Graph invariants | Spanning tree | Matroid theory
In graph theory, a branch of mathematics, the circuit rank, cyclomatic number, cycle rank, or nullity of an undirected graph is the minimum number of edges that must be removed from the graph to break all its cycles, making it into a tree or forest. It is equal to the number of independent cycles in the graph (the size of a cycle basis). Unlike the corresponding feedback arc set problem for directed graphs, the circuit rank r is easily computed using the formula , where m is the number of edges in the given graph, n is the number of vertices, and c is the number of connected components. It is also possible to construct a minimum-size set of edges that breaks all cycles efficiently, either using a greedy algorithm or by complementing a spanning forest. The circuit rank can be explained in terms of algebraic graph theory as the dimension of the cycle space of a graph, in terms of matroid theory as the corank of a graphic matroid, and in terms of topology as one of the Betti numbers of a topological space derived from the graph. It counts the ears in an ear decomposition of the graph, forms the basis of parameterized complexity on almost-trees, and has been applied in software metrics as part of the definition of cyclomatic complexity of a piece of code. Under the name of cyclomatic number, the concept was introduced by Gustav Kirchhoff. (Wikipedia).
Electrical Engineering: Ch 9: 2nd Order Circuits (2 of 76) What is a 2nd Order Circuit? Part 2
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain in a more mathematical approach of what is a second order circuit: part 2. Next video in this series can be seen at: https://youtu.be/B79Kye6U_vw
From playlist ELECTRICAL ENGINEERING 9: SECOND ORDER CIRCUITS
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Visit http://ilectureonline.com for more math and science lectures! http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 In this video I will explain what are second order circuits- a circuit (series or parallel) that contains a resistor and 2-energy storing device
From playlist ELECTRICAL ENGINEERING 9: SECOND ORDER CIRCUITS
This electronics video tutorial answers the question what is current? It explains the concept of electric current by means of electric charge, time, voltage, and resistance. It explains how to calculate the current in a series circuit containing 3 resistors as well as resistors in a para
From playlist Electronic Circuits
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Visit http://ilectureonline.com for more math and science lectures! In this video I will draw the final circuit of a more complicated 2nd order circuit with a current source that is a step-function at t=infinity. (2D) http://www.ilectureonline.com/donate https://www.patreon.com/user?u=32
From playlist ELECTRICAL ENGINEERING 9: SECOND ORDER CIRCUITS
Transistor Amplifiers - Class A, AB, B, & C Circuits
This electronics video tutorial provides a basic introduction into the Class A, AB, B, and C transistor amplifiers. The class A amplifier is the common emitter amplifier which uses a single NPN transistor. The Class B amplifier using two complementary NPN and PNP transistors and yields a
From playlist Electronic Circuits
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From playlist ELECTRICAL ENGINEERING 9: SECOND ORDER CIRCUITS
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Visit http://ilectureonline.com for more math and science lectures! In this video I will summarize 2nd order equations. First we need a set of equations that relates the voltage and the resistor in the circuit, the inductor in the circuit, and the capacitor in the circuit. Second we need
From playlist ELECTRICAL ENGINEERING 9: SECOND ORDER CIRCUITS
Electrical Engineering: Ch 9: 2nd Order Circuits (74 of 76) Duality in a 2nd Order Circuit
Visit http://ilectureonline.com for more math and science lectures! http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will use transform a 2nd order circuit to a duality 2nd order circuit. In other words, a circuit that will do the same thing electronically,
From playlist ELECTRICAL ENGINEERING 9: SECOND ORDER CIRCUITS
Parameterized Lower Bounds on Multilinear Algebraic Models by Purnata Ghosal
Discussion Meeting Workshop on Algebraic Complexity Theory  ORGANIZERS Prahladh Harsha, Ramprasad Saptharishi and Srikanth Srinivasan DATE & TIME 25 March 2019 to 29 March 2019 VENUE Madhava Lecture Hall, ICTS Bangalore Algebraic complexity aims at understanding the computationa
From playlist Workshop on Algebraic Complexity Theory 2019
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From playlist Mathematics
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From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
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From playlist AP Physics 1 - EVERYTHING!!
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From playlist Mathematics
2017 #1 Free Response Question - AP Physics 1 - Exam Solution
My solutions to Free Response Question #1 from the 2017 AP Physics 1 Exam. This is an electric circuits question about ranking electric potential differences and electric power. Also included are my reflections on how to get perform better on the exam. Want Lecture Notes? http://www.flippi
From playlist AP Physics 1 - EVERYTHING!!
Computer Science/Discrete Mathematics Reading Seminar Topic: Tensor Rank Speaker: Avi Wigderson Affiliation: IAS, Herbert H. Maass Professor, School of Mathematics Date: June 22, 2021 Tensors occur throughout mathematics. Their rank, defined in analogy with matrix rank, is however much
From playlist Mathematics
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Proving super-polynomial lower bounds for syntactic multilinear branching programs by Ramya C
Discussion Meeting Workshop on Algebraic Complexity Theory  ORGANIZERS Prahladh Harsha, Ramprasad Saptharishi and Srikanth Srinivasan DATE & TIME 25 March 2019 to 29 March 2019 VENUE Madhava Lecture Hall, ICTS Bangalore Algebraic complexity aims at understanding the computationa
From playlist Workshop on Algebraic Complexity Theory 2019
Physics - E&M: RCL Circuits, Phasors, & Alternating Currents (12 of 24) Phasor Diagram - V Across
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the voltages across each of the components in a RCL circuit. Next video in series: http://youtu.be/0gphIkM2u8A
From playlist PHYSICS 49 RCL CIRCUITS
A PSPACE construction of a hitting set for the closure of small algebraic circuits - Amir Shpilka
Computer Science/Discrete Mathematics Seminar II Topic: A PSPACE construction of a hitting set for the closure of small algebraic circuits Speaker: Amir Shpilka Affiliation: Tel Aviv University Date: December 12, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics