In artificial intelligence and related fields, an argumentation framework is a way to deal with contentious information and draw conclusions from it using formalized arguments. In an abstract argumentation framework, entry-level information is a set of abstract arguments that, for instance, represent data or a proposition. Conflicts between arguments are represented by a binary relation on the set of arguments. In concrete terms, an argumentation framework is represented with a directed graph such that the nodes are the arguments, and the arrows represent the attack relation. There exist some extensions of the Dung's framework, like the logic-based argumentation frameworks or the value-based argumentation frameworks. == Abstract argumentation frameworks == === Formal framework === Abstract argumentation frameworks, also called argumentation frameworks à la Dung, are defined formally as a pair: A set of abstract elements called arguments, denoted A {\displaystyle A} A binary relation on A {\displaystyle A} , called attack relation, denoted R {\displaystyle R} For instance, the argumentation system S = ⟨ A , R ⟩ {\displaystyle S=\langle A,R\rangle } with A = { a , b , c , d } {\displaystyle A=\{a,b,c,d\}} and R = { ( a , b ) , ( b , c ) , ( d , c ) } {\displaystyle R=\{(a,b),(b,c),(d,c)\}} contains four arguments ( a , b , c {\displaystyle a,b,c} and d {\displaystyle d} ) and three attacks ( a {\displaystyle a} attacks b {\displaystyle b} , b {\displaystyle b} attacks c {\displaystyle c} and d {\displaystyle d} attacks c {\displaystyle c} ). Dung defines some notions : an argument a ∈ A {\displaystyle a\in A} is acceptable with respect to E ⊆ A {\displaystyle E\subseteq A} if and only if E {\displaystyle E} defends a {\displaystyle a} , that is ∀ b ∈ A {\displaystyle \forall b\in A} such that ( b , a ) ∈ R , ∃ c ∈ E {\displaystyle (b,a)\in R,\exists c\in E} such that ( c , b ) ∈ R {\displaystyle (c,b)\in R} , a set of arguments E {\displaystyle E} is conflict-free if there is no attack between its arguments, formally : ∀ a , b ∈ E , ( a , b ) ∉ R {\displaystyle \forall a,b\in E,(a,b)\not \in R} , a set of arguments E {\displaystyle E} is admissible if and only if it is conflict-free and all its arguments are acceptable with respect to E {\displaystyle E} . === Different semantics of acceptance === ==== Extensions ==== To decide if an argument can be accepted or not, or if several arguments can be accepted together, Dung defines several semantics of acceptance that allows, given an argumentation system, sets of arguments (called extensions) to be computed. For instance, given S = ⟨ A , R ⟩ {\displaystyle S=\langle A,R\rangle } , E {\displaystyle E} is a complete extension of S {\displaystyle S} only if it is an admissible set and every acceptable argument with respect to E {\displaystyle E} belongs to E {\displaystyle E} , E {\displaystyle E} is a preferred extension of S {\displaystyle S} only if it is a maximal element (with respect to the set-theoretical inclusion) among the admissible sets with respect to S {\displaystyle S} , E {\displaystyle E} is a stable extension of S {\displaystyle S} only if it is a conflict-free set that attacks every argument that does not belong in E {\displaystyle E} (formally, ∀ a ∈ A ∖ E , ∃ b ∈ E {\displaystyle \forall a\in A\backslash E,\exists b\in E} such that ( b , a ) ∈ R {\displaystyle (b,a)\in R} , E {\displaystyle E} is the (unique) grounded extension of S {\displaystyle S} only if it is the smallest element (with respect to set inclusion) among the complete extensions of S {\displaystyle S} . There exists some inclusions between the sets of extensions built with these semantics : Every stable extension is preferred, Every preferred extension is complete, The grounded extension is complete, If the system is well-founded (there exists no infinite sequence a 0 , a 1 , … , a n , … {\displaystyle a_{0},a_{1},\dots ,a_{n},\dots } such that ∀ i > 0 , ( a i + 1 , a i ) ∈ R {\displaystyle \forall i>0,(a_{i+1},a_{i})\in R} ), all these semantics coincide—only one extension is grounded, stable, preferred, and complete. Some other semantics have been defined. One introduce the notation E x t σ ( S ) {\displaystyle Ext_{\sigma }(S)} to note the set of σ {\displaystyle \sigma } -extensions of the system S {\displaystyle S} . In the case of the system S {\displaystyle S} in the figure above, E x t σ ( S ) = { { a , d } } {\displaystyle Ext_{\sigma }(S)=\{\{a,d\}\}} for every Dung's semantic—the system is well-founded. That explains why the semantics coincide, and the accepted arguments are: a {\displaystyle a} and d {\displaystyle d} . ==== Labellings ==== Labellings are a more expressive way than extensions to express the acceptance of the arguments. Concretely, a labelling is a mapping that associates every argument with a label in (the argument is accepted), out (the argument is rejected), or undec (the argument is undefined—not accepted or refused). One can also note a labelling as a set of pairs ( a r g u m e n t , l a b e l ) {\displaystyle ({\mathit {argument}},{\mathit {label}})} . Such a mapping does not make sense without additional constraint. The notion of reinstatement labelling guarantees the sense of the mapping. L {\displaystyle L} is a reinstatement labelling on the system S = ⟨ A , R ⟩ {\displaystyle S=\langle A,R\rangle } if and only if : ∀ a ∈ A , L ( a ) = i n {\displaystyle \forall a\in A,L(a)={\mathit {in}}} if and only if ∀ b ∈ A {\displaystyle \forall b\in A} such that ( b , a ) ∈ R , L ( b ) = o u t {\displaystyle (b,a)\in R,L(b)={\mathit {out}}} ∀ a ∈ A , L ( a ) = o u t {\displaystyle \forall a\in A,L(a)={\mathit {out}}} if and only if ∃ b ∈ A {\displaystyle \exists b\in A} such that ( b , a ) ∈ R {\displaystyle (b,a)\in R} and L ( b ) = i n {\displaystyle L(b)={\mathit {in}}} ∀ a ∈ A , L ( a ) = u n d e c {\displaystyle \forall a\in A,L(a)={\mathit {undec}}} if and only if L ( a ) ≠ i n {\displaystyle L(a)\neq {\mathit {in}}} and L ( a ) ≠ o u t {\displaystyle L(a)\neq {\mathit {out}}} One can convert every extension into a reinstatement labelling: the arguments of the extension are in, those attacked by an argument of the extension are out, and the others are undec. Conversely, one can build an extension from a reinstatement labelling just by keeping the arguments in. Indeed, Caminada proved that the reinstatement labellings and the complete extensions can be mapped in a bijective way. Moreover, the other Datung's semantics can be associated to some particular sets of reinstatement labellings. Reinstatement labellings distinguish arguments not accepted because they are attacked by accepted arguments from undefined arguments—that is, those that are not defended cannot defend themselves. An argument is undec if it is attacked by at least another undec. If it is attacked only by arguments out, it must be in, and if it is attacked some argument in, then it is out. The unique reinstatement labelling that corresponds to the system S {\displaystyle S} above is L = { ( a , i n ) , ( b , o u t ) , ( c , o u t ) , ( d , i n ) } {\displaystyle L=\{(a,{\mathit {in}}),(b,{\mathit {out}}),(c,{\mathit {out}}),(d,{\mathit {in}})\}} . === Inference from an argumentation system === In the general case when several extensions are computed for a given semantic σ {\displaystyle \sigma } , the agent that reasons from the system can use several mechanisms to infer information: Credulous inference: the agent accepts an argument if it belongs to at least one of the σ {\displaystyle \sigma } -extensions—in which case, the agent risks accepting some arguments that are not acceptable together ( a {\displaystyle a} attacks b {\displaystyle b} , and a {\displaystyle a} and b {\displaystyle b} each belongs to an extension) Skeptical inference: the agent accepts an argument only if it belongs to every σ {\displaystyle \sigma } -extension. In this case, the agent risks deducing too little information (if the intersection of the extensions is empty or has a very small cardinal). For these two methods to infer information, one can identify the set of accepted arguments, respectively C r σ ( S ) {\displaystyle Cr_{\sigma }(S)} the set of the arguments credulously accepted under the semantic σ {\displaystyle \sigma } , and S c σ ( S ) {\displaystyle Sc_{\sigma }(S)} the set of arguments accepted skeptically under the semantic σ {\displaystyle \sigma } (the σ {\displaystyle \sigma } can be missed if there is no possible ambiguity about the semantic). Of course, when there is only one extension (for instance, when the system is well-founded), this problem is very simple: the agent accepts arguments of the unique extension and rejects others. The same reasoning can be done with labellings that correspond to the chosen semantic : an argument can be accepted if it is in for each labelling and refused if it is out for each labelling, the others being in an undecided state (the status of the arguments can remind the
