Spatial analysisSpatial analysis is any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques using different analytic approaches, especially spatial statistics. It may be applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, or to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures.
Poisson point processIn probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field.
Spatial databaseA spatial database is a general-purpose database (usually a relational database) that has been enhanced to include spatial data that represents objects defined in a geometric space, along with tools for querying and analyzing such data. Most spatial databases allow the representation of simple geometric objects such as points, lines and polygons. Some spatial databases handle more complex structures such as 3D objects, topological coverages, linear networks, and triangulated irregular networks (TINs).
Boundary problem (spatial analysis)A boundary problem in analysis is a phenomenon in which geographical patterns are differentiated by the shape and arrangement of boundaries that are drawn for administrative or measurement purposes. The boundary problem occurs because of the loss of neighbors in analyses that depend on the values of the neighbors. While geographic phenomena are measured and analyzed within a specific unit, identical spatial data can appear either dispersed or clustered depending on the boundary placed around the data.
Cox processIn probability theory, a Cox process, also known as a doubly stochastic Poisson process is a point process which is a generalization of a Poisson process where the intensity that varies across the underlying mathematical space (often space or time) is itself a stochastic process. The process is named after the statistician David Cox, who first published the model in 1955.
Point processIn statistics and probability theory, a point process or point field is a collection of mathematical points randomly located on a mathematical space such as the real line or Euclidean space. Point processes can be used for spatial data analysis, which is of interest in such diverse disciplines as forestry, plant ecology, epidemiology, geography, seismology, materials science, astronomy, telecommunications, computational neuroscience, economics and others.
Compound Poisson processA compound Poisson process is a continuous-time stochastic process with jumps. The jumps arrive randomly according to a Poisson process and the size of the jumps is also random, with a specified probability distribution. To be precise, a compound Poisson process, parameterised by a rate and jump size distribution G, is a process given by where, is the counting variable of a Poisson process with rate , and are independent and identically distributed random variables, with distribution function G, which are also independent of When are non-negative integer-valued random variables, then this compound Poisson process is known as a stuttering Poisson process.
Geographic data and informationGeographic data and information is defined in the ISO/TC 211 series of standards as data and information having an implicit or explicit association with a location relative to Earth (a geographic location or geographic position). It is also called geospatial data and information, georeferenced data and information, as well as geodata and geoinformation. Approximately 90% of government sourced data has a location component. Location information (known by the many names mentioned here) is stored in a geographic information system (GIS).
Spatial epidemiologySpatial epidemiology is a subfield of epidemiology focused on the study of the spatial distribution of health outcomes; it is closely related to health geography. Specifically, spatial epidemiology is concerned with the description and examination of disease and its geographic variations. This is done in consideration of “demographic, environmental, behavioral, socioeconomic, genetic, and infections risk factors." Disease Mapping Disease maps are visual representations of intricate geographic data that provide a quick overview of said information.
Stochastic processIn probability theory and related fields, a stochastic (stəˈkæstɪk) or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule.
Cell (biology)The cell is the basic structural and functional unit of all forms of life. Every cell consists of cytoplasm enclosed within a membrane, and contains many macromolecules such as proteins, DNA and RNA, as well as many small molecules of nutrients and metabolites. The term comes from the Latin word cellula meaning 'small room'. Cells can acquire specified function and carry out various tasks within the cell such as replication, DNA repair, protein synthesis, and motility. Cells are capable of specialization and mobility within the cell.
EukaryoteThe eukaryotes constitute the domain of Eukaryota (juːˈkærioʊts,_-əts), organisms whose cells have a nucleus. All animals, plants, fungi, and many unicellular organisms are eukaryotes. They constitute a major group of life forms, alongside the two groups of prokaryotes, the Bacteria and the Archaea. Eukaryotes represent a small minority of the number of organisms, but due to their generally much larger size, their collective global biomass is much larger than that of prokaryotes.
Spatial memoryIn cognitive psychology and neuroscience, spatial memory is a form of memory responsible for the recording and recovery of information needed to plan a course to a location and to recall the location of an object or the occurrence of an event. Spatial memory is necessary for orientation in space. Spatial memory can also be divided into egocentric and allocentric spatial memory. A person's spatial memory is required to navigate around a familiar city. A rat's spatial memory is needed to learn the location of food at the end of a maze.
Poisson distributionIn probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson ('pwɑːsɒn; pwasɔ̃). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.
Cell biologyCell biology (also cellular biology or cytology) is a branch of biology that studies the structure, function, and behavior of cells. All living organisms are made of cells. A cell is the basic unit of life that is responsible for the living and functioning of organisms. Cell biology is the study of the structural and functional units of cells. Cell biology encompasses both prokaryotic and eukaryotic cells and has many subtopics which may include the study of cell metabolism, cell communication, cell cycle, biochemistry, and cell composition.
Normal distributionIn statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.
Campbell's theorem (probability)In probability theory and statistics, Campbell's theorem or the Campbell–Hardy theorem is either a particular equation or set of results relating to the expectation of a function summed over a point process to an integral involving the mean measure of the point process, which allows for the calculation of expected value and variance of the random sum. One version of the theorem, also known as Campbell's formula, entails an integral equation for the aforementioned sum over a general point process, and not necessarily a Poisson point process.
Spatial cognitionSpatial cognition is the acquisition, organization, utilization, and revision of knowledge about spatial environments. It is most about how animals including humans behave within space and the knowledge they built around it, rather than space itself. These capabilities enable individuals to manage basic and high-level cognitive tasks in everyday life. Numerous disciplines (such as cognitive psychology, neuroscience, artificial intelligence, geographic information science, cartography, etc.
Ternary Golay codeIn coding theory, the ternary Golay codes are two closely related error-correcting codes. The code generally known simply as the ternary Golay code is an -code, that is, it is a linear code over a ternary alphabet; the relative distance of the code is as large as it possibly can be for a ternary code, and hence, the ternary Golay code is a perfect code. The extended ternary Golay code is a [12, 6, 6] linear code obtained by adding a zero-sum check digit to the [11, 6, 5] code.
Cell wallA cell wall is a structural layer surrounding some types of cells, just outside the cell membrane. It can be tough, flexible, and sometimes rigid. It provides the cell with both structural support and protection, and also acts as a filtering mechanism. Cell walls are absent in many eukaryotes, including animals, but are present in some other ones like fungi, algae and plants, and in most prokaryotes (except mollicute bacteria). A major function is to act as pressure vessels, preventing over-expansion of the cell when water enters.
