Neural cryptography is a branch of cryptography dedicated to analyzing the application of stochastic algorithms, especially artificial neural network algorithms, for use in encryption and cryptanalysis. == Definition == Artificial neural networks are well known for their ability to selectively explore the solution space of a given problem. This feature finds a natural niche of application in the field of cryptanalysis. At the same time, neural networks offer a new approach to attack ciphering algorithms based on the principle that any function could be reproduced by a neural network, which is a powerful proven computational tool that can be used to find the inverse-function of any cryptographic algorithm. The ideas of mutual learning, self learning, and stochastic behavior of neural networks and similar algorithms can be used for different aspects of cryptography, like public-key cryptography, solving the key distribution problem using neural network mutual synchronization, hashing or generation of pseudo-random numbers. Another idea is the ability of a neural network to separate space in non-linear pieces using "bias". It gives different probabilities of activating the neural network or not. This is very useful in the case of Cryptanalysis. Two names are used to design the same domain of research: Neuro-Cryptography and Neural Cryptography. The first work that it is known on this topic can be traced back to 1995 in an IT Master Thesis. == Applications == In 1995, Sebastien Dourlens applied neural networks to cryptanalyze DES by allowing the networks to learn how to invert the S-tables of the DES. The bias in DES studied through Differential Cryptanalysis by Adi Shamir is highlighted. The experiment shows about 50% of the key bits can be found, allowing the complete key to be found in a short time. Hardware application with multi micro-controllers have been proposed due to the easy implementation of multilayer neural networks in hardware. One example of a public-key protocol is given by Khalil Shihab . He describes the decryption scheme and the public key creation that are based on a backpropagation neural network. The encryption scheme and the private key creation process are based on Boolean algebra. This technique has the advantage of small time and memory complexities. A disadvantage is the property of backpropagation algorithms: because of huge training sets, the learning phase of a neural network is very long. Therefore, the use of this protocol is only theoretical so far. == Neural key exchange protocol == The most used protocol for key exchange between two parties A and B in the practice is Diffie–Hellman key exchange protocol. Neural key exchange, which is based on the synchronization of two tree parity machines, should be a secure replacement for this method. Synchronizing these two machines is similar to synchronizing two chaotic oscillators in chaos communications. === Tree parity machine === The tree parity machine is a special type of multi-layer feedforward neural network. It consists of one output neuron, K hidden neurons and K×N input neurons. Inputs to the network take three values: x i j ∈ { − 1 , 0 , + 1 } {\displaystyle x_{ij}\in \left\{-1,0,+1\right\}} The weights between input and hidden neurons take the values: w i j ∈ { − L , . . . , 0 , . . . , + L } {\displaystyle w_{ij}\in \left\{-L,...,0,...,+L\right\}} Output value of each hidden neuron is calculated as a sum of all multiplications of input neurons and these weights: σ i = sgn ( ∑ j = 1 N w i j x i j ) {\displaystyle \sigma _{i}=\operatorname {sgn}(\sum _{j=1}^{N}w_{ij}x_{ij})} Signum is a simple function, which returns −1,0 or 1: sgn ( x ) = { − 1 if x < 0 , 0 if x = 0 , 1 if x > 0. {\displaystyle \operatorname {sgn}(x)={\begin{cases}-1&{\text{if }}x<0,\\0&{\text{if }}x=0,\\1&{\text{if }}x>0.\end{cases}}} If the scalar product is 0, the output of the hidden neuron is mapped to −1 in order to ensure a binary output value. The output of neural network is then computed as the multiplication of all values produced by hidden elements: τ = ∏ i = 1 K σ i {\displaystyle \tau =\prod _{i=1}^{K}\sigma _{i}} Output of the tree parity machine is binary. === Protocol === Each party (A and B) uses its own tree parity machine. Synchronization of the tree parity machines is achieved in these steps Initialize random weight values Execute these steps until the full synchronization is achieved Generate random input vector X Compute the values of the hidden neurons Compute the value of the output neuron Compare the values of both tree parity machines Outputs are the same: one of the suitable learning rules is applied to the weights Outputs are different: go to 2.1 After the full synchronization is achieved (the