A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links between pages. The PageRank of each page can then be generated iteratively from the Google matrix using the power method. However, in order for the power method to converge, the matrix must be stochastic, irreducible and aperiodic. == Adjacency matrix A and Markov matrix S == In order to generate the Google matrix G, we must first generate an adjacency matrix A which represents the relations between pages or nodes. Assuming there are N pages, we can fill out A by doing the following: A matrix element A i , j {\displaystyle A_{i,j}} is filled with 1 if node j {\displaystyle j} has a link to node i {\displaystyle i} , and 0 otherwise; this is the adjacency matrix of links. A related matrix S corresponding to the transitions in a Markov chain of given network is constructed from A by dividing the elements of column "j" by a number of k j = Σ i = 1 N A i , j {\displaystyle k_{j}=\Sigma _{i=1}^{N}A_{i,j}} where k j {\displaystyle k_{j}} is the total number of outgoing links from node j to all other nodes. The columns having zero matrix elements, corresponding to dangling nodes, are replaced by a constant value 1/N. Such a procedure adds a link from every sink, dangling state a {\displaystyle a} to every other node. Now by the construction the sum of all elements in any column of matrix S is equal to unity. In this way the matrix S is mathematically well defined and it belongs to the class of Markov chains and the class of Perron-Frobenius operators. That makes S suitable for the PageRank algorithm. == Construction of Google matrix G == Then the final Google matrix G can be expressed via S as: G i j = α S i j + ( 1 − α ) 1 N ( 1 ) {\displaystyle G_{ij}=\alpha S_{ij}+(1-\alpha ){\frac {1}{N}}\;\;\;\;\;\;\;\;\;\;\;(1)} By the construction the sum of all non-negative elements inside each matrix column is equal to unity. The numerical coefficient α {\displaystyle \alpha } is known as a damping factor. Usually S is a sparse matrix and for modern directed networks it has only about ten nonzero elements in a line or column, thus only about 10N multiplications are needed to multiply a vector by matrix G. == Examples of Google matrix == An example of the matrix S {\displaystyle S} construction via Eq.(1) within a simple network is given in the article CheiRank. For the actual matrix, Google uses a damping factor α {\displaystyle \alpha } around 0.85. The term ( 1 − α ) {\displaystyle (1-\alpha )} gives a surfer probability to jump randomly on any page. The matrix G {\displaystyle G} belongs to the class of Perron-Frobenius operators of Markov chains. The examples of Google matrix structure are shown in Fig.1 for Wikipedia articles hyperlink network in 2009 at small scale and in Fig.2 for University of Cambridge network in 2006 at large scale. == Spectrum and eigenstates of G matrix == For 0 < α < 1 {\displaystyle 0<\alpha <1} there is only one maximal eigenvalue λ = 1 {\displaystyle \lambda =1} with the corresponding right eigenvector which has non-negative elements P i {\displaystyle P_{i}} which can be viewed as stationary probability distribution. These probabilities ordered by their decreasing values give the PageRank vector P i {\displaystyle P_{i}} with the PageRank K i {\displaystyle K_{i}} used by Google search to rank webpages. Usually one has for the World Wide Web that P ∝ 1 / K β {\displaystyle P\propto 1/K^{\beta }} with β ≈ 0.9 {\displaystyle \beta \approx 0.9} . The number of nodes with a given PageRank value scales as N P ∝ 1 / P ν {\displaystyle N_{P}\propto 1/P^{\nu }} with the exponent ν = 1 + 1 / β ≈ 2.1 {\displaystyle \nu =1+1/\beta \approx 2.1} . The left eigenvector at λ = 1 {\displaystyle \lambda =1} has constant matrix elements. With 0 < α {\displaystyle 0<\alpha } all eigenvalues move as λ i → α λ i {\displaystyle \lambda _{i}\rightarrow \alpha \lambda _{i}} except the maximal eigenvalue λ = 1 {\displaystyle \lambda =1} , which remains unchanged. The PageRank vector varies with α {\displaystyle \alpha } but other eigenvectors with λ i < 1 {\displaystyle \lambda _{i}<1} remain unchanged due to their orthogonality to the constant left vector at λ = 1 {\displaystyle \lambda =1} . The gap between λ = 1 {\displaystyle \lambda =1} and other eigenvalue being 1 − α ≈ 0.15 {\displaystyle 1-\alpha \approx 0.15} gives a rapid convergence of a random initial vector to the PageRank approximately after 50 multiplications on G {\displaystyle G} matrix. At α = 1 {\displaystyle \alpha =1} the matrix G {\displaystyle G} has generally many degenerate eigenvalues λ = 1 {\displaystyle \lambda =1} (see e.g. [6]). Examples of the eigenvalue spectrum of the Google matrix of various directed networks is shown in Fig.3 from and Fig.4 from. The Google matrix can be also constructed for the Ulam networks generated by the Ulam method [8] for dynamical maps. The spectral properties of such matrices are discussed in [9,10,11,12,13,15]. In a number of cases the spectrum is described by the