A global computer memory supply shortage started in 2024 due to supply constraints and rapid price escalation in the semiconductor memory market, particularly affecting DRAM and NAND flash memory. This shortage is sometimes labelled by tech media outlets as "RAMmageddon" or the "RAMpocalypse". Unlike the 2020–2023 global chip shortage, which stemmed primarily from pandemic-related supply chain disruptions from COVID-19, this shortage is driven by a structural reallocation of manufacturing capacity toward high-margin products for artificial intelligence infrastructure, creating scarcity of computer memory in consumer and enterprise PC markets. According to a 2026 Kearney's PERLab analysis, the shortage is expected to last at least until 2030, with CEOs agreeing with the timelines. == Background == Following a severe market downturn in 2022–2023, major memory manufacturers—Samsung Electronics, SK Hynix, and Micron Technology—implemented strategic production cuts to stabilize pricing. By mid-2024, the rapid expansion of generative AI services triggered unprecedented demand for specialized memory products, particularly High Bandwidth Memory (HBM) used in AI accelerators and data center GPUs. Specialized components of semiconductor technology are also experiencing supply constraints due to high demand in AI application. For example, glass cloth, a high-performance glass fiber substrate used for power efficient high speed data transfer and a crucial component of semiconductor manufacturing, is experiencing a supply crisis. Nitto Boseki, a Japanese firm having overwhelming monopoly in its production, is not able to meet increased demands, making chip-makers such as Qualcomm, Apple, Nvidia and AMD compete for securing supply. There are also reports of smaller electronics companies struggling to find suppliers for components such as NAND flash. Memory suppliers are adapting to increased demands and market unpredictability by requiring prepayment or shorter time-frame of payment, which makes it more difficult for smaller firms to acquire capital to survive. By 2026, due to steadily increased demand on resources, CPUs are also experiencing shortage issues due to low fabrication capacity, prioritisation of server CPUs, and increased demand, with CPU prices also being forecast to increase by as much as 15%. The demand on memory has also increased strain on other electronic components such as hard disk devices, with reports such as Western Digital's hard disk supply for 2026 being booked for enterprise applications before February 2026. A 2024 McKinsey analysis projected that global demand for AI-ready data center capacity would grow at approximately 33% annually through 2030, with AI workloads consuming roughly 70% of total data center capacity by the decade's end. In addition, according to Kearney's State of Semiconductor 2025 Report, executives were already expecting a shortage in the <8nm wafer size with memory chips being mentioned as an acute source of concern. Multiple companies mentioned being prepared for it through long-term agreements with RAM suppliers or amassing additional inventory. On 24 March 2026, Google announced TurboQuant, a memory compression technology focused on large language models (LLM) and vector search engines, which it claimed achieves 6x lower memory consumption in tested local LLMs and 8x performance enhancement in tests running on H100 accelerators. The technology is also a drop in enhancement for existing inference pipeline. Amid speculation about memory demand trends, memory manufacturers, SanDisk, Micron, Western Digital and Seagate, among other companies involved in memory manufacture experienced stock price declines. Prices of memory kits also reduced in the following months, although still at inflated prices. == Causes == === HBM production displacement === HBM manufacturing requires significantly more wafer capacity per bit than standard DRAM modules. Industry sources reported that as manufacturers allocated increasing wafer capacity to HBM production to meet contracts with AI infrastructure providers, the supply of conventional DDR4 and DDR5 modules for consumer PCs and smartphones contracted sharply. By September 2025, Samsung Electronics had reportedly expanded its 1c DRAM capacity to target 60,000 wafers per month specifically for HBM4 production, further diverting resources from consumer memory lines. === Geopolitical and trade barriers === The supply chain was further constrained by escalating trade tensions between the United States and China. Throughout 2025, fears of U.S. regulatory backlash and new tariff structures led major manufacturers like Samsung and SK Hynix to halt sales of older semiconductor manufacturing equipment to Chinese entities, effectively capping production capacity in the region. Additionally, proposed tariff policies by the U.S. administration in late 2025 prompted supply chain realignments, with Apple reportedly accelerating plans to source all U.S.