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Stress majorization	Stress majorization	Stress majorization is an optimization strategy used in multidimensional scaling (MDS) where, for a set of n m -dimensional data items, a configuration X of n points in r (≪m) -dimensional space is sought that minimizes the so-called stress function σ(X) . Usually r is 2 or 3 , i.e. the (n×r) matrix X lists points in 2− or 3− dimensional Euclidean space so that the result may be visualised (i.e. an MDS plot). The function σ is a cost or loss function that measures the squared differences between ideal ( m -dimensional) distances and actual distances in r-dimensional space. It is defined as: σ(X)=∑i<j≤nwij(dij(X)−δij)2 where wij≥0 is a weight for the measurement between a pair of points (i,j) , dij(X) is the euclidean distance between i and j and δij is the ideal distance between the points (their separation) in the m -dimensional data space. Note that wij can be used to specify a degree of confidence in the similarity between points (e.g. 0 can be specified if there is no information for a particular pair).
Stress majorization	Stress majorization	A configuration X which minimizes σ(X) gives a plot in which points that are close together correspond to points that are also close together in the original m -dimensional data space.
Stress majorization	Stress majorization	There are many ways that σ(X) could be minimized. For example, Kruskal recommended an iterative steepest descent approach. However, a significantly better (in terms of guarantees on, and rate of, convergence) method for minimizing stress was introduced by Jan de Leeuw. De Leeuw's iterative majorization method at each step minimizes a simple convex function which both bounds σ from above and touches the surface of σ at a point Z , called the supporting point. In convex analysis such a function is called a majorizing function. This iterative majorization process is also referred to as the SMACOF algorithm ("Scaling by MAjorizing a COmplicated Function").
Stress majorization	The SMACOF algorithm	The stress function σ can be expanded as follows: σ(X)=∑i<j≤nwij(dij(X)−δij)2=∑i<jwijδij2+∑i<jwijdij2(X)−2∑i<jwijδijdij(X) Note that the first term is a constant C and the second term is quadratic in X (i.e. for the Hessian matrix V the second term is equivalent to tr X′VX ) and therefore relatively easily solved. The third term is bounded by: tr tr X′B(Z)Z where B(Z) has: bij=−wijδijdij(Z) for dij(Z)≠0,i≠j and bij=0 for dij(Z)=0,i≠j and bii=−∑j=1,j≠inbij Proof of this inequality is by the Cauchy-Schwarz inequality, see Borg (pp. 152–153).
Stress majorization	The SMACOF algorithm	Thus, we have a simple quadratic function τ(X,Z) that majorizes stress: tr tr X′B(X)X tr tr X′B(Z)Z=τ(X,Z) The iterative minimization procedure is then: at the kth step we set Z←Xk−1 min Xτ(X,Z) stop if σ(Xk−1)−σ(Xk)<ϵ otherwise repeat.This algorithm has been shown to decrease stress monotonically (see de Leeuw).
Stress majorization	Use in graph drawing	Stress majorization and algorithms similar to SMACOF also have application in the field of graph drawing. That is, one can find a reasonably aesthetically appealing layout for a network or graph by minimizing a stress function over the positions of the nodes in the graph. In this case, the δij are usually set to the graph-theoretic distances between nodes i and j and the weights wij are taken to be δij−α . Here, α is chosen as a trade-off between preserving long- or short-range ideal distances. Good results have been shown for α=2
ZiiLABS	ZiiLABS	ZiiLABS is a global electronics company, producing a line of media-oriented application processors, reference platforms and enabling software, in a series of platforms named ZMS. Its products are found in low-power consumer electronics and embedded devices, including Android-based phones and tablets.
ZiiLABS	History	ZiiLABS was founded in 1994 as 3Dlabs, which became a wholly owned subsidiary of Creative Technology Ltd in 2002. In January 2009 the company re-branded as ZiiLABS. This re-branding reflected 3Dlabs' focus on supplying low-power, media-rich application processors, hardware platforms and middleware, rather than just 3D GPUs as had previously been the case. The company announced its first applications/media processor, the DMS-02 in 2005 and this has been followed by the ZMS-05, ZMS-08 and most recently the ZMS-20 and ZMS-40. The ZMS processors combine ZiiLABS’ core asset, the "Stemcell Computing Array" with ARM cores and integrated peripheral functions to create a system on a chip (SoC). As 3Dlabs the company developed the GLINT and Permedia GPUs used in both personal and workstation graphics cards. In 2002 the company acquired the Intense3D group to become a vertically integrated graphics board vendor supplying workstation graphics card under the RealiZm brand. 3Dlabs stopped developing graphics GPUs and cards in 2006 to focus on its media processor business.
ZiiLABS	History	In November 2012, Creative Technology Limited announced it has entered into an agreement with Intel Corporation for Intel to license certain technology and patents from ZiiLABS Inc. Ltd and acquire certain engineering resources and assets related to its UK branch as a part of a $50 million deal. ZiiLABS (still wholly owned by Creative) continues to retain all ownership of its StemCell media processor technologies and patents, and will continue to supply and support its ZMS series of chips to its customers.
ZiiLABS	Products	The company's products include a range of ARM-based ZMS processors that feature its so-called StemCell media processing architecture, plus a portfolio of tablet reference platforms based on its in-house Android board support package and application software. The most recent platform, the JAGUAR Android reference tablet, was announced in May 2011.
ZiiLABS	Products	StemCell cores The core asset of the ZiiLABS ZMS chips seem to be an array of processing units called StemCells that are programmed to perform media processing. These are described as 32-bit floating-point processing units and are likely some form of digital signal processor cores used to accelerate various operations. All video codec and 3D graphics handling in the ZMS processors is handled by programming this array of coprocessors to do the job.
ZiiLABS	Products	Processors ZMS-40 (quad Cortex-A9 with 96 StemCell cores) ZMS-20 (dual Cortex A9 with 48 StemCell cores) ZMS-08 (single Cortex-A8 with 64 StemCell cores) ZMS-05 (dual ARM9 with 24 StemCell cores) Reference platforms Zii EGG (this product is now end-of-life) JAGUAR (Android 3.2 Reference Tablet) JAGUAR3 (Slim Android 3.2 Reference Tablet)Over the years a number of other development platforms have been made introduced including the Zii Development kits (traditional large form factor systems).
Syntactic hierarchy	Syntactic hierarchy	Syntax is concerned with the way sentences are constructed from smaller parts, such as words and phrases. Two steps can be distinguished in the study of syntax. The first step is to identify different types of units in the stream of speech and writing. In natural languages, such units include sentences, phrases, and words. The second step is to analyze how these units build up larger patterns, and in particular to find general rules that govern the construction of sentences.http://people.dsv.su.se/~vadim/cmnew/chapter2/ch2_21.htm This can be broken down into constituents, which are a group of words that are organized as a unit, and the organization of those constituents. They are organized in a hierarchical structure, by embedding inside one another to form larger constituents.
