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Articles 1 - 28 of 28
Full-Text Articles in Mathematics
The Future Of Brain Tumor Diagnosis: Cnn And Transfer Learning Innovations, Shengyuan Wang
The Future Of Brain Tumor Diagnosis: Cnn And Transfer Learning Innovations, Shengyuan Wang
Mathematics, Statistics, and Computer Science Honors Projects
For the purpose of improving patient survival rates and facilitating efficient treatment planning, brain tumors need to be identified early and accurately classified. This research investigates the application of transfer learning and Convolutional Neural Networks (CNN) to create an automated, high-precision brain tumor segmentation and classification framework. Utilizing large-scale datasets, which comprise MRI images from open-accessible archives, the model exhibits the effectiveness of the method in various kinds of tumors and imaging scenarios. Our approach utilizes transfer learning techniques along with CNN architectures strengths to tackle the intrinsic difficulties of brain tumor diagnosis, namely significant tumor appearance variability and difficult …
An Investigation Into The Causes Of Home Field Advantage In Professional Soccer, Paige E. Tomer
An Investigation Into The Causes Of Home Field Advantage In Professional Soccer, Paige E. Tomer
Mathematics, Statistics, and Computer Science Honors Projects
Home-field advantage is the sporting phenomenon in which the home team outperforms the away team. Despite its widespread occurrence across sports, the underlying reasons for home-field advantage remain uncertain. In this paper, we employ a range of statistical methods to explore the causal relationships of potential determinants of home-field advantage. We measure home-field advantage using match outcomes and differential metrics (e.g., differences in yellow cards received). In an attempt to narrow the research disparity between men’s and women’s sports, we utilize data from the National Women’s Soccer League (NWSL) and the English Premier League (EPL) to investigate potential causes of …
Persistent Relative Homology For Topological Data Analysis, Christian J. Lentz
Persistent Relative Homology For Topological Data Analysis, Christian J. Lentz
Mathematics, Statistics, and Computer Science Honors Projects
A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via the language of persistent homology, which encodes features of interest as holes within a filtration of the data. The recently presented U-Match Decomposition places the standard persistence computation in a flexible form, allowing for straight-forward extensions of the algorithm to variations of persistent homology. We describe U-Match Decomposition in the context of persistent homology, and extend it to an algorithm for persistent relative homology, providing proofs for the correctness and stability of the presented algorithm.
First Order Approximation On The Basilica Julia Set, Xintan Xia, Taryn Flock
First Order Approximation On The Basilica Julia Set, Xintan Xia, Taryn Flock
Mathematics, Statistics, and Computer Science Honors Projects
We consider the basilica Julia set of the quadratic polynomial P (z) = z^2 - 1, with its successive graph approximations defined in terms of the external ray parametrization of the set. Following the model of Kigami and later Strichartz, we exploit these graph approximations to define derivatives of functions defined on the fractal, an endeavor complicated by asymmetric neighborhood behaviors at approximated vertex points across levels, and by the topology of these vertices. We hence differentiate even and odd levels of approximations of the Julia set and construct, accordingly, normal derivatives corresponding to each level category at the vertices, …
Staircase Packings Of Integer Partitions, Melody Arteaga
Staircase Packings Of Integer Partitions, Melody Arteaga
Mathematics, Statistics, and Computer Science Honors Projects
An integer partition is a weakly decreasing sequence of positive integers. We study the family of packings of integer partitions in the triangular array of size n, where successive partitions in the packings are separated by at least one zero. We prove that these are enumerated by the Bell-Like number sequence (OEIS A091768), and investigate its many recursive properties. We also explore their poset (partially ordered set) structure. Finally, we characterize various subfamilies of these staircase packings, including one restriction that connects back to the original patterns of the whole family.
A Brascamp-Lieb–Rary Of Examples, Anina Peersen
A Brascamp-Lieb–Rary Of Examples, Anina Peersen
Mathematics, Statistics, and Computer Science Honors Projects
This paper focuses on the Brascamp-Lieb inequality and its applications in analysis, fractal geometry, computer science, and more. It provides a beginner-level introduction to the Brascamp-Lieb inequality alongside re- lated inequalities in analysis and explores specific cases of extremizable, simple, and equivalent Brascamp-Lieb data. Connections to computer sci- ence and geometric measure theory are introduced and explained. Finally, the Brascamp-Lieb constant is calculated for a chosen family of linear maps.
