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-
- Description:
- This dissertation considers a periodically-forced 1-D Langevin equation that possesses two stable periodic solutions in the absence of noise. We aim at answering the question: is there a most likely noise-induced transition path between these periodic solutions that allows one to identify a preferred phase of the forcing when the...
- Subject:
- Applied mathematics
- Creator:
- Chen, Yuxin
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/12/2020
- Date Created:
- 2019-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:14754 and etdadmin_upload_677031
-
- Description:
- For stochastic simulation optimization in a modern computing era, we introduce a new parallel framework for solving very large-scale problems using a ranking & selection (R&S) approach that simulates all systems or feasible solutions to provide a global statistical guarantee. We propose a parallel adaptive survivor selection (PASS) framework that...
- Keyword:
- master-worker, simulation, parallel, stochastic, large-scale, and optimization
- Subject:
- Applied mathematics, Statistics, and Operations research
- Creator:
- Pei, Linda
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 06/22/2022
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_903888 and http://dissertations.umi.com/northwestern:16108
-
- Description:
- Motivated by rhythms in the brain, we investigate the synchronization of noisy and all-to-all pulse-coupled oscillators. We consider a case where the oscillatory excursions are of varying amplitude and where only sufficiently large excursions result in the output pulses that drive the interactions between the oscillators. In the regime of...
- Keyword:
- Oscillators, Markov Renewal, Events, Mixed-mode, Spiking, and Noise
- Subject:
- Applied mathematics
- Creator:
- Karamchandani, Avinash Jagdish
- 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:16397 and etdadmin_upload_959050
-
- Description:
- We present two novel, computational models of biofilm growth within an experimental flow cell. First, we use asymptotic approximations to develop a reduced model that captures the large-scale dynamics within an entire flow cell. The reduced model's predicted growth and nutrient distribution are close to the values predicted by previous...
- Subject:
- Applied mathematics
- Creator:
- Ford, Noah
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/01/2021
- Date Created:
- 2020-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_764364 and http://dissertations.umi.com/northwestern:15266
-
- Description:
- We present a biophysical model of GCaMP6f calcium fluorescence in CA1 pyramidal neuron dendrites based upon results from imaging and electrophysiology experiments. This work was completed using experimental results from the laboratory of Professor Daniel Dombeck, Department of Neurobiology. Constraining the model to reproduce different objectives --- from in-vitro and...
- Keyword:
- Calcium Model, Dendritic Spines, Computational Neuroscience, Calcium Imaging, and Synaptic Integration
- Subject:
- Applied mathematics and Neurosciences
- Creator:
- Young, Brita Schneiders
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 06/28/2021
- Date Created:
- 2021-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_819855 and http://dissertations.umi.com/northwestern:15589
-
- Description:
- This dissertation is a review of three projects I worked on during my time in the Computational Photography Lab at Northwestern University. First, a source separation problem for the X-Ray Fluorescence images of painted works of art is addressed through the incorporation of Hyperspectral Reflectance data. Following this, a discussion...
- Keyword:
- XRF, Computational Holography, Hypterspectral Imaging, Optical Coherence Tomorgraphy, Computational Imaging, and Cultural Heritage Science
- Subject:
- Applied mathematics
- Creator:
- Fiske, Lionel David
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 05/31/2023
- Date Created:
- 2023-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_961685 and http://dissertations.umi.com/northwestern:16405
-
- Description:
- Many industrial fluid flow problems involve the interaction between heavy, rigid objects and one or more fluid phases. For several decades, there has been a vested interest in simulating these fluid-structure interaction (FSI) problems in order to improve engineering design processes. However, numerical simulations of these problems can be challenging...