Syntactic hierarchy	History	Universal Grammar: the Chomskyan view In Chomsky’s view, humans are born with innate knowledge of certain principles that guide them in developing the grammar of their language. In other words, Chomsky’s theory is that language learning is facilitated by a predisposition that our brains have for certain structures of language. This implies in turn that all languages have a common structural basis: the set of rules known as "universal grammar". The theory of universal grammar entails that humans are born with an innate knowledge (or structural rules) of certain principles that guide them in developing the grammar of their language.
Syntactic hierarchy	History	Structural Linguistics: Saussurean Influences Regarded as the "Founder of Structural Linguistics", which reflects the concept of structuralism, Ferdinand de Saussure stated the ways in which human culture requires an overarching structure to relate to in order to communicate. He defines language to be different than human speech, which is fundamental and essential to language. While speech is a combination of several disciplines (i.e. physical, psychological, etc.) and is part of an individual and their society, language is a system of classification of its own entity.De Saussure argues that in written language, words are chained together in sequence on the chain of speaking, and therefore gain relations based on the linear nature of language. Language, however, is not simply a classification for universal concepts, as translating from one language to another proves to be a difficult task. Each Languages organizes their own world differently, and do not name existing categories, rather articulate their own. This idea explains that though languages can differ within levels of Syntactic Hierarchy, all languages encompass the same set of levels.
Syntactic hierarchy	The Levels of Syntactic Hierarchy	Groups of sentences (text) Separate sentences can combine together to create one sentence. For example, the sentence “The boy chased the ball” and “He didn’t catch it” can be combined together. You can do this in many ways including stringing one sentence after the other or joining the sentences with conjunctions.1. “The boy chased the ball; he didn’t catch it.”2. “The boy chased the ball, but he didn’t catch it.”3. “The boy chased the ball, and he didn’t catch it.” Sentence Phrases combined to form sentences. The phrase “the girl” combines with the phrase “ran away” to form the sentence: “The girl ran away.” Phrases Words combine to form phrases. The word “the” combines with “girl” to form the phrase: “The girl” Words Morphemes combine to form words. Morphemes belong to categories that determine how they combine. For example, the word 'manageable' is made up of two morphemes 'manage' which is a verb and 'able' which is an adjective, these categories tell the morphemes how to combine so they form the word 'manageable.' Morphemes Smallest meaningful unit in a word. For example, “boys” has two morphemes “boy” and “-s.” Phonemes A unit of sound such as individual consonants and vowels of a language. For example, /p/, /t/ and /æ/ are phonemes in English.
Syntactic hierarchy	The Levels of Syntactic Hierarchy	Phonetic form A subset of sounds which demonstrates the different variations of a phoneme. Diacritics can be used to represent this, for example aspiration can be added to the letter /p/ in the word /pʰɪt/. Unsegmented Speech Refers to ambiguous streams of words with spaces in between. For example, this can represent how an infant may hear human speech.
Syntactic hierarchy	Analysis of Syntactic Hierarchy Levels	Sentence Sentences are the hierarchal structure of combined phrases. When constructing a sentence, two types of phrases are always necessary: Noun Phrase (NP) and Verb Phrase (VP), forming the simplest possible sentence. What determines whether a sentence is grammatically constructed (i.e. the sentence makes sense to a native speaker of the language), is its adherence to the language's phrase structure rules, allowing a language to generate large numbers of sentences. Languages cross-linguistically differ in their phrase structure rules, resulting in the difference of order of the NP and VP, and other phrases included in a sentence. Languages which do have the similar phrase structure rules, however, will translate so that a sentence from one language will be grammatical when translated into the target language.
Syntactic hierarchy	Analysis of Syntactic Hierarchy Levels	French example: Sentence: "Le chien a aimé la fille" (translation: "The dog loved the girl") The French sentence directly translates to English, demonstrating that the phrase structures of both languages are very similar.
Syntactic hierarchy	Analysis of Syntactic Hierarchy Levels	Phrase The idea that words combine to form phrases. For example, the word “the” combines with word “dog” to form the phrase “the dog”. A phrase is a sequence of words or a group of words arranged in a grammatical way to combine and form a sentence. There are five commonly occurring types of phrases; Noun phrases (NP), Adjective phrases (AdjP), Verb phrases (VP), Adverb Phrases (AdvP), and Prepositional Phrases (PP).
Syntactic hierarchy	Analysis of Syntactic Hierarchy Levels	Hierarchical combinations of words in their formation of phrasal categories are apparent cross-linguistically- for example, in French: French examples: Noun phrase: "Le chien" (translation: "The dog") Verb phrase: " a aimé la fille" (translation: "loved the girl") Full sentence: "Le chien a aimé la fille" Noun phrase A noun phrase refers to a phrase that is built upon a noun. For example, “ The dog” or “the girl” in the sentence “the dog loved the girl” act as noun phrases.
Syntactic hierarchy	Analysis of Syntactic Hierarchy Levels	Verb phrase Verb phrase refers to a phrase that is composed of at least one main verb and one or more helping/auxiliary verb (every sentence needs at least one main verb). For example, the word “loved the girl” in the sentence “the dog loved the girl” acts as a verb phrase. see also Adjective phrases (AdjP), Adverb phrases (AdvP), and Prepositional phrases (PP) Phrase structure rules A phrase structure tree shows that a sentence is both linear string of words and a hierarchical structure with phrases nested in phrases (combination of phrase structures). A phrase structure tree is a formal device for representing speaker’s knowledge about phrase structure in speech.The syntactic category of each individual word appears immediately above that word. In this way, “the” is shown to be a determiner, “child” is a noun, and so on.
Syntactic hierarchy	Analysis of Syntactic Hierarchy Levels	Word The subdomain that deals with words is morphology, which states that words are made up of morphemes which combine in a regular and rule-governed fashion.For example, the word 'national' is made up of two morphemes 'nation' which is a noun and '-al' which is a suffix that means pertaining to, this meaning helps us in categorizing '-al' as an adjective. These categories aid in arranging the morphemes so they can combine in a way that will form the word 'national,’ which is an adjective.
Syntactic hierarchy	Analysis of Syntactic Hierarchy Levels	Morphology states that words come in categories, and the morphemes that join together to create the word assign the category. The two main categories are open class, where new words can be created and closed class where there is a limited number of members. Within both of these categories there are further sub-categories. Open class includes: nouns, verbs, adjectives, and adverbs, and closed class includes: prepositions, determiners, numerals, complementizers, auxiliaries, modals, coordinators, and negation/affirmation. These sub categories can be further broken down for example, verbs can be either transitive or intransitive. These categories can be identified with semantic criteria about what a word means, for instance nouns are said to be people, places, or things while verbs are actions. Words are all placed in these categories and depending on their category they follow specific rules that determine their word order.Cross-Linguistically other languages form words similarly to English. This is done by having morphemes of different categories combine in a rule governed fashion in order to create the word.