Airfair
AirFair was a mobile travel application that checks flights, and shows whether a traveler is owed compensation. == History == AirFair was developed in 2016 by Allay Logic Ltd; a Newcastle-based tech-company. == Services == AirFair offered a free flight check to see if compensation is owed. The app could indicate how much the person is owed within minutes whether the flight was delayed, cancelled or the traveler is refused boarding.
Media aggregation platform
A Media Aggregation Platform or Media Aggregation Portal (MAP) is an over the top service for distributing web-based streaming media content from multiple sources to a large audience. MAPs consist of networks of sources who host their own content which viewers can choose and access directly from a larger variety of content to choose from than a single source can offer. The service is used by content providers, looking to extend the reach of their content. Unlike multichannel video programming distributor (MVPD) or multiple-system operators (MSO), MAPs rely on the Internet rather than cables or satellite. As more network television channels have moved online in the early 21st century, joining web-native channels like Netflix, MAPs aggregate content the way that MSOs and MVPDs have used cable, and to a lesser extent satellite and IPTV infrastructure. There are companies that offer a similar service for free, including Yidio and StreamingMoviesRight, while others charge a subscription fee like as FreeCast Inc's Rabbit TV Plus. When compared with MSOs and MVPDs, MAP networks have much lower costs due to lack of physical infrastructure. The majority of revenue from MAP services are retained by the content creators, and revenue is instead collected from advertisements, pay-per-view, and subscription-based content offerings instead of licensing and reselling content. MAP service consumers interact and purchase content directly from its source, without the markup added by a middleman.
Best arm identification
Best arm identification (BAI) is a sequential one-player game where the player has to find the best action (arm) among a list of actions (arms) by collecting information in the most efficient way. It is a multi-armed bandit game as a player only gets information about an arm by playing it. The most common objective in multi-armed bandit games is to minimize the regret (i.e., play the best action as much as possible), but in BAI, the goal is to find the best arm as efficiently as possible. This problem naturally arises in scenarios such as adaptive clinical trials where the number of patients is limited and the quantification of the confidence in a treatment is important. It also arises in hyperparameter optimization where the goal is to find the optimal choice of hyperparameters for an algorithm with the smallest possible number of experiments, as it can be costly in terms of time, energy, or money. == Stochastic multi-armed bandit == The stochastic multi-armed bandit (MAB) is a sequential game with one player and K {\displaystyle K} actions (arms). Each arm has an unknown probability distribution associated with it. At each turn, the player has to choose one action and receive an observation from the probability distribution associated with the arm. The more you play an arm, the more you get information on its probability distribution. === Best arm identification === In BAI the goal is to find the arm that has the probability distribution with the highest mean. BAI may be either fixed confidence or fixed horizon. In a fixed-confidence game, a confidence level δ {\displaystyle \delta } is fixed at the beginning of the game and the goal is to find the best arm with this confidence level in as few turns as possible. In a fixed horizon game, the number of turns T {\displaystyle T} is fixed, and the goal is to find the best arm with the highest possible confidence in T {\displaystyle T} turns. === Math formalisation === We have one player and K {\displaystyle K} actions (arms). Behind each arm k ∈ { 1 , … , K } {\displaystyle k\in \{1,\ldots ,K\}} lies an unknown distribution ν k {\displaystyle \nu _{k}} with mean μ k {\displaystyle \mu _{k}} . Each distribution ν k {\displaystyle \nu _{k}} belongs to a known family D {\displaystyle {\mathcal {D}}} (such as the set of Gaussian distributions or Bernoulli distributions). At each time step t {\displaystyle t} , the player selects an arm a t {\displaystyle a_{t}} and observes an independent sample X t ∼ ν a t {\displaystyle X_{t}\sim \nu _{a_{t}}} from the corresponding distribution. We will note μ ∗ := max μ a {\displaystyle \mu ^{}:=\max \mu _{a}} the highest mean. An arm a {\displaystyle a} that satisfies μ a = μ ∗ {\displaystyle \mu _{a}=\mu ^{}} is called an optimal arm; otherwise it is called suboptimal arm. In best arm identification (BAI) the objective is to identify an optimal arm. Two main settings for BAI appear in the literature: Fixed confidence: In this setting, one typically assumes that there exists a unique optimal arm. A confidence level δ ∈ ( 0 , 1 ) {\displaystyle \delta \in (0,1)} is specified at the beginning. The algorithm must stop at some finite stopping time τ δ < + ∞ {\displaystyle \tau _{\delta }<+\infty } and return an arm a ^ τ δ {\displaystyle {\hat {a}}_{\tau _{\delta }}} such that the probability of error is bounded: P ( a ^ τ δ ≠ a ∗ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau _{\delta }}\neq a^{})\leq \delta } . The objective is to minimize the expected sample complexity E [ τ δ ] {\displaystyle \mathbb {E} [\tau _{\delta }]} . Such a setting appears, for example, when a constraint on the confidence is required (for example, if we require a confidence level of 95%, so δ = 1 − 0.95 = 0.05 {\displaystyle \delta =1-0.95=0.05} ). Fixed horizon: In this setting, the number of samples T {\displaystyle T} is fixed in advance. The goal is to design an algorithm that minimizes the probability of misidentifying the optimal arm: P ( a ^ T ≠ a ∗ ) {\displaystyle \mathbb {P} ({\hat {a}}_{T}\neq a^{})} . This setting appears when the number of experiments is limited (for drug tests, the number of patients can be fixed in advance). === Example of simple modelling === In the case where we have K {\displaystyle K} treatments and we want to be sure with a confidence level of 95% which treatment is the best to heal a specific disease. Each treatment heals or does not heal the disease with a probability μ k {\displaystyle \mu _{k}} , which means that each distribution is a Bernoulli distribution, so D {\displaystyle {\mathcal {D}}} is the set of Bernoulli distributions. We can use a BAI algorithm to minimize E [ τ 0.05 ] {\displaystyle \mathbb {E} [\tau _{0.05}]} , the number of patients required to find the best treatment with probability 95%. == Applications == Best arm identification naturally arises in several practical domains: Adaptive clinical trials: The objective is to identify the most effective treatment based on sequentially collected patient data. Each treatment can be modeled as having an underlying distribution of outcomes. The goal is to identify the treatment with the highest expected outcome with high confidence (fixed confidence setting δ {\displaystyle \delta } ) while minimizing the number of drug test patients (minimise E [ τ δ ] {\displaystyle \mathbb {E} [\tau _{\delta }]} ), as it costs to pay patients for this and we would like to use as little as possible less effective drugs. Hyperparameter tuning: Selecting the best configuration for machine learning models efficiently by treating each hyperparameter setting as an arm. The goal is to find the best hyperparameter with as few experiments possible as experiments are costly in time and in energy == Fixed confidence level == In the fixed-confidence setting, the goal is to design an algorithm that identifies the best arm with a prescribed confidence level δ {\displaystyle \delta } while minimizing the expected number of samples. Any such algorithm requires two key components: Stopping rule: A decision criterion that determines when to stop sampling. Formally, this defines a stopping time τ δ {\displaystyle \tau _{\delta }} and returns an arm a ^ τ δ {\displaystyle {\hat {a}}_{\tau _{\delta }}} such that P ( a ^ τ δ ≠ a ⋆ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau _{\delta }}\neq a^{\star })\leq \delta } and P ( τ δ < + ∞ ) = 1 {\displaystyle \mathbb {P} (\tau _{\delta }<+\infty )=1} . Sampling rule: A policy π {\displaystyle \pi } that, at each round t {\displaystyle t} , selects the next arm to sample a t {\displaystyle a_{t}} based on all previous observations ( a s , X s ) s < t {\displaystyle (a_{s},X_{s})_{s The Brian Deer