Automated decision-making (ADM) is the use of data, machines and algorithms to make decisions in a range of contexts, including public administration, business, health, education, law, employment, transport, media and entertainment, with varying degrees of human oversight or intervention. ADM may involve large-scale data from a range of sources, such as databases, text, social media, sensors, images or speech, that is processed using various technologies including computer software, algorithms, machine learning, natural language processing, artificial intelligence, augmented intelligence and robotics. The increasing use of automated decision-making systems (ADMS) across a range of contexts presents many benefits and challenges to human society requiring consideration of the technical, legal, ethical, societal, educational, economic and health consequences. == Overview == There are different definitions of ADM based on the level of automation involved. Some definitions suggests ADM involves decisions made through purely technological means without human input, such as the EU's General Data Protection Regulation (Article 22). However, ADM technologies and applications can take many forms ranging from decision-support systems that make recommendations for human decision-makers to act on, sometimes known as augmented intelligence or 'shared decision-making', to fully automated decision-making processes that make decisions on behalf of individuals or organizations without human involvement. Models used in automated decision-making systems can be as simple as checklists and decision trees through to artificial intelligence and deep neural networks (DNN). Since the 1950s computers have gone from being able to do basic processing to having the capacity to undertake complex, ambiguous and highly skilled tasks such as image and speech recognition, gameplay, scientific and medical analysis and inferencing across multiple data sources. ADM is now being increasingly deployed across all sectors of society and many diverse domains from entertainment to transport. An ADM system (ADMS) may involve multiple decision points, data sets, and technologies (ADMT) and may sit within a larger administrative or technical system such as a criminal justice system or business process. == Data == Automated decision-making involves using data as input to be analyzed within a process, model, or algorithm or for learning and generating new models. ADM systems may use and connect a wide range of data types and sources depending on the goals and contexts of the system, for example, sensor data for self-driving cars and robotics, identity data for security systems, demographic and financial data for public administration, medical records in health, criminal records in law. This can sometimes involve vast amounts of data and computing power. === Data quality === The quality of the available data and its ability to be used in ADM systems is fundamental to the outcomes. It is often highly problematic for many reasons. Datasets are often highly variable; corporations or governments may control large-scale data, restricted for privacy or security reasons, incomplete, biased, limited in terms of time or coverage, measuring and describing terms in different ways, and many other issues. For machines to learn from data, large corpora are often required, which can be challenging to obtain or compute; however, where available, they have provided significant breakthroughs, for example, in diagnosing chest X-rays. == ADM technologies == Automated decision-making technologies (ADMT) are software-coded digital tools that automate the translation of input data to output data, contributing to the function of automated decision-making systems. There are a wide range of technologies in use across ADM applications and systems. ADMTs involving basic computational operations Search (includes 1-2-1, 1-2-many, data matching/merge) Matching (two different things) Mathematical Calculation (formula) ADMTs for assessment and grouping: User profiling Recommender systems Clustering Classification Feature learning Predictive analytics (includes forecasting) ADMTs relating to space and flows: Social network analysis (includes link prediction) Mapping Routing ADMTs for processing of complex data formats Image processing Audio processing Natural Language Processing (NLP) Other ADMT Business rules management systems Time series analysis Anomaly detection Modelling/Simulation === Machine learning === Machine learning (ML) involves training computer programs through exposure to large data sets and examples to learn from experience and solve problems. Machine learning can be used to generate and analyse data as well as make algorithmic calculations and has been applied to image and speech recognition, translations, text, data and simulations. While machine learning has been around for some time, it is becoming increasingly powerful due to recent breakthroughs in training deep neural networks (DNNs), and dramatic increases in data storage capacity and computational power with GPU coprocessors and cloud computing. Machine learning systems based on foundation models run on deep neural networks and use pattern matching to train a single huge system on large amounts of general data