Binary Stars
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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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This lecture deals with Paradise IV, VI and X. At the beginning of Paradise IV, the pilgrim raises two questions to which the remainder of the canto is devoted. The first concerns Piccarda (Paradise III) who was constrained to break her religious vows. The second concerns the arrangement of the souls within the stars. The common thread that emerges from Beatrice's reply is the relationship between intellect and will. Just as Piccarda's...more
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This lecture covers Paradise XXIV-XXVI. In the Heaven of the Fixed Stars, Dante is examined on the three theological virtues by the apostles associated with each: St. Peter with faith (Paradise XXIV), St. James with hope (Paradise XXV), and St. John with love (Paradise XXVI). While mastering these virtues is irrelevant to the elect, it is crucial to the message of reform the pilgrim-turned-poet will relay on his return home. Dante's...more
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In this lecture, Professor Mazzotta examines Paradise XVIII-XIX and XXI-XXII. In Paradise XVIII, Dante enters the Heaven of Jupiter, where the souls of righteous rulers assume the form of an eagle, the emblem of the Roman Empire. The Eagle's outcry against the wickedness of Christian kings leads Dante to probe the boundaries of divine justice by looking beyond the confines of Christian Europe. By contrasting the political with the moral...more
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This lecture focuses on Paradise XXVII-XXIX. St. Peter's invective against the papacy from the Heaven of the Fixed Stars is juxtaposed with Dante's portrayal of its contemporary incumbent, Boniface VIII, in the corresponding canto of Inferno. Recalls of infernal characters proliferate as the pilgrim ascends with Beatrice into the primum mobile. Bid to look back on the world below, Dante perceives the mad track of his uneasy archetype,...more
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Statistical Estimation, Maximum Likelihood Estimation, Examples, Logistic Regression, (Binary) Hypothesis Testing, Scalarization, Experiment Design, D-Optimal Design
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Review of the Dining Philosopher Problem, Modeling Each Philosopher as a Thread, How Deadlock Can Result, How Deadlock Can be Eliminated By Limiting the Number of Philosophers That Can Eat at Once Using a Semaphore, Using a Global Variable and a Binary Lock to Track a Resource Vs. Using a Semaphore, Another Threading Example Involving FTP Downloads of Multiple Files at Once, Where Each File Is Assigned to a Thread and the Total Number of...more
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Guest lecturer Dr. Geoff Marcy gives a lecture entitled, "Planetary Systems Around other Stars," for Professor Lynn Rothschild's Astrobiology and Space Exploration course.
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Rotating Rigid Bodies, Moments of Inertia, Parallel Axis and Perpendicular Axis Theorem. The moment of inertia for a rigid body around an axis of rotation is introduced, and related to its rotational kinetic energy. Flywheels can be used to store energy. Planets and stars have spin rotational kinetic energy, and the Crab Nebula pulsar is presented as a spectacular example.
