AI Chat No Filter App

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Cloud management

Cloud management refers to the administration and oversight of cloud computing products and services. Public clouds are managed by cloud service providers, which operate the underlying infrastructure such as servers, storage, networking, and data center facilities. Users may also opt to manage their public cloud services with a third-party cloud management tool. Users of public cloud services can generally select from three basic cloud provisioning categories: User self-provisioning: Customers purchase cloud services directly from the provider, typically through a web form or console interface. The customer pays on a per-transaction basis. Advanced provisioning: Customers contract in advance a predetermined amount of resources, which are prepared in advance of service. The customer pays a flat fee or a monthly fee. Dynamic provisioning: The provider allocates resources when the customer needs them, then decommissions them when they are no longer needed. The customer is charged on a pay-per-use basis. Managing a private cloud requires software tools to help create a virtualized pool of compute resources, provide a self-service portal for end users and handle security, resource allocation, tracking and billing. Management tools for private clouds tend to be service driven, as opposed to resource driven, because cloud environments are typically highly virtualized and organized in terms of portable workloads. In hybrid cloud environments, compute, network and storage resources must be managed across multiple domains, so a good management strategy should start by defining what needs to be managed, and where and how to do it. Policies to help govern these domains should include configuration and installation of images, access control, and budgeting and reporting. Access control often includes the use of Single sign-on (SSO), in which a user logs in once and gains access to all systems without being prompted to log in again at each of them. == Characteristics of Cloud Management == Cloud management combines software and technologies in a design for managing cloud environments. Software developers have responded to the management challenges of cloud computing with a variety of cloud management platforms and tools. These tools include native tools offered by public cloud providers as well as third-party tools designed to provide consistent functionality across multiple cloud providers. Administrators must balance the competing requirements of efficient consistency across different cloud platforms with access to different native functionality within individual cloud platforms. The growing acceptance of public cloud and increased multicloud usage is driving the need for consistent cross-platform management. Rapid adoption of cloud services is introducing a new set of management challenges for those technical professionals responsible for managing IT systems and services. Cloud-management platforms and tools should have the ability to provide minimum functionality in the following categories. Functionality can be both natively provided or orchestrated via third-party integration. Provisioning and orchestration: create, modify, and delete resources as well as orchestrate workflows and management of workloads Automation: Enable cloud consumption and deployment of app services via infrastructure-as-code and other DevOps concepts Security and compliance: manage role-based access of cloud services and enforce security configurations Service request: collect and fulfill requests from users to access and deploy cloud resources. Monitoring and logging: collect performance and availability metrics as well as automate incident management and log aggregation Inventory and classification: discover and maintain pre-existing brownfield cloud resources plus monitor and manage changes Cost management and optimization: track and rightsize cloud spend and align capacity and performance to actual demand Migration, backup, and DR: enable data protection, disaster recovery, and data mobility via snapshots and/or data replication Organizations may group these criteria into key use cases including Cloud Brokerage, DevOps Automation, Governance, and Day-2 Life Cycle Operations. Enterprises with large-scale cloud implementations may require more robust cloud management tools which include specific characteristics, such as the ability to manage multiple platforms from a single point of reference, or intelligent analytics to automate processes like application lifecycle management. High-end cloud management tools should also have the ability to handle system failures automatically with capabilities such as self-monitoring, an explicit notification mechanism, and include failover and self-healing capabilities. == Multi-Cloud and Hybrid Cloud Management Challenges == Legacy management infrastructures, which are based on the concept of dedicated system relationships and architecture constructs, are not well suited to cloud environments where instances are continually launched and decommissioned. Instead, the dynamic nature of cloud computing requires monitoring and management tools that are adaptable, extensible and customizable. Cloud computing presents a number of management challenges. Companies using public clouds do not have ownership of the equipment hosting the cloud environment, and because the environment is not contained within their own networks, public cloud customers do not have full visibility or control. Users of public cloud services must also integrate with an architecture defined by the cloud provider, using its specific parameters for working with cloud components. Integration includes tying into the cloud APIs for configuring IP addresses, subnets, firewalls and data service functions for storage. Because control of these functions is based on the cloud provider’s infrastructure and services, public cloud users must integrate with the cloud infrastructure management. Capacity management is a challenge for both public and private cloud environments because end users have the ability to deploy applications using self-service portals. Applications of all sizes may appear in the environment, consume an unpredictable amount of resources, then disappear at any time. A possible solution is profiling the applications impact on computational resources. As result, the performance models allow the prediction of how resource utilization changes according to application patterns. Thus, resources can be dynamically scaled to meet the expected demand. This is critical to cloud providers that need to provision resources quickly to meet a growing demand by their applications. Charge-back—or, pricing resource use on a granular basis—is a challenge for both public and private cloud environments. Charge-back is a challenge for public cloud service providers because they must price their services competitively while still creating profit. Users of public cloud services may find charge-back challenging because it is difficult for IT groups to assess actual resource costs on a granular basis due to overlapping resources within an organization that may be paid for by an individual business unit, such as electrical power. For private cloud operators, charge-back is fairly straightforward, but the challenge lies in guessing how to allocate resources as closely as possible to actual resource usage to achieve the greatest operational efficiency. Exceeding budgets can be a risk. Hybrid cloud environments, which combine public and private cloud services, sometimes with traditional infrastructure elements, present their own set of management challenges. These include security concerns if sensitive data lands on public cloud servers, budget concerns around overuse of storage or bandwidth and proliferation of mismanaged images. Managing the information flow in a hybrid cloud environment is also a significant challenge. On-premises clouds must share information with applications hosted off-premises by public cloud providers, and this information may change constantly. Hybrid cloud environments also typically include a complex mix of policies, permissions and limits that must be managed consistently across both public and private clouds. == Cloud Management Platforms (CMP) == CMPs provide a means for a cloud service customer to manage the deployment and operation of applications and associated datasets across multiple cloud service infrastructures, including both on-premises cloud infrastructure and public cloud service provider infrastructure. In other words, CMPs provide management capabilities for hybrid cloud and multi-cloud environments. A cloud management platform (CMP) provides broad cloud management functionality atop both public cloud provider platforms and private cloud platforms. CMPs manage cloud services and resources that are distributed across multiple cloud platforms. The value of CMPs stands in delivering the maximum level of consistency between platforms without comp
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The Visualization Handbook

