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Valuation (geometry)	Operations on translation-invariant valuations	There are several natural operations defined on the subspace of smooth valuations Val Val ⁡(V). The most important one is the product of two smooth valuations. Together with pullback and pushforward, this operation extends to valuations on manifolds. Exterior product Let V,W be finite-dimensional real vector spaces. There exists a bilinear map, called the exterior product, which is uniquely characterized by the following two properties: it is continuous with respect to the usual topologies on Val and Val ∞.
Valuation (geometry)	Operations on translation-invariant valuations	if vol V⁡(∙+A) and vol W⁡(∙+B) where A∈K(V) and B∈K(W) are convex bodies with smooth boundary and strictly positive Gauss curvature, and vol V and vol W are densities on V and W, then Product The product of two smooth valuations Val ∞⁡(V) is defined by where Δ:V→V×V is the diagonal embedding. The product is a continuous map Equipped with this product, Val ∞⁡(V) becomes a commutative associative graded algebra with the Euler characteristic as the multiplicative identity.
Valuation (geometry)	Operations on translation-invariant valuations	Alesker-Poincaré duality By a theorem of Alesker, the restriction of the product is a non-degenerate pairing. This motivates the definition of the k -homogeneous generalized valuation, denoted Val k−∞⁡(V), as Val Dens ⁡(V), topologized with the weak topology. By the Alesker-Poincaré duality, there is a natural dense inclusion Val Val k−∞⁡(V)/ Convolution Convolution is a natural product on Val Dens ⁡(V∗).
Valuation (geometry)	Operations on translation-invariant valuations	For simplicity, we fix a density vol on V to trivialize the second factor. Define for fixed A,B∈K(V) with smooth boundary and strictly positive Gauss curvature There is then a unique extension by continuity to a map called the convolution. Unlike the product, convolution respects the co-grading, namely if Val n−i∞⁡(V), Val n−j∞⁡(V), then Val n−i−j∞⁡(V). For instance, let V(K1,…,Kn) denote the mixed volume of the convex bodies K1,…,Kn⊂Rn. If convex bodies A1,…,An−i in Rn with a smooth boundary and strictly positive Gauss curvature are fixed, then ϕ(K)=V(K[i],A1,…,An−i) defines a smooth valuation of degree i. The convolution two such valuations is where ci,j is a constant depending only on i,j,n. Fourier transform The Alesker-Fourier transform is a natural, GL(V) -equivariant isomorphism of complex-valued valuations discovered by Alesker and enjoying many properties resembling the classical Fourier transform, which explains its name. It reverses the grading, namely Val Val Dens ⁡(V), and intertwines the product and the convolution: Fixing for simplicity a Euclidean structure to identify V=V∗, Dens ⁡(V)=C, we have the identity On even valuations, there is a simple description of the Fourier transform in terms of the Klain embedding: Kl Kl ϕ⁡(E⊥). In particular, even real-valued valuations remain real-valued after the Fourier transform. For odd valuations, the description of the Fourier transform is substantially more involved. Unlike the even case, it is no longer of purely geometric nature. For instance, the space of real-valued odd valuations is not preserved. Pullback and pushforward Given a linear map f:U→V, there are induced operations of pullback Val Val ⁡(U) and pushforward Val Dens Val Dens ⁡(V)∗. The pullback is the simpler of the two, given by f∗ϕ(K)=ϕ(f(K)). It evidently preserves the parity and degree of homogeneity of a valuation. Note that the pullback does not preserve smoothness when f is not injective. The pushforward is harder to define formally. For simplicity, fix Lebesgue measures on U and V. The pushforward can be uniquely characterized by describing its action on valuations of the form vol ⁡(∙+A), for all A∈K(U), and then extended by continuity to all valuations using the Irreducibility Theorem. For a surjective map f, For an inclusion f:U↪V, choose a splitting V=U⊕W. Then Informally, the pushforward is dual to the pullback with respect to the Alesker-Poincaré pairing: for Val ⁡(V) and Val Dens ⁡(U)∗, However, this identity has to be carefully interpreted since the pairing is only well-defined for smooth valuations. For further details, see.
Valuation (geometry)	Valuations on manifolds	In a series of papers beginning in 2006, Alesker laid down the foundations for a theory of valuations on manifolds that extends the theory of valuations on convex bodies. The key observation leading to this extension is that via integration over the normal cycle (1), a smooth translation-invariant valuation may be evaluated on sets much more general than convex ones. Also (1) suggests to define smooth valuations in general by dropping the requirement that the form ω be translation-invariant and by replacing the translation-invariant Lebesgue measure with an arbitrary smooth measure.
Valuation (geometry)	Valuations on manifolds	Let X be an n-dimensional smooth manifold and let PX=P+(T∗X) be the co-sphere bundle of X, that is, the oriented projectivization of the cotangent bundle. Let P(X) denote the collection of compact differentiable polyhedra in X. The normal cycle N(A)⊂PX of A∈P(X), which consists of the outward co-normals to A, is naturally a Lipschitz submanifold of dimension 1.
Valuation (geometry)	Valuations on manifolds	For ease of presentation we henceforth assume that X is oriented, even though the concept of smooth valuations in fact does not depend on orientability. The space of smooth valuations V∞(X) on X consists of functions ϕ:P(X)→C of the form where μ∈Ωn(X) and ω∈Ωn−1(PX) can be arbitrary. It was shown by Alesker that the smooth valuations on open subsets of X form a soft sheaf over X.
Valuation (geometry)	Valuations on manifolds	Examples The following are examples of smooth valuations on a smooth manifold X Smooth measures on X. The Euler characteristic; this follows from the work of Chern on the Gauss-Bonnet theorem, where such μ and ω were constructed to represent the Euler characteristic. In particular, μ is then the Chern-Gauss-Bonnet integrand, which is the Pfaffian of the Riemannian curvature tensor. If X is Riemannian, then the Lipschitz-Killing valuations or intrinsic volumes V0X=χ,V1X,…,VnX=volX are smooth valuations. If f:X→Rm is any isometric immersion into a Euclidean space, then ViX=f∗ViRm, where ViRm denotes the usual intrinsic volumes on Rm (see below for the definition of the pullback). The existence of these valuations is the essence of Weyl's tube formula. Let CPn be the complex projective space, and let GrkC denote the Grassmannian of all complex projective subspaces of fixed dimension k. The function where the integration is with respect to the Haar probability measure on GrkC, is a smooth valuation. This follows from the work of Fu. Filtration The space V∞(X) admits no natural grading in general, however it carries a canonical filtration Here Wn consists of the smooth measures on X, and Wj is given by forms ω in the ideal generated by π∗Ωj(X), where π:PX→X is the canonical projection. The associated graded vector space ⨁i=0nWi/Wi+1 is canonically isomorphic to the space of smooth sections where Val i∞⁡(TX) denotes the vector bundle over X such that the fiber over a point x∈X is Val i∞⁡(TxX), the space of i -homogeneous smooth translation-invariant valuations on the tangent space TxX. Product The space V∞(X) admits a natural product. This product is continuous, commutative, associative, compatible with the filtration: and has the Euler characteristic as the identity element. It also commutes with the restriction to embedded submanifolds, and the diffeomorphism group of X acts on V∞(X) by algebra automorphisms. For example, if X is Riemannian, the Lipschitz-Killing valuations satisfy The Alesker-Poincaré duality still holds. For compact X it says that the pairing V∞(X)×V∞(X)→C, (ϕ,ψ)↦(ϕ⋅ψ)(X) is non-degenerate. As in the translation-invariant case, this duality can be used to define generalized valuations. Unlike the translation-invariant case, no good definition of continuous valuations exists for valuations on manifolds. The product of valuations closely reflects the geometric operation of intersection of subsets. Informally, consider the generalized valuation χA=χ(A∩∙). The product is given by χA⋅χB=χA∩B. Now one can obtain smooth valuations by averaging generalized valuations of the form χA, more precisely ϕ(X)=∫Sχs(A)ds is a smooth valuation if S is a sufficiently large measured family of diffeomorphisms. Then one has see. Pullback and pushforward Every smooth immersion f:X→Y of smooth manifolds induces a pullback map f∗:V∞(Y)→V∞(X). If f is an embedding, then The pullback is a morphism of filtered algebras. Every smooth proper submersion f:X→Y defines a pushforward map f∗:V∞(X)→V∞(Y) by The pushforward is compatible with the filtration as well: dim dim ⁡Y)(Y). For general smooth maps, one can define pullback and pushforward for generalized valuations under some restrictions.
