120 Sentences With "generalise" | Random Sentence Generator

It remains hard to generalise from either set of results.

The paper attacked online articles that "exaggerate and generalise and shout" about China's accomplishments.

So, it is hard to generalise about the influence of social or economic trends on liberalism's popularity.

It took me a long time to realise that … the word "black" can seem to generalise everything.

Yet when it comes to election time, voters behave in ways all too easy to generalise about.

Starter pack memes have been called out as racist, and the starter pack subreddit bans starter packs which generalise about race.

Munro said each SPA with a customer is tailor-made, so it was hard to generalise how an arbitration might play out.

Psychologists are concerned with whether findings generalise beyond student samples, or beyond so-called "WEIRD" (Western, Educated, Industrialised, Rich and Democratic) samples.

But read-across depends on expert analysis and opinion, making it subjective and also difficult to generalise beyond small, well-studied groups of chemicals.

"We studied only a small number of air samples, so to generalise, we need to examine the air from more places," explains lead researcher Joakim Larsson.

"The results are promising on the expanded types of content because we have been developing proprietary techniques to allow the models to generalise across domains," he said.

Background noise remains a big concern; if it is different from that in the training data, the software finds it harder to generalise from what it has learned.

They too would like to win this fight and they too sometimes tend to exaggerate, generalise and over-simplify (as an exception, see the posts of Dapo Akande and Jennifer Trahan).

Any attempt to write a "Hillbilly Elegy" about liberal America quickly runs up against the problem that it is easier to generalise about Republican voters because the groups that make up the party are bigger and have more in common with each other, in terms of ideology and identity.

Its platform uses probabilistic models "to generalise to novel situations and adapt to changing environments by refining their strategies in data-driven ways"; Reinforcement Learning algorithms that estimate and account for uncertainty; and Game Theory to operate in multi-agent settings to infer what humans and other AIs are trying to do.

A city can often generalise where a nation must particularise.

Matching bias has also been shown to generalise to syllogistic reasoning.

The theorem can be used to generalise the Stolarsky mean to more than two variables.

In coding theory, alternant codes form a class of parameterised error- correcting codes which generalise the BCH codes.

Hyperdeterminants generalise many of the properties of determinants. The property of being a discriminant is one of them and it is used in the definition above.

In 2019 DeepMind published a new paper detailing MuZero, a new algorithm able to generalise on AlphaZero work playing both Atari and board games without knowledge of the rules or representations of the game.

However, the Henstock integral depends on specific ordering features of the real line and so does not generalise to allow integration in more general spaces (say, manifolds), while the Lebesgue integral extends to such spaces quite naturally.

In mathematics, moduli of smoothness are used to quantitatively measure smoothness of functions. Moduli of smoothness generalise modulus of continuity and are used in approximation theory and numerical analysis to estimate errors of approximation by polynomials and splines.

It pertains to the classification of finite simple groups, namely the classification of finite primitive permutation groups. The paper contains a complete self-contained proof of the theorem. Praeger later went on to generalise the O'Nan–Scott Theorem to quasiprimitive groups.

Adaptive dynamics is a set of techniques developed during the 1990s for understanding the long-term consequences of small mutations in the traits expressing the phenotype. They link population dynamics to evolutionary dynamics and incorporate and generalise the fundamental idea of frequency- dependent selection from game theory.

We give the construction first in these two cases, under the assumption that we have only two objects. Then we generalise to an arbitrary family of arbitrary modules. The key elements of the general construction are more clearly identified by considering these two cases in depth.

VIII)Mauss 1979 their cultural diversityKleivan 1985:26 makes it hard to generalise how Eskimos and Inuit used masks. The sustenance, mythology, soul concepts, even the languageLawrence Kaplan: Comparative Yupik and Inuit (found on the site of Alaska Native Language Center ) of the different communities were often very different.

They investigated branching chains using a characteristic function. After the war, Ulam would extend and generalise this work. He described Hawkins as "the most talented amateur mathematician I know." Hawkins is credited with the selection of the Alamogordo area for the Trinity nuclear test, but he declined to watch it.

In mathematics, profinite groups are topological groups that are in a certain sense assembled from finite groups. They share many properties with their finite quotients: for example, both Lagrange's theorem and the Sylow theorems generalise well to profinite groups. A non-compact generalization of a profinite group is a locally profinite group.

He worked on Diophantine approximation and geometry of numbers, where he used both classical and p-adic analytic methods.special issue of Annales de l'Institut Fourier (vol. XXIX, Fasc. 1), March 1979, for Chabauty's retirement He introduced the Chabauty topology to generalise Mahler's compactness theorem from Euclidean lattices to more general discrete subgroups.

11 Furthermore, Ang does not attempt to generalise or triangulate the cases study to apply it to other casesYin, Robert K. 2003, Case Study Research. 3rd edn. Sage Publications, Thousand Oaks. instead arguing that it was sufficient to illustrate the audience response to Dallas in this instance alone, a style which is increasing in popularity.

CMA Canberra, 1991. It is possible to generalise the division of space into labyrinths to find triply periodic (but possibly branched) minimal surfaces that divide space into more than two sub-volumes. Quasiperiodic minimal surfaces have been constructed in ℝ2×S1.Laurent Mazet, Martin Traizet, A quasi-periodic minimal surface, Commentarii Mathematici Helvetici, pp.

Jason Hutchens, an "expert in languages", was hired and helped create a "more natural" language compiler.The Making of Black & White, p. 83. A system to generalise each approach to challenges was also needed. The script editor and language were simple enough for non-programmers to use, and was also capable of writing complex scripts.

According to , word-representable graphs are relevant to various fields, thus providing a motivation to study the graphs. These fields are algebra, graph theory, computer science, combinatorics on words, and scheduling. Word-representable graphs are especially important in graph theory, since they generalise several important classes of graphs, e.g. circle graphs, 3-colorable graphs and comparability graphs.

In probability theory, the Palm-Khintchine theorem, the work of Conny Palm and Aleksandr Khinchin, expresses that a large number of renewal processes, not necessarily Poissonian, when combined ("superimposed") will have Poissonian properties. It is used to generalise the behaviour of users or clients in queuing theory. It is also used in dependability and reliability modelling of computing and telecommunications.