The Visualization Handbook is a textbook by Charles D. Hansen and Christopher R. Johnson that serves as a survey of the field of scientific visualization by presenting the basic concepts and algorithms in addition to a current review of visualization research topics and tools. It is commonly used as a textbook for scientific visualization graduate courses. It is also commonly cited as a reference for scientific visualization and computer graphics in published papers, with almost 500 citations documented on Google Scholar. == Table of Contents == PART I - Introduction Overview of Visualization - William J. Schroeder and Kenneth M. Martin PART II - Scalar Field Visualization: Isosurfaces Accelerated Isosurface Extraction Approaches -Yarden Livnat Time-Dependent Isosurface Extraction - Han-Wei Shen Optimal Isosurface Extraction - Paolo Cignoni, Claudio Montani, Robert Scopigno, and Enrico Puppo Isosurface Extraction Using Extrema Graphs - Takayuki Itoh and Koji Koyamada Isosurfaces and Level-Sets - Ross Whitaker PART III - Scalar Field Visualization: Volume Rendering Overview of Volume Rendering - Arie E. Kaufman and Klaus Mueller Volume Rendering Using Splatting - Roger Crawfis, Daqing Xue, and Caixia Zhang Multidimensional Transfer Functions for Volume Rendering - Joe Kniss, Gordon Kindlmann, and Charles D. Hansen Pre-Integrated Volume Rendering - Martin Kraus and Thomas Ertl Hardware-Accelerated Volume Rendering - Hanspeter Pfister PART IV - Vector Field Visualization Overview of Flow Visualization - Daniel Weiskopf and Gordon Erlebacher Flow Textures: High-Resolution Flow Visualization - Gordon Erlebacher, Bruno Jobard, and Daniel Weiskopf Detection and Visualization of Vortices - Ming Jiang, Raghu Machiraju, and David Thompson PART V - Tensor Field Visualization Oriented Tensor Reconstruction - Leonid Zhukov and Alan H. Barr Diffusion Tensor MRI Visualization - Song Zhang, David Laidlaw, and Gordon Kindlmann Topological Methods for Flow Visualization - Gerik Scheuermann and Xavier Tricoche PART VI - Geometric Modeling for Visualization 3D Mesh Compression - Jarek Rossignac Variational Modeling Methods for Visualization - Hans Hagen and Ingrid Hotz Model Simplification - Jonathan D. Cohen and Dinesh Manocha PART VII - Virtual Environments for Visualization Direct Manipulation in Virtual Reality - Steve Bryson The Visual Haptic Workbench - Milan Ikits and J. Dean Brederson Virtual Geographic Information Systems - William Ribarsky Visualization Using Virtual Reality - R. Bowen Loftin, Jim X. Chen, and Larry Rosenblum PART VIII - Large-Scale Data Visualization Desktop Delivery: Access to Large Datasets - Philip D. Heermann and Constantine Pavlakos Techniques for Visualizing Time-Varying Volume Data - Kwan-Liu Ma and Eric B. Lum Large-Scale Data Visualization and Rendering: A Problem-Driven Approach - Patrick McCormick and James Ahrens Issues and Architectures in Large-Scale Data Visualization - Constantine Pavlakos and Philip D. Heermann Consuming Network Bandwidth with Visapult - Wes Bethel and John Shalf PART IX - Visualization Software and Frameworks The Visualization Toolkit - William J. Schroeder and Kenneth M. Martin Visualization in the SCIRun Problem-Solving Environment - David M. Weinstein, Steven Parker, Jenny Simpson, Kurt Zimmerman, and Greg M. Jones Numerical Algorithms Group IRIS Explorer - Jeremy Walton AVS and AVS/Express - Jean M. Favre and Mario Valle Vis5D, Cave5D, and VisAD - Bill Hibbard Visualization with AVS - W. T. Hewitt, Nigel W. John, Matthew D. Cooper, K. Yien Kwok, George W. Leaver, Joanna M. Leng, Paul G. Lever, Mary J. McDerby, James S. Perrin, Mark Riding, I. Ari Sadarjoen, Tobias M. Schiebeck, and Colin C. Venters ParaView: An End-User Tool for Large-Data Visualization - James Ahrens, Berk Geveci, and Charles Law The Insight Toolkit: An Open-Source Initiative in Data Segmentation and Registration - Terry S. Yoo amira: A Highly Interactive System for Visual Data Analysis - Detlev Stalling, Malte Westerhoff, and Hans-Christian Hege PART X - Perceptual Issues in Visualization Extending Visualization to Perceptualization: The Importance of Perception in Effective Communication of Information - David S. Ebert Art and Science in Visualization - Victoria Interrante Exploiting Human Visual Perception in Visualization - Alan Chalmers and Kirsten Cater PART XI - Selected Topics and Applications Scalable Network Visualization - Stephen G. Eick Visual Data-Mining Techniques - Daniel A. Keim, Mike Sips, and Mihael Ankerst Visualization in Weather and Climate Research - Don Middleton, Tim Scheitlin, and Bob Wilhelmson Painting and Visualization - Robert M. Kirby, Daniel F. Keefe, and David Laidlaw Visualization and Natural Control Systems for Microscopy - Russell M. Taylor II, David Borland, Frederick P. Brooks, Jr., Mike Falvo, Kevin Jeffay, Gail Jones, David Marshburn, Stergios J. Papadakis, Lu-Chang Qin, Adam Seeger, F. Donelson Smith, Dianne Sonnenwald, Richard Superfine, Sean Washburn, Chris Weigle, Mary Whitton, Leandra Vicci, Martin Guthold, Tom Hudson, Philip Williams, and Warren Robinett Visualization for Computational Accelerator Physics - Kwan-Liu Ma, Greg Schussman, and Brett Wilson
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Blitter object

A blitter object (Bob) is a graphical element (GEL) used by the Amiga computer. Bobs are hardware sprite-like objects, movable on the screen with the help of the blitter coprocessor. == Overview == The AmigaOS GEL system consists of VSprites, Bobs, AnimComps (animation components) and AnimObs (animation objects), each extending the preceding with additional functionality. While VSprites are a virtualization of hardware sprites Bobs are drawn into a playfield by the blitter, saving and restoring the background of the GEL as required. The Bob with the highest video priority is the last one to be drawn, which makes it appear to be in front of all other Bobs. In contrast to hardware sprites Bobs are not limited in size and number. Bobs require more processing power than sprites, because they require at least one DMA memory copy operation to draw them on the screen. Sometimes three distinct memory copy operations are needed: one to save the screen area where the Bob would be drawn, one to actually draw the Bob, and one later to restore the screen background when the Bob moves away. An AnimComp adds animation to a Bob and an AnimOb groups AnimComps together and assigns them velocity and acceleration.
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Text Database and Dictionary of Classic Mayan

