AI App Like Chat Gpt Free

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  Machine translation software usability

  The sections below give objective criteria for evaluating the usability of machine translation software output. == Stationarity or canonical form == Do repeated translations converge on a single expression in both languages? I.e. does the translation method show stationarity or produce a canonical form? Does the translation become stationary without losing the original meaning? This metric has been criticized as not being well correlated with BLEU (BiLingual Evaluation Understudy) scores. == Adaptive to colloquialism, argot or slang == Is the system adaptive to colloquialism, argot or slang? The French language has many rules for creating words in the speech and writing of popular culture. Two such rules are: (a) The reverse spelling of words such as femme to meuf. (This is called verlan.) (b) The attachment of the suffix -ard to a noun or verb to form a proper noun. For example, the noun faluche means "student hat". The word faluchard formed from faluche colloquially can mean, depending on context, "a group of students", "a gathering of students" and "behavior typical of a student". The Google translator as of 28 December 2006 doesn't derive the constructed words as for example from rule (b), as shown here: Il y a une chorale falucharde mercredi, venez nombreux, les faluchards chantent des paillardes! ==> There is a choral society falucharde Wednesday, come many, the faluchards sing loose-living women! French argot has three levels of usage: familier or friendly, acceptable among friends, family and peers but not at work grossier or swear words, acceptable among friends and peers but not at work or in family verlan or ghetto slang, acceptable among lower classes but not among middle or upper classes The United States National Institute of Standards and Technology conducts annual evaluations [1] Archived 2009-03-22 at the Wayback Machine of machine translation systems based on the BLEU-4 criterion [2]. A combined method called IQmt which incorporates BLEU and additional metrics NIST, GTM, ROUGE and METEOR has been implemented by Gimenez and Amigo [3]. == Well-formed output == Is the output grammatical or well-formed in the target language? Using an interlingua should be helpful in this regard, because with a fixed interlingua one should be able to write a grammatical mapping to the target language from the interlingua. Consider the following Arabic language input and English language translation result from the Google translator as of 27 December 2006 [4]. This Google translator output doesn't parse using a reasonable English grammar: وعن حوادث التدافع عند شعيرة رمي الجمرات -التي كثيرا ما يسقط فيها العديد من الضحايا- أشار الأمير نايف إلى إدخال "تحسينات كثيرة في جسر الجمرات ستمنع بإذن الله حدوث أي تزاحم". ==> And incidents at the push Carbuncles-throwing ritual, which often fall where many of the victims - Prince Nayef pointed to the introduction of "many improvements in bridge Carbuncles God would stop the occurrence of any competing." == Semantics preservation == Do repeated re-translations preserve the semantics of the original sentence? For example, consider the following English input passed multiple times into and out of French using the Google translator as of 27 December 2006: Better a day earlier than a day late. ==> Améliorer un jour plus tôt qu'un jour tard. ==> To improve one day earlier than a day late. ==> Pour améliorer un jour plus tôt qu'un jour tard. ==> To improve one day earlier than a day late. As noted above and in, this kind of round-trip translation is a very unreliable method of evaluation. == Trustworthiness and security == An interesting peculiarity of Google Translate as of 24 January 2008 (corrected as of 25 January 2008) is the following result when translating from English to Spanish, which shows an embedded joke in the English-Spanish dictionary which has some added poignancy given recent events: Heath Ledger is dead ==> Tom Cruise está muerto This raises the issue of trustworthiness when relying on a machine translation system embedded in a Life-critical system in which the translation system has input to a Safety Critical Decision Making process. Conjointly it raises the issue of whether in a given use the software of the machine translation system is safe from hackers. It is not known whether this feature of Google Translate was the result of a joke/hack or perhaps an unintended consequence of the use of a method such as statistical machine translation. Reporters from CNET Networks asked Google for an explanation on January 24, 2008; Google said only that it was an "internal issue with Google Translate". The mistranslation was the subject of much hilarity and speculation on the Internet. If it is an unintended consequence of the use of a method such as statistical machine translation, and not a joke/hack, then this event is a demonstration of a potential source of critical unreliability in the statistical machine translation method. In human translations, in particular on the part of interpreters, selectivity on the part of the translator in performing a translation is often commented on when one of the two parties being served by the interpreter knows both languages. This leads to the issue of whether a particular translation could be considered verifiable. In this case, a converging round-trip translation would be a kind of verification.

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  Data analysis for fraud detection

  Fraud represents a significant problem for governments and businesses and specialized analysis techniques for discovering fraud using them are required. Some of these methods include knowledge discovery in databases (KDD), data mining, machine learning and statistics. They offer applicable and successful solutions in different areas of electronic fraud crimes. In general, the primary reason to use data analytics techniques is to tackle fraud since many internal control systems have serious weaknesses. For example, the currently prevailing approach employed by many law enforcement agencies to detect companies involved in potential cases of fraud consists in receiving circumstantial evidence or complaints from whistleblowers. As a result, a large number of fraud cases remain undetected and unprosecuted. In order to effectively test, detect, validate, correct error and monitor control systems against fraudulent activities, businesses entities and organizations rely on specialized data analytics techniques such as data mining, data matching, the sounds like function, regression analysis, clustering analysis, and gap analysis. Techniques used for fraud detection fall into two primary classes: statistical techniques and artificial intelligence. == Statistical techniques == Examples of statistical data analysis techniques are: Data preprocessing techniques for detection, validation, error correction, and filling up of missing or incorrect data. Calculation of various statistical parameters such as averages, quantiles, performance metrics, probability distributions, and so on. For example, the averages may include average length of call, average number of calls per month and average delays in bill payment. Models and probability distributions of various business activities either in terms of various parameters or probability distributions. Computing user profiles. Time-series analysis of time-dependent data. Clustering and classification to find patterns and associations among groups of data. Data matching Data matching is used to compare two sets of collected data. The process can be performed based on algorithms or programmed loops. Trying to match sets of data against each other or comparing complex data types. Data matching is used to remove duplicate records and identify links between two data sets for marketing, security or other uses. Sounds like Function is used to find values that sound similar. The Phonetic similarity is one way to locate possible duplicate values, or inconsistent spelling in manually entered data. The ‘sounds like’ function converts the comparison strings to four-character American Soundex codes, which are based on the first letter, and the first three consonants after the first letter, in each string. Regression analysis allows you to examine the relationship between two or more variables of interest. Regression analysis estimates relationships between independent variables and a dependent variable. This method can be used to help understand and identify relationships among variables and predict actual results. Gap analysis is used to determine whether business requirements are being met, if not, what are the steps that should be taken to meet successfully. Matching algorithms to detect anomalies in the behavior of transactions or users as compared to previously known models and profiles. Techniques are also needed to eliminate false alarms, estimate risks, and predict future of current transactions or users. Some forensic accountants specialize in forensic analytics which is the procurement and analysis of electronic data to reconstruct, detect, or otherwise support a claim of financial fraud. The main steps in forensic analytics are data collection, data preparation, data analysis, and reporting. For example, forensic analytics may be used to review an employee's purchasing card activity to assess whether any of the purchases were diverted or divertible for personal use. == Artificial intelligence == Fraud detection is a knowledge-intensive activity. The main AI techniques used for fraud detection include: Data mining to classify, cluster, and segment the data and automatically find associations and rules in the data that may signify interesting patterns, including those related to fraud. Expert systems to encode expertise for detecting fraud in the form of rules. Pattern recognition to detect approximate classes, clusters, or patterns of suspicious behavior either automatically (unsupervised) or to match given inputs. Machine learning techniques to automatically identify characteristics of fraud. Neural nets to independently generate classification, clustering, generalization, and forecasting that can then be compared against conclusions raised in internal audits or formal financial documents such as 10-Q. Other techniques such as link analysis, Bayesian networks, decision theory, and sequence matching are also used for fraud detection. A new and novel technique called System properties approach has also been employed where ever rank data is available. Statistical analysis of research data is the most comprehensive method for determining if data fraud exists. Data fraud as defined by the Office of Research Integrity (ORI) includes fabrication, falsification and plagiarism. == Machine learning and data mining == Early data analysis techniques were oriented toward extracting quantitative and statistical data characteristics. These techniques facilitate useful data interpretations and can help to get better insights into the processes behind the data. Although the traditional data analysis techniques can indirectly lead us to knowledge, it is still created by human analysts. To go beyond, a data analysis system has to be equipped with a substantial amount of background knowledge, and be able to perform reasoning tasks involving that knowledge and the data provided. In effort to meet this goal, researchers have turned to ideas from the machine learning field. This is a natural source of ideas, since the machine learning task can be described as turning background knowledge and examples (input) into knowledge (output). If data mining results in discovering meaningful patterns, data turns into information. Information or patterns that are novel, valid and potentially useful are not merely information, but knowledge. One speaks of discovering knowledge, before hidden in the huge amount of data, but now revealed. The machine learning and artificial intelligence solutions may be classified into two categories: 'supervised' and 'unsupervised' learning. These methods seek for accounts, customers, suppliers, etc. that behave 'unusually' in order to output suspicion scores, rules or visual anomalies, depending on the method. Whether supervised or unsupervised methods are used, note that the output gives us only an indication of fraud likelihood. No stand alone statistical analysis can assure that a particular object is a fraudulent one, but they can identify them with very high degrees of accuracy. As a result, effective collaboration between machine learning model and human analysts is vital to the success of fraud detection applications. === Supervised learning === In supervised learning, a random sub-sample of all records is taken and manually classified as either 'fraudulent' or 'non-fraudulent' (task can be decomposed on more classes to meet algorithm requirements). Relatively rare events such as fraud may need to be over sampled to get a big enough sample size. These manually classified records are then used to train a supervised machine learning algorithm. After building a model using this training data, the algorithm should be able to classify new records as either fraudulent or non-fraudulent. Supervised neural networks, fuzzy neural nets, and combinations of neural nets and rules, have been extensively explored and used for detecting fraud in mobile phone networks and financial statement fraud. Bayesian learning neural network is implemented for credit card fraud detection, telecommunications fraud, auto claim fraud detection, and medical insurance fraud. Hybrid knowledge/statistical-based systems, where expert knowledge is integrated with statistical power, use a series of data mining techniques for the purpose of detecting cellular clone fraud. Specifically, a rule-learning program to uncover indicators of fraudulent behaviour from a large database of customer transactions is implemented. Cahill et al. (2000) design a fraud signature, based on data of fraudulent calls, to detect telecommunications fraud. For scoring a call for fraud its probability under the account signature is compared to its probability under a fraud signature. The fraud signature is updated sequentially, enabling event-driven fraud detection. Link analysis comprehends a different approach. It relates known fraudsters to other individuals, using record linkage and social network methods. This type of detection is only able to detect fra