Self-experimentation has value in rapidly obtaining the first results. In some cases, such as with Forssmann's experiments done in defiance of official permission, results may be obtained that would never otherwise have come to light. However, self-experiment lacks the statistical validity of a larger experiment. It is not possible to generalise from an experiment on a single person.

The nature and quality of a purebred dog's coat is important to the dog fancy in the judging of the dog at conformation shows. The exact requirements are detailed in each breed's breed standard and do not generalise in any way, and the terminology may be very different even when referring to similar features. See individual breed articles for specific information.

Due to his use of the normal distribution Thurstone was unable to generalise this binary choice into a multinomial choice framework (which required the multinomial logistic regression rather than probit link function), hence why the method languished for over 30 years. However, in the 1960s through 1980s the method was axiomatised and applied in a variety of types of study.

A systematic review compared smoking control programmes and their effects on smoke exposure in children. The review distinguishes between community-based, ill-child and healthy-child settings and the most common types of interventions were counselling or brief advice during clinical visits. The review did not find superior outcomes for any intervention, and the authors caution that evidence from adult settings may not generalise well to children.

Dkhar, alternatively spelled as Dikhar, is a term used by the Khasis to refer to non-Khasi people in Meghalaya. It is a term used for people from mainland India who come to Meghalaya particularly Shillong to earn a living. It is a general term use to generalise all non tribals who are staying in meghalaya. It is non derogatory but some perceived it as derogatory.

In statistics, Halton sequences are sequences used to generate points in space for numerical methods such as Monte Carlo simulations. Although these sequences are deterministic, they are of low discrepancy, that is, appear to be random for many purposes. They were first introduced in 1960 and are an example of a quasi-random number sequence. They generalise the one-dimensional van der Corput sequences.

There appears to be a greater gender difference when actually presented with the opportunity to perform voyeurism. There is very little research done on voyeurism in women, so very little is known on the subject. One of the few studies deals with a case study of a woman who also had schizophrenia. This limits the degree to which it can generalise to normal populations.

These structures generalise the notion of generalized polygon as every generalized 2n-gon is a near 2n-gon of a particular kind. Near polygons were extensively studied and connection between them and dual polar spaces Cameron, Peter J. "Dual polar spaces". was shown in 1980s and early 1990s. Some sporadic simple groups, for example the Hall-Janko group and the Mathieu groups, act as automorphism groups of near polygons.

Lucio's phenomenon is an unusual reaction seen almost exclusively in patients from the Caribbean and Mexico with diffuse, lepromatous leprosy, especially in untreated cases. It is characterised by recurrent crops of large, sharply demarcated, ulcerative lesions, affecting mainly the lower extremities, but may generalise and become fatal as a result of secondary bacterial infection and sepsis.Kasper DL, Braunwald E, Fauci AS, et al. Harrison's Principles of Internal Medicine.

The Cochrane Collaboration has commissioned two reviews of the evidence for psychological and medical treatments for Narcissistic Personality Disorder (NPD). In both cases, they suspended their initiatives after the authors had made no progress in over a year. There are no clear treatment strategies for NPD, neither medication nor psychotherapy. There is evidence that therapies effective in the treatment of other personality disorders do not generalise to NPD.

It is possible to generalise the class of autoregressive moving average models to incorporate cyclostationary behaviour. For example, TroutmanTroutman, B.M. (1979) "Some results in periodic autoregression." Biometrika, 66 (2), 219-228 treated autoregressions in which the autoregression coefficients and residual variance are no longer constant but vary cyclically with time. His work follows a number of other studies of cyclostationary processes within the field of time series analysis.

Bray, p62 However, it was with Ronald M. Foster that Cauer had much correspondence and it was his work that Cauer recognised as being of such importance. His paper, A reactance theorem,Foster, R M, "A reactance theorem", Bell System Technical Journal, Vol. 3, pp259–267, 1924. is a milestone in filter theory and inspired Cauer to generalise this approach into what has now become the field of network synthesis.

More specifically: when two XPs are Merged and neither one projects, then the structure cannot be computed unless either one moves, thereby forcing the other to project. That's because a single copy is only one link of a bigger chain. This proposal has been formulated as a paper now collected in Moro 2013; see Chomsky 2013 for the proposal to generalise this principle and include it in the standard theory.

The definition of a word-representable graph works both in labelled and unlabelled cases since any labelling of a graph is equivalent to any other labelling. Also, the class of word-representable graphs is hereditary. Word-representable graphs generalise several important classes of graphs such as circle graphs, 3-colorable graphs and comparability graphs. Various generalisations of the theory of word- representable graphs accommodate representation of any graph.

There were three broad criticisms aimed at the idea of maternal deprivation from feminist critics. The first was that Bowlby overstated his case. The studies on which he based his conclusions involved almost complete lack of maternal care and it was unwarranted to generalise from this view that any separation in the first three years of life would be damaging. Subsequent research showed good quality care for part of the day to be harmless.

Much of the theory of rings continues to make sense when applied to arbitrary semirings. In particular, one can generalise the theory of (associative) algebras over commutative rings directly to a theory of algebras over commutative semirings. Then a ring is simply an algebra over the commutative semiring Z of integers. A semiring in which every element is an additive idempotent (that is, a + a = a for all elements a) is called an '.

Negotiations over the terms were carried on by the 1643 to 1653 Westminster Assembly. They were opposed in Parliament by the so-called Independents, who opposed any state-mandated religion, and were heavily represented in the New Model Army. In addition, English Royalists and many who fought for Parliament were neither Presbyterian, nor Independent, but supporters of an Episcopalian Church of England. This makes it difficult to generalise on political and religious views.

Two types of tensor decompositions exist, which generalise the SVD to multi-way arrays. One of them decomposes a tensor into a sum of rank-1 tensors, which is called a tensor rank decomposition. The second type of decomposition computes the orthonormal subspaces associated with the different factors appearing in the tensor product of vector spaces in which the tensor lives. This decomposition is referred to in the literature as the higher-order SVD (HOSVD) or Tucker3/TuckerM.

