In distributed computing and geometric graph theory, greedy embedding is a process of assigning coordinates to the nodes of a telecommunications network in order to allow greedy geographic routing to be used to route messages within the network. Although greedy embedding has been proposed for use in wireless sensor networks, in which the nodes already have positions in physical space, these existing positions may differ from the positions given to them by greedy embedding, which may in some cases be points in a virtual space of a higher dimension, or in a non-Euclidean geometry. In this sense, greedy embedding may be viewed as a form of graph drawing, in which an abstract graph (the communications network) is embedded into a geometric space. The idea of performing geographic routing using coordinates in a virtual space, instead of using physical coordinates, is due to Rao et al. Subsequent developments have shown that every network has a greedy embedding with succinct vertex coordinates in the hyperbolic plane, that certain graphs including the polyhedral graphs have greedy embeddings in the Euclidean plane, and that unit disk graphs have greedy embeddings in Euclidean spaces of moderate dimensions with low stretch factors. == Definitions == In greedy routing, a message from a source node s to a destination node t travels to its destination by a sequence of steps through intermediate nodes, each of which passes the message on to a neighboring node that is closer to t. If the message reaches an intermediate node x that does not have a neighbor closer to t, then it cannot make progress and the greedy routing process fails. A greedy embedding is an embedding of the given graph with the property that a failure of this type is impossible. Thus, it can be characterized as an embedding of the graph with the property that for every two nodes x and t, there exists a neighbor y of x such that d(x,t) > d(y,t), where d denotes the distance in the embedded space. == Graphs with no greedy embedding == Not every graph has a greedy embedding into the Euclidean plane; a simple counterexample is given by the star K1,6, a tree with one internal node and six leaves. Whenever this graph is embedded into the plane, some two of its leaves must form an angle of 60 degrees or less, from which it follows that at least one of these two leaves does not have a neighbor that is closer to the other leaf. In Euclidean spaces of higher dimensions, more graphs may have greedy embeddings; for instance, K1,6 has a greedy embedding into three-dimensional Euclidean space, in which the internal node of the star is at the origin and the leaves are a unit distance away along each coordinate axis. However, for every Euclidean space of fixed dimension, there are graphs that cannot be embedded greedily: whenever the number n is greater than the kissing number of the space, the graph K1,n has no greedy embedding. == Hyperbolic and succinct embeddings == Unlike the case for the Euclidean plane, every network has a greedy embedding into the hyperbolic plane. The original proof of this result, by Robert Kleinberg, required the node positions to be specified with high precision, but subsequently it was shown that, by using a heavy path decomposition of a spanning tree of the network, it is possible to represent each node succinctly, using only a logarithmic number of bits per point. In contrast, there exist graphs that have greedy embeddings in the Euclidean plane, but for which any such embedding requires a polynomial number of bits for the Cartesian coordinates of each point. == Special classes of graphs == === Trees === The class of trees that admit greedy embeddings into the Euclidean plane has been completely characterized, and a greedy embedding of a tree can be found in linear time when it exists. For more general graphs, some greedy embedding algorithms such as the one by Kleinberg start by finding a spanning tree of the given graph, and then construct a greedy embedding of the spanning tree. The result is necessarily also a greedy embedding of the whole graph. However, there exist graphs that have a greedy embedding in the Euclidean plane but for which no spanning tree has a greedy embedding. === Planar graphs === Papadimitriou & Ratajczak (2005) conjectured that every polyhedral graph (a 3-vertex-connected planar graph, or equivalently by Steinitz's theorem the graph of a convex polyhedron) has a greedy embedding into the Euclidean plane. By exploiting the properties of cactus graphs, Leighton & Moitra (2010) proved the conjecture; the greedy embeddings of these graphs can be defined succinctly, with logarithmically many bits per coordinate. However, the greedy embeddings constructed according to this proof are not necessarily planar embeddings, as they may include crossings between pairs of edges. For maximal planar graphs, in which every face is a triangle, a greedy planar embedding can be found by applying the Knaster–Kuratowski–Mazurkiewicz lemma to a weighted version of a straight-line embedding algorithm of Schnyder. The strong Papadimitriou–Ratajczak conjecture, that every polyhedral graph has a planar greedy embedding in which all faces are convex, remains unproven. === Unit disk graphs === The wireless sensor networks that are the target of greedy embedding algorithms are frequently modeled as unit disk graphs, graphs in which each node is represented as a unit disk and each edge corresponds to a pair of disks with nonempty intersection. For this special class of graphs, it is possible to find succinct greedy embeddings into a Euclidean space of polylogarithmic dimension, with the additional property that distances in the graph are accurately approximated by distances in the embedding, so that the paths followed by greedy routing are short.
