Karthik C. S.: Recent Hardness of Approximation results in Parameterized Complexity
In this talk, we survey some recent hardness of approximation results in parameterized complexity such as the inapproximability of the k-clique problem, provide some technical insights, and also highlight some open problems.
From playlist Workshop: Parametrized complexity and discrete optimization
Clément Maria (10/23/19): Parameterized complexity of quantum invariants of knots
Title: Parameterized complexity of quantum invariants of knots Abstract: We give a general fixed parameter tractable algorithm to compute quantum invariants of knots presented by diagrams, whose complexity is singly exponential in the carving-width (or the tree-width) of the knot diagram.
From playlist AATRN 2019
Shmuel Onn: Sparse integer programming is FPT
We show that sparse integer programming, in variable dimension, with linear or separable convex objective, is fixed-parameter tractable. This is a culmination of a long line of research with many colleagues. We also discuss some of the many consequences of this result, which provides a new
From playlist Workshop: Tropical geometry and the geometry of linear programming
The chaotic complexity of natural numbers | Data structures in Mathematics Math Foundations 175
This is a sobering and perhaps disorienting introduction to the fact that arithmetic with bigger numbers starts to look quite different from the familiar arithmetic that we do with the small numbers we are used to. The notion of complexity is key in our treatment of this. We talk about bot
From playlist Math Foundations
Hans Bodlaender: Parameterized Problems Complete for Nondeterministic FPT time and Logarithmic Space
Let XNLP be the class of parameterized problems such that an instance of size n with parameter k can be solved nondeterministically in time f(k)n to the power of O(1) and space f(k) log(n) (for some computable function f). We give a wide variety of XNLP-complete problems, such as List Colo
From playlist Workshop: Parametrized complexity and discrete optimization
Concentration of tempered posteriors and of their variational approximations – Pierre Alquier
Many problems in science and engineering involve an underlying unknown complex process that depends on a large number of parameters. The goal in many applications is to reconstruct, or learn, the unknown process given some direct or indirect observations. Mathematically, such a problem can
From playlist Approximating high dimensional functions
Complex Analysis Episode 14: Parameterizations
Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, but it will help to support my channel. Thank you! Complex Analysis Textbook https://amzn.to/2u5fgl4 (affiliate
From playlist Complex Analysis
Wojciech Chachólski (4/29/20): TDA invariants and model categories
Title: TDA invariants and model categories Abstract: Data analysis is a balancing act of simplification and ignoring most of the information available on the one hand, and retaining what might be meaningful for the particular task on the other. The same balancing act of extracting simplif
From playlist AATRN 2020
Multilevel weighted least squares polynomial approximation – Sören Wolfers, KAUST
Many problems in science and engineering involve an underlying unknown complex process that depends on a large number of parameters. The goal in many applications is to reconstruct, or learn, the unknown process given some direct or indirect observations. Mathematically, such a problem can
From playlist Approximating high dimensional functions
Michael Farber (2/24/22): Topological complexity of spherical bundles
I will start by describing the concept of a parametrized motion planning algorithm which allows to achieve high degree of flexibility and universality. The main part of the talk will focus on the problem of understanding the parametrized topological complexity of sphere bundles. I will exp
From playlist Topological Complexity Seminar
Daniel Kral: Parametrized approach to block structured integer programs
Integer programming is one of the most fundamental problems in discrete optimization. While integer programming is computationally hard in general, there exist efficient algorithms for special instances. In particular, integer programming is fixed parameter tractable when parameterized by
From playlist Workshop: Parametrized complexity and discrete optimization
Complex Numbers and Addition Formulas | Algebraic Calculus One | Wild Egg
Circle geometry and related formulas in calculus are closely connected to the algebra of complex numbers. In particular the all-important rational parametrization of the unit circle has a beautiful interpretation in terms of a quadrance normalization of a square, which gives the natural as
From playlist Old Algebraic Calculus Videos
Barbara Giunti (5/6/2020): Invariants for tame parametrised chain complexes
Title: Invariants for tame parametrised chain complexes Abstract: Along the lines traced by Wojciech Chachólski in the previous talk, we will see that model structures for persistent chain complexes lead to constructions of new and old invariants. In my talk, I will illustrate the usefuln
From playlist AATRN 2020
Michael Farber (7/28/22): Algorithms for automated decision making and topology
Abstract: I will describe topological problems relevant to the task of creating algorithms for automated decision making. My main focus will be on motion planning algorithms in robotics although our mathematical tools are applicable to many other situations.
From playlist Applied Geometry for Data Sciences 2022
Michal Pilipczuk: Introduction to parameterized algorithms, lecture I
The mini-course will provide a gentle introduction to the area of parameterized complexity, with a particular focus on methods connected to (integer) linear programming. We will start with basic techniques for the design of parameterized algorithms, such as branching, color coding, kerneli
From playlist Summer School on modern directions in discrete optimization
Parametrizing Curves in the Complex Plane 1
Complex Analysis: We give a recipe for parametrizing curves in the complex plane. Line segments are the focus of Part 1.
From playlist Complex Analysis
Saket Saurabh: Parametrized Algorithms and possible future directions
In this talk, we will give a short overview of current research directions pursued in Parameterized Complexity and then outline a few potential research directions for further investigations.
From playlist Workshop: Parametrized complexity and discrete optimization
Parametrizing Curves in the Complex Plane 2
Complex Analysis: We give a recipe for parametrizing curves in the complex plane. In this part, we parametrize circles and semicircles.
From playlist Complex Analysis