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4,000 | The Jordan–Hölder theorem is a more precise way of stating this fact about finite groups. However, a significant difference from integer factorization is that such "building blocks" do not necessarily determine a unique group, since there might be many non-isomorphic groups with the same composition series or, put in a... | Classification of finite simple groups | 0.829293 |
4,001 | Groups of sectional 2-rank at most 4, classified by the Gorenstein–Harada theorem.The classification of groups of small 2-rank, especially ranks at most 2, makes heavy use of ordinary and modular character theory, which is almost never directly used elsewhere in the classification. All groups not of small 2 rank can be... | Classification of finite simple groups | 0.829293 |
4,002 | Groups of 2-rank 2. Alperin showed that the Sylow subgroup must be dihedral, quasidihedral, wreathed, or a Sylow 2-subgroup of U3(4). The first case was done by the Gorenstein–Walter theorem which showed that the only simple groups are isomorphic to L2(q) for q odd or A7, the second and third cases were done by the Alp... | Classification of finite simple groups | 0.829293 |
4,003 | The simple groups of low 2-rank are mostly groups of Lie type of small rank over fields of odd characteristic, together with five alternating and seven characteristic 2 type and nine sporadic groups. The simple groups of small 2-rank include: Groups of 2-rank 0, in other words groups of odd order, which are all solvabl... | Classification of finite simple groups | 0.829293 |
4,004 | This is accomplished by the B-theorem, which states that every component of C/O(C) is the image of a component of C. The idea is that these groups have a centralizer of an involution with a component that is a smaller quasisimple group, which can be assumed to be already known by induction. So to classify these groups ... | Classification of finite simple groups | 0.829293 |
4,005 | The rank 1 groups are the thin groups, classified by Aschbacher, and the rank 2 ones are the notorious quasithin groups, classified by Aschbacher and Smith. These correspond roughly to groups of Lie type of ranks 1 or 2 over fields of characteristic 2. Groups of rank at least 3 are further subdivided into 3 classes by ... | Classification of finite simple groups | 0.829293 |
4,006 | In physics, the concept of absolute rotation—rotation independent of any external reference—is a topic of debate about relativity, cosmology, and the nature of physical laws. For the concept of absolute rotation to be scientifically meaningful, it must be measurable. In other words, can an observer distinguish between ... | Absolute rotation | 0.829272 |
4,007 | In classical mechanics, an explanation of this deformation requires external causes in a frame of reference in which the spheroid is not rotating, and these external causes may be taken as "absolute rotation" in classical physics and special relativity. In general relativity, no external causes are invoked. The rotatio... | Absolute rotation | 0.829272 |
4,008 | The South African National Bioinformatics Institute (SANBI) is a non-profit organisation in Cape Town, South Africa dedicated to bioinformatics, biotechnology and genomics in health research. SANBI maintains current collaborations with institutes and laboratories at Harvard University, Oxford University, Cambridge Univ... | South African National Bioinformatics Institute | 0.829261 |
4,009 | From 2000 to 2014, Dr. Frank Plummer was the Scientific Director General of the National Microbiology Laboratory. Under Dr. Plummer's guidance, the NML developed into one of the world's premier institutions in the research, detection, and response to global infectious disease and bio-security threats. Dr. Plummer recei... | National Microbiology Laboratory | 0.829249 |
4,010 | The National Microbiology Laboratory (NML) is part of the Public Health Agency of Canada (PHAC), the agency of the Government of Canada that is responsible for public health, health emergency preparedness and response, and infectious and chronic disease control and prevention. NML is located in several sites across the... | National Microbiology Laboratory | 0.829249 |
4,011 | HIV and Retrovirology - providing laboratory services and scientific expertise relating to HIV and emerging retroviruses. The Science Technology Core and Services Division works with these divisions to provide technological approaches, including genomics, proteomics and bioinformatics. There is also the Public Health R... | National Microbiology Laboratory | 0.829249 |