Syntactic hierarchy	Analysis of Syntactic Hierarchy Levels	French example: "é"- masculine past participle root verb suffix of regular -er verbs "aimer" (translation: to like/love)-> "aim" + "é" = "aimé" (translation: liked)
Syntactic hierarchy	Minimalist Theory of Syntax	Syntactic hierarchy may be the most basic and assumed component of almost all syntactic theories, and yet the minimalist theory of syntax views a clause or group of words as a string, rather than as components of a hierarchical system. While this theory prioritizes linearity over hierarchy, hierarchical structure is still analyzed if it "generates correct data" or if there is "direct evidence for it". In this way, it appears that syntactic hierarchy still plays an important role in even the minimalist theories.
Syntactic hierarchy	Artificial language	In artificial languages, lexemes, tokens, and formulas are usually found among the basic units.
Groundwater flow equation	Groundwater flow equation	Used in hydrogeology, the groundwater flow equation is the mathematical relationship which is used to describe the flow of groundwater through an aquifer. The transient flow of groundwater is described by a form of the diffusion equation, similar to that used in heat transfer to describe the flow of heat in a solid (heat conduction). The steady-state flow of groundwater is described by a form of the Laplace equation, which is a form of potential flow and has analogs in numerous fields.
Groundwater flow equation	Groundwater flow equation	The groundwater flow equation is often derived for a small representative elemental volume (REV), where the properties of the medium are assumed to be effectively constant. A mass balance is done on the water flowing in and out of this small volume, the flux terms in the relationship being expressed in terms of head by using the constitutive equation called Darcy's law, which requires that the flow is laminar. Other approaches are based on Agent Based Models to incorporate the effect of complex aquifers such as karstic or fractured rocks (i.e. volcanic)
Groundwater flow equation	Mass balance	A mass balance must be performed, and used along with Darcy's law, to arrive at the transient groundwater flow equation. This balance is analogous to the energy balance used in heat transfer to arrive at the heat equation. It is simply a statement of accounting, that for a given control volume, aside from sources or sinks, mass cannot be created or destroyed. The conservation of mass states that, for a given increment of time (Δt), the difference between the mass flowing in across the boundaries, the mass flowing out across the boundaries, and the sources within the volume, is the change in storage.
Groundwater flow equation	Diffusion equation (transient flow)	Mass can be represented as density times volume, and under most conditions, water can be considered incompressible (density does not depend on pressure). The mass fluxes across the boundaries then become volume fluxes (as are found in Darcy's law). Using Taylor series to represent the in and out flux terms across the boundaries of the control volume, and using the divergence theorem to turn the flux across the boundary into a flux over the entire volume, the final form of the groundwater flow equation (in differential form) is: Ss∂h∂t=−∇⋅q−G.
Groundwater flow equation	Diffusion equation (transient flow)	This is known in other fields as the diffusion equation or heat equation, it is a parabolic partial differential equation (PDE). This mathematical statement indicates that the change in hydraulic head with time (left hand side) equals the negative divergence of the flux (q) and the source terms (G). This equation has both head and flux as unknowns, but Darcy's law relates flux to hydraulic heads, so substituting it in for the flux (q) leads to Ss∂h∂t=−∇⋅(−K∇h)−G.
Groundwater flow equation	Diffusion equation (transient flow)	Now if hydraulic conductivity (K) is spatially uniform and isotropic (rather than a tensor), it can be taken out of the spatial derivative, simplifying them to the Laplacian, this makes the equation Ss∂h∂t=K∇2h−G. Dividing through by the specific storage (Ss), puts hydraulic diffusivity (α = K/Ss or equivalently, α = T/S) on the right hand side. The hydraulic diffusivity is proportional to the speed at which a finite pressure pulse will propagate through the system (large values of α lead to fast propagation of signals). The groundwater flow equation then becomes ∂h∂t=α∇2h−G. Where the sink/source term, G, now has the same units but is divided by the appropriate storage term (as defined by the hydraulic diffusivity substitution). Rectangular cartesian coordinates Especially when using rectangular grid finite-difference models (e.g. MODFLOW, made by the USGS), we deal with Cartesian coordinates. In these coordinates the general Laplacian operator becomes (for three-dimensional flow) specifically ∂h∂t=α[∂2h∂x2+∂2h∂y2+∂2h∂z2]−G.
Groundwater flow equation	Diffusion equation (transient flow)	MODFLOW code discretizes and simulates an orthogonal 3-D form of the governing groundwater flow equation. However, it has an option to run in a "quasi-3D" mode if the user wishes to do so; in this case the model deals with the vertically averaged T and S, rather than k and Ss. In the quasi-3D mode, flow is calculated between 2D horizontal layers using the concept of leakage.
Groundwater flow equation	Diffusion equation (transient flow)	Circular cylindrical coordinates Another useful coordinate system is 3D cylindrical coordinates (typically where a pumping well is a line source located at the origin — parallel to the z axis — causing converging radial flow). Under these conditions the above equation becomes (r being radial distance and θ being angle), ∂h∂t=α[∂2h∂r2+1r∂h∂r+1r2∂2h∂θ2+∂2h∂z2]−G.
Groundwater flow equation	Diffusion equation (transient flow)	Assumptions This equation represents flow to a pumping well (a sink of strength G), located at the origin. Both this equation and the Cartesian version above are the fundamental equation in groundwater flow, but to arrive at this point requires considerable simplification. Some of the main assumptions which went into both these equations are: the aquifer material is incompressible (no change in matrix due to changes in pressure — aka subsidence), the water is of constant density (incompressible), any external loads on the aquifer (e.g., overburden, atmospheric pressure) are constant, for the 1D radial problem the pumping well is fully penetrating a non-leaky aquifer, the groundwater is flowing slowly (Reynolds number less than unity), and the hydraulic conductivity (K) is an isotropic scalar.Despite these large assumptions, the groundwater flow equation does a good job of representing the distribution of heads in aquifers due to a transient distribution of sources and sinks.
Groundwater flow equation	Laplace equation (steady-state flow)	If the aquifer has recharging boundary conditions a steady-state may be reached (or it may be used as an approximation in many cases), and the diffusion equation (above) simplifies to the Laplace equation. 0=α∇2h This equation states that hydraulic head is a harmonic function, and has many analogs in other fields. The Laplace equation can be solved using techniques, using similar assumptions stated above, but with the additional requirements of a steady-state flow field. A common method for solution of this equations in civil engineering and soil mechanics is to use the graphical technique of drawing flownets; where contour lines of hydraulic head and the stream function make a curvilinear grid, allowing complex geometries to be solved approximately. Steady-state flow to a pumping well (which never truly occurs, but is sometimes a useful approximation) is commonly called the Thiem solution.
Groundwater flow equation	Two-dimensional groundwater flow	The above groundwater flow equations are valid for three dimensional flow. In unconfined aquifers, the solution to the 3D form of the equation is complicated by the presence of a free surface water table boundary condition: in addition to solving for the spatial distribution of heads, the location of this surface is also an unknown. This is a non-linear problem, even though the governing equation is linear.
