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Piranesi is an interactive paint system that enables the user to create artistic images from 3D scenes created using conventional modeling applications. == Image format == Piranesi uses the proprietary EPix file format. For every pixel, additional information is stored, such as distance from the viewer and material settings. EPix files can be rendered from 3D scenes using a fixed viewpoint by Piranesi's companion software, Vedute.
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Dialogflow is a natural language understanding platform used to design and integrate a conversational user interface into mobile apps, web applications, devices, bots, interactive voice response systems and related uses. == History == In May 2012, Speaktoit received a venture round (funding terms undisclosed) from Intel Capital. In July 2014, Speaktoit closed their Series B funding led by Motorola Solutions Venture Capital with participation from new investor Plug and Play Ventures and existing backers Intel Capital and Alpine Technology Fund. In September 2014, Speaktoit released api.ai (the voice-enabling engine that powers Assistant) to third-party developers, allowing the addition of voice interfaces to apps based on Android, iOS, HTML5, and Cordova. The SDK's contain voice recognition, natural language understanding, and text-to-speech. api.ai offers a web interface to build and test conversation scenarios. The platform is based on the natural language processing engine built by Speaktoit for its Assistant application. Api.ai allows Internet of Things developers to include natural language voice interfaces in their products. Assistant and Speaktoit's websites now redirect to api.ai's website Archived 2017-10-10 at the Wayback Machine, which redirects to the Dialogflow website. Google bought the company in September 2016 and was initially known as API.AI; it provides tools to developers building apps ("Actions") for the Google Assistant virtual assistant. The organization discontinued the Assistant app on December 15, 2016. In October 2017, it was renamed as Dialogflow. In November 2017, Dialogflow became part of Google Cloud Platform.
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In the theory of formal languages, the pumping lemma for regular languages is a lemma that describes an essential property of all regular languages. Informally, it says that all sufficiently long strings in a regular language may be pumped—that is, have a middle section of the string repeated an arbitrary number of times—to produce a new string that is also part of the language. The pumping lemma is useful for proving that a specific language is not a regular language, by showing that the language does not have the property. Specifically, the pumping lemma says that for any regular language L {\displaystyle L} , there exists a constant p {\displaystyle p} such that any string w {\displaystyle w} in L {\displaystyle L} with length at least p {\displaystyle p} can be split into three substrings x {\displaystyle x} , y {\displaystyle y} and z {\displaystyle z} ( w = x y z {\displaystyle w=xyz} , with y {\displaystyle y} being non-empty), such that the strings x z , x y z , x y y z , x y y y z , . . . {\displaystyle xz,xyz,xyyz,xyyyz,...} are also in L {\displaystyle L} . The process of repeating y {\displaystyle y} zero or more times is known as "pumping". Moreover, the pumping lemma guarantees that the length of x y {\displaystyle xy} will be at most p {\displaystyle p} , thus giving a "small" substring x y {\displaystyle xy} that has the desired property. Languages with a finite number of strings vacuously satisfy the pumping lemma by having p {\displaystyle p} equal to the maximum string length in L {\displaystyle L} plus one. By doing so, no strings at all in L {\displaystyle L} have length at least p {\displaystyle p} . The pumping lemma was first proven by Michael Rabin and Dana Scott in 1959, and rediscovered shortly after by Yehoshua Bar-Hillel, Micha A. Perles, and Eli Shamir in 1961, as a simplification of their pumping lemma for context-free languages. == Formal statement == Let L {\displaystyle L} be a regular language. Then there exists an integer p ≥ 1 {\displaystyle p\geq 1} depending only on L {\displaystyle L} such that every string w {\displaystyle w} in L {\displaystyle L} of length at least p {\displaystyle p} ( p {\displaystyle p} is called the "pumping length") can be written as w = x y z {\displaystyle w=xyz} (i.e., w {\displaystyle w} can be divided into three substrings), satisfying the following conditions: | y | ≥ 1 {\displaystyle |y|\geq 1} | x y | ≤ p {\displaystyle |xy|\leq p} ( ∀ n ≥ 0 ) ( x y n z ∈ L ) {\displaystyle (\forall n\geq 0)(xy^{n}z\in L)} y {\displaystyle y} is the substring that can be pumped (removed or repeated any number of times, and the resulting string is always in L {\displaystyle L} ). (1) means the loop y {\displaystyle y} to be pumped must be of length at least one, that is, not an empty string; (2) means the loop must occur within the first p {\displaystyle p} characters. | x | {\displaystyle |x|} must be smaller than p {\displaystyle p} (conclusion of (1) and (2)), but apart from that, there is no restriction on x {\displaystyle x} and z {\displaystyle z} . In simple words, for any regular language L {\displaystyle L} , any sufficiently long string w {\displaystyle w} (in L {\displaystyle L} ) can be split into 3 parts, i.e. w = x y z {\displaystyle w=xyz} , such that all the strings x y n z {\displaystyle xy^{n}z} for n ≥ 0 {\displaystyle n\geq 0} are also in L {\displaystyle L} . Below is a formal expression of the pumping lemma. ∀ L ⊆ Σ ∗ , regular ( L ) ⟹ ∃ p ≥ 1 , ∀ w ∈ L , | w | ≥ p ⟹ ∃ x , y , z ∈ Σ ∗ , ( w = x y z ) ∧ ( | y | ≥ 1 ) ∧ ( | x y | ≤ p ) ∧ ( ∀ n ≥ 0 , x y n z ∈ L ) {\displaystyle {\begin{array}{l}\forall L\subseteq \Sigma ^{},{\mbox{regular}}(L)\implies \\\quad \exists p\geq 1,\forall w\in L,|w|\geq p\implies \\\qquad \exists x,y,z\in \Sigma ^{},(w=xyz)\land (|y|\geq 1)\land (|xy|\leq p)\land (\forall n\geq 0,xy^{n}z\in L)\end{array}}} == Use of the lemma to prove non-regularity == The pumping lemma is often used to prove that a particular language is non-regular: a proof by contradiction may consist of exhibiting a string (of the required length) in the language that lacks the property outlined in the pumping lemma. Example: The language L = { a n b n : n ≥ 0 } {\displaystyle L=\{a^{n}b^{n}:n\geq 0\}} over the alphabet Σ = { a , b } {\displaystyle \Sigma =\{a,b\}} can be shown to be non-regular as follows: Assume that some constant p ≥ 1 {\displaystyle p\geq 1} exists as required by the lemma. Let w {\displaystyle w} in L {\displaystyle L} be given by w = a p b p {\displaystyle w=a^{p}b^{p}} , which is a string longer than p {\displaystyle p} . By the pumping lemma, there must exist a decomposition w = x y z {\displaystyle w=xyz} with | x y | ≤ p {\displaystyle |xy|\leq p} and | y | ≥ 1 {\displaystyle |y|\geq 1} such that x y i z {\displaystyle xy^{i}z} in L {\displaystyle L} for every i ≥ 0 {\displaystyle i\geq 0} . Since | x y | ≤ p {\displaystyle |xy|\leq p} , the string y {\displaystyle y} only consists of instances of a {\displaystyle a} . Because | y | ≥ 1 {\displaystyle |y|\geq 1} , it contains at least one instance of the letter a {\displaystyle a} . Pumping y {\displaystyle y} to give x y 2 z {\displaystyle xy^{2}z} gives a word with more instances of the letter a {\displaystyle a} than the letter b {\displaystyle b} , since some instances of a {\displaystyle a} but none of b {\displaystyle b} were added. Therefore, x y 2 z {\displaystyle xy^{2}z} is not in L {\displaystyle L} which contradicts the pumping lemma. Therefore, L {\displaystyle L} cannot be regular. The proof that the language of balanced (i.e., properly nested) parentheses is not regular follows the same idea. Given p {\displaystyle p} , there is a string of balanced parentheses that begins with more than p {\displaystyle p} left parentheses, so that y {\displaystyle y} will consist entirely of left parentheses. By repeating y {\displaystyle y} , a string can be produced that does