Open Media Framework Interchange

Open Media Framework Interchange

Open Media Format (OMF), Open Media Framework, or Open Media Framework Interchange (OMFI), is a platform-independent file format intended for transfer of digital media between different software applications. OMFI is a file format that aids in exchange of digital media across applications and platforms. This framework enables users to import media elements and to edit information and effects summaries. Sequential media representation is the primary concern that is addressed by this format. The primary objective of OMFI is video production. However, there are a number of additional features which can be listed as follows: The origin of the data can be easily backtracked or identified since the import material is in the form of a videotape or film. There are predefined effects and transitions, which paves the way for easy and quick overlapping and sequencing of various track. The format supports motion control. (i.e. enabling a particular segment to play at a ratio of the speed of another segment) Some of the key benefits of OMFI are: It saves time by getting rid of tape-based file transfers. It brings in flexibility owing to its ability to use a number of applications on multiple workstations. The format preserves the best sound and picture quality during all imports. It eliminates the risk of file formatting and incompatibilities, which in turn allows users to spend their productive time on the creative aspects of their work. It preserves the formatting information during file transfers between applications or workstations. Hence, the need for rebuilding the effects and sequences is eliminated. The OMFI format consists of four primary sections namely Header, Object data, Object dictionary and Track data. The header contains an index of all the segments that constitute the file.

Query understanding

Query understanding is the process of inferring the intent of a search engine user by extracting semantic meaning from the searcher’s keywords. Query understanding methods generally take place before the search engine retrieves and ranks results. It is related to natural language processing but specifically focused on the understanding of search queries. == Methods == === Stemming and lemmatization === Many languages inflect words to reflect their role in the utterance they appear in. The variation between various forms of a word is likely to be of little importance for the relatively coarse-grained model of meaning involved in a retrieval system, and for this reason the task of conflating the various forms of a word is a potentially useful technique to increase recall of a retrieval system. Stemming algorithms, also known as stemmers, typically use a collection of simple rules to remove suffixes intended to model the language’s inflection rules. For some languages, there are simple lemmatisation methods to reduce a word in query to its lemma or root form or its stem; for others, this operation involves non-trivial string processing and may require recognizing the word's part of speech or referencing a lexical database. The effectiveness of stemming and lemmatization varies across languages. === Query Segmentation === Query segmentation is a key component of query understanding, aiming to divide a query into meaningful segments. Traditional approaches, such as the bag-of-words model, treat individual words as independent units, which can limit interpretative accuracy. For languages like Chinese, where words are not separated by spaces, segmentation is essential, as individual characters often lack standalone meaning. Even in English, the BOW model may not capture the full meaning, as certain phrases—such as "New York"—carry significance as a whole rather than as isolated terms. By identifying phrases or entities within queries, query segmentation enhances interpretation, enabling search engines to apply proximity and ordering constraints, ultimately improving search accuracy and user satisfaction. === Entity recognition === Entity recognition is the process of locating and classifying entities within a text string. Named-entity recognition specifically focuses on named entities, such as names of people, places, and organizations. In addition, entity recognition includes identifying concepts in queries that may be represented by multi-word phrases. Entity recognition systems typically use grammar-based linguistic techniques or statistical machine learning models. === Query rewriting === Query rewriting is the process of automatically reformulating a search query to more accurately capture its intent. Query expansion adds additional query terms, such as synonyms, in order to retrieve more documents and thereby increase recall. Query relaxation removes query terms to reduce the requirements for a document to match the query, thereby also increasing recall. Other forms of query rewriting, such as automatically converting consecutive query terms into phrases and restricting query terms to specific fields, aim to increase precision. === Spelling Correction === Automatic spelling correction is a critical feature of modern search engines, designed to address common spelling errors in user queries. Such errors are especially frequent as users often search for unfamiliar topics. By correcting misspelled queries, search engines enhance their understanding of user intent, thereby improving the relevance and quality of search results and overall user experience.

