In automata theory, a co-Büchi automaton is a variant of Büchi automaton. The only difference is the accepting condition: a Co-Büchi automaton accepts an infinite word w {\displaystyle w} if there exists a run, such that all the states occurring infinitely often in the run are in the final state set F {\displaystyle F} . In contrast, a Büchi automaton accepts a word w {\displaystyle w} if there exists a run, such that at least one state occurring infinitely often in the final state set F {\displaystyle F} . (Deterministic) Co-Büchi automata are strictly weaker than (nondeterministic) Büchi automata. == Formal definition == Formally, a deterministic co-Büchi automaton is a tuple A = ( Q , Σ , δ , q 0 , F ) {\displaystyle {\mathcal {A}}=(Q,\Sigma ,\delta ,q_{0},F)} that consists of the following components: Q {\displaystyle Q} is a finite set. The elements of Q {\displaystyle Q} are called the states of A {\displaystyle {\mathcal {A}}} . Σ {\displaystyle \Sigma } is a finite set called the alphabet of A {\displaystyle {\mathcal {A}}} . δ : Q × Σ → Q {\displaystyle \delta :Q\times \Sigma \rightarrow Q} is the transition function of A {\displaystyle {\mathcal {A}}} . q 0 {\displaystyle q_{0}} is an element of Q {\displaystyle Q} , called the initial state. F ⊆ Q {\displaystyle F\subseteq Q} is the final state set. A {\displaystyle {\mathcal {A}}} accepts exactly those words w {\displaystyle w} with the run ρ ( w ) {\displaystyle \rho (w)} , in which all of the infinitely often occurring states in ρ ( w ) {\displaystyle \rho (w)} are in F {\displaystyle F} . In a non-deterministic co-Büchi automaton, the transition function δ {\displaystyle \delta } is replaced with a transition relation Δ {\displaystyle \Delta } . The initial state q 0 {\displaystyle q_{0}} is replaced with an initial state set Q 0 {\displaystyle Q_{0}} . Generally, the term co-Büchi automaton refers to the non-deterministic co-Büchi automaton. For more comprehensive formalism see also ω-automaton. == Acceptance Condition == The acceptance condition of a co-Büchi automaton is formally ∃ i ∀ j : j ≥ i ρ ( w j ) ∈ F . {\displaystyle \exists i\forall j:\;j\geq i\quad \rho (w_{j})\in F.} The Büchi acceptance condition is the complement of the co-Büchi acceptance condition: ∀ i ∃ j : j ≥ i ρ ( w j ) ∈ F . {\displaystyle \forall i\exists j:\;j\geq i\quad \rho (w_{j})\in F.} == Properties == Co-Büchi automata are closed under union, intersection, projection and determinization.
Adobe PhotoDeluxe
PhotoDeluxe was a consumer-oriented image editing software line published by Adobe Systems from 1996 until July 8, 2002. At that time it was replaced by Adobe's newly launched consumer-oriented image editing software Photoshop Elements. Adobe no longer provides technical support for the PhotoDeluxe software line. PhotoDeluxe had a range of image processing capabilities for the home photographer and image handler. These included removing red-eye, cropping, and adjusting brightness, contrast, and sharpness. It also included software to extract pictures from an image scanner. Among the functionality included was the ability to dynamically resize photos and export them in a wide range of formats. It also had a range of printing options including printing multiple copies of an image on the same page. It was often bundled free with Epson scanners or as free software with new computers. == Features == Despite the critical concerns regarding the quality of the setup, Photo Deluxe supports layering, blurs, sharpening, cloning, gradient fills, color and background switches, color variations, resizing options, and many other features. Another drawback of PhotoDeluxe was that it was designed for Mac computers, so working on Windows PC was a problem for those who were unable to customize their preferences. == Versions == === Adobe PhotoDeluxe 1.0 === The first version was released in 1996 for Windows and Macintosh computers. In one year, it sold over one million copies. === Adobe PhotoDeluxe 2.0 === The new version was released in 1997 and had added features such as a Clone Tool, red-eye removal, and sample templates for making posters, cards, and calendars. It also had new special effect features. === Adobe PhotoDeluxe 3.0 === The 3rd version was released in 1998. The new features included customizable clipart settings, the ability to import photos on the web, enhanced repair activities following Guided Activities, and Adobe Connectables to add new activities. === Adobe PhotoDeluxe Home Edition (4.0) === Version 4.0 was created by the makers of Photoshop. It