4,012 | Dr. Gilmour spearheaded the partnership that brought these two laboratories together under the National Microbiology Laboratory umbrella. He was previously the Chief, Enteric Diseases and subsequently the Program Director, Bacteriology and Enteric Diseases at the NML. Dr. Gilmour has won a number of scientific awards i... | National Microbiology Laboratory | 0.829249 |
4,013 | Dr. Plummer stepped down as the NML's Scientific Director General to take the position as senior adviser to the Agency's Chief Public Health Officer in 2014. He remained as a distinguished professor at the University of Manitoba prior to his death in February 2020. In 2015, Dr. Matthew Gilmour became the Scientific Dir... | National Microbiology Laboratory | 0.829249 |
4,014 | The National Microbiology Laboratory was preceded by the Bureau of Microbiology which was originally part of the Laboratory Centre for Disease Control of Health Canada in Ottawa. In the 1980s, Health Canada identified both the need to replace existing laboratory space that was reaching the end of its lifespan and the n... | National Microbiology Laboratory | 0.829249 |
4,015 | That is, there is no interaction between the input kernel and the task kernel. The structure on tasks is represented solely by A. Methods for non-separable kernels Γ is a current field of research. For the separable case, the representation theorem is reduced to f ( x ) = ∑ i = 1 N k ( x , x i ) A c i {\textstyle f(x)=... | Multi-task learning | 0.829235 |
4,016 | The Multi-Task Learning via StructurAl Regularization (MALSAR) Matlab package implements the following multi-task learning algorithms: Mean-Regularized Multi-Task Learning Multi-Task Learning with Joint Feature Selection Robust Multi-Task Feature Learning Trace-Norm Regularized Multi-Task Learning Alternating Structura... | Multi-task learning | 0.829235 |
4,017 | Related to multi-task learning is the concept of knowledge transfer. Whereas traditional multi-task learning implies that a shared representation is developed concurrently across tasks, transfer of knowledge implies a sequentially shared representation. Large scale machine learning projects such as the deep convolution... | Multi-task learning | 0.829235 |
4,018 | , T {\displaystyle t\in 1,...,T} . Let n = ∑ t = 1 T n t {\displaystyle n=\sum _{t=1}^{T}n_{t}} . In this setting there is a consistent input and output space and the same loss function L: R × R → R + {\displaystyle {\mathcal {L}}:\mathbb {R} \times \mathbb {R} \rightarrow \mathbb {R} _{+}} for each task: . This result... | Multi-task learning | 0.829235 |
4,019 | Multi-task learning (MTL) is a subfield of machine learning in which multiple learning tasks are solved at the same time, while exploiting commonalities and differences across tasks. This can result in improved learning efficiency and prediction accuracy for the task-specific models, when compared to training the model... | Multi-task learning | 0.829235 |
4,020 | Sulfur oxidation involves the oxidation of reduced sulfur compounds (such as sulfide H2S), inorganic sulfur (S), and thiosulfate (S2O2−3) to form sulfuric acid (H2SO4). A classic example of a sulfur-oxidizing bacterium is Beggiatoa, a microbe originally described by Sergei Winogradsky, one of the founders of environmen... | Heterotrophic microorganism | 0.829234 |
4,021 | Challenging the leading experts of bioinformatics and statistical genetics, the sequence dataset will comprise 6 trillion DNA bases, 60-fold more sequence data than what has been published in DNA databases over the past 25 years.To determine the final design of the full project three pilot studies were designed and wil... | 1000 Genomes Project | 0.829232 |
4,022 | Data generated by the 1000 Genomes Project is widely used by the genetics community, making the first 1000 Genomes Project one of the most cited papers in biology. To support this user community, the project held a community analysis meeting in July 2012 that included talks highlighting key project discoveries, their i... | 1000 Genomes Project | 0.829232 |
4,023 | The 1000 Genomes Project (abbreviated as 1KGP), launched in January 2008, was an international research effort to establish by far the most detailed catalogue of human genetic variation. Scientists planned to sequence the genomes of at least one thousand anonymous participants from a number of different ethnic groups w... | 1000 Genomes Project | 0.829232 |