not contain the same number of left and right parentheses, and so they cannot be balanced. == Proof of the pumping lemma == For every regular language there is a finite-state automaton (FSA) that accepts the language. The number of states in such an FSA are counted and that count is used as the pumping length p {\displaystyle p} . For a string of length at least p {\displaystyle p} , let q 0 {\displaystyle q_{0}} be the start state and let q 1 , . . . , q p {\displaystyle q_{1},...,q_{p}} be the sequence of the next p {\displaystyle p} states visited as the string is emitted. Because the FSA has only p {\displaystyle p} states, within this sequence of p + 1 {\displaystyle p+1} visited states there must be at least one state that is repeated. Write q s {\displaystyle q_{s}} for such a state. The transitions that take the machine from the first encounter of state q s {\displaystyle q_{s}} to the second encounter of state q s {\displaystyle q_{s}} match some string. This string is called y {\displaystyle y} in the lemma, and since the machine will match a string without the y {\displaystyle y} portion, or with the string y {\displaystyle y} repeated any number of times, the conditions of the lemma are satisfied. For example, the following image shows an FSA. The FSA accepts the string: abcd. Since this string has a length at least as large as the number of states, which is four (so the total number of states that the machine passes through to scan abcd would be 5), the pigeonhole principle indicates that there must be at least one repeated state among the start state and the next four visited states. In this example, only q 1 {\displaystyle q_{1}} is a repeated state. Since the substring bc takes the machine through transitions that start at state q 1 {\displaystyle q_{1}} and end at state q 1 {\displaystyle q_{1}} , that portion could be repeated and the FSA would still accept, giving the string abcbcd. Alternatively, the bc portion could be removed and the FSA would still accept giving the string ad. In terms of the pumping lemma, the string abcd is broken into an x {\displaystyle x} portion a, a y {\displaystyle y} portion bc and a z {\displaystyle z} portion d. As a side remark, the problem of checking whether a given string can be accepted by a given nondeterministic finite automaton without visiting any state repeatedly, is NP hard. == General version of pumping lemma for regular languages == If a language L {\displaystyle L} is regular, then there exists a number p ≥ 1 {\displaystyle p\geq 1} (the pumping length) such that every string u w v {\displaystyle uwv} in L {\displaystyle L} with | w | ≥ p {\displaystyle |w|\geq p} can be written in the form u w v = u x y z v {\displaystyle uwv=uxyzv} with strings x {\displaystyle x} , y {\displaystyle y} and z {\displaystyle z} such that | x y | ≤ p {\displaystyle |xy|\leq p} , | y | ≥ 1 {\displaystyle |y|\geq 1} and u x y i z v {\displaystyle uxy^{i}zv} is in L {\displaystyle L} for every integer i ≥ 0 {\displaystyle i\geq 0} . From this, the above standard v
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In search of the best AI code generator? An AI code generator is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI code generator slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
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The Digital Michelangelo Project was a pioneering initiative undertaken during the 1998–1999 academic year to digitize the sculptures and architecture of Michelangelo using advanced laser scanning technology. The project was led by a team of 30 faculty, staff, and students from Stanford University and the University of Washington, with the aim of creating high-resolution 3D models of Michelangelo's works for scholarly, educational, and preservation purposes. == Objectives == The primary goals of the Digital Michelangelo Project were: To apply recent advancements in laser rangefinder technology for digitizing large cultural artifacts. To create detailed digital archives of Michelangelo's sculptures and architectural spaces for future study and analysis. To explore potential educational and curatorial applications for 3D scanned data. === Artworks digitized === The project involved scanning several iconic works by Michelangelo, including: David The Unfinished Slaves (Atlas, Awakening, Bearded, and Youthful) St. Matthew The allegorical statues from the Medici tombs (Night, Day, Dawn, and Dusk) The architectural interiors of the Tribuna del David at the Galleria dell'Accademia and the New Sacristy in the Medici Chapels. == Technology and methodology == === 3D scanning === The project's primary scanner was a laser triangulation rangefinder mounted on a motorized gantry, custom-built by Cyberware Inc. The scanner used a laser sheet to project onto an object, capturing its shape through triangulation. Multiple scans were taken from various angles and combined into a single, detailed 3D mesh. The resolution achieved was fine enough to capture even Michelangelo's chisel marks, with triangles approximately 0.25 mm on each side. In addition to shape data, color data was captured using a spotlight and a secondary camera, enabling the creation of textured 3D models. === Data processing === The project developed a software suite for processing the scanned data. This included: Aligning and merging multiple scans into a seamless 3D model. Filling holes in the geometry caused by inaccessible areas. Correcting color data for lighting inconsistencies and shadowing. Non-photorealistic rendering techniques were also applied, highlighting surface features such as Michelangelo’s chisel marks for enhanced visualization. == Logistical challenges == The scale and complexity of the project presented several challenges: Data size: The dataset for David alone comprised 2 billion polygons and 7,000 color images, occupying 60 GB of storage. Artifact safety: Ensuring the safety of the statues during scanning required extensive crew training, foam-encased equipment, and collision-prevention mechanisms. == Applications and impact == The digitized models have numerous potential applications: Art history: Allowing precise measurements and geometric analysis, such as determining chisel types or evaluating structural balance. Education: Providing new ways to study art, including interactive viewing from unconventional angles and with custom lighting. Museum curation: Enhancing visitor experiences through interactive kiosks and virtual models. The project demonstrated the potential for 3D technology to preserve and disseminate cultural heritage. == Data distribution == The project's models are available through Stanford University for scholarly purposes, under strict licensing due to Italian intellectual property laws. === ScanView === To provide public access to the 3D models while respecting usage restrictions, the project developed ScanView, a client/server rendering system. ScanView allows users to view and interact with high-resolution 3D models without downloading the data. The client component consists of a freely available viewer program and simplified 3D models. Users can navigate these models locally, adjusting position, orientation, lighting, and surface appearance. When a user finalizes a view, the client queries a remote server for a high-resolution rendering of the model, which is sent back to overwrite the simplified version on the user’s screen. A typical query-response cycle takes 1–2 seconds, depending on network conditions. To protect the models from unauthorized reconstruction, the system employs several security measures, including: Encrypting queries Perturbing viewpoint and lighting parameters Adding noise and warping rendered images Compressing images before transmission ScanView operates on Windows-based PCs and provides access to selected models, including David and St. Matthew, as well as other artifacts such as fragments of the Forma Urbis Romae and items from the Stanford 3D Scanning Repository. == Sponsors == The Digital Michelangelo Project was supported by Stanford University, Interval Research Corporation, and the Paul G. Allen Foundation for the Arts.