Classification System (BDC) is a library classification system used to organize materials in libraries with specialized Indigenous collections. The system was created in the mid-1970s by Canadian librarian A. Brian Deer, a Kahnawake Mohawk. It has been adapted for use in a British Columbia version, and also by a small number of First Nations libraries in Canada. == History and usage == Deer designed his classification system while working in the library of the National Indian Brotherhood (now the Assembly of First Nations) from 1974 to 1976. Instead of using a standard library classification scheme, such as that of the Library of Congress, he created a new system to organize the library's historic indigenous research materials and papers. He later worked at the library of the Union of British Columbia Indian Chiefs, where he developed a system for its holdings. He returned to Kahnawake, working at its Cultural Centre at Kahnawake and the Kahnawake Branch branch of the Mohawk Nation Office. His system was flexible, and he created new forms for their collections. The new systems Deer created were designed specifically for the materials in each collection according to the concerns of local Indigenous people at the time (for example, categories included land claims, treaty rights, resource management, and Elders' stories). Between 1978 and 1980, the system was adapted for use in British Columbia by Gene Joseph and Keltie McCall while they were working at the Union of British Columbia Indian Chiefs, becoming known as BDC-BC. Joseph later adapted it further for use in the Xwi7xwa Library at University of British Columbia, Vancouver. Though the Brian Deer Classification was not created as a universal classification solution for Indigenous resources, the system has provided a foundation for specialized libraries to create their own localized classification schemes. Variations of the Brian Deer Classification System are used in a small number of Canadian libraries. One prominent library using BDC is the X̱wi7x̱wa Library at the University of British Columbia, which uses a British Columbia-focused version of BDC along with First Nations House of Learning subject headings. The Union of British Columbia Indian Chiefs Resource Centre issued a revised BDC-BC in 2014, with the goal of providing users with a more flexible and culturally appropriate approach to organizing their resources. The Aanischaaukamikw Cree Cultural Institute in Oujé-Bougoumou, Quebec, implemented a local adaptation of BDC when they opened in 2012. In 2020 the Carrier Sekani Tribal Council in Prince George, British Columbia, shifted from organizing its library with the Dewey Decimal Classification to using a version of the BDC. They added new subject heading categories for topics of local interest such as the crisis of Missing and murdered Indigenous women. Simon Fraser University Library began developing the Indigenous Curriculum Resource Centre (ICRC) in 2020, with the physical space opening in 2023. The ICRC is Call to Action 21 of SFU's Aboriginal Reconciliation Council's final report, Walk This Path With Us. Through its collection, the ICRC supports those interested in learning about how and why decolonizing pedagogy and teaching practices are important. The physical items in the collection are catalogued using a modified Brian Deer Classification system. In 2022 Kwantlen Polytechnic University’s χʷəχʷéy̓əm Indigenous Collection released a revised BDC-BC System. This BDC contains works exclusively with Indigenous authored materials and expands the cuttering systems of previous BDC, with the result that much of the collection reflects a spatial relationality. The implementation of this BDC was possible due to the tireless work at Xwi7xwa Library, Union of British Columbia Indian Chiefs Resource Centre, and Simon Fraser University Library's Indigenous Curriculum Resource Centre. == Structure == The high-level organizational structure of BDC reflects a First Nations worldview, with an emphasis on relationships between and among people, animals, and the land. Subcategories demonstrate the relationships among First Nations by grouping them geographically as opposed to alphabetically; the latter is a practice frequently used for specific topics in the Library of Congress Classification. The top-level hierarchy of the X̱wi7x̱wa Library adaptation of BDC-BC demonstrates the emphasis on access