Taskworld is a cloud-based collaboration platform created by Fred Mouawad. The SaaS (software as a service) is designed to facilitate project and task management, collaboration, delegation, communication, knowledge management, measure progress and provide performance metrics for evidence-based evaluations within teams. It allows team members to assign and receive tasks, add followers, record comments, share and store unlimited files and organize projects. == Background == An initial version of Taskworld was custom-built by the IT team working for Mouawad in 2006. This was done as a way to try and overcome internal issues regarding delegation, accountability and time-management. The application was constructed to prevent tasks from falling through the cracks and make it easy to follow up on-going projects where many individuals throughout various departments of the organization were involved. Mouawad’s Synergia One group of companies later implemented the application internally as the ‘Task Management System’ and found a general improvement in execution across international offices and departments. This successful implementation led Mouawad to found the ‘My Taskworld’ website which later evolved into ‘Taskworld.' The company was officially founded in February 2012, and in June later that year, Mouawad presented a prototype of the Taskworld website to an Executive Program at the Stanford Graduate School of Business. == Reception == The launch of the app was covered by the media as an addition to the Synergia One group of companies founded by CEO Fred Mouawad. The mobile app is currently available on both android and iOS platforms. Google Play gives the app 3.8 out of 5 stars while the Apple App Store gave it 2.9 out of 5 stars. Alex Williams in a 2014 article for Tech Crunch said, “Taskworld’s technology plays to human emotions. As the feedback is continuous, people are compelled to engage with the service. But in some respects, Taskworld is fairly simple and still needing more to make it a potent competitor in the market.” == Features == Taskworld's main features include, but are not limited to: Project &Task Management - Taskworld includes up to five levels of hierarchy including Project Group, Project, Tasklist, Task and Checklist. Some features in this group are assigning tasks, setting due dates, adding followers, task comments, set repeating tasks, tasks in multiple locations, project templates, copy project, archiving, smart notifications, drag and drop Kanban boards, image preview boards, file management, people page and personnel directory, customizable tags and colored labels. Enterprise Messaging - The app includes a native chat application with channels and groups, private and direct messaging capabilities. Other communication features inside of the app include project chat, drag and drop file attachments, an email bridge to send and receive messages and @mentions. Overview & Analytics - Taskworld includes several features under this section including a dashboard, workspace snapshot, workspace filter, interactive calendar, project analytics and health status, project burndown chart, project burn-up chart and interactive timeline. == Languages and customers == Taskworld is used by 4,000 companies in 80 countries. The app is currently available in eight languages: English, French, German, Spanish, Mandarin, Portuguese, Thai and Korean. == Customer support == The Taskworld User Guide offers details on how to use features of the application. Customer support is offered inside of the application for questions and feedback regarding the software, and also via email. The Taskworld customer support team has received a 98% Customer Satisfaction Rating, according to customer ratings on its support platform Zendesk. Free, live demos are also offered for those companies who need assistance.