The so-called classical groups generalise the examples 1 and 2 above. They arise as linear algebraic groups, that is, as subgroups of GLn defined by a finite number of equations. Basic examples are orthogonal, unitary and symplectic groups but it is possible to construct more using division algebras (for example the unit group of a quaternion algebra is a classical group). Note that the projective groups associated to these groups are also linear, though less obviously.

Then f and g are sequences. If Y is a topological space, then f and g have the same limit, or both have none. (When you generalise this to a directed sets, you get the same result, but for nets.) Or, let X be a measure space, and let negligible sets be the null sets. If Y is the real line R, then either f and g have the same integral, or neither integral is defined.

In both the United Kingdom and the Republic of Ireland, the drinking of tea is so varied that it is difficult to generalise. While it is usually served with milk, it is not uncommon to drink it black or with lemon, with sugar being a popular addition to any of the above. Strong ordinary tea (e.g. English Breakfast tea), served in a mug with milk and often sugar, is a popular combination known as builder's tea.

Their classification was the object of the programme of class field theory, which was initiated in the late 19th century (partly by Kronecker and Eisenstein) and carried out largely in 1900–1950. An example of an active area of research in algebraic number theory is Iwasawa theory. The Langlands program, one of the main current large-scale research plans in mathematics, is sometimes described as an attempt to generalise class field theory to non-abelian extensions of number fields.

ZPP, co-RP, BPP, BQP, PP), which generalise P within PSPACE. It is unknown if any of these containments are strict. The definition of RP says that a YES answer is always right and that a NO answer might be wrong (because a question with the YES answer can be sometimes answered NO). In other words, while NO questions are always answered NO, you cannot trust the NO answer, it may be a mistaken answer to a YES question.

The task of revolutionaries was to generalise and politicise such struggles. Kidron was critical of the move within IS to a more traditionally democratic centralist structure in the wake of the events of 1968, and as IS grew, he moved away from its core, both physically, obtaining an academic post in Kingston upon Hull, and politically. Nonetheless, he took no direct part in the factional struggle which saw a split in the central IS cadre in 1975.

On each arc there is a statistical weight. Using back propagation the neural network learns the necessary pattern to recognize the prediction. It is trained by repeatedly exposing it to examples of the problem and learning the significance (weights) of the input nodes. The neural network used by Split_up is said to generalise well if the output of the network is correct (or nearly correct) for examples not seen during training, which classifies it as an intelligent system.

In cymbal making, taper refers to the gradual change in thickness from the bell to the rim of the cymbal. It is one of the key features that determines the tone of the cymbal. This change is typically not uniform, and it is extremely difficult to generalise on the effects of taper, just to say that they are profound. Crash cymbals tend to have the most pronounced taper, with the faster crashes and the richer tones the most pronounced of all.

The idea is to gather knowledge in form of rules or programs, from a set of training instances, which would hopefully generalise to the process of solving unseen instances. Examples of off-line learning approaches within hyper-heuristics are: learning classifier systems, case-base reasoning and genetic programming. An extended classification of selection hyper-heuristics was provided in 2019Drake J. H, Kheiri A., Ozcan E., Burke E. K., (2019) Recent Advances in Selection Hyper- heuristics. European Journal of Operational Research (accepted to appear).

The teaching is based on vocational theory and method and on practical vocational conditions. The aim of the course to be a preparation for higher education studies must be reflected in the organisation of the teaching. Teaching methods included develop the independence of the students and their ability to argue, generalise and make abstractions. The teaching is organised so that the subjects support each other with a view to creating an appropriate and equal distribution of the workload of students.

Fuzzy concepts often play a role in the creative process of forming new concepts to understand something. In the most primitive sense, this can be observed in infants who, through practical experience, learn to identify, distinguish and generalise the correct application of a concept, and relate it to other concepts.Jean Piaget & Bärbel Inhelder, The Growth of Logical Thinking from Childhood to Adolescence. New York: Basic Books, 1958; Philip J. Kelman & Martha E. Arterberry, The cradle of knowledge: development of perception in infancy.

At a larger scale, researchers have attempted to generalize neural networks to the quantum setting. One way of constructing a quantum neuron is to first generalise classical neurons and then generalising them further to make unitary gates. Interactions between neurons can be controlled quantumly, with unitary gates, or classically, via measurement of the network states. This high-level theoretical technique can be applied broadly, by taking different types of networks and different implementations of quantum neurons, such as photonically implemented neuronsA.

Since buckwheat is less glutinous than most grains, buckwheat flour is particularly difficult to knead, roll, and slice into noodles by hand; thus, the noodles are often created in a hand- cranked noodle-making machine instead. It is difficult to generalise regarding makguksu's accompanying ingredients. Ingredients are traditionally determined by the customer rather than the restaurant owner, and many restaurants also carry their own unique flavouring recipes. In most cases, makguksu is very spicy, sometimes seasoned with gochujang (hot chile pepper paste).

Sarkozy's government issued a decree on 7 August 2007 to generalise a voluntary biometric profiling program of travellers in airports. The program, called 'Parafes', was to use fingerprints. The new database would be interconnected with the Schengen Information System (SIS) as well as with a national database of wanted persons (FPR). The Commission nationale de l'informatique et des libertés (CNIL) protested against this new decree, opposing itself to the recording of fingerprints and to the interconnection between the SIS and the FPR.

These included the naphtho and benzo derivatives of pyridocarbazole and beta-carboline, heteroaromatics with sulfur, arsenic or selenium replacements. These were either alone or in association with nitrogen, as well as sulfur and nitrogen containing pseudoazulenes. A series of hydrocarbon-like polynuclear lactones were explored with the intent of establishing a connection between polynuclear aromatics and aflatoxins. Such studies of heteroatomic polynuclears led him to propose a "newer picture" of a carcinogenic hydrocarbon, helping the generalise the classical K-region hypothesis.

A few however, including Steve Freeman and Allan Armstrong, were to generalise their criticisms of the SWP and drifted out of it in 1980/81. Around the same time Steve Jeffries, an industrial organiser for the group and long time leading member, also left in disillusionment. In part his resignation was connected to the final disbandment of the remaining rank and file groups. In many respects the period 1976 to 1981 can best be seen as a transitional period from the IS to the SWP.

