Topological data analysisIn applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challenging. TDA provides a general framework to analyze such data in a manner that is insensitive to the particular metric chosen and provides dimensionality reduction and robustness to noise. Beyond this, it inherits functoriality, a fundamental concept of modern mathematics, from its topological nature, which allows it to adapt to new mathematical tools.
Size theoryIn mathematics, size theory studies the properties of topological spaces endowed with -valued functions, with respect to the change of these functions. More formally, the subject of size theory is the study of the natural pseudodistance between size pairs. A survey of size theory can be found in The beginning of size theory is rooted in the concept of size function, introduced by Frosini. Size functions have been initially used as a mathematical tool for shape comparison in computer vision and pattern recognition.
Crystal structureIn crystallography, crystal structure is a description of the ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter. The smallest group of particles in the material that constitutes this repeating pattern is the unit cell of the structure.
Landscape architectureLandscape architecture is the design of outdoor areas, landmarks, and structures to achieve environmental, social-behavioural, or aesthetic outcomes. It involves the systematic design and general engineering of various structures for construction and human use, investigation of existing social, ecological, and soil conditions and processes in the landscape, and the design of other interventions that will produce desired outcomes.
Molecular solidA molecular solid is a solid consisting of discrete molecules. The cohesive forces that bind the molecules together are van der Waals forces, dipole-dipole interactions, quadrupole interactions, π-π interactions, hydrogen bonding, halogen bonding, London dispersion forces, and in some molecular solids, coulombic interactions. Van der Waals, dipole interactions, quadrupole interactions, π-π interactions, hydrogen bonding, and halogen bonding (2-127 kJ mol−1) are typically much weaker than the forces holding together other solids: metallic (metallic bonding, 400-500 kJ mol−1), ionic (Coulomb’s forces, 700-900 kJ mol−1), and network solids (covalent bonds, 150-900 kJ mol−1).
Landscape ecologyLandscape ecology is the science of studying and improving relationships between ecological processes in the environment and particular ecosystems. This is done within a variety of landscape scales, development spatial patterns, and organizational levels of research and policy. Concisely, landscape ecology can be described as the science of "landscape diversity" as the synergetic result of biodiversity and geodiversity.
English landscape gardenThe English landscape garden, also called English landscape park or simply the English garden (Jardin à l'anglaise, Giardino all'inglese, Englischer Landschaftsgarten, Jardim inglês, Jardín inglés), is a style of "landscape" garden which emerged in England in the early 18th century, and spread across Europe, replacing the more formal, symmetrical French formal garden which had emerged in the 17th century as the principal gardening style of Europe. The English garden presented an idealized view of nature.
Landscape planningLandscape planning is a branch of landscape architecture. According to Erv Zube (1931–2002) landscape planning is defined as an activity concerned with developing landscaping amongst competing land uses while protecting natural processes and significant cultural and natural resources. Park systems and greenways of the type designed by Frederick Law Olmsted are key examples of landscape planning. Landscape designers tend to work for clients who wish to commission construction work.
Size functionSize functions are shape descriptors, in a geometrical/topological sense. They are functions from the half-plane to the natural numbers, counting certain connected components of a topological space. They are used in pattern recognition and topology. In size theory, the size function associated with the size pair is defined in the following way.
Cubic crystal systemIn crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of these crystals: Primitive cubic (abbreviated cP and alternatively called simple cubic) Body-centered cubic (abbreviated cI or bcc) Face-centered cubic (abbreviated cF or fcc) Note: the term fcc is often used in synonym for the cubic close-packed or ccp structure occurring in metals.