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  Deepfake pornography

  Deepfake pornography is a form of non-consensual AI pornography created by altering existing photographs or videos using deepfake technology to modify the appearance of the participants. The use of deepfake pornography has sparked controversy because it involves the making and sharing of realistic videos featuring non-consenting individuals and is sometimes used for revenge porn. Many countries have criminalized this "new voyeurism" through legislative measures and technological solutions. == History == The term "deepfake" was coined in 2017 on a Reddit forum where users shared altered pornographic videos created using machine learning algorithms. It is a combination of the word "deep learning", which refers to the program used to create the videos, and "fake" meaning the videos are not real. Deepfake pornography was originally created on a small individual scale using a combination of machine learning algorithms, computer vision techniques, and AI software. The process began by gathering a large amount of source material (including both images and videos) of a person's face, and then using a deep learning model to train a Generative Adversarial Network to create a fake video that convincingly swaps the face of the source material onto the body of a pornographic performer. However, the production process has significantly evolved since 2018, with the advent of several public apps that have largely automated the process. While several AI "nudification" apps emerged on mainstream platforms like Google Play and the Apple App Store around 2023, major tech storefronts have since implemented stricter policies and automated detection to ban such software. Consequently, the proliferation of non-consensual deepfake pornography has largely shifted to decentralized websites, specialized online forums, and third-party messaging bot ecosystems. Deepfake pornography is sometimes confused with fake nude photography, but the two are mostly different. Fake nude photography typically uses non-sexual images and merely makes it appear that the people in them are nude. == Notable cases == Deepfake technology has been used to create non-consensual and pornographic images and videos of famous women. One of the earliest examples occurred in 2017 when a deepfake pornographic video of Gal Gadot was created by a Reddit user and quickly spread online. Since then, there have been numerous instances of similar deepfake content targeting other female celebrities, such as Emma Watson, Natalie Portman, and Scarlett Johansson. Johansson spoke publicly on the issue in December 2018, condemning the practice but also refusing legal action because she views the harassment as inevitable. === Rana Ayyub === In 2018, Rana Ayyub, an Indian investigative journalist, was the target of an online hate campaign stemming from her condemnation of the Indian government, specifically her speaking out against the rape of an eight-year-old Kashmiri girl. Ayyub was bombarded with rape and death threats, and had a doctored pornographic video of her circulated online. In a Huffington Post article, Ayyub discussed the long-lasting psychological and social effects this experience has had on her. She explained that she continued to struggle with her mental health and how the images and videos continued to resurface whenever she took a high-profile case. === Atrioc controversy === In 2023, Twitch streamer Atrioc stirred controversy when he accidentally revealed deepfake pornographic material featuring female Twitch streamers while on live. The influencer has since admitted to paying for AI generated porn, and apologized to the women and his fans. === Taylor Swift === In January 2024, AI-generated sexually explicit images of American singer Taylor Swift were posted on X (formerly Twitter), and spread to other platforms such as Facebook, Reddit and Instagram. One tweet with the images was viewed over 45 million times before being removed. A report from 404 Media found that the images appeared to have originated from a Telegram group, whose members used tools such as Microsoft Designer to generate the images, using misspellings and keyword hacks to work around Designer's content filters. After the material was posted, Swift's fans posted concert footage and images to bury the deepfake images, and reported the accounts posting the deepfakes. Searches for Swift's name were temporarily disabled on X, returning an error message instead. Graphika, a disinformation research firm, traced the creation of the images back to a 4chan community. A source close to Swift told the Daily Mail that she would be considering legal action, saying, "Whether or not legal action will be taken is being decided, but there is one thing that is clear: These fake AI-generated images are abusive, offensive, exploitative, and done without Taylor's consent and/or knowledge." The controversy drew condemnation from White House Press Secretary Karine Jean-Pierre, Microsoft CEO Satya Nadella, the Rape, Abuse & Incest National Network, and SAG-AFTRA. Several US politicians called for federal legislation against deepfake pornography. Later in the month, US senators Dick Durbin, Lindsey Graham, Amy Klobuchar and Josh Hawley introduced a bipartisan bill that would allow victims to sue individuals who produced or possessed "digital forgeries" with intent to distribute, or those who received the material knowing it was made non-consensually. === 2024 Telegram deepfake scandal === It emerged in South Korea in August 2024, that many teachers and female students were victims of deepfake images created by users who utilized AI technology. Journalist Ko Narin of The Hankyoreh uncovered the deepfake images through Telegram chats. On Telegram, group chats were created specifically for image-based sexual abuse of women, including middle and high school students, teachers, and even family members. Women with photos on social media platforms like KakaoTalk, Instagram, and Facebook are often targeted as well. Perpetrators use AI bots to generate fake images, which are then sold or widely shared, along with the victims' social media accounts, phone numbers, and KakaoTalk usernames. One Telegram group reportedly drew around 220,000 members, according to a Guardian report. Investigations revealed numerous chat groups on Telegram where users, mainly teenagers, create and share explicit deepfake images of classmates and teachers. The issue came in the wake of a troubling history of digital sex crimes, notably the notorious Nth Room case in 2019. The Korean Teachers Union estimated that more than 200 schools had been affected by these incidents. Activists called for a "national emergency" declaration to address the problem. South Korean police reported over 800 deepfake sex crime cases by the end of September 2024, a stark rise from just 156 cases in 2021, with most victims and offenders being teenagers. On September 21, 6,000 people gathered at Marronnier Park in northeastern Seoul to demand stronger legal action against deepfake crimes targeting women. On September 26, following widespread outrage over the Telegram scandal, South Korean lawmakers passed a bill criminalizing the possession or viewing of sexually explicit deepfake images and videos, imposing penalties that include prison terms and fines. Under the new law, those caught buying, saving, or watching such material could face up to three years in prison or fines up to 30 million won ($22,600). At the time the bill was proposed, creating sexually explicit deepfakes for distribution carried a maximum penalty of five years, but the new legislation would increase this to seven years, regardless of intent. By October 2024, it was estimated that "nudify" deep fake bots on Telegram were up to four million monthly users. === 2025–2026 Grok/X chatbot deepfake scandal === In December 2025, Bloomberg reported that X users found Grok would comply with unconsensual requests to digitally undress individuals, including minors, or show them performing sexually explicit acts. The majority of these prompts were targeted at women and girls. An analysis of 20,000 images generated by Grok between December 25, 2025 and January 1, 2026 showed 2% were of people in bikinis or transparent clothes and appeared to be 18 or younger, including 30 of "young or very young" women or girls. A separate analysis conducted over 24 hours from January 5 to 6 calculated that users had Grok create 6,700 sexually suggestive or nudified images per hour. xAI responded to requests for comment from media organizations with the automated reply, "Legacy Media Lies". The bot's image generation sparked an international backlash and calls for legal or regulatory action from officials in the European Union, United Kingdom, Poland, France, India, Malaysia, and Brazil. === Fernandes–Ulmen case === German TV presenter Collien Fernandes, filed a complaint against her ex-husband, actor Christian Ulmen, for several accusation including, ident

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  Generative literature

  Generative literature is poetry or fiction that is automatically generated, often using computers. It is a genre of electronic literature, and also related to generative art. John Clark's Latin Verse Machine (1830–1843) is probably the first example of mechanised generative literature, while Christopher Strachey's love letter generator (1952) is the first digital example. With the large language models (LLMs) of the 2020s, generative literature is becoming increasingly common. == Definitions == Hannes Bajohr defines generative literature as literature involving "the automatic production of text according to predetermined parameters, usually following a combinatory, sometimes aleatory logic, and it emphasizes the production rather than the reception of the work (unlike, say, hypertext)." In his book Electronic Literature, Scott Rettberg connects generative literature to avant-garde literary movements like Dada, Surrealism, Oulipo and Fluxus. Bajohr argues that conceptual art is also an important reference. == Paradigms of generative literature == Bajohr describes two main paradigms of generative literature: the sequential paradigm, where the text generation is "executed as a sequence of rule-steps" and employs linear algorithms, and the connectionist paradigm, which is based on neural nets. The latter leads to what Bajohr calls a algorithmic empathy: "a non-anthropocentric empathy aimed not at the psychological states of the artists but at understanding the process of the work’s material production." == Poetry generation == The first examples of automated generative literature are poetry: John Clark's mechanical Latin Verse Machine (1830–1843) produced lines of hexameter verse in Latin, and Christopher Strachey's love letter generator (1952), programmed on the Manchester Mark 1 computer, generated short, satirical love letters. Examples of generative poetry using artificial neural networks include David Jhave Johnston's ReRites. == Narrative generation == Story generators have often followed specific narratological theories of how stories are constructed. An early example is Grimes' Fairy Tales, the "first to take a grammar-based approach and the first to operationalize Propp's famous model." Mike Sharples and Rafael Peréz y Peréz's book Story Machines gives a detailed history of story generation. Storyland by Nanette Wylde is an example of generative narrative. Jonathan Baillehache compares Storyland to Surrealist writing. Baillehache states, "When compared to earlier uses of chance operation in literature, a piece like this one resembles some of the automatic writings produced by André Breton and Philippe Soupault in their collective work The Magnetic Fields. . . The difference between Nanette Wylde’s Storyland and Breton and Soupault’s Magnetic Fields is that the former is produced according to a computational algorithm involving randomizers and user interaction, and the latter by two free-wheeling human subjects."