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.
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.
Directed-energy weapon wildfire conspiracy theories
The directed-energy weapon wildfire conspiracy theories are claims circulating on social media and in fringe commentary that 2020s wildfires in places such as California, Hawaii and Texas were started or steered by directed-energy weapons or other lasers or directed-energy systems rather than by the documented ignition sources identified by investigators. Fact-checking organisations and newsrooms have repeatedly shown that widely shared images and clips said to depict “beams from the sky” are unrelated, miscaptioned or fabricated, and that official inquiries point to causes such as damaged or re-energised power lines, vegetation and extreme wind conditions. Coverage of the January 2025 Los Angeles fires described a resurgence of familiar hoaxes while local and federal agencies coordinated public rebuttals. == Background == Rumours linking directed-energy weapons to wildfire outbreaks appeared during earlier disaster seasons, then re-emerged at scale during the 2018 Camp Fire and again with the 2023 Maui wildfires and the 2025 Los Angeles fires. Journalists documented how large disasters reliably attract miscaptioned imagery and speculative narratives that portray official explanations as cover stories, while researchers and emergency managers noted that such claims tend to flourish during the information vacuum that accompanies fast-moving events. == Narratives and debunks == Recurring claims include assertions that videos show lasers igniting neighbourhoods, that “green” or “blue” items or roofs were spared because lasers cannot burn those colours, that trees remaining upright indicate precision targeting of houses, and that beams recorded over Hawaii or Texas came from secret platforms. Investigations show that a purported laser-strike video was actually an explosion at a Russian gas station recorded years earlier, that a photograph said to capture an “attack” was an Ohio gas flare from 2018, and that a separate video of green lights over Hawaii was captured months before the Maui fires by an astronomical camera and is unrelated. Fact-checks addressing colour myths have further explained that images of intact blue roofs were either misinterpreted or in at least one widely shared instance artificially generated, and that laser interaction with materials is not governed by such simplistic rules. == Investigations and identified causes == Authorities who examined specific incidents have published findings that contradict DEW narratives. A multi-agency investigation into the Maui disaster concluded that downed and later re-energised lines ignited an initial morning fire that re-kindled under extreme winds in the afternoon, with reports detailing the timeline and infrastructure context; summaries by national outlets echoed those conclusions. Investigators of the February 2024 Smokehouse Creek Fire in the Texas Panhandle reported that power lines ignited both the state’s largest wildfire and another major blaze, and the regional utility acknowledged its facilities appeared to have been involved; subsequent media coverage outlined the findings and regulatory follow-up. For the 2018 Camp Fire in Northern California, public reports from Butte County and subsequent proceedings identified PG&E transmission equipment as the source of ignition, with documentation of maintenance issues on the Caribou–Palermo line preceding the event. == Platform and agency responses == As major fires burned in and around Los Angeles in January 2025, officials from city agencies and national partners pursued a coordinated strategy to counter falsehoods by issuing timely updates, flagging fake imagery and directing residents to verified resources. Reporters described how federal emergency managers and local departments used social channels and briefings to rebut specific rumours, including claims about lasers and targeted ignition, and to clarify that early imagery often misleads during fast-moving disasters.
