William Thurston was an influential American mathematician, renowned for his work in topology, particularly in the field of three-dimensional manifolds. Born on October 30, 1946, and passing away on August 21, 2022, he made significant contributions to the understanding of the structure of 3-manifolds through his groundbreaking ideas and theories.

Word-sense disambiguation (WSD) is a natural language processing (NLP) task that aims to determine which meaning of a word is used in a given context. Many words in the English language (and other languages) have multiple meanings, known as "senses." For instance, the word "bank" can refer to a financial institution or the side of a river, among other meanings.

A working hypothesis is a preliminary assumption or educated guess that serves as a starting point for further investigation or research. It is not a definitive conclusion but rather a proposed explanation that researchers use to guide their study and experiments. Working hypotheses can be adjusted or refined as new data is gathered and as understanding of the topic deepens. In scientific research, a working hypothesis might lead to the formulation of testable predictions and experiments to validate or refute it.

The term "scrambler" can refer to different things depending on the context. Here are a few common interpretations: 1. **Telecommunication Scrambler**: In telecommunications, a scrambler is a device or technology that alters the transmission of signals to enhance security and privacy. It modifies the signal so that it cannot be easily understood by unauthorized listeners. Scrambling is often used in secure phone communications and broadcasting, where the objective is to prevent eavesdropping.

An affine space is a geometric structure that generalizes the idea of a vector space by allowing translation without a fixed origin. It can be thought of as a set of points along with a vector space that describes how to move from one point to another. Here are some key features and concepts related to affine spaces: 1. **Points and Vectors**: In an affine space, there are two distinct types of entities: points and vectors.

The Big M method is a technique used in linear programming, particularly in the context of the Simplex algorithm, to handle problems involving artificial variables and constraints. It is useful when formulating linear programs that include constraints which cannot be easily satisfied by the original feasible region or that are not straightforward to convert into standard forms.

PathoPhenoDB is a specialized database designed to facilitate the study and analysis of phenotypes associated with various pathogenic conditions. It typically aggregates and curates information regarding genetic variants, phenotypic traits, and their relationships to diseases, allowing researchers and clinicians to explore the genetic underpinnings of various disorders. The database may include detailed entries on specific diseases, related genetic information, patient records (in anonymized forms), and data derived from clinical studies and literature.

The conjugate transpose (also known as the Hermitian transpose) of a matrix is an operation that involves two steps: 1. **Transpose**: First, you transpose the matrix, which means you swap its rows and columns. For example, if you have a matrix \( A \) with elements \( a_{ij} \), its transpose \( A^T \) will have elements \( a_{ji} \).