4,024 | Since the completion of the Human Genome Project advances in human population genetics and comparative genomics have made it possible to gain increasing insight into the nature of genetic diversity. However, we are just beginning to understand how processes like the random sampling of gametes, structural variations (in... | 1000 Genomes Project | 0.829232 |
4,025 | In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The Schrödinger equation for a free particle which is restricted to a ring (technically, whose configuration space is the circle S 1 {\displaystyle S^{1}} ) is − ℏ 2 2 m ∇ 2 ψ = E ψ {\displaystyle -{\frac {\hbar ... | Circular potential well | 0.829224 |
4,026 | In organic chemistry, aromatic compounds contain atomic rings, such as benzene rings (the Kekulé structure) consisting of five or six, usually carbon, atoms. So does the surface of "buckyballs" (buckminsterfullerene). This ring behaves like a circular waveguide, with the valence electrons orbiting in both directions. T... | Circular potential well | 0.829224 |
4,027 | Bacterial cells are widely used for cloning processes, genetic modification and small-scale productions. Escherichia coli (E. Coli) is widely utilised due to its highly explored genetics, widely available genetic tools for gene expression, accurate profiling and its ability to grow in inexpensive media at high cell den... | Subunit vaccine | 0.829209 |
4,028 | A peptide-based subunit vaccine employs a peptide instead of a full protein. Peptide-based subunit vaccine mostly used due to many reasons,such as, it is easy and affordable for massive production. Adding to that, its greatest stability, purity and exposed composition. Three steps occur leading to creation of peptide s... | Subunit vaccine | 0.829209 |
4,029 | Reduced immunogenicity compared to attenuated vaccinesRequire adjuvants to improve immunogenicity Often require multiple doses ("booster" doses) to provide long-term immunity Can be difficult to isolate the specific antigen(s) which will invoke the necessary immune response It is not easy to supervise conjugation chemi... | Subunit vaccine | 0.829209 |
4,030 | Ludwig Burmester: theory of linkages Carlo Alberto Castigliano: Elasticity (physics) Ludwig Prandtl: Fluid mechanics, Plasticity Stephen Timoshenko: author of many lasting textbooks, father of modern applied mechanics Theodore von Karman: Fluid mechanics, Structural instability Richard Edler von Mises: Plasticity Geoff... | Mechanician | 0.829206 |
4,031 | After the Sumerians, some of the most famous ancient works on mathematics came from Egypt in the form of the Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus. The more famous Rhind Papyrus has been dated back to approximately 1650 BCE, but it is thought to be a copy of an even older scroll. This papyrus w... | Math education | 0.829203 |
4,032 | Elementary school children need to spend a long time learning to express algebraic properties without symbols before learning algebraic notation. When learning symbols, many students believe letters always represent unknowns and struggle with the concept of variable. They prefer arithmetic reasoning to algebraic equati... | Math education | 0.829203 |
4,033 | Semenya lost her case, in the Court of Arbitration for Sport on 1 May 2019. During proceedings it was revealed that Semenya has 5α-reductase deficiency, and it was argued that although her hormones are different from both normal male and normal female biology, the advantage afforded by testosterone in the male level is... | Testosterone regulations in women's athletics | 0.829198 |
4,034 | Mathematical manipulatives play a key role in young children's mathematics understanding and development. These concrete objects facilitate children's understanding of important math concepts, then later help them link these ideas to representations and abstract ideas. For example, there are manipulatives specifically ... | Mathematical manipulatives | 0.82918 |
4,035 | The major and minor diameters delimit truncations on either side of the sharp V. The nominal diameter of Metric (e.g. M8) and Unified (e.g. 5⁄16 in) threads is the theoretical major diameter of the male thread, which is truncated (diametrically) by 0.866⁄4 of the pitch from the dimension over the tips of the "fundament... | Turn per inch | 0.82916 |