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In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if each of its transitions is uniquely determined by its source state and input symbol, and reading an input symbol is required for each state transition. A nondeterministic finite automaton (NFA), or nondeterministic finite-state machine, does not need to obey these restrictions. In particular, every DFA is also an NFA. Sometimes the term NFA is used in a narrower sense, referring to an NFA that is not a DFA, but not in this article. Using the subset construction algorithm, each NFA can be translated to an equivalent DFA; i.e., a DFA recognizing the same formal language. Like DFAs, NFAs only recognize regular languages. NFAs were introduced in 1959 by Michael O. Rabin and Dana Scott, who also showed their equivalence to DFAs. NFAs are used in the implementation of regular expressions: Thompson's construction is an algorithm for compiling a regular expression to an NFA that can efficiently perform pattern matching on strings. Conversely, Kleene's algorithm can be used to convert an NFA into a regular expression (whose size is generally exponential in the input automaton). NFAs have been generalized in multiple ways, e.g., nondeterministic finite automata with ε-moves, finite-state transducers, pushdown automata, alternating automata, ω-automata, and probabilistic automata. Besides the DFAs, other known special cases of NFAs are unambiguous finite automata (UFA) and self-verifying finite automata (SVFA). == Informal introduction == There are at least two equivalent ways to describe the behavior of an NFA. The first way makes use of the nondeterminism in the name of an NFA. For each input symbol, the NFA transitions to a new state until all input symbols have been consumed. In each step, the automaton nondeterministically "chooses" one of the applicable transitions. If there exists at least one "lucky run", i.e. some sequence of choices leading to an accepting state after completely consuming the input, it is accepted. Otherwise, i.e. if no choice sequence at all can consume all the input and lead to an accepting state, the input is rejected. In the second way, the NFA consumes a string of input symbols, one by one. In each step, whenever two or more transitions are applicable, it "clones" itself into appropriately many copies, each one following a different transition. If no transition is applicable, the current copy is in a dead end, and it "dies". If, after consuming the complete input, any of the copies is in an accept state, the input is accepted, else, it is rejected. == Formal definition == For a more elementary introduction of the formal definition, see automata theory. === Automaton === An NFA is represented formally by a 5-tuple, ( Q , Σ , δ , q 0 , F ) {\displaystyle (Q,\Sigma ,\delta ,q_{0},F)} , consisting of a finite set of states Q {\displaystyle Q} , a finite set of input symbols called the alphabet Σ {\displaystyle \Sigma } , a transition function δ {\displaystyle \delta } : Q × Σ → P ( Q ) {\displaystyle Q\times \Sigma \rightarrow {\mathcal {P}}(Q)} , an initial (or start) state q 0 ∈ Q {\displaystyle q_{0}\in Q} , and a set of accepting (or final) states F ⊆ Q {\displaystyle F\subseteq Q} . Here, P ( Q ) {\displaystyle {\mathcal {P}}(Q)} denotes the power set of Q {\displaystyle Q} . === Recognized language === Given an NFA M = ( Q , Σ , δ , q 0 , F ) {\displaystyle M=(Q,\Sigma ,\delta ,q_{0},F)} , its recognized language is denoted by L ( M ) {\displaystyle L(M)} , and is defined as the set of all strings over the alphabet Σ {\displaystyle \Sigma } that are accepted by M {\displaystyle M} . Loosely corresponding to the above informal explanations, there are several equivalent formal definitions of a string w = a 1 a 2 . . . a n {\displaystyle w=a_{1}a_{2}...a_{n}} being accepted by M {\displaystyle M} : w {\displaystyle w} is accepted if a sequence of states, r 0 , r 1 , . . . , r n {\displaystyle r_{0},r_{1},...,r_{n}} , exists in Q {\displaystyle Q} such that: r 0 = q 0 {\displaystyle r_{0}=q_{0}} r i + 1 ∈ δ ( r i , a i + 1 ) {\displaystyle r_{i+1}\in \delta (r_{i},a_{i+1})} , for i = 0 , … , n − 1 {\displaystyle i=0,\ldots ,n-1} r n ∈ F {\displaystyle r_{n}\in F} . In words, the first condition says that the machine starts in the start state q 0 {\displaystyle q_{0}} . The second condition says that given each character of string w {\displaystyle w} , the machine will transition from state to state according to the transition function δ {\displaystyle \delta } . The last condition says that the machine accepts w {\displaystyle w} if the last input of w {\displaystyle w} causes the machine to halt in one of the accepting states. In order for w {\displaystyle w} to be accepted by M {\displaystyle M} , it is not required that every state sequence ends in an accepting state, it is sufficient if one does. Otherwise, i.e. if it is impossible at all to get from q 0 {\displaystyle q_{0}} to a state from F {\displaystyle F} by following w {\displaystyle w} , it is said that the automaton rejects the string. The set of strings M {\displaystyle M} accepts is the language recognized by M {\displaystyle M} and this language is denoted by L ( M ) {\displaystyle L(M)} . Alternatively, w {\displaystyle w} is accepted if δ ∗ ( q 0 , w ) ∩ F ≠ ∅ {\displaystyle \delta ^{}(q_{0},w)\cap F\not =\emptyset } , where δ ∗ : Q × Σ ∗ → P ( Q ) {\displaystyle \delta ^{}:Q\times \Sigma ^{}\rightarrow {\mathcal {P}}(Q)} is defined recursively by: δ ∗ ( r , ε ) = { r } {\displaystyle \delta ^{}(r,\varepsilon )=\{r\}} where ε {\displaystyle \varepsilon } is the empty string, and δ ∗ ( r , x a ) = ⋃ r ′ ∈ δ ∗ ( r , x ) δ ( r ′ , a ) {\displaystyle \delta ^{}(r,xa)=\bigcup _{r'\in \delta ^{}(r,x)}\delta (r',a)} for all x ∈ Σ ∗ , a ∈ Σ {\displaystyle x\in \Sigma ^{},a\in \Sigma } . In words, δ ∗ ( r , x ) {\displaystyle \delta ^{}(r,x)} is the set of all states reachable from state r {\displaystyle r} by consuming the string x {\displaystyle x} . The string w {\displaystyle w} is accepted if some accepting state in F {\displaystyle F} can be reached from the start state q 0 {\displaystyle q_{0}} by consuming w {\displaystyle w} . === Initial state === The above automaton definition uses a single initial state, which is not necessary. Sometimes, NFAs are defined with a set of initial states. There is an easy construction that translates an NFA with multiple initial states to an NFA with a single initial state, which provides a convenient notation. == Example == The following automaton M, with a binary alphabet, determines if the input ends with a 1. Let M = ( { p , q } , { 0 , 1 } , δ , p , { q } ) {\displaystyle M=(\{p,q\},\{0,1\},\delta ,p,\{q\})} where the transition function δ {\displaystyle \delta } can be defined by this