Honeywell JetWave
Honeywell's JetWave is a piece of satellite communications hardware produced by Honeywell that enables global in-flight internet connectivity. Its connectivity is provided using Inmarsat’s GX Aviation network. The JetWave platform is used in business and general aviation, as well as defense and commercial airline users. == History == In 2012, Honeywell announced it would provide Inmarsat with the hardware for its GX Ka-band in-flight connectivity network. The Ka-band (pronounced either "kay-ay band" or "ka band") is a portion of the microwave part of the electromagnetic spectrum defined as frequencies in the range 27.5 to 31 gigahertz (GHz). In satellite communications, the Ka-band allows higher bandwidth communication. In 2017, after five years and more than 180 flight hours and testing, JetWave was launched as part of GX Aviation with Lufthansa Group. Honeywell’s JetWave was the exclusive terminal hardware option for the Inmarsat GX Aviation network; however, the exclusivity clause in that contract has expired. In July 2019, the United States Air Force selected Honeywell’s JetWave satcom system for 70 of its C-17 Globemaster III cargo planes. In December 2019, it was reported that six AirAsia aircraft had been fitted with Inmarsat’s GX Aviation Ka-band connectivity system and is slated to be implemented fleetwide across AirAsia’s Airbus A320 and A330 models in 2020, requiring installation of JetWave atop AirAsia’s fuselages. Today, Honeywell’s JetWave hardware is installed on over 1,000 aircraft worldwide. In August 2021, the Civil Aviation Administration of China approved a validation of Honeywell’s MCS-8420 JetWave satellite connectivity system for Airbus 320 aircraft. In December 2021, Honeywell, SES, and Hughes Network Systems demonstrated multi-orbit high-speed airborne connectivity for military customers using Honeywell’s JetWave MCX terminal with a Hughes HM-series modem, and SES satellites in both medium Earth orbit (MEO) and geostationary orbit (GEO). The tests achieved full duplex data rates of more than 40 megabits per second via a number of SES' (GEO) satellites including GovSat-1, and the high-throughput, low-latency O3b MEO satellite constellation, with connections moving between GEO/MEO links in under 30 sec. == Uses == === Commercial aviation === Honeywell’s JetWave enables air transport and regional aircraft to connect to Inmarsat’s GX Aviation network. The multichannel satellite (MSC) JetWave terminals share the same antenna controller, modem and router hardware with the business market, but have an MCS-8200 fuselage-mounted antenna. === Business aviation === Honeywell’s JetWave hardware allows users to connect to Inmarsat’s Jet ConneX, a business aviation broadband connectivity offering to provide Wi-Fi for connected devices. JetWave offers a tail-mount antenna for business jets. === Defense === Honeywell’s JetWave satellite communications system for defense allows users to connect to the Inmarsat GX network, offering global coverage for military airborne operators, including over water, over nontraditional flight paths and in remote areas. JetWave and the Inmarsat GX network enable mission-critical applications like real-time weather; videoconferencing; large file transfers; encryption capabilities; in-flight briefings; intelligence, surveillance, and reconnaissance video; and secure communications. JetWave is configurable for a variety of military platforms and offers antennas for large and small airframes.
TeaOnHer
TeaOnHer is a male-oriented dating surveillance mobile app that allows men to anonymously rate and comment on women they are dating. It was set up in response to the existence of Tea, a female-oriented dating app that allowed women to rate and comment on men. In 2025, Cosmopolitian magazine described it as America's second most popular mobile app, with it being the second most popular app in the lifestyle section of Apple's App Store. The TeaOnHer app has fewer features than the rival Tea app, focusing instead on anonymous commenting. It is listed as having been developed by a company called Newville Media Corporation. TechCrunch reported in 2025 that TeaOnHer had leaked credentials of some of its users.
Rider Spoke
Rider Spoke developed by Blast Theory in collaboration with the Mixed Reality Lab was first staged at the Barbican, London in October 2007. Created for cyclists, it combines elements of theatre, performance, game play and state of the art technology. Rider Spoke was built in the IPerG project on the EQUIP architecture. Rider Spoke has since been presented in Athens (2008), Brighton (2008), Budapest (2008), Sydney (2009, Adelaide (2009) and Liverpool (2010).