- Keyword:
- Aquatic locomotion, Adaptive mesh refinement, Fluid-structure interaction, Multiphase flow, Computational fluid dynamics, and Vehicle aerodynamics
- Subject:
- Applied mathematics, Computational physics, and Fluid mechanics
- Creator:
- Nangia, Nishant
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/12/2020
- Date Created:
- 2019-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_637421 and http://dissertations.umi.com/northwestern:14506
-
- Description:
- The ever growing desire for accurate estimation and efficient learning necessitates the efforts to quantitatively characterize uncertainties for models. In this thesis, four problems pertaining to uncertainty quantification are discussed: A sequential stopping framework of constructing fixed-precision confidence regions is proposed for a class of multivariate simulation problems where variance...
- Keyword:
- Ranking and Selection, Reinforcement Learning, Statistical Learning, Stochastic Gradient Descent, and Uncertainty Quantification
- Subject:
- Applied mathematics, Statistics, and Computer science
- Creator:
- Zhu, Yi
- 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:15080 and etdadmin_upload_741745
-
- Description:
- This dissertation presents two projects with the goal of understanding how to quantitatively describe biological data, particularly data that is highly dynamic. The first study presents an improved quantitative tool for the analysis of particulate trajectories. Particulate trajectory data appears in several different biological contexts, and the majority of analyses...
- Keyword:
- Differential Equations Modeling, Quantitative Biology, Data Driven Methods, Jump Distance Distribution, and C. elegans
- Subject:
- Applied mathematics
- Creator:
- Menssen, Rebecca
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/12/2020
- Date Created:
- 2019-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_684514 and http://dissertations.umi.com/northwestern:14797
-
- Description:
- Mixing by cutting-and-shuffling (like that for a deck of cards or a Rubik's cube) is a paradigm that has not been studied in detail even though it can be applied in a variety of situations including the mixing of granular materials. Mathematically, cutting- and-shuffling is described by piecewise isometries (PWIs),...
- Keyword:
- granular materials, mixing, machine learning, piecewise isometries, cutting-and-shuffling, and interval exchange transforms
- Subject:
- Applied mathematics, Chemical engineering, and Mechanical engineering
- Creator:
- Lynn, Thomas Ferguson
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 06/22/2022
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_881325 and http://dissertations.umi.com/northwestern:15951
-
- Description:
- To survive, animals, including human beings, have developed an amazing ability to learn the constantly changing environment. Specifically, detecting specific odorants in a noisy, variable background is crucial for finding food and water, mating, and avoiding potential dangers. For this purpose, rodents have developed an olfactory system that is powerful...
- Keyword:
- Synchronization, Olfactory Bulb, Neuron, Structural Plasticity, Learning, and Rhythms
- Subject:
- Applied mathematics and Neurosciences
- Creator:
- Meng, Hongyu
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 04/28/2020
- Date Created:
- 2019-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:14966 and etdadmin_upload_713722
-
- Description:
- Cells are often precisely organized into patterns within developing tissues. This precision must emerge from biochemical processes within, and between cells, that are inherently stochastic. I investigated the impact of stochastic gene expression on self-organized pattern formation, focusing on Senseless (Sens), a key target of Wnt and Notch signaling during...
- Keyword:
- gene expression, microRNA, cell fate, Drosophila, self-organization, and noise
- Subject:
- Applied mathematics, Statistics, and Developmental biology
- Creator:
- Giri, Ritika
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/01/2021
- Date Created:
- 2020-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_763812 and http://dissertations.umi.com/northwestern:15251
-
- Description:
- Soft matter is the field of science concerning soft and deformable materials: such as liquids, gels, and foams. Active matter is a sub-field of soft matter that considers systems that contain active agents or particles that consume energy for self-propulsion or to exert mechanical stress on the surrounding system. In...
- Keyword:
- Spinners, Models, Dynamics, Soft Matter, Cell Motility, and Active Matter
- Subject:
- Applied mathematics
- Creator:
- Reeves, Cody Jordan
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/01/2021
- Date Created:
- 2020-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_772543 and http://dissertations.umi.com/northwestern:15339
-
- Description:
- Circadian rhythms — physiological, behavioral, and metabolic oscillations with an approximate 24-h period — are controlled by an evolutionarily conserved set of core clock genes operating at the transcriptional and protein level. Entrainable by Zeitgebers (external environmental stimuli such as light, temperature, and food) that modulate time-of-day specific functions, the...