-bound iPhones from India to avoid potential levies. === NAND flash capacity constraints === In the NAND flash segment, manufacturers prioritized higher-margin enterprise SSDs for data center applications while phasing out older process nodes more rapidly than anticipated. In November 2025, contract prices for NAND wafers increased by more than 60% month-over-month for certain product categories, with 512GB TLC experiencing the steepest rise as legacy manufacturing capacity was retired. == Impact on industry and consumers == === Manufacturer responses === Major PC manufacturers responded to component cost increases with significant price adjustments and supply chain strategies. Dell Technologies Chief Operating Officer Jeff Clarke stated during a November 2025 analyst call that the company had "never witnessed costs escalating at the current pace," describing tighter availability across DRAM, hard drives, and NAND flash memory. Analysts at Morgan Stanley downgraded Dell Technologies stock from "Overweight" to "Underweight" in late 2025, citing the company's heavy exposure to rising server memory costs. The firm warned that skyrocketing memory prices could significantly erode margins for server and PC OEMs. Conversely, Apple Inc. was reportedly less affected than its competitors, having secured long-term supply agreements for DRAM through the first quarter of 2026. Lenovo Chief Financial Officer Winston Cheng described the cost surge as "unprecedented" and disclosed that the company's memory inventories were approximately 50% above normal levels in anticipation of further price increases. === Consumer electronics sector === The shortage particularly affected smartphone manufacturers and other consumer electronics producers. DRAM prices reportedly rose by 172% throughout 2025, leading manufacturers like Samsung to halt new orders for DDR5 modules to reassess pricing structures and Micron to exit its 'Crucial' brand of consumer products. In Tokyo's Akihabara electronics district, retailers began limiting purchases of memory products to prevent hoarding, with prices for popular DDR5 memory modules more than doubling in some cases. Despite the broad trend of rising hardware costs, some companies engaged in aggressive pricing strategies to maintain market share; for example, Sony reduced the price of the PlayStation 5 by $100 for Black Friday 2025, potentially absorbing increased component costs to stimulate software ecosystem growth. Due to memory prices more than doubling in a single quarter, HP revealed in its Q1 2026 earnings call that memory costs account for 35% of PC build materials up from 15-18% previous quarter. Despite showing strong Q1 2026 earning driven by Windows 11 upgrade cycle and AI PC adoption, HP warned investors of low operating margins and up to double digit percentage decline for coming quarter. Trendforce, an IT analytics company, updated its forecast from 1.7% year-over-year growth in PC market to 2.6% year-over-year decline for 2026, amid backdrop of steadily increasing prices and supply crisis. Research and analytics firms, Gartner and IDC expect worldwide PC market to decline 10-11% and smartphone market to decline 8-9% in 2026. Gartner also projects that rising memory prices will make low-margin entry level laptops under 500 USD financially unviable in two years. The RAM shortage has delayed the release of Valve's second Steam Machine due to increased memory prices. The device was originally set to launch in early 2026. === AI infrastructure competition === Technology companies including Google, Amazon, Microsoft, and Meta Platforms placed open-ended orders with memory suppliers, indicating they would accept as much supply as available regardless of cost, according to Reuters sources. The limited supply of AI chips has been cited as a reason for the slow down in compute growth. In October 2025, OpenAI formally announced a strategic partnership using letters of intent with Samsung Electronics and SK Hynix
Evntlive
Evntlive was an interactive digital concert venue that allowed music fans worldwide to stream concerts to their computer, tablet, or phone. Based in Redwood City, CA, EVNTLIVE Beta launched on April 15, 2013. EVNTLIVE provided users with the ability to switch camera angles, view All Access interviews and clips from artists, buy music, and chat with other online concert-goers in the in-app feature. Users could watch live and on-demand concerts with both free and pay-per-view concerts offered. In its first two months, EVNTLIVE streamed live performances of popular artists ranging from Bon Jovi to Wale, as well as music festivals such as Taste of Country and Mountain Jam; including performances by The Lumineers, Gary Clark Jr., Phil Lesh & Friends, Primus, and more. On December 6, 2013, Evntlive was acquired and absorbed by Yahoo!. The site ceased operations and redirected viewers to Yahoo! Music and Yahoo! Screen promptly afterwards. == About the Platform == EvntLive is an HTML5, web-based platform available on laptops, iPads, and mobile devices. Users must register for a free account on Evntlive’s website in order to reserve tickets and access live and on-demand content. Once they reserve tickets, they can view All Access features from their favorite artists or bands, purchase music, and interact with other online audience members using Buzz. Users can also switch between alternate camera angles as though they are on the concert floor - sharing the experience with their friends online in real-time. EvntLive was acquired by Yahoo in December 2013 == Artists == Bon Jovi Wale Escape the Fate The Parlotones === Taste of Country Music Festival === Trace Adkins Willie Nelson Justin Moore Montgomery Gentry Craig Campbell Blackberry Smoke Gloriana Dustin Lynch LoCash Cowboys Rachel Farley Parmalee Joe Nichols === Mountain Jam Music Festival === Source: The Lumineers Primus Widespread Panic Gov't Mule Phil Lesh The Avett Brothers Dispatch Rubblebucket Michael Franti Jackie Greene Deer Tick Gary Clark Jr. ALO The London Souls Nicki Bluhm Amy Helm The Lone Bellow The Revivalists Swear and Shake Roadkill Ghost Choir Michael Bernard Fitzgerald Michele Clark 's Sunset Sessions Semi Precious Weapons Dale Earnhardt Jr. Jr. DigiTour Media Pentatonix Allstar Weekend Tyler Ward === Launch Music Festival ===