Collision detection
Collision detection is the computational problem of detecting an intersection of two or more objects in virtual space. More precisely, it deals with the questions of if, when, and where two or more objects intersect. Collision detection is a classic problem of computational geometry with applications in computer graphics, physical simulation, video games, robotics (including autonomous driving), and computational physics. Collision detection algorithms can be divided into operating on 2D or 3D spatial objects. == Overview == Collision detection is closely linked to calculating the distance between objects, as objects collide when the distance between them is less than or equal to zero. Negative distances indicate that one object has penetrated another. Performing collision detection requires more context than just the distance between the objects. Accurately identifying the points of contact on both objects' surfaces is also essential for computing a physically accurate collision response. The complexity of this task increases with the level of detail in the objects' representations: the more intricate the model, the greater the computational cost. Collision detection frequently involves dynamic objects, adding a temporal dimension to distance calculations. Instead of simply measuring distance between static objects, collision detection algorithms often aim to determine whether the objects' motion will bring them to a point in time when their distance is zero—an operation that adds significant computational overhead. In collision detection involving multiple objects, a naive approach would require detecting collisions for all pairwise combinations of objects. As the number of objects increases, the number of required comparisons grows rapidly: for n {\displaystyle n} objects, n ( n − 1 ) / 2 {n(n-1)}/{2} intersection tests are needed with a naive approach. This quadratic growth makes such an approach computationally expensive as n {\displaystyle n} increases. Due to the complexity mentioned above, collision detection is a computationally intensive process. Nevertheless, it is essential for interactive applications like video games, robotics, and real-time physics engines. To manage these computational demands, extensive efforts have gone into optimizing collision detection algorithms. A commonly used approach towards accelerating the required computations is to divide the process into two phases: the broad phase and the narrow phase. The broad phase aims to answer the question of whether objects might collide, using a conservative but efficient approach to rule out pairs that clearly do not intersect, thus avoiding unnecessary calculations. Objects that cannot be definitively separated in the broad phase are passed to the narrow phase. Here, more precise algorithms determine whether these objects actually intersect. If they do, the narrow phase often calculates the exact time and location of the intersection. == Broad phase == This phase aims at quickly finding objects or parts of objects for which it can be quickly determined that no further collision test is needed. A useful property of such approach is that it is output sensitive. In the context of collision detection this means that the time complexity of the collision detection is proportional to the number of objects that are close to each other. An early example of that is the I-COLLIDE where the number of required narrow phase collision tests was O ( n + m ) {\displaystyle O(n+m)} where n {\displaystyle n} is the number of objects and m {\displaystyle m} is the number of objects at close proximity. This is a significant improvement over the quadratic complexity of the naive approach. === Spatial partitioning === Several approaches can be grouped under the spatial partitioning umbrella, which includes octrees (for 3D), quadtrees (for 2D), binary space partitioning (or BSP trees) and other, similar approaches. If one splits space into a number of simple cells, and if two objects can be shown not to be in the same cell, then they need not be checked for intersection. Dynamic scenes and deformable objects require updating the partitioning which can add overhead. === Bounding volume hierarchy === Bounding Volume Hierarchy (BVH) is a tree structure over a set of bounding volumes. Collision is determined by doing a tree traversal starting from the root. If the bounding volume of the root doesn't intersect with the object of interest, the traversal can be stopped. If, however there is an intersection, the traversal proceeds and checks the branches for each there is an intersection. Branches for which there is no intersection with the bounding volume can be culled from further intersection test. Therefore, multiple objects can be determined to not intersect at once. BVH can be used with deformable objects such as cloth or soft-bodies but the volume