weights wij of both tree parity machines are same), A and B can use their weights as keys. This method is known as a bidirectional learning. One of the following learning rules can be used for the synchronization: Hebbian learning rule: w i + = g ( w i + σ i x i Θ ( σ i τ ) Θ ( τ A τ B ) ) {\displaystyle w_{i}^{+}=g(w_{i}+\sigma _{i}x_{i}\Theta (\sigma _{i}\tau )\Theta (\tau ^{A}\tau ^{B}))} Anti-Hebbian learning rule: w i + = g ( w i − σ i x i Θ ( σ i τ ) Θ ( τ A τ B ) ) {\displaystyle w_{i}^{+}=g(w_{i}-\sigma _{i}x_{i}\Theta (\sigma _{i}\tau )\Theta (\tau ^{A}\tau ^{B}))} Random walk: w i + = g ( w i + x i Θ ( σ i τ ) Θ ( τ A τ B ) ) {\displaystyle w_{i}^{+}=g(w_{i}+x_{i}\Theta (\sigma _{i}\tau )\Theta (\tau ^{A}\tau ^{B}))} Where: Θ ( a , b ) = 0 {\displaystyle \Theta (a,b)=0} if a ≠ b {\displaystyle a\neq b} otherwise Θ ( a , b ) = 1 {\displaystyle \Theta (a,b)=1} And: g ( x ) {\displaystyle g(x)} is a function that keeps the w i {\displaystyle w_{i}} in the range { − L , − L + 1 , . . . , 0 , . . . , L − 1 , L } {\displaystyle \{-L,-L+1,...,0,...,L-1,L\}} === Attacks and security of this protocol === In every attack it is considered, that the attacker E can eavesdrop messages between the parties A and B, but does not have an opportunity to change them. ==== Brute force ==== To provide a brute force attack, an attacker has to test all possible keys (all possible values of weights wij). By K hidden neurons, K×N input neurons and boundary of weights L, this gives (2L+1)KN possibilities. For example, the configuration K = 3, L = 3 and N = 100 gives us 310253 key possibilities, making the attack impossible with today's computer power. ==== Learning with own tree parity machine ==== One of the basic attacks can be provided by an attacker, who owns the same tree parity machine as the parties A and B. He wants to synchronize his tree parity machine with these two parties. In each step there are three situations possible: Output(A) ≠ Output(B): None of the parties updates its weights. Output(A) = Output(B) = Output(E): All the three parties update weights in their tree parity machines. Output(A) = Output(B) ≠ Output(E): Parties A and B update their tree parity machines, but the attacker can not do that. Because of this situation his learning is slower than the synchronization of parties A and B. It has been proven, that the synchronization of two parties is faster than learning of an attacker. It can be improved by increasing of the synaptic depth L of the neural network. That gives this protocol enough security and an attacker can find out the key only with small probability. ==== Other attacks ==== For conventional cryptographic systems, we can improve the security of the protocol by increasing of the key length. In the case of neural cryptography, we improve it by increasing of the synaptic depth L of the neural networks. Changing this parameter increases the cost of a successful attack exponentially, while the effort for the users grows polynomially. Therefore, breaking the security of neural key exchange belongs to the complexity class NP. Alexander Klimov, Anton Mityaguine, and Adi Shamir say that the original neural synchronization scheme can be broken by at least three different attacks—geometric, probabilistic analysis, and using genetic algorithms. Even though this particular implementation is insecure, the ideas behind chaotic synchronization could potentially lead to a secure implementation. === Permutation parity machine === The permutation parity machine is a binary variant of the tree parity machine. It consists of one input layer, one hidden layer and one output layer. The number of neurons in the output layer depends on the number of hidden units K. Each hidden neuron has N binary input neurons: x i j ∈ { 0 , 1 } {\displaystyle x_{ij}\in \left\{0,1\right\}} The weights between input and hidden neurons are also binary: w i j ∈ { 0 , 1 } {\displaystyle w_{ij}\in \left\{0,1\right\}} Output value of each hidden neuron is calculated as a sum of all exclusive disjunctions (exclusive or) of input neurons and these weights: σ i = θ N ( ∑ j = 1 N w i j ⊕ x i j ) {\displaystyle \sigma _{i}=\theta _{N}(\sum _{j=1}^{N}w_{ij}\oplus x_{ij})} (⊕ means XOR). Th
VoxForge
VoxForge is a free speech corpus and acoustic model repository for open source speech recognition engines. VoxForge was set up to collect transcribed speech to create a free GPL speech corpus in order to be uses with open source speech recognition engines. The speech audio files will be 'compiled' into acoustic models for use with open source speech recognition engines such as Julius, ISIP, and Sphinx and HTK (note: HTK has distribution restrictions). VoxForge has used LibriVox as a source of audio data since 2007.
