Hylogenesis is a term that is not widely used in mainstream biology, so its meaning can vary depending on the context in which it is used. Generally, it can be understood as a concept related to the evolutionary development of organisms or the origin and diversification of biological forms based on their lineage and evolutionary history.

Light dark matter refers to a class of hypothetical dark matter candidates that have a relatively low mass compared to traditional dark matter models like Weakly Interacting Massive Particles (WIMPs). While WIMPs are typically on the scale of hundreds of GeV (giga-electronvolts), light dark matter candidates can have masses that are much smaller, often in the range of a few MeV (mega-electronvolts) to a few GeV.

The Axiom of Determinacy (AD) is a principle in set theory that relates to the behavior of certain games and the existence of winning strategies in those games. More specifically, the Axiom of Determinacy posits that for certain kinds of infinite games involving two players, one player can always have a winning strategy.

Primordial black holes (PBHs) are hypothetical black holes that may have formed soon after the Big Bang, during the early universe. Unlike stellar black holes, which form from the gravitational collapse of massive stars at the end of their life cycles, primordial black holes are thought to have formed from density fluctuations in the very early universe.

A DNA microarray, also known as a gene chip or DNA chip, is a powerful tool used in molecular biology and genetics for the simultaneous analysis of thousands of genes. It consists of a small solid surface—typically a glass slide or a silicon chip—that has been populated with numerous DNA probes. Each probe is a short, single-stranded nucleic acid that is complementary to a specific DNA sequence corresponding to a gene of interest.

The Runge-Gross theorem is a fundamental result in the field of many-body quantum mechanics, specifically in the context of time-dependent density functional theory (TDDFT). It establishes a mathematical connection between the time-dependent electron density of a system and the external potential acting on it.

The Banach-Mazur game is a two-player game in the field of set theory and topology, particularly in the context of functional analysis. It is named after mathematicians Stefan Banach and Juliusz Mazur, who introduced the game in the early 20th century. ### Rules of the Game: 1. **Players**: There are two players, typically called Player I and Player II.

A Homogeneously Suslin set refers to a specific type of subset of a Polish space (a separable completely metrizable topological space), particularly in the context of descriptive set theory. The notion is related to the concepts of Suslin sets and the general theory of analytic sets. A subset of a Polish space is called a Suslin set if it can be obtained from Borel sets through a continuous image or by countable unions and intersections.

Differential algebraic geometry is a field of mathematics that combines concepts from differential geometry and algebraic geometry. Specifically, it studies sets of algebraic equations and inequalities that define geometric objects and incorporates differentiability conditions. Here are some of the key components and concepts related to differential algebraic geometry: 1. **Algebraic Geometry**: This branch of mathematics focuses on the study of geometric properties of solutions to polynomial equations.

A Differential Graded Lie Algebra (DGLA) is a mathematical structure that is a generalized form of a Lie algebra. It combines the properties of a Lie algebra with those of a graded vector space and a differential operator.

Macintosh operating systems, commonly referred to as macOS, are a series of graphical operating systems developed by Apple Inc. for their Macintosh line of computers. The first version, called System Software, was released in 1984, and subsequent versions have evolved significantly over the years. **Key Features of macOS:** 1. **User Interface**: macOS is known for its user-friendly graphical interface, featuring a desktop, icons, and a menu bar, allowing for intuitive navigation.

"Digitality" is a term that often refers to the condition or state of being digital, typically encompassing the ways in which digital technologies influence society, culture, and individuals. It captures the essence of living in a world increasingly mediated by digital technologies, including the internet, social media, and various digital platforms. Key aspects of digitality include: 1. **Interconnectivity**: The ability to connect and communicate through digital means, leading to global networks of interaction.

"Software wars" generally refers to the competitive landscape and conflicts among software companies, technologies, or platforms in various sectors of the tech industry. This term can apply to several contexts: 1. **Operating Systems**: The competition between major operating systems like Microsoft Windows, macOS, and various distributions of Linux can be described as software wars, as each system strives for market dominance and user preference. 2. **Application Software**: Various applications compete for user attention and market share.

Birch's theorem, also known as the Birch and Swinnerton-Dyer conjecture, is a famous conjecture in number theory related to elliptic curves. It posits a deep relationship between the number of rational points on an elliptic curve and the behavior of an associated L-function.

The discrepancy of hypergraphs is a concept in combinatorial mathematics that deals with how evenly one can color or distribute a set of points (or elements) among different subsets (or hyperedges) of a hypergraph. More formally, it is concerned with the maximum imbalance that can arise when assigning colors, typically two colors, to the vertices of the hypergraph with respect to the hyperedges.