Staircase Arrangements Of Pillars With Distinct Heights, Andrea L. Simmons
Staircase Arrangements Of Pillars With Distinct Heights, Andrea L. Simmons
Mathematics, Statistics, and Computer Science Honors Projects
We study the family An of sequences (a1, a2, ..., an) where 0 ≤ ak ≤ k and nonzero entries are distinct. We show that these sequences are in bijection with the set partitions of [n + 1]. These sequences have a natural poset structure, and we analyze the maximal chains within this poset. Finally, we explore various subfamilies of An, including sequences whose largest entry is k and sequences missing the value k.
Mixing Measures For Trees Of Fixed Diameter, Ari Holcombe Pomerance
Mixing Measures For Trees Of Fixed Diameter, Ari Holcombe Pomerance
Mathematics, Statistics, and Computer Science Honors Projects
A mixing measure is the expected length of a random walk in a graph given a set of starting and stopping conditions. We determine the tree structures of order n with diameter d that minimize and maximize for a few mixing measures. We show that the maximizing tree is usually a broom graph or a double broom graph and that the minimizing tree is usually a seesaw graph or a double seesaw graph.
Sharp Inequalities Of The X-Ray Transform And The Competing Symmetries Argument, Arthur D. Dressenwall
Sharp Inequalities Of The X-Ray Transform And The Competing Symmetries Argument, Arthur D. Dressenwall
Mathematics, Statistics, and Computer Science Honors Projects
We examine the $k=1$ case of a conjecture by Baernstein and Loss pertaining to the operator norm of the $k$-plane transform from $L^p(\R^d)$ space to $L^q(\M)$ space. Previous work on this problem by Carlen and Loss, as well as by Drouot, has used an iterative technique known as the ``competing symmetries argument’’ to prove this conjecture in the $q=2$ and $q=d+1$ cases. We summarize the conjecture and this proof technique, then perform work that strongly suggest that no sufficiently ``nice” transformation exists that can be used to apply the competing symmetries argument to other cases of the conjecture.
Don’T Beep At Me: Using Google Maps Apis To Reduce Driving Anxiety, Daniel Chechelnitsky
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.
A Comparison Of Stacking Methods To Estimate Survival Using Residual Lifetime Data From Prevalent Cohort Studies, Zhaoheng Li
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.
The Eagle Programming Language, Samuel G. Horlbeck Olsen
The Eagle Programming Language, Samuel G. Horlbeck Olsen
Mathematics, Statistics, and Computer Science Honors Projects
C remains the dominant systems programming language despite many new languages attempting to take its place. Modern languages generally value abstraction and safety over speed and direct control of hardware. They are therefore not well suited to the low-level tasks for which C was designed. This paper introduces a novel programming language, Eagle, which represents a fast, elegant alternative to C. It allows low-level programming while providing optional modern features like reference counting, closures, generators, and classes. In addition to specifying this language and reviewing the current alternatives, the paper describes the implementation of a working Eagle compiler. The language …
Building Voters: Exploring Interdependent Preferences In Binary Contexts, Ian Calaway
Building Voters: Exploring Interdependent Preferences In Binary Contexts, Ian Calaway
Mathematics, Statistics, and Computer Science Honors Projects
In this thesis we develop a new method for constructing binary preference orders for given interdependent structures, called characters. We introduce the preference space, which is a vector space of preference vectors. The preference vectors correspond to binary preference orders. We show that the hyperoctahedral group, Z2 o Sn, describes the symmetries of binary preferences orders and then define an action of Z2 o Sn on our preference vectors. We find a natural basis for a preference space. These basis vectors are indexed by subsets of proposals. We show that when completely separable binary preference vectors are decomposed using this …
Bases For Mckay Centralizer Algebras, Lucas Gagnon
Bases For Mckay Centralizer Algebras, Lucas Gagnon
Mathematics, Statistics, and Computer Science Honors Projects
The finite subgroups of the special unitary group SU2 have been classified to be isomorphic to one of the following groups: cyclic, binary dihedral, binary tetrahedral, binary octahedral, and binary icosahedral, of order n, 4n, 24, 48, and 120, respectively. Associated to each group is a representation graph, which by the McKay correspondence is a Dynkin diagram of type Aˆ n−1, Dˆ n+2, Eˆ 6, Eˆ 7, or Eˆ 8. The centralizer algebra Zk(G) = EndG(V ⊗k ) is the algebra of transformations that commute with G acting on the k-fold tensor product of the defining representation V = C …
Blossom: A Language Built To Grow, Jeffrey Lyman
Blossom: A Language Built To Grow, Jeffrey Lyman
Mathematics, Statistics, and Computer Science Honors Projects
No abstract provided.
