Tag Archives: Mathematics

Evolutionary Game Theory

July 31, 2012Article6107 vuesEdit
Evolutionary Game Theory is a relatively recent branch of game theory which studies the dynamics of games. Originally used to describe populations of species in biology, and more particularly, the consequences of their interactions to the evolution of their populations, this field now produces interesting results for economic and environmental modelings.

P versus NP: A Crucial Open Problem

June 28, 2012Article7312 vuesEdit
P=NP is probably today's most crucial open problem. Not only is it a very theoretical question in computer science and mathematics, but it also has major implications to real world. Its resolution could revolutionize the world. This article gives the definition and major results of P=NP.

From Divide and Conquer to Parallelization

June 26, 2012Article1744 vuesEdit
Divide and conquer is a extremely powerful concept that is being used a lot in computer science, and that can also be applied in real life. We present its application to sorting algorithms. Then we'll talk about a major fundamental open mathematical problem, called P=NC.

Duality in Linear Programming

June 23, 2012Article22533 vuesEdit
Duality in linear programming yields plenty of amazing results that help understand and improve algorithms of resolution. This article shows the construction of the dual and its interpretation, as well as major results. In particular, matching of primal and dual bases will be dealt, before presenting the issue of degeneracy and its dual interpretation.

Primal and Dual Simplex Methods

June 23, 2012Article26456 vuesEdit
The simplex method is one of the major algorithm of the 20th century, as it enables the resolution of linear problems with millions of variables. An intuitive approach is given. But that's not all. We present an important variant called the dual simplex. Finally, we'll explain its main default, that is, when facing degeneracy.

Dual Variable Stabilization

June 22, 2012Article899 vuesEdit
Simplex methods face issues in case of degeneracy. The dual variable stabilization is a very recent state-of-the-art way to deal with degeneracy. An intuitive understanding is given in this article.

Marriage Assignment Problem and Variants

June 03, 2012Article7208 vuesEdit
Marriage problems consist in matching boys and girls. They are a very interesting class of problems that include assignment problems, which have a very large range of applications. Additional results have been found for variants which include the introduction of boys and girls' preferences, and cases where people cannot be categorized into two groups.

Optimization by Linear Programming

May 23, 2012Article7851 vuesEdit
Operations Research deals with optimizing industrial systems. Those systems can be very complex and their modeling may require the use of hundreds, thousands or even millions of variables. Optimizing over millions of variables may seem impossible, but it can be done if the optimization problem has a linear structure. Learn more on this linear structure and optimization solutions!

From Britain’s coast to Julia set: an introduction to fractals

May 20, 2012Article4772 vuesEdit
Introduction I could have started this article by showing you beautiful examples of fractals, found in nature or invented by mathematicians, in two or three dimensions, constructed deterministically or not. But I won’t. In fact, you wouldn’t need to read this article to find such examples. I’d rather start by telling you a story. It […]

Mechanism Design and the Revelation Principle

April 19, 2012Article7173 vuesEdit
Whenever you need to make a group of people interact, you are designing a mechanism. If you want to achieve a good interaction, you need to make sure your mechanism is well designed. In this article, I'll show you main features of mechanisms through various examples. I'll also talk about a great mathematical tool for mechanism design: the revelation principle.

Fair Division and Cake-Cutting

April 10, 2012Article6305 vuesEdit
Cutting a cake to satisfy everyone is no piece of cake! In the article, we focus on classical definitions of fair divisions. I'll criticize those definitions and conclude by extrapolating them to fairness in society.