Fake nude photography is the creation of nude photographs designed to appear as genuine nudes of an individual. The motivations for the creation of these modified photographs include curiosity, sexual gratification, the stigmatization or embarrassment of the subject, and commercial gain, such as through the sale of the photographs via pornographic websites. Fakes can be created using image editing software or through machine learning. Fake images created using the latter method are called deepfakes. == History == Magazines such as Celebrity Skin published non-fake paparazzi shots and illicitly obtained nude photos, showing there was a market for such images. Subsequently, some websites hosted fake nude or pornographic photos of celebrities, which are sometimes referred to as celebrity fakes. In the 1990s and 2000s, fake nude images of celebrities proliferated on Usenet and on websites, leading to campaigns to take legal action against the creators of the images and websites dedicated to determining the veracity of nude photos. "Deepfakes", which use artificial neural networks to superimpose one person's face into an image or video of someone else, were popularized in the late 2010s, leading to concerns about the technology's use in fake news and revenge porn. Fake nude photography is sometimes confused with Deepfake pornography, but the two are distinct. Fake nude photography typically starts with human-made non-sexual images, and merely makes it appear that the people in them are nude (but not having sex). Deepfake pornography typically starts with human-made sexual (pornographic) images or videos, and alters the actors' facial features to make the participants in the sexual act look like someone else. === DeepNude === In June 2019, a downloadable Windows and Linux application called DeepNude was released which used a Generative Adversarial Network to remove clothing from images of women. The images it produced were typically not pornographic, merely nude. Because there were more images of nude women than men available to its creator, the images it produced were all female, even when the original was male. The app had both a paid and unpaid version. A few days later, on June 27, the creators removed the application and refunded consumers, although various copies of the app, both free and for charge, continue to exist. On GitHub, the open-source version of this program called "open-deepnude" was deleted. The open-source version had the advantage of allowing it to be trained on a larger dataset of nude images to increase the resulting nude image's accuracy level. A successor free software application, Dreamtime, was later released, and some copies of it remain available, though some have been suppressed. === Deepfake Telegram Bot === In July 2019 a deepfake bot service was launched on messaging app Telegram that used AI technology to create nude images of women. The service was free and enabled users to submit photos and receive manipulated nude images within minutes. The service was connected to seven Telegram channels, including the main channel that hosts the bot, technical support, and image sharing channels. While the total number of users was unknown, the main channel had over 45,000 members. As of July 2020, it is estimated that approximately 24,000 manipulated images had been shared across the image sharing channels. === Nudify websites === By late 2024, most ways to produce nude images from photographs of clothed people were accessible at websites rather than in apps, and required payment. == Purposes == The reasons for the creation of nude photos may range from a need to discredit the target publicly, personal hatred for the target, or the promise of pecuniary gains for such work on the part of the creator of such photos. Fake nude photos often target prominent figures such as businesspeople or politicians. == Notable cases == In 2010, 97 people were arrested in Korea after spreading fake nude pictures of the group Girls' Generation on the internet. In 2011, a 53-year-old Incheon man was arrested after spreading more fake pictures of the same group. In 2012, South Korean police identified 157 Korean artists of whom fake nudes were circulating. In 2012, when Liu Yifei's fake nude photography released on the network, Liu Yifei Red Star Land Company declared a legal search to find out who created and released the photos. In the same year, Chinese actor Huang Xiaoming released nude photos that sparked public controversy, but they were ultimately proven to be real pictures. In 2014, supermodel Kate Upton threatened to sue a website for posting her fake nude photos. Previously, in 2011, this page was threatened by Taylor Swift. In November 2014, singer Rain was angry because of a fake nude photo that spread throughout the internet. Information reveals that: "Rain's nude photo was released from Kim Tae-hee's lost phone." Rain's label, Cube Entertainment, stated that the person in the nude photo is not Rain and the company has since stated that it will take strict legal action against those who post photos together with false comments. In July 2018, Seoul police launched an investigation after a fake nude photo of President Moon Jae-in was posted on the website of the Korean radical feminist group WOMAD. In early 2019, Alexandria Ocasio-Cortez, a Democratic politician, was berated by other political parties over a fake nude photo of her in the bathroom. The picture created a huge wave of media controversy in the United States. == Methods == Fake nude images can be created using image editing software or neural network applications. There are two basic methods: Combine and superimpose existing images onto source images, adding the face of the subject onto a nude model. Remove clothes from the source image to make it look like a nude photo. == Impact == Images of this type may have a negative psychological impact on the victims and may be used for extortion purposes.