Groundwater flow equation	Two-dimensional groundwater flow	An alternative formulation of the groundwater flow equation may be obtained by invoking the Dupuit–Forchheimer assumption, where it is assumed that heads do not vary in the vertical direction (i.e., ∂h/∂z=0 ). A horizontal water balance is applied to a long vertical column with area δxδy extending from the aquifer base to the unsaturated surface. This distance is referred to as the saturated thickness, b. In a confined aquifer, the saturated thickness is determined by the height of the aquifer, H, and the pressure head is non-zero everywhere. In an unconfined aquifer, the saturated thickness is defined as the vertical distance between the water table surface and the aquifer base. If ∂h/∂z=0 , and the aquifer base is at the zero datum, then the unconfined saturated thickness is equal to the head, i.e., b=h.
Groundwater flow equation	Two-dimensional groundwater flow	Assuming both the hydraulic conductivity and the horizontal components of flow are uniform along the entire saturated thickness of the aquifer (i.e., ∂qx/∂z=0 and ∂K/∂z=0 ), we can express Darcy's law in terms of integrated groundwater discharges, Qx and Qy: Qx=∫0bqxdz=−Kb∂h∂x Qy=∫0bqydz=−Kb∂h∂y Inserting these into our mass balance expression, we obtain the general 2D governing equation for incompressible saturated groundwater flow: ∂nb∂t=∇⋅(Kb∇h)+N.
Groundwater flow equation	Two-dimensional groundwater flow	Where n is the aquifer porosity. The source term, N (length per time), represents the addition of water in the vertical direction (e.g., recharge). By incorporating the correct definitions for saturated thickness, specific storage, and specific yield, we can transform this into two unique governing equations for confined and unconfined conditions: S∂h∂t=∇⋅(Kb∇h)+N. (confined), where S=Ssb is the aquifer storativity and Sy∂h∂t=∇⋅(Kh∇h)+N. (unconfined), where Sy is the specific yield of the aquifer. Note that the partial differential equation in the unconfined case is non-linear, whereas it is linear in the confined case. For unconfined steady-state flow, this non-linearity may be removed by expressing the PDE in terms of the head squared: ∇⋅(K∇h2)=−2N. Or, for homogeneous aquifers, ∇2h2=−2NK. This formulation allows us to apply standard methods for solving linear PDEs in the case of unconfined flow. For heterogeneous aquifers with no recharge, Potential flow methods may be applied for mixed confined/unconfined cases.
Celestine (mineral)	Celestine (mineral)	Celestine (the IMA-accepted name) or celestite is a mineral consisting of strontium sulfate (SrSO4). The mineral is named for its occasional delicate blue color. Celestine and the carbonate mineral strontianite are the principal sources of the element strontium, commonly used in fireworks and in various metal alloys.
Celestine (mineral)	Etymology	Celestine derives its name from the Latin word caelestis meaning celestial which in turn is derived from the Latin word caelum meaning sky or heaven.
Celestine (mineral)	Occurrence	Celestine occurs as crystals, and also in compact massive, and fibrous forms. It is mostly found in sedimentary rocks, often associated with the minerals gypsum, anhydrite, and halite. On occasion in some localities, it may also be found with sulfur inclusions. The mineral is found worldwide, usually in small quantities. Pale blue crystal specimens are found in Madagascar. White and orange variants also occurred at Yate, Bristol, UK, where it was extracted for commercial purposes until April 1991.The skeletons of the protozoan Acantharea are made of celestine, unlike those of other radiolarians which are made of silica. In carbonate marine sediments, burial dissolution is a recognized mechanism of celestine precipitation. It is sometimes used as a gemstone.
Celestine (mineral)	Geodes	Celestine crystals are found in some geodes. The world's largest known geode, a celestine geode 35 feet (11 m) in diameter at its widest point, is located near the village of Put-in-Bay, Ohio, on South Bass Island in Lake Erie. The geode has been converted into a viewing cave, Crystal Cave, with the crystals which once composed the floor of the geode removed. The geode has celestine crystals as wide as 18 inches (46 cm) across, estimated to weigh up to 300 pounds (140 kg) each.
Celestine (mineral)	Geodes	Celestine geodes are understood to form by replacement of alabaster nodules consisting of the calcium sulfates gypsum or anhydrite. Calcium sulfate is sparingly soluble, but strontium sulfate is mostly insoluble. Strontium-bearing solutions that come into contact with calcium sulfate nodules dissolve the calcium away, leaving a cavity. The strontium is immediately precipitated as celestine, with the crystals growing into the newly-formed cavity.
Apple Pencil	Apple Pencil	Apple Pencil is a line of wireless stylus pen accessories designed and developed by Apple Inc. for use with supported iPad tablets.
Apple Pencil	Apple Pencil	The first-generation Apple Pencil was announced alongside the first iPad Pro on September 9, 2015. It communicates wirelessly via Bluetooth and has a removable cap that conceals a Lightning connector used for charging. The Pencil is compatible with the first- and second-generation iPad Pro models, and the sixth through tenth-generation iPad models (with the latter requiring a USB-C adapter).The second-generation Apple Pencil was announced on October 30, 2018, alongside the third-generation iPad Pro, and is used with most iPad models that contain a USB-C port (excluding the tenth-generation iPad). It uses a magnetic connector on the side of the tablet for charging rather than a Lightning connector, and includes touch-sensitive areas that can be tapped to perform actions within supported apps.
Apple Pencil	Apple Pencil	Apple has promoted the Pencil as being oriented towards creative work and productivity; during its unveiling, the Pencil's drawing capabilities were demonstrated using the mobile version of Adobe Photoshop, and its document-annotation capabilities were shown on several Microsoft Office apps.
Apple Pencil	Specifications	First generation The Apple Pencil has pressure sensitivity and angle detection, and it was designed for low latency to enable smooth marking on the screen. The Pencil and the user's fingers can be used simultaneously while rejecting input from the user's palm. One end of the device has a magnetically-fastened removable cap which covers a Lightning connector which is used for charging from an iPad's Lightning port. The initial charge lasts about twelve hours, but fifteen seconds of charging provides sufficient power for 30 minutes of use. It also ships with a female-to-female Lightning adapter that allows it to be used with charging cables.The Apple Pencil uses an STMicroelectronics STM32L151UCY6 Ultra-low-power 32-bit RISC ARM-based Cortex-M3 MCU running at 32 MHz with 64 KB of flash memory, a Bosch Sensortech BMA280 3‐axis accelerometer and a Cambridge Silicon Radio (Qualcomm) CSR1012A05 Bluetooth Smart IC for its Bluetooth connection to the iPad. It is powered by a rechargeable 3.82 V, 0.329 Wh lithium-ion battery.