hierarchy has to be adjusted as the shape deforms. For deformable objects we need to be concerned about self-collisions or self intersections. BVH can be used for that end as well. Collision between two objects is computed by computing intersection between the bounding volumes of the root of the tree as there are collision we dive into the sub-trees that intersect. Exact collisions between the actual objects, or its parts (often triangles of a triangle mesh) need to be computed only between intersecting leaves. The same approach works for pair wise collision and self-collisions. === Exploiting temporal coherence === During the broad-phase, when the objects in the world move or deform, the data-structures used to cull collisions have to be updated. In cases where the changes between two frames or time-steps are small and the objects can be approximated well with axis-aligned bounding boxes, the sweep and prune algorithm can be a suitable approach. Several key observation make the implementation efficient: Two bounding-boxes intersect if, and only if, there is overlap along all three axes; overlap can be determined, for each axis separately, by sorting the intervals for all the boxes; and lastly, between two frames updates are typically small (making sorting algorithms optimized for almost-sorted lists suitable for this application). The algorithm keeps track of currently intersecting boxes, and as objects move, re-sorting the intervals helps keep track of the status. === Pairwise pruning === Once a pair of physical bodies has been selected for further investigation, collisions need to be checked more carefully. However, in many applications, individual objects (if they are not too deformable) are described by a set of smaller primitives, mainly triangles. So there are two sets of triangles, S = S 1 , S 2 , … , S n {\displaystyle S={S_{1},S_{2},\dots ,S_{n}}} and T = T 1 , T 2 , … , T n {\displaystyle T={T_{1},T_{2},\dots ,T_{n}}} (for simplicity, each set has the same number of triangles.) The obvious thing to do is to check all triangles S j {\displaystyle S_{j}} against all triangles T k {\displaystyle T_{k}} for collisions, but this involves n 2 {\displaystyle n^{2}} comparisons, which is highly inefficient. If possible, it is desirable to use a pruning algorithm to reduce the number of pairs of triangles that need to be checked. The most widely used family of algorithms is known as the hierarchical bounding volumes method. As a preprocessing step, for each object (e.g., S {\displaystyle S} and T {\displaystyle T} ) calculates a hierarchy of bounding volumes. Then, at each time step, when collisions need to be checked between S {\displaystyle S} and T {\displaystyle T} , the hierarchical bounding volumes are used to reduce the number of pairs of triangles under consideration. For simplicity, provide an example using bounding spheres, although it has been noted that spheres are undesirable in many cases. If E {\displaystyle E} is a set of triangles, a bounding sphere is pre-calculated. B ( E ) {\displaystyle B(E)} . There are many ways of choosing B ( E ) {\displaystyle B(E)} , B ( E ) {\displaystyle B(E)} is a sphere that completely contains E {\displaystyle E} and is as small as possible. Ahead of time, B ( S ) {\displaystyle B(S)} and B ( T ) {\displaystyle B(T)} can be computed. Clearly, if these two spheres do not intersect (and that is very easy to test), then neither do S {\displaystyle S} and T {\displaystyle T} . This is not much better than an n-body pruning algorithm, however. If E = E 1 , E 2 , … , E m {\displaystyle E={E_{1},E_{2},\dots ,E_{m}}} is a set of triangles, then split it into two halves L ( E ) := E 1 , E 2 , … , E m / 2 {\displaystyle L(E):={E_{1},E_{2},\dots ,E_{m/2}}} and R ( E ) := E m / 2 + 1 , … , E m − 1 , E m {\displaystyle R(E):={E_{m/2+1},\dots ,E_{m-1},E_{m}}} . Apply this to S {\displaystyle S} and T {\displaystyle T} , and calculate (ahead of time) the bounding spheres B ( L ( S ) ) , B ( R ( S ) ) {\displaystyle B(L(S)),B(R(S))} and B ( L ( T ) ) , B ( R ( T ) ) {\displaystyle B(L(T)),B(R(T))} . T
Fuzzy mathematics
Fuzzy mathematics is a branch of mathematics that extends classical set theory and logic to model reasoning under uncertainty. Initiated by Lotfi Asker Zadeh in 1965 with the introduction of fuzzy sets, the field has since evolved to include fuzzy set theory, fuzzy logic, and various fuzzy analogues of traditional mathematic structures. Unlike classical mathematics, which usually relies on binary membership (an element either belongs to a set or it does not), fuzzy mathematics allows elements to partially belong to a set, with degrees of membership represented by values in the interval [0, 1]. This framework enables more flexible modeling of imprecise or vague concepts. Fuzzy mathematics has found applications in numerous domains, including control theory, artificial