state transition table (cf. upper left picture): State Input 0 1 p { p } { p , q } q ∅ ∅ {\displaystyle {\begin{array}{|c|cc|}{\bcancel {{}_{\text{State}}\quad {}^{\text{Input}}}}&0&1\\\hline p&\{p\}&\{p,q\}\\q&\emptyset &\emptyset \end{array}}} Since the set δ ( p , 1 ) {\displaystyle \delta (p,1)} contains more than one state, M is nondeterministic. The language of M can be described by the regular language given by the regular expression (0|1)1. All possible state sequences for the input string "1011" are shown in the lower picture. The string is accepted by M since one state sequence satisfies the above definition; it does not matter that other sequences fail to do so. The picture can be interpreted in a couple of ways: In terms of the above "lucky-run" explanation, each path in the picture denotes a sequence of choices of M. In terms of the "cloning" explanation, each vertical column shows all clones of M at a given point in time, multiple arrows emanating from a node indicate cloning, a node without emanating arrows indicating the "death" of a clone. The feasibility to read the same picture in two ways also indicates the equivalence of both above explanations. Considering the first of the above formal definitions, "1011" is accepted since when reading it M may traverse the state sequence ⟨ r 0 , r 1 , r 2 , r 3 , r 4 ⟩ = ⟨ p , p , p , p , q ⟩ {\displaystyle \langle r_{0},r_{1},r_{2},r_{3},r_{4}\rangle =\langle p,p,p,p,q\rangle } , which satisfies conditions 1 to 3. Concerning the second formal definition, bottom-up computation shows that δ ∗ ( p , ε ) = { p } {\displaystyle \delta ^{}(p,\varepsilon )=\{p\}} , hence δ ∗ ( p , 1 ) = δ ( p , 1 ) = { p , q } {\displaystyle \delta ^{}(p,1)=\delta (p,1)=\{p,q\}} , hence δ ∗ ( p , 10 ) = δ ( p , 0 ) ∪ δ ( q , 0 ) = { p } ∪ { } {\displaystyle \delta ^{}(p,10)=\delta (p,0)\cup \delta (q,0)=\{p\}\cup \{\}} , hence δ ∗ ( p , 101 ) = δ ( p , 1 ) = { p , q } {\displaystyle \delta ^{}(p,101)=\delta (p,1)=\{p,q\}} , and hence δ ∗ ( p , 1011 ) = δ ( p , 1 ) ∪ δ ( q , 1 ) = { p , q } ∪ { } {\displaystyle \delta ^{}(p,1011)=\delta (p,1)\cup \delta (q,1)=\{p,q\}\cup \{\}} ; since that set is
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In dual decomposition a problem is broken into smaller subproblems and a solution to the relaxed problem is found. This method can be employed for MRF optimization. Dual decomposition is applied to markov logic programs as an inference technique. == Background == Discrete MRF Optimization (inference) is very important in Machine Learning and Computer vision, which is realized on CUDA graphical processing units. Consider a graph G = ( V , E ) {\displaystyle G=(V,E)} with nodes V {\displaystyle V} and Edges E {\displaystyle E} . The goal is to assign a label l p {\displaystyle l_{p}} to each p ∈ V {\displaystyle p\in V} so that the MRF Energy is minimized: (1) min Σ p ∈ V θ p ( l p ) + Σ p q ∈ ε θ p q ( l p ) ( l q ) {\displaystyle \min \Sigma _{p\in V}\theta _{p}(l_{p})+\Sigma _{pq\in \varepsilon }\theta _{pq}(l_{p})(l_{q})} Major MRF Optimization methods are based on Graph cuts or Message passing. They rely on the following integer linear programming formulation (2) min x E ( θ , x ) = θ . x = ∑ p ∈ V θ p . x p + ∑ p q ∈ ε θ p q . x p q {\displaystyle \min _{x}E(\theta ,x)=\theta .x=\sum _{p\in V}\theta _{p}.x_{p}+\sum _{pq\in \varepsilon }\theta _{pq}.x_{pq}} In many applications, the MRF-variables are {0,1}-variables that satisfy: x p ( l ) = 1 {\displaystyle x_{p}(l)=1} ⇔ {\displaystyle \Leftrightarrow } label l {\displaystyle l} is assigned to p {\displaystyle p} , while x p q ( l , l ′ ) = 1 {\displaystyle x_{pq}(l,l^{\prime })=1} , labels l , l ′ {\displaystyle l,l^{\prime }} are assigned to p , q {\displaystyle p,q} . == Dual Decomposition == The main idea behind decomposition is surprisingly simple: decompose your original complex problem into smaller solvable subproblems, extract a solution by cleverly combining the solutions from these subproblems. A sample problem to decompose: min x Σ i f i ( x ) {\displaystyle \min _{x}\Sigma _{i}f^{i}(x)} where x ∈ C {\displaystyle x\in C} In this problem, separately minimizing every single f i ( x ) {\displaystyle f^{i}(x)} over x {\displaystyle x} is easy; but minimizing their sum is a complex problem. So the problem needs to get decomposed using auxiliary variables { x i } {\displaystyle \{x^{i}\}} and the problem will be as follows: min { x i } , x Σ i f i ( x i ) {\displaystyle \min _{\{x^{i}\},x}\Sigma _{i}f^{i}(x^{i})} where x i ∈ C , x i = x {\displaystyle x^{i}\in C,x^{i}=x} Now we can relax the constraints by multipliers { λ i } {\displaystyle \{\lambda ^{i}\}} which gives us the following Lagrangian dual function: g ( { λ i } ) = min { x i ∈ C } , x Σ i f i ( x i ) + Σ i λ i . ( x i − x ) = min { x i ∈ C } , x Σ i [ f i ( x i ) + λ i . x i ] − ( Σ i λ i ) x {\displaystyle g(\{\lambda ^{i}\})=\min _{\{x^{i}\in C\},x}\Sigma _{i}f^{i}(x^{i})+\Sigma _{i}\lambda ^{i}.(x^{i}-x)=\min _{\{x^{i}\in C\},x}\Sigma _{i}[f^{i}(x^{i})+\lambda ^{i}.x^{i}]-(\Sigma _{i}\lambda ^{i})x} Now we eliminate x {\displaystyle x} from the dual function by minimizing over x {\displaystyle x} and dual function becomes: g ( { λ i } ) = min { x i ∈ C } Σ i [ f i ( x i ) + λ i . x i ] {\displaystyle g(\{\lambda ^{i}\})=\min _{\{x^{i}\in C\}}\Sigma _{i}[f^{i}(x^{i})+\lambda ^{i}.x^{i}]} We can set up a Lagrangian dual problem: (3) max { λ i } ∈ Λ g ( λ i ) = Σ i g i ( x i ) , {\displaystyle \max _{\{\lambda ^{i}\}\in \Lambda }g({\lambda ^{i}})=\Sigma _{i}g^{i}(x^{i}),} The Master problem (4) g i ( x i ) = m i n x i f i ( x i ) + λ i . x i {\displaystyle g^{i}(x^{i})=min_{x^{i}}f^{i}(x^{i})+\lambda ^{i}.x^{i}} where x i ∈ C {\displaystyle x^{i}\in C} The Slave problems == MRF optimization via Dual Decomposition == The original MRF optimization problem is NP-hard and we need to transform it into something easier. τ {\displaystyle \tau } is a set of sub-trees of graph G {\displaystyle G} where its trees cover all nodes and edges of the main graph. And MRFs defined for every tree T {\displaystyle T} in τ {\displaystyle \tau } will be smaller. The vector of MRF parameters is θ T {\displaystyle \theta ^{T}} and the vector of MRF variables is x T {\displaystyle x^{T}} , these two are just smaller in comparison with original MRF vectors θ , x {\displaystyle \theta ,x} . For all vectors θ T {\displaystyle \theta ^{T}} we'll have the following: (5) ∑ T ∈ τ ( p ) θ p T = θ p , ∑ T ∈ τ ( p q ) θ p q T = θ p q . {\displaystyle \sum _{T\in \tau (p)}\theta _{p}^{T}=\theta _{p},\sum _{T\in \tau (pq)}\theta _{pq}^{T}=\theta _{pq}.