had advanced abilities such as tools to add animation, voice, and music to a picture. It also had features to restore photos to their original position. == History == Adobe PhotoDeluxe 1.0 was released in 1996 for Macintosh computers, initially retailing for an MSRP of $49. The software did quite well, reportedly selling over a million copies by February of the next year, primarily due to bundles with companies like Apple and Hewlett-Packard. PhotoDeluxe was primarily advertised to consumers as a way to do basic photo manipulation, such as cropping and rotating images, or creating simple cards and calendars. PhotoDeluxe 2.0 was released in 1997, and was the last version of PhotoDeluxe that Adobe made that worked on Macs. PhotoDeluxe 2.0 became the "number one selling consumer photo-editing software product in the world." PhotoDeluxe 3.0 was released in 1998, where it was rebranded as "3.0 Home Edition", as Adobe released PhotoDeluxe Business Edition later that year for a higher price. PhotoDeluxe Home Edition, unofficially called PhotoDeluxe 4.0, was released in 1999 and was the last version of PhotoDeluxe to be released. Adobe officially cancelled PhotoDeluxe on July 8, 2002, citing the presence of Photoshop and Photoshop Elements, with support being officially cancelled in mid-2003. No version of PhotoDeluxe is compatible with Windows 10, rendering the program obsolete. == Pricing == All home versions of PhotoDeluxe retailed for an MSRP of $49. PhotoDeluxe 2.0 and onwards allowed users to upgrade from a previous version of PhotoDeluxe or a competing piece of graphics software for $39. Additionally PhotoDeluxe Business Edition allowed a similar deal, allowing users to upgrade from other versions of PhotoDeluxe or a competing software for $59, instead of its normal price of $99. Adobe also offered a bundle allowing users of 1.0 or 2.0 to get 3.0 and Business Edition for $79.
Subvocal recognition
Subvocal recognition (SVR) is the process of taking subvocalization and converting the detected results to a digital output, aural or text-based. A silent speech interface is a device that allows speech communication without using the sound made when people vocalize their speech sounds. It works by the computer identifying the phonemes that an individual pronounces from nonauditory sources of information about their speech movements. These are then used to recreate the speech using speech synthesis. == Input methods == Silent speech interface systems have been created using ultrasound and optical camera input of tongue and lip movements. Electromagnetic devices are another technique for tracking tongue and lip movements. The detection of speech movements by electromyography of speech articulator muscles and the larynx is another technique. Another source of information is the vocal tract resonance signals that get transmitted through bone conduction called non-audible murmurs. They have also been created as a brain–computer interface using brain activity in the motor cortex obtained from intracortical microelectrodes. == Uses == Such devices are created as aids to those unable to create the sound phonation needed for audible speech such as after laryngectomies. Another use is for communication when speech is masked by background noise or distorted by self-contained breathing apparatus. A further practical use is where a need exists for silent communication, such as when privacy is required in a public place, or hands-free data silent transmission is needed during a military or security operation. In 2002, the Japanese company NTT DoCoMo announced it had created a silent mobile phone using electromyography and imaging of lip movement. The company stated that "the spur to developing such a phone was ridding public places of noise," adding that, "the technology is also expected to help people who have permanently lost their voice." The feasibility of using silent speech interfaces for practical communication has since then been shown. In 2019, Arnav Kapur, a researcher from the Massachusetts Institute of Technology, conducted a study known as AlterEgo. Its implementation of the silent speech interface enables direct communication between the human brain and external devices through stimulation of the speech muscles. By leveraging neural signals associated with speech and language, the AlterEgo system deciphers the user's intended words and translates them into text or commands without the need for audible speech. == Research and patents == With a grant from the U.S. Army, research into synthetic telepathy