intelligence, decision theory, pattern recognition, and linguistics, where the modeling of gradations and uncertainty is essential. == Definition == A fuzzy subset A of a set X is defined by a function A: X → L, where L is typically the interval [0, 1]. This function is called the membership function of the fuzzy subset and assigns to each element x in X a degree of membership A(x) in the fuzzy set A. In classical set theory, a subset of X can be represented by an indicator function (also known as a characteristic function), which maps elements to either 0 or 1, indicating non-membership or full membership, respectively. Fuzzy subsets generalize this concept by allowing any real value between 0 and 1, thereby enabling partial membership. More generally, the codomain L of the membership function can be replaced with any complete lattice, resulting in the broader framework of L-fuzzy sets. == Fuzzification == The development of fuzzification in mathematics can be broadly divided into three historical stages: Initial, straightforward fuzzifications (1960s–1970s), Expansion of generalization techniques (1980s), Standardization, axiomatization, and L-fuzzification (1990s). Fuzzification generally involves extending classical mathematical concepts from binary (crisp) logic, where membership is determined by characteristic functions, to fuzzy logic, where membership is expressed by values in the interval [0, 1] via membership functions. Let A and B be fuzzy subsets of a set X. The fuzzy versions of set-theoretic operations are commonly defined as: ( A ∩ B ) ( x ) = min ( A ( x ) , B ( x ) ) {\displaystyle (A\cap B)(x)=\min(A(x),B(x))} ( A ∪ B ) ( x ) = max ( A ( x ) , B ( x ) ) {\displaystyle (A\cup B)(x)=\max(A(x),B(x))} for all x ∈ X {\displaystyle x\in X} . These operations can be generalized using t-norms and t-conorms, respectively. For example, the minimum operation can be replaced by multiplication: ( A ∩ B ) ( x ) = A ( x ) ⋅ B ( x ) {\displaystyle (A\cap B)(x)=A(x)\cdot B(x)} Fuzzification of algebraic structures often relies on generalizing the closure property. Let ∗ {\displaystyle } be a binary operation on X, and let A be a fuzzy subset of X. Then A is said to satisfy fuzzy closure if: A ( x ∗ y ) ≥ min ( A ( x ) , A ( y ) ) {\displaystyle A(xy)\geq \min(A(x),A(y))} for all x , y ∈ X {\displaystyle x,y\in X} . If ( G , ∗ ) {\displaystyle (G,)} is a group, then a fuzzy subset A of G is a fuzzy subgroup if: A ( x ∗ y − 1 ) ≥ min ( A ( x ) , A ( y − 1 ) ) {\displaystyle A(xy^{-1})\geq \min(A(x),A(y^{-1}))} for all x , y ∈ G {\displaystyle x,y\in G} . Similar generalizations apply to relational properties. For example, for example, for fuzzification of the transitivity property, a fuzzy relation R {\displaystyle R} on X {\displaystyle X} (i.e., a fuzzy subset of X × X {\displaystyle X\times X} ) is said to be fuzzy transitive if: R ( x , z ) ≥ min ( R ( x , y ) , R ( y , z ) ) {\displaystyle R(x,z)\geq \min(R(x,y),R(y,z))} for all x , y , z ∈ X {\displaystyle x,y,z\in X} . == Fuzzy analogues == Fuzzy subgroupoids and fuzzy subgroups were introduced in 1971 by A. Rosenfeld. Analogues of other mathematical subjects have been translated to fuzzy mathematics, such as fuzzy field theory and fuzzy Galois theory, fuzzy topology, fuzzy geometry, fuzzy orderings, and fuzzy graphs.
Dry Drowning
Dry Drowning is a cyberpunk mystery visual novel developed by Studio V and published by VLG Publishing and WhisperGames for Microsoft Windows on August 2, 2019. It was released on the Nintendo Switch on February 22, 2021. == Gameplay == The player takes control of Mordred Foley and has to read through the story, while making decisions at certain points. Depending on the choices, the player can influence the relationship to other characters as well as the course of the game, discovering more than 150 story branches, and eventually reach one out of three different endings with variations. The game also includes passages where the player has to find clues or items on the screen by clicking on them. These can be used in interrogation scenes with certain characters in order to unmask them and discover their lies. Throughout the game, the player has access to an in-game operating system called AquaOS. With that, they can re-read their conversations, look at their found items, and read biographies of the characters encountered. == Plot == The game is set in the fictional and totalitarian city Nova Polemos in Europa in 2066. Mordred Foley and Hera Kairis are private investigators and before the events of the game, they sent two of the most dangerous serial killers ever, Jennifer Kingston and Robert Herrington, to the electric chair. However, after their execution, their agency underwent an investigation for falsifying the evidence presented during the case, which completely destroyed its reputation. Now they want to restart their careers and lives, while