Secret London
Secret London is a Facebook group started by 21-year-old Bristol University graduate, Tiffany Philippou, on 19 January 2010 in response to a Saatchi & Saatchi competition. The group grew rapidly (180,000 members as of 8 February 2010) and is composed mostly of Londoners who use the site to share suggestions and photos of London. After the group's early success, the founder announced her intention to launch a website of the same name by crowdsourcing the design and development. The website was launched on 16 February 2010. == Other secret cities == Following the initial success of Secret London, a number of other secret groups were independently started around the world, some of which already have over 100,000 users. As of 19 February 2010, the list of other groups includes: Secret Frankfurt, Secret Tel Aviv, Secret Paris, Secret New York, Secret Tokyo, Secret Toronto, Secret Los Angeles, Secret Exeter, Secret Boston, Secret Norwich, Secret Singapore, Secret Brighton, Secret Minneapolis, Secret Sydney, Secret Canberra, Secret Brisbane, Secret Wellington, Secret Christchurch, Secret Madeira, Secret Funchal, Secret Bristol and Secret Cardiff. == Controversy == Some commentators have questioned whether it possible to share secrets without compromising them, and whether sharing tips publicly will lead to over-exposure of the businesses who are recommended.
Public Services Network
The Public Services Network (PSN) is a UK government's high-performance network, which helps public sector organisations work together, reduce duplication and share resources. It unified the provision of network infrastructure across the United Kingdom public sector into an interconnected "network of networks" to increase efficiency and reduce overall public expenditure. It is now a legacy network and public sector organisations are being migrated to using services on the public internet. == Origins == The Public Services Network (PSN) was launched officially as part of the Transformational Government Strategy commencing in 2005, under the original name of the Public Sector Network. Prior to this, some parts of local government had already successfully implemented the concept. The Hampshire Public Services Network (HPSN) was the first PSN, launched in 1999, followed closely by Kent County Councils partnerships with the KPSN. The HPSN, encompassing all of the borough, district and unitary councils, with the County Council, as well as the Fire Services, the Isle of Wight Council and 540 schools. National PSN technical and architecture compliance criteria were established from 2007, by GDS working with local government leaders from Socitm (the Society of Information Technology Management) on the National CIO Council and the Local CIO Council. The PSN's aim was to bring public services organisations with a common interest onto a single, coherent and standards-based ‘network of networks’. This would create influence, economies of scale and a commonality of standards for secure and easy inter-connection between public service organisations. The original concept of a network of networks strategy was based upon the work already undertaken in local government and recognition of Communities of Interest (COI) within the Criminal Justice Sector during work by the Office for Criminal Justice Reform (OCJR) between 2005 and 2007 to enable data sharing across business units. In this context a COI was defined as groups of Government departments and external partners who in combination provided services within a specific area of operation and used the same data, with a similar risk profile, shared risk appetite and common governance framework. Historically each group member had implemented their own networks and standards of operation in isolation with little or no consideration as to how services and data may be shared and resulting in increased costs of operation. The Network of Networks strategy proposed within OCJR recommended the creation of specific networks based upon these Communities of Interest which were joined together through data interchange gateways supporting common standards. Under this approach networks would be arranged by data type and business functions such as Criminal Justice, Health and Social Care, Defence and Intelligence or Public Finance rather than solely on established departmental boundaries. Within a COI, trust relationships and data interchange are readily supported, enabling data sharing without a need to cross network boundaries and providing benefits of scale without the challenges and compromises intrinsic to homogeneous cross sector networks. Data is made available without a need to transport it between organisations and control is retained by the data originator. In early 2007 a group of UK Government department CTOs in conjunction with the Office for Government Commerce Buying Solutions (OGC BS) established the vision for a single commonly provided, procured and managed public sector voice and data network infrastructure to replace the multitude of separately procured and managed networks serving various segments of the UK public sector; Education, Health, Central Government, Local Government etc. In 2008 an Industry Working Group was established to document the objectives and requirements more clearly. Their report set out the architectural and commercial principles as well as anticipated security, service management, governance and transition arrangements. == Architecture == The PSN comprises a core network, the Government Conveyancing Network or GCN provided by GCN Service Providers or GCNSPs. The GCN interconnects multiple operator networks, termed Direct Network Service Providers or DNSPs. Subscriber organisations contract to a connection from a local participating DNSP, connect via that to GCN and hence onwards to other interconnected networks and services. The GCN network is entirely based on IPv4 and MPLS and the GCNSPs are not currently mandated to provide IPv6, though they should have a roadmap to implementing it if and when required. == Commercial framework == In 2010 Virgin Media Business, BT, Cable & Wireless and Global Crossing signed Deeds of Undertaking (DoU) and subsequently achieved accreditation for providing GCN and IP VPN services. In March 2012, BT, Cable & Wireless, Capita Business Services, Eircom, Fujitsu, Kcom, Level 3, Logicalis, MDNX, Thales, Updata and Virgin Media Business were successful bidders for the initial two-year PSN Connectivity framework. In June 2012, 29 companies were confirmed as suppliers of ICT services to the UK public sector under the Government's PSN Services framework contract. Apart from most of the previous suppliers, additional companies also included 2e2, Airwave Solutions, Azzurri Communications, Cassidian, CSC Computer Sciences, Computacenter, Daisy Communications, Easynet Global Services, EE, Freedom Communications, Icom Holdings, NextiraOne, PageOne Communications, Phoenix IT Group, Siemens Communications, Specialist Computer Centres, Telefónica, telent Technology Services, Uniworld Communications and Vodafone. == Governance == The PSN is managed within the Cabinet Office where it is part of the Government Digital Service. == Early implementations == There were already notable initiatives in progress in county council areas, demonstrating public sector network integration in both the Hampshire HPSN2 network and in Kent's community network. Project Pathway was established as a pilot linking these two county-wide networks, with Virgin Media Business and Global Crossing the subscriber and GCN network elements. Staffordshire County Council was the first council in England to establish a PSN that included the county's NHS Health partners. Other county councils have since followed the leads of these councils. == Transition == Centrally procured public sector networks are expected to migrate across to the PSN framework as they reach the end of their contract terms, either through an interim framework or directly. The Government Secure Intranet (GSi) contracts expired in September 2011, running on to 12 February 2012 and were replaced by the transitional Government Secure Intranet Convergence Framework (GCF). The Managed Telephony Service (MTS) contract expired on 31 December 2011 and was replaced by the Managed Telephony Convergence Framework (MTCF). == Future plan == In a blog post published on 20 January 2017, Government Digital Service announced that the Technology Leaders Network (TLN) had agreed that government was starting a journey away from the PSN. This was because using the Internet was considered suitable for the vast majority of the work that the public sector does. The blog post confirmed that the 'move was not going to happen immediately' and stated that 'there's quite a bit of work to do across the public sector to prepare for the changes'. It also stated that it was too early for a full timeline to be provided, although all PSN-connected organisations would be updated as the process evolved. The blog post confirmed that organisations that need to access services that are only available on the PSN would still need to connect to it for the time being and continue to meet its assurance requirements. In a blog post published on 16 March 2017, Government Digital Service (GDS) set out its plans for PSN assurance. The blog post confirmed that the PSN compliance process wasn't 'going anywhere, certainly for a while yet'. It explained that the TLN agreed that – as one of the only recognised, externally accredited, cross-government common assurance standards – it 'needs to live on far beyond the end of the physical PSN network'. Government Digital Service, along with the National Cyber Security Centre (NCSC) and the Cyber and Government Security Directorate, are now looking at ways to expand and reframe PSN compliance in a new context that, while retaining the assurance principles that are the basis of the existing process, will aim to improve the process. A GDS blog post titled 'The road to closing down the PSN' published on 8 September 2020 describes how the public sector will migrate away from the PSN. The Cabinet Office has set up a programme called Future Networks for Government (FN4G) to help organisations move away from the PSN.