Evidence-based practice is a philosophical approach that is in opposition to tradition. Some degree of reliance on "the way it was always done" can be found in almost every profession, even when those practices are contradicted by new and better information. Some critics argue that since research is conducted on a population level, results may not generalise to each individual within the population. Therefore, evidence-based practices may fail to provide the best solution to each individual, and traditional practices may better accommodate individual differences.

In category theory, n-ary functions generalise to n-ary morphisms in a multicategory. The interpretation of an n-ary morphism as an ordinary morphisms whose domain is some sort of product of the domains of the original n-ary morphism will work in a monoidal category. The construction of the derived morphisms of one variable will work in a closed monoidal category. The category of sets is closed monoidal, but so is the category of vector spaces, giving the notion of bilinear transformation above.

Artificial neural networks are computational models that excel at machine learning and pattern recognition. Neural networks must be trained with example data before being able to generalise for experimental data, and tested against benchmark data. Neural networks are able to come up with approximate solutions to problems that are hard to solve algorithmically, provided there is sufficient training data. When applied to gene prediction, neural networks can be used alongside other ab initio methods to predict or identify biological features such as splice sites.

Kroll used the four phases to give an explanation and generalise about the development of these two aspects of language. The highest significance is placed on the second and third phase, consolidation and differentiation respectively. It could be concluded that children's written and spoken language, in certain respects, become more similar to age, maturation, and experience; however, they are also increasingly different in other respects. The content of the skills are more similar, but the approach used for both writing and speaking are different.

Tarbat Ness from the south across the Moray Firth Given the scattered nature of the county it is difficult to generalise. The original shire consisted of a portion of the Black Isle peninsula bordering on Cromarty Firth, across which lay the Tarbart peninsula, of which several portions belonged to Cromartyshire, including Tarbat Ness. The interior sections consist of several enclaves within Ross-shire which are mountainous, remote and sparsely populated. To the west are various sections around Little Loch Broom, including the southern tip of Gruinard Island.

TDIQ (also known as 6,7-methylenedioxy-1,2,3,4-tetrahydroisoquinoline or MDTHIQ) is a drug used in scientific research, which has anxiolytic and anorectic effects in animals. It has an unusual effects profile in animals, with the effects generalising to cocaine and partially to MDMA and ephedrine, but the effects did not generalise to amphetamine and TDIQ does not have any stimulant effects. It is thought these effects are mediated via a partial agonist action at Alpha-2 adrenergic receptors, and TDIQ has been suggested as a possible drug for the treatment of cocaine dependence.

So there was a desire to generalise the nonabelian fundamental group to all dimensions. In 1932, Eduard Čech submitted a paper on higher homotopy groups to the International Congress of Mathematics at Zürich. However, Pavel Alexandroff and Heinz Hopf quickly proved these groups were abelian for n > 1, and on these grounds persuaded Cech to withdraw his paper, so that only a small paragraph appeared in the Proceedings. It is said that Witold Hurewicz attended this conference, and his first work on higher homotopy groups appeared in 1935.

To generalise this to universal algebra, normal subgroups need to be replaced by congruence relations. A congruence on an algebra A is an equivalence relation \Phi\subseteq A \times A that forms a subalgebra of A \times A considered as an algebra with componentwise operations. One can make the set of equivalence classes A/\Phi into an algebra of the same type by defining the operations via representatives; this will be well-defined since \Phi is a subalgebra of A \times A. The resulting structure is the quotient algebra.

Simonds d'Ewes is perhaps best known for his work as an antiquarian, and particularly for his transcriptions of important historical documents, originals of which do not survive today, and the Journals of all the Parliaments during the Reign of Queen Elizabeth. Although d'Ewes was ambitious in this field, he lacked the ability to generalise or construct effectively, and died without publishing any major work, except The Primitive Practice for Preserving Truth (1645) and a few speeches. The Journals were published posthumously in 1682 by his nephew, the lawyer and antiquary Paul Bowes.

Once his interest in the publication waned The Journal began to generalise, satirising medicine, theology, theatre, justice, and other social issues. It often contained contradictory accounts of events reported by the previous week's newspapers, its writers inserting sarcastic remarks on the inaccuracies printed by their rivals. It ran until 1737 when it became the Literary Courier of Grub-street, which lingered for a further six months before vanishing altogether. legal battle against the executive power of the state was an influential factor in the Fourth Amendment to the United States Constitution.

Profitability of production measured by surplus value (Saari 2006,3) The scale of success run by a going concern is manifold, and there are no criteria that might be universally applicable to success. Nevertheless, there is one criterion by which we can generalise the rate of success in production. This criterion is the ability to produce surplus value. As a criterion of profitability, surplus value refers to the difference between returns and costs, taking into consideration the costs of equity in addition to the costs included in the profit and loss statement as usual.

It seems that the Buddha's teaching on nonviolence was not interpreted or put into practice in an uncompromisingly pacifist or anti-military-service way by early Buddhists. The early texts assume war to be a fact of life, and well-skilled warriors are viewed as necessary for defensive warfare.Bartholomeusz, p. 50. In Pali texts, injunctions to abstain from violence and involvement with military affairs are directed at members of the sangha; later Mahayana texts, which often generalise monastic norms to laity, require this of lay people as well.

In his career, Teichmüller wrote 34 papers in the space of around 6 years. His early algebraic investigations dealt with the valuation theory of fields and the structure of algebras. In valuation theory, he introduced multiplicative systems of representatives of the residue field of valuation rings, which led to a characterisation of the structure of the whole field in terms of the residue field. In the theory of algebras, he started to generalise Emmy Noether's concept of crossed products from fields to certain kind of algebras, gaining new insights into the structure of p-algebras.

Other theorists may try to unify, formalise, reinterpret or generalise extant theories, or create completely new ones altogether.Arguably these are the most celebrated theories in physics: Newton's theory of gravitation, Einstein's theory of relativity and Maxwell's theory of electromagnetism share some of these attributes. Sometimes the vision provided by pure mathematical systems can provide clues to how a physical system might be modeled;This approach is often favoured by (pure) mathematicians and mathematical physicists. e.g., the notion, due to Riemann and others, that space itself might be curved.