Verge3D
Verge3D is a real-time renderer and a toolkit used for creating interactive 3D experiences running on websites. == Overview == Verge3D enables users to convert content from 3D modelling tools (Blender, 3ds Max, and Maya are currently supported) to view in a web browser. Verge3D was created by the same core group of software engineers that previously created the Blend4Web framework. == Features == Verge3D uses WebGL for rendering. It incorporates components of the Three.js library and exposes its API to application developers. Puzzles Application functionality can be added via JavaScript, either by writing code directly or by using Puzzles, Verge3D’s visual programming environment based on Google Blockly. Puzzles is aimed primarily at non-programmers allowing quick creation of interactive scenarios in a drag-and-drop fashion. App Manager and web publishing App Manager is a lightweight web-based tool for creating, managing and publishing Verge3D projects, running on top of the local development server. Verge3D Network service integrated in the App Manager allows for publishing Verge3D applications via Amazon S3 and EC2 cloud services. PBR For purposes of authoring materials, a glTF 2.0-compliant physically based rendering pipeline is offered alongside the standard shader-based approach. PBR textures can be authored using external texturing software such as Substance Painter for which Verge3D offers the corresponding export preset. Besides the glTF 2.0 model, Verge3D supports physical materials of 3ds Max and Maya (with Autodesk Arnold as reference), and Blender's real-time Eevee materials. glTF and DCC software integration Verge3D integrates directly with Blender, 3ds Max, and Maya, enabling users to create 3D geometry, materials, and animations inside the software, then export them in the JSON-based glTF format. The Sneak Peek feature allows for exporting and viewing scenes from the DCC tool environment. Facebook 3D posts For Facebook publishing, Verge3D offers a specific GLB export option. The exported GLB files are displayed and can be opened in the App Manager. Asset compression Exported files can optionally use LZMA compression, resulting in a reduction in file size of up to 6x. UI and website layouts Interface layouts, created using external WYSIWYG editors, can be linked with Puzzles to trigger changes to a 3D scene being rendered in the browser and vice versa. Animation Verge3D supports skeletal animation, including animation of bipeds and character rigs, and allows for animation of material parameters. Model parts can also be set up to be dragged by the user. Physics The physics module can be linked separately to enable collision detection, dynamically moving objects, support for characters and vehicles, springs, ropes and cloth simulation. As of version 2.11, simple physics simulations can be created and controlled without coding via Puzzles, the visual programming system used by Verge3D. AR/VR The 2.10 update added support for WebXR, an in-development open technology designed to enable virtual reality and augmented reality experiences to be displayed in web browsers. It works with both headsets with controllers, like the HTC Vive and Oculus Rift, and those without, like Google Cardboard. AR/VR experiences can enabled via Puzzles or JavaScript. == Workflow == Verge3D's workflow differs substantially from other mainstream WebGL frameworks. Development of a new Verge3D application is usually started from modeling, texturing and animating 3D objects. The models are assembled in the 3D authoring tool. The scene file is then used as a basis for a Verge3D project initialized from the App Manager. An interactive scenario is optionally added using the Puzzles editor. A Verge3D application can be previewed in the web browser at any development stage using the App Manager. The finished web application can be deployed on the Verge3D Network, on Facebook or on the user's website. == Notable uses == NASA's Jet Propulsion Laboratory used Verge3D to create an interactive 3D visualization of the Mars InSight lander. The web application allows for exploring and interacting with the real-time model of the spacecraft, with the possibility to move different parts and unfurl the solar panels. NASA's older interactive web application Experience Curiosity was ported to Verge3D from Blend4Web. The application makes it possible to operate the rover, control its cameras and the robotic arm and reproduces some of the prominent events of the Mars Science Laboratory mission. Route 66 Digital's Escape Room used Verge3D and Blender. This interactive short explores how users can navigate 3D spaces and interact with objects without the need for instruction.
Mortimer Rogoff
Mortimer Alan Rogoff (May 2, 1921 – August 1, 2008) was an American inventor, businessman, and author as well as an amateur photographer and radio operator. He is recognized for his work in spread spectrum technology which is the technology that modern cell phones and GPS systems are based on. He is also considered the grandfather of the electronic navigation chart. == Early life == Rogoff was born in Brooklyn, New York. He earned his B.S.E.E. from Rensselaer Polytechnic Institute in 1943 and his M.S.E.E. from Columbia University in 1948. While at Rensselaer he was a member of Kappa Nu fraternity and the Features Editor for the student newspaper. During World War II, he enlisted in the United States Navy and worked on developing radio communication and aerial navigation systems. One of the techniques he developed was undetectable by Axis forces because its power was below that of the background noise and its frequency varied in random ways. This secure transmission was the beginning of spread spectrum technology which would become the basis for GPS and CDMA cellular telephone systems. Although he was never able to patent the technology because it was a military secret he did get some recognition for it almost forty years later when he received the Institute of Electrical and Electronics Engineers’ Pioneer Award in 1981. == Career == Rogoff worked for twenty-two years (1946 to 1968) for ITT Laboratories in New Jersey. In 1958, he became their deputy director of Engineering. He was Vice President of ITT Laboratories from 1962 to 1963. From 1963 to 1968, he was promoted to the corporate staff where he became head of European operations. In 1968 he left ITT to work for the Diebold Group where he became an Executive Vice President. After leaving the Diebold Group he founded several technology and automation businesses, including his own consulting firm, and Teletext Communications Corporation. Later in the 1970s, he was a Principal with Booz Allen Hamilton. In 1979, his book ‘’Calculator Navigation’’ was published. This book demonstrated practical methods for calculating precise ship locations using radio navigation with a consumer calculator. In 1981, he founded a new company, Navigation Sciences Inc., in Bethesda, Maryland. With this company he patented a method for marine navigation that combined radar maps with electronic charts in 1986. This was a major advancement in field. Today, this system is known as the Electronic Chart Display and Information System (ECDIS). Rogoff had seen the need for a new charting system in 1968 from his apartment at 180 East End Avenue in New York City. From there, he saw a boating accident where a life was lost and decided there had to be a way to automate navigation. Rogoff then became of member of the International Maritime Organization’s (IMO) sub-committee on Safety of Navigation, a representative to the International Electrotechnical Commission, and became the chairman of the Radio Technical Commission for Maritime Services Special Committee 109 on Electronic Charts. He was able to use his influence on these boards to push through a proposal of ECDIS standards in 1989 where none has been before. As his friend Giuseppe Carnevali said, “Although nobody could argue against the need for a standard, no one was ready to endorse one; however, nobody was brave enough to oppose it.” A Test Bed project on these proposals was conducted by the United States Coast Guard. The amended standards were accepted by the IMO in November, 1995. In 2000, he was named as a Fellow of the Institute of Navigation. He was also a Fellow of the Institute of Electrical and Electronics Engineers. During this time, he was also president of the Navigational Electronic Charts System Association. == Personal == In 1979, he moved to Washington, D.C. and bought a home in Nantucket, Massachusetts. He married Sheila Zunser in 1943 and they were together for sixty-five years. They had three daughters: Louisa Thompson, Alice Rogoff, and Julia Peach. His sister was sociologist Natalie Rogoff Ramsøy of the University of Oslo. He was a member of the Cosmos Club and President of The Navigational Electronic Chart System Association (NECSA). He was a very good amateur photographer and liked amateur radio (call sign W2EE). He died in Nantucket from bladder cancer. == Patents == Patent number: 4176316 – Secure Communication System – November 27, 1979 With Louis A. DeRosa Patent number: 4590569 – Electronic Navigation System – May 20, 1986 With Peter M. Winkler and John N. Ackley Patent number: RE34004 – Secure Communication System – July 21, 1992 With Louis A. DeRosa == Publications == Rogoff, Mortimer September 1957. Automatic Analysis of Infrared Spectra. Annals of the New York Academy of Sciences; vol. 69: no. 1: 27–37. Gen. P.C. Sandretto and Mortimer Rogoff. 1958 “A Novel Concept for Application to the Control of Airways Traffic.” NAVIGATION: Journal of The Institute of Navigation; vol. 6: no. 2: 102–107 Rogoff, Mortimer 1979. Calculator Navigation; ISBN 0-393-03192-6. Published by W.W. Norton & Company (New York and London). Rogoff, Mortimer December 1985. Electronic Charting. Yachting; vol. 158: no. 6: 54–57. Rogoff, Mortimer Winter 1990. Electronic Charts in the Nineties. NAVIGATION: Journal of The Institute of Navigation; vol. 37: no. 4: 305–318.