Apple Pencil	Specifications	The first-generation Apple Pencil is compatible with iPad models with a Lightning port released since 2018, including the first- and second-generation iPad Pro models, third-generation iPad Air, fifth-generation iPad Mini, sixth-generation 9.7-inch iPad, and the seventh, eighth, and ninth-generation 10.2-inch iPad models. It also supports the tenth-generation, 10.9-inch iPad released in 2022, but requires a dongle (similar to the aforementioned Lightning adapter) to connect it to a USB-C cable for charging. Apple began to bundle this dongle with Pencil units in October 2022, and it can be purchased separately by existing owners.
Apple Pencil	Specifications	Second generation On October 30, 2018, Apple announced an updated Pencil alongside the third-generation iPad Pro. It is similar in design and specifications to the first model, but without the detachable connector, and part of the stylus is flattened to inhibit rolling. It contains tap-sensitive zones on its sides that can be mapped to functions within apps. The sixth-generation iPad Pro added the ability (known as Hover) to detect the position and angle of Pencil up to 12 millimetres (0.47 in) above the screen. Custom laser engraving is available when purchased via the Apple Store online.Rather than a physical Lightning connector, the second-generation Pencil is paired and charged using a proprietary magnetic wireless charging connector on the tablet instead. As such, it is only supported by the third-, fourth-, fifth- and sixth-generation iPad Pro, sixth-generation iPad Mini, and the fourth- and fifth-generation iPad Air. All of these models have USB-C connectors instead of Lightning, making them physically incompatible with the first-generation Pencil.
Rabbit pie	Rabbit pie	Rabbit pie is a game pie consisting of rabbit meat in a gravy with other ingredients (typically onions, celery and carrots) enclosed in a pastry crust. Rabbit pie is part of traditional American and English cuisine. It has recently found renewed popularity.
Rabbit pie	Ingredients	Wild rabbit, as opposed to farmed, is most often used as it is easily and affordably obtained, and is described as more flavoursome.Along with rabbit meat, ingredients of the filling of a rabbit pie typically include onions, celery and carrots. Other ingredients may include prunes, bacon and cider.Australian recipes for rabbit pie sometimes include the food paste Vegemite as an ingredient.
Rabbit pie	In culture	Rabbit pie was a staple dish of the American pioneers. Thanks to the increasing demand for wild and fresh ingredients, rabbit pie is often seen on the menus of fashionable restaurants and gastropubs.Two huge rabbit pies are part of traditional Easter celebrations in the English village of Hallaton, Leicestershire.In Beatrix Potter's children's book The Tale of Peter Rabbit, Peter Rabbit and his siblings are warned "[not to] go into Mr. McGregor's garden" because their father "had an accident there; he was put in a pie by Mrs. McGregor.""Rabbit pie day" is ostensibly invoked in the song Run, Rabbit, Run.
SureThing	SureThing	SureThing is a line of label printing software created by MicroVision Development.Its most popular program is SureThing CD Labeler, which is designed to produce CD and DVD labels as well as LightScribe writing. SureThing CD Labeler's allows clipart and images to the labels to improve the label's design. The program supports playlists as well. SureThing has pre-produced templates for labels for LightScribe, 45-inch vinyl, CD, DVD, pocket CDs. It allows customers to create song labels electronically from the playlist of a CD player or other device.In 1999, Electronic Musician's David Rubin wrote that the "SureThing label applicator is arguably the weakest part of the package. Designed around a CD jewel case, it's awkward to use and susceptible to damage" and that "[c]learly, the SureThing software is the main reason that someone would buy this kit". Katherine Stevenson wrote in a 2002 review of SureThing that the "handy preview and browse capabilities make the vast number of options manageable" and that "Depending how flat the label lies, and how evenly you apply pressure with your fingers, you may still end up with wrinkles". In 2002, the SureThing CD Labeler received awards from SharewareJunkies for "Best Program of the Year", as well as the "Best Windows Program".In a 2005 review, "SureThing is a bit better, but lacks niceties like the alignment tools we've all grown accustomed to from the menu design functions in DVD-authoring programs." Sally Wiener Grotta and Daniel Grotta wrote in a 2009 PC World that "SureThing CD Labeler is an intuitive, easy-to-learn program" and "SureThing can make the difference between having your CDs and DVDs look homemade or professional".
Semantic lexicon	Semantic lexicon	A semantic lexicon is a digital dictionary of words labeled with semantic classes so associations can be drawn between words that have not previously been encountered. Semantic lexicons are built upon semantic networks, which represent the semantic relations between words. The difference between a semantic lexicon and a semantic network is that a semantic lexicon has definitions for each word, or a "gloss".
Semantic lexicon	Structure	Semantic lexicons are made up of lexical entries. These entries are not orthographic, but semantic, eliminating issues of homonymy and polysemy. These lexical entries are interconnected with semantic relations, such as hyperonymy, hyponymy, meronymy, or troponymy. Synonymous entries are grouped together in what the Princeton WordNet calls "synsets" Most semantic lexicons are made up of four different "sub-nets": nouns, verbs, adjectives, and adverbs, though some researchers have taken steps to add an "artificial node" interconnecting the sub-nets.
Semantic lexicon	Structure	Nouns Nouns are ordered into a taxonomy, structured into a hierarchy where the broadest and most encompassing noun is located at the top, such as "thing", with the nouns becoming more and more specific the further they are from the top. The very top noun in a semantic lexicon is called a unique beginner. The most specific nouns (those that do not have any subordinates), are terminal nodes.Semantic lexicons also distinguish between types, where a type of something has characteristics of a thing such as a Rhodesian Ridgeback being a type of dog, and instances, where something is an example of said thing, such as Dave Grohl is an instance of a musician. Instances are always terminal nodes because they are solitary and don’t have other words or ontological categories belonging to them.Semantic lexicons also address meronymy, which is a “part-to-whole” relationship, such as keys are part of a laptop. The necessary attributes that define a specific entry are also necessarily present in that entry’s hyponym. So, if a computer has keys, and a laptop is a type of computer, then a laptop must have keys. However, there are many instances where this distinction can become vague. A good example of this is the item chair. Most would define a chair as having legs and a seat (as in the part one sits on). However, there are some very “artistic” and “modern” chairs in overpriced boutiques that do not have legs at all. Beanbags also do not have legs, but few would argue that they aren't chairs. Questions like this are the core questions that drive research and work in the fields of taxonomy and ontology.
Semantic lexicon	Structure	Verbs Verb synsets are arranged much like their noun counterparts: the more general and encompassing verbs are near the top of the hierarchy while troponyms (verbs that describe a more specific way of doing something) are grouped beneath. Verb specificity moves along a vector, with the verbs becoming more and more specific in reference to a certain quality. For example. The set "walk / run / sprint" becomes more specific in terms of the speed, and "dislike / hate / abhor" becomes more specific in terms of the intensity of the emotion.
Semantic lexicon	Structure	The ontological groupings and separations of verbs is far more arguable than their noun counterparts. It is widely accepted that a dog is a type of animal and that a stool is a type of chair, but it can be argued that abhor is on the same emotional plane as hate (that they are synonyms and not super/subordinates). It can also be argued that love and adore are synonyms, or that one is more specific than the other. Thus, the relations between verbs are not as agreed-upon as that of nouns.