Valuation (geometry)	Applications in Integral Geometry	Let M be a Riemannian manifold and let G be a Lie group of isometries of M acting transitively on the sphere bundle SM. Under these assumptions the space V∞(M)G of G -invariant smooth valuations on M is finite-dimensional; let ϕ1,…,ϕm be a basis. Let A,B∈P(M) be differentiable polyhedra in M.
Valuation (geometry)	Applications in Integral Geometry	Then integrals of the form ∫Gϕi(A∩gB)dg are expressible as linear combinations of ϕk(A)ϕl(B) with coefficients cikl independent of A and B : Formulas of this type are called kinematic formulas. Their existence in this generality was proved by Fu. For the three simply connected real space forms, that is, the sphere, Euclidean space, and hyperbolic space, they go back to Blaschke, Santaló, Chern, and Federer.
Valuation (geometry)	Applications in Integral Geometry	Describing the kinematic formulas explicitly is typically a difficult problem. In fact already in the step from real to complex space forms, considerable difficulties arise and these have only recently been resolved by Bernig, Fu, and Solanes. The key insight responsible for this progress is that the kinematic formulas contain the same information as the algebra of invariant valuations V∞(M)G.
Valuation (geometry)	Applications in Integral Geometry	For a precise statement, let be the kinematic operator, that is, the map determined by the kinematic formulas (2). Let denote the Alesker-Poincaré duality, which is a linear isomorphism. Finally let mG∗ be the adjoint of the product map The Fundamental theorem of algebraic integral geometry relating operations on valuations to integral geometry, states that if the Poincaré duality is used to identify V∞(M)G with V∞(M)G∗, then kG=mG∗
Trial graphics	Trial graphics	Trial graphics are images that have been designed by expert graphic artists for use in legal trials and procedures. Graphs and other images can be created to use as evidential support in a court of law by utilizing current graphic design technology. Effective jury presentations are a key point to creating a strong legal case. High quality legal graphics are a relatively new tool that can be utilized by lawyers looking to add clear forms of analytic data or other designed images for jury review.
Standard Geographical Classification code (Canada)	Standard Geographical Classification code (Canada)	The Standard Geographical Classification (SGC) is a system maintained by Statistics Canada for categorizing and enumerating the census geographic units of Canada. Each geographic area receives a unique numeric code ranging from one to seven digits, which extend telescopically to refer to increasingly small areas. This geocode is roughly analogous to the ONS coding system in use in the United Kingdom.
Standard Geographical Classification code (Canada)	Regions	The SGC code format for regions is X, where X is a unique identifier incrementing from east to west, then north. 1: Atlantic Canada2: Quebec3: Ontario4: Prairies5: British Columbia6: Northern Canada
Standard Geographical Classification code (Canada)	Provinces and Territories	The SGC code format for provinces and territories is XY, where X is the above regional prefix, and Y is a further identifier incrementing from east to west. Taken as a single digit, each value of Y is unique within the province group, or unique within the territory group. 10: Newfoundland and Labrador11: Prince Edward Island12: Nova Scotia13: New Brunswick24: Quebec35: Ontario46: Manitoba47: Saskatchewan48: Alberta59: British Columbia60: Yukon61: Northwest Territories62: Nunavut
Standard Geographical Classification code (Canada)	Census divisions	The SGC code format for census divisions is XX YY, where XX is the above province/territory code, and YY is the census division's code, unique within its own province. Census divisions are generally numbered from east to west. In some locations, a similar policy to American FIPS county codes has been adopted, with even-numbered slots being left vacant for future expansion.
Standard Geographical Classification code (Canada)	Census divisions	Examples:10 04: Division No. 4, Newfoundland and Labrador10 05: Division No. 5, Newfoundland and Labrador13 08: Kent County, New Brunswick13 09: Northumberland County, New Brunswick13 10: York County, New Brunswick24 64: Les Moulins Regional County Municipality, Quebec24 65: Territoire équivalent of Laval, Quebec24 66: Territoire équivalent of Montreal, Quebec24 67: Roussillon Regional County Municipality, Quebec24 68: Les Jardins-de-Napierville Regional County Municipality, Quebec35 07: Leeds and Grenville United Counties, Ontario35 08: [vacant slot]35 09: Lanark County, Ontario35 10: Frontenac Census Division, Ontario47 04: Division No. 4, Saskatchewan48 05: Division No. 5, Alberta59 01: Regional District of East Kootenay, British Columbia59 02: [vacant slot]59 03: Regional District of Central Kootenay, British Columbia59 04: [vacant slot]59 05: Regional District of Kootenay Boundary, British Columbia
Standard Geographical Classification code (Canada)	Census subdivisions	The SGC code format for census subdivisions is XX YY ZZZ, where XX is the province/territory code, YY is the census division code, and ZZZ is the census subdivision's code, unique within its own census division. Census subdivisions are again generally numbered from east to west, and the practice has been to leave even-numbered slots vacant for future expansion. Examples:35 12 001: Tyendinaga, Ontario35 12 002: Deseronto, Ontario35 12 003: [vacant slot]35 12 004: Tyendinaga Mohawk Territory, Ontario35 12 005: Belleville, Ontario35 12 006: [vacant slot]62 04 001: Sanikiluaq, Nunavut62 04 002: [vacant slot]62 04 003: Iqaluit, Nunavut62 04 004: [vacant slot]62 04 005: Kimmirut, Nunavut62 04 006: [vacant slot]
MAP3K8	MAP3K8	Mitogen-activated protein kinase kinase kinase 8 is an enzyme that in humans is encoded by the MAP3K8 gene.
MAP3K8	Function	The gene was identified by its oncogenic transforming activity in cells. The encoded protein is a member of the serine/threonine-specific protein kinase family. This kinase can activate ERK1, ERK2 and p38 MAP kinases. This kinase was shown to activate IkappaB kinases, and thus induce the nuclear production of NF-kappaB. This kinase was also found to promote the production of TNF-alpha and IL-2 during T lymphocyte activation. Studies of a similar gene in rat suggested the direct involvement of this kinase in the proteolysis of NF-kappaB1, p105 (NFKB1). This gene may also start transcription at a downstream in-frame translation start codon, and thus produce an isoform containing a shorter N-terminus. The shorter isoform has been shown to display weaker transforming activity. In mice, the gene is known as TPL2 and is a tumor-suppressor gene whose absence contributes to the development and progression of cancer. However, it functions in other organs as a oncogene, promoting cancer.