using subvocalization is taking place at the University of California, Irvine under lead scientist Mike D'Zmura. NASA's Ames Research Laboratory in Mountain View, California, under the supervision of Charles Jorgensen is conducting subvocalization research. The Brain Computer Interface R&D program at Wadsworth Center under the New York State Department of Health has confirmed the existing ability to decipher consonants and vowels from imagined speech, which allows for brain-based communication using imagined speech, however using EEGs instead of subvocalization techniques. US Patents on silent communication technologies include: US Patent 6587729 "Apparatus for audibly communicating speech using the radio frequency hearing effect", US Patent 5159703 "Silent subliminal presentation system", US Patent 6011991 "Communication system and method including brain wave analysis and/or use of brain activity", US Patent 3951134 "Apparatus and method for remotely monitoring and altering brain waves". Latter two rely on brain wave analysis. == In fiction == The decoding of silent speech using a computer played an important role in Arthur C. Clarke's story and Stanley Kubrick's associated film A Space Odyssey. In this, HAL 9000, a computer controlling spaceship Discovery One, bound for Jupiter, discovers a plot to deactivate it by the mission astronauts Dave Bowman and Frank Poole through lip reading their conversations. In Orson Scott Card's series (including Ender's Game), the artificial intelligence can be spoken to while the protagonist wears a movement sensor in his jaw, enabling him to converse with the AI without making noise. He also wears an ear implant. In Speaker for the Dead and subsequent novels, author Orson Scott Card described an ear implant, called a "jewel", that allows subvocal communication with computer systems. Author Robert J. Sawyer made use of subvocal recognition to allow silent commands to the cybernetic 'companion implants' used by the advanced Neanderthal characters in his Neanderthal Parallax trilogy of science fiction novels. In Earth, David Brin depicts this technology and its uses as a normal gear in the near future. In Down and Out in the Magic Kingdom, Cory Doctorow has cellphone technology become silent through a cochlear implant and miking the throat to pick up subvocalization. William Gibson's Sprawl Trilogy frequently uses sub-vocalization systems in various devices. In Kage Baker's Company novels, the immortal cyborgs communicate subvocally. In the Hugo Award-winning Hyperion Cantos by Dan Simmons, the characters often use subvocalization to communicate. In the Culture novels by Iain M. Banks, more highly advanced species often communicate subvocally through their technology. In Deus Ex: Human Revolution (2011), the protagonist is augmented with a subvocalization implant for sending covert communications (and a corresponding cochlear implant for receiving covert communications). In the tabletop RPG and video game series Shadowrun, player characters can communicate via subvocal microphones in some instances. In Paranoia, all citizens can speak to the computer via their "cerebral cortech" implants. Alistair Reynolds Revelation Space trilogy frequently uses sub-vocalization systems in various devices.
RagTime
RagTime is a frame-oriented business publishing software which combines word processing, spreadsheets, simple drawings, image processing, and charts, in a single document/program, integrated software. It is often used to create forms, reports, documentation, desktop publishing, and in office environments. Typical users are business clients, educational institutions, administrations, architects, and also private users. Ragtime includes the following modules: Page layout (forms, templates etc.) Word processing Image processing Spreadsheets, similar to Microsoft Excel Formulas and functions which can be used throughout, in text, graphics, and spreadsheets Charts in different types of diagrams Drawings in vector graphics including lines, polygons, Bézier curves and more Slide show (presentation of RagTime documents) Audio/video Buttons (pop-up menus, switches, and more) that can be used within RagTime documents Import/export of various file formats Support of the AppleScript scripting language available system-wide under macOS == Principle == RagTime differs from most other comparable programs or software packages in its strict frame-oriented design: all content is contained within frames on each page. The content can have a fixed position within its frame or, if it is