4,036 | This fact is intrinsic to the geometry of an equilateral triangle — a direct result of the basic trigonometric functions. It is independent of measurement units (inch vs mm). However, UTS and ISO threads are not sharp threads. | Turn per inch | 0.82916 |
4,037 | In theoretical computer science and formal language theory, the equivalence problem is the question of determining, given two representations of formal languages, whether they denote the same formal language. The complexity and decidability of this decision problem depend upon the type of representation under considera... | Equivalence problem | 0.829155 |
4,038 | Isfahan Mathematics House (Persian:خانه ریاضیات اصفهان) is a non-formal education institute in Iran, focusing primarily on statistics, biology, physics, maths, AI, computer programming courses. Established 1998 mainly priority of the Isfahan mathematics house is to offer students training. | Math house | 0.829153 |
4,039 | In molecular biology, the myogenic determination factor 5 proteins are a family of proteins found in eukaryotes. This family includes the Myf5 protein, which is responsible for directing cells to the skeletal myocyte lineage during development. Myf5 is likely to act in a similar way to the other MRF4 proteins such as M... | Myogenic determination factor 5 | 0.82915 |
4,040 | Discriminative training of linear classifiers usually proceeds in a supervised way, by means of an optimization algorithm that is given a training set with desired outputs and a loss function that measures the discrepancy between the classifier's outputs and the desired outputs. Thus, the learning algorithm solves an o... | Linear classification | 0.829148 |
4,041 | In the field of machine learning, the goal of statistical classification is to use an object's characteristics to identify which class (or group) it belongs to. A linear classifier achieves this by making a classification decision based on the value of a linear combination of the characteristics. An object's characteri... | Linear classification | 0.829148 |
4,042 | In particle physics, the most important hierarchy problem is the question that asks why the weak force is 1024 times as strong as gravity. Both of these forces involve constants of nature, the Fermi constant for the weak force and the Newtonian constant of gravitation for gravity. Furthermore, if the Standard Model is ... | Hierarchy problem | 0.829137 |
4,043 | If the universe came to exist by chance, and perhaps vast numbers of other universes exist or have existed, then life capable of physics experiments only arose in universes that by chance had very balanced forces. All of the universes where the forces were not balanced didn't develop life capable of asking this questio... | Hierarchy problem | 0.829137 |
4,044 | We might also wonder if one force is so much weaker than the others that it needs a factor of 4×1029 to allow it to be related to them in terms of effects, how did our universe come to be so exactly balanced when its forces emerged? In current particle physics, the differences between some parameters are much larger th... | Hierarchy problem | 0.829137 |
4,045 | Suppose a physics model requires four parameters which allow it to produce a very high-quality working model, generating predictions of some aspect of our physical universe. Suppose we find through experiments that the parameters have values: 1.2, 1.31, 0.9 and 404,331,557,902,116,024,553,602,703,216.58 (roughly 4×1029... | Hierarchy problem | 0.829137 |
4,046 | (Note that the contribution here is positive. This is because of the spin-statistics theorem, which means that fermions will have a negative contribution and bosons a positive contribution. This fact is exploited.) This gives a total contribution to the Higgs mass to be zero if we include both the fermionic and bosonic... | Hierarchy problem | 0.829137 |
4,047 | We only need to prove the theorem for the 2-dimensional case, since we can then generalize it to n-dimensions by applying the theorem sequentially to each pair of coordinates. Since rotating by 90 degrees preserves the joint distribution, both X 1 , X 2 {\displaystyle X_{1},X_{2}} has the same probability measure. Let ... | Maxwell's theorem | 0.829136 |
4,048 | In probability theory, Maxwell's theorem (known also as Herschel-Maxwell's theorem and Herschel-Maxwell's derivation) states that if the probability distribution of a random vector in R n {\displaystyle \mathbb {R} ^{n}} is unchanged by rotations, and if the components are independent, then the components are identical... | Maxwell's theorem | 0.829136 |
4,049 | Now assume that it is not. By Lebesgue's decomposition theorem, we decompose it to a sum of regular measure and an atomic measure: μ = μ r + μ s {\displaystyle \mu =\mu _{r}+\mu _{s}} . We need to show that μ s = 0 {\displaystyle \mu _{s}=0} , with a proof by contradiction. | Maxwell's theorem | 0.829136 |
4,050 | If the probability distribution of a vector-valued random variable X = ( X1, ..., Xn )T is the same as the distribution of GX for every n×n orthogonal matrix G and the components are independent, then the components X1, ..., Xn are normally distributed with expected value 0 and all have the same variance. This theorem ... | Maxwell's theorem | 0.829136 |
4,051 | James Clerk Maxwell proved the theorem in Proposition IV of his 1860 paper.Ten years earlier, John Herschel also proved the theorem.The logical and historical details of the theorem may be found in. | Maxwell's theorem | 0.829136 |
4,052 | The education part of NBIC, BioWise, organizes courses and trainings at different levels. They provide awareness training at schools, collaborate with the different bioinformatics education programs at the universities in the Netherlands, and organize trainings for PhD students. Also, subject-specific trainings and con... | Netherlands Bioinformatics Centre | 0.829134 |
4,053 | In 2003 NBIC was launched as a not-for-profit organization, to strengthen and organize the bioinformatics research in the Netherlands. NBIC is one of the four enabling technology centres that were initiated by the Netherlands Genomics Initiative (NGI) to improve the genomics-based research in the Netherlands. The other... | Netherlands Bioinformatics Centre | 0.829134 |
4,054 | First steps have been made to include commercial entities, among others, via the Bioinformatics Industrial Users Platform (BIUP). The BIUP, though still in its start-up phase in mid-2011, has already attracted partners such as DSM. | Netherlands Bioinformatics Centre | 0.829134 |
4,055 | A wide variety of bioinformatics software has been created by people involved in NBIC. NBIC also hosts a service to coordinate software development (Trac server with software releases and project documentation). Many tools are also made available through NBIC's own open Galaxy server | Netherlands Bioinformatics Centre | 0.829134 |
4,056 | A large part of NBIC's efforts focus on developing new or strengthening existing bio-informatics communities. For example, NBIC hosted the 2011 Galaxy Community Conference. The Netherlands Bioinformatics for Proteomics Platform (for short NBPP) is a joint initiative of the Netherlands Bioinformatics Centre (NBIC) and t... | Netherlands Bioinformatics Centre | 0.829134 |
4,057 | The Netherlands Bioinformatics Centre or NBIC (2003-2013) was a Dutch, government-funded organization, that coordinated all academic work on bioinformatics in the Netherlands. NBIC consisted of programs for research (BioRange), for education (BioWise), and for support (BioAssist). NBIC partners are all Dutch universiti... | Netherlands Bioinformatics Centre | 0.829134 |
4,058 | So far, NBIC has achieved its goal of bringing together the different bioinformatics research groups in the Netherlands. It is now also partnering up with Dutch universities of Applied Sciences (UAS) in the LOBIN network. in July 2011, four UASes have joined. | Netherlands Bioinformatics Centre | 0.829134 |
4,059 | The support department of NBIC, BioAssist, consists of task forces that bring together experts in the different fields of Bioinformatics. Together, these people identify common problems in their field that they set out to solve in a collaborative way. BioAssist also has a group, BioInformatics Research Support (BRS), t... | Netherlands Bioinformatics Centre | 0.829134 |
4,060 | The Netherlands Bioinformatics Centre was funded by the Dutch government through the Netherlands Genomics Initiative (NGI) and the BSIK(knowledge infrastructures) programme. | Netherlands Bioinformatics Centre | 0.829134 |
4,061 | However, knowing the true mean and standard deviation of a population is often an unrealistic expectation, except in cases such as standardized testing, where the entire population is measured. When the population mean and the population standard deviation are unknown, the standard score may be estimated by using the s... | Standardized variable | 0.829125 |