MAP3K8	Interactions	MAP3K8 has been shown to interact with AKT1, CHUK, NFKB2, NFKB1, C22orf25 and TNIP2.
Textile bleaching	Textile bleaching	The textile bleaching (or bleaching of textiles) is one of the steps in the textile manufacturing process. The objective of bleaching is to remove the natural color for the following steps such as dyeing or printing or to achieve full white. All raw textile materials, when they are in natural form, are known as 'greige' material. They have their natural color, odor and impurities that are not suited to clothing materials. Not only the natural impurities will remain in the greige material, but also the add-ons that were made during its cultivation, growth and manufacture in the form of pesticides, fungicides, worm killers, sizes, lubricants, etc. The removal of these natural coloring matters and add-ons during the previous state of manufacturing is called scouring and bleaching.: 193 A continuous bleaching range is a set of machines to carry out bleaching action. It consists of several compartments in which fabric moves from one side to another with the help of guide rollers and is treated with chemicals, heated, rinsed, and squeezed. Continuous bleaching is possible for the fabrics in open-width or rope form.
Textile bleaching	History	Bleaching can be dated back to at least 1000BC from an Egyptian list found in the tomb of Rekh-mi-re at Thebes, which mentioned both bleached and unbleached linen. Mulrooney dates it back as far as 5000BC, while Walton claims it was introduced to Egypt from Asia. It’s plausible that it was discovered independently by different cultures. It’s generally assumed to have developed after noticing that garments are naturally bleached by sunlight and washing. Wood ash (potash, or impure potassium hydroxide) was an early form of soap, known to have been used in bleaching since at least 1AD. This process of washing cloth in a solution of ashes (lye) and left in the sun, known as Grassing, is one of the oldest methods of bleaching textile goods. To bleach linen and cotton-based fabrics, the Grassing method has been used. Linen has long been bleached in Europe with Grassing method. The linens were laid out on the grass for over seven days after boiling with the ''lyes of ashes and rinsing''. Bleachfield was an open area to spread cloth, it was a field near watercourse used by a bleachery. Bleachfields were common in and around the mill towns during the British Industrial RevolutionThe Dutch were bleaching by about the 12th century and are credited with soaking the bleached cloth in a bath of soured milk for 5 - 8 days. This softened and neutralised the harsh effects of the caustic lye. By the 17th century the Dutch were renowned for their bleaching skills and much of their trade was for customers abroad. Around 1756 an alternative to soured milk was proposed by the Scottish doctor, Francis Home using a weak solution of sulphuric acid. This was made commercially viable by John Roebuck's manufacture of sulphuric acid and reduced the soaking time to 12 - 24 hours. A final rinse and drying finished the bleaching process. The English East India Company imported bleached, painted and printed calico from India during the 17th century. This disrupted the English silk and wool trades and an act of parliament (11 Will III Cap X) was passed in 1700 that prohibited the wearing of printed calicos manufactured in China, India or Persia. This inadvertently established a calico bleaching and printing industry using unbleached Indian calico. A second law in 1721 prohibited the use and wear of all printed, painted, stained or dyed calicoes which stimulated demand for linen and fustian. The calico acts were repealed in 1774 when cloth was made using imported cotton from America.
Textile bleaching	History	Discovery of Chlorine After discovering Chlorine in the late 18th century, when chemical bleaching came into existence, the chemical bleaching rose above Grassing, as it was quicker and possible in indoors.The French chemist Claude Louis Berthollet first demonstrated the bleaching properties of chlorine and subsequently developed liquid bleaches around 1789. James Watt is credited with bringing it to Britain, and a fellow Scot, Charles Tennant patented a more practical bleaching powder that made chlorine-based bleaching a commercial success.
Textile bleaching	Scouring	Scouring is the first process carried out with or without chemicals, at room temperature or at suitable higher temperatures with the addition of suitable wetting agents, alkali and so on. Scouring removes the impurities such as waxes, pectins and makes the textile material hydrophilichy or water absorbent.: 78 Scouring is then followed by the bleaching process.: 169 : 193
Textile bleaching	Bleaching	Bleaching is the process of decolorizing the material after it has been scoured.: 169 Bleaching textiles can be classified as oxidative bleaching and reductive bleaching which can be carried out with oxidizing and reductive bleaching agents.: 161 Bleaching agents attack the chromophores and alter the color absorbing properties of the objects. Oxidative bleaching Generally oxidative bleachings are carried out using sodium hypochlorite, sodium chlorite or sulfuric acid. Vegetable fibres, animal fibers, and mineral fibres are the three major types of natural fibers. Natural fibers such as cotton, ramie, jute, wool, and regenerated fibers such as bamboo are all generally bleached with oxidative methods.
Textile bleaching	Bleaching	Oxygen bleaching action It is the conjugated double bonds of the substrate that makes the substrate capable of absorbing visible light. Hence, it looks yellower and need bleaching. When bleaching action carries out with oxygen, it removes the chromophoric sites and makes the cloths whiter. Oxygen is a degrading bleaching agent. Its bleaching action is based on ''destroying the phenolic groups and the carbon–carbon double bonds.''. The major source of chemical bleaching is Hydrogen peroxide H2O2 that contains a single bond, (–O–O–). When this breaks down it gives rise to very reactive oxygen specie, which is the active agent of the bleach. Around sixty percent of the world Hydrogen peroxide is used in chemical bleaching of textiles and wood pulp.
Textile bleaching	Bleaching	Reductive bleaching Reductive bleaching is done with sodium hydrosulphite, a powerful reducing agent. Fibres like polyamides, polyacrylics and polyacetates can be bleached using reductive bleaching technology.
Textile bleaching	Bleaching	Textile whitening Bleaching of textiles may include an additional application of optical brighteners (OBAs). Optical brightening agents are chemical compounds that absorb light in the ultraviolet and violet region (usually 340-370 nm) of the electromagnetic spectrum, and re-emit light in the blue region (typically 420-470 nm) by fluorescence. After scouring and bleaching, optical brightening agents are applied to make the textile material appear a more brilliant white. These OBAs are available in different tints such as blue, violet and red.
Textile bleaching	Whiteness	Whiteness in colorimetry is the degree to which a surface is white. The term "whiteness" refers to the degree to which a surface resembles the properties of a perfect reflecting diffuser, i.e. an ideal reflecting surface that neither absorbs nor transmits light, but instead reflects it evenly in all directions. CIE Whiteness CIE Whiteness is a formula that measures the degree of whiteness. The CIE Whiteness Index is a measure or methodology developed by the Commission on illumination.
Occupancy grid mapping	Occupancy grid mapping	Occupancy Grid Mapping refers to a family of computer algorithms in probabilistic robotics for mobile robots which address the problem of generating maps from noisy and uncertain sensor measurement data, with the assumption that the robot pose is known. Occupancy grids were first proposed by H. Moravec and A. Elfes in 1985.The basic idea of the occupancy grid is to represent a map of the environment as an evenly spaced field of binary random variables each representing the presence of an obstacle at that location in the environment. Occupancy grid algorithms compute approximate posterior estimates for these random variables.