text or a spreadsheet, flow into another frame that is connected to the first frame via a so-called “pipeline”. RagTime has no different document types for different types of data; all content is stored in a single compound document type. Thus, a RagTime document not only can contain multiple pages, but also multiple layouts within the same document; e.g. spreadsheets in addition to text and images. The RagTime filename extension is .rtd (RagTime document); for templates the extension is .rtt (RagTime template). The current version is RagTime 6.6.5. It is available for OS X (10.6-10.14) and Windows (XP/Vista/7/8/10). == Extensions == FileTime – allows accessing “FileMaker Pro” databases from RagTime documents under OS X RagTime Connect – ODBC database connection for RagTime 6 (Mac and Windows) Johannes – print extension for the simple creation of stapled or folded brochures, booklets etc. PowerFunctions – additional functions for a more effective creation of intelligent documents for exchanging data and for use in mixed Mac/Windows environments MetaFormula – SYLK-based extension that allows calculating text as formula == History == RagTime has been developed since 1985 for the Macintosh – originally named MacFrame – and was published in 1986. When released, it already had the present name, which was chosen following the then-available software package Lotus Jazz. In the European Macintosh market, RagTime quickly gained a prominent position that continues to this day, even though the market share has decreased. Despite repeated attempts, the program could not gain acceptance in the North American market due to its high cost ($395 in 1990). The North American sales office closed in 1991, shortly after Claris Corporation released ClarisWorks which duplicated much of the functionality of RagTime for a lower price. After the manufacturer – first Brüning & Everth, followed by B&E Software and today RagTime.de Development – had focused on the Macintosh only for a very long time, it also released a Windows version, RagTime 5.0, in 1999. However, the program could not assume great significance against established competitors, especially Microsoft Office. Until mid-2006 RagTime was, in addition to the commercial version, also available as a free version (RagTime Solo) for personal use. RagTime Solo included the same features and performance (except for spelling and Syllabification) dictionaries), but was not allowed for use in commercial environments. In other languages RagTime Solo was distributed as RagTime Privat. In a press release from July 5, 2006, RagTime announced the discontinuation of RagTime Solo: “… the RagTime Solo license conditions were often misinterpreted or deliberately flouted. Therefore we discontinued RagTime Solo, there will be no private version of RagTime 6 anymore.” After a successful start of the RagTime 6.0 software, sales edged significantly lower in the following years. Disagreements arose among the shareholders about the continuation of the company, which filed for bankruptcy in July 2007. As a result, the rights to RagTime were taken over by the newly established company RagTime.de Development GmbH, which was responsible for the development. The sales partner RagTime.de Sales GmbH distributed the RagTime products until October 2015. Today RagTime.de Development GmbH is also responsible for sales. The last level of development is the extensively revamped version RagTime 6.6 of 8 October 2015, which also includes new OS X features (e.g. high-resolution “Retina” displays) and supports Windows 10. == Programming == RagTime 1-3 were developed in Pascal, since version 4 the development is completely coded in C++. External programming and automation can be implemented via AppleScript on a Mac, and via OLE/COM-API (e.g. Visual Basic) under Windows. On a Mac, RagTime provides a comprehensive AppleScript library, for the automation of almost any task, from automatic document creation to the export of PDF documents. RagTime also supports “recordings” by use of the “AppleScript Editor”, which allows recording the interactive RagTime operation as an AppleScript program sequence. AppleScripts can be saved in the RagTime document and called via menu or shortcut keys. On Windows, RagTime (since version 6) disposes over an OLE/COM API, which allows automating many RagTime components via external programming. For that purpose there is a type library that installs the available RagTime OLE/COM object catalogue. Programming can be realized in all programming languages supported by Microsoft.