The project Text Database and Dictionary of Classic Mayan (abbr. TWKM) promotes research on the writing and language of pre-Hispanic Maya culture. It is housed in the Faculty of Arts at the University of Bonn and was established with funding from the North Rhine-Westphalian Academy of Sciences, Humanities and the Arts. The project has a projected run-time of fifteen years and is directed by Nikolai Grube from the Department of Anthropology of the Americas at the University of Bonn. The goal of the project is to conduct computer-based studies of all extant Maya hieroglyphic texts from an epigraphic and cultural-historical standpoint, and to produce and publish a database and a comprehensive dictionary of the Classic Mayan language. == Subject of the Project == The text database, as well as the dictionary that will be compiled by the conclusion of the project, will be assembled based on all known texts from the pre-Hispanic Maya culture. These texts were produced and used between approximately the third century B.C. through A.D. 1500, in a region that today includes parts of the countries of Mexico, Guatemala, Belize, and Honduras. The thousands of hieroglyphic inscriptions on monuments, ceramics, or daily objects that have survived into the present offer insight into the language's vocabulary and structure. The project's database and dictionary will digitally represent original spellings using the logo-syllabic Maya hieroglyphs, as well as their transcription and transliteration in the Roman alphabet. The data will be additionally annotated with various epigraphic analyses, translations, and further object-specific information. == Project Partners == TWKM will employ digital technologies in order to compile and make available the data and metadata, as well as to publish the project's research results. The project thereby methodologically positions itself in the field of the digital humanities. The project will be conducted in cooperation with the project partners (below), the research association for the eHumanities TextGrid, as well as the University and Regional Library of Bonn (ULB). The working environment that is currently under construction, in which the data and metadata will be compiled and annotated, will be realized in theTextGrid Laboratory, a software of the virtual research environment. A further component of this software, the TextGrid Repository, will make the data that are authorized for publication freely available online and ensure their long-term storage. The tools for data compilation and annotation attained from the modularly constructed and extended TextGrid lab thereby provide all the necessary materials for facilitating the research team's the typical epigraphic workflow. The workflow usually begins by documenting the texts and the objects on which they are preserved, and by compiling descriptive data. It then continues with the various levels of epigraphic and linguistic analysis, and concludes in the best case scenario with a translation of the analyzed inscription and a corresponding publication. In cooperation with the ULB, selected data will additionally be made available. The project's Virtual Inscription Archive will present online, in the Digital Collections of the ULB, hieroglyphic inscriptions selected from the published data in the repository, including an image of and brief information about the texts and the objects on which they are written, epigraphic analysis, and translation. == Project Goal == One of the project's goals is to produce a dictionary of Classic Mayan, in both digital and print form, towards the end of the project run-time. Additionally, a database with a corpus of inscriptions, including their translations and epigraphic analyses, will be made freely available online. The database furthermore will provide an ontology-like link of the contextual object data with the inscriptions and with each other, thereby allowing a cultural-historical arrangement of all contents within the periods of pre-Hispanic Maya culture. The contents of the database are additionally linked to citations of relevant literature. As a result, the database will also make freely available to both the scientific community and other interested parties a bibliography representing the research history and a base of knowledge concerning ancient Maya culture and script. In addition, the Classic Maya script, in its temporally defined stages of language development, will be gathered into and documented in a comprehensive language corpus with the aid of the information gathered by the project. In collaboration with all project participants, the corpus data can be used, together with the aid of various comparable analyses and also computational linguistic methods, such as inference-based methods, to confirm readings of some hieroglyphs that are currently only partially confirmed, and to eventually completely decipher the Classic Maya script.
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Cloudflare