4,062 | In mathematical statistics, a random variable X is standardized by subtracting its expected value E {\displaystyle \operatorname {E} } and dividing the difference by its standard deviation σ ( X ) = Var ( X ): {\displaystyle \sigma (X)={\sqrt {\operatorname {Var} (X)}}:} Z = X − E σ ( X ) {\displaystyle Z={X-\o... | Standardized variable | 0.829125 |
4,063 | Kinematic dynamo can be also viewed as the phenomenon of the spontaneous breakdown of the topological supersymmetry of the associated stochastic differential equation related to the flow of the background matter. Within stochastic supersymmetric theory, this supersymmetry is an intrinsic property of all stochastic diff... | Dynamo mechanism | 0.829121 |
4,064 | Linear combinations are especially useful in contexts where straightforward addition would violate some normalization rule, such as mixing of strategies in game theory or superposition of states in quantum mechanics.Convolution is used to add two independent random variables defined by distribution functions. Its usual... | Addition | 0.829114 |
4,065 | In modular arithmetic, the set of available numbers is restricted to a finite subset of the integers, and addition "wraps around" when reaching a certain value, called the modulus. For example, the set of integers modulo 12 has twelve elements; it inherits an addition operation from the integers that is central to musi... | Addition | 0.829114 |
4,066 | In mathematics, in the realm of group theory, the term complemented group is used in two distinct, but similar ways. In (Hall 1937), a complemented group is one in which every subgroup has a group-theoretic complement. Such groups are called completely factorizable groups in the Russian literature, following (Baeva 195... | Complemented group | 0.829097 |
4,067 | In particular, support vector machines find a hyperplane that separates the feature space into two classes with the maximum margin. If the problem is not originally linearly separable, the kernel trick can be used to turn it into a linearly separable one, by increasing the number of dimensions. Thus a general hypersurf... | Decision boundary | 0.829093 |
4,068 | In the case of backpropagation based artificial neural networks or perceptrons, the type of decision boundary that the network can learn is determined by the number of hidden layers the network has. If it has no hidden layers, then it can only learn linear problems. If it has one hidden layer, then it can learn any con... | Decision boundary | 0.829093 |
4,069 | In such a situation, the distributed charges taken as a group always carries a whole number of elementary charge units. Yet one can point to zones within the assemblage where less than a full charge resides, such as the area around an atom's nucleus. This is possible in part because particles are not like mathematical ... | Atomic charge | 0.829081 |
4,070 | In atomic physics, a partial charge (or net atomic charge) is a non-integer charge value when measured in elementary charge units. It is represented by the Greek lowercase delta (𝛿), namely 𝛿− or 𝛿+. Partial charges are created due to the asymmetric distribution of electrons in chemical bonds. For example, in a pola... | Atomic charge | 0.829081 |
4,071 | Partial atomic charges are used in molecular mechanics force fields to compute the electrostatic interaction energy using Coulomb's law, even though this leads to substantial failures for anisotropic charge distributions. Partial charges are also often used for a qualitative understanding of the structure and reactivit... | Atomic charge | 0.829081 |
4,072 | Ritonavir was initially derived from a moderately potent and orally bioavailable small molecule, A-80987. The P3 and P2′ heterocyclic groups of A-80987 were redesigned to create an analogue, now known as ritonavir, with improved pharmacokinetic properties to the original.Full details of the synthesis of ritonavir were ... | Ritonavir | 0.829074 |
4,073 | A prompt for a text-to-text model can be a query such as "what is Fermat's little theorem?" a command such as "write a poem about leaves falling", a short statement of feedback (for example, "too verbose", "too formal", "rephrase again", "omit this word") or a longer statement including context, instructions, and input... | In-context learning (natural language processing) | 0.829071 |
