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Description:: The purpose of this thesis is to study the empirical measure of the t-distributed stochastic neighbor embedding algorithm (t-SNE) when the input is given by n independent, identically distributed inputs.We show that this sequence of measures converges to an equilibrium measure, which can be described as the solution of a...
Keyword:: Probability and Unsupervised Machine Learning
Subject:: Mathematics
Creator:: Fletcher, Daniel
Owner:: Scholarly Digital Publishing
Language:: en
Date Uploaded:: 05/31/2023
Date Created:: 2023-01-01
Resource Type:: Dissertation
Alternate Identifier:: http://dissertations.umi.com/northwestern:16523 and etdadmin_upload_983853

Description:: The purpose of this thesis is to derive three results in probability theory. The first is a proof that small powers of the normalized absolute characteristic polynomial of a random matrix sampled from either the Gaussian Orthogonal or Symplectic Ensemble converges in law to a Gaussian multiplicative chaos measure. The...
Keyword:: Probability and Random Matrices
Subject:: Mathematics
Creator:: Kivimae, Pax
Owner:: Scholarly Digital Publishing
Language:: en
Date Uploaded:: 09/22/2022
Date Created:: 2022-01-01
Resource Type:: Dissertation
Alternate Identifier:: etdadmin_upload_923657 and http://dissertations.umi.com/northwestern:16191

Description:: This thesis is composed of two major parts. The first major part includes the first two chapters. In Chapter 1, we go over the history and background of spin glass theory and introduce the Sherrington-Kirkpatrick (SK) model and the Ghatak-Sherrington (GS) model. In Chapter 2, we introduce the Thouless-Anderson-Palmer (TAP)...
Keyword:: Probability and Spin Glass
Subject:: Mathematics
Creator:: Chen, Xi
Owner:: Scholarly Digital Publishing
Language:: en
Date Uploaded:: 06/22/2022
Date Created:: 2022-01-01
Resource Type:: Dissertation
Alternate Identifier:: http://dissertations.umi.com/northwestern:16090 and etdadmin_upload_903175

Description:: The staggered (or imbricated) lamellar ``brick-and-mortar" nanostructure of nacre endows nacre with strength and fracture toughness values exceeding by an order of magnitude those of the constituents, and inspires the advent of new robust biomimetic materials. While many deterministic studies clarified these advantageous features in the mean sense, a closed-form...
Keyword:: Nacre, Strength, Probability, Octet-truss, Architected Material, and Size Effect
Subject:: Mechanics, Mechanical engineering, and Civil engineering
Creator:: Luo, Wen
Owner:: Scholarly Digital Publishing
Language:: en
Date Uploaded:: 01/21/2021
Date Created:: 2020-01-01
Resource Type:: Dissertation
Alternate Identifier:: http://dissertations.umi.com/northwestern:15081 and etdadmin_upload_741756

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