Psychological stressIn psychology, stress is a feeling of emotional strain and pressure. Stress is a type of psychological pain. Small amounts of stress may be beneficial, as it can improve athletic performance, motivation and reaction to the environment. Excessive amounts of stress, however, can increase the risk of strokes, heart attacks, ulcers, and mental illnesses such as depression and also aggravation of a pre-existing condition.
Definite matrixIn mathematics, a symmetric matrix with real entries is positive-definite if the real number is positive for every nonzero real column vector where is the transpose of . More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number is positive for every nonzero complex column vector where denotes the conjugate transpose of Positive semi-definite matrices are defined similarly, except that the scalars and are required to be positive or zero (that is, nonnegative).
Complex post-traumatic stress disorderComplex post-traumatic stress disorder (CPTSD) is a stress-related mental disorder generally occurring in response to complex traumas, i.e. commonly prolonged or repetitive exposures to a series of traumatic events, within which individuals perceive little or no chance to escape. In the ICD-11 classification, CPTSD is a category of post-traumatic stress disorder (PTSD) with three additional clusters of significant symptoms: emotional dysregulations, negative self-beliefs (e.g.
Post-traumatic stress disorderPost-traumatic stress disorder (PTSD) is a mental and behavioral disorder that develops from experiencing a traumatic event, such as sexual assault, warfare, traffic collisions, child abuse, domestic violence, or other threats on a person's life or well-being. Symptoms may include disturbing thoughts, feelings, or dreams related to the events, mental or physical distress to trauma-related cues, attempts to avoid trauma-related cues, alterations in the way a person thinks and feels, and an increase in the fight-or-flight response.
Self-medicationSelf-medication is a human behavior in which an individual uses a substance or any exogenous influence to self-administer treatment for physical or psychological conditions: for example headaches or fatigue. The substances most widely used in self-medication are over-the-counter drugs and dietary supplements, which are used to treat common health issues at home. These do not require a doctor's prescription to obtain and, in some countries, are available in supermarkets and convenience stores.
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Rank (linear algebra)In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number of linearly independent columns of A. This, in turn, is identical to the dimension of the vector space spanned by its rows. Rank is thus a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by A. There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics.
Electron densityElectron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial variables and is typically denoted as either or . The density is determined, through definition, by the normalised -electron wavefunction which itself depends upon variables ( spatial and spin coordinates). Conversely, the density determines the wave function modulo up to a phase factor, providing the formal foundation of density functional theory.
Semidefinite programmingSemidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron. Semidefinite programming is a relatively new field of optimization which is of growing interest for several reasons. Many practical problems in operations research and combinatorial optimization can be modeled or approximated as semidefinite programming problems.
Nonlinear programmingIn mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear.
