Types of artificial neural networksThere are many types of artificial neural networks (ANN). Artificial neural networks are computational models inspired by biological neural networks, and are used to approximate functions that are generally unknown. Particularly, they are inspired by the behaviour of neurons and the electrical signals they convey between input (such as from the eyes or nerve endings in the hand), processing, and output from the brain (such as reacting to light, touch, or heat). The way neurons semantically communicate is an area of ongoing research.
Index of a subgroupIn mathematics, specifically group theory, the index of a subgroup H in a group G is the number of left cosets of H in G, or equivalently, the number of right cosets of H in G. The index is denoted or or . Because G is the disjoint union of the left cosets and because each left coset has the same size as H, the index is related to the orders of the two groups by the formula (interpret the quantities as cardinal numbers if some of them are infinite). Thus the index measures the "relative sizes" of G and H.
Focal subgroup theoremIn abstract algebra, the focal subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced in and is the "first major application of the transfer" according to . The focal subgroup theorem relates the ideas of transfer and fusion such as described in . Various applications of these ideas include local criteria for p-nilpotence and various non-simplicity criteria focussing on showing that a finite group has a normal subgroup of index p.
NociceptorA nociceptor ("pain receptor" from Latin nocere 'to harm or hurt') is a sensory neuron that responds to damaging or potentially damaging stimuli by sending "possible threat" signals to the spinal cord and the brain. The brain creates the sensation of pain to direct attention to the body part, so the threat can be mitigated; this process is called nociception. Nociceptors were discovered by Charles Scott Sherrington in 1906. In earlier centuries, scientists believed that animals were like mechanical devices that transformed the energy of sensory stimuli into motor responses.
Molecular pathological epidemiologyMolecular pathological epidemiology (MPE, also molecular pathologic epidemiology) is a discipline combining epidemiology and pathology. It is defined as "epidemiology of molecular pathology and heterogeneity of disease". Pathology and epidemiology share the same goal of elucidating etiology of disease, and MPE aims to achieve this goal at molecular, individual and population levels. Typically, MPE utilizes tissue pathology resources and data within existing epidemiology studies.
Sylow theoremsIn mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow that give detailed information about the number of subgroups of fixed order that a given finite group contains. The Sylow theorems form a fundamental part of finite group theory and have very important applications in the classification of finite simple groups. For a prime number , a Sylow p-subgroup (sometimes p-Sylow subgroup) of a group is a maximal -subgroup of , i.
Conjugacy classIn mathematics, especially group theory, two elements and of a group are conjugate if there is an element in the group such that This is an equivalence relation whose equivalence classes are called conjugacy classes. In other words, each conjugacy class is closed under for all elements in the group. Members of the same conjugacy class cannot be distinguished by using only the group structure, and therefore share many properties. The study of conjugacy classes of non-abelian groups is fundamental for the study of their structure.
Host–parasite coevolutionHost–parasite coevolution is a special case of coevolution, where a host and a parasite continually adapt to each other. This can create an evolutionary arms race between them. A more benign possibility is of an evolutionary trade-off between transmission and virulence in the parasite, as if it kills its host too quickly, the parasite will not be able to reproduce either. Another theory, the Red Queen hypothesis, proposes that since both host and parasite have to keep on evolving to keep up with each other, and since sexual reproduction continually creates new combinations of genes, parasitism favours sexual reproduction in the host.
Central seriesIn mathematics, especially in the fields of group theory and Lie theory, a central series is a kind of normal series of subgroups or Lie subalgebras, expressing the idea that the commutator is nearly trivial. For groups, the existence of a central series means it is a nilpotent group; for matrix rings (considered as Lie algebras), it means that in some basis the ring consists entirely of upper triangular matrices with constant diagonal. This article uses the language of group theory; analogous terms are used for Lie algebras.
Porter's five forces analysisPorter's Five Forces Framework is a method of analysing the operating environment of a competition of a business. It draws from industrial organization (IO) economics to derive five forces that determine the competitive intensity and, therefore, the attractiveness (or lack thereof) of an industry in terms of its profitability. An "unattractive" industry is one in which the effect of these five forces reduces overall profitability. The most unattractive industry would be one approaching "pure competition", in which available profits for all firms are driven to normal profit levels.