Vue.js

Vue.js (commonly referred to as Vue; pronounced "view") is an open-source model–view–viewmodel front end JavaScript framework for building user interfaces and single-page applications. It was created by Evan You and is maintained by him and the rest of the active core team members. == Overview == Vue.js features an incrementally adaptable architecture that focuses on declarative rendering and component composition. The core library is focused on the view layer only. Advanced features required for complex applications such as routing, state management and build tooling are offered via officially maintained supporting libraries and packages. Vue.js allows for extending HTML with HTML attributes called directives. The directives offer functionality to HTML applications, and come as either built-in or user defined directives. == History == Vue was created by Evan You after working for Google using AngularJS in several projects. He later summed up his thought process: "I figured, what if I could just extract the part that I really liked about Angular and build something really lightweight." The first source code commit to the project was dated July 2013, at which time it was originally named "Seed". Vue was first publicly announced the following February, in 2014. Version names are often derived from manga and anime series, with the first letters arranged in alphabetical order. === Versions === When a new major is released i.e. v3.y.z, the last minor i.e. 2.x.y will become a LTS release for 18 months (bug fixes and security patches) and for the following 18 months will be in maintenance mode (security patches only). Vue 3 was officially released in September 2020. According to the State of Vue.js Report 2025, 96% of surveyed developers reported having used Vue 3.x. However, 35% also indicated that they used Vue 2.7.x in the past year, reflecting continued reliance on Vue 2 despite its end of support. The report also noted that more than a quarter of respondents encountered challenges when migrating from Vue 2 to Vue 3. === State management evolution === 2015 - Vuex introduced as official state management solution 2021 - Pinia development begins as Vuex 5 experiment 2022 - Pinia becomes officially recommended for new projects 2023 - Vue team announces Vuex maintenance mode transition According to the State of Vue.js Report 2025, the Vue's core team recommendation is reflected in developer adoption–over 80% of surveyed developers reported using Pinia while Vuex still had 38.4% usage, indicating ongoing reliance on the older library. == Features == === Components === Vue components extend basic HTML elements to encapsulate reusable code. At a high level, components are custom elements to which the Vue's compiler attaches behavior. In Vue, a component is essentially a Vue instance with pre-defined options. The code snippet below contains an example of a Vue component. The component presents a button and prints the number of times the button is clicked: === Templates === Vue uses an HTML-based template syntax that allows binding the rendered DOM to the underlying Vue instance's data. All Vue templates are valid HTML that can be parsed by specification-compliant browsers and HTML parsers. Vue compiles the templates into virtual DOM render functions. A virtual Document Object Model (or "DOM") allows Vue to render components in its memory before updating the browser. Combined with the reactivity system, Vue can calculate the minimal number of components to re-render and apply the minimal amount of DOM manipulations when the app state changes. Vue users can use template syntax or choose to directly write render functions using hyperscript either through function calls or JSX. Render functions allow applications to be built from software components. === Reactivity === Vue features a reactivity system that uses plain JavaScript objects and optimized re-rendering. Each component keeps track of its reactive dependencies during its render, so the system knows precisely when to re-render, and which components to re-render. === Transitions === Vue provides a variety of ways to apply transition effects when items are inserted, updated, or removed from the DOM. This includes tools to: Automatically apply classes for CSS transitions and animations Integrate third-party CSS animation libraries, such as Animate.css Use JavaScript to directly manipulate the DOM during transition hooks Integrate third-party JavaScript animation libraries, such as Velocity.js When an element wrapped in a transition component is inserted or removed, this is what happens: Vue will automatically sniff whether the target element has CSS transitions or animations applied. If it does, CSS transition classes will be added/removed at appropriate timings. If the transition component provided JavaScript hooks, these hooks will be called at appropriate timings. If no CSS transitions/animations are detected and no JavaScript hooks are provided, the DOM operations for insertion and/or removal will be executed immediately on next frame. === Routing === A traditional disadvantage of single-page applications (SPAs) is the inability to share links to the exact "sub" page within a specific web page. Because SPAs serve their users only one URL-based response from the server (it typically serves index.html or index.vue), bookmarking certain screens or sharing links to specific sections is normally difficult if not impossible. To solve this problem, many client-side routers delimit their dynamic URLs with a "hashbang" (#!), e.g. page.com/#!/. However, with HTML5 most modern browsers support routing without hashbangs. Vue provides an interface to change what is displayed on the page based on the current URL path – regardless of how it was changed (whether by emailed link, refresh, or in-page links). Additionally, using a front-end router allows for the intentional transition of the browser path when certain browser events (i.e. clicks) occur on buttons or links. Vue itself doesn't come with front-end hashed routing. But the open-source "vue-router" package provides an API to update the application's URL, supports the back button (navigating history), and email password resets or email verification links with authentication URL parameters. It supports mapping nested routes to nested components and offers fine-grained transition control. With Vue, developers are already composing applications with small building blocks building larger components. With vue-router added to the mix, components must merely be mapped to the routes they belong to, and parent/root routes must indicate where children should render. The code above: Sets a front-end route at websitename.com/user/. Which will render in the User component defined in (const User...) Allows the User component to pass in the particular id of the user which was typed into the URL using the $route object's params key: $route.params.id. This template (varying by the params passed into the router) will be rendered into inside the DOM's div#app. The finally generated HTML for someone typing in: websitename.com/user/1 will be: == Ecosystem == The core library comes with tools and libraries both developed by the core team and contributors. === Official tooling === Devtools – Browser devtools extension for debugging Vue.js applications Vite – Standard Tooling for rapid Vue.js development Vue Loader – a webpack loader that allows the writing of Vue components in a format called Single-File Components (SFCs) Vue.js Plugins Collection - Collection of almost 100 plugins and ecosystem libraries across various categories. === Official libraries === Vue Router – The official router, suitable for building SPAs Pinia – The official state management solution === Video courses === Vue School – Expert-led courses on Vue.js and its ecosystem. === State management libraries === Pinia – Official state management solution with modular architecture Vuex – Legacy state management library, now in maintenance mode VueUse – Collection of 200+ composition utilities including state management helpers === Community & Core Teams Resources === The State of Vue.js Report - A comprehensive publication about Vue.js created since 2017 by Monterail, Vue & Nuxt Official Partner. Each edition includes unique data from developer survey, key ecosystem trends and case studies. The latest 5th edition released in March 2025 was co-created with Evan You and Vue&Nuxt Core Teams. Although the Vue.js Ecosystem is generally very well-developed, developers point to some ecosystem gaps as one of the most important thing missing (as of March 2025 Developer Survey in the State of Vue.js Report 2025). 22% of respondents mentioned the lack of robust, official component libraries like MUI or Radix, and the need for better testing utilities. There was also demand for more modular, enterprise-ready solutions for dashboards, e-commerce, and animation libraries similar to Fr