Social network game
A social network game (sometimes simply referred to as a social media game, social gaming, or online social game) is a type of online game that is played through social networks or social media. They typically feature gamification systems with multiplayer gameplay mechanics. Social network games were originally implemented as browser games. As mobile gaming took off, the games moved to mobile as well. While they share many aspects of traditional video games, social network games often employ additional ones that make them distinct. Traditionally they are oriented to be social games and casual games. The first cross-platform "Facebook-to-Mobile" social network game was developed in 2011 by a Finnish company Star Arcade. Social network games are amongst the most popular games played in the world, with several products with tens of millions of players. (Lil) Green Patch, Happy Farm, and Mob Wars were some of the first successful games of this genre. FarmVille, Mafia Wars, Kantai Collection, and The Sims Social are more recent examples of popular social network game. Major companies that made or published social network games include Zynga, Wooga and Bigpoint Games. == Demographics == As of 2010, it was reported that 55 percent of the social network gaming demographic in the United States consisted of women while in the United Kingdom, women made up nearly 60 percent of the demographic. In addition, most social gamers were around the 30 to 59 age range, with the average social gamer being 43 years old. Social gaming may appeal more to the older demographic because it is free, easier to advance through in a short period, does not involve as much violence as traditional video games, and is easier to grasp. Other games target certain demographics that use social media, such as Pot Farm creating a community by involving elements of cannabis subculture in its gameplay. == Technology and platforms == A social network video game is a client-server application. The client in the web era was implemented with a mix of web technologies like Flash, HTML5, PHP and JavaScript. When mobile games moved to mobile, social game front ends were developed using mobile platform technologies like Java, Objective-C, Swift and C++. The back end was a mix of programming languages and systems, including PHP, Ruby, C++ and go. Where social network video games diverged from traditional game development was the combination of real-time analytics to continuously optimize game mechanics to drive growth, revenue, and engagement. == Distinct features == The following table outlines common characteristics of social games, mentioned by Björk at the 2010 GCO Games Convention Online: A social network game may employ any of the following features: asynchronous gameplay, which allows rules to be resolved without needing players to play at the same time. gamification, which video game mechanics such as achievements and points are applied to those experienced when playing games in order to motivate and engage users. community, as one of the most distinct features of social video games is in leveraging the player's social network. Quests or game goals may only be possible if a player "shares" with friends connected by the social network hosting the game or gets them to play, as well as "neighbors" or "allies". a lack of victory conditions: there are generally no victory conditions since most developers count on users playing their games often. The game never ends and no one is ever declared winner. Instead, many casual games have "quests" or "missions" for players to complete. This is not true for board game-like social games, such as Scrabble. a virtual currency which players usually must purchase with real-world money. With the in-game currency, players can buy upgrades that would otherwise take much longer to earn through in-game achievements. In many cases, some upgrades are only available with the virtual currency. == Engagement strategies == Since social network games are often less challenging than console games and they have relatively shorter game play, they use different techniques to stretch game play and tools to retain users. Continuous goals: The games assign specific goals for users to achieve. As they advance in the game, the goals become more challenging and time-consuming. They also provide frequent feedback with their performance. Every action will translate towards a certain goal that will be used to attain higher gaming capitals. Gaming capitals: Players are encouraged to earn different badges, trophies, and accolades that indicate their progress and accomplishments. Some achievements are unlocked just by advancing in the game while others may significantly alter the rationale behind the game and require extensive investment from players. The ways of gaining gaming capital are not limited to playing games but the games-related productive activities that are appreciated in the player's social circle too. By accumulating