Occupancy grid mapping	Algorithm outline	There are four major components of occupancy grid mapping approach. They are: Interpretation Integration Position estimation Exploration
Occupancy grid mapping	Occupancy grid mapping algorithm	The goal of an occupancy mapping algorithm is to estimate the posterior probability over maps given the data: p(m∣z1:t,x1:t) , where m is the map, z1:t is the set of measurements from time 1 to t, and x1:t is the set of robot poses from time 1 to t. The controls and odometry data play no part in the occupancy grid mapping algorithm since the path is assumed known.
Occupancy grid mapping	Occupancy grid mapping algorithm	Occupancy grid algorithms represent the map m as a fine-grained grid over the continuous space of locations in the environment. The most common type of occupancy grid maps are 2d maps that describe a slice of the 3d world. If we let mi denote the grid cell with index i (often in 2d maps, two indices are used to represent the two dimensions), then the notation p(mi) represents the probability that cell i is occupied. The computational problem with estimating the posterior p(m∣z1:t,x1:t) is the dimensionality of the problem: if the map contains 10,000 grid cells (a relatively small map), then the number of possible maps that can be represented by this gridding is 10 000 . Thus calculating a posterior probability for all such maps is infeasible.
Occupancy grid mapping	Occupancy grid mapping algorithm	The standard approach, then, is to break the problem down into smaller problems of estimating p(mi∣z1:t,x1:t) for all grid cells mi . Each of these estimation problems is then a binary problem. This breakdown is convenient but does lose some of the structure of the problem, since it does not enable modelling dependencies between neighboring cells. Instead, the posterior of a map is approximated by factoring it into p(m∣z1:t,x1:t)=∏ip(mi∣z1:t,x1:t) .Due to this factorization, a binary Bayes filter can be used to estimate the occupancy probability for each grid cell. It is common to use a log-odds representation of the probability that each grid cell is occupied.
Christopher Burge	Christopher Burge	Christopher Boyce Burge is Professor of Biology and Biological Engineering at Massachusetts Institute of Technology.
Christopher Burge	Education	Burge completed his Bachelor of Science at Stanford University in 1990, and continued graduate studies in computational biology at Stanford University, gaining his PhD in 1997 under the supervision of Samuel Karlin. During his time at Stanford he was responsible for developing algorithms for GENSCAN used in gene prediction for example the initial analysis of the Human Genome Project. His PhD thesis was titled Identification of genes in human genomic DNA.
Christopher Burge	Research	From 1997 to 1999 Burge worked as a postdoc in the laboratory of Phillip Allen Sharp, working in the fields of RNA splicing and molecular evolution. Burge joined the Massachusetts Institute of Technology in 1999 as a Bioinformatics Fellow. He became Assistant Professor in 2002, Associate Professor in 2004, was tenured in 2006, and was promoted to full Professor in 2010. He has been an Associate Member of the Broad Institute since 2004. His current research interests include genomics, RNA splicing and microRNA regulation.Burge has also served on the editorial boards of the academic journals RNA, PLOS Computational Biology, BMC Bioinformatics and BMC Genomics.
Christopher Burge	Awards	In 2001 he was awarded the Overton Prize for Computational Biology by the International Society for Computational Biology. He was awarded a Searle Scholar Award in 2003 for his research in the computational biology of gene expression. In 2007 he was awarded the Schering-Plough Research Institute Award (now known as the ASBMB Young Investigator Award) by the American Society for Biochemistry and Molecular Biology for his outstanding research contributions to biochemistry and molecular biology.
Median (geometry)	Median (geometry)	In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length.
Median (geometry)	Median (geometry)	The concept of a median extends to tetrahedra.
Median (geometry)	Relation to center of mass	Each median of a triangle passes through the triangle's centroid, which is the center of mass of an infinitely thin object of uniform density coinciding with the triangle. Thus the object would balance on the intersection point of the medians. The centroid is twice as close along any median to the side that the median intersects as it is to the vertex it emanates from.
Median (geometry)	Equal-area division	Each median divides the area of the triangle in half; hence the name, and hence a triangular object of uniform density would balance on any median. (Any other lines which divide the area of the triangle into two equal parts do not pass through the centroid.) The three medians divide the triangle into six smaller triangles of equal area. Proof of equal-area property Consider a triangle ABC. Let D be the midpoint of AB¯ , E be the midpoint of BC¯ , F be the midpoint of AC¯ , and O be the centroid (most commonly denoted G). By definition, AD=DB,AF=FC,BE=EC . Thus [ADO]=[BDO],[AFO]=[CFO],[BEO]=[CEO], and [ABE]=[ACE] , where [ABC] represents the area of triangle △ABC ; these hold because in each case the two triangles have bases of equal length and share a common altitude from the (extended) base, and a triangle's area equals one-half its base times its height.
Median (geometry)	Equal-area division	We have: [ABO]=[ABE]−[BEO] [ACO]=[ACE]−[CEO] Thus, [ABO]=[ACO] and [ADO]=[DBO],[ADO]=12[ABO] Since [AFO]=[FCO],[AFO]=12[ACO]=12[ABO]=[ADO] , therefore, [AFO]=[FCO]=[DBO]=[ADO] Using the same method, one can show that [AFO]=[FCO]=[DBO]=[ADO]=[BEO]=[CEO] Three congruent triangles In 2014 Lee Sallows discovered the following theorem: The medians of any triangle dissect it into six equal area smaller triangles as in the figure above where three adjacent pairs of triangles meet at the midpoints D, E and F. If the two triangles in each such pair are rotated about their common midpoint until they meet so as to share a common side, then the three new triangles formed by the union of each pair are congruent.
Median (geometry)	Formulas involving the medians' lengths	The lengths of the medians can be obtained from Apollonius' theorem as: where a,b, and c are the sides of the triangle with respective medians ma,mb, and mc from their midpoints. These formulas imply the relationships:
Median (geometry)	Other properties	Let ABC be a triangle, let G be its centroid, and let D, E, and F be the midpoints of BC, CA, and AB, respectively. For any point P in the plane of ABC then The centroid divides each median into parts in the ratio 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex.
Median (geometry)	Other properties	For any triangle with sides a,b,c and medians ma,mb,mc, The medians from sides of lengths a and b are perpendicular if and only if a2+b2=5c2. The medians of a right triangle with hypotenuse c satisfy ma2+mb2=5mc2. Any triangle's area T can be expressed in terms of its medians ma,mb , and mc as follows. If their semi-sum (ma+mb+mc)/2 is denoted by σ then
Median (geometry)	Tetrahedron	A tetrahedron is a three-dimensional object having four triangular faces. A line segment joining a vertex of a tetrahedron with the centroid of the opposite face is called a median of the tetrahedron. There are four medians, and they are all concurrent at the centroid of the tetrahedron. As in the two-dimensional case, the centroid of the tetrahedron is the center of mass. However contrary to the two-dimensional case the centroid divides the medians not in a 2:1 ratio but in a 3:1 ratio (Commandino's theorem).