} Where τ ( p ) {\displaystyle \tau (p)} and τ ( p q ) {\displaystyle \tau (pq)} denote all trees of τ {\displaystyle \tau } than contain node p {\displaystyle p} and edge p q {\displaystyle pq} respectively. We simply can write: (6) E ( θ , x ) = ∑ T ∈ τ E ( θ T , x T ) {\displaystyle E(\theta ,x)=\sum _{T\in \tau }E(\theta ^{T},x^{T})} And our constraints will be: (7) x T ∈ χ T , x T = x | T , ∀ T ∈ τ {\displaystyle x^{T}\in \chi ^{T},x^{T}=x_{|T},\forall T\in \tau } Our original MRF problem will become: (8) min { x T } , x Σ T ∈ τ E ( θ T , x T ) {\displaystyle \min _{\{x^{T}\},x}\Sigma _{T\in \tau }E(\theta ^{T},x^{T})} where x T ∈ χ T , ∀ T ∈ τ {\displaystyle x^{T}\in \chi ^{T},\forall T\in \tau } and x T ∈ x | T , ∀ T ∈ τ {\displaystyle x^{T}\in x_{|T},\forall T\in \tau } And we'll have the dual problem we were seeking: (9) max { λ T } ∈ Λ g ( { λ T } ) = ∑ T ∈ τ g T ( λ T ) , {\displaystyle \max _{\{\lambda ^{T}\}\in \Lambda }g(\{\lambda ^{T}\})=\sum _{T\in \tau }g^{T}(\lambda ^{T}),} The Master problem where each function g T ( . ) {\displaystyle g^{T}(.)} is defined as: (10) g T ( λ T ) = min x T E ( θ T + λ T , x T ) {\displaystyle g^{T}(\lambda ^{T})=\min _{x^{T}}E(\theta ^{T}+\lambda ^{T},x^{T})} where x T ∈ χ T {\displaystyle x^{T}\in \chi ^{T}} The Slave problems == Theoretical Properties == Theorem 1. Lagrangian relaxation (9) is equivalent to the LP relaxation of (2). min { x T } , x { E ( x , θ ) | x p T = s p , x T ∈ CONVEXHULL ( χ T ) } {\displaystyle \min _{\{x^{T}\},x}\{E(x,\theta )|x_{p}^{T}=s_{p},x^{T}\in {\text{CONVEXHULL}}(\chi ^{T})\}} Theorem 2. If the sequence of multipliers { α t } {\displaystyle \{\alpha _{t}\}} satisfies α t ≥ 0 , lim t → ∞ α t = 0 , ∑ t = 0 ∞ α t = ∞ {\displaystyle \alpha _{t}\geq 0,\lim _{t\to \infty }\alpha _{t}=0,\sum _{t=0}^{\infty }\alpha _{t}=\infty } then the algorithm converges to the optimal solution of (9). Theorem 3. The distance of the current solution { θ T } {\displaystyle \{\theta ^{T}\}} to the optimal solution { θ ¯ T } {\displaystyle \{{\bar {\theta }}^{T}\}} , which decreases at every iteration. Theorem 4. Any solution obtained by the method satisfies the WTA (weak tree agreement) condition. Theorem 5. For binary MRFs with sub-modular energies, the method computes a globally optimal solution.
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In software, a spell checker (or spelling checker or spell check) is a software feature that checks for misspellings in a text. Spell-checking features are often embedded in software or services, such as a word processor, email client, electronic dictionary, or search engine. == Design == A basic spell checker carries out the following processes: It scans the text and extracts the words contained in it. It then compares each word with a known list of correctly spelled words (i.e. a dictionary). This might contain just a list of words, or it might also contain additional information, such as hyphenation points or lexical and grammatical attributes. An additional step is a language-dependent algorithm for handling morphology. Even for a lightly inflected language like English, the spell checker will need to consider different forms of the same word, such as plurals, verbal forms, contractions, and possessives. For many other languages, such as those featuring agglutination and more complex declension and conjugation, this part of the process is more complicated. It is unclear whether morphological analysis—allowing for many forms of a word depending on its grammatical role—provides a significant benefit for English, though its benefits for highly synthetic languages such as German, Hungarian, or Turkish are clear. As an adjunct to these components, the program's user interface allows users to approve or reject replacements and modify the program's operation. Spell checkers can use approximate string matching algorithms such as Levenshtein distance to find correct spellings of misspelled words. An alternative type of spell checker uses solely statistical information, such as n-grams, to recognize errors instead of correctly-spelled words. This approach usually requires a lot of effort to obtain sufficient statistical information. Key advantages include needing less runtime storage and the ability to correct errors in words that are not included in a dictionary. In some cases, spell checkers use a fixed list of misspellings and suggestions for those misspellings; this less flexible approach is often used in paper-based correction methods, such as the see also entries of encyclopedias. Clustering algorithms have also been used for spell checking combined with phonetic information. == History == === Pre-PC === In 1961, Les Earnest, who headed the research on this budding technology, saw it necessary to include the first spell checker that accessed a list of 10,000 acceptable words. Ralph Gorin, a graduate student under Earnest at the time, created the first true spelling checker program written as an applications program (rather than research) for general English text: SPELL for the DEC PDP-10 at Stanford University's Artificial Intelligence Laboratory, in February 1971. Gorin wrote SPELL in assembly language, for faster action; he made the first spelling corrector by searching the word list for plausible correct spellings that differ by a single letter or adjacent letter transpositions and presenting them to the user. Gorin made SPELL publicly accessible, as was done with most SAIL (Stanford Artificial Intelligence Laboratory) programs, and it soon spread around the world via the new ARPAnet, about ten years before personal computers came into general use. SPELL, its algorithms and data structures inspired the Unix ispell program. The first spell checkers were widely available on mainframe computers in the late 1970s. A group of six linguists from Georgetown University developed the first spell-check system for the IBM corporation. Henry Kučera invented one for the VAX machines of Digital Equipment Corp in 1981. === Unix === The International Ispell program commonly used in Unix is based on R. E. Gorin's SPELL. It was converted to C by Pace Willisson at MIT. The GNU project has its spell checker GNU Aspell. Aspell's main improvement is that it can more accurately suggest correct alternatives for misspelled English words. Due to the inability of traditional spell checkers to check words in complex inflected languages, Hungarian László Németh developed Hunspell, a spell checker that supports agglutinative languages and complex compound words. Hunspell also uses Unicode in its dictionaries. Hunspell replaced the previous MySpell in OpenOffice.org in version 2.0.2. Enchant is another general spell checker, derived from AbiWord. Its goal is to combine programs supporting different languages such as Aspell, Hunspell, Nuspell, Hspell (Hebrew), Voikko (Finnish), Zemberek (Turkish) and AppleSpell under one interface. === PCs === The first spell checkers for personal computers appeared in 1980, such as "WordCheck" for Commodore