- Keyword:
- Differential Dynamics Detection, Time-Series Analysis, Dynamical Systems Theory, Circadian Rhythms, Topological Analysis, and Cycle Detection
- Subject:
- Biostatistics, Applied mathematics, and Bioinformatics
- Creator:
- Ness-Cohn, Elan Meir
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 06/22/2022
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_875611 and http://dissertations.umi.com/northwestern:15905
-
- Description:
- Perhaps because of the influence of the central limit theorem, it is common for scientists to assume distributions in the real world are singly peaked and unimodal. However, many quantities in nature are actually better represented by multimodal distributions. One must provide an explanation for this disconnect between the central...
- Keyword:
- Multimodality, Ecology, Economics, Dynamical Systems, Applied Mathematics, and Coupled Oscillators
- Subject:
- Ecology, Applied mathematics, and Economics
- Creator:
- Johnson, Joseph Davis
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/01/2021
- Date Created:
- 2020-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:15298 and etdadmin_upload_765238
-
- Description:
- There is a rich history on the study of the interplay between symmetry and synchronization in networks. At the most fundamental level, many synchronization patterns are induced by underlying network symmetries. However, when stability is taken into account, the relation between symmetry and synchronization is far from monotonic. In this...
- Keyword:
- complex systems, nonlinear dynamics, networks, chimeras, symmetry, and synchronization
- Subject:
- Applied mathematics, Statistical physics, and Systems science
- Creator:
- Zhang, Yuanzhao
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/01/2021
- Date Created:
- 2020-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_764987 and http://dissertations.umi.com/northwestern:15288
-
Recurrent inhibition within olfactory networks shapes noise correlations and stimulus discrimination
- Description:
- Each second, living organisms take in sensory input from an ever-changing environment and respond appropriately. Identifying and contextualizing stimuli is critical for survival, and it often necessitates distinguishing between sensory experiences that are similar to each other. Pattern separation characterizes the mechanisms by which neuronal networks extract and highlight differences...
- Keyword:
- Sensory processing, Neuroscience, and Olfaction
- Subject:
- Applied mathematics
- Creator:
- Wang, Angelia Feiyang
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/16/2023
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_945895 and http://dissertations.umi.com/northwestern:16353
-
- Description:
- Recently, machine learning and deep learning, which have made many theoretical and empir- ical breakthroughs and is widely applied in various fields, attract a great number of researchers and practitioners. They have become one of the most popular research directions and plays a sig- nificant role in many fields, such...
- Keyword:
- Algorithm Design, Deep Learning, Optimization, and Machine Learning
- Subject:
- Applied mathematics and Operations research
- Creator:
- Fang, Biyi
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/02/2022
- Date Created:
- 2021-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:15817 and etdadmin_upload_855647
-
- Description:
- Modern data sets are increasingly vast, not only in the number of samples, but also in the number of measurements, or features, that they contain. This high-dimensionality poses a unique set of problems for data analysis due to a set of phenomena known as ``the curse of dimensionality.'' This thesis...
- Keyword:
- Data Visualization, Circular Linear Regression, Dimensionality Reduction, Curse of Dimensionality, and Quality Assessment
- Subject:
- Applied mathematics, Bioinformatics, and Computer science
- Creator:
- Johnson, Eric Mitchell
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 06/22/2022
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_892588 and http://dissertations.umi.com/northwestern:15988
-
- Description:
- Motivated by rhythms in the brain, we investigate the synchronization of noisy and all-to-all pulse-coupled oscillators. We consider a case where the oscillatory excursions are of varying amplitude and where only sufficiently large excursions result in the output pulses that drive the interactions between the oscillators. In the regime of...
- Keyword:
- Oscillators, Markov Renewal, Events, Mixed-mode, Spiking, and Noise
- Subject:
- Applied mathematics
- Creator:
- Karamchandani, Avinash Jagdish
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 03/24/2023
- Date Created:
- 2023-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:16397 and etdadmin_upload_959050