Matrix (mathematics)In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.
Extracellular matrixIn biology, the extracellular matrix (ECM), also called intercellular matrix, is a network consisting of extracellular macromolecules and minerals, such as collagen, enzymes, glycoproteins and hydroxyapatite that provide structural and biochemical support to surrounding cells. Because multicellularity evolved independently in different multicellular lineages, the composition of ECM varies between multicellular structures; however, cell adhesion, cell-to-cell communication and differentiation are common functions of the ECM.
Triangular matrixIn mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called if all the entries above the main diagonal are zero. Similarly, a square matrix is called if all the entries below the main diagonal are zero. Because matrix equations with triangular matrices are easier to solve, they are very important in numerical analysis. By the LU decomposition algorithm, an invertible matrix may be written as the product of a lower triangular matrix L and an upper triangular matrix U if and only if all its leading principal minors are non-zero.
Stenotrophomonas maltophiliaStenotrophomonas maltophilia is an aerobic, nonfermentative, Gram-negative bacterium. It is an uncommon bacterium and human infection is difficult to treat. Initially classified as Bacterium bookeri, then renamed Pseudomonas maltophilia, S. maltophilia was also grouped in the genus Xanthomonas before eventually becoming the type species of the genus Stenotrophomonas in 1993. S. maltophilia is slightly smaller (0.7–1.8 × 0.4–0.7 μm) than other members of the genus.
Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
BiofilmA biofilm comprises any syntrophic consortium of microorganisms in which cells stick to each other and often also to a surface. These adherent cells become embedded within a slimy extracellular matrix that is composed of extracellular polymeric substances (EPSs). The cells within the biofilm produce the EPS components, which are typically a polymeric conglomeration of extracellular polysaccharides, proteins, lipids and DNA. Because they have three-dimensional structure and represent a community lifestyle for microorganisms, they have been metaphorically described as "cities for microbes".
Pseudomonas aeruginosaPseudomonas aeruginosa is a common encapsulated, Gram-negative, aerobic–facultatively anaerobic, rod-shaped bacterium that can cause disease in plants and animals, including humans. A species of considerable medical importance, P. aeruginosa is a multidrug resistant pathogen recognized for its ubiquity, its intrinsically advanced antibiotic resistance mechanisms, and its association with serious illnesses – hospital-acquired infections such as ventilator-associated pneumonia and various sepsis syndromes.
T helper cellThe T helper cells (Th cells), also known as CD4+ cells or CD4-positive cells, are a type of T cell that play an important role in the adaptive immune system. They aid the activity of other immune cells by releasing cytokines. They are considered essential in B cell antibody class switching, breaking cross-tolerance in dendritic cells, in the activation and growth of cytotoxic T cells, and in maximizing bactericidal activity of phagocytes such as macrophages and neutrophils.
T cellT cells are one of the important types of white blood cells of the immune system and play a central role in the adaptive immune response. T cells can be distinguished from other lymphocytes by the presence of a T-cell receptor (TCR) on their cell surface. T cells are born from hematopoietic stem cells, found in the bone marrow. Developing T cells then migrate to the thymus gland to develop (or mature). T cells derive their name from the thymus. After migration to the thymus, the precursor cells mature into several distinct types of T cells.
Extracellular polymeric substanceExtracellular polymeric substances (EPSs) are natural polymers of high molecular weight secreted by microorganisms into their environment. EPSs establish the functional and structural integrity of biofilms, and are considered the fundamental component that determines the physicochemical properties of a biofilm. EPS in the matrix of biofilms provides compositional support and protection of microbial communities from the harsh environments. Components of EPS can be of different classes of polysaccharides, lipids, nucleic acids, proteins, lipopolysaccharides, and minerals.
Covariance matrixIn probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. Any covariance matrix is symmetric and positive semi-definite and its main diagonal contains variances (i.e., the covariance of each element with itself). Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions.
Invertible matrixIn linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.
Potassium channelPotassium channels are the most widely distributed type of ion channel found in virtually all organisms. They form potassium-selective pores that span cell membranes. Potassium channels are found in most cell types and control a wide variety of cell functions. Potassium channels function to conduct potassium ions down their electrochemical gradient, doing so both rapidly (up to the diffusion rate of K+ ions in bulk water) and selectively (excluding, most notably, sodium despite the sub-angstrom difference in ionic radius).
Matrix multiplicationIn mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB.
Diagonal matrixIn linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is , while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size).
Natural killer cellNatural killer cells, also known as NK cells or large granular lymphocytes (LGL), are a type of cytotoxic lymphocyte critical to the innate immune system that belong to the rapidly expanding family of known innate lymphoid cells (ILC) and represent 5–20% of all circulating lymphocytes in humans. The role of NK cells is analogous to that of cytotoxic T cells in the vertebrate adaptive immune response. NK cells provide rapid responses to virus-infected cell and other intracellular pathogens acting at around 3 days after infection, and respond to tumor formation.
B cellB cells, also known as B lymphocytes, are a type of white blood cell of the lymphocyte subtype. They function in the humoral immunity component of the adaptive immune system. B cells produce antibody molecules which may be either secreted or inserted into the plasma membrane where they serve as a part of B-cell receptors. When a naïve or memory B cell is activated by an antigen, it proliferates and differentiates into an antibody-secreting effector cell, known as a plasmablast or plasma cell.
Calcium channelA calcium channel is an ion channel which shows selective permeability to calcium ions. It is sometimes synonymous with voltage-gated calcium channel, although there are also ligand-gated calcium channels. The following tables explain gating, gene, location and function of different types of calcium channels, both voltage and ligand-gated. voltage-gated calcium channel the receptor-operated calcium channels (in vasoconstriction) P2X receptors L-type calcium channel blockers are used to treat hypertension.
Chloride channelChloride channels are a superfamily of poorly understood ion channels specific for chloride. These channels may conduct many different ions, but are named for chloride because its concentration in vivo is much higher than other anions. Several families of voltage-gated channels and ligand-gated channels (e.g., the CaCC families) have been characterized in humans. Voltage-gated chloride channels perform numerous crucial physiological and cellular functions, such as controlling pH, volume homeostasis, transporting organic solutes, regulating cell migration, proliferation, and differentiation.
Vibrio choleraeVibrio cholerae is a species of Gram-negative, facultative anaerobe and comma-shaped bacteria. The bacteria naturally live in brackish or saltwater where they attach themselves easily to the chitin-containing shells of crabs, shrimp, and other shellfish. Some strains of V. cholerae are pathogenic to humans and cause a deadly disease called cholera, which can be derived from the consumption of undercooked or raw marine life species. V. cholerae was first described by Félix-Archimède Pouchet in 1849 as some kind of protozoa.
