Resource-Constrained Environments, Martinson Ofori
Transfer-Learned Pruned Deep Convolutional Neural Networks For Efficient Plant Classification In Resource-Constrained Environments, Martinson Ofori
Masters Theses & Doctoral Dissertations
Traditional means of on-farm weed control mostly rely on manual labor. This process is time-consuming, costly, and contributes to major yield losses. Further, the conventional application of chemical weed control can be economically and environmentally inefficient. Site-specific weed management (SSWM) counteracts this by reducing the amount of chemical application with localized spraying of weed species. To solve this using computer vision, precision agriculture researchers have used remote sensing weed maps, but this has been largely ineffective for early season weed control due to problems such as solar reflectance and cloud cover in satellite imagery. With the current advances in artificial …
On A Multistage Discrete Stochastic Optimization Problem With Stochastic Constraints And Nested Sampling, Thuy Anh Ta, Tien Mai, Fabian Bastin, Pierre L'Ecuyer
On A Multistage Discrete Stochastic Optimization Problem With Stochastic Constraints And Nested Sampling, Thuy Anh Ta, Tien Mai, Fabian Bastin, Pierre L'Ecuyer
Research Collection School Of Computing and Information Systems
We consider a multistage stochastic discrete program in which constraints on any stage might involve expectations that cannot be computed easily and are approximated by simulation. We study a sample average approximation (SAA) approach that uses nested sampling, in which at each stage, a number of scenarios are examined and a number of simulation replications are performed for each scenario to estimate the next-stage constraints. This approach provides an approximate solution to the multistage problem. To establish the consistency of the SAA approach, we first consider a two-stage problem and show that in the second-stage problem, given a scenario, the …
Span-Level Emotion Cause Analysis With Neural Sequence Tagging, Xiangju Li, Wei Gao, Shi Feng, Daling Wang, Shafiq Joty
Span-Level Emotion Cause Analysis With Neural Sequence Tagging, Xiangju Li, Wei Gao, Shi Feng, Daling Wang, Shafiq Joty
Research Collection School Of Computing and Information Systems
This paper addresses the task of span-level emotion cause analysis (SECA). It is a finer-grained emotion cause analysis (ECA) task, which aims to identify the specific emotion cause span(s) behind certain emotions in text. In this paper, we formalize SECA as a sequence tagging task for which several variants of neural network-based sequence tagging models to extract specific emotion cause span(s) in the given context. These models combine different types of encoding and decoding approaches. Furthermore, to make our models more "emotionally sensitive'', we utilize the multi-head attention mechanism to enhance the representation of context. Experimental evaluations conducted on two …
Expediting The Accuracy-Improving Process Of Svms For Class Imbalance Learning, Bin Cao, Yuqi Liu, Chenyu Hou, Jing Fan, Baihua Zheng, Jianwei Jin
Expediting The Accuracy-Improving Process Of Svms For Class Imbalance Learning, Bin Cao, Yuqi Liu, Chenyu Hou, Jing Fan, Baihua Zheng, Jianwei Jin
Research Collection School Of Computing and Information Systems
To improve the classification performance of support vector machines (SVMs) on imbalanced datasets, cost-sensitive learning methods have been proposed, e.g., DEC (Different Error Costs) and FSVM-CIL (Fuzzy SVM for Class Imbalance Learning). They relocate the hyperplane by adjusting the costs associated with misclassifying samples. However, the error costs are determined either empirically or by performing an exhaustive search in the parameter space. Both strategies can not guarantee effectiveness and efficiency simultaneously. In this paper, we propose ATEC, a solution that can efficiently find a preferable hyperplane by automatically tuning the error cost for between-class samples. ATEC distinguishes itself from all …
Adaptive Posterior Knowledge Selection For Improving Knowledge-Grounded Dialogue Generation, Weichao Wang, Wei Gao, Shi Feng, Ling Chen, Daling Wang
Adaptive Posterior Knowledge Selection For Improving Knowledge-Grounded Dialogue Generation, Weichao Wang, Wei Gao, Shi Feng, Ling Chen, Daling Wang
Research Collection School Of Computing and Information Systems
In open-domain dialogue systems, knowledge information such as unstructured persona profiles, text descriptions and structured knowledge graph can help incorporate abundant background facts for delivering more engaging and informative responses. Existing studies attempted to model a general posterior distribution over candidate knowledge by considering the entire response utterance as a whole at the beginning of decoding process for knowledge selection. However, a single smooth distribution could fail to model the variability of knowledge selection patterns over different decoding steps, and make the knowledge expression less consistent. To remedy this issue, we propose an adaptive posterior knowledge selection framework, which sequentially …
Span-Level Emotion Cause Analysis By Bert-Based Graph Attention Network, Xiangju Li, Wei Gao, Shi Feng, Daling Wang, Shafiq Joty
Span-Level Emotion Cause Analysis By Bert-Based Graph Attention Network, Xiangju Li, Wei Gao, Shi Feng, Daling Wang, Shafiq Joty
Research Collection School Of Computing and Information Systems
We study the task of span-level emotion cause analysis (SECA), which is focused on identifying the specific emotion cause span(s) triggering a certain emotion in the text. Compared to the popular clause-level emotion cause analysis (CECA), it is a finer-grained emotion cause analysis (ECA) task. In this paper, we design a BERT-based graph attention network for emotion cause span(s) identification. The proposed model takes advantage of the structure of BERT to capture the relationship information between emotion and text, and utilizes graph attention network to model the structure information of the text. Our SECA method can be easily used for …
Fuzzy Multi Criteria Decision Making Approach For Technology Selection For Emissions Reduction From Seaborne Transportation Under Uncertainty And Vagueness, Rachid Mouaici
World Maritime University Dissertations
No abstract provided.