Surface Reconstruction Using Differential Invariant Signatures, Sophors Khut
Surface Reconstruction Using Differential Invariant Signatures, Sophors Khut
Mathematics, Statistics, and Computer Science Honors Projects
This thesis addresses the problem of reassembling a broken surface. Three di- mensional curve matching is used to determine shared edges of broken pieces. In practice, these pieces may have different orientation and position in space, so edges cannot be directly compared. Instead, a differential invariant signature is used to make the comparison. A similarity score between edge signatures determines if two pieces share an edge. The Procrustes algorithm is applied to find the translations and rotations that best fit shared edges. The method is implemented in Matlab, and tested on a broken spherical surface.
Hurdle Models And Age Effects In The Major League Baseball Draft, Justin Sims
Hurdle Models And Age Effects In The Major League Baseball Draft, Justin Sims
Mathematics, Statistics, and Computer Science Honors Projects
Major League Baseball (MLB) franchises expend an abundance of resources on scouting in preparation for the June Amateur Draft. In addition to the classic "tools" assessed, another factor considered is age: younger players may get selected over older players of equal ability because of anticipated development, whereas college players may get selected over high school players due to a shortened latency before reaching the majors. Additionally, Little League rules in effect until 2006 operated on an August 1-July 31 year, meaning that, in their youth, players born on August 1 were the eldest relative to their cohort. We examine the …
Parallel Design Patterns And Program Performance, Yu Zhao
Parallel Design Patterns And Program Performance, Yu Zhao
Mathematics, Statistics, and Computer Science Honors Projects
With the rapid advancement of parallel and distributed computing (PDC), three types of hardware and their corresponding software (hardware-software pairs) are becoming more and more popular: Distributed Memory Systems with the Message Passing Interface (MPI) library, Shared Memory Systems with the OpenMP library and Co-processor Systems with a general purpose parallel computing library. Alongside the development of both hardware and software aspects of PDC, the process of designing parallel programs has also improved significantly over the years. A consequence of this is that researchers have been able to describe many parallel design patterns, which are recurring solutions to well-known problems …
How Ideas Grow: Critical Mass In The Linear Threshold Model, Hossein Alidaee
How Ideas Grow: Critical Mass In The Linear Threshold Model, Hossein Alidaee
Mathematics, Statistics, and Computer Science Honors Projects
We study how ideas spread through a social network using the Linear Threshold Model. Each node i on the complete graph Kn is given a threshold Ɵi chosen uniformly at random from (0, 1]. This threshold indicates the fraction of the social network that must be active (or believe the idea) prior to node i becoming active. We start with an activated group of early adopters, called the seed set. Considering various scenarios, we use the probabilistic method to find lower bounds on size of a seed set which guarantees that all nodes become active with high …
The Rook-Brauer Algebra, Elise G. Delmas
The Rook-Brauer Algebra, Elise G. Delmas
Mathematics, Statistics, and Computer Science Honors Projects
We introduce an associative algebra RBk(x) that has a basis of rook-Brauer diagrams. These diagrams correspond to partial matchings on 2k vertices. The rook-Brauer algebra contains the group algebra of the symmetric group, the Brauer algebra, and the rook monoid algebra as subalgebras. We show that the basis of RBk(x) is generated by special diagrams si, ti (1 <= i < k) and pj (1 <= j <= k), where the si are the simple transpositions that generated the symmetric group Sk, the ti are the "contraction maps" which generate the …
Elliptic Curves Of High Rank, Cecylia Bocovich
Elliptic Curves Of High Rank, Cecylia Bocovich
Mathematics, Statistics, and Computer Science Honors Projects
The study of elliptic curves grows out of the study of elliptic functions which dates back to work done by mathematicians such as Weierstrass, Abel, and Jacobi. Elliptic curves continue to play a prominent role in mathematics today. An elliptic curve E is defined by the equation, y2 = x3 + ax + b, where a and b are coefficients that satisfy the property 4a3 + 27b2 = 0. The rational solutions of this curve form a group. This group, denoted E(Q), is known as the Mordell-Weil group and was proved by Mordell to be isomorphic …
Characterizing Conflict In Wikipedia, Nathaniel Miller
Characterizing Conflict In Wikipedia, Nathaniel Miller
Mathematics, Statistics, and Computer Science Honors Projects
Wikipedia serves as the Internet's most widely viewed reference. In order to ensure its success, editors who create and maintain articles must resolve conflicts over appropriate article content. Previous research has measured Wikipedia conflict at two levels: single articles and categories of pages. I observe conflicts within small groups of articles, identifying their frequency, size, and intensity. Additionally, I identify individual conflicts spanning multiple articles and effects of conflict upon users' editing habits. I analyze cross-article conflict in three stages. First, I cluster a group of 1.4 million Wikipedia articles. Next, I find individual user conflicts within each article cluster …