Pulse-coupled networks
Pulse-coupled networks or pulse-coupled neural networks (PCNNs) are neural models proposed by modeling a cat's visual cortex, and developed for high-performance biomimetic image processing. In 1989, Eckhorn introduced a neural model to emulate the mechanism of cat's visual cortex. The Eckhorn model provided a simple and effective tool for studying small mammal’s visual cortex, and was soon recognized as having significant application potential in image processing. In 1994, Johnson adapted the Eckhorn model to an image processing algorithm, calling this algorithm a pulse-coupled neural network. The basic property of the Eckhorn's linking-field model (LFM) is the coupling term. LFM is a modulation of the primary input by a biased offset factor driven by the linking input. These drive a threshold variable that decays from an initial high value. When the threshold drops below zero it is reset to a high value and the process starts over. This is different than the standard integrate-and-fire neural model, which accumulates the input until it passes an upper limit and effectively "shorts out" to cause the pulse. LFM uses this difference to sustain pulse bursts, something the standard model does not do on a single neuron level. It is valuable to understand, however, that a detailed analysis of the standard model must include a shunting term, due to the floating voltages level in the dendritic compartment(s), and in turn this causes an elegant multiple modulation effect that enables a true higher-order network (HON). A PCNN is a two-dimensional neural network. Each neuron in the network corresponds to one pixel in an input image, receiving its corresponding pixel's color information (e.g. intensity) as an external stimulus. Each neuron also connects with its neighboring neurons, receiving local stimuli from them. The external and local stimuli are combined in an internal activation system, which accumulates the stimuli until it exceeds a dynamic threshold, resulting in a pulse output. Through iterative computation, PCNN neurons produce temporal series of pulse outputs. The temporal series of pulse outputs contain information of input images and can be used for various image processing applications, such as image segmentation and feature generation. Compared with conventional image processing means, PCNNs have several significant merits, including robustness against noise, independence of geometric variations in input patterns, capability of bridging minor intensity variations in input patterns, etc. A simplified PCNN called a spiking cortical model was developed in 2009. == Applications == PCNNs are useful for image processing, as discussed in a book by Thomas Lindblad and Jason M. Kinser. PCNNs have been used in a variety of image processing applications, including: image segmentation, pattern recognition, feature generation, face extraction, motion detection, region growing, image denoising and image enhancement Multidimensional pulse image processing of chemical structure data using PCNN has been discussed by Kinser, et al. They have also been applied to an all pairs shortest path problem.
Learning rate
In machine learning and statistics, the learning rate is a tuning parameter in an optimization algorithm that determines the step size at each iteration while moving toward a minimum of a loss function. Since it influences to what extent newly acquired information overrides old information, it metaphorically represents the speed at which a machine learning model "learns". In the adaptive control literature, the learning rate is commonly referred to as gain. In setting a learning rate, there is a trade-off between the rate of convergence and overshooting. While the descent direction is usually determined from the gradient of the loss function, the learning rate determines how big a step is taken in that direction. Too high a learning rate will make the learning jump over minima, but too low a learning rate will either take too long to converge or get stuck in an undesirable local minimum. In order to achieve faster convergence, prevent oscillations and getting stuck in undesirable local minima the learning rate is often varied during training either in accordance to a learning rate schedule or by using an adaptive learning rate. The learning rate and its adjustments may also differ per parameter, in which case it is a diagonal matrix that can be interpreted as an approximation to the inverse of the Hessian matrix in Newton's method. The learning rate is related to the step length determined by inexact line search in quasi-Newton methods and related optimization algorithms. == Learning rate schedule == Initial rate can be left as system default or can be selected using a range of techniques. A learning rate schedule changes the learning rate during learning and is most often changed between epochs/iterations. This is mainly done with two parameters: decay and momentum. There are many different learning rate schedules but the most common are time-based, step-based and exponential. Decay serves to settle the learning in a nice place and avoid oscillations, a situation that may arise when too high a constant learning rate makes the learning jump back and forth over a minimum, and is controlled by a hyperparameter. Momentum is analogous to a ball rolling down a hill; we want the