4,074 | Phylogenomics draws information by comparing entire genomes, or at least large portions of genomes. Phylogenetics compares and analyzes the sequences of single genes, or a small number of genes, as well as many other types of data. Four major areas fall under phylogenomics: Prediction of gene function Establishment and... | Phylogenomics | 0.82907 |
4,075 | Phylogenomics is the intersection of the fields of evolution and genomics. The term has been used in multiple ways to refer to analysis that involves genome data and evolutionary reconstructions. It is a group of techniques within the larger fields of phylogenetics and genomics. | Phylogenomics | 0.82907 |
4,076 | These elements can be a point, line or plane with respect to which the symmetry operation is carried out. The symmetry operations of a molecule determine the specific point group for this molecule. In chemistry, there are five important symmetry operations. | Infinite group theory | 0.829064 |
4,077 | In chemistry and materials science, point groups are used to classify regular polyhedra, and the symmetries of molecules, and space groups to classify crystal structures. The assigned groups can then be used to determine physical properties (such as chemical polarity and chirality), spectroscopic properties (particular... | Infinite group theory | 0.829064 |
4,078 | The identity keeping the object fixed is always a symmetry of an object. Existence of inverses is guaranteed by undoing the symmetry and the associativity comes from the fact that symmetries are functions on a space, and composition of functions is associative. Frucht's theorem says that every group is the symmetry gro... | Infinite group theory | 0.829064 |
4,079 | Conformal maps give rise to Kleinian groups, for example. Symmetries are not restricted to geometrical objects, but include algebraic objects as well. For instance, the equation x 2 − 3 = 0 {\displaystyle x^{2}-3=0} has the two solutions 3 {\displaystyle {\sqrt {3}}} and − 3 {\displaystyle -{\sqrt {3}}} . | Infinite group theory | 0.829064 |
4,080 | Galois theory uses groups to describe the symmetries of the roots of a polynomial (or more precisely the automorphisms of the algebras generated by these roots). The fundamental theorem of Galois theory provides a link between algebraic field extensions and group theory. It gives an effective criterion for the solvabil... | Infinite group theory | 0.829064 |
4,081 | (For example the Hodge conjecture (in certain cases).) The one-dimensional case, namely elliptic curves is studied in particular detail. They are both theoretically and practically intriguing. In another direction, toric varieties are algebraic varieties acted on by a torus. Toroidal embeddings have recently led to adv... | Infinite group theory | 0.829064 |
4,082 | Algebraic geometry likewise uses group theory in many ways. Abelian varieties have been introduced above. The presence of the group operation yields additional information which makes these varieties particularly accessible. They also often serve as a test for new conjectures. | Infinite group theory | 0.829064 |
4,083 | A Lie group is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Sophus Lie, who laid the foundations of the theory of continuous transformation groups. The term groupes de Lie first appeared in French in 1893... | Infinite group theory | 0.829064 |
4,084 | A significant source of abstract groups is given by the construction of a factor group, or quotient group, G/H, of a group G by a normal subgroup H. Class groups of algebraic number fields were among the earliest examples of factor groups, of much interest in number theory. If a group G is a permutation group on a set ... | Infinite group theory | 0.829064 |
4,085 | In physics, groups are important because they describe the symmetries which the laws of physics seem to obey. According to Noether's theorem, every continuous symmetry of a physical system corresponds to a conservation law of the system. Physicists are very interested in group representations, especially of Lie groups,... | Infinite group theory | 0.829064 |
4,086 | Often, an additional objective expression (i.e., an optimization equation) is given, that is to be minimized or maximized by an optimal solution.For example, 0 ≤ x 1 ≤ 690 − 1.5 ⋅ x 2 ∧ 0 ≤ x 2 ≤ 530 − x 1 ∧ x 1 ≤ 640 − 0.75 ⋅ x 2 {\displaystyle 0\leq x_{1}\leq 690-1.5\cdot x_{2}\;\land \;0\leq x_{2}\leq 530-x_{1}\;\la... | Inequation | 0.829055 |