Zero-overhead looping

In computer architecture, zero-overhead looping is a hardware feature found in some processors that enables loops to execute without the performance cost of traditional loop control instructions. Instead of software managing loop iterations, the processor's hardware handles repetition automatically, saving clock cycles and improving efficiency. This technique is commonly employed in digital signal processors (DSPs) and certain complex instruction set computer (CISC) architectures. == Background == In many instruction sets, a loop must be implemented by using instructions to increment or decrement a counter, check whether the end of the loop has been reached, and if not jump to the beginning of the loop so it can be repeated. Although this typically only represents around 3–16 bytes of space for each loop, even that small amount could be significant depending on the size of the CPU caches. More significant is that those instructions each take time to execute, time which is not spent doing useful work. The overhead of such a loop is apparent compared to a completely unrolled loop, in which the body of the loop is duplicated exactly as many times as it will execute. In that case, no space or execution time is wasted on instructions to repeat the body of the loop. However, the duplication caused by loop unrolling can significantly increase code size, and the larger size can even impact execution time due to cache misses. (For this reason, it's common to only partially unroll loops, such as transforming it into a loop which performs the work of four iterations in one step before repeating. This balances the advantages of unrolling with the overhead of repeating the loop.) Moreover, completely unrolling a loop is only possible for a limited number of loops: those whose number of iterations is known at compile time. For example, the following C code could be compiled and optimized into the following x86 assembly code: == Implementation == Processors with zero-overhead looping have machine instructions and registers to automatically repeat one or more instructions. Depending on the instructions available, these may only be suitable for count-controlled loops ("for loops") in which the number of iterations can be calculated in advance, or only for condition-controlled loops ("while loops") such as operations on null-terminated strings. === Examples === ==== PIC ==== In the PIC instruction set, the REPEAT and DO instructions implement zero-overhead loops. REPEAT only repeats a single instruction, while DO repeats a specified number of following instructions. ==== Blackfin ==== Blackfin offers two zero-overhead loops. The loops can be nested; if both hardware loops are configured with the same "loop end" address, loop 1 will behave as the inner loop and repeat, and loop 0 will behave as the outer loop and repeat only if loop 1 would not repeat. Loops are controlled using the LTx and LBx registers (x either 0 to 1) to set the top and bottom of the loop — that is, the first and last instructions to be executed, which can be the same for a loop with only one instruction — and LCx for the loop count. The loop repeats if LCx is nonzero at the end of the loop, in which case LCx is decremented. The loop registers can be set manually, but this would typically consume 6 bytes to load the registers, and 8–16 bytes to set up the values to be loaded. More common is to use the loop setup instruction (represented in assembly as either LOOP with pseudo-instruction LOOP_BEGIN and LOOP_END, or in a single line as LSETUP), which optionally initializes LCx and sets LTx and LBx to the desired values. This only requires 4–6 bytes, but can only set LTx and LBx within a limited range relative to where the loop setup instruction is located. ==== x86 ==== The x86 assembly language REP prefixes implement zero-overhead loops for a few instructions (namely MOVS/STOS/CMPS/LODS/SCAS). Depending on the prefix and the instruction, the instruction will be repeated a number of times with (E)CX holding the repeat count, or until a match (or non-match) is found with AL/AX/EAX or with DS:[(E)SI]. This can be used to implement some types of searches and operations on null-terminated strings.