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  Cobocards

  CoboCards is a web application for creation, study and sharing of flashcards. They also provide mobile application for Android and iOS mobile devices, to help study of flashcards on the move. Based on the freemium model, CoboCards provides users a free account with two card sets compared to paid subscription with premium features such as unlimited card sets, Leitner system based trainer and collaborative learning. == History == CoboCards is a project of Jamil Soufan and Tamim Swaid. Tamim Swaid has developed the concept and interface of a collaboratively usable e-learning platform in his diploma thesis at the University of Applied Sciences in February 2007. In January 2010 they founded the CoboCards GmbH (limited company) together with Ali Yildirim. CoboCards is supported by its strategic partners Prof. Schroeder (RWTH Aachen University), Prof. Oliver Wrede (University for Applied Sciences Aachen) and Prof. Klaus Gasteier (University of Arts Berlin). With the idea of creating and studying flashcards online and offering an active control of learning progress they won the start2grow business idea competition in September 2009 (€25.000 ). Additionally CoboCards was funded by German Authorities with approximately €100.000 .

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  Blended artificial intelligence

  Blended artificial intelligence (blended AI) refers to the blending of different artificial intelligence techniques or approaches to achieve more robust and practical solutions. It involves integrating multiple AI models, algorithms, and technologies to leverage their respective strengths and compensate for their weaknesses. == Background == In the context of machine learning, blended AI can involve using different types of models, such as generative AI, decision trees, neural networks, and support vector machines. By combining their results, predictions are more accurate and reliable. This blending of models can be done through techniques like ensemble learning, where multiple models are trained independently and their predictions are combined to make a final decision. Blended AI can also involve combining different AI techniques or technologies, such as natural language processing, computer vision, and expert systems, to tackle complex problems that require a multi-dimensional approach. For example, in a sales scenario AI could be used for lead generation and gathering information from social media such as LinkedIn posts, or understanding a prospect's hobbies and interests. Another blended AI could achieve customer profiling including past interactions and purchasing habits, by them, their industry and growth areas. Blended AI could be used to do predictive analytics to look at historical sales data, market trends, and external factors to generate accurate sales forecasts. This method is critical to gauge and increase "efficiency, revenue, and productivity". Lastly, another could integrate all the information into the CRM to build and maintain better prospect and customer profiles. Blended AI aims to leverage the strengths of different AI techniques and technologies, allowing them to complement each other and create more powerful and comprehensive AI solutions. By combining multiple approaches, blended AI aims to achieve better performance, higher accuracy, improved robustness, and enhanced capabilities in solving diverse and challenging problems.

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  Batch normalization

  In artificial neural networks, batch normalization (also known as batch norm) is a normalization technique used to make training faster and more stable by adjusting the inputs to each layer—re-centering them around zero and re-scaling them to a standard size. It was introduced by Sergey Ioffe and Christian Szegedy in 2015. Experts still debate why batch normalization works so well. It was initially thought to tackle internal covariate shift, a problem where parameter initialization and changes in the distribution of the inputs of each layer affect the learning rate of the network. However, newer research suggests it doesn’t fix this shift but instead smooths the objective function—a mathematical guide the network follows to improve—enhancing performance. In very deep networks, batch normalization can initially cause a severe gradient explosion—where updates to the network grow uncontrollably large—but this is managed with shortcuts called skip connections in residual networks. Another theory is that batch normalization adjusts data by handling its size and path separately, speeding up training. == Internal covariate shift == Each layer in a neural network has inputs that follow a specific distribution, which shifts during training due to two main factors: the random starting values of the network’s settings (parameter initialization) and the natural variation in the input data. This shifting pattern affecting the inputs to the network’s inner layers is called internal covariate shift. While a strict definition isn’t fully agreed upon, experiments show that it involves changes in the means and variances of these inputs during training. Batch normalization was first developed to address internal covariate shift. During training, as the parameters of preceding layers adjust, the distribution of inputs to the current layer changes accordingly, such that the current layer needs to constantly readjust to new distributions. This issue is particularly severe in deep networks, because small changes in shallower hidden layers will be amplified as they propagate within the network, resulting in significant shift in deeper hidden layers. Batch normalization was proposed to reduced these unwanted shifts to speed up training and produce more reliable models. Beyond possibly tackling internal covariate shift, batch normalization offers several additional advantages. It allows the network to use a higher learning rate—a setting that controls how quickly the network learns—without causing problems like vanishing or exploding gradients, where updates become too small or too large. It also appears to have a regularizing effect, improving the network’s ability to generalize to new data, reducing the need for dropout, a technique used to prevent overfitting (when a model learns the training data too well and fails on new data). Additionally, networks using batch normalization are less sensitive to the choice of starting settings or learning rates, making them more robust and adaptable. == Procedures == === Transformation === In a neural network, batch normalization is achieved through a normalization step that fixes the means and variances of each layer's inputs. Ideally, the normalization would be conducted over the entire training set, but to use this step jointly with stochastic optimization methods, it is impractical to use the global information. Thus, normalization is restrained to each mini-batch in the training process. Let us use B to denote a mini-batch of size m of the entire training set. The empirical mean and variance of B could thus be denoted as μ B = 1 m ∑ i = 1 m x i {\displaystyle \mu _{B}={\frac {1}{m}}\sum _{i=1}^{m}x_{i}} and σ B 2 = 1 m ∑ i = 1 m ( x i − μ B ) 2 {\displaystyle \sigma _{B}^{2}={\frac {1}{m}}\sum _{i=1}^{m}(x_{i}-\mu _{B})^{2}} . For a layer of the network with d-dimensional input, x = ( x ( 1 ) , . . . , x ( d ) ) {\displaystyle x=(x^{(1)},...,x^{(d)})} , each dimension of its input is then normalized (i.e. re-centered and re-scaled) separately, x ^ i ( k ) = x i ( k ) − μ B ( k ) ( σ B ( k ) ) 2 + ϵ {\displaystyle {\hat {x}}_{i}^{(k)}={\frac {x_{i}^{(k)}-\mu _{B}^{(k)}}{\sqrt {\left(\sigma _{B}^{(k)}\right)^{2}+\epsilon }}}} , where k ∈ [ 1 , d ] {\displaystyle k\in [1,d]} and i ∈ [ 1 , m ] {\displaystyle i\in [1,m]} ; μ B ( k ) {\displaystyle \mu _{B}^{(k)}} and σ B ( k ) {\displaystyle \sigma _{B}^{(k)}} are the per-dimension mean and standard deviation, respectively. ϵ {\displaystyle \epsilon } is added in the denominator for numerical stability and is an arbitrarily small positive constant. The resulting normalized activation x ^ ( k ) {\displaystyle {\hat {x}}^{(k)}} have zero mean and unit variance, if ϵ {\displaystyle \epsilon } is not taken into account. To restore the representation power of the network, a transformation step then follows as y i ( k ) = γ ( k ) x ^ i ( k ) + β ( k ) {\displaystyle y_{i}^{(k)}=\gamma ^{(k)}{\hat {x}}_{i}^{(k)}+\beta ^{(k)}} , where the parameters γ ( k ) {\displaystyle \gamma ^{(k)}} and β ( k ) {\displaystyle \beta ^{(k)}} are subsequently learned in the optimization process. Formally, the operation that implements batch normalization is a transform B N γ ( k ) , β ( k ) : x 1... m ( k ) → y 1... m ( k ) {\displaystyle BN_{\gamma ^{(k)},\beta ^{(k)}}:x_{1...m}^{(k)}\rightarrow y_{1...m}^{(k)}} called the Batch Normalizing transform. The output of the BN transform y ( k ) = B N γ ( k ) , β ( k ) ( x ( k ) ) {\displaystyle y^{(k)}=BN_{\gamma ^{(k)},\beta ^{(k)}}(x^{(k)})} is then passed to other network layers, while the normalized output x ^ i ( k ) {\displaystyle {\hat {x}}_{i}^{(k)}} remains internal to the current layer. === Backpropagation === The described BN transform is a differentiable operation, and the gradient of the loss l {\displaystyle l} with respect to the different parameters can be computed directly with the chain rule. Specifically, ∂ l ∂ y i ( k ) {\displaystyle {\frac {\partial l}{\partial y_{i}^{(k)}}}} depends on the choice of activation function, and the gradient against other parameters could be expressed as a function of ∂ l ∂ y i ( k ) {\displaystyle {\frac {\partial l}{\partial y_{i}^{(k)}}}} : ∂ l ∂ x ^ i ( k ) = ∂ l ∂ y i ( k ) γ ( k ) {\displaystyle {\frac {\partial l}{\partial {\hat {x}}_{i}^{(k)}}}={\frac {\partial l}{\partial y_{i}^{(k)}}}\gamma ^{(k)}} , ∂ l ∂ γ ( k ) = ∑ i = 1 m ∂ l ∂ y i ( k ) x ^ i ( k ) {\displaystyle {\frac {\partial l}{\partial \gamma ^{(k)}}}=\sum _{i=1}^{m}{\frac {\partial l}{\partial y_{i}^{(k)}}}{\hat {x}}_{i}^{(k)}} , ∂ l ∂ β ( k ) = ∑ i = 1 m ∂ l ∂ y i ( k ) {\displaystyle {\frac {\partial l}{\partial \beta ^{(k)}}}=\sum _{i=1}^{m}{\frac {\partial l}{\partial y_{i}^{(k)}}}} , ∂ l ∂ σ B ( k ) 2 = ∑ i = 1 m ∂ l ∂ y i ( k ) ( x i ( k ) − μ B ( k ) ) ( − γ ( k ) 2 ( σ B ( k ) 2 + ϵ ) − 3 / 2 ) {\displaystyle {\frac {\partial l}{\partial \sigma _{B}^{(k)^{2}}}}=\sum _{i=1}^{m}{\frac {\partial l}{\partial y_{i}^{(k)}}}(x_{i}^{(k)}-\mu _{B}^{(k)})\left(-{\frac {\gamma ^{(k)}}{2}}(\sigma _{B}^{(k)^{2}}+\epsilon )^{-3/2}\right)} , ∂ l ∂ μ B ( k ) = ∑ i = 1 m ∂ l ∂ y i ( k ) − γ ( k ) σ B ( k ) 2 + ϵ + ∂ l ∂ σ B ( k ) 2 1 m ∑ i = 1 m ( − 2 ) ⋅ ( x i ( k ) − μ B ( k ) ) {\displaystyle {\frac {\partial l}{\partial \mu _{B}^{(k)}}}=\sum _{i=1}^{m}{\frac {\partial l}{\partial y_{i}^{(k)}}}{\frac {-\gamma ^{(k)}}{\sqrt {\sigma _{B}^{(k)^{2}}+\epsilon }}}+{\frac {\partial l}{\partial \sigma _{B}^{(k)^{2}}}}{\frac {1}{m}}\sum _{i=1}^{m}(-2)\cdot (x_{i}^{(k)}-\mu _{B}^{(k)})} , and ∂ l ∂ x i ( k ) = ∂ l ∂ x ^ i ( k ) 1 σ B ( k ) 2 + ϵ + ∂ l ∂ σ B ( k ) 2 2 ( x i ( k ) − μ B ( k ) ) m + ∂ l ∂ μ B ( k ) 1 m {\displaystyle {\frac {\partial l}{\partial x_{i}^{(k)}}}={\frac {\partial l}{\partial {\hat {x}}_{i}^{(k)}}}{\frac {1}{\sqrt {\sigma _{B}^{(k)^{2}}+\epsilon }}}+{\frac {\partial l}{\partial \sigma _{B}^{(k)^{2}}}}{\frac {2(x_{i}^{(k)}-\mu _{B}^{(k)})}{m}}+{\frac {\partial l}{\partial \mu _{B}^{(k)}}}{\frac {1}{m}}} . === Inference === During the training stage, the normalization steps depend on the mini-batches to ensure efficient and reliable training. However, in the inference stage, this dependence is not useful any more. Instead, the normalization step in this stage is computed with the population statistics such that the output could depend on the input in a deterministic manner. The population mean, E [ x ( k ) ] {\displaystyle E[x^{(k)}]} , and variance, Var ⁡ [ x ( k ) ] {\displaystyle \operatorname {Var} [x^{(k)}]} , are computed as: E [ x ( k ) ] = E B [ μ B ( k ) ] {\displaystyle E[x^{(k)}]=E_{B}[\mu _{B}^{(k)}]} , and Var ⁡ [ x ( k ) ] = m m − 1 E B [ ( σ B ( k ) ) 2 ] {\displaystyle \operatorname {Var} [x^{(k)}]={\frac {m}{m-1}}E_{B}[\left(\sigma _{B}^{(k)}\right)^{2}]} . The population statistics thus is a complete representation of the mini-batches. The BN transform in the inference step thus becomes y ( k ) = B N γ ( k ) , β ( k ) inf ( x ( k ) ) = γ ( k ) x ( k ) − E [ x ( k ) ] Var ⁡ [ x ( k ) ] + ϵ + β

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  Evolutionary computation

  Evolutionary computation (EC) from computer science is a family of algorithms for global optimization inspired by biological evolution, and a subfield of computational intelligence and soft computing studying these algorithms. In technical terms, they are a family of population-based trial and error problem solvers with a metaheuristic or stochastic optimization character. In evolutionary computation, an initial set of candidate solutions is generated and iteratively updated. Each new generation is produced by stochastically removing less desired solutions, and introducing small random changes as well as, depending on the method, mixing parental information. In biological terminology, a population of solutions is subjected to natural selection (or artificial selection), mutation and possibly recombination. These biological functions serve as role models for the genetic operators - mutation, crossover, and selection - used in the EC procedures. As a result, the population will gradually evolve to increase in fitness, in this case the chosen fitness function of the algorithm. Evolutionary computation techniques can produce highly optimized solutions in a wide range of problem settings, making them popular in computer science. Many variants and extensions exist, suited to more specific families of problems and data structures. Evolutionary computation is also sometimes used in evolutionary biology as an in silico experimental procedure to study common aspects of general evolutionary processes. == History == The concept of mimicking evolutionary processes to solve problems originates before the advent of computers, such as when Alan Turing proposed a method of genetic search in 1948 . Turing's B-type u-machines resemble primitive neural networks, and connections between neurons were learnt via a sort of genetic algorithm. His P-type u-machines resemble a method for reinforcement learning, where pleasure and pain signals direct the machine to learn certain behaviors. However, Turing's paper went unpublished until 1968, and he died in 1954, so this early work had little to no effect on the field of evolutionary computation that was to develop. Evolutionary computing as a field began in earnest in the 1950s and 1960s. There were several independent attempts to use the process of evolution in computing at this time, which developed separately for roughly 15 years. Three branches emerged in different places to attain this goal: evolution strategies, evolutionary programming, and genetic algorithms. A fourth branch, genetic programming, eventually emerged in the early 1990s. These approaches differ in the method of selection, the permitted mutations, and the representation of genetic data. By the 1990s, the distinctions between the historic branches had begun to blur, and the term 'evolutionary computing' was coined in 1991 to denote a field that exists over all four paradigms. In 1962, Lawrence J. Fogel initiated the research of Evolutionary Programming in the United States, which was considered an artificial intelligence endeavor. In this system, finite state machines are used to solve a prediction problem: these machines would be mutated (adding or deleting states, or changing the state transition rules), and the best of these mutated machines would be evolved further in future generations. The final finite state machine may be used to generate predictions when needed. The evolutionary programming method was successfully applied to prediction problems, system identification, and automatic control. It was eventually extended to handle time series data and to model the evolution of gaming strategies. In 1964, Ingo Rechenberg and Hans-Paul Schwefel introduce the paradigm of evolution strategies in Germany. Since traditional gradient descent techniques produce results that may get stuck in local minima, Rechenberg and Schwefel proposed that random mutations (applied to all parameters of some solution vector) may be used to escape these minima. Child solutions were generated from parent solutions, and the more successful of the two was kept for future generations. This technique was first used by the two to successfully solve optimization problems in fluid dynamics. Initially, this optimization technique was performed without computers, instead relying on dice to determine random mutations. By 1965, the calculations were performed wholly by machine. John Henry Holland introduced genetic algorithms in the 1960s, and it was further developed at the University of Michigan in the 1970s. While the other approaches were focused on solving problems, Holland primarily aimed to use genetic algorithms to study adaptation and determine how it may be simulated. Populations of chromosomes, represented as bit strings, were transformed by an artificial selection process, selecting for specific 'allele' bits in the bit string. Among other mutation methods, interactions between chromosomes were used to simulate the recombination of DNA between different organisms. While previous methods only tracked a single optimal organism at a time (having children compete with parents), Holland's genetic algorithms tracked large populations (having many organisms compete each generation). By the 1990s, a new approach to evolutionary computation that came to be called genetic programming emerged, advocated for by John Koza among others. In this class of algorithms, the subject of evolution was itself a program written in a high-level programming language (there had been some previous attempts as early as 1958 to use machine code, but they met with little success). For Koza, the programs were Lisp S-expressions, which can be thought of as trees of sub-expressions. This representation permits programs to swap subtrees, representing a sort of genetic mixing. Programs are scored based on how well they complete a certain task, and the score is used for artificial selection. Sequence induction, pattern recognition, and planning were all successful applications of the genetic programming paradigm. Many other figures played a role in the history of evolutionary computing, although their work did not always fit into one of the major historical branches of the field. The earliest computational simulations of evolution using evolutionary algorithms and artificial life techniques were performed by Nils Aall Barricelli in 1953, with first results published in 1954. Another pioneer in the 1950s was Alex Fraser, who published a series of papers on simulation of artificial selection. As academic interest grew, dramatic increases in the power of computers allowed practical applications, including the automatic evolution of computer programs. Evolutionary algorithms are now used to solve multi-dimensional problems more efficiently than software produced by human designers, and also to optimize the design of systems. == Techniques == Evolutionary computing techniques mostly involve metaheuristic optimization algorithms. Broadly speaking, the field includes: Agent-based modeling Ant colony optimization Particle swarm optimization Swarm intelligence Artificial immune systems Artificial life Digital organism Cultural algorithms Differential evolution Dual-phase evolution Estimation of distribution algorithm Evolutionary algorithm Genetic algorithm Evolutionary programming Genetic programming Gene expression programming Grammatical evolution Evolution strategy Learnable evolution model Learning classifier system Memetic algorithms Neuroevolution Self-organization such as self-organizing maps, competitive learning Over recent years many dubious algorithms have been proposed, that are often just copies of existing algorithms (frequently Particle Swarm Optimization), where only the metaphor changed, but the algorithm itself is not new at all. A thorough catalogue with many of these dubious algorithms has been published in the Evolutionary Computation Bestiary. It is also important to note that many of these dubiously 'novel' algorithms have poor experimental validation. == Evolutionary algorithms == Evolutionary algorithms form a subset of evolutionary computation in that they generally only involve techniques implementing mechanisms inspired by biological evolution such as reproduction, mutation, recombination and natural selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the cost function determines the environment within which the solutions "live" (see also fitness function). Evolution of the population then takes place after the repeated application of the above operators. In this process, there are two main forces that form the basis of evolutionary systems: Recombination (e.g. crossover) and mutation create the necessary diversity and thereby facilitate novelty, while selection acts as a force increasing quality. Many aspects of such an evolutionary process are stochastic. Changed pieces of information due to recombination and mutati