such as text and images. Early models tended to start from scratch for each new problem however since the early 2020s many are able to be adapted to new problems. Examples of these technologies include Open AI's DALL-E (an image creation program) and their various GPT language models, and Google's PaLM language model program. == Applications == ADM is being used to replace or augment human decision-making by both public and private-sector organisations for a range of reasons including to help increase consistency, improve efficiency, reduce costs and enable new solutions to complex problems. === Debate === Research and development are underway into uses of technology to assess argument quality, assess argumentative essays and judge debates. Potential applications of these argument technologies span education and society. Scenarios to consider, in these regards, include those involving the assessment and evaluation of conversational, mathematical, scientific, interpretive, legal, and political argumentation and debate. === Law === In legal systems around the world, algorithmic tools such as risk assessment instruments (RAI), are being used to supplement or replace the human judgment of judges, civil servants and police officers in many contexts. In the United States RAI are being used to generate scores to predict the risk of recidivism in pre-trial detention and sentencing decisions, evaluate parole for prisoners and to predict "hot spots" for future crime. These scores may result in automatic effects or may be used to inform decisions made by officials within the justice system. In Canada ADM has been used since 2014 to automate certain activities conducted by immigration officials and to support the evaluation of some immigrant and visitor applications. === Economics === Automated decision-making systems are used in certain computer programs to create buy and sell orders related to specific financial transactions and automatically submit the orders in the international markets. Computer programs can automatically generate orders based on predefined set of rules using trading strategies which are based on technical analyses, advanced statistical and mathematical computations, or inputs from other electronic sources. === Business === ==== Continuous auditing ==== Continuous auditing uses advanced analytical tools to automate auditing processes. It can be utilized in the private sector by business enterprises and in the public sector by governmental organizations and municipalities. As artificial intelligence and machine learning continue to advance, accountants and auditors may make use of increasingly sophisticated algorithms which make decisions such as those involving determining what is anomalous, whether to notify personnel, and how to prioritize those tasks assigned to personnel. === Media and entertainment === Digital media, entertainment platforms, and information services increasingly provide content to audiences via automated recommender systems based on demographic information, previous selections, collaborative filtering or content-based filtering. This includes music and video platforms, publishing, health information, product databases and search engines. Many recommender systems also provide some agency to users in accepting recommendations and incorporate data-driven algorithmic feedback loops based on the actions of the system user. Large-scale machine learning language models and image creation programs being developed by companies such as OpenAI and Google in the 2020s have restricted access however they are likely to have widespread application in fields such as advertising, copywriting, stock imagery and gra
TigerGraph
TigerGraph is a private company headquartered in Redwood City, California. It provides graph database and graph analytics software. == History == TigerGraph was founded in 2012 by programmer Yu, Ruoming, Li, Like and Mingxi, under the name GraphSQL. In September 2017, the company came out of stealth mode under the name TigerGraph with $33 million in funding. It raised an additional $32 million in funding in September 2019 and another $105 million in a series C round in February 2021. Cumulative funding as of March 2021 is $170 million. == Products == TigerGraph's hybrid transactional/analytical processing database and analytics software can scale to hundreds of terabytes of data with trillions of edges, and is used for data intensive applications such as fraud detection, customer data analysis (customer 360), IoT, artificial intelligence and machine learning. It is available using the cloud computing delivery model. The analytics uses C++ based software and a parallel processing engine to process algorithms and queries. It has its own graph query language that is similar to SQL. TigerGraph also provides a software development kit for creating graphs and visual representations. As of Mar 2024, TigerGraph version is up to version 4.2.0 TigerGraph offers free Community Edition for developers, researchers, and educators. It can be obtained from https://dl.tigergraph.com/ == Query Language == GSQL , designed by Mingxi Wu and Alin Deutsch in 2015, is a SQL-like Turing complete query language. GSQL includes additions to make it compliant with the Graph Query Language standard.
