Set theory | Graph algorithms | Graph theory
In the mathematical field of graph theory, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges as possible, such that for all pairs of vertices v, w a (directed) path from v to w in D exists if and only if such a path exists in the reduction. Transitive reductions were introduced by , who provided tight bounds on the computational complexity of constructing them. More technically, the reduction is a directed graph that has the same reachability relation as D. Equivalently, D and its transitive reduction should have the same transitive closure as each other, and the transitive reduction of D should have as few edges as possible among all graphs with that property. The transitive reduction of a finite directed acyclic graph (a directed graph without directed cycles) is unique and is a subgraph of the given graph. However, uniqueness fails for graphs with (directed) cycles, and for infinite graphs not even existence is guaranteed. The closely related concept of a minimum equivalent graph is a subgraph of D that has the same reachability relation and as few edges as possible. The difference is that a transitive reduction does not have to be a subgraph of D. For finite directed acyclic graphs, the minimum equivalent graph is the same as the transitive reduction. However, for graphs that may contain cycles, minimum equivalent graphs are NP-hard to construct, while transitive reductions can be constructed in polynomial time. Transitive reduction can be defined for an abstract binary relation on a set, by interpreting the pairs of the relation as arcs in a directed graph. (Wikipedia).
Reduction of Order - Linear Second Order Homogeneous Differential Equations Part 2
This video explains how to apply the method of reduction of order to solve a linear second order homogeneous differential equations. Site: http://mathispower4u
From playlist Second Order Differential Equations: Reduction of Order
Reduction of Order - Linear Second Order Homogeneous Differential Equations Part 1
This video explains how to apply the method of reduction of order to solve a linear second order homogeneous differential equations. Site: http://mathispower4u
From playlist Second Order Differential Equations: Reduction of Order
Using two multipliers when solving a system of equations using the addition method
đŸ‘‰Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Using Two Multipliers to Solve a System of Equations with Elimination
đŸ‘‰Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Using Multipliers to Solve a System of Equations Using Elimination
đŸ‘‰Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Graphing a System of Equations by Eliminating the Fractions
đŸ‘‰Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Solve a System of Equations Using Elimination
đŸ‘‰Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Hydroxyl-directed 1,3 Reductions of Ketones - Organic Chemistry, Reaction Mechanism
Three named reactions in organic chemistry that are highly diastereoselective reductions of beta-hydroxyketones. This video discussed the synthetic chemistry aspects and the appropriate transition states for these kinetically controlled reactions. #chemistry #organicchemistry #orgo #ochem
From playlist Organic Chemistry Mechanisms
Stochastic Analysis and Applications in Gene Networks by Chunhe Li
PROGRAM TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID) ORGANIZERS: Partha Sharathi Dutta (IIT Ropar, India), Vishwesha Guttal (IISc, India), Mohit Kumar Jolly (IISc, India) and Sudipta Kumar Sinha (IIT Ropar, India) DATE: 19 September 2022 to 30 September 2022 VENUE: Ramanujan Lecture Hall an
From playlist TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID, 2022)
CBS Reduction, Enantioselective Catalysis - Organic Chemistry, Reaction Mechanism
Another introductory video on enantioselective catalysis in Organic Chemistry. Here secondary ketones can be synthesised in high enantiomeric excess from the parent ketone by a CBS reduction reaction. Essentially the CBS reduction is a chiral version of the more familiar reagent sodium bor
From playlist Organic Chemistry Mechanisms
Solve a system of equation when they are the same line
đŸ‘‰Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Medium
Max Tschaikowski, Aalborg University
March 1, Max Tschaikowski, Aalborg University Lumpability for Uncertain Continuous-Time Markov Chains
From playlist Spring 2022 Online Kolchin seminar in Differential Algebra
Solve a System of Equations with Elimination when Your Solutions are Fractions
đŸ‘‰Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Slava Rychkov - Random Field Ising Model and Parisi-Sourlas Supersymmetry (1/4)
Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any d. I will present a recent theory, developed in 2019
From playlist Slava Rychkov - Random Field Ising Model and Parisi-Sourlas Supersymmetry
Lec 36 | MIT 5.111 Principles of Chemical Science, Fall 2005
Review (Prof. Catherine Drennan) View the complete course: http://ocw.mit.edu/5-111F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 5.111 Principles of Chemical Science, Fall 2005
Nickel-Catalyzed Anti-Markovnikov Hydroarylation of Unactivated Alkenes with Dr. Noam Saper
In our first ever Research Spotlight episode, we are joined by Dr. Noam Saper, who takes us through his recent work on anti-Markovnikov hydroarylation. Parent reference:Â Nature Chem. 2020, 12, 276-283. Other references: Science 2011, 332, 439. Organometallics 2012, 31, 1300. Angew. Chem.
From playlist Special Topics: Organometallics
Synthesis Workshop: Deuterium + Tritium Labeling with Sara Kopf and Florian Bourriquen (Episode 94)
In this Research Spotlight episode, Sara Kopf and Florian Bourriquen (Beller group) join us to take us through some recent developments in the field of deuterium and tritium labeling of organic molecules. Key paper: Chem. Rev. 2022, 122, 6634-6718. https://doi.org/10.1021/acs.chemrev.1c00
From playlist Research Spotlights
Lattice Studies of Three-Dimensional Super-Yang--Mills by David Schaich
PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II
From playlist NUMSTRING 2022
How to Solve a System by Using Two Multipliers for Elimination
đŸ‘‰Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Introduction to Fiber Bundles Part 5.1: Steenrod's Theorem
This video is about how to reduce structure groups of fiber bundles.
From playlist Fiber bundles