Abandoned mine	Abandoned mine	An abandoned mine refers to a former mining or quarrying operation that is no longer in use and has no responsible entity to finance the cost of remediation and/or restoration of the mine feature or site. Such mines are typically left unattended and may pose safety hazards or cause environmental damage without proper maintenance. The term incorporates all types of old mines, including underground shaft mines and drift mines, and surface mines, including quarries and placer mining. Typically, the cost of addressing the mine's hazards is borne by the public/taxpayers/the government.An abandoned mine may be a hazard to health, safety or environment.
Abandoned mine	Hazards	Abandoned mines contain many hazards, including: Subsidence, or collapsing ground Blasting caps and other unexploded explosives Blackdamp, which accumulates in old mines and can cause suffocation Hidden mine shafts, often hidden beneath bushes, grasses, and other vegetation that has grown up around the mine entrance Unstable roofs and passageways, which are prone to cave-ins
Abandoned mine	Abandoned mines in the United States	Definitions Department of the Interior – Bureau of Land Management – Abandoned mines are those mines that were abandoned before January 1, 1981, the effective date of the Bureau of Land Management's Surface Management regulations issued under the authority of the Federal Land Policy and Management Act of 1976, as amended (43 U.S.C. 1701 et seq.) Environmental Protection Agency – Abandoned mine lands (AMLs) are those lands, waters, and surrounding watersheds where extraction, beneficiation or, processing of ores and minerals has occurred.In the United States, there are thousands of abandoned mines. The precise number of abandoned mines in the United States remains unknown, ranging "from the National Park Service's tally of 2,500 on its lands to the Mineral Policy Center's assessment of 560,000 abandoned mines on public and privately owned lands." Many of these abandoned mines are associated with abandoned neighboring towns often referred to as ghost towns. Experts strongly warn against entering or exploring old or abandoned mines. In California, Nevada, Colorado, New Mexico, and Arkansas, there are over 6,500 abandoned mines, according to infographic.
Abandoned mine	Abandoned mines in the United States	In the U.S., the estimation is that approximately 80% of the abandoned mine lands (AML) sites pose physical safety hazards and require more work in determining the proper safety of these lands.Every year, dozens are injured or killed in recreational accidents on mine property. While exploring abandoned mines can be dangerous, the majority of deaths on mine property are actually unrelated to mine exploration. The leading causes of accidental deaths on abandoned mine properties are drownings in open quarries and ATV accidents. These types of accidents often occur when people engage in recreational activities on abandoned mine sites without taking proper precautions or following safety guidelines. It is important for individuals to recognize the risks associated with these activities and to take steps to ensure their safety. Property owners and managers also have a role to play in preventing accidents by implementing safety measures and providing adequate warning signs and barriers. The U.S. Department of Labor notes that since 1999, "more than 200 people have died in recreational accidents at the surface and underground active and abandoned operations across the country." Due to these circumstances, the Mine Safety and Health Administration launched the "Stay Out – Stay Alive" campaign, which is a national public awareness campaign aimed at warning and educating children and adults about the dangers of exploring and playing on active and abandoned mine sites.
Abandoned mine	Abandoned mines in the United States	In the U.S., the Abandoned Mine Land Initiative, launched by the Western Governor's Association and the National Mining Association is also an effort focusing on reporting the number of high-priority AML sites. The initiative identifies, measures, and reports on the progress of current reclamation cleanup programs on an annual basis. In the Americas region, the United Nations Environment Programme (UNEP) and the Chilean Copper Commission (COHILCO) co-hosted a workshop to address the problem of abandoned or "orphaned" mines. Including a representative from the UN, ten countries were represented from North, Central, and South America with an eleventh participant being Japan.
Abandoned mine	Abandoned mines in the United States	Legislation Surface Mining Control and Reclamation Act It can be hazardous and detrimental to reside close to an abandoned coal mining site. The Surface Mining Control and Reclamation Act (SMCRA) was passed in 1977 in two parts: one to control the effects of active mines, and one to regulate abandoned mines. SMCRA also initiated an abandoned mine land fund, in which a fee was charged for each ton of coal produced. This revenue was distributed in part to the United Mine Workers Association (UMWA) towards retirement funds, as well as to the Office of Surface Mining Reclamation and Enforcement (OSMRE) to continue operations. There is still around $2 billion in undistributed funds thus far.
Abandoned mine	Abandoned mines in Canada	Definitions National Orphaned/Abandoned Mines Initiative – Orphaned or abandoned mines are those mines for which the owner cannot be found or, the owner is financially unable or unwilling to carry out clean-up. They pose environmental, health, safety, and economic problems to communities, the mining industry, and governments in many countries, including Canada. The Ontario Mining Act describes "abandoned mines" as old land previously used for coal mining unused due to hazardous environmental and health effects.There are approximately 10,139 abandoned mines currently in Canada. Research is being done to utilize geothermal systems in these abandoned mines as a renewable heating source and has shown to be quite cost-efficient.
Abandoned mine	Reuse of abandoned mines	Abandoned mines may be reused for other purposes, such as pumped-storage hydropower.
Nude calendar	Nude calendar	Nude calendars are a type of wall calendar that feature nude models in a variety of scenes and locations. Predominantly in the United Kingdom, nude calendars are produced to raise money for charity.
Nude calendar	Types	Calendars featuring pin-up models Commercial advertising on calendars started in the late 19th century and has often been linked to pictures or photographs of pin-up models. The products being advertised may be incorporated via product placement in the pictures themselves or separate via logos and corporate in-house style. Calendars featuring female nudes became a common feature in workplaces which were predominantly male (e.g. garages, car dealerships, etc.), although many employers have banned or restricted their display considering them a form of sex discrimination.
Nude calendar	Types	An example is the Pirelli Calendar. Sports nude calendars Some sports teams have produced nude calendars, often to raise their profile or increase funding. Examples include the Australian women's football team prior to the 2000 Summer Olympics in Sydney, the Canadian cross-country ski team in 2001 and 2002, and a group of Canadian women biathletes in 2008.
Nude calendar	Types	Charity nude calendars The first nude charity calendar was made by a group of middle-aged Englishwomen, members of a local branch of the Women's Institute, who were posing nude to raise funds for Leukaemia Research. The calendar was released in 1999, and became an international sensation, and also inspired the movie Calendar Girls. Following this lead, charity nude calendars proliferated in the 2000s. Proceeds usually go to various health or social causes. Participants may include artists, celebrities, sportsmen and sportswomen, firefighters, military forces, the police, or members of a group such as farmers, Women's Institute members who wish to raise funds for a chosen charity.
Nude calendar	Types	The women's rugby match Oxford and Cambridge, which was played at Twickenham in 2015, was publicised by the Oxford team making a nude calendar.Successful charity nude calendars include: Rylstone Women's Institute 2000 Alternative WI Calendar, the first ever nude charity calendar Dieux du Stade (France) Men of the Long Tom Grange (United States) in aid of Junction City, Oregon public schools (2004-2006) League of Their Own (Australia) in aid of the Koori Kids Foundation (2006) Naked Rugby League (Australia) in aid of the National Breast Cancer Foundation of Australia (2007/2008) Naked For A Cause (Australia) in aid of breast cancer research (2008) Gods of Football (Australia) featuring Australian Football League and Australian Rugby League players in aid of the McGrath Foundation (2009) University of Warwick Boat Club (United Kingdom) in aid of Macmillan Cancer Support (2013) EastEnders (United Kingdom) featuring actors and actresses from the BBC TV show in aid of Children in Need (2015) The Magnet Tavern, in Lincolnshire (United Kingdom), in aid of the Air Ambulance (2016)
Vruk	Vruk	The Vruk is a proprietary bass drum pedal design produced by Vruk Corporation. The term vruk also refers to playing techniques associated with this design, and related accessories produced by the corporation for attachment to other brands of pedal. Proponents claim that the technique gives greater control and in particular allows greater speed. The name VRUK (capitalised) is also used by Vineyard Records UK.