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  Sprite (computer graphics)

  In computer graphics, a sprite is a two-dimensional bitmap that is integrated into a larger scene, most often in a 2D video game. Originally, the term sprite referred to fixed-sized objects composited together, by hardware, with a background. Use of the term has since become more general. Systems with hardware sprites include arcade video games of the 1970s and 1980s; game consoles including as the Atari VCS (1977), ColecoVision (1982), Famicom (1983), Genesis/Mega Drive (1988); and home computers such as the TI-99/4 (1979), Atari 8-bit computers (1979), Commodore 64 (1982), MSX (1983), Amiga (1985), and X68000 (1987). Hardware varies in the number of sprites supported, the size and colors of each sprite, and special effects such as scaling or reporting pixel-precise overlap. Hardware composition of sprites occurs as each scan line is prepared for the video output device, such as a cathode-ray tube, without involvement of the main CPU and without the need for a full-screen frame buffer. Sprites can be positioned or altered by setting attributes used during the hardware composition process. The number of sprites which can be displayed per scan line is often lower than the total number of sprites a system supports. For example, the Texas Instruments TMS9918 chip supports 32 sprites, but only four can appear on the same scan line. The CPUs in modern computers, video game consoles, and mobile devices are fast enough that bitmaps can be drawn into a frame buffer without special hardware assistance. Beyond that, GPUs can render vast numbers of scaled, rotated, anti-aliased, partially translucent, very high resolution images in parallel with the CPU. == Etymology == According to Karl Guttag, one of two engineers for the 1979 Texas Instruments TMS9918 video display processor, this use of the word sprite came from David Ackley, a manager at TI. It was also used by Danny Hillis at Texas Instruments in the late 1970s. The term was derived from the fact that sprites "float" on top of the background image without overwriting it, much like a ghost or mythological sprite. Some hardware manufacturers used different terms, especially before sprite became common: Player/Missile Graphics was a term used by Atari, Inc. for hardware sprites in the Atari 8-bit computers (1979) and Atari 5200 console (1982). The term reflects the use for both characters ("players") and smaller associated objects ("missiles") that share the same color. The earlier Atari Video Computer System and some Atari arcade games used player, missile, and ball. Stamp was used in some arcade hardware in the early 1980s, including Ms. Pac-Man. Movable Object Block, or MOB, was used in MOS Technology's graphics chip literature. Commodore, the main user of MOS chips and the owner of MOS for most of the chip maker's lifetime, instead used the term sprite for the Commodore 64. OBJs (short for objects) is used in the developer manuals for the NES, Super NES, and Game Boy. The region of video RAM used to store sprite attributes and coordinates is called OAM (Object Attribute Memory). This also applies to the Game Boy Advance and Nintendo DS. == History == === Arcade video games === The use of sprites originated with arcade video games. Nolan Bushnell came up with the original concept when he developed the first arcade video game, Computer Space (1971). Technical limitations made it difficult to adapt the early mainframe game Spacewar! (1962), which performed an entire screen refresh for every little movement, so he came up with a solution to the problem: controlling each individual game element with a dedicated transistor. The rockets were essentially hardwired bitmaps that moved around the screen independently of the background, an important innovation for producing screen images more efficiently and providing the basis for sprite graphics. The earliest video games to represent player characters as human player sprites were arcade sports video games, beginning with Taito's TV Basketball, released in April 1974 and licensed to Midway Manufacturing for release in North America. Designed by Tomohiro Nishikado, he wanted to move beyond simple Pong-style rectangles to character graphics, by rearranging the rectangle shapes into objects that look like basketball players and basketball hoops. Ramtek released another sports video game in October 1974, Baseball, which similarly displayed human-like characters. The Namco Galaxian arcade system board, for the 1979 arcade game Galaxian, displays animated, multi-colored sprites over a scrolling background. It became the basis for Nintendo's Radar Scope and Donkey Kong arcade hardware and home consoles such as the Nintendo Entertainment System. According to Steve Golson from General Computer Corporation, the term "stamp" was used instead of "sprite" at the time. === Home systems === Signetics devised the first chips capable of generating sprite graphics (referred to as objects by Signetics) for home systems. The Signetics 2636 video processors were first used in the 1978 1292 Advanced Programmable Video System and later in the 1979 Elektor TV Games Computer. The Atari VCS, released in 1977, has a hardware sprite implementation where five graphical objects can be moved independently of the game playfield. The term sprite was not in use at the time. The VCS's sprites are called movable objects in the programming manual, further identified as two players, two missiles, and one ball. These each consist of a single row of pixels that are displayed on a scan line. To produce a two-dimensional shape, the sprite's single-row bitmap is altered by software from one scan line to the next. The 1979 Atari 400 and 800 home computers have similar, but more elaborate, circuitry capable of moving eight single-color objects per scan line: four 8-bit wide players and four 2-bit wide missiles. Each is the full height of the display—a long, thin strip. DMA from a table in memory automatically sets the graphics pattern registers for each scan line. Hardware registers control the horizontal position of each player and missile. Vertical motion is achieved by moving the bitmap data within a player or missile's strip. The feature was called player/missile graphics by Atari. Texas Instruments developed the TMS9918 chip with sprite support for its 1979 TI-99/4 home computer. An updated version is used in the 1981 TI-99/4A. === In 2.5D and 3D games === Sprites remained popular with the rise of 2.5D games (those which recreate a 3D game space from a 2D map) in the late 1980s and early 1990s. A technique called billboarding allows 2.5D games to keep onscreen sprites rotated toward the player view at all times. Some 2.5D games, such as 1993's Doom, allow the same entity to be represented by different sprites depending on its rotation relative to the viewer, furthering the illusion of 3D. Fully 3D games usually present world objects as 3D models, but sprites are supported in some 3D game engines, such as GoldSrc and Unreal, and may be billboarded or locked to fixed orientations. Sprites remain useful for small details, particle effects, and other applications where the lack of a third dimension is not a major detriment. == Systems with hardware sprites == These are base hardware specs and do not include additional programming techniques, such as using raster interrupts to repurpose sprites mid-frame.

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  Supreme Commander (video game)