ball to settle at the lowest point of the hill (corresponding to the lowest error). Momentum both speeds up the learning (increasing the learning rate) when the error cost gradient is heading in the same direction for a long time and also avoids local minima by 'rolling over' small bumps. Momentum is controlled by a hyperparameter analogous to a ball's mass which must be chosen manually—too high and the ball will roll over minima which we wish to find, too low and it will not fulfil its purpose. The formula for factoring in the momentum is more complex than for decay but is most often built in with deep learning libraries such as Keras. Time-based learning schedules alter the learning rate depending on the learning rate of the previous time iteration. Factoring in the decay the mathematical formula for the learning rate is: η n + 1 = η 0 1 + d n {\displaystyle \eta _{n+1}={\frac {\eta _{0}}{1+dn}}} where η {\displaystyle \eta } is the learning rate, η 0 {\displaystyle \eta _{0}} is the original learning rate, d {\displaystyle d} is a decay parameter and n {\displaystyle n} is the iteration step. Step-based learning schedules changes the learning rate according to some predefined steps. The decay application formula is here defined as: η n = η 0 d ⌊ 1 + n r ⌋ {\displaystyle \eta _{n}=\eta _{0}d^{\left\lfloor {\frac {1+n}{r}}\right\rfloor }} where η n {\displaystyle \eta _{n}} is the learning rate at iteration n {\displaystyle n} , η 0 {\displaystyle \eta _{0}} is the initial learning rate, d {\displaystyle d} is how much the learning rate should change at each drop (0.5 corresponds to a halving) and r {\displaystyle r} corresponds to the drop rate, or how often the rate should be dropped (10 corresponds to a drop every 10 iterations). The floor function ( ⌊ … ⌋ {\displaystyle \lfloor \dots \rfloor } ) here drops the value of its input to 0 for all values smaller than 1. Exponential learning schedules are similar to step-based, but instead of steps, a decreasing exponential function is used. The mathematical formula for factoring in the decay is: η n = η 0 e − d n {\displaystyle \eta _{n}=\eta _{0}e^{-dn}} where d {\displaystyle d} is a decay parameter. == Adaptive learning rate == The issue with learning rate schedules is that they all depend on hyperparameters that must be manually chosen for each given learning session and may vary greatly depending on the problem at hand or the model used. To combat this, there are many different types of adaptive gradient descent algorithms such as Adagrad, Adadelta, RMSprop, and Adam which are generally built into deep learning libraries such as Keras.
GamePigeon
GamePigeon is a mobile app for iOS devices, developed by Vitalii Zlotskii and released on September 13, 2016. The game takes advantage of the iOS 10 update, which expanded how users could interact with Apple's Messages app. GamePigeon is only available through the Messages app, which allows players to start and respond to different party games in conversations. == Release == The app was first released on September 13, 2016, coinciding with the launch of iOS 10. The app was released for free, although it includes in-app purchases to unlock additional items, such as cosmetic skins, avatar items, new game modes, and an option to remove ads. == Games in the app == The following is a list of games that users can play within GamePigeon: Sources: Poker was one of the games included in GamePigeon at launch, although it has since been removed and is no longer listed on the game's App Store description. == Reception == GamePigeon has enjoyed commercial success, with VentureBeat noting that GamePigeon was ranked number-one in the "Top Free" category of the iMessage App Store, six months after its release. Critically, GamePigeon has been generally well received, being highlighted by online media publications early on shortly after the iOS 10 launch. It has since been included on many "best iMessage apps" lists. Based on over 162,000 ratings, the game holds a 4.0 out of 5 rating on the App Store. Julian Chokkattu of Digital Trends wrote "GamePigeon should be like the pre-installed versions of Solitaire and Minesweeper that used to come with older iterations of Windows." On its launch day, Boy Genius Report included it on a list of "10 of the best iMessage apps, games and stickers for iOS 10 on launch day." The Daily Dot wrote, "GamePigeon is easily the best current gaming option within iMessages." 8-ball and cup pong have been particularly well received by media outlets. The Daily Dot had specific praise for the app's billiards game: "8-Ball controls shockingly smoothly with your fingers, and there’s nothing quite like destroying a dear friend in poker." During his 2020 U.S. presidential campaign, Cory Booker was cited as playing the game with his family. In 2017, CNBC cited one teenager who expressed that GamePigeon was one of just a few reasons that those in her age range use the iMessage app. The game has received particular positive reception for allowing introverted individuals to exercise a form social activity; similarly, the game was highlighted as a way to maintain social distancing guidelines during the COVID-19 pandemic. As an April Fools' Day joke in 2020, The Chronicle, a Duke University newspaper, published that Duke's athletic program adopted GamePigeon's Cup Pong as an official varsity sport.