Cloudflare, Inc., is an American technology company headquartered in San Francisco, California, that provides a range of internet services, including content delivery network (CDN) services, cloud cybersecurity, DDoS mitigation, and ICANN-accredited domain registration. The company's services act primarily as a reverse proxy between website visitors and a customer's hosting provider, improving performance and protecting against malicious traffic. Cloudflare was founded in 2009 by Matthew Prince, Lee Holloway, and Michelle Zatlyn. The company went public on the New York Stock Exchange in 2019 under the ticker symbol NET. Cloudflare has since expanded its offerings to include edge computing through its Workers platform, a public DNS resolver (1.1.1.1), and a VPN-like service known as WARP. In recent years, the company has integrated artificial intelligence into its infrastructure, acquiring companies such as Replicate and launching tools to manage AI bots and scrapers. According to W3Techs, Cloudflare is used by approximately 21.3% of all websites on the Internet as of January 2026. The company has been the subject of controversy regarding its policy of content neutrality. While Cloudflare executives have historically advocated for remaining a neutral infrastructure provider, the company has terminated services for specific high-profile websites associated with hate speech and violence, including The Daily Stormer, 8chan, and Kiwi Farms, following significant public pressure. Cloudflare has also faced criticism and litigation regarding copyright infringement by websites using its services, notably losing a lawsuit against Japanese publishers in 2025. The company experienced significant global outages in late 2025 which disrupted services for major platforms internationally. == History == Cloudflare was founded on July 26, 2009, by Matthew Prince, Lee Holloway, and Michelle Zatlyn. Prince and Holloway had previously collaborated on Project Honey Pot, a product of Unspam Technologies that partly inspired the basis of Cloudflare. In 2009, the company was venture-capital funded. On August 15, 2019, Cloudflare submitted its S-1 filing for an initial public offering on the New York Stock Exchange under the stock ticker NET. It opened for public trading on September 13, 2019, at $15 per share. According to the company, the name 'Cloudflare' was chosen, over the initial 'WebWall', because it best described what they were trying to do: build a "firewall in the cloud." In 2020, Cloudflare co-founder and COO Michelle Zatlyn was named president. Cloudflare has acquired web-services and security companies, including StopTheHacker (February 2014), CryptoSeal (June 2014), Eager Platform Co. (December 2016), Neumob (November 2017), S2 Systems (January 2020), Linc (December 2020), Zaraz (December 2021), Vectrix (February 2022), Area 1 Security (February 2022), Nefeli Networks (March 2024), BastionZero (May 2024), and Kivera (October 2024). Replicate (November 2025), and Human Native (January 2026). Since at least 2017, Cloudflare has used a wall of lava lamps at its San Francisco headquarters as a source of randomness for encryption keys, alongside double pendulums at its London offices and a Geiger counter at its Singapore offices. The lava lamp installation implements the Lavarand method, where a camera transforms the unpredictable shapes of the "lava" blobs into a digital image. In Q4 2022, Cloudflare provided paid services to 162,086 customers. In October 2024, Cloudflare won a lawsuit against patent troll Sable Networks. Sable paid Cloudflare $225,000, granted it a royalty-free license to its patent portfolio, and dedicated its patents to the public by abandoning its patent rights. In November 2025, it was announced Cloudflare had agreed to acquire Replicate, a San Francisco–based platform that enables software developers to run, fine-tune, and deploy open-source machine-learning models via an API without managing infrastructure. In January 2026, Cloudflare released an analysis regarding BGP routing leaks observed from the Venezuelan state-owned ISP CANTV (AS8048), which occurred on January 2 coincides with the arrest of Nicolás Maduro. While some security researchers had speculated that the outages were linked to U.S. cyber operations, Cloudflare's data indicated that the anomalies were consistent with a pattern of "insufficient routing export and import policies" by the ISP rather than malicious external interference. In January 2026, Cloudflare acquired Human Native, an AI data marketplace that brokers transactions between developers and content creators, for an undisclosed amount. On January 16, 2026, Cloudflare acquired The Astro Technology Company, the developers behind the open-source web framework Astro. In May 2026, Cloudflare announced the elimination of approximately 1,100 positions, around 20 percent of its workforce, in a restructuring the company attributed to the rapid adoption of artificial intelligence tools. The announcement coincided with the company's first-quarter 2026 earnings, which reported a record $639.8 million in quarterly revenue, a 34 percent year-over-year increase. CEO Matthew Prince stated the cuts were not driven by performance concerns but reflected roles made obsolete by AI, and that Cloudflare expected to employ more people by the end of 2027 than at any point during 2026. == Products == Cloudflare provides network and security products for consumers and businesses, utilizing edge computing, reverse proxies for web traffic, data center interconnects, and a content distribution network to serve content across its network of servers. It supports transport layer protocols TCP, UDP, QUIC, and many application layer protocols such as DNS over HTTPS, SMTP, and HTTP/2 with support for HTTP/2 Server Push. As of 2023, Cloudflare handles an average of 45 million HTTP requests per second. As of 2024, Cloudflare servers are powered by AMD EPYC 9684X processors. Cloudflare also provides analysis and reports on large-scale outages, including Verizon's October 2024 outage. === Artificial intelligence === In 2023, Cloudflare launched "Workers AI", a framework allowing for use of Nvidia GPU's within Cloudflare's network. In 2024, Cloudflare launched a tool that prevents bots from scraping websites. To build automatic bot detector models, the company analyzed "AI" bots and crawler traffic. The company also launched an "AI" assistant to generate charts based on queries by leveraging "Workers AI". Cloudflare announced plans in September 2024 to launch a marketplace where website owners can sell "AI" model providers access to scrape their site's content. In March 2025, Cloudflare announced a new feature called "AI Labyrinth", which combats unauthorized "AI" data scraping by serving fake "AI"-generated content to LLM bots. In July, the company rolled out a permission-based setting to allow websites to automatically block online bots from scraping data and content. Cloudflare released AutoRAG into beta in 2025. AutoRAG (retrieval augmented generation) creates a vector database of a website's unstructured content to identify relationships between concepts. It is part of an initiative with Microsoft, alongside their NLWeb standard, to make websites easier for people and automated systems to query. Cloudflare and GoDaddy partnered in April 2026 to enable AI Crawl Control features on GoDaddy hosted websites. This would allow site owners to decide how AI bot crawlers interact with their content. === DDoS mitigation === Cloudflare provides free and paid DDoS mitigation services that protect customers from distributed denial of service (DDoS) attacks. Cloudflare received media attention in June 2011 for providing DDoS mitigation for the website of LulzSec, a black hat hacking group. In March 2013, The Spamhaus Project was targeted by a DDoS attack that Cloudflare reported exceeded 300 gigabits per second (Gbit/s). Patrick Gilmore, of Akamai, stated that at the time it was "the largest publicly announced DDoS attack in the history of the Internet". While trying to defend Spamhaus against the DDoS attacks, Cloudflare ended up being attacked as well; Google and other companies eventually came to Spamhaus' defense and helped it to absorb the unprecedented amount of attack traffic. In 2014, Cloudflare began providing free DDoS mitigation for artists, activists, journalists, and human rights groups under the name "Project Galileo". In 2017, it extended the service to electoral infrastructure and political campaigns under the name "Athenian Project". By 2025, more than 2,900 users and organizations were participating in Project Galileo, including 31 US states. In February 2014, Cloudflare claimed to have mitigated an NTP reflection attack against an unnamed European customer, which it stated peaked at 400 Gbit/s. In November 2014, it reported a 500 Gbit/s DDoS attack in Hong Kong. In July 2021, the company claimed to have absorbed a DDoS atta
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Thermal attack

A thermal attack (aka thermal imaging attack) is an approach that exploits heat traces to uncover the entered credentials. These attacks rely on the phenomenon of heat transfer from one object to another. During authentication, heat transfers from the users' hands to the surface they are interacting with, leaving heat traces behind that can be analyzed using thermal cameras that operate in the far-infrared spectrum. These traces can be recovered and used to reconstruct the passwords. In some cases, the attack can be successful even 30 seconds after the user has authenticated. Thermal attacks can be performed after the victim had authenticated, alleviating the need for in-situ observation attacks (e.g., shoulder surfing attacks) that can be affected by hand occlusions. While smudge attacks can reveal the order of entries of graphical passwords, such as the Android Lock Patterns, thermal attacks can reveal the order of entries even in the case of PINs or alphanumeric passwords. The reason thermal attacks leak information about the order of entry is because keys and buttons that the user touches first lose heat over time, while recently touched ones maintain the heat signature for a longer time. This results in distinguishable heat patterns that can tell the attacker which entry was entered first. Thermal attacks were shown to be effective against plastic keypads, such as the ones used to enter credit card's PINs in supermarkets and restaurants, and on handheld mobile devices such as smartphones and tablets. In their paper published at the Conference on Human Factors in Computing Systems (CHI 2017), Abdelrahman et al. showed that the attack is feasible on today's smartphones. They also proposed some ways to mitigate the attack, such as swiping randomly on the screen to distort the heat traces, or forcing maximum CPU usage for a few seconds. Thermal attacks can also infer passwords from heat traces on keyboards. Researchers at the University of Glasgow showed that attackers who use AI methods can be more effective in performing thermal attacks. Their study presents a new tool called ThermoSecure and evaluates it in two user studies. The results show that ThermoSecure can successfully attack passwords with an average accuracy of 92% to 55%, depending on the length of the password. The effectiveness of thermal attacks also depends on typing behavior and the material of the keycaps. ABS keycaps, which retain heat traces longer, are more vulnerable to thermal attacks. The study also discusses ways to protect against thermal attacks and presents seven potential mitigation approaches. Dr Khamis, who led the development of the technology with Norah Alotaibi and John Williamson, said with thermal imaging cameras more affordable than ever and machine learning becoming more accessible, it was "very likely that people around the world are developing systems along similar lines to ThermoSecure in order to steal passwords". == Thermal Attack Mitigation == === Simple and Practical Measures === One basic and effective way to mitigate thermal attacks is to deliberately create heat noise over the input interface, such as a keypad or keyboard, after entering a password. For instance, placing one's palm over the entire interface for a few seconds after use can obscure the thermal pattern left by the fingers, making it much more difficult for an unauthorized user to interpret the heat traces. === Range of Proposed Strategies === In addition to simple methods, researchers have developed a spectrum of mitigation strategies to counter thermal attacks. These strategies encompass 15 different approaches including: Use of Biometrics: Replacing traditional pin codes or passwords with biometric authentication, such as fingerprint recognition or facial recognition, eliminates the issue of residual heat on keypads. Heating the Interface: Implementing technology to slightly warm up the keypad can effectively neutralize the heat traces left by fingers, preventing thermal cameras from capturing the pattern. Randomizing Key Layouts: Employing dynamic key layouts that change positions every time the interface is used, making it impossible to correlate heat patterns with static input positions. === Technological Intervention on Thermal Cameras === Another avenue for mitigation is to address the issue at the source by modifying thermal cameras. Proposals have been made to develop thermal cameras that can automatically detect vulnerable interfaces such as keyboards or keypads. When these interfaces are detected within the camera's field of view, the camera would be programmed to prevent the user from recording images of them. This solution, however, would require widespread adoption by thermal camera manufacturers. Additionally, the approach is particularly viable for thermal cameras connected to a computing device, such as a smartphone, which can process the images in real time. Many affordable thermal cameras are standalone and do not have connectivity or processing capabilities. However, thermal cameras designed for connection to mobile devices can utilize the smartphone's processing power, making this mitigation approach feasible for such devices.
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Tensor glyph