  Supreme Commander (sometimes SupCom) is a 2007 real-time strategy video game designed by Chris Taylor and developed by his company, Gas Powered Games. The game is considered to be a spiritual successor, not a direct sequel, to Taylor's 1997 game Total Annihilation. First announced in the August 2005 edition of PC Gamer magazine, the game was released in Europe on February 16, 2007, and in North America on February 20. The standalone expansion Supreme Commander: Forged Alliance was released on November 6 of the same year. The sequel, Supreme Commander 2, was released in 2010. Nowadays, the original Supreme Commander is played through the community client called Forged Alliance Forever; the game has been further developed and balanced, and offers a wide variety of community mods. The gameplay of Supreme Commander focuses on using a giant bipedal mech called an Armored Command Unit (ACU), the so-called "Supreme Commander", to build a base, upgrading units to reach higher technology tiers, and conquering opponents. The player can command one of three factions: the Aeon Illuminate, the Cybran Nation, or the United Earth Federation (UEF). The expansion game added the Seraphim faction. Supreme Commander was highly anticipated in pre-release previews, and was well received by critics, with a Metacritic average of 86 out of 100. == Gameplay == Supreme Commander, like its spiritual predecessors, Total Annihilation and Spring, begins with the player solely possessing a single, irreplaceable construction unit called the "Armored Command Unit," or ACU, the titular Supreme Commander. Normally the loss of this unit results in the loss of the game (Skirmish missions can be set for a variety of victory conditions). These mech suits are designed to be transported through quantum gateways across the galaxy and contain all the materials and blueprints necessary to create an army from a planet's native resources in hours. All standard units except Commanders and summoned Support Commanders (sACU) are self-sufficient robots. All units and structures belong to one of four technology tiers, or "Tech" levels, each tier being stronger and/or more efficient than the previous. Certain lower-tier structures can be upgraded into higher ones without having to rebuild them. The first tier is available at the start of the game and consists of small, relatively weak units and structures. The second tier expands the player's abilities greatly, especially in terms of stationary weapons and shielding, and introduces upgraded versions of tier one units. The third tier level has very powerful assault units designed to overcome the fortifications of the most entrenched player. The fourth tier is a limited range of "experimental" technology. These are usually massive units which take a lot of time and energy to produce, but provide a significant tactical advantage. Supreme Commander features a varied skirmish AI. The typical Easy' and Normal modes are present, but the Hard difficulty level has four possible variants. Horde AI will swarm the player with hordes of lower level units, Tech AI will upgrade its units as fast as possible and assault the player with advanced units, the Balanced AI attempts to find a balance between the two, and the Supreme AI decides which of the three hard strategies is best for the map. The single player campaign consists of eighteen missions, six for each faction. The player is an inexperienced Commander who plays a key role in their faction's campaign to bring the "Infinite War" to an end. Despite the low number of campaign missions, each mission can potentially last hours. At the start of a mission, objectives are assigned for the player to complete. Once the player accomplishes them, the map is expanded, sometimes doubling or tripling in size, and new objectives are assigned. As the mission is commonly divided into three segments, the player will often have to overcome several enemy positions to achieve victory. === Resource management === Because humans have developed replication technology, making advanced use of rapid prototyping and nanotechnology, only two types of resources are required to wage war: Energy and Mass. Energy is obtained by constructing power generators on any solid surface (except fuel generators, which can only be built on fuel deposits), while Mass is obtained either by placing mass extractors on limited mass deposit spots (the most efficient method, although it requires map control) or by building mass fabricators to convert energy into mass. Constructor units can gather energy by "reclaiming" it from organic debris such as trees and mass from rocks and wrecked units. Each player has a certain amount of resource storage, which can be expanded by the construction of storage structures. This gives the player reserves in times of shortage or allows them to stockpile resources. If the resource generation exceeds the player's capacity, the material is wasted. On the contrary, if the storages are depleted and the demand of one of the resources exceeds the production, then all the productions speed is reduced. In addition, if an energy deficit occurs, shields will stop working. An adjacency system allows certain structures to benefit from being built directly adjacent to others. Energy-consuming structures will use less energy when built adjacent to power generators and power generators will produce more energy when built adjacent to power storage structures. The same applies to their mass-producing equivalents. Likewise, factories will consume less energy and mass when built adjacent to power generators and mass fabricators/extractors, respectively. However, by placing structures in close proximity, they become more vulnerable to collateral damage if an adjacent structure is destroyed. Furthermore, most resource generation structures can cause chain reactions when destroyed (especially Tier III structures, which produce large amounts of resources but often have large detonations that can wipe out a nearby army). === Warfare === Supreme Commander uses a "strategic zoom" system that allows the player to seamlessly zoom from a detailed close up view of an individual unit all the way out to a view of the entire map, at which point it resembles a fullscreen version of the minimap denoting individual units with icons. The camera also has a free movement mode and can be slaved to track a selected unit and there is a split screen mode which also supports multiple monitors. This system allows Supreme Commander to use vast maps up to 80 km x 80 km, with players potentially controlling a thousand units each. Units in Supreme Commander are built to scale as they would be in the real world. For example, battleships dwarf submarines. Late into the game, the larger "experimental" units, such as the Cybran Monkeylord, an enormous spider-shaped assault unit, can actually crush smaller enemy units by stepping on them. Because of the wide range of planets colonized by humanity in the setting, the theatres of war range from desert to arctic, and all battlespaces are employed. Technologies emerging in modern warfare are frequently employed in Supreme Commander. For example, stealth technology and both tactical and strategic missile and missile defense systems can be used. Supreme Commander introduced several innovations designed to reduce the amount of micromanagement inherent in many RTS games. Engineers units have the command "assist", that will help follow other engineers and help them finish their orders or improve production rate of factories. In addition, engineers with the order "patrol" will repair units, buildings and recycle wrecks in their along their patrol route. Holding the shift key causes any orders given to a unit (or group of units) to be queued. In this manner a unit may be ordered to attack several targets in succession, or to make best speed to a given point on the map and then attack towards a specified location engaging any hostiles it encounters along the way. After orders have been issued, holding the shift key causes all issued orders to be displayed on the map where they can be subsequently modified to accommodate a change of plan. Further, when a unit is ordered to attack a target, the player can issue an order to perform a coordinated attack to another unit. This order coordinates the arrival time of the units at the target automatically by adjusting the speed of the units involved. As in other RTS games, air transports can be used to convey units to specified destinations, in Supreme Commander though by shift queuing orders a transport containing several units can be ordered to drop specific units at subsequent waypoints. An air transport can also be ordered to create a ferry route, an airbridge wherein any land units ordered to the start of the ferry route will be conveyed by the air transport to the specified destination. The output from a production factory can be routed to a ferry route causing all units co

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  AI Seoul Summit 2024

  The AI Seoul Summit 2024 was an event in May 2024 co-hosted by the South Korean and British governments. The Seoul Declaration was adopted to address artificial intelligence technology and related challenges and opportunities. == Background == The AI Seoul Summit is the second such meeting following the AI Safety Summit held in the United Kingdom in November 2023. In the Bletchley Declaration, the participating countries agreed to prioritize identifying AI safety risks of shared concern, a shared concern, but at the Seoul Summit, the leaders also recognized the importance of AI. == Notable attendees == The summit was attended by the leaders of Group of Seven countries, including the United States, Canada, France, and Germany, South Korea, Singapore and Australia, representatives of the United Nations, the Organisation for Economic Co-operation and Development, and the European Union. Also in attendance were representatives of global companies such as Tesla CEO Elon Musk, Samsung Electronics Chairman Lee Jae-yong, ChatGPT maker OpenAI, Google, Microsoft, Meta, and South Korea's top portal operator Naver. == Topics == === South Korean AI safety center === "South Korea will push forward with the establishment of an AI safety research center in Korea and join a network to boost the global safety of AI." Minister of Science, Lee Jong-ho said that South Korea was planning to open an AI Safety Institute in 2024. He also expressed his intention to strengthen cooperation for the development of international standards. === Seoul Declaration for Safe, Innovative and Inclusive AI === The Seoul Declaration was adopted at the summit by leaders representing the EU, the US, the UK, Australia, Canada, Germany, France, Italy, Japan, South Korea, and Singapore. The declaration is a commitment to foster international cooperation to help develop AI governance frameworks that are interoperable between countries, partly by integrating the Hiroshima Process International Code of Conduct for Organizations Developing Advanced AI Systems. It advocates for the development of human-centric AI in collaboration with the private sector, academia, and civil society. === Seoul Ministerial Statement for advancing AI safety === At the ministerial meeting of the summit, the Seoul Ministerial Statement, a joint statement calling for the improvement of the safety, innovation, and inclusivity of AI technologies, was adopted by ministers from Australia, Canada, Chile, France, Germany, India, Indonesia, Israel, Italy, Japan, Kenya, Mexico, the Netherlands, Nigeria, New Zealand, the Philippines, South Korea, Rwanda, Saudi Arabia, Singapore, Spain, Switzerland, Turkey, Ukraine, the United Arab Emirates, the UK, and the US, as well as an EU representative. It aims to develop low-power chips as the AI industry rapidly expands and massive consumption is expected. == Global AI Summit series ==

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  AI Seoul Summit 2024

  The AI Seoul Summit 2024 was an event in May 2024 co-hosted by the South Korean and British governments. The Seoul Declaration was adopted to address artificial intelligence technology and related challenges and opportunities. == Background == The AI Seoul Summit is the second such meeting following the AI Safety Summit held in the United Kingdom in November 2023. In the Bletchley Declaration, the participating countries agreed to prioritize identifying AI safety risks of shared concern, a shared concern, but at the Seoul Summit, the leaders also recognized the importance of AI. == Notable attendees == The summit was attended by the leaders of Group of Seven countries, including the United States, Canada, France, and Germany, South Korea, Singapore and Australia, representatives of the United Nations, the Organisation for Economic Co-operation and Development, and the European Union. Also in attendance were representatives of global companies such as Tesla CEO Elon Musk, Samsung Electronics Chairman Lee Jae-yong, ChatGPT maker OpenAI, Google, Microsoft, Meta, and South Korea's top portal operator Naver. == Topics == === South Korean AI safety center === "South Korea will push forward with the establishment of an AI safety research center in Korea and join a network to boost the global safety of AI." Minister of Science, Lee Jong-ho said that South Korea was planning to open an AI Safety Institute in 2024. He also expressed his intention to strengthen cooperation for the development of international standards. === Seoul Declaration for Safe, Innovative and Inclusive AI === The Seoul Declaration was adopted at the summit by leaders representing the EU, the US, the UK, Australia, Canada, Germany, France, Italy, Japan, South Korea, and Singapore. The declaration is a commitment to foster international cooperation to help develop AI governance frameworks that are interoperable between countries, partly by integrating the Hiroshima Process International Code of Conduct for Organizations Developing Advanced AI Systems. It advocates for the development of human-centric AI in collaboration with the private sector, academia, and civil society. === Seoul Ministerial Statement for advancing AI safety === At the ministerial meeting of the summit, the Seoul Ministerial Statement, a joint statement calling for the improvement of the safety, innovation, and inclusivity of AI technologies, was adopted by ministers from Australia, Canada, Chile, France, Germany, India, Indonesia, Israel, Italy, Japan, Kenya, Mexico, the Netherlands, Nigeria, New Zealand, the Philippines, South Korea, Rwanda, Saudi Arabia, Singapore, Spain, Switzerland, Turkey, Ukraine, the United Arab Emirates, the UK, and the US, as well as an EU representative. It aims to develop low-power chips as the AI industry rapidly expands and massive consumption is expected. == Global AI Summit series ==

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  Adrozek

  Adrozek is malware that injects fake ads into online search results. Microsoft announced the malware threat on 10 December 2020, and noted that many different browsers are affected, including Google Chrome, Microsoft Edge, Mozilla Firefox and Yandex Browser. The malware was first detected in May 2020 and, at its peak in August 2020, controlled over 30,000 devices a day. But during the December 2020 announcement, Microsoft claimed "hundreds of thousands" of infected devices worldwide between May and September 2020. According to Microsoft, if not detected and blocked, Adrozek adds browser extensions, modifies a specific DLL per target browser, and changes browser settings to insert additional, unauthorized ads into web pages, often on top of legitimate ads from search engines. For each user tricked into clicking on the fake ads, the scammers earn affiliate advertising dollars. The malware has been observed to extract device data and, in some cases, steal credentials, sending them to remote servers. Users may unintentionally install the malware because of a drive-by download, by visiting a tampered website, opening an e-mail attachment, or clicking on a deceptive link or a deceptive pop-up window. The main malware program is downloaded to the “Programs Files” folder using file names such as Audiolava.exe, QuickAudio.exe, and converter.exe. According to PC Magazine, a good way to avoid, or mitigate, infection by Adrozek is to keep browser and related software programs up to date.

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  Trevor Paglen

  Trevor Paglen (born 1974) is an American artist, geographer, and author whose work covers mass surveillance and data collection. In 2016, Paglen won the Deutsche Börse Photography Foundation Prize and he has also won The Cultural Award from the German Society for Photography. In 2017, he was a recipient of a MacArthur Fellowship. On March 17, 2026, Paglen was awarded the 2026 LG Guggenheim Award (a collaboration between LG and Guggenheim New York). == Early life and education == Paglen earned a B.A. degree in religious studies in 1998 from the University of California at Berkeley, a M.F.A. degree in 2002 from the School of the Art Institute of Chicago, and a Ph.D. in Geography in 2008 from the University of California at Berkeley. While at UC Berkeley, Paglen lived in the Berkeley Student Cooperative, residing in Chateau, Fenwick, and Rochdale co-ops. == Work == Sean O'Hagan, writing in The Guardian in 2015, said that Paglen, whose "ongoing grand project [is] the murky world of global state surveillance and the ethics of drone warfare", "is one of the most conceptually adventurous political artists working today, and has collaborated with scientists and human rights activists on his always ambitious multimedia projects." His visual work such as his "Limit Telephotography" and "The Other Night Sky" series have received widespread attention for both his technical innovations and for his conceptual project that involves simultaneously making and negating documentary-style truth-claims. Paglen’s work relies on contemporary technology in two meaningful ways. Firstly, the views he photographs would be impossible to shoot without media tech, that includes the cameras, the microscopes, and even helicopters. But interestingly enough, the shots would not be possible if not for the existence of the subject. The contrasts between secrecy and revelation, evidence and abstraction distinguish Paglen's work. With that the artist presents not so much "evidence" as admonitions to awareness. He was an Eyebeam Commissioned Artist in 2007. In 2008 the Berkeley Art Museum devoted a comprehensive solo exhibition to his work. In the next year, Paglen took part in the Istanbul Biennial, and in 2010 he exhibited at the Vienna Secession. Autonomy Cube was a project by Paglen and Jacob Appelbaum that placed relays for the anonymous communication network Tor in traditional art museums. He contributed to the Oscar-winning documentary film Citizenfour (2014), directed by Laura Poitras. Paglen features in the nerd-culture documentary Traceroute (2016). Orbital Reflector was a reflective, mylar sculpture by Paglen intended to be the first "purely artistic" object in space. The temporary satellite, containing an inflatable mylar balloon with reflective surface, launched into space 3 December 2018. A mid-career survey in 2018–2019, Trevor Paglen: Sites Unseen, was a traveling exhibition shown at the Smithsonian American Art Museum in Washington DC and the Museum of Contemporary Art San Diego. In September 2020, Pace Gallery in London held an exhibition of Paglen's work, exploring "the weird, partial ways computers look back at us". His work is included in the permanent collections of the San Francisco Museum of Modern Art, the Columbus Museum of Art, and the Metropolitan Museum. === Experimental Geography === Paglen is credited with coining the term "Experimental Geography" to describe practices coupling experimental cultural production and art-making with ideas from critical human geography about the production of space, materialism, and praxis. The 2009 book Experimental Geography: Radical Approaches to Landscape, Cartography, and Urbanism is largely inspired by Paglen's work. == Publications == Paglen has published a number of books. Torture Taxi (2006) (co-authored with investigative journalist A. C. Thompson) was the first book to comprehensively describe the CIA's extraordinary rendition program. I Could Tell You But Then You Would Have to be Destroyed by Me (2007), is a look at the world of black projects through unit patches and memorabilia created for top-secret programs. Blank Spots on the Map: The Dark Geography of the Pentagon's Secret World (2009) is a broader look at secrecy in the United States. The Last Pictures (2012) is a collection of 100 images to be placed on permanent media and launched into space on EchoStar XVI, as a repository available for future civilizations (alien or human) to find. === Publications by Paglen === I Could Tell You But Then You Would Have to be Destroyed by Me. Brooklyn, NY: Melville House, 2007. ISBN 1-933633-32-8. Blank Spots on the Map: The Dark Geography of the Pentagon's Secret World. New York: Dutton, 2009. ISBN 9781101011492. Invisible: Covert Operations and Classified Landscapes, Photographs by Trevor Paglen. New York: Aperture, 2010. ISBN 9781597111300. With an essay by Rebecca Solnit. The Last Pictures. Oakland, CA: University of California, 2012. ISBN 9780520275003. Trevor Paglen. London: Phaidon, 2018. ISBN 0714873446. With essays by Laren Cornell, Julia Bryan-Wilson, Omar Kholeif. === Publications co-authored === Torture Taxi. Co-authored with A. C. Thompson. Brooklyn, NY: Melville House Publishing, 2006. ISBN 1-933633-09-3. Icon, 2007. ISBN 9781840468304. === Publications with contributions by Paglen === Experimental Geography: Radical Approaches to Landscape, Cartography, and Urbanism. Brooklyn, NY: Melville House, 2009. ISBN 978-0091636586. Edited by Nato Thompson. With essays by Paglen, Thompson, and Jeffrey Kastner. Trevor Paglen and Jacob Appelbaum – Autonomy Cube. Revolver, 2016. ISBN 978-3957633026. Essays by Luke Skrebowski and Keller Easterling on Autonomy Cube, a piece of sculpture by Paglen and Jacob Appelbaum. In English and German. == Exhibitions == Bellwether Gallery, New York, November–December 2006 The Other Night Sky, Berkeley Art Museum, 2008 A Compendium of Secrets, Cologne Still Revolution: Suspended in Time, Museum of Contemporary Canadian Art, Toronto, May–June 2009. Group exhibition with Paglen, Barbara Astman, Walead Beshty, Mat Collishaw, Stan Douglas, Idris Khan, Martha Rosler, and Mikhael Subotzky A Hidden Landscape, Aksioma, Ljubljana, Slowenia Geographies of Seeing, Lighthouse, Brighton, England, October–November 2012 The Last Pictures, New York, 2012–13 Trevor Paglen, Altman Siegel gallery, San Francisco, CA, March–May 2015 The Octopus, Frankfurter Kunstverein, Frankfurt am Main, 2015 Autonomy Cube, Edith-Russ-Haus, Oldenburg, Germany, October 2015 – January 2016. Sculpture by Paglen and Jacob Appelbaum. Deutsche Börse Photography Foundation Prize 2016, The Photographers' Gallery, London, April–July 2016. Deutsche Börse Photography Prize shortlist with Paglen, Erik Kessels, Laura El-Tantawy, and Tobias Zielony. Radical Landscapes, di Rosa, Napa, February–April 2016 L’Image volée, Americas II, Bahamas Internet Cable System (BICS-1) and Globenet, Fondazione Prada, Milan (group exhibition), 2016 A Study of Invisible Images, Metro Pictures, New York, September–October 2017 == Awards == 2014: Pioneer Award from the Electronic Frontier Foundation. 2015: The Cultural Award from the German Society for Photography (DGPh) 2015: Academy Award as cameraman and director for the documentary film Citzenfour. 2016: Deutsche Börse Photography Foundation Prize 2017: MacArthur Fellowship, John D. and Catherine T. MacArthur Foundation, Chicago, IL 2018: Nam June Paik Art Center Prize == Films about Paglen == Unseen Skies (2021) == Works ==

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  Residuated Boolean algebra