Mini-STX
Mini-STX (mSTX, Mini Socket Technology EXtended, originally "Intel 5x5") is a computer motherboard form factor that was released by Intel in 2015 (as "Intel 5x5"). These motherboards measure 147mm by 140mm (5.8" x 5.5"), making them larger than "4x4" NUC (102x102mm / 4.01" x 4.01" inches) and Nano-ITX (120x120mm / 4.7" x 4.7") boards, but notably smaller than the more common Mini-ITX (170x170mm / 6.7" x 6.7") boards. Unlike these standards, which use a square shape, the Mini-STX form factor is 7mm longer from front-to-rear, making it slightly rectangular. == Mini-STX design elements == The Mini-STX design suggests (but does not require) support for: Socketed processors (e.g. LGA or PGA CPUs) Onboard power regulation circuitry, enabling direct DC power input IO ports embedded on the front and rear of the motherboard (akin to NUC, but unlike typical motherboards which often use headers instead to connect built-in ports on enclosures) == Adoption by manufacturers == This motherboard form factor is still not in particularly common use with consumer-PC manufacturers, although there are a few offerings: ASRock offers both DeskMini kits (that use mini-STX boards) and standalone motherboards, Asus offer VivoMini kits (that use mini-STX boards) and standalone motherboards, Gigabyte offers a few motherboards, and industrial PC suppliers (e.g. Kontron, Iesy, ASRock Industrial) also provide some options for mini-STX equipment. == Derivatives == ASRock developed a derivative of mini-STX, dubbed micro-STX, for their 'DeskMini GTX/RX' small form-factor PCs and industrial motherboards. Micro-STX adds an MXM slot which allows the use of special PCI Express expansion cards, including graphics or machine learning accelerators, but increases the width of the board to be extended two inches, resulting in measurements of 147 x 188 mm (5.8" x 7.4")
Dynamic Graphics Project
The Dynamic Graphics Project (commonly referred to as DGP) is an interdisciplinary research laboratory at the University of Toronto devoted to projects involving computer graphics, computer vision, human computer interaction, and visualization. The lab began as the computer graphics research group of Department of Computer Science Professor Leslie Mezei in 1967. Mezei invited Bill Buxton, a pioneer of human–computer interaction (HCI) to join. In 1972, Ronald Baecker, another HCI pioneer joined, establishing DGP as the first Canadian university group focused on computer graphics and human-computer interaction. According to csrankings.org, the DGP is the top research institution in the world for the combined subfields of computer graphics, HCI, and visualization. Since then, DGP has hosted many well known faculty and students in computer graphics, computer vision and HCI (e.g., Alain Fournier, Bill Reeves, Jos Stam, Demetri Terzopoulos, Marilyn Tremaine). DGP also occasionally hosts artists in residence (e.g., Oscar-winner Chris Landreth). Many past and current researchers at Autodesk (and before that Alias Wavefront) graduated after working at DGP. DGP is located in the St. George campus of University of Toronto in the Bahen Centre for Information Technology. DGP researchers regularly publish at ACM SIGGRAPH, ACM SIGCHI and ICCV. DGP hosts the Toronto User Experience (TUX) Speaker Series and the Sanders Series Lectures. == Notable alumni == Bill Buxton (MS 1978) James McCrae (PhD 2013) Dimitris Metaxas (PhD 1992) Bill Reeves (MS 1976, Ph.D. 1980) Jos Stam (MS 1991, Ph.D. 1995)
Usage share of operating systems
The usage share of an operating system is the percentage of computers running that operating system (OS). These statistics are estimates as wide scale OS usage data is difficult to obtain and measure. Reliable primary sources are limited and data collection methodology is not formally agreed. Currently devices connected to the internet allow for web data collection to approximately measure OS usage. As of December 2025, Android, which uses the Linux kernel, is the world's most popular operating system with 38.94% of the global market, followed by Windows with 29.99%, iOS with 15.66%, macOS with 2.14%, and other operating systems with 