Network theory | Stochastic models | Graph theory | Applied mathematics
Physicists often use various lattices to apply their favorite models in them. For instance, the most favorite lattice is perhaps the square lattice. There are 14 Bravais space lattice where every cell has exactly the same number of nearest, next nearest, nearest of next nearest etc. neighbors and hence they are called regular lattice. Often physicists and mathematicians study phenomena which require disordered lattice where each cell do not have exactly the same number of neighbors rather the number of neighbors can vary wildly. For instance, if one wants to study the spread of disease, viruses, rumors etc. then the last thing one would look for is the square lattice. In such cases a disordered lattice is necessary. One way of constructing a disordered lattice is by doing the following. Starting with a square, say of unit area, and dividing randomly at each step only one block, afterpicking it preferentially with respect to ares, into four smaller blocks creates weighted planar stochastic lattice (WPSL). Essentially it is a disordered planar lattice as its block size and their coordination number are random. (Wikipedia).
Dihedral Group (Abstract Algebra)
The Dihedral Group is a classic finite group from abstract algebra. It is a non abelian groups (non commutative), and it is the group of symmetries of a regular polygon. This group is easy to work with computationally, and provides a great example of one connection between groups and geo
From playlist Abstract Algebra
Prob & Stats - Markov Chains (9 of 38) What is a Regular Matrix?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a regular matrix. Next video in the Markov Chains series: http://youtu.be/loBUEME5chQ
From playlist iLecturesOnline: Probability & Stats 3: Markov Chains & Stochastic Processes
Prob & Stats - Markov Chains (8 of 38) What is a Stochastic Matrix?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a stochastic matrix. Next video in the Markov Chains series: http://youtu.be/YMUwWV1IGdk
From playlist iLecturesOnline: Probability & Stats 3: Markov Chains & Stochastic Processes
Abstract Algebra | The dihedral group
We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
On Crossing Probabilities in Critical Random-Cluster Models - Eveliina Peltola
Probability Seminar Topic: On Crossing Probabilities in Critical Random-Cluster Models Speaker: Eveliina Peltola Affiliation: University of Bonn Date: February 10, 2023 I will discuss exact solvability results (in a sense) for scaling limits of interface crossings in critical random-clus
From playlist Mathematics
Multivariate Gaussian distributions
Properties of the multivariate Gaussian probability distribution
From playlist cs273a
Coalescence of geodesics and the BKS midpoint problem in planar first-passage percolation- Ron Peled
Probability Seminar Topic: Coalescence of geodesics and the BKS midpoint problem in planar first-passage percolation Speaker: Ron Peled 11:15am|Simonyi 101 and Remote Access Date: September 30, 2022 First-passage percolation studies the geometry obtained from a random perturbation of Euc
From playlist Mathematics
Anter El-Azab: Mesoscale crystal plasticity based on continuum dislocation dynamics
Anter El-Azab: Mesoscale crystal plasticity based on continuum dislocation dynamics: mathematical formalism and numerical solution The lecture was held within the framework of the Hausdorff Trimester Program Multiscale Problems: Workshop on Non-local Material Models and Concurrent Multisc
From playlist HIM Lectures: Trimester Program "Multiscale Problems"
Courses - R. SUN "Brownian web, Brownian net, and their universality"
The Brownian web is the collection of one-dimensional coalescing Brownian motions starting from every point in space-time. Originally conceived by Arratia in the context of the one-dimensional voter model and its dual coalescing random walks, the Brownian web has since been shown to arise
From playlist T1-2015 : Disordered systems, random spatial processes and some applications
Busemann Functions in Random Growth and Polymer Models by Timo Seppäläinen
PROGRAM FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS: Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE: 11 July 2022 to 29 July 2022 VENUE: Ramanujan Lecture Hall and online This
From playlist First-Passage Percolation and Related Models 2022 Edited
Steffen Borgwardt: The role of partition polytopes in data analysis
The field of optimization, and polyhedral theory in particular, provides a powerful point of view on common tasks in data analysis. In this talk, we highlight the role of the so-called partition polytopes and their studies in clustering and classification. The geometric properties of parti
From playlist Workshop: Tropical geometry and the geometry of linear programming
Eveliina Peltola - On crossing probabilities in critical random-cluster models
I will discuss exact solvability results (in a sense) for scaling limits of interface crossings in critical random-cluster models in the plane with various boundary conditions. The results are rigorous for the FK-Ising model, Bernoulli percolation, and the spin-Ising model in appropriate s
From playlist 100…(102!) Years of the Ising Model
Noise Sensitivity and Chaos in Random Planar Geometry by Shirshendu Ganguly
PROGRAM : FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS : Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE : 11 July 2022 to 29 July 2022 VENUE : Ramanujan Lecture Hall and online T
From playlist First-Passage Percolation and Related Models 2022 Edited
Algorithms you Need for Deep Learning: Stochastic Gradient Updates for Logistic Regression
Guest: https://hhexiy.github.io/ This is a single lecture from a course. If you you like the material and want more context (e.g., the lectures that came before), check out the whole course: https://go.umd.edu/jbg-inst-808 (Including homeworks and reading.) Music: https://soundcloud.co
From playlist Deep Learning for Information Scientists
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Blume-Capel and the Tricritical Point - Trishen Gunaratnam
Analysis and Mathematical Physics Topic: Blume-Capel and the Tricritical Point Speaker: Trishen Gunaratnam Affiliation: University of Geneva Date: February 22, 2023 This talk will be about a ferromagnetic spin system called the Blume-Capel model. It was introduced in the '60s to model a
From playlist Mathematics
Firas Rassoul-Agha: "Geometry of Last Passage Percolation"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop IV: Stochastic Analysis Related to Hamilton-Jacobi PDEs "Geometry of Last Passage Percolation" Firas Rassoul-Agha - University of Utah Abstract: We consider planar directed last-passage percolation on the square lattice with general i.i
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
Gourab Ray : Universality of fluctuations of the dimer model
Recording during the thematic meeting : "Pre-School on Combinatorics and Interactions" the January 13, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Combinatorics
AlgTopReview4: Free abelian groups and non-commutative groups
Free abelian groups play an important role in algebraic topology. These are groups modelled on the additive group of integers Z, and their theory is analogous to the theory of vector spaces. We state the Fundamental Theorem of Finitely Generated Commutative Groups, which says that any such
From playlist Algebraic Topology