Semantic lexicon	Structure	Another attribute of verb synset relations is that there are also ordered into verb pairs. In these pairs, one verb necessarily entails the other in the way that massacre entails kill, and know entails believe. These verb pairs can be troponyms and their superordinates, as is the case in the first example, or they can be in completely different ontological categories, as in the case in the second example.
Semantic lexicon	Structure	Adjectives Adjective synset relations are very similar to verb synset relations. They are not quite as neatly hierarchical as the noun synset relations, and they have fewer tiers and more terminal nodes. However, there are generally less terminal nodes per ontological category in adjective synset relations than that of verbs. Adjectives in semantic lexicons are organized in word pairs as well, with the difference being that their word pairs are antonyms instead of entailments. More generic polar adjectives such as hot and cold, or happy and sad are paired. Then other adjectives that are semantically similar are linked to each of these words. Hot is linked to warm, heated, sizzling, and sweltering, while cold is linked to cool, chilly, freezing, and nippy. These semantically similar adjectives are considered indirect antonyms to the opposite polar adjective (i.e. nippy is an indirect antonym to hot). Adjectives that are derived from a verb or a noun are also directly linked to said verb or noun across sub-nets. For example, enjoyable is linked to the semantically similar adjectives agreeable, and pleasant, as well as to its origin verb, enjoy.
Semantic lexicon	Structure	Adverbs There are very few adverbs accounted for in semantic lexicons. This is because most adverbs are taken directly from their adjective counterparts, in both meaning and form, and changed only morphologically (i.e. happily is derived from happy, and luckily is derived from lucky, which is derived from luck). The only adverbs that are accounted for specifically are ones without these connections, such as really, mostly, and hardly.
Semantic lexicon	Challenges facing semantic lexicons	The effects of the Princeton WordNet project extend far past English, though most research in the field revolves around the English language. Creating a semantic lexicon for other languages has proved to be very useful for Natural Language Processing applications. One of the main focuses of research in semantic lexicons is linking lexicons of different languages to aid in machine translation. The most common approach is to attempt to create a shared ontology that serves as a “middleman” of sorts between semantic lexicons of two different languages. This is an extremely challenging and as-of-yet unsolved issue in the Machine Translation field. One issue arises from the fact that no two languages are word-for-word translations of each other. That is, every language has some sort of structural or syntactic difference from every other. In addition, languages often have words that don’t translate easily into other languages, and certainly not with an exact word-to-word match. Proposals have been made to create a set framework for wordnets. Research has shown that every known human language has some sort of concept resembling synonymy, hyponymy, meronymy, and antonymy. However, every idea so far proposed has been met with criticism for using a pattern that works best for English and less for other languages.Another obstacle in the field is that no solid guidelines exist for semantic lexicon framework and contents. Each lexicon project in each different language has had a slightly (or not so slightly) different approach to their wordnet. There is not even an agreed-upon definition of what a “word” is. Orthographically, they are defined as a string of letters with spaces on either side, but semantically it becomes a very debated subject. For example, though it is not difficult to define dog or rod as words, but what about guard dog or lightning rod? The latter two examples would be considered orthographically separate words, though semantically they make up one concept: one is a type of dog and one is a type of rod. In addition to these confusions, wordnets are also idiosyncratic, in that they do not consistently label items. They are redundant, in that they often have several words assigned to each meaning (synsets). They are also open-ended, in that they often focus on and extend into terminology and domain-specific vocabulary.
Semantic lexicon	List of semantic lexicons	WordNet EuroWordNet Multilingual Central Repository Global Wordnet MindNet
Device configuration overlay	Device configuration overlay	Device configuration overlay (DCO) is a hidden area on many of today's hard disk drives (HDDs). Usually when information is stored in either the DCO or host protected area (HPA), it is not accessible by the BIOS (or UEFI), OS, or the user. However, certain tools can be used to modify the HPA or DCO. The system uses the IDENTIFY_DEVICE command to determine the supported features of a given hard drive, but the DCO can report to this command that supported features are nonexistent or that the drive is smaller than it actually is. To determine the actual size and features of a disk, the DEVICE_CONFIGURATION_IDENTIFY command is used, and the output of this command can be compared to the output of IDENTIFY_DEVICE to see if a DCO is present on a given hard drive. Most major tools will remove the DCO in order to fully image a hard drive, using the DEVICE_CONFIGURATION_RESET command. This permanently alters the disk, unlike with the host protected area (HPA), which can be temporarily removed for a power cycle.
Device configuration overlay	Uses	The Device Configuration Overlay (DCO), which was first introduced in the ATA-6 standard, "allows system vendors to purchase HDDs from different manufacturers with potentially different sizes, and then configure all HDDs to have the same number of sectors. An example of this would be using DCO to make an 80-gigabyte HDD appear as a 60-gigabyte HDD to both the (OS) and the BIOS.... Given the potential to place data in these hidden areas, this is an area of concern for computer forensics investigators. An additional issue for forensic investigators is imaging the HDD that has the HPA and/or DCO on it. While certain vendors claim that their tools are able to both properly detect and image the HPA, they are either silent on the handling of the DCO or indicate that this is beyond the capabilities of their tool."
Device configuration overlay	DCO Software tools	Detection tools HDAT2 a free software program for MS-DOS. It can be used to create/remove Host Protected Area (HPA) (using command SET MAX) and create/remove DCO hidden area (using command DCO MODIFY). It also can do other functions on the DCO. Data Synergy's freeware ATATool utility can be used to detect a DCO from a Windows environment. Recent versions allow a DCO to be created, removed or frozen.
Device configuration overlay	DCO Software tools	Software imaging tools Guidance Software's EnCase comes with a Linux-based tool that images hard drives called LinEn. LinEn 6.01 was validated by the National Institute of Justice (NIJ) in October 2008, and they found that "The tool does not remove either Host Protected Areas (HPAs) or DCOs. However, the Linux test environment automatically removed the HPA on the test drive, allowing the tool to image sectors hidden by an HPA. The tool did not acquire sectors hidden by a DCO."AccessData's FTK Imager 2.5.3.14 was validated by the National Institute of Justice (NIJ) in June 2008. Their findings indicated that "If a physical acquisition is made of a drive with hidden sectors in either a Host Protected Area or a Device Configuration Overlay, the tool does not remove either an HPA or a DCO. The tool did not acquire sectors hidden by an HPA." Hardware imaging tools A variety of hardware imaging tools have been found to successfully detect and remove DCOs. The NIJ routinely tests digital forensics tools and these publications can be found at www.ojp.gov (Link needs checking by other Wikipedians! For this particular European reader using locked-down non-JavaScript Firefox on 2021-11-30 this link unhelpfully shows: "Access Denied. You are not authorized to access this page") or from NIST at https://www.nist.gov/itl/ssd/software-quality-group/computer-forensics-tool-testing-program-cftt
1-Testosterone	1-Testosterone	1-Testosterone (abbreviated and nicknamed as 1-Testo, 1-T), also known as δ1-dihydrotestosterone (δ1-DHT), as well as dihydroboldenone, is a synthetic anabolic–androgenic steroid (AAS) and a 5α-reduced derivative of boldenone (Δ1-testosterone). It differs from testosterone by having a 1(2)-double bond instead of a 4(5)-double bond in its A ring. It was legally sold online in the United States until 2005, when it was reclassified as a Schedule III drug.