10.78%. This is for all device types excluding embedded devices. For smartphones and other mobile devices, Android has 72% market share, and Apple's iOS has 28%. For desktop computers and laptops, Microsoft Windows has 60.8%, followed by unknown operating systems at 19.7%, Mac OS at 14.4%, desktop Linux at 3.2%, then Google's ChromeOS at 1.6%, as of March 2026. For tablets, Apple's iPadOS (a variant of iOS) has 52% share and Android has 48% worldwide. For the top 500 most powerful supercomputers, Linux distributions have had 100% of the market share since 2017. The global server operating system market share has Linux leading with a 63.1% marketshare, followed by Windows, Unix and other operating systems. Linux is also most used for web servers, and the most common Linux distribution is Ubuntu, followed by Debian. Linux has almost caught up with the second-most popular (desktop) OS, macOS, in some regions, such as in South America, and in Asia it's at 6.4% (7% with ChromeOS) vs 9.7% for macOS. In the US, ChromeOS is third at 5.5%, followed by (desktop) Linux at 4.3%. The most numerous type of device with an operating system are embedded systems. Not all embedded systems have operating systems, instead running their application code on the "bare metal"; of those that do have operating systems, a high percentage are standalone or do not have a web browser, which makes their usage share difficult to measure. Some operating systems used in embedded systems are more widely used than some of those mentioned above; for example, modern Intel microprocessors contain an embedded management processor running a version of the Minix operating system. == Worldwide device shipments == Shipments (to stores) do not necessarily translate to sales to consumers, therefore suggesting the numbers indicate popularity and/or usage could be misleading. Not only do smartphones sell in higher numbers than PCs, but also a lot more by dollar value, with the gap only projected to widen, to well over double. According to Gartner, the following is the worldwide device shipments (referring to wholesale) by operating system from 2012 to 2016, which includes smartphones, tablets, laptops and PCs together. On 27 January 2016, Paul Thurrott summarized the operating system market, the day after Apple announced "one billion devices": Apple's "active installed base" is now one billion devices. [..] Granted, some of those Apple devices were probably sold into the marketplace years ago. But that 1 billion figure can and should be compared to the numbers Microsoft touts for Windows 10 (200 million, most recently) or Windows more generally (1.5 billion active users, a number that hasn’t moved, magically, in years), and that Google touts for Android (over 1.4 billion, as of September). My understanding of iOS is that the user base was previously thought to be around 800 million strong, and when you factor out Macs and other non-iOS Apple devices, that's probably about right. But as you can see, there are three big personal computing platforms. And only one of them is actually declining. We’ll see how Windows 10 fares over the long term, but even if Microsoft hits the 1 billion figure in 1-2 years as promised, it will by then still be the smallest of those three platforms. In 2018, Apple stopped revealing unit sales in its reports. Since 2018, the company have been publishing only revenues per device models which, nonetheless, allowed the analysers to extrapolate the unit sales from the model revenues by applying the wholesale device prices. Other hardware manufacturers usually do not report unit sales. === PC shipments === For 2015 (and earlier), Gartner reports for "the year, worldwide PC shipments declined for the fourth consecutive year, which started in 2012 with the launch of tablets" with an 8% decline in PC sales for 2015 (not including cumulative decline in sales over the previous years). Microsoft backed away from their goal of one billion Windows 10 devices in three years (or "by the middle of 2018") and reported on 26 September 2016 that Windows 10 was running on over 400 million devices, and in March 2019, on more than 800 million. In