In scientific visualization a tensor glyph is an object that can visualize all or most of the nine degrees of freedom, such as acceleration, twist, or shear – of a 3 × 3 {\displaystyle 3\times 3} matrix. It is used for tensor field visualization, where a data-matrix is available at every point in the grid. "Glyphs, or icons, depict multiple data values by mapping them onto the shape, size, orientation, and surface appearance of a base geometric primitive." Tensor glyphs are a particular case of multivariate data glyphs. There are certain types of glyphs that are commonly used: Ellipsoid Cuboid Cylindrical Superquadrics According to Thomas Schultz and Gordon Kindlmann, specific types of tensor fields "play a central role in scientific and biomedical studies as well as in image analysis and feature-extraction methods."
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Jeremy Renner Official

Jeremy Renner Official (or Jeremy Renner on the Google Play Store) was a mobile app created by American actor Jeremy Renner. He created the app in March 2017 to hear the input and comments of his fans. The app was shut down in September 2019 in part due to the frequent bullying and trolling that the platform had experienced. The app featured optional microtransactions, with some ranging up to roughly US$400 despite the app itself being free. Upon shutting down the app, Renner issued a mass-refund for the collectible "stars" in the app for purchases made within the last ninety days, from the day the announcement was posted. He then posted an apology to the app itself, and the app was deleted from both the Google Play Store and the App Store shortly after. == Usage == Upon downloading the app, the user was faced with a video of Renner speaking about his fans and superfans, regular giveaways, and real-life updates. While the app was active, Renner posted regular questions and comments for fans. Renner occasionally livestreamed about his work and day-to-day life. The community developed to include memes, selfies, and a "Happy Rennsday" event on Wednesdays. == History == === 2017–2019 === The app launched in March 2017 with a promotional contest. Renner's fans were encouraged to download the app and create comments about being Renner's biggest fan; Renner would then choose a winner and transport the winner and a guest to have lunch with him at the Calgary Expo. In the first few months Renner teased behind-the-scenes of projects he was working on, which he now sporadically does on Instagram. The app was similarly designed to Instagram as well, with a near identically styled layout. Around midway through 2019, a hoax account of Renner was made to mock the celebrity, joking about masturbating to porn and defending another hoax account of Casey Anthony. FastCompany wrote extensively about Renner's app in April 2019, calling it "a surprising new kind of social media". The Ringer stated "Jeremy Renner's Jeremy Renner app is the Jeremy Renner of apps." === After deletion (2019–2020) === After the shutdown of the app, a comedy-based pseudo-app with modular endings was released, called "The Jeremy Renner App Experience", in which the player plays as Jeremy Renner on the day of the Jeremy Renner Official app's shutdown. The app details several different choices on how Renner handles the situation. A six-part podcast was also created to mock the app's deletion, called The Renner Files, featuring Carolyn Goldfarb and Sarah Ramos. == Controversies == === Marketing === One of the main controversies of Renner's app was its marketing. The app's developers, Escapex, specialized in and grew famous for making similar monetized apps for celebrities. The marketing campaign was based on direct contact with Renner, whose chances were increased with regular payments for "stars", although very few encounters seemed to happen with Renner himself. The multiple problems with the app led the CEO of Escapex, Sephi Shapira, to call the app a "freak situation", and added "Am I concerned about this? Not more than I'm concerned about 50 other things I'm dealing with as a startup company." Along with the marketing failures, the app was seen as misrepresenting itself as seemingly erotic with some advertisements featuring Renner suggestively staring at the camera, despite the actual app being initially considered safe for children. === Harassment === After its release in 2017, the app was met with waves of harassment and bullying by many users on the app, most frequently by using impersonation — referenced in Renner's apology/deletion notice. Some death threats were made across the app by fraud accounts pretending to be several controversial celebrities, including O. J. Simpson and Casey Anthony. As early as October 2017, there were claims of censorship, bullying, and "contest-rigging". In September 2019, comedian Stefan Heck publicized his discovery of the fact that replies through the app appeared as if they were sent by Renner himself in push notifications. After several users abused this feature, Renner asked Escapex to shut down the app.
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Brave Leo

Brave Leo is a large language model-based chatbot developed by Brave Software and included with the Brave browser. == History == In November 2023, the company said versions for iOS and Android would be available "in the coming months". == Features == Since January 2024, Leo has used the open-source Mixtral 8x7B from Mistral AI as its default large language model, in addition to LLaMA 2 from Meta Platforms and Claude from Anthropic, both of which have been used previously. Leo can suggest follow-up questions, and summarize webpages, PDFs, and videos. Leo has a $15 (US) per month premium version that enables more requests and uses larger LLMs. == Privacy == The answers given by Leo are not saved. Brave uses the slogan Love Privacy to emphasize its focus on user privacy and data protection. The phrase has been featured in Brave's official marketing campaigns and has been cited in media coverage of the browser's privacy-first approach. == Controversies == In 2023, PC World reported that Leo evades questions about US elections.
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Security type system