Self-brand	Self-brand	Throughout the long history of consumer research, there has been much interest regarding how consumers choose which brand to buy and why they continue to purchase these brands. Self-branding describes the process in which consumers match their own self-concept with the images of a certain brand.
Self-brand	Self-brand	People engaged in consumption do not merely buy certain products to satisfy basic needs. In fact, consumer buying habits are at a much deeper level. Owning a certain brand can help consumers to express and build their own self-concept. Specifically, consumers will often only purchase certain trademarks when he/she finds a match between the brand image (communicated through advertisement, design of retail shop, or even package design) and his/her own self-concept. Thereby, the value of a brand also depends on its ability to help consumer to build and create self-concept.
Self-brand	Formation of connections	Based on self-congruity theory The above explanation for self-branding can be summarized by Sirgy's self-congruity theory. It is proposed that consumer behavior is partially determined by the similarity between consumers' psychological comparisons of the brand-user-image. This self-congruity affects consumption behavior of consumers through motives such as need for self-consistency (e.g. "I am a good student because I work hard to prepare for examinations and I always get good grades") and self-esteem. On the other hand, high self-congruity occurs when the consumers find appropriate match between their own self-image and the brand-image. Only high self-congruity would help consumers maintain and enhance self in a positive direction. Further from the above notions, high self-congruity will lead to positive attitudes towards the brand and repeated purchase.
Self-brand	Formation of connections	Brand evaluation Besides assisting consumer to choose which product and brand to buy, the matching process between self-concept and image of brand and product also determines how consumers evaluate the brand and product. When we say that a brand has a positive brand-image, it means that the brand has established some strong, favorable and unique associations with the consumer's self-image (e.g. iPods have a strong and explicit image of being trendy, fashionable and high-tech, a combination of brand image that is unique and valued by young people). These strong, favorable and unique associations can be mainly divided into two parts. They are image of users and the psychological benefits experienced by the users in buying this particular brand or product. Firstly, image of users means that when consumer evaluate the brand they will image the typical user of this particular brand and see whether they are similar to the typical user. Demographic and psychological profile of the typical user is usually a good source of information for consumer to make these comparisons. (e.g. if someone perceived themselves as a trendy youngster and valued advanced technology, the chance that they will buy an iPod for their own use is very high). Secondly, psychological benefits experienced by consumers include increase recognition by the peer group (i.e. social approval) and expression of how one would like other people to see and think of oneself (i.e. personal expression).
Self-brand	Constructing a self-concept	When the set of brand associations are linked or connected to the self, these associations can help consumers achieve certain goals. These goals include what they might become, what they would like to become, and what they are afraid of becoming. People are motivated to create a favorable and consistent self-identity based on self-enhancement (i.e. people over-emphasize favorable evaluations and minimize critical assessment of themselves) self-verification (i.e. people want to be known and understood by others according to their firmly held beliefs and feelings about themselves respectively).
Self-brand	Constructing a self-concept	Self-enhancement In self-enhancement, the impressions individuals hold about themselves are often biased towards a positive direction. Therefore, they over-emphasize favorable evaluations and minimize critical assessment of self. People use brand to represent favorable self-images to others or to themselves.
Self-brand	Constructing a self-concept	The first aspect in self-enhancement is the need to maintain and enhance self-esteem. Another aspect is about social interaction (e.g. staff meetings). In terms of impression management, people actively manage their presentation (e.g. the brand of garment) in front of other people so as to maximize the opportunity to gain positive feedback. On the other hand, people are also motivated to create a good impression (e.g. wearing a watch of big brand) in order to gain social approval and intrinsic satisfaction. This is especially true when the person has very high self-esteem.
Self-brand	Constructing a self-concept	Self-verification Self-verification refers to seek accurate information about self. In general, people seek and interpret situations and behavioral strategies that match their present self-conceptions. In contrast, they avoid situations and behaviors that derive contradictory information.Self-verification can be achieved by two primary strategies. The first strategy is seeing more self-confirmatory evidence than actually exists. The second strategy is striving to affect the reactions of other people by developing a self-confirmatory environment, which includes displaying identity cues such as driving a certain brand of automobile.It is found that people choose products and brand by imagining the prototypical users for each item in the choice set and choosing the items that maximizes their similarity to a desired prototypical user.
Self-brand	Constructing a self-concept	Compatibility of self-enhancement and self-verification It seems that it is incompatible to seek feedback that is favorable (self-enhancement) and at the same time seek accurate feedback regardless of favorability (self-verification). Social psychology shows that there are factors affecting the relative degree to which each feedback satisfied, e.g. cognitive resources, stable versus malleable aspects of personality, intuitive-experiential versus analytical-rational modes of thought, or cognitive versus affective processes. More specifically, it is found that people with high self-esteem, high self-monitors (i.e. regulate their own behavior in order to "look good"), narcissists (i.e. self-love), and Type B personalities (i.e. patient, relaxed, and easy-going) are more likely than their counterparts to be influenced by self-enhancement motives as opposed to self-verification motives.
Self-brand	Use of YouTube to promote a brand	YouTube has become an increasingly popular platform for self-branding. As self-branding is known for its strategic placement of oneself through a media outlet, it is a commonplace for many individuals to post videos, clips, tutorials, and other visual aides under their channels. YouTube especially gives the individual the opportunity to upload and control the information that is distributed on themselves – as they are the ones creating, editing, and uploading the content. By controlling the information being displayed on their channels, it is possible to promote and market themselves on a wider scale as YouTube has millions cross paths with their site daily. Through self-branding, developing one's self is not the only aspect of this self-marketing tactic. There is also the aspect of "authenticity" to validate their specialties, and also a "business-targeted self presentation". This can be done through addressing the proper credentials or years of practice that has past throughout their practice of the topic or talent they relate themselves to.
Self-brand	Use of YouTube to promote a brand	The concept of self-branding a product can be seen particularly in the case of physical exercise gurus, beauty gurus, health gurus, food expert, and other gurus as well. This concept can be seen in the successful Michelle Phan, who is a beauty guru on YouTube. Michelle Phan has a record of revealing intimate facts about her life through interviews, blogs, and YouTube videos. On her website michellephan.com, she has created an "about me" section to further her self-branding in efforts to give a brief introduction about herself and her passion for beauty related topics, tips, and advice. She states, "I'm passionate about being a makeup artist and teaching others how to look and feel fabulous in their own skin". She also claims to help women raise their self-esteem and confidence levels. This is all done through "a safe space where makeup enthusiasts, fashion lovers, trendsetters, and beauty aficionados alike, can find inspiration, how-to advice, style news, easy DIY ideas, and tips".YouTube gurus like Michelle Phan carry an image and a created identity. In an interview with fashionista.com, Michelle Phan stated that success in the blogging and video industry has to do with sending a message, vision, and brand identity. She has said to be cautious of what she is affiliated with, as it can affect the relationship she has formed with her followers. Through presenting an identity through her YouTube channel, she and other YouTube gurus alike have launched their own products. For instance, Michelle Phan has created a line of cosmetics that include eye shadows, lipsticks, eyeliners, foundation, contour sticks, concealer, and other forms of makeup that are related to the content she chooses to upload on her personal YouTube channel. Michelle Phan's ability to self-brand through media such as YouTube gives her a competitive advantage. YouTube reports that "more than 1 billion unique users visit YouTube each month". It also states "over 6 billion hours of video are watched each month on YouTube". Michelle Phan's channel is one of the channels YouTube claims is among the "thousands of channels that are making six figures a year".
