In algorithmic information theory, sophistication is a measure of complexity related to algorithmic entropy. When K is the Kolmogorov complexity and c is a constant, the sophistication of x can be defined as The constant c is called significance. The S variable ranges over finite sets. Intuitively, sophistication measures the complexity of a set of which the object is a "generic" member. (Wikipedia).
Complexity Theory, Quantified Boolean Formula
Theory of Computation 15. Complexity Theory, Quantified Boolean Formula ADUni
From playlist [Shai Simonson]Theory of Computation
Simple groups, Lie groups, and the search for symmetry I | Math History | NJ Wildberger
During the 19th century, group theory shifted from its origins in number theory and the theory of equations to describing symmetry in geometry. In this video we talk about the history of the search for simple groups, the role of symmetry in tesselations, both Euclidean, spherical and hyper
From playlist MathHistory: A course in the History of Mathematics
Clojure Conj 2012 - Whence Complexity?
Whence Complexity? by: Michael Nygard Quantum Mechanics and General Relativity don't agree on much, but both claim that every physical process is perfectly reversible. The Second Law of Themodynamics says, "Not likely!" The Second Law may win in the long run, but today, at (nearly) every
From playlist Clojure Conf 2012
The Complexity of Distributions - Emanuele Viola
Emanuele Viola Northeastern University March 5, 2012 Complexity theory, with some notable exceptions, typically studies the complexity of computing a function h(x) of a *given* input x. We advocate the study of the complexity of generating -- or sampling -- the output distribution h(x) for
From playlist Mathematics
Simple groups, Lie groups, and the search for symmetry II | Math History | NJ Wildberger
This is the second video in this lecture on simple groups, Lie groups and manifestations of symmetry. During the 19th century, the role of groups shifted from its origin in number theory and the theory of equations to its role in describing symmetry in geometry. In this video we talk abou
From playlist MathHistory: A course in the History of Mathematics
What are complex numbers? | Essence of complex analysis #2
A complete guide to the basics of complex numbers. Feel free to pause and catch a breath if you feel like it - it's meant to be a crash course! Complex numbers are useful in basically all sorts of applications, because even in the real world, making things complex sometimes, oxymoronicall
From playlist Essence of complex analysis
Results and open problems in theory of quantum complexity - Anindya De
Andris Ambainis University of Latvia; Member, School of Mathematics April 22, 2014 I will survey recent results and open problems in several areas of quantum complexity theory, with emphasis on open problems which can be phrased in terms of classical complexity theory or mathematics but ha
From playlist Mathematics
What We've Learned from NKS Chapter 12: The Principle of Computational Equivalence [Part 1]
In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th
From playlist Science and Research Livestreams
Mathematical modeling of evolving systems
Discover the multidisciplinary nature of the dynamical principles at the core of complexity science. COURSE NUMBER: CAS 522 COURSE TITLE: Dynamical Systems LEVEL: Graduate SCHOOL: School of Complex Adaptive Systems INSTRUCTOR: Enrico Borriello MODE: Online SEMESTER: Fall 2021 SESSION:
From playlist What is complex systems science?
Why Mathematicians are Essential for National Security
Oxford Sedleian Professor of Natural Philosophy Jon Keating discusses his research in Quantum Theory and his work with GCHQ – the UK intelligence agency. Jon starts by discussing his current work on random matrices and how they are linked to Quantum Theory, as well as Number Theory via t
From playlist Interviews
Structure vs Randomness in Complexity Theory - Rahul Santhanam
Computer Science/Discrete Mathematics Seminar I Topic: Structure vs Randomness in Complexity Theory Speaker: Rahul Santhanam Affiliation: University of Oxford Date: April 20, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Upscaling and Automation: New Opportunities for Multiscale Systems Modeling
SIAM Geosciences Webinar Series Date and Time: Wednesday, March 8, 2023, 12:00pm Eastern time zone Speaker: Ilenia Battiato, Stanford University Abstract: The accurate modeling of energy and geologic systems has challenged generations of computational physicists due to the mathematical an
From playlist SIAM Geosciences Webinar Series
Some recent developments in Kähler geometry and exceptional holonomy – Simon Donaldson – ICM2018
Plenary Lecture 1 Some recent developments in Kähler geometry and exceptional holonomy Simon Donaldson Abstract: This article is a broad-brush survey of two areas in differential geometry. While these two areas are not usually put side-by-side in this way, there are several reasons for d
From playlist Plenary Lectures
Paul Root Wolpe: Kurzweil's Singularity Prediction is Wrong (YouTube Geek Week!) | Big Think
Paul Root Wolpe: Kurzweil's Singularity Prediction is Wrong (YouTube Geek Week!) Watch the newest video from Big Think: https://bigth.ink/NewVideo Join Big Think Edge for exclusive videos: https://bigth.ink/Edge ------------------------------------------------------------------------------
From playlist The future: artificial intelligence | Big Think
Nikita Nekrasov - Non-perturbative Dyson-Schwinger equations...
Nikita NEKRASOV (Simons Center for Geometry and Physics, Stony Brook, USA)
From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur
Primes, Complexity and Computation: How Big Number theory resolves the Goldbach Conjecture
This lecture, which begins at 2:45, shows how Big Number theory, together with an understanding of prime numbers and their distribution resolves the Goldbach Conjecture, which states that every even number greater than two is the sum of two primes. Notions of complexity and computation,
From playlist MathSeminars
Ep 1: Stanford PhD student Joseph Bakarji on Machine Learning and the Hard Sciences
Broadcasted live on Twitch -- Watch live at https://www.twitch.tv/formalsystem
From playlist Interviews
Said Hamoun (2/23/23): On the rational topological complexity of coformal elliptic spaces
We establish some upper and lower bounds of the rational topological complexity for certain classes of elliptic spaces. Our techniques permit us in particular to show that the rational topological complexity coincides with the dimension of the rational homotopy for some special families of
From playlist Topological Complexity Seminar
Rob Moore Public Lecture: Building a Future From the Atoms Up
In his Apr. 4 public lecture at Perimeter Institute, Rob Moore (Assistant Director of the Stanford Institute for Materials and Energy Sciences) explored how the next great “age” of humankind may well be forged in this new quantum world of materials. Perimeter Institute (charitable registr
From playlist Public Lecture Series