In graph theory, a family of graphs is said to have bounded expansion if all of its shallow minors are sparse graphs. Many natural families of sparse graphs have bounded expansion. A closely related but stronger property, polynomial expansion, is equivalent to the existence of separator theorems for these families. Families with these properties have efficient algorithms for problems including the subgraph isomorphism problem and model checking for the first order theory of graphs. (Wikipedia).
Convergent sequences are bounded
Convergent Sequences are Bounded In this video, I show that if a sequence is convergent, then it must be bounded, that is some part of it doesn't go to infinity. This is an important result that is used over and over again in analysis. Enjoy! Other examples of limits can be seen in the
From playlist Sequences
Definite Integral Using Limit Definition
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definite Integral Using Limit Definition. In this video we compute a definite integral using the limit definition.
From playlist Calculus
What are Bounded Sequences? | Real Analysis
What are bounded sequences? We go over the definition of bounded sequence in today's real analysis video lesson. We'll see examples of sequences that are bounded, and some that are bounded above or bounded below, but not both. We say a sequence is bounded if the set of values it takes on
From playlist Real Analysis
Local Maximum and Local Minimum of a Definite Integral Function (Accumulation Function)
This video provides an example of how to determine when a definite integral function would have local maximums or local minimums. Site: http://mathispower4u.com
From playlist Definite Integrals and The Fundamental Theorem of Calculus
Monotonic Sequences and Bounded Sequences - Calculus 2
This calculus 2 video tutorial provides a basic introduction into monotonic sequences and bounded sequences. A monotonic sequence is a sequence that is always increasing or decreasing. You can prove that a sequence is always increasing by showing that the next term is greater than the p
From playlist New Calculus Video Playlist
Proof: Convergent Sequence is Bounded | Real Analysis
Any convergent sequence must be bounded. We'll prove this basic result about convergent sequences in today's lesson. We use the definition of the limit of a sequence, a useful equivalence involving absolute value inequalities, and then considering a maximum and minimum will help us find an
From playlist Real Analysis
Infinite Limits With Equal Exponents (Calculus)
#Calculus #Math #Engineering #tiktok #NicholasGKK #shorts
From playlist Calculus
Bounded Area: With Respect to y
This area explains how to determine bounded area by integrating with respect to y.
From playlist Area Bounded by Two Functions
Expanders and Communication-Avoiding Algorithms - Oded Schwartz
Oded Schwartz Technical University Berlin January 25, 2010 Algorithms spend time on performing arithmetic computations, but often more on moving data, between the levels of a memory hierarchy and between parallel computing entities. Judging by the hardware evolution of the last few decades
From playlist Mathematics
Vaughn Climenhaga: Beyond Bowen specification property - lecture 2
Rufus Bowen introduced the specification property for uniformly hyperbolic dynamical systems and used it to establish uniqueness of equilibrium states, including the measure of maximal entropy. After reviewing Bowen's argument, we will present our recent work on extending Bowen's approach
From playlist Dynamical Systems and Ordinary Differential Equations
Elliot Paquette : Anchored expansion in the hyperbolic Poisson Voronoi tessellation
Abstract: We show that random walk on a stationary random graph with positive anchored expansion and exponential volume growth has positive speed. We also show that two families of random triangulations of the hyperbolic plane, the hyperbolic Poisson Voronoi tessellation and the hyperbolic
From playlist Combinatorics
Nexus trimester - Yitong Yin (Nanjing University)
Rectangle inequalities for data structure lower bounds Yitong Yin (Nanjing University) February 23, 2016 Abstract: The richness lemma is a classic rectangle-based technique for asymmetric communication complexity and cell-probe lower bounds. The technique was enhanced by the Patrascu-Thoru
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Construction of Real Numbers using Decimal Expansions In this video, I construct the real numbers using decimal expansions instead of Dedekind Cuts. This way is much more direct, but of course makes proving the least upper bound property a bit harder. Enjoy! Dedekind Cut Construction of
From playlist Sequences
Dissipation-based uncertainty bounds for currents by Todd Gingrich
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
Graph expansion and communication complexity of algorithms - Olga Holtz
Olga Holtz University of California, Berkeley; Member, School of Mathematics March 18, 2014 In joint work with Ballard, Demmel, and Schwartz, we showed the communication cost of algorithms (also known as I/O-complexity) to be closely related to the small-set expansion properties of the cor
From playlist Mathematics
Expansion in Linear Groups and Applications - Jean Bourgain
Jean Bourgain, Professor, School of Mathematics Institute for Advanced Study September 24, 2010 This lecture was part of the Institute for Advanced Study’s celebration of its eightieth anniversary, and took place during the events related to the Schools and Mathematics and Natural Science
From playlist Mathematics
Valentin Blomer - 4/4 Automorphic forms in higher rank
Valentin Blomer - Automorphic forms in higher rank
From playlist École d'été 2014 - Théorie analytique des nombres
Ex: Properties of Definite Integrals - Zero Interval
This video provides an example of how to evaluate a definite integral when the upper and lower limit of integration are equal. Site: http://mathispower4u.com
From playlist Applications of Definite Integration