Self-brand	Development of concepts	In the process of consumer socialization, self-brand connections develop throughout childhood as a result of developmental changes. Major changes occur in the representation of self-concepts between early childhood and adolescence. As children grow older, they conceptualize the self in less concrete and more abstract terms. For example, a concrete thinker can recognize that John likes clothes; more abstract thinker can reflect on emotions, like affection. Self-concepts become more complex as children mature, with a greater variety of self-constructs used to describe the self. In the Dixon and Street (1975) study, possessions were not part of self-concept descriptions for 6- to 8-year-olds but surfaced and increased in importance from 8 to 16 years of age.
Self-brand	Development of concepts	Children recognize brand at an early age, as young as 3 or 4 years of age. John and Sujan (1990) found that children 4–7 years of age used perceptual cues (shape, package color), whereas older children (8–10 years) used no observable conceptual cues (taste) as a basis for classifying products. They, in middle childhood (7–8 years of age) can name multiple brand products and request products by brand name. Their comparisons of the self-concept with brand take place on a concrete level that self-brand connections are straightforward in nature. For example, self-brand connections might be made on the basis of simply being familiar with or owning a brand.
Self-brand	Development of concepts	Late childhood (10–12 years of age) begin heightened appreciation for subtle meanings imbedded in brand images converges with a trend toward defining the self in more abstract and complex terms. Brands gain recognition as useful devices for characterizing the self in terms of personality traits, user characteristics, and reference groups.
Self-brand	Development of concepts	As children move into adolescence, children have deeper self-brand connections because they think about brand in a very specific way—as having personalities and symbolizing group membership—that provides a natural link to their self-concepts. A greater understanding of the self, combined with social pressures to "fit in" and signal group membership, leads adolescents to be more vigilant about the social implications of owning certain brand. As a result, adolescents possess an even larger number of self-brand connections, which may be even more complex in nature.
Self-brand	Reference group	As mentioned in the social comparison theory proposed by social psychologist Leon Festinger in 1954, humans have a drive to evaluate themselves by examining their opinions and abilities in comparison to others. Consumers often use the images of other brands' users as a source of information for evaluating their own beliefs and perceptions about their own and others' social identities. They also actively construct self-concept using brand associations that arise through reference group.
Self-brand	Reference group	In many consumer researches, reference group is a key concept for demonstrating the congruency between group membership and brand usage. It refers to the social groups that are important to a consumer and against which he/she compares oneself. With different personal goals, individuals would take different types of reference groups. For example, if someone would like to verify his own current social identities, he tends to compare himself with a 'member group', to which it supposes he belongs to. For example, if a person considers himself to be intellectual and his member group of intellectuals tends to drive a Volvos, he may choose to drive Volvo too. Similarly, an 'aspiration group' is another type of reference group to which an individual aspires to belong. If a consumer wishes to be more hip, and he sees hip people wearing Versace clothing, he may choose to wear Versace clothing in an attempt to appropriate the hip associations of that brand.
Self-brand	Use	On the marketing level, companies gain an enduring competitive advantage by utilizing the association between brand and self-concept. This type of association is difficult for competitors to imitate. For example, in a sport consumption context, when consumer fans identify with the team (i.e., a branded organization) and rally together in expectation of victory, the team image is emphasized. On the individual level, brand symbolism provides moderation effects for in-group and out-group association. For in-groups, a symbolic brand has a stronger communicating effect than a non-symbolic brand; for out-groups, only a symbolic brand used to differentiate one from out-group.
Id Tech 7	Id Tech 7	id Tech 7 is a multiplatform proprietary game engine developed by id Software. As part of the id Tech series of game engines, it is the successor to id Tech 6. The software was first demonstrated at QuakeCon 2018 as part of the id Software announcement of Doom Eternal.
Id Tech 7	Technology	id Tech 7 features ten times the geometric detail, and higher texture fidelity of id Tech 6. Moreover the capabilities of the game engine allow it to have a new system called "Destructible Demons", in which enemies' bodies become progressively destroyed and deteriorated in combat as they suffer damage. On PC, id Tech 7 supports Vulkan rendering only. Ray tracing and DLSS were added in June 2021. According to engine developer Axel Gneiting, the engine doesn't have a "main thread"; everything is implemented as jobs.
Id Tech 7	Technology	Improvements in comparison to id Tech 6 1 million fewer lines of code, due in part to the removal of the OpenGL render-engine Unified HDR lighting and shadowing Full HDR-support on PS4, PS4 Pro, PS5, Xbox One S, Xbox One X, Xbox Series S, Xbox Series X, PC and Stadia Multi PBR material compositing, blending, and painting Increased texture fidelity and geometric detail due to removal of MegaTexture pipeline, used since id Tech 4 Enhanced global illumination quality Majorly improved particle system as more particles are running on the GPU, which allows for bigger explosions, more atmospheric volumetrics and more vibrant particle effects The framerate limit has been increased to 1000 FPS. The frame limit was 250 FPS in id Tech 6.
Id Tech 7	Technology	Rewritten jobs-system to use all available CPU-cores more efficiently Improved post-processing effects, including more detailed anti-aliasing and enhanced motion blur Support for gameplay areas twice the size of those in id Tech 6 Improved image streaming Expanded decal system Improved LOD system New GPU triangle-, light- and occlusion-culling system to not render what isn't on-screen Dramatically improved compression Improved level loading times, including after death screens DLSS 2.3.0 Ray-traced reflections on PlayStation 5, Xbox Series X (not available on Xbox Series S) and PCs with hardware accelerated ray tracing Variable rate shading on Xbox Series X and Xbox Series S
Id Tech 7	Games using id Tech 7	Doom Eternal (2020) – id Software
TASB (psychedelics)	TASB (psychedelics)	TASB, or thioasymbescaline, is a series of lesser-known psychedelic drugs similar in structure to asymbescaline and to mescaline. They were first synthesized by Alexander Shulgin and written up in his book PiHKAL (Phenethylamines i Have Known And Loved). Very little is known about their dangers or toxicity.
TASB (psychedelics)	TASB compounds	3-TASB Dosage: 160 mg or greater Duration: 10–18 hours Effects: Mild stimulative effects 4-TASB Dosage: 60–100 mg Duration: 10–15 hours Effects: Negative effects 5-TASB Dosage: 160 mg or greater Duration: 8 hours Effects: Warmth at extremities, diarrhea
Sequence assembly	Sequence assembly	In bioinformatics, sequence assembly refers to aligning and merging fragments from a longer DNA sequence in order to reconstruct the original sequence. This is needed as DNA sequencing technology might not be able to 'read' whole genomes in one go, but rather reads small pieces of between 20 and 30,000 bases, depending on the technology used. Typically, the short fragments (reads) result from shotgun sequencing genomic DNA, or gene transcript (ESTs).