Quantum Artificial Intelligence Lab
The Quantum Artificial Intelligence Lab (also called the Quantum AI Lab or QuAIL) is a joint initiative of NASA, Universities Space Research Association, and Google (specifically, Google Research) whose goal is to pioneer research on how quantum computing might help with machine learning and other difficult computer science problems. The lab is hosted at NASA's Ames Research Center. == History == The Quantum AI Lab was announced by Google Research in a blog post on May 16, 2013. At the time of launch, the Lab was using the most advanced commercially available quantum computer, D-Wave Two from D-Wave Systems. On October 10, 2013, Google released a short film describing the current state of the Quantum AI Lab. On October 18, 2013, Google announced that it had incorporated quantum physics into Minecraft. In January 2014, Google reported results comparing the performance of the D-Wave Two in the lab with that of classical computers. The results were ambiguous and provoked heated discussion on the Internet. On 2 September 2014, it was announced that the Google Quantum AI Lab, in partnership with UC Santa Barbara, would be launching an initiative to create quantum information processors based on superconducting electronics. On the 23rd of October 2019, the Quantum AI Lab announced in a paper that it had achieved quantum supremacy with their Sycamore processor. The claim of quantum supremacy achievement has since been debated, with a far more accurate simulation on a classical computer being possible in 2.5 days as a conservative estimate. == Present == On December 9, 2024, Google introduced the Willow processor, describing it as a "state-of-the-art quantum chip". Google claims that this new chip takes just five minutes to solve a problem that takes traditional supercomputers ten septillion years. However, experts say Willow is, for now, a largely experimental device.
Pinakes
The Pinakes (Ancient Greek: Πίνακες 'tables', plural of πίναξ pinax) is a lost bibliographic work composed by Callimachus (310/305–240 BCE) that is popularly considered to be the first library catalog in the West; its contents were based upon the holdings of the Library of Alexandria during Callimachus's tenure there during the third century BCE. == History == The Library of Alexandria had been founded by Ptolemy I Soter about 306 BCE. The first recorded librarian was Zenodotus of Ephesus. During Zenodotus' tenure, Callimachus, who was never the head librarian, compiled many catalogues/lists, each called Pinakes. His most famous one listed authors and their works; thus he became the first known bibliographer and the scholar who organized the library by authors and subjects about 245 BCE. His work was 120 volumes long. Apollonius of Rhodes was the successor to Zenodotus. Eratosthenes of Cyrene succeeded Apollonius in 235 BCE and compiled his tetagmenos epi teis megaleis bibliothekeis, the 'scheme of the great bookshelves'. In 195 BCE Aristophanes of Byzantium, Eratosthenes' successor, was the librarian and updated the Pinakes, although it is also possible that his work was not a supplement of Callimachus' Pinakes themselves, but an independent polemic against, or commentary upon, their contents. == Description == The collection at the Library of Alexandria contained nearly 500,000 papyrus scrolls, which were grouped together by subject matter and stored in bins. Each bin carried a label with painted tablets hung above the stored papyri. Pinakes was named after these tablets and are a set of index lists. The bins gave bibliographical information for every roll. A typical entry started with a title and also provided the author's name, birthplace, father's name, any teachers trained under, and educational background. It contained a brief biography of the author and a list of the author's publications. The entry had the first line of the work, a summary of its contents, the name of the author, and information about the origin of the roll, as well as any doubts about the genuineness of the ascription. Callimachus' system divided works into six genres of poetry and five sections of prose: rhetoric, law, epic, tragedy, comedy, lyric poetry, history, medicine, mathematics, natural science, and miscellanies. Each category was alphabetized by author. Callimachus composed two other works that were referred as pinakes and were probably somewhat similar in format to the Pinakes (of which they "may or may not be subsections"), but were concerned with individual topics. These are listed by the Suda as: A Chronological Pinax and Description of Didaskaloi from the Beginning and Pinax of the Vocabulary and Treatises of Democritus. == Later bibliographic pinakes == The term pinax was used for bibliographic catalogs beyond Callimachus. For example, Ptolemy-el-Garib's catalog of Aristotle's writings comes to us with the title Pinax (catalog) of Aristotle's writings. == Legacy == The Pinakes proved indispensable to librarians for centuries, and they became a model for organizing knowledge throughout the Mediterranean. Their later influence can be traced to medieval times, even to the Arabic counterpart of the tenth century: Ibn al-Nadim's Al-Fihrist ("Index"). Local variations for cataloging and library classification continued through the late 19th century, when Anthony Panizzi and Melvil Dewey paved the way for more shared and standardized approaches.
Business rules engine
A business rules engine is a software system that executes one or more business rules in a runtime production environment. The rules might come from legal regulation ("An employee can be fired for any reason or no reason but not for an illegal reason"), company policy ("All customers that spend more than $100 at one time will receive a 10% discount"), or other sources. A business rule system enables these company policies and other operational decisions to be defined, tested, executed and maintained separately from application code. Rule engines typically support rules, facts, priority (score), mutual exclusion, preconditions, and other functions. Rule engine software is commonly provided as a component of a business rule management system which, among other functions, provides the ability to: register, define, classify, and manage all the rules, verify consistency of rules definitions (”Gold-level customers are eligible for free shipping when order quantity > 10” and “maximum order quantity for Silver-level customers = 15” ), define the relationships between different rules, and relate some of these rules to IT applications that are affected or need to enforce one or more of the rules. == IT use case == In any IT application, business rules can change more frequently than other parts of the application code. Rules engines or inference engines serve as pluggable software components which execute business rules that a business rules approach has externalized or separated from application code. This externalization or separation allows business users to modify the rules without the need for IT intervention. The system as a whole becomes more easily adaptable with such external business rules, but this does not preclude the usual requirements of QA and other testing. == History == An article in Computerworld traces rules engines to the early 1990s and to products from the likes of Pegasystems, Fair Isaac Corp, ILOG and eMerge from Sapiens. == Design strategies == Many organizations' rules efforts combine aspects of what is generally considered workflow design with traditional rule design. This failure to separate the two approaches can lead to problems with the ability to re-use and control both business rules and workflows. Design approaches that avoid this quandary separate the role of business rules and workflows as follows: Business rules produce knowledge; Workflows perform business work. Concretely, that means that a business rule may do things like detect that a business situation has occurred and raise a business event (typically carried via a messaging infrastructure) or create higher level business knowledge (e.g., evaluating the series of organizational, product, and regulatory-based rules concerning whether or not a loan meets underwriting criteria). On the other hand, a workflow would respond to an event that indicated something such as the overloading of a routing point by initiating a series of activities. This separation is important because the same business judgment (mortgage meets underwriting criteria) or business event (router is overloaded) can be reacted to by many different workflows. Embedding the work done in response to rule-driven knowledge creation into the rule itself greatly reduces the ability of business rules to be reused across an organization because it makes them work-flow specific. To create an architecture that employs a business rules engine it is essential to establish the integration between a BPM (Business Process Management) and a BRM (Business Rules Management) platform that is based upon processes responding to events or examining business judgments that are defined by business rules. There are some products in the marketplace that provide this integration natively. In other situations this type of abstraction and integration will have to be developed within a particular project or organization. Most Java-based rules engines provide a technical call-level interface, based on the JSR-94 application programming interface (API) standard, in order to allow for integration with different applications, and many rule engines allow for service-oriented integrations through Web-based standards such as WSDL and SOAP. Most rule engines provide the ability to develop a data abstraction that represents the business entities and relationships that rules should be written against. This business entity model can typically be populated from a