The Maximum Agreement Subtree (MAST) problem is a computational problem in the field of comparative genomics and bioinformatics. It involves identifying a subtree that is common to multiple phylogenetic trees (or evolutionary trees) that represent the relationships between a given set of species or taxa. Specifically, the goal is to find a subtree that maximizes the number of leaves (species) that are consistent across the input trees.

Quadratic pseudo-Boolean optimization refers to the optimization of a specific type of mathematical function known as a quadratic pseudo-Boolean function. These functions are special cases of polynomial functions and are defined over binary variables (typically taking values of 0 or 1).

The Set Traveling Salesman Problem (Set TSP) is a variant of the classic Traveling Salesman Problem (TSP), which is a well-known problem in combinatorial optimization. In the standard TSP, a salesman is required to visit a set of cities exactly once and return to the starting point while minimizing the total distance traveled.

A star system, often referred to as a stellar system, is a group of celestial bodies that are gravitationally bound to a central star. The most recognizable type of star system is a solar system, which includes a star (or multiple stars in the case of binary or multiple star systems) and various objects such as planets, moons, asteroids, comets, and meteoroids that orbit the star.

Bifurcation theory, a branch of mathematics and dynamical systems, studies how the qualitative or topological structure of a given system changes as parameters vary. This theory has several biological applications across various fields. Here are some notable ones: 1. **Population Dynamics**: Bifurcation theory is often used to model changes in population dynamics of species in ecological systems.

The Bogdanov–Takens bifurcation is a significant phenomenon in the study of dynamical systems, particularly in the context of the behavior of nonlinear systems. It describes a scenario in which a system undergoes a bifurcation, leading to the simultaneous occurrence of a transcritical bifurcation (where the stability of fixed points is exchanged) and a Hopf bifurcation (where a fixed point becomes unstable and bifurcates into a periodic orbit).

Pitchfork bifurcation is a type of bifurcation that occurs in dynamical systems, particularly in the study of nonlinear systems. It describes a situation where a system's stable equilibrium point becomes unstable and gives rise to two new stable equilibrium points as a parameter is varied. In more technical terms, a pitchfork bifurcation typically occurs in systems described by equations where the steady-state solutions undergo a change in stability.

The Horseshoe map is a well-known example of a one-dimensional dynamical system that exhibits chaotic behavior. It is a type of chaotic map that is used in the study of chaos theory and nonlinear dynamics. The Horseshoe map illustrates how simple deterministic systems can exhibit complex, unpredictable behavior. ### Definition The Horseshoe map can be defined on the unit interval \( [0, 1] \) and involves a transformation that stretches and folds the interval to create a "horseshoe" shape.

The Hénon–Heiles system is a classic model in dynamical systems and astrophysics that describes the motion of a particle in a two-dimensional potential well. This system is specifically notable for its chaotic behavior and is often used as a prototypical example of non-integrable Hamiltonian systems.

The Lorenz system is a set of three nonlinear ordinary differential equations originally studied by mathematician and meteorologist Edward Lorenz in 1963. It is famous for its chaotic solutions, which exhibit sensitive dependence on initial conditions—an essential feature of chaotic systems, often referred to as the "butterfly effect." The Lorenz system is defined by the following equations: 1. \(\frac{dx}{dt} = \sigma (y - x)\) 2.

A solid angle is a measure of how large an object appears to an observer from a particular point of view, and it indicates the two-dimensional angle in three-dimensional space. Solid angles are measured in steradians (sr), where one steradian corresponds to the solid angle subtended at the center of a sphere by an area on its surface equal to the square of the sphere's radius.

Warren B. Mori is a prominent physicist known for his significant contributions to the field of plasma physics and computational science. He is particularly noted for his work on advanced simulation techniques, including the development of particle-in-cell (PIC) methods, which are widely used in modeling plasma behavior and interactions. Mori's research has implications in various areas, including astrophysics, fusion energy, and laser-plasma interactions. In addition to his research, Warren B.

Homology theory is a branch of algebraic topology that studies topological spaces through the use of algebraic structures, primarily by associating a sequence of abelian groups or modules, called homology groups, to a topological space. These groups encapsulate information about the space's shape, connectivity, and higher-dimensional features.

Knot theory is a branch of mathematics that studies mathematical knots, which are loops in three-dimensional space that do not intersect themselves. It is a part of the field of topology, specifically dealing with the properties of these loops that remain unchanged through continuous deformations, such as stretching, twisting, and bending, but not cutting or gluing. In knot theory, a "knot" is defined as an embedded circle in three-dimensional Euclidean space \( \mathbb{R}^3 \).

An **Abelian 2-group** is a specific type of group in the field of abstract algebra. Let’s break down the main characteristics: 1. **Group**: A set equipped with a binary operation that satisfies four fundamental properties: closure, associativity, the existence of an identity element, and the existence of inverses.