systems which was released in late 1980 in time for advertisements to go to print in January 1981. Developers such as Maria Mariani and Random House rushed OEM packages or end-user products into the rapidly expanding software market. On the pre-Windows PCs, these spell checkers were standalone programs, many of which could be run in terminate-and-stay-resident mode from within word-processing packages on PCs with sufficient memory. However, the market for standalone packages was short-lived, as by the mid-1980s developers of popular word-processing packages like WordStar and WordPerfect had incorporated spell checkers in their packages, mostly licensed from the above companies, who quickly expanded support from just English to many European and eventually even Asian languages. However, this required increasing sophistication in the morphology routines of the software, particularly with regard to heavily-agglutinative languages like Hungarian and Finnish. Although the size of the word-processing market in a country like Iceland might not have justified the investment of implementing a spell checker, companies like WordPerfect nonetheless strove to localize their software for as many national markets as possible as part of their global marketing strategy. When Apple developed "a system-wide spelling checker" for Mac OS X so that "the operating system took over spelling fixes," it was a first: one "didn't have to maintain a separate spelling checker for each" program. Mac OS X's spellcheck coverage includes virtually all bundled and third party applications. Visual Tools' VT Speller, introduced in 1994, was "designed for developers of applications that support Windows." It came with a dictionary but had the ability to build and incorporate use of secondary dictionaries. === Browsers === Web browsers such as Firefox and Google Chrome offer spell checking support, using Hunspell. Prior to using Hunspell, Firefox and Chrome used MySpell and GNU Aspell, respectively. === Specialties === Some spell checkers have separate support for medical dictionaries to help prevent medical errors. == Functionality == The first spell checkers were "verifiers" instead of "correctors." They offered no suggestions for incorrectly spelled words. This was helpful for typos but it was not so helpful for logical or phonetic errors. The challenge the developers faced was the difficulty in offering useful suggestions for misspelled words. This requires reducing words to a skeletal form and applying pattern-matching algorithms. It might seem logical that where spell-checking dictionaries are concerned, "the bigger, the better," so that correct words are not marked as incorrect. In practice, however, an optimal size for English appears to be around 90,000 entries. If there are more than this, incorrectly spelled words may be skipped because they are mistaken for others. For example, a linguist might determine on the basis of corpus linguistics that the word baht is more frequently a misspelling of bath or bat than a reference to the Thai currency. Hence, it would typically be more useful if a few people who write about Thai currency were slightly inconvenienced than if the spelling errors of the many more people who discuss baths were overlooked. The first MS-DOS spell checkers were mostly used in proofing mode from within word processing packages. After preparing a document, a user scanned the text looking for misspellings. Later, however, batch processing was offered in such packages as Oracle's short-lived CoAuthor and allowed a user to view the results after a document was processed and correct only the words that were known to be wrong. When memory and processing power became abundant, spell checking was performed in the background in an interactive way, such as has been the case with the Sector Software produced Spellbound program released in 1987 and Microsoft Word since Word 95. Spell checkers became increasingly sophisticated; now capable of recognizing grammatical errors. However, even at their best, they rarely catch all the errors in a text (such as homophone errors) and will flag neologisms and foreign words as misspellings. Nonetheless, spell checkers can be considered as a type of foreign language writing aid that non-native language lea
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A distributional–relational database, or word-vector database, is a database management system (DBMS) that uses distributional word-vector representations to enrich the semantics of structured data. As distributional word-vectors can be built automatically from large-scale corpora, this enrichment supports the construction of databases which can embed large-scale commonsense background knowledge into their operations. Distributional-Relational models can be applied to the construction of schema-agnostic databases (databases in which users can query the data without being aware of its schema), semantic search, schema-integration and inductive and abductive reasoning as well as different applications in which a semantically flexible knowledge representation model is needed. The main advantage of distributional–relational models over purely logical or semantic web models is the fact that the core semantic associations can be automatically captured from corpora, in contrast to the definition of manually curated ontologies and rule knowledge bases. == Distributional–relational models == Distributional–relational models were first formalized as a mechanism to cope with the vocabulary/semantic gap between users and the schema behind the data. In this scenario, distributional semantic relatedness measures, combined with semantic pivoting heuristics can support the approximation between user queries (expressed in their own vocabulary), and data (expressed in the vocabulary of the designer). In this model, the database symbols (entities and relations) are embedded into a distributional semantic space and have a geometric interpretation under a latent or explicit semantic space. The geometric aspect supports the semantic approximation between entities from different databases, or between a query term and a database entity. The distributional relational model then becomes a double layered model where the semantics of the structured data provides the fine-grained semantics intended by the database designer, which is extended by the distributional semantic model which contains the semantic associations expressed at a broader use. These models support the generalization from a closed communication scenario (in which database designers and users live in the same context, e.g. the same organization) to an open communication scenario (e.g. different organizations, the Web), creating an abstraction layer between users and the specific representation of the conceptual model.