Digital Cinema Package

A Digital Cinema Package (DCP) is a collection of digital files used to store and convey digital cinema (DC) audio, image, and data streams. The term was popularized by Digital Cinema Initiatives, LLC in its original recommendation for packaging DC contents. However, the industry tends to apply the term to the structure more formally known as the composition. A DCP is a container format for compositions, a hierarchical file structure that represents a title version. The DCP may carry a partial composition (e.g. not a complete set of files), a single complete composition, or multiple and complete compositions. The composition consists of a Composition Playlist (in XML format) that defines the playback sequence of a set of Track Files. Track Files carry the essence (audio, image, subtitles), which is wrapped using Material eXchange Format (MXF). Track Files must contain only one essence type. Two track files at a minimum must be present in every composition (see SMPTE ST429-2 D-Cinema Packaging – DCP Constraints, or Cinepedia): a track file carrying picture essence, and a track file carrying audio essence. The composition, consisting of a Composition Playlist (CPL) and associated track files, are distributed as a Digital Cinema Package (DCP). A composition is a complete representation of a title version, while the DCP need not carry a full composition. However, as already noted, it is commonplace in the industry to discuss the title in terms of a DCP, as that is the deliverable to the cinema. The Picture Track File essence is compressed using JPEG 2000 and the Audio Track File carries a 24-bit linear PCM uncompressed multichannel WAV file. Encryption may optionally be applied to the essence of a track file to protect it from unauthorized use. The encryption used is AES 128-bit in CBC mode. In practice, there are two versions of composition in use. The original version is called Interop DCP. In 2009, a specification was published by SMPTE (SMPTE ST 429-2 Digital Cinema Packaging – DCP Constraints) for what is commonly referred to as SMPTE DCP. SMPTE DCP is similar but not backwards compatible with Interop DCP, resulting in an uphill effort to transition the industry from Interop DCP to SMPTE DCP. SMPTE DCP requires significant constraints to ensure success in the field, as shown by ISDCF. While legacy support for Interop DCP is necessary for commercial products, new productions are encouraged to be distributed in SMPTE DCP. == Technical specifications == The DCP root folder (in the storage medium) contains a number of files, some used to store the image and audio contents, and some other used to organize and manage the whole playlist. === Picture MXF files === Picture contents may be stored in one or more reels corresponding to one or more MXF files. Each reel contains pictures as MPEG-2 or JPEG 2000 essence, depending on the adopted codec. MPEG-2 is no longer compliant with the DCI specification. JPEG 2000 is the only accepted compression format. Supported frame rates are: SMPTE (JPEG 2000) 24, 25, 30, 48, 50, and 60 fps @ 2K 24, 25, and 30 fps @ 4K 24 and 48 fps @ 2K stereoscopic MXF Interop (JPEG 2000) – Deprecated 24 and 48 fps @ 2K (MXF Interop can be encoded at 25 frame/s but support is not guaranteed) 24 fps @ 4K 24 fps @ 2K stereoscopic MXF Interop (MPEG-2) – Deprecated 23.976 and 24 fps @ 1920 × 1080 Maximum frame sizes are 2048 × 1080 for 2K DC, and 4096 × 2160 for 4K DC. Common formats are: SMPTE (JPEG 2000) Flat (1998 × 1080 or 3996 × 2160), = 1.85:1 aspect ratio Scope (2048 × 858 or 4096 × 1716), ~2.39:1 aspect ratio HDTV (1920 × 1080 or 3840 × 2160), 16:9 aspect ratio (~1.78:1) (although not specifically defined in the DCI specification, this resolution is DCI compliant per section 8.4.3.2). Full (2048 × 1080 or 4096 × 2160) (~1.9:1 aspect ratio, official name by DCI is Full Container. Not widely accepted in cinemas.) MXF Interop (MPEG-2) – Deprecated Full Frame (1920 × 1080) 12 bits per component precision (36 bits total per pixel) XYZ' colorspace; the prime mark indicates gamma encoding (gamma=2.6) Maximum bit rate is 250 Mbit/s (1.3 MBytes per frame at 24 frame per second) === Sound MXF files === Sound contents are also stored in reels corresponding to picture reels in number and duration. In case of multilingual features, separate reels are required to convey different languages. Each file contains linear PCM essence. Sampling rate is 48,000 or 96,000 samples per second Sample precision