dealing with their past traumas. Soon, Mordred is caught up in several cases that all led him to believe that the dreaded serial killer named Pandora has returned. In order to solve these cases, both Mordred and Hera have to face their pasts and fears, all while a racist political party is about to make the lives of refugees in Nova Polemos even worse. == Development == The game was initially conceived by Giacomo Masi and Samuele Zolfanelli, then developed by Studio V and directed and written by Giacomo Masi. It was originally written in Italian and translated into English, Chinese, Japanese, Korean, and German. The soundtrack was composed, written, and performed by Giorgio Maioli. The ending theme and Hera's pieces, performed on piano, were created by Alessandro Masi. The background and character artworks were made by Giulia Carli, other graphic elements such as the UI were created by Samuele Zolfanelli. The developers cited L.A. Noire, Ace Attorney, Blade Runner and Heavy Rain as some of their inspirations for the game. === Releases === Dry Drowning was originally released on Microsoft Windows through Steam, GOG, Itch.io, and Utomik in August 2019. In July 2019, Giacomo Masi announced the game would be released for Xbox One in 2020, though it was not released that year. A Nintendo Switch port was released on February 22, 2021, and a version for PlayStation 4 is set to release in 2021. == Reception == According to review aggregator platform Metacritic, Dry Drowning received "mixed or average reviews" for PC based on 11 reviews and "generally favorable reviews" for Nintendo Switch based on 6 reviews. Fellow review aggregator OpenCritic assessed that the game received fair approval, being recommended by 55% of critics. 4players.de gave a positive rating of 80% and wrote: "Stylish noir thriller with an interesting story, but mechanical limitations – despite a variety of possible interactions." Screen Rant gave a mixed rating of 3 out of 5 stars and wrote, "Dry Drowning may be a fair bit messy, but there's charm here. Players who are willing to embrace the cheesier elements will find some joy in its well-crafted setting and a decent murder mystery plot. The game is constrictive and lacks the genuine shock and engagement of top tier visual novels like Doki Doki Literature Club!, but there are some moments of clever world building and a strong enough mystery propelling it." The Italian review site SpazioGames gave a positive rating of 8.5 out of 10 points and wrote: "Dry Drowning is a very good game with great narrative experience. Every relationship between the characters is layered to increase player involvement, and each choice has different consequences. A thriller game that deserves to be played." === Awards === The game won Best of EGS 2019 and Best of JOIN 2019 awards, an honorable mention at GAMEROME and was nominated as "Best Italian Debut Game" at the Italian Video Game Awards 2020. It was also declared Best Game at Join The Indie 2019.
Smart speaker
A smart speaker is a type of loudspeaker and voice command device with an integrated virtual assistant that offers interactive actions and hands-free activation with the help of one "wake word" (or several "wake words"). Some smart speakers also act as smart home hubs by using Wi-Fi, Bluetooth, Thread, and other protocol standards to extend usage beyond audio playback and control home automation devices connected through a local area network. == History == Early voice-activated devices began in 2013 with MIT's Jasper project, which used multiple microphones and cloud software to power hands-free interactions from across a room. The first commercial smart speaker was the Amazon Echo, which was released in 2014 powered by Alexa and a ring of far-field microphones. Google followed in 2016 with Home, powered by Google Assistant. By 2017, devices like the Echo Show and Home Hub (later called Nest Hub) added touchscreens and video, creating the "smart display" subcategory. In 2018, Apple joined the smart speaker trend by launching the HomePod, which focused on high-quality audio alongside their built-in assistant Siri. ASUS release its own smart Speaker Xiao-Bu in 2019 with Artificial Intelligence, it terminates the Cloud Service on June 1st, 2025, which means all real-time service such as weather, news, currency conversion is affected. Sonos's 1st smart speaker Sonos One released in 2017, powered by Alexa. Invoke by Harman Kardon was powered by Microsoft's intelligent personal assistant, Cortana. In the early 2020s, smart speakers gained on-device voice processing for faster responses and improved privacy. New standards such as Matter and Thread allowed multitudes of smart-home devices (even from completely different brands) to work together. == Features == === Audio and Voice === Smart speakers use multiple microphones along with noise-cancelling software to pick up your voice