variety of sources including XML, POJOs, flat files, etc. There is no standard language for writing the rules themselves. Many engines use a Java-like syntax, while some allow the definition of custom business-friendly languages. Most rules engines function as a callable library. However, it is becoming more popular for them to run as a generic process akin to the way that RDBMSs behave. Most engines treat rules as a configuration to be loaded into their process instance, although some are actually code generators for the whole rule execution instance and others allow the user to choose. == Types of rule engines == There are a number of different types of rule engines. These types (generally) differ in how Rules are scheduled for execution. Most rules engines used by businesses are forward chaining, which can be further divided into two classes: The first class processes so-called production/inference rules. These types of rules are used to represent behaviors of the type IF condition THEN action. For example, such a rule could answer the question: "Should this customer be allowed a mortgage?" by executing rules of the form "IF some-condition THEN allow-customer-a-mortgage". The other type of rule engine processes so-called reaction/Event condition action rules. The reactive rule engines detect and react to incoming events and process event patterns. For example, a reactive rule engine could be used to alert a manager when certain items are out of stock. The biggest difference between these types is that production rule engines execute when a user or application invokes them, usually in a stateless manner. A reactive rule engine reacts automatically when events occur, usually in a stateful manner. Many (and indeed most) popular commercial rule engines have both production and reaction rule capabilities, although they might emphasize one class over another. For example, most business rules engines are primarily production rules engines, whereas complex event processing rules engines emphasize reaction rules. In addition, some rules engines support backward chaining. In this case a rules engine seeks to resolve the facts to fit a particular goal. It is often referred to as being goal driven because it tries to determine if something exists based on existing information. Another kind of rule engine automatically switches between back- and forward-chaining several times during a reasoning run, e.g. the Internet Business Logic system, which can be found by searching the web. A fourth class of rules engine might be called a deterministic engine. These rules engines may forgo both forward chaining and backward chaining, and instead utilize domain-specific language approaches to better describe policy. This approach is often easier to implement and maintain, and provides performance advantages over forward or backward chaining systems. There are some circumstance where fuzzy logic based inference may be more appropriate, where heuristics are used in rule processing, rather than Boolean rules. Examples might include customer classification, missing data inference, customer value calculations, etc. The DARL language and the associated inference engine and editors is an example of this approach. == Rules engines for access control / authorization == One common use case for rules engines is standardized access control to applications. OASIS defines a rules engine architecture and standard dedicated to access control called XACML (eXtensible Access Control Markup Language). One key difference between a XACML rule engine and a business rule engine is the fact that a XACML rule engine is stateless and cannot change the state of any data. The XACML rule engine, called a Policy Decision Point (PDP), expects a binary Yes/No question e.g. "Can Alice view document D?" and returns a decision e.g. Permit / deny.
Scale space implementation
