Goal programming is a branch of multi-criteria decision-making and optimization that involves finding solutions to problems that have multiple, often conflicting objectives. It extends linear programming by allowing decision-makers to prioritize and balance those competing goals rather than focusing on a single objective. ### Key Features of Goal Programming: 1. **Multiple Goals**: Unlike traditional linear programming, which typically optimizes a single objective function, goal programming allows for the consideration of several goals simultaneously.

In the context of network theory and graph theory, the **average path length** is a metric that measures the average number of steps (or edges) along the shortest paths for all possible pairs of nodes (vertices) in a graph. It provides an indication of how "far apart" nodes are on average, which can help characterize the structure and efficiency of the network.

Community search refers to various methods or approaches used to identify, engage, and leverage communities based on shared interests, characteristics, or needs. This concept is used in different contexts, such as social media, data analysis, marketing, and more. Here are a few key applications of community search: 1. **Social Media and Online Forums**: In social media platforms and online communities, community search helps users find groups or individuals with similar interests or hobbies.

Degree distribution is a fundamental concept in network theory and graph theory, describing the distribution of the degrees (the number of connections) of the nodes (vertices) in a graph. In simpler terms, degree distribution provides insights into how many links each node in a network has. Here's a brief overview of key aspects related to degree distribution: 1. **Degree of a Node**: The degree of a node is the number of edges that connect to it.

An **evolving network** generally refers to a type of network that changes over time, where nodes (such as individuals, organizations, or systems) can join or leave the network, and the connections (or edges) between them can also change. Evolving networks are an important area of study in network theory, complex systems, and various fields such as sociology, biology, and computer science.

The Human Disease Network is a conceptual and analytical framework used to understand the complex relationships between various human diseases, their genetic underpinnings, and the biological pathways involved. It is often represented as a network in which nodes correspond to diseases and edges represent various types of relationships, such as shared genes, biological pathways, or clinical features.

Gephi is an open-source software platform designed for network visualization and analysis. It is widely used by researchers, data scientists, and analysts to explore and understand complex data structures represented as networks or graphs. Gephi allows users to visualize relationships and patterns in data through interactive graphical representations. Key features of Gephi include: 1. **Visualization**: Users can create and manipulate various types of graphs, including static and dynamic visualizations, which help in identifying trends, clusters, and anomalies.

Link-centric preferential attachment is a concept that arises in the context of network theory and complex systems, particularly in the study of how networks grow and evolve. It builds on the foundational idea of preferential attachment, which was introduced by the Barabási-Albert (BA) model for network growth. ### Definitions: 1. **Preferential Attachment:** This principle suggests that new nodes in a network are more likely to connect to existing nodes that already have a high degree (i.e., many connections).

Network Description Language (NDL) is a formal language used to describe the topology and configuration of networked systems. It provides a structured way to represent various aspects of networks, including nodes (such as routers, switches, servers) and their interconnections (links). NDL is often employed in network modeling and simulation, allowing for the specification of network characteristics, protocols, and behaviors in a way that can be processed by software tools.

Non-linear preferential attachment is a concept that extends the idea of preferential attachment in network theory. Preferential attachment is a mechanism often used to explain the formation and growth of complex networks, such as social networks, the World Wide Web, or citation networks. The basic principle of preferential attachment is that nodes (or vertices) in a network have a probability of attracting new connections proportional to their current degree (number of connections). This results in some nodes becoming "hubs" that accumulate many connections over time.

A sparse network typically refers to a type of network in which the connections or edges between nodes (or vertices) are limited in number compared to the total possible connections. In other words, most nodes in the network have relatively few connections. This concept can be applied to various fields such as computer science, graph theory, telecommunications, and social network analysis. ### Characteristics of Sparse Networks: 1. **Low Edge Density**: The ratio of the number of edges to the maximum number of edges is low.

Ginestra Bianconi, also known as Ginestra, is a plant from the family of the leguminous plants (Fabaceae). Its scientific name is *Genista* or *Cytisus* depending on the classification. It's commonly known as "broom" due to its characteristic bushy appearance and yellow flowers. Ginestra species are native to various regions, primarily in Europe and the Mediterranean.

Greg Moore is a theoretical physicist known for his work in the fields of string theory and mathematical physics. He is a professor at Rutgers University and has made significant contributions to our understanding of various aspects of string theory, including the study of dualities, topological field theories, and the relationship between physics and mathematics. Moore has been involved in research that explores the connections between string theory and other areas of physics, as well as the implications for our understanding of fundamental forces in the universe.

Jean-Pierre Eckmann is a Swiss physicist and mathematician known for his contributions to various fields, including statistical physics, nonlinear dynamics, and complex systems. He has also been involved in research related to the mathematics of networks and chaos. Additionally, Eckmann has engaged in interdisciplinary studies that bridge the gap between mathematics and computational sciences.

Hilbrand J. Groenewold is a Dutch physicist known for his contributions to the field of theoretical physics, particularly in statistical mechanics and quantum theory. He is well known for the Groenewold theorem, which relates to the foundations of quantum mechanics and has implications in the study of quantum observables and their measurements. His work has also involved the development of techniques in the field of quantum statistical mechanics.

Huzihiro Araki appears to be a misspelling or an incorrect reference. There might be a misunderstanding or confusion with "Hiroshi Araki," a common name, or perhaps "Hajime Araki," who might be associated with a particular field like literature, art, or a specific cultural context.

Jacob Biamonte is a name that may refer to different individuals. One well-known Jacob Biamonte is a mathematician known for his work in the fields of algebra, operator theory, and their applications. He has made contributions to areas such as quantum probability and information theory.

Krzysztof Gawedzki is a notable figure in the field of theoretical physics, particularly known for his work in mathematical physics and quantum field theory. His research often focuses on topics such as gauge theories, topological field theories, and the mathematical foundations of quantum mechanics. Gawedzki has also contributed to the study of exact results in quantum field theory and string theory, exploring the interplay between mathematics and physical concepts.

Leonid Berlyand is a mathematician and professor known for his work in applied mathematics, dynamical systems, and mathematical biology. He has contributed to various fields including mathematical modeling and analysis of complex systems.

Louis Michel is a Belgian physicist known for his work in the field of particle physics and cosmology. He is notable for his contributions to the understanding of the fundamental forces and particles in the universe. Michel has engaged in research related to the properties of neutrinos and other elementary particles, and he has been involved in various theoretical and experimental studies aimed at exploring the fundamental aspects of matter and energy.