In computer science, a type system can be described as a syntactic framework which contains a set of rules that are used to assign a type property (int, boolean, char etc.) to various components of a computer program, such as variables or functions. A security type system works in a similar way, only with a main focus on the security of the computer program, through information flow control. Thus, the various components of the program are assigned security types, or labels. The aim of a such system is to ultimately be able to verify that a given program conforms to the type system rules and satisfies non-interference. Security type systems is one of many security techniques used in the field of language-based security, and is tightly connected to information flow and information flow policies. In simple terms, a security type system can be used to detect if there exists any kind of violation of confidentiality or integrity in a program, i.e. the programmer wants to detect if the program is in line with the information flow policy or not. == A simple information flow policy == Suppose there are two users, A and B. In a program, the following security classes (SC) are introduced: SC = {∅, {A}, {B}, {A,B}}, where ∅ is the empty set. The information flow policy should define the direction that information is allowed to flow, which is dependent on whether the policy allows read or write operations. This example considers read operations (confidentiality). The following flows are allowed: → = {({A}, {A}), ({B}, {B}), ({A,B}, {A,B}), ({A,B}, {A}), ({A,B}, {B}), ({A}, ∅), ({B}, ∅), ({A,B}, ∅)} This can also be described as a superset (⊇). In words: information is allowed to flow towards stricter levels of confidentiality. The combination operator (⊕) can express how security classes can perform read operations with respect to other security classes. For example: {A} ⊕ {A,B} = {A} — the only security class that can read from both {A} and {A,B} is {A}. {A} ⊕ {B} = ∅ — neither {A} nor {B} are allowed to read from both {A} and {B}. This can also be described as an intersection (∩) between security classes. An information flow policy can be illustrated as a Hasse diagram. The policy should also be a lattice, that is, it has a greatest lower-bound and least upper-bound (there always exists a combination between security classes). In the case of integrity, information will flow in the opposite direction, thus the policy will be inverted. == Information flow policy in security type systems == Once the policy is in place, the software developer can apply the security classes to the program components. Use of a security type system is usually combined with a compiler that can perform the verification of the information flow according to the type system rules. For the sake of simplicity, a very simple computer program, together with the information flow policy as described in the previous section, can be used as a demonstration. The simple program is given in the following pseudocode: if y{A} = 1 then x{A,B} := 0 else x{A,B} := 1 Here, an equality check is made on a variable y that is assigned the security class {A}. A variable x with a lower security class ({A,B}) is influenced by this check. This means that information is leaking from class {A} to class {A,B}, which is a violation of the confidentiality policy. This leak should be detected by the security type system. === Example === Designing a security type system requires a function (also known as a security environment) that creates a mapping from variables to security types, or classes. This function can be called Γ, such that Γ(x) = τ, where x is a variable and τ is the security class, or type. Security classes are assigned (also called "judgement") to program components, using the following notation: Types are assigned to read operations by: Γ ⊢ e : τ. Types are assigned to write operations by: Γ ⊢ S : τ cmd. Constants can be assigned any type. The following bottom-up notation can be used to decompose the program: ⁠assumption1 ... assumptionn/conclusion⁠. Once the program is decomposed into trivial judgements, by which the type can easily be determined, the types for the less trivial parts of the program can be derived. Each "numerator" is considered in isolation, looking at the type of each statement to see if an allowed type can be derived for the "denominator", based on the defined type system "rules". ==== Rules ==== The main part of the security type system is the rules. They say how the program should be decomposed and how type verification should be performed. This toy program consists of a conditional test and two possible variable assignments. Rules for these two events are defined as follows: Applying this to the simple program introduced above yields: The type system detects the policy violation in line 2, where a read operation of security class {A} is performed, followed by two write operations of a less strict security class {A,B}. In more formalized terms, {A} ⋢ {A,B}, {A,B} (from the rule of the conditional test). Thus, the program is classified as "not typeable". === Soundness === The soundness of a security type system can be informally defined as: If program P is well typed, P satisfies non-interference. Volpano, Smith and Irvine were the first to prove soundness of a security type system for a deterministic imperative programming language with a standard (non-instrumented) semantics using the notion of non-interference.
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Digital supply chain security

Digital supply chain security refers to efforts to enhance cyber security within the supply chain. It is a subset of supply chain security and is focused on the management of cyber security requirements for information technology systems, software and networks, which are driven by threats such as cyber-terrorism, malware, data theft and the advanced persistent threat (APT). Typical supply chain cyber security activities for minimizing risks include buying only from trusted vendors, disconnecting critical machines from outside networks, and educating users on the threats and protective measures they can take. The acting deputy undersecretary for the National Protection and Programs Directorate for the United States Department of Homeland Security, Greg Schaffer, stated at a hearing that he is aware that there are instances where malware has been found on imported electronic and computer devices sold within the United States. == Examples of supply chain cyber security threats == Network or computer hardware that is delivered with malware installed on it already. Malware that is inserted into software or hardware (by various means) Vulnerabilities in software applications and networks within the supply chain that are discovered by malicious hackers Counterfeit computer hardware == Related U.S. government efforts == Comprehensive National Cyber Initiative Defense Procurement Regulations: Noted in section 806 of the National Defense Authorization Act International Strategy for Cyberspace: White House lays out for the first time the U.S.’s vision for a secure and open Internet. The strategy outlines three main themes: diplomacy, development and defense. Diplomacy: The strategy sets out to “promote an open, interoperable, secure and reliable information and communication infrastructure” by establishing norms of acceptable state behavior built through consensus among nations. Development: Through this strategy the government seeks to “facilitate cybersecurity capacity-building abroad, bilaterally and through multilateral organizations.” The objective is to protect the global IT infrastructure and to build closer international partnerships to sustain open and secure networks. Defense: The strategy calls out that the government “will ensure that the risks associated with attacking or exploiting our networks vastly outweigh the potential benefits” and calls for all nations to investigate, apprehend and prosecute criminals and non-state actors who intrude and disrupt network systems. == Related government efforts around the world == Common Criteria offers with Evaluation Assurance Level(EAL) 4 an opportunity to evaluate all relevant aspects of the digital supply chain security like the product, the development environment, IT systems security, the processes in human resource, physical security and with the module ALC_FLR.3 (Systematic Flaw Remediation) also security update processes and methods even by physical site visits. EAL 4 is mutually recognized in countries that signed the SOGIS-MRA and up to ELA 2 in countries the signed the CCRA but including ALC_FRL.3. Russia: Russia has had non-disclosed functionality certification requirements for several years and has recently initiated the National Software Platform effort based on open-source software. This reflects the apparent desire for national autonomy, reducing dependence on foreign suppliers. India: Recognition of supply chain risk in its draft National Cybersecurity Strategy. Rather than targeting specific products for exclusion, it is considering Indigenous Innovation policies, giving preferences to domestic ITC suppliers in order to create a robust, globally competitive national presence in the sector. China: Deriving from goals in the 11th Five Year Plan (2006–2010), China introduced and pursued a mix of security-focused and aggressive Indigenous Innovation policies. China is requiring an indigenous innovation product catalog be used for its government procurement and implementing a Multi-level Protection Scheme (MLPS) which requires (among other things) product developers and manufacturers to be Chinese citizens or legal persons, and product core technology and key components must have independent Chinese or indigenous intellectual property rights. == Private sector efforts == SLSA (Supply-chain Levels for Software Artifacts) is an end-to-end framework for ensuring the integrity of software artifacts throughout the software supply chain. The requirements are inspired by Google’s internal "Binary Authorization for Borg" that has been in use for the past 8+ years and that is mandatory for all of Google's production workloads. The goal of SLSA is to improve the state of the industry, particularly open source, to defend against the most pressing integrity threats. With SLSA, consumers can make informed choices about the security posture of the software they consume. == Other references == Financial Sector Information Sharing and Analysis Center International Strategy for Cyberspace (from the White House) NSTIC SafeCode Whitepaper Archived 2013-10-21 at the Wayback Machine Trusted Technology Forum and the Open Trusted Technology Provider Standard (O-TTPS) Archived 2012-01-03 at the Wayback Machine Cyber Supply Chain Security Solution Malware Implants in Firmware Supply Chain in the Software Era INFORMATION AND COMMUNICATIONS TECHNOLOGY SUPPLY CHAIN RISK MANAGEMENT TASK FORCE: INTERIM REPORT
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Halloween Problem