gaming capitals, they provide an intrinsic benefit to gamers as there is an avenue to boost their accomplishment and showcase their expertise of the game. The achievements are visible to their network of friends. Gaming capitals are a way for developers to increase replay value provides extended play time, and players get more value from the game. Motivation for collecting gaming capitals: 1. Legitimization: refers to society's willingness to approve or condone certain behavior. Collecting is about channeling one's materialistic desires into more meaningful pursuits. Game achievements serve a similar purpose, allowing players to justify the hours spent playing the game. 2. Self-extension: Gathering and controlling meaningful objects or experiences can work to gain one an improved sense of self. The collector's goal to complete a collection is symbolically about completing the self too. Events timed to real world: Popular games such as Dragon City and Wild Ones require users to wait a certain time period before their "energy bars" replenish. Without energy, they are unable to conduct any form of action. Gamers are forced to wait and return after their energy replenishes to continue playing. == Monetization == Social network games frequently monetize based on virtual good transactions, but other games are emerging that utilize newer economic models. === Virtual goods === Gamers will be able to purchase in game items like power-ups, avatar accessories, or decorative items users purchase within the game itself. This is realized by monetize products that do not technically exist. Virtual goods account for over 90% of all revenue generated by the world's top social game developers. Designers optimize user experience through additional gameplay, missions, and quests, without having to worry about overhead or unused stock. == Advertising == The following are common ways of advertising in social network games: === Banner advertisements === As banner ads within social networks tend to be where ad response is low, they tend to be priced at bottom-of-the-barrel CPMs of around $2. However, because social games generate so many page views, they are the biggest part of advertising revenue for the social gaming industry. === Video ads === Videos are the ad format with the most revenue per view. They tend to be higher-priced, either by CPMs ($35+ CPM in social games) or cost-per-completed-view. According to studies, video ads result in highest brand recall thus a good return on investment for advertisers. Video ads are shown either in in-game interstitials (e.g. when the game is loading a new screen) or through incentive-based advertising, i.e. you will get either an in-game reward or Facebook credits for watching an advertisement. === Product placement === A brand or product will be injected in a game in some way. Due to the variety of ways in which product placement can be accomplished in any media, and because the category is nascent, this category is not standardized at all, but some examples include branded in-game goods or even in-game quests. For example, in a game where you run a restaurant, you might be asked to collect ingredients to make a Starbucks Frappuccino, and receive in-game rewards for doing so. As these product placement deals are non-standard, they are largely charged with a production fee, which can be $350,000 to $750,000 depending on the type of placement and the popularity of the game. === Lead generation offers === Another form of advertising that is prevalent in many social games are lead generation offers. In this form of advertising, companies, usually from different industries, aim to convince players to sign up for their goods or services and in exchange, players will receive virtual gifts or advance in the game as a reward. === Sponsorship === ==== White label games ==== Applications that are built once, then individualized and licensed again and again. Developer can create a quality app focused on fun while leaving the edge
Focus recovery based on the linear canonical transform
For digital image processing, the Focus recovery from a defocused image is an ill-posed problem since it loses the component of high frequency. Most of the methods for focus recovery are based on depth estimation theory. The Linear canonical transform (LCT) gives a scalable kernel to fit many well-known optical effects. Using LCTs to approximate an optical system for imaging and inverting this system, theoretically permits recovery of a defocused image. == Depth of field and perceptual focus == In photography, depth of field (DOF) means an effective focal length. It is usually used for stressing an object and deemphasizing the background (and/or the foreground). The important measure related to DOF is the lens aperture. Decreasing the diameter of aperture increases focus and lowers resolution and vice versa. == The Huygens–Fresnel principle and DOF == The Huygens–Fresnel principle describes diffraction of wave propagation between two fields. It belongs to Fourier optics rather than geometric optics. The disturbance of diffraction depends on two circumstance parameters, the size of aperture and the interfiled distance. Consider a source field and a destination field, field 1 and field 0, respectively. P1(x1,y1) is the position in the source field, P0(x0,y0) is the position in the destination field. The Huygens–Fresnel principle gives the diffraction formula for two fields U(x0,y0), U(x1,y1) as following: U ( x 0 , y 0 ) = 1 j λ ∫ ∫ U ( x 1 , y 1 ) e j k r 01 r 01 cos θ d x 1 d y 1 {\displaystyle \mathbf {U} (x_{0},y_{0})={\frac {1}{j\lambda }}\int \!