Size is a key factor in determining the potential toxicity of a particle. However it is not the only important factor. Other properties of nanomaterials that influence toxicity include: chemical composition, shape, surface structure, surface charge, aggregation and solubility, and the presence or absence of functional groups of other chemicals. The large number of variables influencing toxicity means that it is difficult to generalise about health risks associated with exposure to nanomaterials – each new nanomaterial must be assessed individually and all material properties must be taken into account.

Ludwigsburg Palace in Württemberg To the west of Austria and Prussia stood the remaining, major, part of Germany. The existence of the two big powers precluded a serious reform of the confederate structure of Germany; but reform of the individual state governments and administrations was not excluded. The general picture was as varied as the political map of the Holy Roman Empire, and it is difficult to generalise. But the impression prevails that, overall, after 1750 and especially after 1770, the general situation of the middle classes improved slightly, both economically and politically.

In probability theory, an empirical process is a stochastic process that describes the proportion of objects in a system in a given state. For a process in a discrete state space a population continuous time Markov chain or Markov population model is a process which counts the number of objects in a given state (without rescaling). In mean field theory, limit theorems (as the number of objects becomes large) are considered and generalise the central limit theorem for empirical measures. Applications of the theory of empirical processes arise in non-parametric statistics.

Letting u be an ordered binary pattern we thus get the notion of a u-representable graph. So, word-representable graphs are just the class of 11-representable graphs. Intriguingly, any graph can be u-represented assuming u is of length at least 3 S. Kitaev. Existence of u-representation of graphs, Journal of Graph Theory 85 (2017) 3, 661−668.. Another way to generalise the notion of a word-representable graph, again suggested by Jeff Remmel, is to introduce the "degree of tolerance" k for occurrences of a pattern p defining edges/non-edges.

Just as one can generalise a vector bundle to the notion of a Higgs bundle, it is possible to formulate a definition of a principal G-Higgs bundle. The above definition of stability for principal bundles generalises to these objects by requiring the reductions of structure group are compatible with the Higgs field of the principal Higgs bundle. It was shown by Anchouche and Biswas that the analogue of the nonabelian Hodge correspondence for Higgs vector bundles is true for principal G-Higgs bundles in the case where the base manifold (X,\omega) is a complex projective variety.

" In a BBC interview, Longley said that "it's never been the practice of the Catholic Church, as it were, to 'means-test' people before admitting them to the celebration of the Eucharist. It would be a mistake to jump to conclusions or to generalise about anybody's particular lifestyle, or their state of grace." Longley is the head of the Diocesan Pastoral Board and has responsibilities for the Deaneries of Camden, Hackney, Islington, Marylebone, Tower Hamlets, and Westminster. He is considered to be a conservative who is "friendly" to the traditional Latin Mass, but also a "born diplomat.

When boiler pressure had exceeded 60psi, compound engines achieved a thermo-dynamic advantage, but it was the mechanical advantages of the smoother stroke that was the deciding factor in the adoption of compounds. In 1859, there was 75,886 ihp (indicated horsepower) of engines in mills in the Manchester area, of which 32,282 ihp was provided by compounds though only 41,189 ihp was generated from boilers operated at over 60psi. To generalise, between 1860 and 1926 all Lancashire mills were driven by compounds. The last compound built was by Buckley and Taylor for Wye No.2 mill, Shaw.

It is possible to generalise this selection principle even beyond the domain of pitch. The diatonic idea has been applied in analysis of some traditional African rhythms, for example. Some selection or other is made from an underlying superset of metrical beats, to produce a "diatonic" rhythmic "scale" embedded in an underlying metrical "matrix". Some of these selections are diatonic in a way similar to the traditional diatonic selections of pitch classes (that is, a selection of seven beats from a matrix of twelve beats – perhaps even in groupings that match the tone-and-semitone groupings of diatonic scales).

Social conservatism in the United States is a right-wing political ideology that opposes social progressivism. It is centered on the preservation of what adherents often call 'traditional' or 'family values', though the accepted aims of the movement often vary amongst the organisations it comprises, making it hard to generalise about ideological preferences. There are, however, a number of general principles to which at least a majority of social conservatives adhere, such as opposition to abortion and opposition to same- sex marriage. The Republican Party is the largest political party with socially conservative ideals incorporated into its platform.

Despite the numerous advantages offered by on-site renewable energy generation, wastewater utilities are experiencing several difficulties in integrating renewables in their facilities. From a survey conducted by Beca it emerged that one of the biggest barrier is that energy generation is not core business for wastewater utilities and renewable energy projects come with technical challenges and high initial investment costs. Moreover, each plant presents differences and it requires a customised solution for each situation, making it hard to generalise solution for the all sector. There is a lack of guidelines and roadmaps to follow, so each utility has to create specific solutions for their wastewater treatment plants.

One of the subjects that Reynolds studied in the 1880s was the properties of granular materials, including dilatant materials. In 1903 appeared his 250-page book The Sub-Mechanics of the Universe, in which he tried to generalise the mechanics of granular materials to be "capable of accounting for all the physical evidence, as we know it, in the Universe". His aim seems to have been to construct a theory of aether, which he considered to be in a liquid state. The ideas were extremely difficult to understand or evaluate, and in any case were overtaken by other developments in physics around the same time.

Since we have the prior knowledge that we are looking at an experiment for which both success and failure are possible, our estimate is as if we had observed one success and one failure for sure before we even started the experiments. In a sense we made n + 2 observations (known as pseudocounts) with s+1 successes. Although this may seem the simplest and most reasonable assumption, which also happens to be true, it still requires a proof. Indeed, assuming a pseudocount of one per possibility is one way to generalise the binary result, but has unexpected consequences — see Generalization to any number of possibilities, below.

Sutherland had developed the idea of the "self" as a social construct, as when a person's self-image is continuously being reconstructed especially when interacting with other people. Phenomenology and ethnomethodology also encouraged people to debate the certainty of knowledge and to make sense of their everyday experiences using indexicality methods. People define their lives by reference to their experiences, and then generalise those definitions to provide a framework of reference for deciding on future action. From a researcher's perspective, a subject will view the world very differently if employed as opposed to unemployed, if in a supportive family or abused by parents or those close to the individual.