In computing, the Halloween Problem refers to a phenomenon in databases in which an update operation causes a change in the physical location of a row, potentially allowing the row to be visited again later in the same update operation. This could even cause an infinite loop in some cases where updates continually place the updated record ahead of the scan performing the update operation. The potential for this database error was first discovered by Don Chamberlin, Pat Selinger, and Morton Astrahan in the mid-1970s, on Halloween day, while working on query optimization. They wrote a SQL query supposed to give a ten percent raise to every employee who earned less than $25,000. This query would run successfully, with no errors, but when finished all the employees in the database earned at least $25,000, because it kept giving them a raise until they reached that level. The expectation was that the query would iterate over each of the employee records with a salary less than $25,000 precisely once. In fact, because even updated records were visible to the query execution engine and so continued to match the query's criteria, salary records were matching multiple times and each time being given a 10% raise until they were all greater than $25,000. Contrary to what some believe, the name is not descriptive of the nature of the problem but rather was given due to the day it was discovered on. As recounted by Don Chamberlin: Pat and Morton discovered this problem on Halloween... I remember they came into my office and said, "Chamberlin, look at this. We have to make sure that when the optimizer is making a plan for processing an update, it doesn't use an index that is based on the field that is being updated. How are we going to do that?" It happened to be on a Friday, and we said, "Listen, we are not going to be able to solve this problem this afternoon. Let's just give it a name. We'll call it the Halloween Problem and we'll work on it next week." And it turns out it has been called that ever since.
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MoFA Mitra

MoFA Mitra is a mobile application launched by the Ministry of Foreign Affairs of Nepal to provide digital consular services, emergency support, rescue coordination, and complaint registration facilities for Nepali citizens living and working abroad. The application allows Nepali migrant workers, students, tourists, and Non-Resident Nepalis (NRNs) to access embassy services, emergency help, and official information directly from their smartphones. == Background == The need for a centralized digital support platform for Nepalis abroad had been discussed for several years due to increasing complaints related to labor exploitation, rescue delays, documentation problems, and lack of communication with Nepali diplomatic missions. Media organizations and migrant rights advocates had continuously highlighted issues faced by Nepali workers abroad, including human trafficking, fraudulent recruitment, delayed repatriation, and difficulties in receiving emergency assistance. In response, the Ministry of Foreign Affairs developed the MoFA Mitra app to digitize complaint handling, improve communication between embassies and citizens, and make emergency response faster and more accessible. == Features == The app includes several services and features for Nepali citizens abroad, including complaint registration, rescue coordination, embassy communication, and digital consular support services. Features of the application include: Online complaint registration Emergency rescue request system Direct contact with Nepali embassies and consulates Digital consular information Passport and document-related assistance Labor and migration support information Emergency hotline access Real-time notifications and alerts Location-based embassy information Tracking and coordination support for stranded citizens According to reports, the application was designed to simplify access to diplomatic services and strengthen emergency response coordination for Nepalis abroad. == Launch == The application was officially launched by Nepal’s Ministry of Foreign Affairs in Kathmandu in May 2026. Government officials stated that the app would strengthen Nepal’s digital governance system and improve support mechanisms for Nepali citizens residing overseas. Officials said the platform would help improve communication between Nepali diplomatic missions and citizens during emergencies and rescue operations. == Reception == The launch of the app received positive coverage from Nepali and international media outlets. Commentators described the initiative as a significant step toward modernization of Nepal’s diplomatic and consular services and digital governance infrastructure. Some observers also emphasized the importance of effective implementation, rapid response mechanisms, and continuous monitoring to ensure practical benefits for migrant workers abroad.
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Data commingling

Data commingling, in computer science, occurs when different items or kinds of data are stored in such a way that they become commonly accessible when they are supposed to remain separated. In cloud computing, this can occur where different customer data sits on the same server. Data that is commingled can present a security vulnerability. Data commingling can also occur due to high speed data transmission mixing. In this situation, data of one security level can inadvertently or purposely be mixed with data of a lower or higher security level on the same transmission portal. Portal vehicles can be wire, fiber optics, microwave or various radio frequency transmission portals. This commingling can cause breaches of security and become a source of legal issues to any entity, corporation or individual. Data commingling can also occur when personal computers and personal software programs are used for business, security, government, etc. uses. In the early formulation stages of entities, non-profit or profit corporations, LLC's, LLP's, etc., the creation and use of stand-alone computers and stand-alone networks, "absolutely unconnected" to involved individuals, is the easiest, and safest way to prevent Data Commingling.
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Hexagonal sampling