May 2020, Gartner predicted further decline in all market segments for 2020 due to COVID-19, predicting a decline of 13.6% for all devices. while the "Work from Home Trend Saved PC Market from Collapse", with only a decline of 10.5% predicted for PCs. However, in the end, according to Gartner, PC shipments grew 10.7% in the fourth quarter of 2020 and reached 275 million units in 2020, a 4.8% increase from 2019 and the highest growth in ten years." Apple in 4th place for PCs had the largest growth in shipments for a company in Q4 of 31.3%, while "the fourth quarter of 2020 was another remarkable period of growth for Chromebooks, with shipments increasing around 200% year over year to reach 11.7 million units. In 2020, Chromebook shipments increased over 80% to total nearly 30 million units, largely due to demand from the North American education market." Chromebooks sold more (30 million) than Apple's Macs worldwide (22.5 million) in pandemic year 2020. According to the Catalyst group, the year 2021 had record high PC shipments with total shipments of 341 million units (including Chromebooks), 15% higher than 2020 and 27% higher than 2019, while being the largest shipment total since 2012. According to Gartner, worldwide PC shipments declined by 16.2% in 2022, the largest annual decrease since the mid-1990s, due to geopolitical, economic, and supply chain challenges. In 2024 and 2025, due to lower adoption of Windows 11 and Microsoft ending its support to Windows 10, the number of PCs shipped with pre-installed Windows OS dropped. Pundits attribute the low Windows 11 acceptance to its steep hardware requirements and especially the TPM 2.0 ready chipset requirement and the 2024 CrowdStrike-related IT outages. Meanwhile, the macOS device market share in PC device shipments increased to new heights, with improved numbers seen for Linux devices too. In Q3 2025, the macOS pre-installed device shipments increased by 14.9% year-over-year (YoY), while the overall PC-shipments increased only by 8.1%, in Q2 2025, it grew 21.4% YoY while the global PC-shipments increased only by 6.5%, and in Q1 2025, it grew 7% YoY while the global PC-shipments increased by 4.8%. === Tablet computers shipments === In 2015, eMarketer estimated at the beginning of the year that the tablet installed base would hit one billion for the first time (with China's use at 328 million, which Google Play doesn't serve or track, and the United States's use second at 156 million). At the end of the year, because of cheap tablets – not counted by all analysts – that goal was met (even excluding cumulative sales of previous years) as: Sales quintupled to an expected 1 billion units worldwide this year, from 216 million units in 2014, according to projections from the Envisioneering Group. While that number is far higher than the 200-plus million units globally projected by research firms IDC, Gartner and Forrester, Envisioneering analyst Richard Doherty says the rival estimates miss all the cheap Asian knockoff tablets that have been churning off assembly lines.[..] Forrester says its definition of tablets "is relatively narrow" while IDC says it includes some tablets by Amazon — but not all.[..] The top tech purchase of the year continued to be the smartphone, with an expected 1.5 billion sold worldwide, according to projections from researcher IDC. Last year saw some 1.2 billion sold.[..] Computers didn’t fare as well, despite the introduction of Microsoft's latest software upgrade, Windows 10, and the expected but not realized bump it would provide for consumers looking to skip the upgrade and just get a new computer instead. Some 281 million PCs were expected to be sold, according to IDC, down from 308 million in 2014. Folks tend to be happy with the older computers and keep them for longer, as more of our daily computing activities have moved to the smartphone.[..] While Windows 10 got good reviews from tech critics, only 11% of the 1-billion-plus Windows user base opted to do the upgrade, according to Microsoft. This suggests Microsoft has a ways to go before the software gets "hit" status. Apple's new operating system El Capitan has been