460–62, 464 (including footnote 44).Joseph Priestley, The History and Present State of Electricity, with Original Experiments (London, England: 1767), p. 732 : > May we not infer from this experiment, that the attraction of electricity is > subject to the same laws with that of gravitation, and is therefore > according to the squares of the distances; since it is easily demonstrated, > that were the earth in the form of a shell, a body in the inside of it would > not be attracted to one side more than another? However, he did not generalise or elaborate on this, and the general law was enunciated by French physicist Charles-Augustin de Coulomb in the 1780s.

The connection with induced representations is that the permutation representation on cosets is the special case of induced representation, in which a representation is induced from a trivial representation. The structure, combinatorial in this case, respected by translation shows that either K is a maximal subgroup of G, or there is a system of imprimitivity (roughly, a lack of full 'mixing'). In order to generalise this to other cases, the concept is re-expressed: first in terms of functions on G constant on K-cosets, and then in terms of projection operators (for example the averaging over K-cosets of elements of the group algebra). Mackey also used the idea for his explication of quantization theory based on preservation of relativity groups acting on configuration space.

Membership of Solidarity was open to anyone who agreed with the statement As We See It, later elaborated in As We Don't See It, some key points of which were: Solidarity rejected what it saw as the economic determinism and elitism of most of the Marxist left and committed itself to a view of socialism based on self-management. Supporting those who were in conflict with bureaucratic capitalist society "in industry and elsewhere", the group tried to generalise their experiences to develop a mass revolutionary consciousness, which it believed was essential for a total transformation of society. Crucially, the group did not see itself as another political leadership. On the contrary, it believed that the workers themselves should decide on the objectives of their struggles.

The Ceratopogonidae (biting midges) include serious blood-sucking pests, feeding both on humans and other mammals. Some of them spread the livestock diseases blue tongue and African horse sickness - other species though, are at least partly nectar feeders, and some even suck insect bodily fluids. A midge in the family Ceratopogonidae sitting on the dexter (right-hand-side) femorotibial joint of a feeding mantis and sucking its blood Most other midge families are bloodsuckers, but it is not possible to generalise rigidly because of the vagueness of the term "midge". There is, for example, no objective basis for excluding the Psychodidae from the list, and some of them (or midge-like taxa commonly included in the family, such as Phlebotomus) are blood-sucking pests and disease vectors.

"Greater China" is the informal geographic area that shares commercial and cultural ties to Han Chinese.MTV Channels In Southeast Asia and Greater China To Exclusively Air The Youth Inaugural Ball - MTV AsiaJune 1, 2008, Universal Music Group realigns presence in Greater China , Television Asia The area described by this term is not always clear, but it normally encompasses mainland China, Hong Kong, Macau, and Taiwan - areas where the majority identify as Han Chinese and primarily use Chinese. Some analysts also include other Chinese-speaking communities throughout the world, where Chinese is not the only tongue, such as Malaysia, Singapore (where it makes up 76% of the population) and Chinese communities in Thailand. They may further generalise the term to encompass "linkages among regional Chinese communities".

For example, they could cause overload on phagocytes, cells that ingest and destroy foreign matter, thereby triggering stress reactions that lead to inflammation and weaken the body's defense against other pathogens. Apart from what happens if non-degradable or slowly degradable nanoparticles accumulate in organs, another concern is their potential interaction with biological processes inside the body: because of their large surface, nanoparticles on exposure to tissue and fluids will immediately adsorb onto their surface some of the macromolecules they encounter. This may, for instance, affect the regulatory mechanisms of enzymes and other proteins. The large number of variables influencing toxicity means that it is difficult to generalise about health risks associated with exposure to nanomaterials – each new nanomaterial must be assessed individually and all material properties must be taken into account.

It is somewhat difficult to generalise about how field guides are intended to be used, because this varies from one guide to another, partly depending on how expert the targeted reader is expected to be. For general public use, the main function of a field guide is to help the reader identify a bird, plant, rock, butterfly or other natural object down to at least the popular naming level. To this end some field guides employ simple keys and other techniques: the reader is usually encouraged to scan illustrations looking for a match, and to compare similar-looking choices using information on their differences. Guides are often designed to first lead readers to the appropriate section of the book, where the choices are not so overwhelming in number.

Galton also devised a technique called "composite portraiture" (produced by superimposing multiple photographic portraits of individuals' faces registered on their eyes) to create an average face (see averageness). In the 1990s, a hundred years after his discovery, much psychological research has examined the attractiveness of these faces, an aspect that Galton had remarked on in his original lecture. Others, including Sigmund Freud in his work on dreams, picked up Galton's suggestion that these composites might represent a useful metaphor for an Ideal type or a concept of a "natural kind" (see Eleanor Rosch)—such as Jewish men, criminals, patients with tuberculosis, etc.—onto the same photographic plate, thereby yielding a blended whole, or "composite", that he hoped could generalise the facial appearance of his subject into an "average" or "central type".

As evidence it has been shown that flies can differentiate between two odor molecules which only differ in hydrogen isotope (which will drastically change vibrational energy levels of the molecule). Not only could the flies distinguish between the deuterated and non-deuterated forms of an odorant, they could generalise the property of "deuteratedness" to other novel molecules. In addition, they generalised the learned avoidance behaviour to molecules which were not deuterated but did share a significant vibration stretch with the deuterated molecules, a fact which the differential physics of deuteration (below) has difficulty in accounting for. Deuteration changes the heats of adsorption and the boiling and freezing points of molecules (boiling points: 100.0 °C for H2O vs. 101.42 °C for D2O; melting points: 0.0 °C for H2O, 3.82 °C for D2O), pKa (i.e.