\int \mathbf {U} (x_{1},y_{1}){\frac {e^{jkr_{01}}}{r_{01}}}\cos \theta dx_{1}dy_{1}} where θ denotes the angle between r 01 {\displaystyle r_{01}} and z {\displaystyle z} . Replace cos θ by r 01 z {\displaystyle {\frac {r_{01}}{z}}} and r 01 {\displaystyle r_{01}} by [ ( x 0 − x 1 ) 2 + ( y 0 − y 1 ) 2 + z 2 ] 1 / 2 {\displaystyle [(x_{0}-x_{1})^{2}+(y_{0}-y_{1})^{2}+z^{2}]^{1/2}} we get U ( x 0 , y 0 ) = 1 j λ z ∫ ∫ U ( x 1 , y 1 ) exp ( j k z [ 1 + ( x 0 − x 1 z ) 2 + ( y 0 − y 1 z ) 2 ] 1 / 2 ) 1 + ( x 0 − x 1 z ) 2 + ( y 0 − y 1 z ) 2 d x 1 d y 1 {\displaystyle \mathbf {U} (x_{0},y_{0})={\frac {1}{j\lambda z}}\int \!\int \mathbf {U} (x_{1},y_{1}){\frac {\exp(jkz[1+({\frac {x_{0}-x_{1}}{z}})^{2}+({\frac {y_{0}-y_{1}}{z}})^{2}]^{1/2})}{1+({\frac {x_{0}-x_{1}}{z}})^{2}+({\frac {y_{0}-y_{1}}{z}})^{2}}}dx_{1}dy_{1}} The further distance z or the smaller aperture (x1,y1) causes a greater diffraction. A larger DOF can lead to a more effective focused wave distribution. This seems to be a conflict. Here are the notations: Diffraction In a real imaging environment, the depths of objects comparing to the aperture are usually not enough to lead to serious diffraction. However, a long enough depth of the object can truly blurs the image. Effective Focus Small aperture, small blurring radius, few wave information. Loses details in comparing to a large aperture. In conclusion, diffraction explains a micro behavior whereas DOF shows a macro behavior. Both of them are related to aperture size. == Linear canonical transform == As the meaning of "canonical", the linear canonical transform (LCT) is a scalable transform that connects to many important kernels such as the Fresnel transform, Fraunhofer transform and the fractional Fourier transform. It can be easily controlled by its four parameters, a, b, c, d (3 degrees of freedom). The definition: L M ( f ( u ) ) = ∫ L M ( u , u ′ ) f ( u ′ ) d u ′ {\displaystyle L_{M}(f(u))=\int L_{M}(u,u')f(u')du'} where L M ( u , u ′ ) = { 1 b e − j π / 4 e [ j π ( d b u 2 ) − 2 1 b u u ′ + a b u ′ 2 ] , if b ≠ 0 d e j 2 c d u 2 δ ( u ′ − d u ) , if b = 0 {\displaystyle L_{M}(u,u')={\begin{cases}{\sqrt {\frac {1}{b}}}e^{-j\pi /4}e^{[j\pi ({\frac {d}{b}}u^{2})-2{\frac {1}{b}}uu'+{\frac {a}{b}}u'^{2}]},&{\mbox{if }}b\neq 0\\{\sqrt {d}}e^{{\frac {j}{2}}cdu^{2}}\delta (u'-du),&{\mbox{if }}b=0\end{cases}}} Consider a general imaging system with object distance z0, focal length of the thin lens f and an imaging distance z1. The effect of the propagation in freespace acts as nearly a chirp convolution, that is, the formula of diffraction. Besides, the effect of the propagation in thin lens acts as a chirp multiplication. The parameters are all simplified as paraxial approximations while meeting the freespace propagation. It does not consider aperture size. From the properties of the LCT, it is possible to obtain those 4 parameters for this optical system as: [ 1 − z 1 f λ z 0 − λ z 0 z 1 f + λ z 1 − 1 λ f 1 − z 0 f ] {\displaystyle {\begin{bmatrix}1-{\frac {z_{1}}{f}}\quad &\lambda z_{0}-{\frac {\lambda z_{0}z_{1}}{f}}+\lambda z_{1}\\-{\frac {1}{\lambda f}}\quad &1-{\frac {z_{0}}{f}}\end{bmatrix}}} Once the values of z1, z0 and f are known, the LCT can simulate any optical system.
Big memory
Big-memory computers are machines with a large amount of random-access memory (RAM). The computers are required for databases, graph analytics, or more generally, high-performance computing, data science, and big data. Some database systems called in-memory databases are designed to run mostly in memory, rarely if ever retrieving data from disk or flash memory. See list of in-memory databases. == Details == The performance of big-memory systems depends on how the central processing units (CPUs) access the memory, via a conventional memory controller or via non-uniform memory access (NUMA). Performance also depends on the size and design of the CPU cache. Performance also depends on operating system (OS) design. The huge pages feature in Linux and other OSes can improve the efficiency of virtual memory. The transparent huge pages feature in Linux can offer better performance for some big-memory workloads. The "Large-Page Support" in Microsoft Windows enables server applications to establish large-page memory regions which are typically three orders of magnitude larger than the native page size.