Amazon Elastic Compute Cloud
Amazon Elastic Compute Cloud (EC2) is a part of Amazon's cloud-computing platform, Amazon Web Services (AWS), that allows users to rent virtual computers on which to run their own computer applications. EC2 encourages scalable deployment of applications by providing a web service through which a user can boot an Amazon Machine Image (AMI) to configure a virtual machine, which Amazon calls an "instance", containing any software desired. A user can create, launch, and terminate server-instances as needed, paying by the second for active servers – hence the term "elastic". EC2 provides users with control over the geographical location of instances that allows for latency optimization and high levels of redundancy. In November 2010, Amazon switched its own retail website platform to EC2 and AWS. == History == Amazon announced a limited public beta test of EC2 on August 25, 2006, offering access on a first-come, first-served basis. Amazon added two new instance types (Large and Extra-Large) on October 16, 2007. On May 29, 2008, two more types were added, High-CPU Medium and High-CPU Extra Large. There were twelve types of instances available. Amazon added three new features on March 27, 2008: static IP addresses, availability zones, and user-selectable kernels. On August 20, 2008, Amazon added Elastic Block Store (EBS). This provides persistent storage, a feature that had been lacking since the service was introduced. Amazon EC2 went into full production when it dropped the beta label on October 23, 2008. On the same day, Amazon announced the following features: a service level agreement for EC2, Microsoft Windows in beta form on EC2, Microsoft SQL Server in beta form on EC2, plans for an AWS management console, and plans for load balancing, autoscaling, and cloud monitoring services. These features were subsequently added on May 18, 2009. Amazon EC2 was developed mostly by a team in Cape Town, South Africa led by Chris Pinkham. Pinkham provided the initial architecture guidance for EC2 and then built the team and led the development of the project along with Willem van Biljon. == Instance types == Initially, EC2 used Xen virtualization exclusively. However, on November 6, 2017, Amazon announced the new C5 family of instances that were based on a custom architecture around the KVM hypervisor, called Nitro. Each virtual machine, called an "instance", functions as a virtual private server. Amazon sizes instances based on "Elastic Compute Units". The performance of otherwise identical virtual machines may vary. On November 28, 2017, AWS announced a bare-metal instance, a departure from exclusively offering virtualized instance types. As of January 2019, the following instance types were offered: General Purpose: A1, T3, T2, M5, M5a, M4, T3a Compute Optimized: C5, C5n, C4 Memory Optimized: R5, R5a, R4, X1e, X1, High Memory, z1d Accelerated Computing: P3, P2, G3, F1 Storage Optimized: H1, I3, D2 As of April 2018, the following payment methods by instance were offered: On-demand: pay by the hour without commitment. Reserved: rent instances with one-time payment receiving discounts on the hourly charge. Spot: bid-based service: runs the jobs only if the spot price is below the bid specified by bidder. The spot price is claimed to be supply-demand based, however a 2011 study concluded that the price was generally not set to clear the market, but was dominated by an undisclosed reserve price. In 2025, AWS expanded EC2 with the compute-optimized C8gn family, powered by Graviton4 and offering up to 600 Gbit/s network bandwidth (about 30% higher compute performance than C7gn), and introduced G6f fractional-GPU instances that let customers provision one-eighth, one-quarter, or one-half of an NVIDIA L4 GPU for right-sized graphics/ML workloads. === Cost === As of April 2018, Amazon charged about $0.0058 per hour ($4.176 per month) for the smallest "Nano Instance" (t2.nano) virtual machine running Linux or Windows. Storage-optimized instances cost as much as $4.992 per hour (i3.16xlarge). "Reserved" instances can go as low as $2.50 per month for a three-year prepaid plan. The data transfer charge ranges from free to $0.12 per gigabyte, depending on the direction and monthly volume (inbound data transfer is free on all AWS services). EC2 costs can be analyzed using the Amazon Cost and Usage Report. There are many different cost categories for EC2 including: hourly Instance Charges, Data Transfer, EBS Volumes, EBS Volume Snapshots, and Nat Gateway. === Free tier === As of December 2010 Amazon offered a bundle of free resource credits to new account holders. The credits are designed to run a "micro" sized server, storage (EBS), and bandwidth for one year. Unused credits cannot be carried over from one month to the next. === Reserved instances === Reserved instances enable EC2 or RDS service users to reserve an instance for one or three years. The corresponding hourly rate charged by Amazon to operate the instance is 35 to 75% lower than the rate charged for on-demand instances. Reserved instances can be purchased with three different payment options: All Upfront, Partial Upfront and No Upfront. The different purchase options allow for different structuring of payment models, with a larger discount given to customers that pay their reservation upfront. Reserved Instances are purchased based on a resource commitment. These reservations are made based on an instance type and a count of that instance type. For example, you could reserve 100 i3.large instances for a 3-year term. In September 2016, AWS announced several enhancements to Reserved instances, introducing a new feature called scope and a new reservation type called a Convertible. In October 2017, AWS announced the allowance to subdivide the instances purchased for more flexibility. === Spot instances === Cloud providers maintain large amounts of excess capacity they have to sell or risk incurring losses. Amazon EC2 Spot instances are spare compute capacity in the AWS cloud available at up to 90% discount compared to On-Demand prices. As a trade-off, AWS offers no SLA on these instances and customers take the risk that it can be interrupted with only two minutes of notification when Amazon needs the capacity back. Researchers from the Israeli Institute of Technology found that "they (Spot instances) are typically generated at random from within a tight price interval via a dynamic hidden reserve price". Some companies, like Spotinst, are using machine learning to predict spot interruptions up to 15 minutes in advance. === Savings Plans === In November 2019, Amazon announced Savings Plans. Savings Plans are an alternative to Reserved Instances that come in two different plan types: Compute Savings Plans and EC2 Instances Savings Plans. Compute Savings Plans allow an organization to commit to EC2 and Fargate usage with the freedom to change region, family, size, availability zone, OS and tenancy inside the lifespan of the commitment. EC2 Instance Savings plans provide a larger discount than Compute Savings Plans but are less flexible meaning a user must commit to individual instance families within a region to take advantage, but with the freedom to change instances within the family in that region. AWS uses the Cost Explorer to automatically calculate recommendations for the commitments you should make how that commitment will look like as a monthly charge on your AWS bill. AWS Savings Plans are purchased based on hourly spend commitment. This hourly commitment is made using the discounted pricing of the savings plan you are purchasing. For example, you could commit to spending $5 per hour, on a Compute Savings Plan, for a 3-year term. == Features == === Operating systems === When it launched in August 2006, the EC2 service offered Linux and later Sun Microsystems' OpenSolaris and Solaris Express Community Edition. In October 2008, EC2 added the Windows Server 2003 and Windows Server 2008 operating systems to the list of available operating systems. In March 2011, NetBSD AMIs became available. In November 2012, Windows Server 2012 support was added. Since 2006, Colin Percival, a FreeBSD developer and Security Officer, solicited Amazon to add FreeBSD. In November 2012, Amazon officially supported running FreeBSD in EC2. The FreeBSD/EC2 platform is maintained by Percival who also developed the secure deduplicating Amazon S3-cloud based backup service Tarsnap. Amazon has their own Linux distribution based on Fedora and Red Hat Enterprise Linux as a low cost offering known as the Amazon Linux AMI. Version 2013.03 included: Linux kernel, Java OpenJDK Runtime Environment and GNU Compiler Collection. On November 30, 2020, Amazon announced that it would be adding macOS to the EC2 service. Initial support was announced for macOS Mojave and macOS Catalina running on Mac Mini. === Managed Container and Kubernetes Services === Amazon Elastic Container Registry (ECR) is a Docker registry service for Amazon EC2
Eigenmoments
EigenMoments is a set of orthogonal, noise robust, invariant to rotation, scaling and translation and distribution sensitive moments. Their application can be found in signal processing and computer vision as descriptors of the signal or image. The descriptors can later be used for classification purposes. It is obtained by performing orthogonalization, via eigen analysis on geometric moments. == Framework summary == EigenMoments are computed by performing eigen analysis on the moment space of an image by maximizing signal-to-noise ratio in the feature space in form of Rayleigh quotient. This approach has several benefits in Image processing applications: Dependency of moments in the moment space on the distribution of the images being transformed, ensures decorrelation of the final feature space after eigen analysis on the moment space. The ability of EigenMoments to take into account distribution of the image makes it more versatile and adaptable for different genres. Generated moment kernels are orthogonal and therefore analysis on the moment space becomes easier. Transformation with orthogonal moment kernels into moment space is analogous to projection of the image onto a number of orthogonal axes. Nosiy components can be removed. This makes EigenMoments robust for classification applications. Optimal information compaction can be obtained and therefore a few number of moments are needed to characterize the images. == Problem formulation == Assume that a signal vector s ∈ R n {\displaystyle s\in {\mathcal {R}}^{n}} is taken from a certain distribution having correlation C ∈ R n × n {\displaystyle C\in {\mathcal {R}}^{n\times n}} , i.e. C = E [ s s T ] {\displaystyle C=E[ss^{T}]} where E[.] denotes expected value. Dimension of signal space, n, is often too large to be useful for practical application such as pattern classification, we need to transform the signal space into a space with lower dimensionality. This is performed by a two-step linear transformation: q = W T X T s , {\displaystyle q=W^{T}X^{T}s,} where q = [ q 1 , . . . , q n ] T ∈ R k {\displaystyle q=[q_{1},...,q_{n}]^{T}\in {\mathcal {R}}^{k}} is the transformed signal, X = [ x 1 , . . . , x n ] T ∈ R n × m {\displaystyle X=[x_{1},...,x_{n}]^{T}\in {\mathcal {R}}^{n\times m}} a fixed transformation matrix which transforms the signal into the moment space, and W = [ w 1 , . . . , w n ] T ∈ R m × k {\displaystyle W=[w_{1},...,w_{n}]^{T}\in {\mathcal {R}}^{m\times k}} the transformation matrix which we are going to determine by maximizing the SNR of the feature space resided by q {\displaystyle q} . For the case of Geometric Moments, X would be the monomials. If m = k = n {\displaystyle m=k=n} , a full rank transformation would result, however usually we have m ≤ n {\displaystyle m\leq n} and k ≤ m {\displaystyle k\leq m} . This is specially the case when n {\displaystyle n} is of high dimensions. Finding W {\displaystyle W} that maximizes the SNR of the feature space: S N R t r a n s f o r m = w T X T C X w w T X T N X w , {\displaystyle SNR_{transform}={\frac {w^{T}X^{T}CXw}{w^{T}X^{T}NXw}},} where N is the correlation matrix of the noise signal. The problem can thus be formulated as w 1 , . . . , w k = a r g m a x w w T X T C X w w T X T N X w {\displaystyle {w_{1},...,w_{k}}=argmax_{w}{\frac {w^{T}X^{T}CXw}{w^{T}X^{T}NXw}}} subject to constraints: w i T X T N X w j = δ i j , {\displaystyle w_{i}^{T}X^{T}NXw_{j}=\delta _{ij},} where δ i j {\displaystyle \delta _{ij}} is the Kronecker delta. It can be observed that this maximization is Rayleigh quotient by letting A = X T C X {\displaystyle A=X^{T}CX} and B = X T N X {\displaystyle B=X^{T}NX} and therefore can be written as: w 1 , . . . , w k = a r g m a x x w T A w w T B w {\displaystyle {w_{1},...,w_{k}}={\underset {x}{\operatorname {arg\,max} }}{\frac {w^{T}Aw}{w^{T}Bw}}} , w i T B w j = δ i j {\displaystyle w_{i}^{T}Bw_{j}=\delta _{ij}} === Rayleigh quotient === Optimization of Rayleigh quotient has the form: max w R ( w ) = max w w T A w w T B w {\displaystyle \max _{w}R(w)=\max _{w}{\frac {w^{T}Aw}{w^{T}Bw}}} and A {\displaystyle A} and B {\displaystyle B} , both are symmetric and B {\displaystyle B} is positive definite and therefore invertible. Scaling w {\displaystyle w} does not change the value of the object function and hence and additional scalar constraint w T B w = 1 {\displaystyle w^{T}Bw=1} can be imposed on w {\displaystyle w} and no solution would be lost when the objective function is optimized. This constraint optimization problem can be solved using Lagrangian multiplier: max w w T A w {\displaystyle \max _{w}{w^{T}Aw}} subject to w T B w = 1 {\displaystyle {w^{T}Bw}=1} max w L ( w ) = max w ( w T A w − λ w T B w ) {\displaystyle \max _{w}{\mathcal {L}}(w)=\max _{w}(w{T}Aw-\lambda w^{T}Bw)} equating first derivative to zero and we will have: A w = λ B w {\displaystyle Aw=\lambda Bw} which is an instance of Generalized Eigenvalue Problem (GEP). The GEP has the form: A w = λ B w {\displaystyle Aw=\lambda Bw} for any pair ( w , λ ) {\displaystyle (w,\lambda )} that is a solution to above equation, w {\displaystyle w} is called a generalized eigenvector and λ {\displaystyle \lambda } is called a generalized eigenvalue. Finding w {\displaystyle w} and λ {\displaystyle \lambda } that satisfies this equations would produce the result which optimizes Rayleigh quotient. One way of maximizing Rayleigh quotient is through solving the Generalized Eigen Problem. Dimension reduction can be performed by simply choosing the first components w i {\displaystyle w_{i}} , i = 1 , . . . , k {\displaystyle i=1,...,k} , with the highest values for R ( w ) {\displaystyle R(w)} out of the m {\displaystyle m} components, and discard the rest. Interpretation of this transformation is rotating and scaling the moment space, transforming it into a feature space with maximized SNR and therefore, the first k {\displaystyle k} components are the components with highest k {\displaystyle k} SNR values. The other method to look at this solution is to use the concept of simultaneous diagonalization instead of Generalized Eigen Problem. === Simultaneous diagonalization === Let A = X T C X {\displaystyle A=X^{T}CX} and B = X T N X {\displaystyle B=X^{T}NX} as mentioned earlier. We can write W {\displaystyle W} as two separate transformation matrices: W = W 1 W 2 . {\displaystyle W=W_{1}W_{2}.} W 1 {\displaystyle W_{1}} can be found by first diagonalize B: P T B P = D B {\displaystyle P^{T}BP=D_{B}} . Where D B {\displaystyle D_{B}} is a diagonal matrix sorted in increasing order. Since B {\displaystyle B} is positive definite, thus D B > 0 {\displaystyle D_{B}>0} . We can discard those eigenvalues that large and retain those close to 0, since this means the energy of the noise is close to 0 in this space, at this stage it is also possible to discard those eigenvectors that have large eigenvalues. Let P ^ {\displaystyle {\hat {P}}} be the first k {\displaystyle k} columns of P {\displaystyle P} , now P T ^ B P ^ = D B ^ {\displaystyle {\hat {P^{T}}}B{\hat {P}}={\hat {D_{B}}}} where D B ^ {\displaystyle {\hat {D_{B}}}} is the k × k {\displaystyle k\times k} principal submatrix of D B {\displaystyle D_{B}} . Let W 1 = P ^ D B ^ − 1 / 2 {\displaystyle W_{1}={\hat {P}}{\hat {D_{B}}}^{-1/2}} and hence: W 1 T B W 1 = ( P ^ D B ^ − 1 / 2 ) T B ( P ^ D B ^ − 1 / 2 ) = I {\displaystyle W_{1}^{T}BW_{1}=({\hat {P}}{\hat {D_{B}}}^{-1/2})^{T}B({\hat {P}}{\hat {D_{B}}}^{-1/2})=I} . W 1 {\displaystyle W_{1}} whiten B {\displaystyle B} and reduces the dimensionality from m {\displaystyle m} to k {\displaystyle k} . The transformed space resided by q ′ = W 1 T X T s {\displaystyle q'=W_{1}^{T}X^{T}s} is called the noise space. Then, we diagonalize W 1 T A W 1 {\displaystyle W_{1}^{T}AW_{1}} : W 2 T W 1 T A W 1 W 2 = D A {\displaystyle W_{2}^{T}W_{1}^{T}AW_{1}W_{2}=D_{A}} , where W 2 T W 2 = I {\displaystyle W_{2}^{T}W_{2}=I} . D A {\displaystyle D_{A}} is the matrix with eigenvalues of W 1 T A W 1 {\displaystyle W_{1}^{T}AW_{1}} on its diagonal. We may retain all the eigenvalues and their corresponding eigenvectors since most of the noise are already discarded in previous step. Finally the transformation is given by: W = W 1 W 2 {\displaystyle W=W_{1}W_{2}} where W {\displaystyle W} diagonalizes both the numerator and denominator of the SNR, W T A W = D A {\displaystyle W^{T}AW=D_{A}} , W T B W = I {\displaystyle W^{T}BW=I} and the transformation of signal s {\displaystyle s} is defined as q = W T X T s = W 2 T W 1 T X T s {\displaystyle q=W^{T}X^{T}s=W_{2}^{T}W_{1}^{T}X^{T}s} . === Information loss === To find the information loss when we discard some of the eigenvalues and eigenvectors we can perform following analysis: η = 1 − t r a c e ( W 1 T A W 1 ) t r a c e ( D B − 1 / 2 P T A P D B − 1 / 2 ) = 1 − t r a c e ( D B ^ − 1 / 2 P ^ T A P ^ D B ^ − 1 / 2 ) t r a c e ( D B − 1 / 2 P T A P D B − 1 / 2 ) {\displaystyle {\begin{array}{lll}\eta &=&
ChatGPT
ChatGPT is a generative artificial intelligence chatbot developed by OpenAI. Originally released in November 2022, the product uses large language models—specifically generative pre-trained transformers (GPTs)—to generate text, speech, and images in response to user prompts. ChatGPT accelerated the AI boom, an ongoing period marked by rapid investment and public attention toward the field of artificial intelligence (AI). OpenAI operates the service on a freemium model. Users can interact with ChatGPT through text, audio, and image prompts. ChatGPT was quickly adopted, reaching 100 million monthly active users two months after its release and 900 million weekly active users in February 2026. It has been lauded for its potential to transform numerous professional fields, and has instigated public debate about the nature of creativity and the future of knowledge work. The chatbot has also been criticized for its limitations and potential for unethical use. It can generate plausible-sounding but incorrect or nonsensical answers, known as hallucinations. Biases in its training data have been reflected in its responses. The chatbot can facilitate academic dishonesty, generate misinformation, and create malicious code. The ethics of its development, particularly the use of copyrighted content as training data, have also drawn controversy. == Features == ChatGPT is a chatbot and AI assistant built on large language model (LLM) technology. It is designed to generate human-like text and can carry out a wide variety of tasks. These include, among many others, writing and debugging computer programs, composing music, scripts, fairy tales, and essays, answering questions (sometimes at a level exceeding that of an average human test-taker), and generating business concepts. ChatGPT is frequently used for translation and summarization tasks, and can simulate interactive environments such as a Linux terminal, a multi-user chat room, or simple text-based games such as tic-tac-toe. Users interact with ChatGPT through conversations which consist of text, audio, and image inputs and outputs. The user's inputs to these conversations are referred to as prompts. An optional "Memory" feature allows users to tell ChatGPT to memorize specific information. Another option allows ChatGPT to recall old conversations. GPT-based moderation classifiers are used to reduce the risk of harmful outputs being presented to users. In March 2023, OpenAI added support for plugins for ChatGPT. This includes both plugins made by OpenAI, such as web browsing and code interpretation, and external plugins from developers such as Expedia, OpenTable, and Zapier. From October to December 2024, ChatGPT Search was deployed. It allows ChatGPT to search the web in an attempt to make more accurate and up-to-date responses. It increased OpenAI's direct competition with major search engines. OpenAI allows businesses to tailor how their content appears in the ChatGPT Search results and influence what sources are used. In December 2024, OpenAI launched a new feature allowing users to call ChatGPT with a telephone for up to 15 minutes per month for free. In September 2025, OpenAI added a feature called Pulse, which generates a daily analysis of a user's chats and connected apps such as Gmail and Google Calendar. In October 2025, OpenAI launched ChatGPT Atlas, a browser integrating the ChatGPT assistant directly into web navigation, to compete with existing browsers such as Google Chrome. It has an additional feature called "agentic mode" that allows it to take online actions for the user. === Paid tier === ChatGPT was initially free to the public and remains free in a limited capacity. In February 2023, OpenAI launched a premium service, ChatGPT Plus, that costs US$20 per month. What was offered on the paid plan versus the free tier changed as OpenAI has continued to update ChatGPT, and a Pro tier at $200/mo was introduced in December 2024. The Pro launch coincided with the release of the o1 model. In August 2025, ChatGPT Go was offered in India for ₹399 per month. The plan has higher limits than the free version. === Mobile apps === In May-July 2023, OpenAI began offering ChatGPT iOS and Android apps. ChatGPT can also power Android's assistant. An app for Windows launched on the Microsoft Store on October 15, 2024. === Languages === OpenAI met Icelandic President Guðni Th. Jóhannesson in 2022. In 2023, OpenAI worked with a team of 40 Icelandic volunteers to fine-tune ChatGPT's Icelandic conversation skills as a part of Iceland's attempts to preserve the Icelandic language. ChatGPT (based on GPT-4) was better able to translate Japanese to English when compared to Bing, Bard, and DeepL Translator in 2023. In December 2023, the Albanian government decided to use ChatGPT for the rapid translation of European Union documents and the analysis of required changes needed for Albania's accession to the EU. Several studies have shown that ChatGPT can outperform Google Translate in some mainstream translation tasks. However, as of 2024, no machine translation services match human expert performance. In August 2024, a representative of the Asia Pacific wing of OpenAI made a visit to Taiwan, during which a demonstration of ChatGPT's Chinese abilities was made. ChatGPT's Mandarin Chinese abilities were lauded, but the ability of the AI to produce content in Mandarin Chinese in a Taiwanese accent was found to be "less than ideal" due to differences between mainland Mandarin Chinese and Taiwanese Mandarin. === GPT Store === In November 2023, OpenAI released GPT Builder, a tool allowing users to customize ChatGPT's behavior for a specific use case. The customized systems are referred to as GPTs. In January 2024, OpenAI launched the GPT Store, a marketplace for GPTs. At launch, OpenAI included more than 3 million GPTs created by GPT Builder users in the GPT Store. === ChatGPT Apps === In September 2025, OpenAI added support for Model Context Protocol (MCP) to ChatGPT apps. When enabled in developer mode, this allows for improved third-party access to ChatGPT tools and servers. === Deep Research === In February 2025, OpenAI released Deep Research, a feature that generates reports based on extensive web searches. It was initially based on the reasoning model o3 and took 5 to 30 minutes per report. === Images === In October 2023, OpenAI's image generation model DALL-E 3 was integrated into ChatGPT. The integration used ChatGPT to write prompts for DALL-E guided by conversations with users. In March 2025, OpenAI updated ChatGPT to generate images using GPT Image instead of DALL-E. One of the most significant improvements was in the generation of text within images, which is especially useful for branded content. However, this ability is noticeably worse in non-Latin alphabets. The model can also generate new images based on existing ones provided in the prompt. These images are generated with C2PA metadata, which can be used to verify that they are AI-generated. OpenAI has emplaced additional safeguards to prevent what the company deems to be harmful image generation. === Agents === In 2025, OpenAI added several features to make ChatGPT more agentic (capable of autonomously performing longer tasks). In January, Operator was released. It was capable of autonomously performing tasks through web browser interactions, including filling forms, placing online orders, scheduling appointments, and other browser-based tasks. It was controlling a software environment inside a virtual machine with limited internet connectivity and with safety restrictions. It struggled with complex user interfaces. In May 2025, OpenAI introduced an agent for coding named Codex. It is capable of writing software, answering codebase questions, running tests, and proposing pull requests. It is based on a fine-tuned version of OpenAI o3. It has two versions, one running in a virtual machine in the cloud, and one where the agent runs in the cloud, but performs actions on a local machine connected via API. In July 2025, OpenAI released ChatGPT agent, an AI agent that can perform multi-step tasks. Like Operator, it controls a virtual computer. It also inherits from Deep Research's ability to gather and summarize significant volumes of information. The user can interrupt tasks or provide additional instructions as needed. In September 2025, OpenAI partnered with Stripe, Inc. to release Agentic Commerce Protocol, enabling purchases through ChatGPT. At launch, the feature was limited to purchases on Etsy from US users with a payment method linked to their OpenAI account. OpenAI takes an undisclosed cut from the merchant's payment. === ChatGPT Health === On January 7, 2026, OpenAI introduced a feature called "ChatGPT Health", whereby ChatGPT can discuss the user's health in a way that is separate from other chats. The feature is not available for users in the United Kingdom, Switzerland, or the European Economic Area, and is available on a waitli
Universal portfolio algorithm
The universal portfolio algorithm is a portfolio selection algorithm from the field of machine learning and information theory. The algorithm learns adaptively from historical data and maximizes log-optimal growth rate in the long run, per the Kelly criterion. It was introduced by the late Stanford University information theorist Thomas M. Cover. The algorithm rebalances the portfolio at the beginning of each trading period. At the beginning of the first trading period it starts with a naive diversification. In the following trading periods the portfolio composition depends on the historical total return of all possible constant-rebalanced portfolios. The universal portfolio algorithm is the predecessor of the various online portfolio selection methodologies.
Color vision
Color vision (CV), a feature of visual perception, is an ability to perceive differences between light composed of different frequencies independently of light intensity. Color perception is a part of the larger visual system and is mediated by a complex process between neurons that begins with differential stimulation of different types of photoreceptors by light entering the eye. Those photoreceptors then emit outputs that are propagated through many layers of neurons ultimately leading to higher cognitive functions in the brain. Color vision is found in many animals and is mediated by similar underlying mechanisms with common types of biological molecules and a complex history of the evolution of color vision within different animal taxa. In primates, color vision may have evolved under selective pressure for a variety of visual tasks including the foraging for nutritious young leaves, ripe fruit, and flowers, as well as detecting predator camouflage and emotional states in other primates. == Wavelength == Isaac Newton discovered that white light after being split into its component colors when passed through a dispersive prism could be recombined to make white light by passing them through a different prism. The visible light spectrum ranges from about 380 to 740 nanometers. Spectral colors (colors that are produced by a narrow band of wavelengths) such as red, orange, yellow, green, cyan, blue, and violet can be found in this range. These spectral colors do not refer to a single wavelength, but rather to a set of wavelengths: red, 625–740 nm; orange, 590–625 nm; yellow, 565–590 nm; green, 500–565 nm; cyan, 485–500 nm; blue, 450–485 nm; violet, 380–450 nm. Wavelengths longer or shorter than this range are called infrared or ultraviolet, respectively. Humans cannot generally see these wavelengths, but other animals may. === Hue detection === Sufficient differences in wavelength cause a difference in the perceived hue; the just-noticeable difference in wavelength varies from about 1 nm in the blue-green and yellow wavelengths to 10 nm and more in the longer red and shorter blue wavelengths. Although the human eye can distinguish up to a few hundred hues, when those pure spectral colors are mixed together or diluted with white light, the number of distinguishable chromaticities can be much higher. In very low light levels, vision is scotopic: light is detected by rod cells of the retina. Rods are maximally sensitive to wavelengths near 500 nm and play little, if any, role in color vision. In brighter light, such as daylight, vision is photopic: light is detected by cone cells which are responsible for color vision. Cones are sensitive to a range of wavelengths, but are most sensitive to wavelengths near 555 nm. Between these regions, mesopic vision comes into play and both rods and cones provide signals to the retinal ganglion cells. The shift in color perception from dim light to daylight gives rise to differences known as the Purkinje effect. The perception of "white" is formed by the entire spectrum of visible light, or by mixing colors of just a few wavelengths in animals with few types of color receptors. In humans, white light can be perceived by combining wavelengths such as red, green, and blue, or just a pair of complementary colors such as blue and yellow. === Non-spectral colors === There are a variety of colors in addition to spectral colors and their hues. These include grayscale colors, shades of colors obtained by mixing grayscale colors with spectral colors, violet-red colors, impossible colors, and metallic colors. Grayscale colors include white, gray, and black. Rods contain rhodopsin, which reacts to light intensity, providing grayscale coloring. Shades include colors such as pink or brown. Pink is obtained from mixing red and white. Brown may be obtained from mixing orange with gray or black. Navy is obtained from mixing blue and black. Violet-red colors include hues and shades of magenta. The light spectrum is a line on which violet is one end and the other is red, and yet we see hues of purple that connect those two colors. Impossible colors are a combination of cone responses that cannot be naturally produced. For example, medium cones cannot be activated completely on their own; if they were, we would see a 'hyper-green' color. == Dimensionality == Color vision is categorized foremost according to the dimensionality of the color gamut, which is defined by the number of primaries required to represent the color vision. This is generally equal to the number of photopsins expressed: a correlation that holds for vertebrates but not invertebrates. The common vertebrate ancestor possessed four photopsins (expressed in cones) plus rhodopsin (expressed in rods), so was tetrachromatic. However, many vertebrate lineages have lost one or many photopsin genes, leading to lower-dimension color vision. The dimensions of color vision range from 1-dimensional and up: == Physiology of color perception == Perception of color begins with specialized retinal cells known as cone cells. Cone cells contain different forms of opsin – a pigment protein – that have different spectral sensitivities. Humans contain three types, resulting in trichromatic color vision. Each individual cone contains pigments composed of opsin apoprotein covalently linked to a light-absorbing prosthetic group: either 11-cis-hydroretinal or, more rarely, 11-cis-dehydroretinal. The cones are conventionally labeled according to the ordering of the wavelengths of the peaks of their spectral sensitivities: short (S), medium (M), and long (L) cone types. These three types do not correspond well to particular colors as we know them. Rather, the perception of color is achieved by a complex process that starts with the differential output of these cells in the retina and which is finalized in the visual cortex and associative areas of the brain. For example, while the L cones have been referred to simply as red receptors, microspectrophotometry has shown that their peak sensitivity is in the greenish-yellow region of the spectrum. Similarly, the S cones and M cones do not directly correspond to blue and green, although they are often described as such. The RGB color model, therefore, is a convenient means for representing color but is not directly based on the types of cones in the human eye. The peak response of human cone cells varies, even among individuals with typical color vision; in some non-human species this polymorphic variation is even greater, and it may well be adaptive. === Theories === Two complementary theories of color vision are the trichromatic theory and the opponent process theory. The trichromatic theory, or Young–Helmholtz theory, proposed in the 19th century by Thomas Young and Hermann von Helmholtz, posits three types of cones preferentially sensitive to blue, green, and red, respectively. Others have suggested that the trichromatic theory is not specifically a theory of color vision but a theory of receptors for all vision, including color but not specific or limited to it. Equally, it has been suggested that the relationship between the phenomenal opponency described by Ewald Hering and the physiological opponent processes are not straightforward (see below), making of physiological opponency a mechanism that is relevant to the whole of vision, and not just to color vision alone. Hering proposed the opponent process theory in 1872. It states that the visual system interprets color in an antagonistic way: red vs. green, blue vs. yellow, black vs. white. Both theories are generally accepted as valid, describing different stages in visual physiology, visualized in the adjacent diagram. Green–magenta and blue–yellow are scales with mutually exclusive boundaries. In the same way that there cannot exist a "slightly negative" positive number, a single eye cannot perceive a bluish-yellow or a reddish-green. Although these two theories are both currently widely accepted theories, past and more recent work has led to criticism of the opponent process theory, stemming from a number of what are presented as discrepancies in the standard opponent process theory. For example, the phenomenon of an after-image of complementary color can be induced by fatiguing the cells responsible for color perception, by staring at a vibrant color for a length of time, and then looking at a white surface. This phenomenon of complementary colors shows that cyan, rather than green, is the complement of red, and that magenta, rather than red, is the complement of green. It therefore also shows that the reddish-green color supposed to be impossible by opponent process theory is actually the color yellow. Although this phenomenon is more readily explained by the trichromatic theory, explanations for the discrepancy may include alterations to the opponent process theory, such as redefining the opponent colors as red vs. cyan, to reflect this effect. Despite such criticis
Luxafor
Luxafor () is a brand of office productivity tools designed to improve efficiency and communication in workplaces. The brands main product is LED status indicators for use in office settings. Luxafor is a product line under the company SIA Greynut, based in Riga, Latvia. == History == Luxafor was developed by the technology company SIA Greynut. The brand first gained attention through a Kickstarter campaign in 2015, which aimed to fund its initial product, the Luxafor Flag. Although the campaign was unsuccessful in reaching its funding goal, the product was still brought to market. In 2017, Luxafor launched another Kickstarter campaign for the Luxafor Bluetooth, a wireless version of its LED status indicator. This campaign also did not meet its funding goal, but like its predecessor, the product was still developed and released. Despite initial setbacks, Luxafor Bluetooth has become one of the brand's leading products. == Products == Luxafors main product range is LED status indicators, including: === Luxafor Flag === A USB-powered LED indicator that shows different colors to signal the user's availability. === Luxafor Bluetooth === A wireless LED indicator controlled via Bluetooth, integrating with productivity tools like Slack and Microsoft Teams. === Luxafor Switch === An advanced status indicator designed to manage room and workspace availability. === Other === Other Luxafor products include CO2 Dongle, Smart Button, Mute Button, Pomodoro Timer and others. == Features == Luxafor products are known for their customizable indicators, integration capabilities with IFTTT, Zapier, and remote control features. They are compatible with various operating systems, including Windows and macOS, and can be integrated with numerous communication and productivity platforms, like Microsoft Teams and Cisco Jabber.