fractal Weyl law [10,12]. The Google matrix can be constructed also for other directed networks, e.g. for the procedure call network of the Linux Kernel software introduced in [15]. In this case the spectrum of λ {\displaystyle \lambda } is described by the fractal Weyl law with the fractal dimension d ≈ 1.3 {\displaystyle d\approx 1.3} (see Fig.5 from ). Numerical analysis shows that the eigenstates of matrix G {\displaystyle G} are localized (see Fig.6 from ). Arnoldi iteration method allows to compute many eigenvalues and eigenvectors for matrices of rather large size [13]. Other examples of G {\displaystyle G} matrix include the Google matrix of brain [17] and business process management [18], see also. Applications of Google matrix analysis to DNA sequences is described in [20]. Such a Google matrix approach allows also to analyze entanglement of cultures via ranking of multilingual Wikipedia articles abouts persons [21] == Historical notes == The Google matrix with damping factor was described by Sergey Brin and Larry Page in 1998 [22], see also articles on PageRank history [23], [24].
Histogram of oriented displacements
Histogram of oriented displacements (HOD) is a 2D trajectory descriptor. The trajectory is described using a histogram of the directions between each two consecutive points. Given a trajectory T = {P1, P2, P3, ..., Pn}, where Pt is the 2D position at time t. For each pair of positions Pt and Pt+1, calculate the direction angle θ(t, t+1). Value of θ is between 0 and 360. A histogram of the quantized values of θ is created. If the histogram is of 8 bins, the first bin represents all θs between 0 and 45. The histogram accumulates the lengths of the consecutive moves. For each θ, a specific histogram bin is determined. The length of the line between Pt and Pt+1 is then added to the specific histogram bin. To show the intuition behind the descriptor, consider the action of waving hands. At the end of the action, the hand falls down. When describing this down movement, the descriptor does not care about the position from which the hand started to fall. This fall will affect the histogram with the appropriate angles and lengths, regardless of the position where the hand started to fall. HOD records for each moving point: how much it moves in each range of directions. HOD has a clear physical interpretation. It proposes that, a simple way to describe the motion of an object, is to indicate how much distance it moves in each direction. If the movement in all directions are saved accurately, the movement can be repeated from the initial position to the final destination regardless of the displacements order. However, the temporal information will be lost, as the order of movements is not stored-this is what we solve by applying the temporal pyramid, as shown in section \ref{sec:temp-pyramid}. If the angles quantization range is small, classifiers that use the descriptor will overfit. Generalization needs some slack in directions-which can be done by increasing the quantization range.
Report generator
A report generator is a computer program whose purpose is to take data from a source such as a database, XML stream or a spreadsheet, and use it to produce a document in a format which satisfies a particular human readership. Report generation functionality is almost always present in database systems, where the source of the data is the database itself. It can also be argued that report generation is part of the purpose of a spreadsheet. Standalone report generators may work with multiple data sources and export reports to different document formats. Information systems theory specifies that information delivered to a target human reader must be timely, accurate and relevant. Report generation software targets the final requirement by making sure that the information delivered is presented in the way most readily understood by the target reader. == History == An early report writer was part of NOMAD developed in the 1970s. The evolution of reporting software has a rich history dating back to the mid-20th century, driven by the increasing need for businesses to efficiently analyze and present data. Initially, manual extraction and tabulation were commonplace, but the advent of computers in the 1960s marked a transformative phase with the emergence of basic reporting tools. The 1980s saw the widespread adoption of database management systems, laying the groundwork for more sophisticated reporting capabilities. Notable dedicated reporting software, such as Crystal Reports and BusinessObjects, gained prominence in the 1990s amidst the growing demand for business intelligence. The 21st century witnessed a paradigm shift towards web-based reporting solutions and the rise of self-service BI tools, empowering users to create reports independently. Presently, reporting software continues to evolve with a focus on data visualization, integration of artificial intelligence, and the imperative for real-time analytics in decision-making.