of 24 bits Linear mapping (no companding) Up to 16 independent channels === Asset map file === List of all files included in the DCP, in XML format. === Composition playlist file === Defines the playback order during presentation. The order is saved in XML format in this file; each picture and sound reel is identified by its UUID. In the following example, a reel is composed by picture and sound: === Packing list file or package key list (PKL) === All files in the composition are hashed and their hash is stored here, in XML format. This file is generally used during ingestion in a digital cinema server to verify if data have been corrupted or tampered with in some way. For example, an MXF picture reel is identified by the following element: The hash value is the Base64 encoding of the SHA-1 checksum. It can be calculated with the command: openssl sha1 -binary "FILE_NAME" | openssl base64 === Volume index file === A single DCP may be stored in more than one medium (e.g., multiple hard disks). The XML file VOLINDEX is used to identify the volume order in the series. == 3D DCP == The DCP format is also used to store stereoscopic (3D) contents for 3D films. In this case, 48 frames exist for every second – 24 frames for the left eye, 24 frames for the right. Depending on the projection system used, the left eye and right eye pictures are either shown alternately (double or triple flash systems) at 48 fps or, on 4k systems, both left and right eye pictures are shown simultaneously, one above the other, at 24 fps. In triple flash systems, active shutter glasses are required whereas optical filtering such as circular polarisation is used in conjunction with passive glasses on polarized systems. Since the maximum bit rate is always 250 Mbit/s, this results in a net 125 Mbit/s for single frame, but the visual quality decrease is generally unnoticeable. == D-Box == D-Box codes for motion controlled seating (labelled as "Motion Data" in the DCP specification), if present, are stored as a monoaural WAV file on Sound Track channel 13. Motion Data tracks are unencrypted and not watermarked. == Creation == Most film producers and distributors rely on digital cinema encoding facilities to produce and quality control check a digital cinema package before release. Facilities follow strict guidelines set out in the DCI recommendations to ensure compatibility with all digital cinema equipment. For bigger studio release films, the facility will usually create a Digital Cinema Distribution Master (DCDM). A DCDM is the post-production step prior to a DCP. The frames are in XYZ TIFF format and both sound and picture are not yet wrapped into MXF files. A DCP can be encoded directly from a DCDM. A DCDM is useful for archiving purposes and also facilities can share them for international re-versioning purposes. They can easily be turned into alternative version DCPs for foreign territories. For smaller release films, the facility will usually skip the creation of a DCDM and instead encode directly from the Digital Source Master (DSM) the original film supplied to the encoding facility. A DSM can be supplied in a multitude of formats and color spaces. For this reason, the encoding facility needs to have extensive knowledge in color space handling including, on occasion, the use of 3D LUTs to carefully match the look of the finished DCP to a celluloid film print. This can be a highly involved process in which the DCP and the film print are "butterflied" (shown side by side) in a highly calibrated cinema. Less demanding DCPs are encoded from tape formats such as HDCAM SR. Quality control checks are always performed in calibrated cinemas and carefully checked for errors. QC checks are often attended by colorists, directors, sound mixers and other personnel to check for correct picture and sound reproduction in the finished DCP. == Accessibility == === Hearing impaired audio === A Hearing Impaired (HI) audio track is designed for people who are hearing-impaired to better hear dialog. Moviegoers can wear headphones which play this audio track synchronized with the film. Hearing Impaired audio is stored in the DCP on Sound Track channel 7. === Audio description === Audio description is narration for people who are blind or visually impaired. Audio description is stored in the DCP as "Visually Impaired-Native" (VI-N) audio on Sound Track channel 8. === Sign Language Video === A Sign Language Video track can be included in a DCP to allow for display of sign la

