A quasi-homogeneous polynomial is a type of polynomial that exhibits a certain kind of symmetry in terms of its variable degrees. Specifically, a polynomial \( f(x_1, x_2, \ldots, x_n) \) is called quasi-homogeneous of degree \( d \) if it can be expressed as a sum of terms, each of which has the same "weighted degree".

Stanley decomposition is a concept related to combinatorial geometry and enumerative combinatorics, specifically in the context of polyhedral combinatorics. It is named after Richard P. Stanley, a prominent mathematician who has made significant contributions to these fields. The Stanley decomposition provides a way to express a polyhedron, especially a convex polytope, as a combination of combinatorial objects, typically through the use of face lattices.

In algebraic geometry and commutative algebra, a Weierstrass ring is a type of local ring that can be used to study singularities of algebraic varieties. More specifically, it is a particular kind of ring that arises in the context of the Weierstrass preparation theorem. A Weierstrass ring is defined as follows: 1. **Local Ring**: It is a local ring, which means it has a unique maximal ideal.

Group theory is a branch of mathematics that studies algebraic structures known as groups. A group is defined as a set equipped with a single binary operation that satisfies four fundamental properties: 1. **Closure**: If \( a \) and \( b \) are elements of the group, then the result of the operation \( a * b \) is also in the group.

The Price of Anarchy (PoA) is a concept from game theory, particularly in the context of auctions and other competitive scenarios. It measures how the efficiency of a given outcome in a strategic game (where players act out of self-interest) compares to the optimal outcome that could be achieved if all players acted in a cooperative manner.

Win rate is a metric commonly used in various fields such as gaming, sports, finance, and business to quantify the percentage of wins relative to the total number of attempts or events.

Barga Jazz is an annual jazz festival that takes place in the town of Barga, located in the Tuscany region of Italy. This festival is known for its picturesque setting and its celebration of jazz music, attracting both local and international artists. It typically features a variety of performances, including concerts, jam sessions, and workshops, catering to jazz enthusiasts and musicians of all levels.

Derek Barton was a notable British chemist, best known for his work in the field of organic chemistry and his contributions to the understanding of molecular conformations and stereochemistry. Born on September 8, 1918, Barton made significant advancements in the study of conformational analysis, particularly with the introduction of the concept of "conformational energy," which helped explain how the three-dimensional shape of molecules affects their chemical behavior.

Game artificial intelligence (AI) refers to the techniques and methods used to create responsive, adaptive, and intelligent behavior in non-player characters (NPCs) or game elements within video games. The primary goal of game AI is to enhance the player experience by making the game world more immersive, challenging, and engaging. Here are some key aspects of game AI: 1. **Pathfinding:** - Game AI often involves pathfinding algorithms that help characters navigate the game world efficiently.

Organizations related to game theory typically focus on the study and application of strategic interactions among rational decision-makers. These organizations may be academic institutions, research centers, think tanks, or professional associations that emphasize the theoretical underpinnings and practical applications of game theory in various fields, such as economics, political science, biology, and computer science. Here are some examples: 1. **Academic Institutions**: Many universities have departments or programs in economics, mathematics, or political science that focus on game theory.