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Articles 1 - 11 of 11
Full-Text Articles in Mathematics
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.
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.
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.
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 …