A multidimensional signal is a function of M independent variables where M ≥ 2 {\displaystyle M\geq 2} . Real world signals, which are generally continuous time signals, have to be discretized (sampled) in order to ensure that digital systems can be used to process the signals. It is during this process of discretization where sampling comes into picture. Although there are many ways of obtaining a discrete representation of a continuous time signal, periodic sampling is by far the simplest scheme. Theoretically, sampling can be performed with respect to any set of points. But practically, sampling is carried out with respect to a set of points that have a certain algebraic structure. Such structures are called lattices. Mathematically, the process of sampling an N {\displaystyle N} -dimensional signal can be written as: w ( t ^ ) = w ( V . n ^ ) {\displaystyle w({\hat {t}})=w(V.{\hat {n}})} where t ^ {\displaystyle {\hat {t}}} is continuous domain M-dimensional vector (M-D) that is being sampled, n ^ {\displaystyle {\hat {n}}} is an M-dimensional integer vector corresponding to indices of a sample, and V is an N × N {\displaystyle N\times N} sampling matrix. == Motivation == Multidimensional sampling provides the opportunity to look at digital methods to process signals. Some of the advantages of processing signals in the digital domain include flexibility via programmable DSP operations, signal storage without the loss of fidelity, opportunity for encryption in communication, lower sensitivity to hardware tolerances. Thus, digital methods are simultaneously both powerful and flexible. In many applications, they act as less expensive alternatives to their analog counterparts. Sometimes, the algorithms implemented using digital hardware are so complex that they have no analog counterparts. Multidimensional digital signal processing deals with processing signals represented as multidimensional arrays such as 2-D sequences or sampled images.[1] Processing these signals in the digital domain permits the use of digital hardware where in signal processing operations are specified by algorithms. As real world signals are continuous time signals, multidimensional sampling plays a crucial role in discretizing the real world signals. The discrete time signals are in turn processed using digital hardware to extract information from the signal. == Preliminaries == === Region of Support === The region outside of which the samples of the signal take zero values is known as the Region of support (ROS). From the definition, it is clear that the region of support of a signal is not unique. === Fourier transform === The Fourier transform is a tool that allows us to simplify mathematical operations performed on the signal. The transform basically represents any signal as a weighted combination of sinusoids. The Fourier and the inverse Fourier transform of an M-dimensional signal can be defined as follows: X a ( Ω ^ ) = ∫ − ∞ + ∞ x a ( t ^ ) e − j Ω ^ T t ^ d t ^ {\displaystyle X_{a}({\hat {\Omega }})=\int _{-\infty }^{+\infty }\!x_{a}({\hat {t}})e^{-j{\hat {\Omega }}^{T}{\hat {t}}}d{\hat {t}}} x a ( t ^ ) = 1 2 π M ∫ − ∞ + ∞ X ( Ω ^ ) e ( j Ω ^ T t ^ ) d Ω ^ {\displaystyle x_{a}({\hat {t}})={\frac {1}{2\pi ^{M}}}\int _{-\infty }^{+\infty }\!X({\hat {\Omega }})e^{(j{\hat {\Omega }}^{T}{\hat {t}})}\,\mathrm {d} {\hat {\Omega }}} The cap symbol ^ indicates that the operation is performed on vectors. The Fourier transform of the sampled signal is observed to be a periodic extension of the continuous time Fourier transform of the signal. This is mathematically represented as: X ( ω ) = 1 | d e t ( V ) | ∑ k X a ( Ω ^ − U k ) {\displaystyle X(\omega )={\frac {1}{|det(V)|}}\sum _{k}\!X_{a}({\hat {\Omega }}-Uk)} where ω = V ~ Ω {\displaystyle \omega ={\tilde {V}}\Omega } and U = 2 π V ~ {\displaystyle U=2\pi {\tilde {V}}} is the periodicity matrix where ~ denotes matrix transposition. Thus sampling in the spatial domain results in periodicity in the Fourier domain. === Aliasing === A band limited signal may be periodically replicated in many ways. If the replication results in an overlap between replicated regions, the signal suffers from aliasing. Under such conditions, a continuous time signal cannot be perfectly recovered from its samples. Thus in order to ensure perfect recovery of the continuous signal, there must be zero overlap multidimensional sampling of the replicated regions in the transformed domain. As in the case of 1-dimensional signals, aliasing can be prevented if the continuous time signal is sampled at an adequate sufficiently high rate. === Sampling density === It is a measure of the number of samples per unit area. It is defined as: S . D = 1 | d e t ( V ) | = | d e t ( U ) | 4 π 2 {\displaystyle S.D={\frac {1}{|det(V)|}}={\frac {|det(U)|}{4\pi ^{2}}}} . The minimum number of samples per unit area required to completely recover the continuous time signal is termed as optimal sampling density. In applications where memory or processing time are limited, emphasis must be given to minimizing the number of samples required to represent the signal completely. == Existing approaches == For a bandlimited waveform, there are infinitely many ways the signal can be sampled without producing aliases in the Fourier domain. But only two strategies are commonly used: rectangular sampling and hexagonal sampling. === Rectangular and Hexagonal sampling === In rectangular sampling, a 2-dimensional signal, for example, is sampled according to the following V matrix: V r e c t = [ T 1 0 0 T 2 ] {\displaystyle V_{rect}={\begin{bmatrix}T1&0\\0&T2\end{bmatrix}}} where T1 and T2 are the sampling periods along the horizontal and vertical direction respectively. In hexagonal sampling, the V matrix assumes the following general form: V h e x = [ T 1 T 1 − T 2 T 2 ] {\displaystyle V_{hex}={\begin{bmatrix}T1&T1\\-T2&T2\end{bmatrix}}} The difference in the efficiency of the two schemes is highlighted using a bandlimited signal with a circular region of support of radius R. The circle can be inscribed in a square of length 2R or a regular hexagon of length 2 R 3 {\displaystyle {\frac {2R}{\sqrt {3}}}} . Consequently, the region of support is now transformed into a square and a hexagon respectively. If these regions are periodically replicated in the frequency domain such that there is zero overlap between any two regions, then by periodically replicating the square region of support, we effectively sample the continuous signal on a rectangular lattice. Similarly periodic replication of the hexagonal region of support maps to sampling the continuous signal on a hexagonal lattice. From U, the periodicity matrix, we can calculate the optimal sampling density for both the rectangular and hexagonal schemes. It is found that in order to completely recover the circularly band-limited signal, the hexagonal sampling scheme requires 13.4% fewer samples than the rectangular sampling scheme. The reduction may appear to be of little significance for a 2-dimensional signal. But as the dimensionality of the signal increases, the efficiency of the hexagonal sampling scheme will become far more evident. For instance, the reduction achieved for an 8-dimensional signal is 93.8%. To highlight the importance of the obtained result [2], try and visualize an image as a collection of infinite number of samples. The primary entity responsible for vision, i.e. the photoreceptors (rods and cones) are present on the retina of all mammals. These cells are not arranged in rows and columns. By adapting a hexagonal sampling scheme, our eyes are able to process images much more efficiently. The importance of hexagonal sampling lies in the fact that the photoreceptors of the human vision system lie on a hexagonal sampling lattice and, thus, perform hexagonal sampling.[3] In fact, it can be shown that the hexagonal sampling scheme is the optimal sampling scheme for a circularly band-limited signal. == Applications == === Aliasing effects minimized by the use of optimal sampling grids === Recent advances in the CCD technology has made hexagonal sampling feasible for real life applications. Historically, because of technology constraints, detector arrays were implemented only on 2-dimensional rectangular sampling lattices with rectangular shape detectors. But the super [CCD] detector introduced by Fuji has an octagonal shaped pixel in a hexagonal grid. Theoretically, the performance of the detector was greatly increased by introducing an octagonal pixel. The number of pixels required to represent the sample was reduced and there was significant improvement in the Signal-to-Noise Ratio (SNR) when compared with that of a rectangular pixel. But the drawback of using hexagonal pixels is that the associated fill factor will be less than 82%. An alternative method would be to interpolate hexagonal pixels in such a manner that we ultimately end up with a rectangular grid. The Spot 5 satellite incorporates a
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