to subjects prioritized by a First Nation collection: Reference Materials Local History History International Education Economic Development Housing and Community Development Criminal Justice System Constitution (Canada) and First Nations Self Government Rights and Title Natural Resources Community Resources Health World View Fine Arts Languages Literature The system is not designed to provide a comprehensive description of all topics of interest to North American Indigenous peoples; in addition, its use is limited in scope, being intended for small and specialized libraries. While English is used in the classification scheme as a common language among First Nations peoples and non-Indigenous library users, Indigenous spellings and terminology that local library users would expect to find are used to provide access. Short and easily remembered call numbers are used to facilitate use by both library workers and patrons, with the recognition that Indigenous libraries often have a small staff and limited resources to devote to cataloging. Beyond its simplicity, one potential drawback of the system is its shortage of clear guidelines for application, which provides flexibility but can also result in inconsistencies within and between library catalogs. Because few libraries use the BDC and there are limited examples for use as case studies, implementing the system and keeping it up-to-date can prove a challenge for libraries with limited resources. However, X̱wi7x̱wa Library head librarian Ann Doyle describes the system as "an important part of the body of Indigenous scholarship" that should be retained as a reflection of Indigenous worldviews, as well as for ease of access for Indigenous library users. 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. Collective operations are building blocks for interaction patterns, that are often used in SPMD algorithms in the parallel programming context. Hence, there is an interest in efficient realizations of these operations. A realization of the collective operations is provided by the Message Passing Interface (MPI). == Definitions == In all asymptotic runtime functions, we denote the latency α {\displaystyle \alpha } (or startup time per message, independent of message size), the communication cost per word β {\displaystyle \beta } , the number of processing units p {\displaystyle p} and the input size per node n {\displaystyle n} . In cases where we have initial messages on more than one node we assume that all local messages are of the same size. To address individual processing units we use p i ∈ { p 0 , p 1 , … , p p − 1 } {\displaystyle p_{i}\in \{p_{0},p_{1},\dots ,p_{p-1}\}} . If we do not have an equal distribution, i.e. node p i {\displaystyle p_{i}} has a message of size n i {\displaystyle n_{i}} , we get an upper bound for the runtime by setting n = max ( n 0 , n 1 , … , n p − 1 ) {\displaystyle n=\max(n_{0},n_{1},\dots ,n_{p-1})} . A distributed memory model is assumed. The concepts are similar for the shared memory model. However, shared memory systems can provide hardware support for some operations like broadcast (§ Broadcast) for example, which allows convenient concurrent read. Thus, new algorithmic possibilities can become available. == Broadcast == The broadcast pattern is used to distribute data from one processing unit to all processing units, which is often needed in SPMD parallel programs to dispense input or global values. Broadcast can be interpreted as an inverse version of the reduce pattern (§ Reduce). Initially only root r {\displaystyle r} with i d {\displaystyle id} 0 {\displaystyle 0} stores message m {\displaystyle m} . During broadcast m {\displaystyle m} is sent to the remaining processing units, so that eventually m {\displaystyle m} is available to all processing units. Since an implementation by means of a sequential for-loop with p − 1 {\displaystyle p-1} iterations becomes a bottleneck, divide-and-conquer approaches are common. One possibility is to utilize a binomial tree structure with the requirement that p {\displaystyle p} has to be a power of two. When a processing unit is responsible for sending m {\displaystyle m} to processing units i . . j {\displaystyle i..j} , it sends m {\displaystyle m} to processing unit ⌈ ( i + j ) / 2 ⌉ {\displaystyle \left\lceil (i+j)/2\right\rceil } and delegates responsibility for the processing units ⌈ ( i + j ) / 2 ⌉ . . j {\displaystyle \left\lceil (i+j)/2\right\rceil ..j} to it, while its own responsibility is cut down to i . . ⌈ ( i + j ) / 2 ⌉ − 1 {\displaystyle i..