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In search of the best AI customer-support bot? An AI customer-support bot is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI customer-support bot slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
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In theoretical computer science and formal language theory, a tree transducer (TT) is an abstract machine taking as input a tree, and generating output – generally other trees, but models producing words or other structures exist. Roughly speaking, tree transducers extend tree automata in the same way that word transducers extend word automata. Manipulating tree structures instead of words enable TT to model syntax-directed transformations of formal or natural languages. However, TT are not as well-behaved as their word counterparts in terms of algorithmic complexity, closure properties, etcetera. In particular, most of the main classes are not closed under composition. The main classes of tree transducers are: == Top-Down Tree Transducers (TOP) == A TOP T is a tuple (Q, Σ, Γ, I, δ) such that: Q is a finite set, the set of states; Σ is a finite ranked alphabet, called the input alphabet; Γ is a finite ranked alphabet, called the output alphabet; I is a subset of Q, the set of initial states; and δ is a set of rules of the form q ( f ( x 1 , … , x n ) ) → u {\displaystyle q(f(x_{1},\dots ,x_{n}))\to u} , where f is a symbol of Σ, n is the arity of f, q is a state, and u is a tree on Γ and Q × 1.. n {\displaystyle Q\times 1..n} , such pairs being nullary. === Examples of rules and intuitions on semantics === For instance, q ( f ( x 1 , … , x 3 ) ) → g ( a , q ′ ( x 1 ) , h ( q ″ ( x 3 ) ) ) {\displaystyle q(f(x_{1},\dots ,x_{3}))\to g(a,q'(x_{1}),h(q''(x_{3})))} is a rule – one customarily writes q ( x i ) {\displaystyle q(x_{i})} instead of the pair ( q , x i ) {\displaystyle (q,x_{i})} – and its intuitive semantics is that, under the action of q, a tree with f at the root and three children is transformed into g ( a , q ′ ( x 1 ) , h ( q ″ ( x 3 ) ) ) {\displaystyle g(a,q'(x_{1}),h(q''(x_{3})))} where, recursively, q ′ ( x 1 ) {\displaystyle q'(x_{1})} and q ″ ( x 3 ) {\displaystyle q''(x_{3})} are replaced, respectively, with the application of q ′ {\displaystyle q'} on the first child and with the application of q ″ {\displaystyle q''} on the third. === Semantics as term rewriting === The semantics of each state of the transducer T, and of T itself, is a binary relation between input trees (on Σ) and output trees (on Γ). A way of defining the semantics formally is to see δ {\displaystyle \delta } as a term rewriting system, provided that in the right-hand sides the calls are written in the form q ( x i ) {\displaystyle q(x_{i})} , where states q are unary symbols. Then the semantics [ [ q ] ] {\displaystyle [\![q]\!]} of a state q is given by [ [ q ] ] = { u ↦ v ∣ u is a tree on Σ , v is a tree on Γ , and q ( u ) → δ ∗ v } . {\displaystyle [\![q]\!]=\{u\mapsto v\mid u{\text{ is a tree on }}\Sigma ,\ v{\text{ is a tree on }}\Gamma {\text{, and }}q(u)\to _{\delta }^{}v\}.} The semantics of T is then defined as the union of the semantics of its initial states: [ [ T ] ] = ⋃ q ∈ I [ [ q ] ] . {\displaystyle [\![T]\!]=\bigcup _{q\in I}[\![q]\!].} === Determinism and domain === As with tree automata, a TOP is said to be deterministic (abbreviated DTOP) if no two rules of δ share the same left-hand side, and there is at most one initial state. In that case, the semantics of the DTOP is a partial function from input trees (on Σ) to output trees (on Γ), as are the semantics of each of the DTOP's states. The domain of a transducer is the domain of its semantics. Likewise, the image of a transducer is the image of its semantics. === Properties of DTOP === DTOP are not closed under union: this is already the case for deterministic word transducers. The domain of a DTOP is a regular tree language. Furthermore, the domain is recognisable by a deterministic top-down tree automaton (DTTA) of size at most exponential in that of the initial DTOP. That the domain is DTTA-recognizable is not surprising, considering that the left-hand sides of DTOP rules are the same as for DTTA. As for the reason for the exponential explosion in the worst case (that does not exist in the word case), consider the rule q ( f ( x 1 , x 2 ) ) → g ( p 1 ( x 1 ) , p 2 ( x 1 ) , p 3 ( x 2 ) ) {\displaystyle q(f(x_{1},x_{2}))\to g(p_{1}(x_{1}),p_{2}(x_{1}),p_{3}(x_{2}))} . In order for the computation to succeed, it must succeed for both children. That means that the right child must be in the domain of p 3 {\displaystyle p_{3}} . As for the left child, it must be in the domain of both p 1 {\displaystyle p_{1}} and p 2 {\displaystyle p_{2}} . Generally, since subtrees can be copied, a single subtree can be evaluated by multiple states during a run, despite the determinism, and unlike DTTA. Thus the construction of the DTTA recognising the domain of a DTOP must account for sets of states and compute the intersections of their domains, hence the exponential. In the special case of linear DTOP, that is to say DTOP where each x i {\displaystyle x_{i}} appears at most once in the right-hand side of each rule, the construction is linear in time and space. The image of a DTOP is not a regular tree language. Consider the transducer coding the transformation f ( x ) → g ( x , x ) {\displaystyle f(x)\to g(x,x)} ; that is, duplicate the child of the input. This is easily done by a rule q ( f ( x 1 ) ) → g ( p ( x 1 ) , p ( x 1 ) ) {\displaystyle q(f(x_{1}))\to g(p(x_{1}),p(x_{1}))} , where p encodes the identity. Then, absent any restrictions on the first child of the input, the image is a classical non-regular tree language. However, the domain of a DTOP cannot be restricted to a regular tree language. That is to say, given a DTOP T and a language L, one cannot in general build a DTOP T ′ {\displaystyle T'} such that the semantics of T ′ {\displaystyle T'} is that of T, restricted to L. This property is linked to the reason deterministic top-down tree automata are less expressive than bottom-up automata: once you go down a given path, information from other paths is inaccessible. Consider the transducer coding the transformation f ( x , y ) → y {\displaystyle f(x,y)\to y} ; that is, output the right child of the input. This is easily done by a rule q ( f ( x 1 , x 2 ) ) → p ( x 2 ) {\displaystyle q(f(x_{1},x_{2}))\to p(x_{2})} , where p encodes the identity. Now let's say we want to restrict this transducer to the finite (and thus, in particular, regular) domain { f ( c , a ) , f ( c , b ) } {\displaystyle \{f(c,a),\ f(c,b)\}} . We must use the rules q ( f ( x 1 , x 2 ) ) → p ( x 2 ) , p ( a ) → a , p ( b ) → b {\displaystyle q(f(x_{1},x_{2}))\to p(x_{2}),\ p(a)\to a,\ p(b)\to b} . But in the first rule, x 1 {\displaystyle x_{1}} does not appear at all, since nothing is produced from the left child. Thus, it is not possible to test that the left child is c. In contrast, since we produce from the right child, we can test that it is a or b. In general, the criterion is that DTOP cannot test properties of subtrees from which they do not produce output. DTOP are not closed under composition. However this problem can be solved by the addition of a lookahead: a tree automaton, coupled to the transducer, that can perform tests on the domain which the transducer is incapable of. This follows from the point about domain restriction: composing the DTOP encoding identity on { f ( c , a ) , f ( c , b ) } {\displaystyle \{f(c,a),\ f(c,b)\}} with the one encoding f ( x , y ) → y {\displaystyle f(x,y)\to y} must yield a transducer with the semantics { f ( c , a ) ↦ a , f ( c , b ) ↦ b } {\displaystyle \{f(c,a)\mapsto a,\ f(c,b)\mapsto b\}} , which we know is not expressible by a DTOP. The typechecking problem—testing whether the image of a regular tree language is included in another regular tree language—is decidable. The equivalence problem—testing whether two DTOP define the same functions—is decidable. == Bottom-Up Tree Transducers (BOT) == As in the simpler case of tree automata, bottom-up tree transducers are defined similarly to their top-down counterparts, but proceed from the leaves of the tree to the root, instead of from the root to the leaves. Thus the main difference is in the form of the rules, which are of the form f ( q 1 ( x 1 ) , … , q n ( x n ) ) → q ( u ) {\displaystyle f(q_{1}(x_{1}),\dots ,q_{n}(x_{n}))\to q(u)} .