  In mathematics, a residuated Boolean algebra is a residuated lattice whose lattice structure is that of a Boolean algebra. Examples include Boolean algebras with the monoid taken to be conjunction, the set of all formal languages over a given alphabet Σ {\displaystyle \Sigma } under concatenation, the set of all binary relations on a given set X {\displaystyle X} under relational composition, and more generally the power set of any equivalence relation, again under relational composition. The original application was to relation algebras as a finitely axiomatized generalization of the binary relation example, but there exist interesting examples of residuated Boolean algebras that are not relation algebras, such as the language example. == Definition == A residuated Boolean algebra is an algebraic structure ( L , ∧ , ∨ , ¬ , 0 , 1 , ∙ , I , / , ∖ ) {\displaystyle (L,\wedge ,\vee ,\neg ,0,1,\bullet ,\mathbf {I} ,/,\backslash )} such that An equivalent signature better suited to the relation algebra application is ( L , ∧ , ∨ , ¬ , 0 , 1 , ∙ , I , ▹ , ◃ ) {\displaystyle (L,\wedge ,\vee ,\neg ,0,1,\bullet ,\mathbf {I} ,\triangleright ,\triangleleft )} where the unary operations x ∖ {\displaystyle x\backslash } and x ▹ {\displaystyle x\triangleright } are intertranslatable in the manner of De Morgan's laws via x ∖ y = ¬ ( x ▹ ¬ y ) {\displaystyle x\backslash y=\neg (x\triangleright \neg y)} , x ▹ y = ¬ ( x ∖ ¬ y ) {\displaystyle x\triangleright y=\neg (x\backslash \neg y)} , and dually / y {\displaystyle /y} and ◃ y {\displaystyle \triangleleft y} as x / y = ¬ ( ¬ x ◃ y ) {\displaystyle x/y=\neg (\neg x\triangleleft y)} , x ◃ y = ¬ ( ¬ x / y ) {\displaystyle x\triangleleft y=\neg (\neg x/y)} , with the residuation axioms in the residuated lattice article reorganized accordingly (replacing z {\displaystyle z} by ¬ z {\displaystyle \neg z} ) to read ( x ▹ z ) ∧ y = 0 ⇔ ( x ∙ y ) ∧ z = 0 ⇔ ( z ◃ y ) ∧ x = 0 {\displaystyle (x\triangleright z)\wedge y=0\ \Leftrightarrow \ (x\bullet y)\wedge z=0\ \Leftrightarrow \ (z\triangleleft y)\wedge x=0} This De Morgan dual reformulation is motivated and discussed in more detail in the section below on conjugacy. Since residuated lattices and Boolean algebras are each definable with finitely many equations, so are residuated Boolean algebras, whence they form a finitely axiomatizable variety. == Examples == Any Boolean algebra, with the monoid multiplication ∙ {\displaystyle \bullet } taken to be conjunction and both residuals taken to be material implication x → y {\displaystyle x\to y} . Of the remaining 15 binary Boolean operations that might be considered in place of conjunction for the monoid multiplication, only five meet the monotonicity requirement, namely 0 , 1 , x , y {\displaystyle 0,1,x,y} and x ∨ y {\displaystyle x\vee y} . Setting y = z = 0 {\displaystyle y=z=0} in the residuation axiom y ≤ x ∖ z ⇔ x ∙ y ≤ z {\displaystyle y\leq x\backslash z\ \Leftrightarrow \ x\bullet y\leq z} , we have 0 ≤ x ∖ 0 ⇔ x ∙ 0 ≤ 0 {\displaystyle 0\leq x\backslash 0\ \Leftrightarrow \ x\bullet 0\leq 0} , which is falsified by taking x = 1 {\displaystyle x=1} when x ∙ y = 1 {\displaystyle x\bullet y=1} , x {\displaystyle x} , or x ∨ y {\displaystyle x\vee y} . The dual argument for z / y {\displaystyle z/y} rules out x ∙ y = y {\displaystyle x\bullet y=y} . This just leaves x ∙ y = 0 {\displaystyle x\bullet y=0} (a constant binary operation independent of x {\displaystyle x} and y {\displaystyle y} ), which satisfies almost all the axioms when the residuals are both taken to be the constant operation x / y = x ∖ y = 1 {\displaystyle x/y=x\backslash y=1} . The axiom it fails is x ∙ I = x = I ∙ x {\displaystyle x\bullet \mathbf {I} =x=\mathbf {I} \bullet x} , for want of a suitable value for I {\displaystyle \mathbf {I} } . Hence conjunction is the only binary Boolean operation making the monoid multiplication that of a residuated Boolean algebra. The power set 2 X 2 {\displaystyle 2^{X^{2}}} made a Boolean algebra as usual with ∩ {\displaystyle \cap } , ∪ {\displaystyle \cup } and complement relative to X 2 {\displaystyle X^{2}} , and made a monoid with relational composition. The monoid unit I {\displaystyle \mathbf {I} } is the identity relation { ( x , x ) | x ∈ X } {\displaystyle \{(x,x)|x\in X\}} . The right residual R ∖ S {\displaystyle R\backslash S} is defined by x ( R ∖ S ) y ⇔ ∀ z ∈ X , z R x ⇒ z S y {\displaystyle x(R\backslash S)y\ \Leftrightarrow \ \forall z\in X,zRx\Rightarrow zSy} . Dually the left residual S / R {\displaystyle S/R} is defined by y ( S / R ) x ⇔ ∀ z ∈ X , x R z ⇒ y S z {\displaystyle y(S/R)x\ \Leftrightarrow \ \forall z\in X,xRz\Rightarrow ySz} . The power set 2 Σ ∗ {\displaystyle 2^{\Sigma ^{}}} made a Boolean algebra as for Example 2, but with language concatenation for the monoid. Here the set Σ {\displaystyle \Sigma } is used as an alphabet while Σ ∗ {\displaystyle \Sigma ^{}} denotes the set of all finite (including empty) words over that alphabet. The concatenation L M {\displaystyle LM} of languages L {\displaystyle L} and M {\displaystyle M} consists of all words u v {\displaystyle uv} such that u ∈ L {\displaystyle u\in L} and v ∈ M {\displaystyle v\in M} . The monoid unit is the language { ε } {\displaystyle \{\varepsilon \}} consisting of just the empty word ε {\displaystyle \varepsilon } . The right residual M ∖ L {\displaystyle M\backslash L} consists of all words w {\displaystyle w} over Σ {\displaystyle \Sigma } such that M w ⊆ L {\displaystyle Mw\subseteq L} . The left residual L / M {\displaystyle L/M} is the same with w M {\displaystyle wM} in place of M w {\displaystyle Mw} . == Conjugacy == The De Morgan duals ▹ {\displaystyle \triangleright } and ◃ {\displaystyle \triangleleft } of residuation arise as follows. Among residuated lattices, Boolean algebras are special by virtue of having a complementation operation ¬ {\displaystyle \neg } . This permits an alternative expression of the three inequalities y ≤ x ∖ z ⇔ x ∙ y ≤ z ⇔ x ≤ z / y {\displaystyle y\leq x\backslash z\ \Leftrightarrow \ x\bullet y\leq z\ \Leftrightarrow \ x\leq z/y} in the axiomatization of the two residuals in terms of disjointness, via the equivalence x ≤ y ⇔ x ∧ ¬ y = 0 {\displaystyle x\leq y\ \Leftrightarrow \ x\wedge \neg y=0} . Abbreviating x ∧ y = 0 {\displaystyle x\wedge y=0} to x # y {\displaystyle x\#y} as the expression of their disjointness, and substituting ¬ z {\displaystyle \neg z} for z {\displaystyle z} in the axioms, they become with a little Boolean manipulation ¬ ( x ∖ ¬ z ) # y ⇔ x ∙ y # z ⇔ ¬ ( ¬ z / y ) # x {\displaystyle \neg (x\backslash \neg z)\#y\ \Leftrightarrow \ x\bullet y\#z\ \Leftrightarrow \ \neg (\neg z/y)\#x} Now ¬ ( x ∖ ¬ z ) {\displaystyle \neg (x\backslash \neg z)} is reminiscent of De Morgan duality, suggesting that x ∖ {\displaystyle x\backslash } be thought of as a unary operation f {\displaystyle f} , defined by f ( y ) = x ∖ y {\displaystyle f(y)=x\backslash y} , that has a De Morgan dual ¬ f ( ¬ y ) {\displaystyle \neg f(\neg y)} , analogous to ∀ x ϕ ( x ) = ¬ ∃ x ¬ ϕ ( x ) {\displaystyle \forall x\phi (x)=\neg \exists x\neg \phi (x)} . Denoting this dual operation as x ▹ {\displaystyle x\triangleright } , we define x ▹ z {\displaystyle x\triangleright z} as ¬ x ∖ ¬ z {\displaystyle \neg x\backslash \neg z} . Similarly we define another operation z ◃ y {\displaystyle z\triangleleft y} as ¬ ( ¬ z / y ) {\displaystyle \neg (\neg z/y)} . By analogy with x ∖ {\displaystyle x\backslash } as the residual operation associated with the operation x ∙ {\displaystyle x\bullet } , we refer to x ▹ {\displaystyle x\triangleright } as the conjugate operation, or simply conjugate, of x ∙ {\displaystyle x\bullet } . Likewise ◃ y {\displaystyle \triangleleft y} is the conjugate of ∙ y {\displaystyle \bullet y} . Unlike residuals, conjugacy is an equivalence relation between operations: if f {\displaystyle f} is the conjugate of g {\displaystyle g} then g {\displaystyle g} is also the conjugate of f {\displaystyle f} , i.e. the conjugate of the conjugate of f {\displaystyle f} is f {\displaystyle f} . Another advantage of conjugacy is that it becomes unnecessary to speak of right and left conjugates, that distinction now being inherited from the difference between x ∙ {\displaystyle x\bullet } and ∙ x {\displaystyle \bullet x} , which have as their respective conjugates x ▹ {\displaystyle x\triangleright } and ◃ x {\displaystyle \triangleleft x} . (But this advantage accrues also to residuals when x ∖ {\displaystyle x\backslash } is taken to be the residual operation to x ∙ {\displaystyle x\bullet } .) All this yields (along with the Boolean algebra and monoid axioms) the following equivalent axiomatization of a residuated Boolean algebra. y # x ▹ z ⇔ x ∙ y # z ⇔ x # z ◃ y {\displaystyle y\#x\triangleright z\ \Leftrightarrow \ x\bullet y\#z\ \Leftrightarrow \ x\#z\triangleleft y} With this signature it remains the case that this axiomatization can be expressed as

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