4,087 | In computer science, X + Y {\displaystyle {\boldsymbol {X}}+{\boldsymbol {Y}}} sorting is the problem of sorting pairs of numbers by their sums. Applications of the problem include transit fare minimisation, VLSI design, and sparse polynomial multiplication. As with comparison sorting and integer sorting more generally... | X + Y sorting | 0.829053 |
4,088 | Merge the sorted results A + A {\displaystyle A+A} , B + B {\displaystyle B+B} , and A + B {\displaystyle A+B} together.The number of comparisons C ( n ) {\displaystyle C(n)} needed to perform this recursive algorithm on an input of n {\displaystyle n} items can be analyzed using the recurrence relation where the 2 C (... | X + Y sorting | 0.829053 |
4,089 | Several other problems in computational geometry have equivalent or harder complexity to X + Y {\displaystyle X+Y} sorting, including constructing Minkowski sums of staircase polygons, finding the crossing points of an arrangement of lines in sorted order by their x {\displaystyle x} -coordinates, listing pairs of poin... | X + Y sorting | 0.829053 |
4,090 | A well-known lower bound for unstructured sorting, in the decision tree model, is based on the factorial number of sorted orders that an unstructured list may have. Because each comparison can at best reduce the number of possible orderings by a factor of two, sorting requires a number of comparisons at least equal to ... | X + Y sorting | 0.829053 |
4,091 | In 2016, the Welsh government issued a statement of intent and is considering participating in the 100,000 Genomes Project.The initial participants were recruited from Cambridge University Hospitals, University College London Partners, and Newcastle upon Tyne NHS Foundation Trust. The following medical centres joined t... | 100,000 Genomes Project | 0.829046 |
4,092 | The Genomics England Clinical Interpretation Partnership (GeCIP) includes 2,500 UK and international clinicians and scientists from approximately 300 institutions in 24 countries. There are plans to increase this number. Researchers are organised in "domains" formed around particular conditions, cancer types and resear... | 100,000 Genomes Project | 0.829046 |
4,093 | The human body can adapt to high altitude by breathing faster, having a higher heart rate, and adjusting its blood chemistry. It can take days or weeks to adapt to high altitude. However, above 8,000 metres (26,000 ft), (in the "death zone"), altitude acclimatization becomes impossible.There is a significantly lower ov... | Altitude | 0.829045 |
4,094 | A TK Solver model can include up to 32,000 rules, and the library that ships with the current version includes utilities for higher mathematics, statistics, engineering and science, finances, and programming. Variables in a rule are automatically posted to the Variable Sheet when the rule is entered and the rule is dis... | TK Solver | 0.829043 |
4,095 | TK Solver's core technologies are a declarative programming language, algebraic equation solver, an iterative equation solver, and a structured, object-based interface, using a command structure. The interface comprises nine classes of objects that can be shared between and merged into other TK files: Rules: equations,... | TK Solver | 0.829043 |
4,096 | TK Solver includes roughly 150 built-in functions: mathematical, trigonometric, Boolean, numerical calculus, matrix operations, database access, and programming functions, including string handling and calls to externally compiled routines. Users may also define three types of functions: declarative rule functions; lis... | TK Solver | 0.829043 |
4,097 | TK Solver has three ways of solving systems of equations. The "direct solver" solves a system algebraically by the principle of consecutive substitution. When multiple rules contain multiple unknowns, the program can trigger an iterative solver which uses the Newton–Raphson algorithm to successively approximate based o... | TK Solver | 0.829043 |
4,098 | Since photosynthesis, transpiration and stomatal conductance are an integral part of basic plant physiology, estimates of these parameters can be used to investigate numerous aspects of plant biology. The plant-scientific community has generally accepted photosynthetic systems as reliable and accurate tools to assist r... | Photosynthesis system | 0.829042 |
4,099 | The algorithm is useful in examining large data streams for patterns. This is particularly useful in applications of data compression, sight and sound recognition, and other artificial intelligence applications. | Approximate counting algorithm | 0.82902 |
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