The Best Mixing Time For Trees, Jeanmarie Youngblood
The Best Mixing Time For Trees, Jeanmarie Youngblood
Mathematics, Statistics, and Computer Science Honors Projects
A graph G consists of a set of vertices connected in pairs by edges. Two vertices connected by an edge are called neighbors. A random walk on G is a sequence of vertices, where the next vertex is chosen randomly from the neighbors of the current vertex. Under mild assumptions, the distribution of a walk's current location converges to the stationary distribution. In this distribution, the probability of being at a given vertex is proportional to the size of its neighbor set. The expected time to convergence is called a mixing measure of G. There are a variety …
Comparison Study Between Mapreduce (Mr) And Parallel Data Management Systems (Dbms) In Large Scale Data Analysis, Miriam Lawrence Mchome
Comparison Study Between Mapreduce (Mr) And Parallel Data Management Systems (Dbms) In Large Scale Data Analysis, Miriam Lawrence Mchome
Mathematics, Statistics, and Computer Science Honors Projects
As the quantity of structured and unstructured data increases, data processing
experts have turned to systems that analyze data using many computers in parallel.
This study looks at two systems designed for these needs: MapReduce and parallel
databases. In the MapReduce programming model, users express their problem in
terms of a map function and a reduce function. Parallel databases organize data as a
system of tables representing entities and relationships between them. Previous
comparison studies have focused on performance, concluding that these two
systems are complimentary. Parallel databases scored high on performance and
MapReduce scored high on flexibility in handling …
Extremal Random Walks On Trees, Meng Wang
Extremal Random Walks On Trees, Meng Wang
Mathematics, Statistics, and Computer Science Honors Projects
We study random walks on trees, where we iteratively move from one vertex to a randomly chosen adjacent vertex. We study two quantities arising in random walks: the hitting time and the mixing time. The hitting time is the expected number of steps to walk between a chosen pair of vertices. The mixing time is the expected number of steps before the distribution of the current state is proportional to its degree. For a fixed tree size, we prove that the star is the unique minimizing structure and the path is the unique maximizing structure for both quantities.
Shadowing Chaos Via Optimization, Henrik Haakonsen
Shadowing Chaos Via Optimization, Henrik Haakonsen
Mathematics, Statistics, and Computer Science Honors Projects
A prominent idea in the theory of chaos is that of shadowing, which says that, in many cases, the numerical results one sees after accuracy is lost are not total nonsense, but are in fact very close to the exact trajectory for an initial value that is near the one used. Using high-precision computation, I have researched the use of optimization as a way of finding exact shadows for several chaotic systems, such as the quadratic map r x (1 - x) and a billiard problem from the SIAM 100-Digit Challenge.
Implementing Bluetooth Support In Wifi-Based Mobile Ad-Hoc Networks, Christopher Dragga
Implementing Bluetooth Support In Wifi-Based Mobile Ad-Hoc Networks, Christopher Dragga
Mathematics, Statistics, and Computer Science Honors Projects
Mobile ad-hoc networks (MANETs) provide a useful means of connecting computers in unusual situations, such as search and rescue. However, they ignore those small, highly mobile devices that only support Bluetooth, a low-range, low-bandwidth Wifi alternative that consumes significantly less power. Allowing these devices to connect to Wifi MANETs could permit a variety of applications, from text messaging to VOIP to parallel processing. Bluetooth features several unusual characteristics that could make this difficult, though. In this project, I implemented this kind of integration and analyzed its success through physical testing and models both analytical and simulated.
Representations Of The Temperley-Lieb Algebra, Anne Moore
Representations Of The Temperley-Lieb Algebra, Anne Moore
Mathematics, Statistics, and Computer Science Honors Projects
This paper gives an introduction to Temperley-Lieb algebra that is easily accessible to undergraduates, presenting TL diagrams, the method for multiplying the diagrams, and the properties of the multiplication that it is necessary to preserve in a representation. The paper also gives a method for finding representations of the TL monoids (sets of diagrams classified by number of vertices) using Young tableaux, and shows that these representations are all of the irreducible representations. While ideas of Hecke algebra imply the fact that this method produces representations, this paper provides a direct proof, strictly within the field of representation theory. It …