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Open Access

Author:: Ginsburg, Victor
Title:: Morse–Bott Theory and Diameters of Immersed Submanifolds of Euclidean Space
Area of Honors:: Mathematics
Keywords:: Morse theory
Morse–Bott theory
diameters
double normals
File:: Download Morse_Bott_Theory_and_Diameters_of_Immersed_Submanifolds_of_Euclidean_Space.pdf
Thesis Supervisors:: Sergei Tabachnikov, Thesis Supervisor
Nathanial Patrick Brown, Thesis Honors Advisor

Open Access

Author:: Jin, Xin
Title:: Solution of Problems in Quadratic Programming Using Dykstra's Algorithm
Area of Honors:: Mathematics
Keywords:: quadratic programming
best approximation
dykstra algorithm
ellipsoid method
File:: Download latex_thesis_template-combined.pdf
Thesis Supervisors:: Ludmil Tomov Zikatanov, Thesis Supervisor
Ludmil Tomov Zikatanov, Thesis Honors Advisor
Xiantao Li, Faculty Reader

Open Access

Author:: Tomasko, Jessica
Title:: Odd Grassmannian Permutations Avoiding Patterns of Size Three
Area of Honors:: Mathematics
Keywords:: Grassmannian
permutations
pattern-avoidance
Dyck paths
odd
File:: Download Tomasko_Thesis_Final.pdf
Thesis Supervisors:: Juan Bautista Gil, Thesis Supervisor
Laura Rotunno, Thesis Honors Advisor

Open Access

Author:: Lou, Chenyu
Title:: Detecting Ischemic Stroke: A Topological Approach
Area of Honors:: Mathematics
Keywords:: Time-series classification
Topological Data Analysis
Gaussian Process Regression
File:: Download Lou_Honors_Thesis_Apr7.pdf
Thesis Supervisors:: Matthew Logan Reimherr, Thesis Supervisor
Luen-Chau Li, Thesis Honors Advisor

Open Access

Author:: Zhang, Yifei
Title:: Zeta Function of Curves Over Finite Field and Its Rationality
Area of Honors:: Mathematics
Keywords:: In this thesis
we are set to explore a zeta function over finite field: an analogy to Riemann zeta function
and prove its rationality with techniques of p-adic numbers.
zeta function
p-adic
finite field
File:: Download Zeta_Function_of_Curves_Over_Finite_Field_and_Its_Rationality.pdf
Thesis Supervisors:: Mihran Papikian, Thesis Supervisor
Nathanial Patrick Brown, Thesis Honors Advisor

Open Access

Author:: Wang, Yancheng
Title:: Solving the Lady in the Lake Problem and Its Fastest Optimal Strategy
Area of Honors:: Mathematics
Keywords:: Differential Game Theory
Lady in the Lake
numerical approximation
File:: Download thesis_final_version.pdf
Thesis Supervisors:: Jessica Maral Conway, Thesis Supervisor
Luen-Chau Li, Thesis Honors Advisor

Open Access

Author:: Lloyd, Owen
Title:: Time Alignment of Biological Data: Numerical Modeling and Stochastic Processes
Area of Honors:: Mathematics
Keywords:: stochastic processes
numerical modeling
single-cell RNA sequencing
pseudotime analysis
trajectory inference
Brownian motion
File:: Download Lloyd_Owen_Thesis.pdf
Thesis Supervisors:: Andrew Belmonte, Thesis Supervisor
Sergei Tabachnikov, Thesis Honors Advisor

Open Access

Author:: Piazza, Jack
Title:: A Topological Approach to Selection Rule Stochasticity
Area of Honors:: Mathematics
Keywords:: logic
computability
topology
randomness
File:: Download Piazza_Jack_SelectionTopology.pdf
Thesis Supervisors:: Jan S Reimann, Thesis Supervisor
Sergei Tabachnikov, Thesis Honors Advisor

Open Access

Author:: Stepler, Isabelle
Title:: Analysis of the SIR Model on a Network of Nodes
Area of Honors:: Mathematics
Keywords:: SIR
Infectious disease
asymptotic analysis
parameter estimation
File:: Download Schreyer_Honors_Thesis_final.pdf
Thesis Supervisors:: Pierre-Emmanuel Jabin, Thesis Supervisor
Diane Marie Henderson, Thesis Honors Advisor

Restricted (Penn State Only)

Author:: Song, Zitao
Title:: Predicting Volatility of Stocks Using Time Series Models
Area of Honors:: Mathematics
Keywords:: GARCH
Volatility
Time Series
Stock
File:: Login to Download
Thesis Supervisors:: Mauricio Fernandes Nascimento, Jr., Thesis Supervisor
Sergei Tabachnikov, Thesis Honors Advisor

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