Scripped
Scripped was an online screenplay services company offering three services: script writing, script registration, and script coverage. Scripped did not facilitate collaboration among screenwriters. It combined with Zhura in 2010. According to Techcrunch, Scripped had more than 60,000 writers as of March 2010. Scripped was administered by Sunil Rajaraman, Ryan Buckley and Zak Freer. Actor, writer, and director Edward Burns and screenwriter Steven E. de Souza joined Scripped's Board of Advisers in May 2008. In 2008, the company formed a partnership with Write Brothers, makers of Movie Magic Screenwriter software. On March 29, 2010, Scripped announced that it closed $250,000 in private investment and merged with competitor Zhura. Scripped's CEO, Sunil Rajaraman, remains the merged company's Chief Executive Officer. On April 1, 2015, citing a serious technical failure, Scripped shuttered its service. As part of the announcement, it was disclosed that their backup servers had failed as well, losing all of its users' stored scripts. The website URL currently redirects to WriterDuet's website, another online scriptwriting service; Scripped had advertised WriterDuet in Scripped's shutdown open letter. == Features == The Scripped Writer provided a built-in screenplay template which formatted the document to a standard for scripts as recommended by the AMPAS. The screenplay document was composed of seven elements: scene, action, character, dialog, parenthetical, transition and general. Each element had a specific style to which the Scripped Writer conformed as text was entered. Like other client-side screenplay software, Scripped offered Tab-Enter toggling between screenplay elements, making the writing process much faster. Text files could be imported into the Scripped Writer and automatically conformed to the screenplay template. Completed scripts could be exported as PDF files. In May 2011 the administrators of Scripped launched Scripted.com - a sister site focused on freelance writing jobs. Subsequent to the service's launch, the company was renamed to Scripted, Inc.
Toad (software)
Toad is a database management toolset from Quest Software for managing relational and non-relational databases using SQL aimed at database developers, database administrators, and data analysts. The Toad toolset runs against Oracle, SQL Server, IBM DB2 (LUW & z/OS), SAP and MySQL. A Toad product for data preparation supports many data platforms. == History == A practicing Oracle DBA, Jim McDaniel, designed Toad for his own use in the mid-1990s. He called it Tool for Oracle Application Developers, shortened to "TOAD". McDaniel initially distributed the tool as shareware and later online as freeware. Quest Software acquired TOAD in October 1998. Quest Software itself was acquired by Dell in 2012 to form Dell Software. In June 2016, Dell announced the sale of their software division, including the Quest business, to Francisco Partners and Elliott Management Corporation. On October 31, 2016, the sale was finalized. On November 1, 2016, the sale of Dell Software to Francisco Partners and Elliott Management was completed, and the company re-launched as Quest Software. == Features == Connection Manager - Allow users to connect natively to the vendor’s database whether on-premise or DBaaS. Browser - Allow users to browse all the different database/schema objects and their properties effective management. Editor - A way to create and maintain scripts and database code with debugging and integration with source control. Unit Testing (Oracle) - Ensures code is functionally tested before it is released into production. Static code review (Oracle) - Ensures code meets required quality level using a rules-based system. SQL Optimization - Provides developers with a way to tune and optimize SQL statements and database code without relying on a DBA. Advanced optimization enables DBAs to tune SQL effectively in production. Scalability testing and database workload replay - Ensures that database code and SQL will scale properly before it gets released into production. == Books == Toad Pocket Reference for Oracle plsql 1st Edition by Jim McDaniel and Patrick McGrath, O'Reilly, 2002 (ISBN 0596003374, ISBN 978-0-596-00337-1) Toad Pocket Reference for Oracle 2nd Edition by Jeff Smith, Bert Scalzo, and Patrick McGrath, O'Reilly, 2005 (ISBN 0596009712, ISBN 978-0-596-00971-7) TOAD Handbook by Bert Scalzo and Dan Hotka, Sams, 2003 (ISBN 0672324865, ISBN 978-0-672-32486-4) TOAD Handbook 2nd Edition by Bert Scalzo and Dan Hotka, Addison-Wesley Professional, 2009 (ISBN 0321649109, ISBN 978-0-321-64910-2). TOAD Handbook 2nd Edition by Bert Scalzo and Dan Hotka, Addison-Wesley Professional, 2009 (ISBN 0321649109, ISBN 978-0-321-64910-2).