1-Testosterone	Pharmacology	Pharmacodynamics A 2006 study determined that 1-testosterone has a high androgenic and anabolic potency even without being metabolized, so it can be characterized as a typical anabolic steroid. 1-Testosterone binds in a manner that is highly selective to the androgen receptor (AR) and has a high potency to stimulate AR-dependent transactivation. In vivo, an equimolar dose of 1-testosterone has the same potency to stimulate the growth of the prostate, the seminal vesicles and the androgen-sensitive levator ani muscle as the reference anabolic steroid testosterone propionate, but, unlike testosterone propionate, 1-testosterone also increases liver weight.
1-Testosterone	Chemistry	1-Testosterone, IUPAC name 17β-hydroxy-5α-androst-1-en-3-one, also known as 4,5α-dihydro-δ1-testosterone (Δ1-DHT) or as 5α-androst-1-en-17β-ol-3-one, is a synthetic androstane steroid and a derivative of dihydrotestosterone (DHT). Derivatives Two prohormones of 1-testosterone are 1-androstenediol and 1-androstenedione, the latter of which may be synthesized from stanolone acetate.Mesabolone is a ketal made from 1-testosterone. 1-Testosterone also is known to be used to synthesize mestanolone and metenolone.Methyl-1-testosterone is the 17α-methyl derivative of 1-testosterone. Detection in body fluids Doping with 1-testosterone can be detected in urine samples using gas chromatography.
Gallium(III) fluoride	Gallium(III) fluoride	Gallium(III) fluoride (GaF3) is a chemical compound. It is a white solid that melts under pressure above 1000 °C but sublimes around 950 °C. It has the FeF3 structure where the gallium atoms are 6-coordinate. GaF3 can be prepared by reacting F2 or HF with Ga2O3 or by thermal decomposition of (NH4)3GaF6. GaF3 is virtually insoluble in water. Solutions of GaF3 in HF can be evaporated to form the trihydrate, GaF3·3H2O, which on heating gives a hydrated form of GaF2(OH). Gallium(III) fluoride reacts with mineral acids to form hydrofluoric acid.
C1orf141	C1orf141	Chromosome 1 open reading frame 141, or C1orf141 is a protein which, in humans, is encoded by gene C1orf141. It is a precursor protein that becomes active after cleavage. The function is not yet well understood, but it is suggested to be active during development
C1orf141	Gene	Locus This gene is located on chromosome 1 at position 1p31.3. It is encoded on the antisense strand of DNA spanning from 67,092,176 to 67,141,646 and has 10 total exons. It overlaps slightly with the gene IL23R being encoded on the sense strand.
C1orf141	Gene	Transcription regulation A specific promoter region has not been predicted for C1orf141 so the 1000 base pairs upstream of the start of transcription was analyzed for transcription factor binding sites. The transcription factors below represent a subset of the transcription factor binding sites found within this region that give an idea of the kind of factors that could bind to the promoter Vertebrate TATA binding protein factor CCAAT binding factor Lim homeodomain factor Cart-1 Homeodomain transcription factor Fork head domain factor Nuclear receptor subfamily Brn POU domain
C1orf141	mRNA	Alternative Splicing The C1orf141 gene appears to have two common isoforms and seven less common transcript variants.
C1orf141	Protein	The primary encoded precursor protein (C1orf141 Isoform 1) consists of 400 amino acid residues and is 2177 base pairs long. It consists of 7 exons and a domain of unknown function DUF4545. Its predicted molecular mass is 54.4 kDa and predicted isoelectric point is 9.63. Composition The C1orf141 precursor protein has more lysine amino acid residues and less glycine amino acid residues than expected when compared to other human proteins. The sequence has 11.7% lysine and only 2.1% glycine. Post-translational modifications C1orf141 is modified post translation to form a mature protein product. It undergoes O-linked glycosylation, sumoylation, glycation, and phosphorylation. One N-terminal cleavage occurs followed by acetylation. Propeptide cleavage occurs at the start site of the final exon.
C1orf141	Protein	Structure The secondary structure for uncleaved C1orf141 consists primarily of alpha helices with a few small segments of beta sheets. These helices can be seen in the model of the tertiary structure predicted by the I-TASSER program. The program Phyre2 also predicts the protein to be made up primarily of alpha helices. After propeptide cleavage of C1orf141, I-TASSER predicts that only alpha helices remain.
C1orf141	Protein	Interactions There are currently no experimentally confirmed interactions for C1orf141. The STRING database for protein interactions identified ten potential proteins that interact with C1orf141 through text mining. These include SALT1, C8orf74, SHCBP1L, ACTL9, RBM44, CCDC116, ADO, WDR78, ZNF365, SPATA45. Through investigation of the papers where these interaction predictions were found, a solid link was not clear for any of the identified proteins.
C1orf141	Expression	C1orf141 is expressed in 30 different tissues but primarily in the testes. Other tissues where expression is above baseline levels are the brain, lungs, and ovaries. Localization The subcellular localization for C1orf141 is predicted to be in the nucleus. There are two nuclear localization signals within the protein sequence, one of which stays present after propeptide cleavage.
C1orf141	Function	The function of C1orf141 is not yet fully understood and has not been experimentally confirmed. However, expression data shows that the protein is active in some developmental stages. RNA-Seq data taken at different stages of development show expression at varying levels throughout. Expression rates are seen at higher levels in the fetal developmental stage than the adult in the protein's ETS profile. Microarray data for cumulus cells during natural and stimulated in vitro fertilization show relatively high levels of expression. There is no significant change in expression in adult tissue disease states.
C1orf141	Homology	Paralogs There are no paralogs for C1orf141 Orthologs Orthologous sequences are seen primarily in other mammalian species. The most distant ortholog identified through a NCBI BLAST search is a Reptilian species, but that is the only non-mammalian species. This list contains a subset of the species identified as orthologs to display the diversity of the species where orthologs can be found. Each species was compared to the human C1orf141 isoform that includes each coding exon, isoform X1.
C1orf141	Homology	Evolutionary History Using the Molecular Clock Hypothesis, the m value (the number of corrected amino acid changes per 100 residues) was calculated for C1orf141 and plotted against the divergence of species. When compared to the same m value plot for hemoglobin, fibrinogen alpha chain, and cytochrome c, it is clear that the C1orf141 gene is evolving at a faster rate than all three.