Sequence assembly	Sequence assembly	The problem of sequence assembly can be compared to taking many copies of a book, passing each of them through a shredder with a different cutter, and piecing the text of the book back together just by looking at the shredded pieces. Besides the obvious difficulty of this task, there are some extra practical issues: the original may have many repeated paragraphs, and some shreds may be modified during shredding to have typos. Excerpts from another book may also be added in, and some shreds may be completely unrecognizable.
Sequence assembly	Genome assemblers	The first sequence assemblers began to appear in the late 1980s and early 1990s as variants of simpler sequence alignment programs to piece together vast quantities of fragments generated by automated sequencing instruments called DNA sequencers. As the sequenced organisms grew in size and complexity (from small viruses over plasmids to bacteria and finally eukaryotes), the assembly programs used in these genome projects needed increasingly sophisticated strategies to handle: terabytes of sequencing data which need processing on computing clusters; identical and nearly identical sequences (known as repeats) which can, in the worst case, increase the time and space complexity of algorithms quadratically; DNA read errors in the fragments from the sequencing instruments, which can confound assembly.Faced with the challenge of assembling the first larger eukaryotic genomes—the fruit fly Drosophila melanogaster in 2000 and the human genome just a year later,—scientists developed assemblers like Celera Assembler and Arachne able to handle genomes of 130 million (e.g., the fruit fly D. melanogaster) to 3 billion (e.g., the human genome) base pairs. Subsequent to these efforts, several other groups, mostly at the major genome sequencing centers, built large-scale assemblers, and an open source effort known as AMOS was launched to bring together all the innovations in genome assembly technology under the open source framework.
Sequence assembly	EST assemblers	Expressed sequence tag or EST assembly was an early strategy, dating from the mid-1990s to the mid-2000s, to assemble individual genes rather than whole genomes. The problem differs from genome assembly in several ways. The input sequences for EST assembly are fragments of the transcribed mRNA of a cell and represent only a subset of the whole genome. A number of algorithmical problems differ between genome and EST assembly. For instance, genomes often have large amounts of repetitive sequences, concentrated in the intergenic regions. Transcribed genes contain many fewer repeats, making assembly somewhat easier. On the other hand, some genes are expressed (transcribed) in very high numbers (e.g., housekeeping genes), which means that unlike whole-genome shotgun sequencing, the reads are not uniformly sampled across the genome.
Sequence assembly	EST assemblers	EST assembly is made much more complicated by features like (cis-) alternative splicing, trans-splicing, single-nucleotide polymorphism, and post-transcriptional modification. Beginning in 2008 when RNA-Seq was invented, EST sequencing was replaced by this far more efficient technology, described under de novo transcriptome assembly.
Sequence assembly	Types of sequence assembly	There are three approaches to assembling sequencing data: De-novo: assembling sequencing reads to create full-length (sometimes novel) sequences, without using a template (see de novo sequence assemblers, de novo transcriptome assembly) Mapping/Aligning: assembling reads by aligning reads against a template (AKA reference). The assembled consensus may not be identical to the template.
Sequence assembly	Types of sequence assembly	Reference-guided: grouping of reads by similarity to the most similar region within the reference (step wise mapping). Reads within each group are then shortened down to mimic short reads quality. A typical method to do so is the k-mer approach. Reference-guided assembly is most useful using long-reads.Referenced-guided assembly is a combination of the other types. This type is applied on long reads to mimic short reads advantages (i.e. call quality). The logic behind it is to group the reads by smaller windows within the reference. Reads in each group will then be reduced in size using the k-mere approach to select the highest quality and most probable contiguous (contig). Contigs will then will be joined together to create a scaffold. The final consense is made by closing any gaps in the scaffold.
Sequence assembly	De-novo vs. mapping assembly	In terms of complexity and time requirements, de-novo assemblies are orders of magnitude slower and more memory intensive than mapping assemblies. This is mostly due to the fact that the assembly algorithm needs to compare every read with every other read (an operation that has a naive time complexity of O(n2)). Current de-novo genome assemblers may use different types of graph-based algorithms, such as the: Overlap/Layout/Consensus (OLC) approach, which was typical of the Sanger-data assemblers and relies on an overlap graph.
Sequence assembly	De-novo vs. mapping assembly	de Bruijn Graph (DBG) approach, which is most widely applied to the short reads from the Solexa and SOLiD platforms. It relies on K-mer graphs, which performs well with vast quantities of short reads.
Sequence assembly	De-novo vs. mapping assembly	Greedy graph-based approach, which may also use one of the OLC or DBG approaches. With greedy graph-based algorithms, the contigs grow by greedy extension, always taking on the read that is found by following the highest-scoring overlap.Referring to the comparison drawn to shredded books in the introduction: while for mapping assemblies one would have a very similar book as a template (perhaps with the names of the main characters and a few locations changed), de-novo assemblies present a more daunting challenge in that one would not know beforehand whether this would become a science book, a novel, a catalogue, or even several books. Also, every shred would be compared with every other shred.
Sequence assembly	De-novo vs. mapping assembly	Handling repeats in de-novo assembly requires the construction of a graph representing neighboring repeats. Such information can be derived from reading a long fragment covering the repeats in full or only its two ends. On the other hand, in a mapping assembly, parts with multiple or no matches are usually left for another assembling technique to look into.
Sequence assembly	Sequence assembly pipeline (bioinformatics)	In general, there are three steps in assembling sequencing reads into a scaffold: 1) Pre-assembly: this step is essential to ensure the integrity of downline analysis such as variant calling or final scaffold sequence. This step consists of two chronological workflow: A) Quality check: Depending on the types of sequencing technology, different errors might arise that would lead to a false base call. For example, sequencing "NAAAAAAAAAAAAN" and "NAAAAAAAAAAAN" which include 12 adenine might be wrongfully called with 11 adenine instead. Sequencing a highly repetitive segment of the target DNA/RNA might result in a call that is one short or one more base. Read quality is typically measured by Phred which is an encoded score of each nucleotide quality within a read's sequence. Some sequencing technologies such as PacBio do not have a scoring method for the their sequenced reads. A common tool used in this step is FastQC.B) Filtering of reads: Reads that failed to pass the quality check should be removed from the FastQ file to get the best assembly contigs. 2) Assembly: during this step, reads alignment will be utilized with different criteria to map each read to the possible location. The predicted position of a read is based on either how much of its sequence aligns with other reads or a reference. Different alignment algorithms are used for reads from different sequencing technologies. Some of the commonly used approaches in the assembly are de Bruijn graph and overlapping. Read length, coverage, quality, and the sequencing technique used plays a major role in choosing the best alignment algorithm in the case of Next Generation Sequencing. On the other hand, algorithms aligning 3rd generation sequencing reads requires advance approaches to account for the high error rate associated with them. 3) Post assembly: This step focusing on extracting valuable information from the assembled sequence. Comparative genomics, and population analysis are examples go post-assemble analysis.

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