Plane Finder
Plane Finder is a United Kingdom-based real-time flight tracking service launched in 2009, that is able to show flight data globally. The data available includes flight numbers, how fast an aircraft is moving, its elevation and destination of travel. Several variants of the service are available as mobile apps including free, premium 3D and augmented reality versions. The flight tracking map and database can be accessed by web browsers. Plane Finder allows registered users to share their ADS-B and MLAT data via the Plane Finder ADS-B Client, available for macOS, Windows and Linux. Plane Finder supports VFR charts from NATS, and was the first major flight tracking app to introduce a replay feature, allowing users to replay flights dating back to 2011. == Flight tracking == Plane Finder collects data from its own global network of receivers, using the following sources. === Automatic dependent surveillance-broadcast (ADS-B) === A network of automatic dependent surveillance-broadcast (ADS-B) receivers gathers aircraft data such as callsign, position and speed. Plane Finder serves to supplement this data with additional information, including aircraft registration/tail number, departure airport, destination, artwork, and photographs. Plane Finder users can apply for an ADS-B receiver in exchange for their flight data. === Multilateration (MLAT) === To deliver aircraft position data where ADS-B is unavailable, Plane Finder uses multilateration (MLAT). Using three or more receivers running Plane Finder client software, monitoring the aircraft simultaneously, the aircraft’s position is calculated using receiver location and accurate timestamps. While European airspace is widely covered, only some parts of North American airspace are covered. === Federal Aviation Administration (FAA) feed === ADS-B is prevalent across Europe and Australia, but not in North America. Where MLAT or ADS-B data is unavailable, a feed from the Federal Aviation Administration provides flight information. The FAA feed covers United States and Canadian airspace, including bordering areas of the Atlantic and Pacific Oceans. === FLARM feed === Plane Finder collects data from a centralised FLARM feed, for monitoring small aircraft and gliders. == Flight data source == The Plane Finder website and database is widely used as an information source to support articles in the media. The Independent used Plane Finder flight tracking to demonstrate to readers the flight path of flight MT2706, which turned back as a result of last minute Egyptian government flight restrictions on 6 November 2015. The Independent also used Plane Finder information to demonstrate a timeline of the speed/altitude of flight 7K 9268, a Russian plane which crashed on 31 October 2015. The BBC cited Plane Finder in regard to the point at which at British Airways flight turned back to Heathrow Airport to make an emergency landing after smoke was seen coming from its engines. Plane Finder data has also been used to create original imagery for the media, such as the Washington Post, which used Plane Finder as a source to show flight patterns immediately after the Brussels bombings in March 2016.
Viaweb
Viaweb was a web-based application that allowed users to build and host their own online stores with little technical expertise using a web browser. The company was started in July 1995 by Paul Graham, Robert Morris (using the pseudonym "John McArtyem"), and Trevor Blackwell. Graham claims Viaweb was the first application service provider. Viaweb was also unusual for being partially written in the Lisp programming language. The software was originally called Webgen, but another company was using the same name, so the company renamed it to Viaweb, "because it worked via the Web". In 1998, Yahoo! Inc. bought Viaweb for 455,000 shares of Yahoo! capital stock, valued at about $49 million, and renamed it Yahoo! Store. Viaweb's example has been influential in Silicon Valley's entrepreneurial culture, largely due to Graham's widely read essays and his subsequent career as a successful venture capitalist.