Topological deep learning

Topological deep learning (TDL) is a research field that extends deep learning to handle complex, non-Euclidean data structures. Traditional deep learning models, such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs), excel in processing data on regular grids and sequences. However, scientific and real-world data often exhibit more intricate data domains encountered in scientific computations, including point clouds, meshes, time series, scalar fields graphs, or general topological spaces like simplicial complexes and CW complexes. TDL addresses this by incorporating topological concepts to process data with higher-order relationships, such as interactions among multiple entities and complex hierarchies. This approach leverages structures like simplicial complexes and hypergraphs to capture global dependencies and qualitative spatial properties, offering a more nuanced representation of data. TDL also encompasses methods from computational and algebraic topology that permit studying properties of neural networks and their training process, such as their predictive performance or generalization properties. The mathematical foundations of TDL are algebraic topology, differential topology, and geometric topology. Therefore, TDL can be generalized for data on differentiable manifolds, knots, links, tangles, curves, etc. == History and motivation == Traditional techniques from deep learning often operate under the assumption that a dataset is residing in a highly-structured space (like images, where convolutional neural networks exhibit outstanding performance over alternative methods) or a Euclidean space. The prevalence of new types of data, in particular graphs, meshes, and molecules, resulted in the development of new techniques, culminating in the field of geometric deep learning, which originally proposed a signal-processing perspective for treating such data types. While originally confined to graphs, where connectivity is defined based on nodes and edges, follow-up work extended concepts to a larger variety of data types, including simplicial complexes and CW complexes, with recent work proposing a unified perspective of message-passing on general combinatorial complexes. An independent perspective on different types of data originated from topological data analysis, which proposed a new framework for describing structural information of data, i.e., their "shape," that is inherently aware of multiple scales in data, ranging from local information to global information. While at first restricted to smaller datasets, subsequent work developed new descriptors that efficiently summarized topological information of datasets to make them available for traditional machine-learning techniques, such as support vector machines or random forests. Such descriptors ranged from new techniques for feature engineering over new ways of providing suitable coordinates for topological descriptors, or the creation of more efficient dissimilarity measures. Contemporary research in this field is largely concerned with either integrating information about the underlying data topology into existing deep-learning models or obtaining novel ways of training on topological domains. == Learning on topological spaces == One of the core concepts in topological deep learning is considering the domain upon which this data is defined and supported. In case of Euclidean data, such as images, this domain is a grid, upon which the pixel value of the image is supported. In a more general setting this domain might be a topological domain. Studying and developing deep learning models that are supported ln topological domains constitute the essence of topological deep learning. Next, we introduce the most common topological domains that are encountered in a deep learning setting. These domains include, but not limited to, graphs, simplicial complexes, cell complexes, combinatorial complexes and hypergraphs. Given a finite set S of abstract entities, a neighborhood function N {\displaystyle {\mathcal {N}}} on S is an assignment that attach to every point x {\displaystyle x} in S a subset of S or a relation. Such a function can be induced by equipping S with an auxiliary structure. Edges provide one way of defining relations among the entities of S. More specifically, edges in a graph allow one to define the notion of neighborhood using, for instance, the one hop neighborhood notion. Edges however, limited in their modeling capacity as they can only be used to model binary relations among entities of S since every edge is connected typically to two entities. In many applications, it is desirable to permit relations that incorporate more than two entities. The idea of using relations that involve more than two entities is central to topological domains. Such higher-order relations allow for a broader range of neighborhood functions to be defined on S to capture multi-way interactions among entities of S. Next we review the main