Insignificant Details of a Random Episode	Insignificant Details of a Random Episode	Insignificant Details of a Random Episode (Russian: Незначительные подробности случайного эпизода) is a 2011 Russian comedy short film directed by Mikhail Mestetsky.
Insignificant Details of a Random Episode	Plot	The two trains stopped opposite each other and strange relationships began to develop between the passengers.
Insignificant Details of a Random Episode	Cast	Kirill Käro Miriam Sekhon Ilya Zaslavskiy
Flux balance analysis	Flux balance analysis	Flux balance analysis (FBA) is a mathematical method for simulating metabolism in genome-scale reconstructions of metabolic networks. In comparison to traditional methods of modeling, FBA is less intensive in terms of the input data required for constructing the model. Simulations performed using FBA are computationally inexpensive and can calculate steady-state metabolic fluxes for large models (over 2000 reactions) in a few seconds on modern personal computers. The related method of metabolic pathway analysis seeks to find and list all possible pathways between metabolites.
Flux balance analysis	Flux balance analysis	FBA finds applications in bioprocess engineering to systematically identify modifications to the metabolic networks of microbes used in fermentation processes that improve product yields of industrially important chemicals such as ethanol and succinic acid. It has also been used for the identification of putative drug targets in cancer and pathogens, rational design of culture media, and host–pathogen interactions. The results of FBA can be visualized using flux maps similar to the image on the right, which illustrates the steady-state fluxes carried by reactions in glycolysis. The thickness of the arrows is proportional to the flux through the reaction.
Flux balance analysis	Flux balance analysis	FBA formalizes the system of equations describing the concentration changes in a metabolic network as the dot product of a matrix of the stoichiometric coefficients (the stoichiometric matrix S) and the vector v of the unsolved fluxes. The right-hand side of the dot product is a vector of zeros representing the system at steady state. Linear programming is then used to calculate a solution of fluxes corresponding to the steady state.
Flux balance analysis	History	Some of the earliest work in FBA dates back to the early 1980s. Papoutsakis demonstrated that it was possible to construct flux balance equations using a metabolic map. It was Watson, however, who first introduced the idea of using linear programming and an objective function to solve for the fluxes in a pathway. The first significant study was subsequently published by Fell and Small, who used flux balance analysis together with more elaborate objective functions to study the constraints in fat synthesis.
Flux balance analysis	Simulations	FBA is not computationally intensive, taking on the order of seconds to calculate optimal fluxes for biomass production for a typical network (around 2000 reactions). This means that the effect of deleting reactions from the network and/or changing flux constraints can be sensibly modelled on a single computer.
Flux balance analysis	Simulations	Gene/reaction deletion and perturbation studies Single reaction deletion A frequently used technique to search a metabolic network for reactions that are particularly critical to the production of biomass. By removing each reaction in a network in turn and measuring the predicted flux through the biomass function, each reaction can be classified as either essential (if the flux through the biomass function is substantially reduced) or non-essential (if the flux through the biomass function is unchanged or only slightly reduced).
Flux balance analysis	Simulations	Pairwise reaction deletion Pairwise reaction deletion of all possible pairs of reactions is useful when looking for drug targets, as it allows the simulation of multi-target treatments, either by a single drug with multiple targets or by drug combinations. Double deletion studies can also quantify the synthetic lethal interactions between different pathways providing a measure of the contribution of the pathway to overall network robustness.
Flux balance analysis	Simulations	Single and multiple gene deletions Genes are connected to enzyme-catalyzed reactions by Boolean expressions known as Gene-Protein-Reaction expressions (GPR). Typically a GPR takes the form (Gene A AND Gene B) to indicate that the products of genes A and B are protein sub-units that assemble to form the complete protein and therefore the absence of either would result in deletion of the reaction. On the other hand, if the GPR is (Gene A OR Gene B) it implies that the products of genes A and B are isozymes. Therefore, it is possible to evaluate the effect of single or multiple gene deletions by evaluation of the GPR as a Boolean expression. If the GPR evaluates to false, the reaction is constrained to zero in the model prior to performing FBA. Thus gene knockouts can be simulated using FBA.
Flux balance analysis	Simulations	Interpretation of gene and reaction deletion results The utility of reaction inhibition and deletion analyses becomes most apparent if a gene-protein-reaction matrix has been assembled for the network being studied with FBA. The gene-protein-reaction matrix is a binary matrix connecting genes with the proteins made from them. Using this matrix, reaction essentiality can be converted into gene essentiality indicating the gene defects which may cause a certain disease phenotype or the proteins/enzymes which are essential (and thus what enzymes are the most promising drug targets in pathogens). However, the gene-protein-reaction matrix does not specify the Boolean relationship between genes with respect to the enzyme, instead it merely indicates an association between them. Therefore, it should be used only if the Boolean GPR expression is unavailable.
Flux balance analysis	Simulations	Reaction inhibition The effect of inhibiting a reaction, rather than removing it entirely, can be simulated in FBA by restricting the allowed flux through it. The effect of an inhibition can be classified as lethal or non-lethal by applying the same criteria as in the case of a deletion where a suitable threshold is used to distinguish “substantially reduced” from “slightly reduced”. Generally the choice of threshold is arbitrary but a reasonable estimate can be obtained from growth experiments where the simulated inhibitions/deletions are actually performed and growth rate is measured.
Flux balance analysis	Simulations	Growth media optimization To design optimal growth media with respect to enhanced growth rates or useful by-product secretion, it is possible to use a method known as Phenotypic Phase Plane analysis. PhPP involves applying FBA repeatedly on the model while co-varying the nutrient uptake constraints and observing the value of the objective function (or by-product fluxes). PhPP makes it possible to find the optimal combination of nutrients that favor a particular phenotype or a mode of metabolism resulting in higher growth rates or secretion of industrially useful by-products. The predicted growth rates of bacteria in varying media have been shown to correlate well with experimental results, as well as to define precise minimal media for the culture of Salmonella typhimurium.Host-pathogen interactions The human microbiota is a complex system with as many as 400 trillion microbes and bacteria interacting with each other and the host. To understand key factors in this system; a multi-scale, dynamic flux-balance analysis is proposed as FBA is classified as less computationally intensive.
Flux balance analysis	Mathematical description	In contrast to the traditionally followed approach of metabolic modeling using coupled ordinary differential equations, flux balance analysis requires very little information in terms of the enzyme kinetic parameters and concentration of metabolites in the system. It achieves this by making two assumptions, steady state and optimality. The first assumption is that the modeled system has entered a steady state, where the metabolite concentrations no longer change, i.e. in each metabolite node the producing and consuming fluxes cancel each other out. The second assumption is that the organism has been optimized through evolution for some biological goal, such as optimal growth or conservation of resources. The steady-state assumption reduces the system to a set of linear equations, which is then solved to find a flux distribution that satisfies the steady-state condition subject to the stoichiometry constraints while maximizing the value of a pseudo-reaction (the objective function) representing the conversion of biomass precursors into biomass.

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