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### Introduction and Case Studies

01:13:50Gerbrand CederWe revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

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### Potentials, Supercells, Relaxation, Methodology

01:16:59Gerbrand CederWe revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

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### Potentials 2: Potentials for Organic Materials and Oxides - It's a Quantum World!

01:22:16Gerbrand CederWe revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

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### First Principles Energy Methods: The Many-Body Problem

01:19:57Nicola Marzari - Play ►
### First Principles Energy Methods: Hartree-Fock and DFT

01:22:04Nicola Marzari - Play ►
### Technical Aspects of Density Functional Theory

01:19:05Nicola Marzari - Play ►
### Case Studies of DFT

01:20:06Nicola Marzari - Play ►
### Advanced DFT: Success and FailureDFT Applications and Performance

01:22:27Nicola Marzari - Play ►
### Finite Temperature: Excitations in Materials and How to Sample Them

01:13:20Gerbrand Ceder - Play ►
### Molecular Dynamics I

01:23:31Nicola Marzari - Play ►
### Molecular Dynamics II

01:21:53Nicola Marzari - Play ►
### Molecular Dynamics III: First Principles

01:21:47Nicola Marzari - Play ►
### Monte Carlo Simulations: Application to Lattice Models, Sampling Errors, Metastability

01:14:31Gerbrand Ceder - Play ►
### Monte Carlo Simulation II and Free Energies

01:15:27Gerbrand Ceder - Play ►
### Free Energies and Physical Coarse-Graining

01:16:49Gerbrand Ceder - Play ►
### Model Hamiltonions

01:20:00Nicola Marzari - Play ►
### Ab-Initio Thermodynamics and Structure Prediction

01:19:13Gerbrand Ceder - Play ►
### Accelerated Molecular Dynamics, Kinetic Monte Carlo, and Inhomogeneous Spatial Coarse Graining

01:10:52Gerbrand Ceder - Play ►
### Case Studies: High PressureConclusions

01:01:52Nicola Marzari