At The National Personal Protective Technology Laboratory of NIOSH, studies investigating the filter penetration of nanoparticles on NIOSH-certified and EU marked respirators, as well as non- certified dust masks have been conducted. These studies found that the most penetrating particle size range was between 30 and 100 nanometers, and leak size was the largest factor in the number of nanoparticles found inside the respirators of the test dummies. Other properties of nanomaterials that influence toxicity include: chemical composition, shape, surface structure, surface charge, aggregation and solubility, and the presence or absence of functional groups of other chemicals. The large number of variables influencing toxicity means that it is difficult to generalise about health risks associated with exposure to nanomaterials – each new nanomaterial must be assessed individually and all material properties must be taken into account.

The name comes from projective geometry, where the projective group acting on homogeneous coordinates (x0:x1: ... :xn) is the underlying group of the geometry.This is therefore PGL(n + 1, F) for projective space of dimension n Stated differently, the natural action of GL(V) on V descends to an action of PGL(V) on the projective space P(V). The projective linear groups therefore generalise the case PGL(2, C) of Möbius transformations (sometimes called the Möbius group), which acts on the projective line. Note that unlike the general linear group, which is generally defined axiomatically as "invertible functions preserving the linear (vector space) structure", the projective linear group is defined constructively, as a quotient of the general linear group of the associated vector space, rather than axiomatically as "invertible functions preserving the projective linear structure".

The characteristic features of the geometry of non- positively curved Riemann surfaces are used to generalize the notion of non- positive beyond the study of Riemann surfaces. In the study of manifolds or orbifolds of higher dimension, the notion of sectional curvature is used wherein one restricts one's attention to two-dimensional subspaces of the tangent space at a given point. In dimensions greater than 2 the Mostow–Prasad rigidity theorem ensures that a hyperbolic manifold of finite area has a unique complete hyperbolic metric so the study of hyperbolic geometry in this setting is integral to the study of topology. In an arbitrary geodesic metric space the notions of being Gromov hyperbolic or of being a CAT(0) space generalise the notion that on a Riemann surface of non-positive curvature, triangles whose sides are geodesics appear thin whereas in settings of positive curvature they appear fat.

Australian anthropologists willing to generalise suggest Aboriginal myths still being performed across Australia by Aboriginal peoples serve an important social function amongst their intended audiences: justifying the received ordering of their daily lives; helping shape peoples' ideas; and assisting to influence others' behaviour. In addition, such performance often continuously incorporates and "mythologises" historical events in the service of these social purposes in an otherwise rapidly changing modern world. > It is always integral and common... that the Law (Aboriginal law) is > something derived from ancestral peoples or Dreamings and is passed down the > generations in a continuous line. While... entitlements of particular human > beings may come and go, the underlying relationships between foundational > Dreamings and certain landscapes are theoretically eternal ... the > entitlements of people to places are usually regarded strongest when those > people enjoy a relationship of identity with one or more Dreamings of that > place.

On the one hand, figures such as Karl Radek argued that a stagist strategy was correct for China, although their writings are only known to us now second hand, having perished in the 1930s (if original copies exist in the archives, they have not been located since the dissolution of the Soviet Union in December 1991). On the other hand, Trotsky generalised his theory of permanent revolution which had only been applied in the case of Russia previously and argued that the proletariat needed to take power in a process of uninterrupted and permanent revolution in order to not only carry out the tasks of the bourgeois-democratic revolution, but to implement socialism. His position was put forward in his essay entitled The Permanent Revolution which can be found today in a single book together with Results and Prospects. Not only did Trotsky generalise his theory of permanent revolution in this essay, but he also grounded it in the idea of uneven and combined development.

He also published speculative works on hybridisation in evolution: Larvae and Evolution (1992, a book foreworded by Lynn Margulis and Alfred I. Tauber), The Origins of Larvae (2003, a revised and extended edition of Larvae and Evolution, not to be confounded with his 2007 article of same title published in the magazine American Scientist), and some articles on the same subject. In Larvae and Evolution Williamson developed a controversial hypothesis proposing the acquisition of larval stages in some marine organisms by hybridisation between two distant animal species (a speciation process referred to as hybridogenesis by Williamson). The fraction of the genome of one of the contributor species would be restricted to lead the developmental program of a newly acquired larva whereas the genome of the other contributor would drive the development of most of the adult anatomical structures. During the following years he would generalise his theory to other animal groups featuring a holometabolous development.

In 1827, he republished his Lettres sur l'histoire de France, with the addition of fifteen new ones, in which he described some of the more striking episodes in the history of the rise of the medieval communes. The chronicles of the 11th and 12th centuries and a few communal charters provided him with materials for a solid work. For this reason his work on the communes has not become so out of date as his Norman Conquest; but he was too apt to generalise from the facts furnished by a few striking cases which occurred in a small portion of France, and helped to spread among the public, and even among professional historians, mistaken ideas concerning one of the most complex problems relating to the social origins of France. Thierry ardently supported the July Revolution and the triumph of liberal ideas; at this time, too, his brother Amédée was appointed prefect, and he went to live with him for four years.

Arithmetic zeta functions generalise the Riemann and Dedekind zeta functions as well as the zeta functions of varieties over finite fields to every arithmetic scheme or a scheme of finite type over integers. The arithmetic zeta function of a regular connected equidimensional arithmetic scheme of Kronecker dimension n can be factorized into the product of appropriately defined L-factors and an auxiliary factor . Assuming a functional equation and meromorphic continuation, the generalized Riemann hypothesis for the L-factor states that its zeros inside the critical strip \Re(s)\in (0,n) lie on the central line. Correspondingly, the generalized Riemann hypothesis for the arithmetic zeta function of a regular connected equidimensional arithmetic scheme states that its zeros inside the critical strip lie on vertical lines \Re(s)=1/2,3/2,\dots,n-1/2 and its poles inside the critical strip lie on vertical lines \Re(s)=1, 2, \dots,n-1.

Bonnie Anne (96 bars), MacDonald of Sleat (128 bars)). In fact, the figures and arrangement of modern Scottish country dances, while derived from a 300-year tradition, make it difficult to generalise because many newer dances feature new ideas such as partner changes (you dance with a new partner on each new time through the dance, as in "Nighean Donn" (by Peter Hastings) or "Caddam Wood" (by John Mitchell)), palindromic structure (the sequence of figures is similar seen from the end to the beginning as it is seen from the beginning to the end, as in "The White Heather Jig" by Cosh), fugues (the sequence of figures for each couple is intricately intertwined to resemble the structure of a musical fugue), canons (a new couple begins their time through even though the couple before have not finished theirs yet) and others, such as John Drewry's "Crossing the Line", where the bottom of the set becomes the top for the next time through. Dance devisers seem to enjoy blending new ideas with the traditional though the results vary in popularity.