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Dropbox Paper, or simply Paper, is a collaborative document-editing service developed by Dropbox. Originating from the company's acquisition of document collaboration company Hackpad in April 2014, Dropbox Paper was officially announced in October 2015, and launched in January 2017. It offers a web application, as well as mobile apps for Android and iOS. Dropbox Paper was described in the official announcement post as "a flexible workspace that brings people and ideas together. With Paper, teams can create, review, revise, manage, and organize — all in shared documents". Reception of Dropbox Paper has been mixed. Critics praised collaboration functionality, including content available immediately, the ability to mention specific collaborators, assign tasks, write comments, as well as editing attribution, and revision history. It received particular praise for its support for rich media from a variety of sources, with one reviewer noting that the Paper's support for rich media exceeds the capabilities of most of its competitors. However, it was criticized for a lack of formatting options and editing features. While the user interface was liked for being minimal, reviewers cited the lack of a fixed formatting bar and missing features present in competitors' products as making Dropbox Paper seem like a "light" tool. == History == Dropbox acquired document collaboration company Hackpad in April 2014. A year later, Dropbox launched a Dropbox Notes note-taking product in beta testing phase. Dropbox Paper was officially announced on October 15, 2015, followed by an open beta and release of mobile Android and iOS apps in August 2016. Dropbox Paper was officially released on January 30, 2017. == Reception == In a comparison between Dropbox Paper and Evernote, PC World's Michael Ansaldo wrote that "With its emphasis on document creation, you might expect formatting to be front and center in Dropbox Paper. That's not the case." Ansaldo noted the lack of a "fixed formatting toolbar as you'd find in Evernote or a word processor like Google Docs or Microsoft Word. Instead, the text editor appears as a floating ribbon only when you highlight selected text." The only formatting options available for emphasis were bolding, strikethrough, bulleted and numbered lists, and H1 and H2 tags. Users can also add links, convert text to checklists, and add comments. Ansaldo wrote that "Both Evernote and Dropbox Paper make it easy to add images to a document", but also noted that "Dropbox Paper doesn't support any image editing". Paper supports rich media, and users can "add rich content to your document just by pasting a link to the file. In addition to Dropbox, Paper supports media from a variety of popular services including YouTube, Spotify, Vimeo, SoundCloud, Facebook, and Google's productivity suite. Once the file appears, you can delete the link for a cleaner display." To start working with other people, Paper "allows you to invite people via email from within a document", with sharing options for who can view the link (anyone with the link or just the invited person), and action permissions (edit or only comment). Regarding collaboration, Ansaldo wrote that "Creative collaboration is Paper’s marquee feature, and it provides a variety of ways to work effectively with others in real time". Users can "make any content immediately visible and accessible to a specific collaborator with "@mentions"", and "You can also use @mentions to create and assign task lists within a document." Paper also "boasts essential collaboration tools including comments, editing attribution, and revision history." Writing for TechRadar, John Brandon wrote that Dropbox Paper "might be a 'light' tool for now without the extensive templates of Microsoft Office or the integration with other apps in the Zoho suite, but it does work well with the Dropbox storage service that's so popular with office workers these days." Kyle Wiggers of Digital Trends wrote that Paper is "all about minimizing distractions. Its interface is quite literally a big, blank canvas on which you tap out your agenda. You can organize notes by title and create to-do lists, but even basic formatting tools are obscured from view", noting Paper's "floating box above words and phrases highlighted by your cursor". Wiggers stated that "Paper is not a to-do organizer", but that it's "well suited to the purpose thanks to a bevy of labor-saving conveniences", highlighting that Paper "supports more media than most of its to-do and note-taking counterparts". He praised the collaboration tools, writing that they "are as extensive as you'd hope, and then some", citing its invitation system with permission controls, lists of changes and revision history, comment and chat support, and "perhaps best of all", the ability to assign tasks with a "@" mention. Business Insider's Alex Heath praised that "Paper's interface is spotless and friendly to write in. You don't feel overwhelmed with formatting options", but criticized the available features, writing that "Google Docs is much more full-featured in the formatting department, so Paper has some catching up to do if it wants to be on par with the competition". Writing for The Verge, Casey Newton praised Paper's handling of rich media, complimenting it for being "great", and added that "I imagine that creative types who work on teams will appreciate having rich media embedded in the documents they're working on rather than in a series of infinite tabs".
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Xuedong David Huang (born October 20, 1962) is a Chinese-American computer scientist and technology executive who has made contributions to spoken language processing and artificial intelligence, including Azure AI Services. He is Zoom's chief technology officer after serving as Microsoft's Technical Fellow and Azure AI Chief Technology Officer for 30 years. Huang is a strong advocate of AI for Accessibility, and AI for Cultural Heritage. == Education == Huang received his PhD from the University of Edinburgh in 1989 (sponsored by the British ORS and Edinburgh University Scholarship), his MS from Tsinghua University in 1984, and BS from Hunan University in 1982. == Career == After receiving his PhD in 1989, Huang joined Carnegie Mellon University and worked with Raj Reddy and Kai-Fu Lee on speech recognition. At CMU, he directed the Sphinx-II speech system research which achieved the best performance in every category of DARPA's 1992 benchmarking. Microsoft Research recruited him to found and lead Microsoft's spoken language initiatives in 1993. His co-authored book Spoken Language Processing and his Historical speech recognition review succinctly summarize several generations of spoken language research. As Microsoft's Mr. Speech for three decades, Huang has been instrumental in creating Microsoft's Speech Application Programming Interface (SAPI), shipping Microsoft Speech Server, and modernizing spoken language and integrative AI services via Azure AI, which not only enables millions of 3rd party customers but also powers up Microsoft's Windows, Office, Teams, and Azure OpenAI Services. Huang helped Microsoft and Azure Cognitive Services achieve multiple industry's first human parity milestones on the following open research tasks: transcribing conversational speech, machine translation, conversational QnA, and computer vision image captioning. Huang has made significant contributions to the software and AI industry through his executive leadership and his scientific publications, owning more than 170 US patents and impacting billions through Azure AI enabled products and services. In 2016, Wired magazine named him one of 25 Geniuses. In 2021, Azure AI was named the winner of InfoWorld's Technology of the Year Award. Huang was awarded the Allen Newell research excellence medal in 1992, and IEEE Speech Processing Best Paper in 1993. He was recognized as an IEEE Fellow by Institute of Electrical and Electronics Engineers in 2000, named ACM Fellow by Association for Computing Machinery in 2017, and a member of Washington State Academy of Sciences. Huang received 2022 Asian American Corporate Leadership Award, and IEEE Amar Bose Industrial Leader Award. In 2023, he was elected a member of the US National Academy of Engineering (NAE), and a member of the American Academy of Arts and Sciences.
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A stochastic grammar (statistical grammar) is a grammar framework with a probabilistic notion of grammaticality: Stochastic context-free grammar Statistical parsing Data-oriented parsing Hidden Markov model (or stochastic regular grammar) Estimation theory The grammar is realized as a language model. Allowed sentences are stored in a database together with the frequency how common a sentence is. Statistical natural language processing uses stochastic, probabilistic and statistical methods, especially to resolve difficulties that arise because longer sentences are highly ambiguous when processed with realistic grammars, yielding thousands or millions of possible analyses. Methods for disambiguation often involve the use of corpora and Markov models. "A probabilistic model consists of a non-probabilistic model plus some numerical quantities; it is not true that probabilistic models are inherently simpler or less structural than non-probabilistic models." == Examples == A probabilistic method for rhyme detection is implemented by Hirjee & Brown in their study in 2013 to find internal and imperfect rhyme pairs in rap lyrics. The concept is adapted from a sequence alignment technique using BLOSUM (BLOcks SUbstitution Matrix). They were able to detect rhymes undetectable by non-probabilistic models.
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