In the areas of computer vision, image analysis and signal processing, the notion of scale-space representation is used for processing measurement data at multiple scales, and specifically enhance or suppress image features over different ranges of scale (see the article on scale space). A special type of scale-space representation is provided by the Gaussian scale space, where the image data in N dimensions is subjected to smoothing by Gaussian convolution. Most of the theory for Gaussian scale space deals with continuous images, whereas one when implementing this theory will have to face the fact that most measurement data are discrete. Hence, the theoretical problem arises concerning how to discretize the continuous theory while either preserving or well approximating the desirable theoretical properties that lead to the choice of the Gaussian kernel (see the article on scale-space axioms). This article describes basic approaches for this that have been developed in the literature, see also for an in-depth treatment regarding the topic of approximating the Gaussian smoothing operation and the Gaussian derivative computations in scale-space theory, and for a complementary treatment regarding hybrid discretization methods. == Statement of the problem == The Gaussian scale-space representation of an N-dimensional continuous signal, f C ( x 1 , ⋯ , x N , t ) , {\displaystyle f_{C}\left(x_{1},\cdots ,x_{N},t\right),} is obtained by convolving fC with an N-dimensional Gaussian kernel: g N ( x 1 , ⋯ , x N , t ) . {\displaystyle g_{N}\left(x_{1},\cdots ,x_{N},t\right).} In other words: L ( x 1 , ⋯ , x N , t ) = ∫ u 1 = − ∞ ∞ ⋯ ∫ u N = − ∞ ∞ f C ( x 1 − u 1 , ⋯ , x N − u N , t ) ⋅ g N ( u 1 , ⋯ , u N , t ) d u 1 ⋯ d u N . {\displaystyle L\left(x_{1},\cdots ,x_{N},t\right)=\int _{u_{1}=-\infty }^{\infty }\cdots \int _{u_{N}=-\infty }^{\infty }f_{C}\left(x_{1}-u_{1},\cdots ,x_{N}-u_{N},t\right)\cdot g_{N}\left(u_{1},\cdots ,u_{N},t\right)\,du_{1}\cdots du_{N}.} However, for implementation, this definition is impractical, since it is continuous. When applying the scale space concept to a discrete signal fD, different approaches can be taken. This article is a brief summary of some of the most frequently used methods. == Separability == Using the separability property of the Gaussian kernel g N ( x 1 , … , x N , t ) = G ( x 1 , t ) ⋯ G ( x N , t ) {\displaystyle g_{N}\left(x_{1},\dots ,x_{N},t\right)=G\left(x_{1},t\right)\cdots G\left(x_{N},t\right)} the N-dimensional convolution operation can be decomposed into a set of separable smoothing steps with a one-dimensional Gaussian kernel G along each dimension L ( x 1 , ⋯ , x N , t ) = ∫ u 1 = − ∞ ∞ ⋯ ∫ u N = − ∞ ∞ f C ( x 1 − u 1 , ⋯ , x N − u N , t ) G ( u 1 , t ) d u 1 ⋯ G ( u N , t ) d u N , {\displaystyle L(x_{1},\cdots ,x_{N},t)=\int _{u_{1}=-\infty }^{\infty }\cdots \int _{u_{N}=-\infty }^{\infty }f_{C}(x_{1}-u_{1},\cdots ,x_{N}-u_{N},t)G(u_{1},t)\,du_{1}\cdots G(u_{N},t)\,du_{N},} where G ( x , t ) = 1 2 π t e − x 2 2 t {\displaystyle G(x,t)={\frac {1}{\sqrt {2\pi t}}}e^{-{\frac {x^{2}}{2t}}}} and the standard deviation of the Gaussian σ is related to the scale parameter t according to t = σ2. Separability will be assumed in all that follows, even when the kernel is not exactly Gaussian, since separation of the dimensions is the most practical way to implement multidimensional smoothing, especially at larger scales. Therefore, the rest of the article focuses on the one-dimensional case. == The sampled Gaussian kernel == When implementing the one-dimensional smoothing step in practice, the presumably simplest approach is to convolve the discrete signal fD with a sampled Gaussian kernel: L ( x , t ) = ∑ n = − ∞ ∞ f ( x − n ) G ( n , t ) {\displaystyle L(x,t)=\sum _{n=-\infty }^{\infty }f(x-n)\,G(n,t)} where G ( n , t ) = 1 2 π t e − n 2 2 t {\displaystyle G(n,t)={\frac {1}{\sqrt {2\pi t}}}e^{-{\frac {n^{2}}{2t}}}} (with t = σ2) which in turn is truncated at the ends to give a filter with finite impulse response L ( x , t ) = ∑ n = − M M f ( x − n ) G ( n , t ) {\displaystyle L(x,t)=\sum _{n=-M}^{M}f(x-n)\,G(n,t)} for M chosen sufficiently large (see error function) such that 2 ∫ M ∞ G ( u , t ) d u = 2 ∫ M t ∞ G ( v , 1 ) d v < ε . {\displaystyle 2\int _{M}^{\infty }G(u,t)\,du=2\int _{\frac {M}{\sqrt {t}}}^{\infty }G(v,1)\,dv<\varepsilon .} A common choice is to set M to a constant C times the standard deviation of the Gaussian kernel M = C σ + 1 = C t + 1 {\displaystyle M=C\sigma +1=C{\sqrt {t}}+1} where C is often chosen somewhere between 3 and 6. Using the sampled Gaussian kernel can, however, lead to implementation problems, in particular when computing higher-order derivatives at finer scales by applying sampled derivatives of Gaussian kernels. When accuracy and robustness are primary design criteria, alternative implementation approaches should therefore be considered. For small values of ε (10−6 to 10−8) the errors introduced by truncating the Gaussian are usually negligible. For larger values of ε, however, there are many