Analysis Of Linear Systems
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Recap: Branch And Bound Methods, Basic Idea, Unconstrained, Nonconvex Minimization
Stanford / Mathematics
Announcements, Recap: Branch And Bound Methods, Basic Idea, Unconstrained, Nonconvex Minimization, Lower And Upper Bound Functions, Branch And Bound Algorithm, Comment: Picture Of Branch And Bound Algorithm In R^2, Comment: Binary Tree, Example, Pruning, Convergence Analysis, Bounding Condition Number, Small Volume Implies Small Size, Mixed Boolean-Convex Problem, Solution Methods, Lower Bound Via Convex Relaxation, Upper Bounds,...more
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Addendum: Hit-And-Run CG Algorithm, Maximum Volume Ellipsoid Method, Chebyshev Center Method, Analytic Center Cutting-Plane Method, Extensions (Of Cutting-Plane Methods), Dropping Constraints, Epigraph Cutting-Plane Method, PWL Lower Bound On Convex Function, Lower Bound, Analytic Center Cutting-Plane Method, ACCPM Algorithm, Constructing Cutting-Planes, Computing The Analytic Center, Infeasible Start Newton Method Algorithm, Properties...more
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Although molecular mechanics is imperfect, it is useful for discussing molecular structure and energy in terms of standard covalent bonds. Analysis of the Cambridge Structural Database shows that predicting bond distances to within 1% required detailed categorization of bond types. Early attempts to predict heats of combustion in terms of composition proved adequate for physiology, but not for chemistry. Group- or bond-additivity schemes...more
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Recap: Conjugate Gradient Method, Recap: Krylov Subspace, Spectral Analysis Of Krylov Sequence, A Bound On Convergence Rate, Convergence, Residual Convergence, CG Algorithm, Efficient Matrix-Vector Multiply, Shifting, Preconditioned Conjugate Gradient Algorithm, Choice Of Preconditioner, CG Summary, Truncated Newton Method, Approximate Or Inexact Newton Methods, CG Initialization, Hessian And Gradient, Methods, Convergence Versus...more
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After discussing the statistical basis of the law of mass action, the lecture turns to developing a framework for understanding reaction rates. A potential energy surface that associates energy with polyatomic geometry can be realized physically for a linear, triatomic system, but it is more practical to use collective energies for starting material, transition state, and product, together with Eyring theory, to predict rates....more
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In 1989, following the year when Dell, Inc. went public, Dell explains how the company had a large problem with inventory management. As a result, the company failed to transition properly in the industry from one technology to the other. However, because of this critical mistake, the company learned how to correctly manage their inventory, and according to Dell, became the best in the world at it. Later on, Dell also notes the company...more
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The most prominent chemist in the generation following Lavoisier was Berzelius in Sweden. Together with Gay-Lussac in Paris and Davy in London, he discovered new elements, and improved atomic weights and combustion analysis for organic compounds. Invention of electrolysis led not only to new elements but also to the theory of dualism, with elements being held together by electrostatic attraction. Wöhler's report on the synthesis of urea...more
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May 16, 2008 lecture by Rob Miller for the Stanford University Human Computer Interaction Seminar (CS547). Rob Miller discusses some of the explorations into keyword programming in the web automation domain, and also in other domains such as Java development. One surprising result is that programming language syntax often has relatively little information content, and can be inferred automatically from only a handful of keywords --...more
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Geography is very important in ecology. Two major systems have been designed to model this, island biogeography and metapopulations. The idea of metapopulations is more recent, and has emerged as the dominant theory. Metapopulations are populations in multiple neighboring areas. The population of a species in any individual area may go extinct, but the metapopulation still survives. The theory of metapopulations has gained momentum in...more
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Continuous-Time Reachability, General State Transfer, Observability And State Estimation, State Estimation Set Up, State Estimation Problem, Observability Matrix, Least-Squares Observers, Some Parting Thoughts..., Linear Algebra, Levels Of Understanding, What's Next
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Continue On Unconstrained Minimization, Self-Concordance, Convergence Analysis For Self-Concordant Functions, Implementation, Example Of Dense Newton System With Structure, Equality Constrained Minimization, Eliminating Equality Constraints, Newton Step, Newton's Method With Equality Constraints
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Complementary Slackness, Karush-Kuhn-Tucker (KKT) Conditions, KKT Conditions For Convex Problem, Perturbation And Sensitivity Analysis, Global Sensitivity Result, Local Sensitivity, Duality And Problem Reformulations, Introducing New Variables And Equality Constraints, Implicit Constraints, Semidefinite Program