from across the room, even when music is playing or the assistant is already talking. Noise suppression and echo cancellation is also used by the speaker so it can focus in on who is talking and ignore any background noises. Most smart speaker models can recognize who is speaking by voiceprint, which allows the speaker to grab information from that person's calendar, preferences, or music playlists. Listening to music on a speaker is when importance for good audio quality becomes apparent. Entry-level (cheaper) speakers such as the Home Mini or the Echo Dot have a single full-range driver. These lower-end speakers typically aren't great for listening to music as the audio quality is pretty poor. More advanced units such as the Home Max or Echo Studio have separate tweeters and woofers meant for listening to music in high quality. === Connectivity and smart-home control === Most connect over Wi-Fi or Bluetooth and support hub protocols like Thread and Matter. That lets them not only stream and play music but also allows you to control various brands of smart lights, thermostats, door locks, cameras, and much more-all from one point of control. Each can have its own designated interface and features in-house, usually launched or controlled via application or home automation software. These devices are able to communicate with each other via peer-to-peer connection through mesh networking. These speakers and related smart devices are typically controlled with one smartphone application. === Assistant services and skills === The built-in assistants handle timers, alarms, reminders, news briefings, weather updates, send messages to other smart devices, send texts, make calls, and simple questions. You can combine actions together in what are typically known as routines (for example saying "good morning" turns on lights, starts the coffee, says the weather, and reads the news) and add extra functions known as skills or actions (for things like ordering food or playing trivia games). This hands-free use of smart speakers can help assist those with disabilities. Most other technologies need the user to be able to physically interact with the device. Smart speakers are not bound by these limitations and can serve as an excellent tool for those who are unable to use their arms or legs or have vision issues. Although these tasks can be completed by a phone or computer, consumers tend to lean towards smart speakers due to factors such as their range being much greater than that of a phone and the need to not have to physically interact with the speaker to get the voice assistant as with most smartphones, certain parts of a phone may need to be interacted with to activate the speaking assistant. === Smart displays === Some smart speakers also include a screen to show the user a visual response. A smart speaker with a touchscreen is known as a smart display; these integrate a conversational user interface with display screens to augment voice interaction with images and video. They are powered by one of the common voice assistants and offer additional controls for smart home devices, feature streaming apps, and web browsers with touch controls for selecting content. The first smart displays were introduced in 2017 by Amazon (Amazon Echo Show) and Google (Google/Nest Home Hub). Hotel chain Marriott International partnered with Amazon to install Echo devices in select hotels since 2018. A Taiwanese startup, Aiello, launched the Aiello Voice Assistant (AVA) in the Asian hotel market in 2019, claiming it is powered by a multi-AI model system. Angie by Nomadix, which is similar to the Amazon Echo, launched its first product in 2017, specifically targeting hotel properties in the North America. In May 2019, Angie Hospitality acquired the assets of Roxy, a competitor that also built its own speech-enabled virtual assistant technology for hotels. This acquisition merged two proprietary NLP stacks into the current Nomadix product. === Artificial intelligence === The newest speakers can use on-device AI or cloud-based generative models to allow the smart speaker to carry on much more natural conversations, draft emails or recipes, suggest ideas based on context, or even create short pieces of music or art. This AI evolution allows these speakers to do far more than what they could do before. == Accuracy == According to a study by Proceedings of the National Academy of Sciences of the United States of America released In March 2020, the six biggest tech development companies, Amazon, Apple, Google, Yandex, IBM and Microsoft, have misidentified more words spoken by "black people" than "white people". The systems tested errors and unreadability, with a 19 and 35 percent discrepancy for the former and a 2 and 20 percent discrepancy for the latter. The North American Chapter of the Association for Computational Linguistics (NAACL) also identified a