properties, advantages, and disadvantages of some commonly studied topological domains in the context of deep learning, including (abstract) simplicial complexes, regular cell complexes, hypergraphs, and combinatorial complexes. ==== Comparisons among topological domains ==== Each of the enumerated topological domains has its own characteristics, advantages, and limitations: Simplicial complexes Simplest form of higher-order domains. Extensions of graph-based models. Admit hierarchical structures, making them suitable for various applications. Hodge theory can be naturally defined on simplicial complexes. Require relations to be subsets of larger relations, imposing constraints on the structure. Cell Complexes Generalize simplicial complexes. Provide more flexibility in defining higher-order relations. Each cell in a cell complex is homeomorphic to an open ball, attached together via attaching maps. Boundary cells of each cell in a cell complex are also cells in the complex. Represented combinatorially via incidence matrices. Hypergraphs Allow arbitrary set-type relations among entities. Relations are not imposed by other relations, providing more flexibility. Do not explicitly encode the dimension of cells or relations. Useful when relations in the data do not adhere to constraints imposed by other models like simplicial and cell complexes. Combinatorial Complexes : Generalize and bridge the gaps between simplicial complexes, cell complexes, and hypergraphs. Allow for hierarchical structures and set-type relations. Combine features of other complexes while providing more flexibility in modeling relations. Can be represented combinatorially, similar to cell complexes. ==== Hierarchical structure and set-type relations ==== The properties of simplicial complexes, cell complexes, and hypergraphs give rise to two main features of relations on higher-order domains, namely hierarchies of relations and set-type relations. ===== Rank function ===== A rank function on a higher-order domain X is an order-preserving function rk: X → Z, where rk(x) attaches a non-negative integer value to each relation x in X, preserving set inclusion in X. Cell and simplicial complexes are common examples of higher-order domains equipped with rank functions and therefore with hierarchies of relations. ===== Set-type relations ===== Relations in a higher-order domain are called set-type relations if the existence of a relation is not implied by another relation in the domain. Hypergraphs constitute examples of higher-order domains equipped with set-type relations. Given the modeling limitations of simplicial complexes, cell complexes, and hypergraphs, we develop the combinatorial complex, a higher-order domain that features both hierarchies of relations and set-type relations. The learning tasks in TDL can be broadly classified into three categories: Cell classification: Predict targets for each cell in a complex. Examples include triangular mesh segmentation, where the task is to predict the class of each face or edge in a given mesh. Complex classification: Predict targets for an entire complex. For example, predict the class of each input mesh. Cell prediction: Predict properties of cell-cell interactions in a complex, and in some cases, predict whether a cell exists in the complex. An example is the prediction of linkages among entities in hyperedges of a hypergraph. In practice, to perform the aforementioned tasks, deep learning models designed for specific topological spaces must be constructed and implemented. These models, known as topological neural networks, are tailored to operate effectively within these spaces. === Topological neural networks === Central to TDL are topological neural networks (TNNs), specialized architectures designed to operate on data structured in topological domains. Unlike traditional neural networks tailored for grid-like structures, TNNs are adept at handling more intricate data representations, such as graphs

TheFWA

FWA (Favourite Website Awards) is an international award platform that honors and rewards web designers, developers and agencies around the world for excellence within the field of web design and development. The FWA was founded in May 2000 by Rob Ford. In November 2012, The FWA was the most visited website award program in the history of the internet, with over 170 millions site visits. == Jury == The FWA jury is composed of more than 500 web professionals (200 women + 200 men) from 35 countries. == Awards granted == FWA of the Day (FOTD) : Every day, the FWA jury selects the best project, FWA of the Month (FOTM): Every month, the FWA jury selects the best project, People's Choice Award (PCA) : Every year, a public vote selects the people's favourite project, FWA of the Year (FOTY) : Every year, the FWA jury selects the best project. == Hall Of Fame == The FWA Hall of Fame was established in May 2007 (to celebrate the seventh anniversary of the FWA), as a recognition of web's greatest individuals and companies.