\left\lceil (i+j)/2\right\rceil -1} . Binomial trees have a problem with long messages m {\displaystyle m} . The receiving unit of m {\displaystyle m} can only propagate the message to other units, after it received the whole message. In the meantime, the communication network is not utilized. Therefore pipelining on binary trees is used, where m {\displaystyle m} is split into an array of k {\displaystyle k} packets of size ⌈ n / k ⌉ {\displaystyle \left\lceil n/k\right\rceil } . The packets are then broadcast one after another, so that data is distributed fast in the communication network. Pipelined broadcast on balanced binary tree is possible in O ( α log p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} , whereas for the non-pipelined case it takes O ( ( α + β n ) log p ) {\displaystyle {\mathcal {O}}((\alpha +\beta n)\log p)} cost. == Reduce == The reduce pattern is used to collect data or partial results from different processing units and to combine them into a global result by a chosen operator. Given p {\displaystyle p} processing units, message m i {\displaystyle m_{i}} is on processing unit p i {\displaystyle p_{i}} initially. All m i {\displaystyle m_{i}} are aggregated by ⊗ {\displaystyle \otimes } and the result is eventually stored on p 0 {\displaystyle p_{0}} . The reduction operator ⊗ {\displaystyle \otimes } must be associative at least. Some algorithms require a commutative operator with a neutral element. Operators like s u m {\displaystyle sum} , m i n {\displaystyle min} , m a x {\displaystyle max} are common. Implementation considerations are similar to broadcast (§ Broadcast). For pipelining on binary trees the message must be representable as a vector of smaller object for component-wise reduction. Pipelined reduce on a balanced binary tree is possible in O ( α log p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} . == All-Reduce == The all-reduce pattern (also called allreduce) is used if the result of a reduce operation (§ Reduce) must be distributed to all processing units. Given p {\displaystyle p} processing units, message m i {\displaystyle m_{i}} is on processing unit p i {\displaystyle p_{i}} initially. All m i {\displaystyle m_{i}} are aggregated by an operator ⊗ {\displaystyle \otimes } and the result is eventually stored on all p i {\displaystyle p_{i}} . Analog to the reduce operation, the operator ⊗ {\displaystyle \otimes } must be at least associative. All-reduce can be interpreted as a reduce operation with a subsequent broadcast (§ Broadcast). For long messages a corresponding implementation is suitable, whereas for short messages, the latency can be reduced by using a hypercube (Hypercube (communication pattern) § All-Gather/ All-Reduce) topology, if p {\displaystyle p} is a power of two. All-reduce can also be implemented with a butterfly algorithm and achieve optimal latency and bandwidth. All-reduce is possible in O ( α log p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} , since reduce and broadcast are possible in O ( α log p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} with pipelining on balanced binary trees. All-reduce implemented with a butterfly algorithm achieves the same asymptotic runtime. == Prefix-Sum/Scan == The prefix-sum or scan operation is used to collect data or partial results from different processing units and to compute intermediate results by an operator, which are stored on those processing units. It can be seen as a generalization of the reduce operation (§ Reduce). Given p {\displaystyle p} processing units, message m i {\displaystyle m_{i}} is on processing unit p i {\displaystyle p_{i}} . The operator ⊗ {\displaystyle \otimes } must be at least associative, whereas some algorithms require also a commutative operator and a neutral element. Common operators are s u m {\displaystyle sum} , m i n {\displaystyle min} and m a x {\displaystyle max} . Eventually processing unit p i {\displaystyle p_{i}} stores the prefix sum ⊗ i ′ <= i {\displaystyle \otimes _{i'<=i}} m i ′ {\displaystyle m_{i'}} . In the case of the so-called exclusive prefix sum, processing unit p i {\displaystyle p_{i}} stores the prefix sum ⊗ i ′ < i {\displaystyle \otimes _{i'Brian Deer Classification System
RagTime
Collective operation