discrepancy between male and female voices. According to their research, Google's speech recognition software is 13 percent more accurate for men than women. It performs better than the systems used by Bing, AT&T, and IBM. == Privacy concerns == The built-in microphone in smart speakers is continuously listening for wake words followed by a command. However, these continuously listening microphones also raise privacy concerns among users. According to a survey taken by 1,007 people in Western Europe, it is clear that privacy is the biggest concern holding consumers back from buying "smart" products. these concerns include what is being recorded, how the data will be used, how it will be protected, and whether it will be used for invasive advertising. Furthermore, an analysis of Amazon Echo Dots showed that 30–38% of "spurious audio recordings were human conversations", suggesting that these devices capture audio other than strictly detection of the wake word. === As a wiretap === There are strong concerns that the ever-listening microphone of smart speakers presents a perfect candidate for wiretapping. In 2017, British security researcher Mark Barnes showed that pre-2017 Echos have exposed pins which allow for a compromised OS to be booted. According to Umar Iqbal, an assistant professor at Washington University in St. Louis, research indicates that data from consumer interactions with Alexa was used to targeted advertisements and products to consumer with over 40% of transmitted data lacking proper encryption raising privacy concerns. Further data indicates that due to the Smart Speakers ability to always capture audio, it begins to pick up on external conversations from consumers not related to commands given to the smart speaker. Things such as other members in the household, consumers on the phone and even TV audio can be picked up by these speakers and stored for future use by companies. === Voice assistance vs privacy === While voice assistants provide a valuable service, there can be some hesitation towards using them in various social contexts, such as in public or around other users. However, only more recently have users begun interac
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.
Combs method
The Combs method is a rule base reduction method of writing fuzzy logic rules described by William E. Combs in 1997. It is designed to prevent combinatorial explosion in fuzzy logic rules. The Combs method takes advantage of the logical equality ( ( p ∧ q ) ⇒ r ) ⟺ ( ( p ⇒ r ) ∨ ( q ⇒ r ) ) {\displaystyle ((p\land q)\Rightarrow r)\iff ((p\Rightarrow r)\lor (q\Rightarrow r))} . == Equality proof == The simplest proof of given equality involves usage of truth tables: == Combinatorial explosion == Suppose we have a fuzzy system that considers N variables at a time, each of which can fit into at least one of S sets. The number of rules necessary to cover all the cases in a traditional fuzzy system is S N {\displaystyle S^{N}} , whereas the Combs method would need only S × N {\displaystyle S\times N} rules. For example, if we have five sets and five variables to consider to produce one output, covering all the cases would require 3125 rules in a traditional system, while the Combs method would require only 25 rules, taming the combinatorial explosion that occurs when more inputs or more sets are added to the system. This article will focus on the Combs method itself. To learn more about the way rules are traditionally formed, see fuzzy logic and fuzzy associative matrix. == Example == Suppose we were designing an artificial personality system that determined how friendly the personality is supposed to be towards a person in a strategic video game. The personality would consider its own fear, trust, and love in the other person. A set of rules in the Combs system might look like this: The table translates to: [IF Fear IS Unafraid THEN Friendship IS Enemies OR IF Fear IS ModerateFear THEN Friendship IS Neutral OR IF Fear IS Afraid THEN Friendship IS GoodFriends ] OR [IF Trust IS Distrusting THEN Friendship IS Enemies OR IF Trust IS ModerateTrust THEN Friendship IS Neutral OR IF Trust IS Trusting THEN Friendship IS GoodFriends] OR [IF Love IS Unloving THEN Friendship IS Enemies OR IF Love IS ModerateLove THEN Friendship IS Neutral OR IF Love IS Loving THEN Friendship IS GoodFriends] In this case, because the table follows a straightforward pattern in the output, it could be rewritten as: Each column of the table maps to the output provided in the last row. To obtain the output of the system, we just average the outputs of each rule for that output. For example, to calculate how much the computer is Enemies with the player, we take the average of how much the computer is Unafraid, Distrusting, and Unloving of the player. When all three averages are obtained, the result can then be defuzzified by any of the traditional means.