Multi-Valued Solutions For The Equation Of Motion, Darcy-Jordan Model, As A Cauchy Problem: A Shocking Event, Chandler Shimp
Multi-Valued Solutions For The Equation Of Motion, Darcy-Jordan Model, As A Cauchy Problem: A Shocking Event, Chandler Shimp
Master's Theses
Shocks are physical phenomenon that occur quite often around us. In this thesis we examine the occurrence of shocks in finite amplitude acoustic waves from a numerical perspective. These waves, or jump discontinuities, yield ill-behaved solutions when solved numerically. This study takes on the challenge of finding both single- and multi-valued solutions.
The previously unsolved problem in this study is the representation of the Equation of Motion (EoM) in the form of the Darcy-Jordan model (DJM) and expressed as a dimensionless IVP Cauchy problem. Prior attempts to solve have resulted only in implicit solutions or explicit solutions with certain initial …
Introduction To Discrete Mathematics: An Oer For Ma-471, Mathieu Sassolas
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 …
Tradao: A Visual Analytics System For Trading Algorithm Optimization, Ka Wing Tsang, Haotian Li, Fuk Ming Lam, Yifan Mu, Yong Wang, Huamin Qu
Tradao: A Visual Analytics System For Trading Algorithm Optimization, Ka Wing Tsang, Haotian Li, Fuk Ming Lam, Yifan Mu, Yong Wang, Huamin Qu
Research Collection School Of Computing and Information Systems
With the wide applications of algorithmic trading, it has become critical for traders to build a winning trading algorithm to beat the market. However, due to the lack of efficient tools, traders mainly rely on their memory to manually compare the algorithm instances of a trading algorithm and further select the best trading algorithm instance for the real trading deployment. We work closely with industry practitioners to discover and consolidate user requirements and develop an interactive visual analytics system for trading algorithm optimization. Structured expert interviews are conducted to evaluateTradAOand a representative case study is documented for illustrating the system …
Disentangling Hate In Online Memes, Ka Wei, Roy Lee, Rui Cao, Ziqing Fan, Jing Jiang, Wen Haw Chong
Disentangling Hate In Online Memes, Ka Wei, Roy Lee, Rui Cao, Ziqing Fan, Jing Jiang, Wen Haw Chong
Research Collection School Of Computing and Information Systems
Hateful and offensive content detection has been extensively explored in a single modality such as text. However, such toxic information could also be communicated via multimodal content such as online memes. Therefore, detecting multimodal hateful content has recently garnered much attention in academic and industry research communities. This paper aims to contribute to this emerging research topic by proposing DisMultiHate, which is a novel framework that performed the classification of multimodal hateful content. Specifically, DisMultiHate is designed to disentangle target entities in multimodal memes to improve the hateful content classification and explainability. We conduct extensive experiments on two publicly available …
Quantum-Inspired Algorithm For Vehicle Sharing Problem, Whei Yeap Suen, Chun Yat Lee, Hoong Chuin Lau
Quantum-Inspired Algorithm For Vehicle Sharing Problem, Whei Yeap Suen, Chun Yat Lee, Hoong Chuin Lau
Research Collection School Of Computing and Information Systems
Recent hardware developments in quantum technologies have inspired a myriad of special-purpose hardware devices tasked to solve optimization problems. In this paper, we explore the application of Fujitsu’s quantum-inspired CMOS-based Digital Annealer (DA) in solving constrained routing problems arising in transportation and logistics. More precisely in this paper, we study the vehicle sharing problem and show that the DA as a QUBO solver can potentially fill the gap between two common methods: exact solvers like Cplex and heuristics. We benchmark the scalability and quality of solutions obtained by DA with Cplex and with a greedy heuristic. Our results show that …
Novel Theorems And Algorithms Relating To The Collatz Conjecture, Michael R. Schwob, Peter Shiue, Rama Venkat
Novel Theorems And Algorithms Relating To The Collatz Conjecture, Michael R. Schwob, Peter Shiue, Rama Venkat
Mathematical Sciences Faculty Research
Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and algorithms that explore relationships and properties between the natural numbers, their peak values, and the conjecture. These contributions primarily analyze the number of Collatz iterations it takes for a given integer to reach 1 or a number less than itself, or the relationship between a starting number and its peak value.