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Search.setIndex({"alltitles":{"1) Analyzing data on a manifold reduces the degrees of freedom of the system, making computations less complicated.":[[32,"1)-Analyzing-data-on-a-manifold-reduces-the-degrees-of-freedom-of-the-system,-making-computations-less-complicated."]],"1. A first example in 2D":[[42,"1.-A-first-example-in-2D"]],"1. Introduction":[[33,null]],"1. Introduction and Motivation":[[43,"1.-Introduction-and-Motivation"],[50,"1.-Introduction-and-Motivation"]],"1. What is a Connection?":[[34,null]],"1.1 General Mathematical Definition of the Connection":[[34,"1.1-General-Mathematical-Definition-of-the-Connection"]],"1.2 What does the Connection actually do? \u2013 a more friendly description of the connection, with an example":[[34,"1.2-What-does-the-Connection-actually-do?----a-more-friendly-description-of-the-connection,-with-an-example"]],"2) Knowing the manifold that a data set belongs to may give you a deeper understanding of your data\u2019s evolution or \u201cwhy your data looks/evolves the way it does\u201d":[[32,"2)-Knowing-the-manifold-that-a-data-set-belongs-to-may-give-you-a-deeper-understanding-of-your-data's-evolution-or-%22why-your-data-looks/evolves-the-way-it-does%22"]],"2. Dataset Description":[[43,"2.-Dataset-Description"]],"2. Dataset description":[[50,"2.-Dataset-description"]],"2. Focus on quotienting out reparametrizations":[[42,"2.-Focus-on-quotienting-out-reparametrizations"]],"2. What is a Manifold?":[[33,"2.-What-is-a-Manifold?"]],"2. Why is the Connection important (big picture)? \u2013 parallel transport, parallel vector fields":[[34,"2.-Why-is-the-Connection-important-(big-picture)?----parallel-transport,-parallel-vector-fields"]],"2.1 Parallel Vector Fields":[[34,"2.1-Parallel-Vector-Fields"]],"2.1 Precise Mathematical Definition":[[33,"2.1-Precise-Mathematical-Definition"]],"2.1. Comparing parametrized curves":[[42,"2.1.-Comparing-parametrized-curves"]],"2.2 Imprecise \u201cLayman\u2019s Terms\u201d Definition:":[[33,"2.2-Imprecise-%22Layman's-Terms%22-Definition:"]],"2.2 Parallel Transport":[[34,"2.2-Parallel-Transport"]],"2.2. 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Why do we care about manifolds?":[[33,"3.-Why-do-we-care-about-manifolds?"]],"3.1 Intuitive Definition of a Geodesic":[[34,"3.1-Intuitive-Definition-of-a-Geodesic"]],"3.1. Road representation: introduction to the Gamma manifold.":[[50,"3.1.-Road-representation:-introduction-to-the-Gamma-manifold."]],"3.1.1. Hypotheses":[[50,"3.1.1.-Hypotheses"]],"3.1.2. Model":[[50,"3.1.2.-Model"]],"3.2 Defining a geodesic with the connection":[[34,"3.2-Defining-a-geodesic-with-the-connection"]],"3.2. Mathematical representation of renovation efforts":[[50,"3.2.-Mathematical-representation-of-renovation-efforts"]],"3.2.1. Hypotheses":[[50,"3.2.1.-Hypotheses"]],"3.2.2. Model":[[50,"3.2.2.-Model"]],"3.3 Building Intuition with Physics":[[34,"3.3-Building-Intuition-with-Physics"]],"3.3. Optimization problem":[[50,"3.3.-Optimization-problem"]],"4 Data Analysis":[[43,"4-Data-Analysis"]],"4. Dataset processing":[[50,"4.-Dataset-processing"]],"4. 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