In October 2006, they performed at The Secret Policeman's Ball. On New Year's Eve 2006, the Zutons appeared on Jools Holland's annual Hootenanny on BBC television on which they performed their songs "Valerie", "Why Don't You Give Me Your Love?" and "It's The Little Things We Do." Abi Harding playing the saxophone in 2008 As the November tour began, the band gave an interview to STV discussing songwriting, making videos and their American dates with The Killers. In a separate interview, Payne complained about the tendency of music writers and magazines to generalise a particular city as the breeding ground of new 'movements', "A lot of bands get lumped in when they’re in the same neck of the woods and journalists–especially in England–like to make a big deal out of that and make it into a scene, as if the individual bands aren’t good enough to write about." The band announced on 13 July 2007 that guitarist Boyan Chowdhury had left The Zutons, citing "musical differences".

The first published concerns came from Ludwig Rütimeyer, a professor of zoology and comparative anatomy at the University of Basel who had placed fossil mammals in an evolutionary lineage early in the 1860s and had been sent a complimentary copy. At the end of 1868 his review in the Archiv für Anthropologie wondered about the claim that the work was "popular and scholarly", doubting whether the second was true, and expressed horror about such public discussion of man's place in nature with illustrations such as the evolutionary trees being shown to non-experts. Though he made no suggestion that embryo illustrations should be directly based on specimens, to him the subject demanded the utmost "scrupulosity and conscientiousness" and an artist must "not arbitrarily model or generalise his originals for speculative purposes" which he considered proved by comparison with works by other authors. In particular, "one and the same, moreover incorrectly interpreted woodcut, is presented to the reader three times in a row and with three different captions as [the] embryo of the dog, the chick, [and] the turtle".

In mathematics, the Hurwitz problem, named after Adolf Hurwitz, is the problem of finding multiplicative relations between quadratic forms which generalise those known to exist between sums of squares in certain numbers of variables. There are well-known multiplicative relationships between sums of squares in two variables : (x^2+y^2)(u^2+v^2) = (xu-yv)^2 + (xv+yu)^2 \ , (known as the Brahmagupta–Fibonacci identity), and also Euler's four-square identity and Degen's eight-square identity. These may be interpreted as multiplicativity for the norms on the complex numbers, quaternions and octonions respectively.Charles W. Curtis (1963) "The Four and Eight Square Problem and Division Algebras" in Studies in Modern Algebra edited by A.A. Albert, pages 100–125, Mathematical Association of America, Solution of Hurwitz’s Problem on page 115 The Hurwitz problem for the field K is to find general relations of the form : (x_1^2+\cdots+x_r^2) \cdot (y_1^2+\cdots+y_s^2) = (z_1^2 + \cdots + z_n^2) \ , with the z being bilinear forms in the x and y: that is, each z is a K-linear combination of terms of the form xiyj.

Graham, Russ J London Calling , Television House from Transdiffusion 1 January 2004, accessed 27 November 2008 In that time, he supervised the conversion of the former headquarters of the Air Ministry, Adastral House, into Television House, A-R studios and administration headquarters, which also served as the headquarters for ITN, the TV Times and, at first, Associated TeleVision, A-R's main rival. At the same time, he was also actively involved in defining the station's identity, formulating the programme plans, creating an advertising market for television, chairing ITN and negotiating industrial relations with the film and broadcasting unions. Many stories are told by old ITV hands about Brownrigg's idiosyncrasies, especially his dominant - or domineeringBromsgrove, Mark Brian Masters MBE , TV Heroes from Transdiffusion, accessed 27 November 2008 \- manner, his name- dropping, his willingness to outrageously generalise on any subject and his requirement for very junior staff to salute him and his fellow directors. However, personal friends also point out that he had a great sense of humour and an ability to laugh at himself \- many of the anecdotes about him may therefore have derived from him in the first place.

Aboriginal specialists willing to generalise believe all Aboriginal myths across Australia, in combination, represent a kind of unwritten (oral) library within which Aboriginal peoples learn about the world and perceive a peculiarly Aboriginal 'reality' dictated by concepts and values vastly different from those of western societies: > Aboriginal people learned from their stories that a society must not be > human-centred but rather land centred, otherwise they forget their source > and purpose ... humans are prone to exploitative behaviour if not constantly > reminded they are interconnected with the rest of creation, that they as > individuals are only temporal in time, and past and future generations must > be included in their perception of their purpose in life. > People come and go but the Land, and stories about the Land, stay. This is a > wisdom that takes lifetimes of listening, observing and experiencing ... > There is a deep understanding of human nature and the environment... sites > hold 'feelings' which cannot be described in physical terms... subtle > feelings that resonate through the bodies of these people... It is only when > talking and being with these people that these 'feelings' can truly be > appreciated. This is... the intangible reality of these people...

There are two families of conjectures, formulated for general classes of L-functions (the very general setting being for L-functions L(s) associated to Chow motives over number fields), the division into two reflecting the questions of: :(a) how to replace π in the Leibniz formula by some other "transcendental" number (whether or not it is yet possible for transcendental number theory to provide a proof of the transcendence); and :(b) how to generalise the rational factor in the formula (class number divided by number of roots of unity) by some algebraic construction of a rational number that will represent the ratio of the L-function value to the "transcendental" factor. Subsidiary explanations are given for the integer values of n for which such formulae L(n) can be expected to hold. The conjectures for (a) are called Beilinson's conjectures, for Alexander Beilinson.Peter Schneider, Introduction to the Beilinson Conjectures (PDF)Jan Nekovář, Beilinson's Conjectures (PDF) The idea is to abstract from the regulator of a number field to some "higher regulator" (the Beilinson regulator), a determinant constructed on a real vector space that comes from algebraic K-theory.