better alternatives to a rectangular window function. For example, for a given number of points, a Hamming window, Blackman window, or Kaiser window will do less damage to the spectral and other properties of the Gaussian than a simple truncation will. Notwithstanding this, since the Gaussian kernel decreases rapidly at the tails, the main recommendation is still to use a sufficiently small value of ε such that the truncation effects are no longer important. == The discrete Gaussian kernel == A more refined approach is to convolve the original signal with the discrete Gaussian kernel T(n, t) L ( x , t ) = ∑ n = − ∞ ∞ f ( x − n ) T ( n , t ) {\displaystyle L(x,t)=\sum _{n=-\infty }^{\infty }f(x-n)\,T(n,t)} where T ( n , t ) = e − t I n ( t ) {\displaystyle T(n,t)=e^{-t}I_{n}(t)} and I n ( t ) {\displaystyle I_{n}(t)} denotes the modified Bessel functions of integer order, n. This is the discrete counterpart of the continuous Gaussian in that it is the solution to the discrete diffusion equation (discrete space, continuous time), just as the continuous Gaussian is the solution to the continuous diffusion equation. This filter can be truncated in the spatial domain as for the sampled Gaussian L ( x , t ) = ∑ n = − M M f ( x − n ) T ( n , t ) {\displaystyle L(x,t)=\sum _{n=-M}^{M}f(x-n)\,T(n,t)} or can be implemented in the Fourier domain using a closed-form expression for its discrete-time Fourier transform: T ^ ( θ , t ) = ∑ n = − ∞ ∞ T ( n , t ) e − i θ n = e t ( cos θ − 1 ) . {\displaystyle {\widehat {T}}(\theta ,t)=\sum _{n=-\infty }^{\infty }T(n,t)\,e^{-i\theta n}=e^{t(\cos \theta -1)}.} With this frequency-domain approach, the scale-space properties transfer exactly to the discrete domain, or with excellent approximation using periodic extension and a suitably long discrete Fourier transform to approximate the discrete-time Fourier transform of the signal being smoothed. Moreover, higher-order derivative approximations can be computed in a straightforward manner (and preserving scale-space properties) by applying small support central difference operators to the discrete scale space representation. As with the sampled Gaussian, a plain truncation of the infinite impulse response will in most cases be a sufficient approximation for small values of ε, while for larger values of ε it is better to use either a decomposition of the discrete Gaussian into a cascade of generalized binomial filters or alternatively to construct a finite approximate kernel by multiplying by a window function. If ε has been chosen too large such that effects of the truncation error begin to appear (for example as spurious extrema or spurious responses to higher-order derivative operators), then the options are to decrease the value of ε such that a larger finite kernel is used, with cutoff where the support is very small, or to use a tapered window. == Recursive filters == Since computational efficiency is often important, low-order recursive filters are often used for scale-space smoothing. For example, Young and van Vliet use a third-order recursive filter with one real pole and a pair of complex poles, applied forward and backward to make a sixth-order symmetric approximation to the Gaussian with low computational complexity for any smoothing scale. By relaxing a few of the axioms, Lindeberg concluded that good smoothing filters would be "normalized Pólya frequency sequences", a family of discrete kernels that includes all filters with real poles at 0 < Z < 1 and/or Z > 1, as well as with real zeros at Z < 0. For symmetry, which leads to approximate directional homogeneity, these filters must be further restricted to pairs of poles and zeros that lead to zero-phase filters. To match the transfer function curvature at zero frequency of the discrete Gaussian, which ensures an approximate semi-group property of additive t, two poles at Z = 1 + 2 t − ( 1 + 2 t ) 2 − 1 {\displaystyle
Texas Senate Bill 20
Texas Senate Bill 20 (S.B. 20), also known as the "Stopping AI-Generated Child Pornography Act", is a 2025 law in the state of Texas that creates new criminal offenses for those who possess, promote, or view visual material deemed obscene, which is said to depict a child, whether it is an actual person, animated or cartoon depiction, or an image of someone created through computer software or artificial intelligence. It was passed by the Texas Legislature on May 28, 2025, unanimously in both chambers. It was signed into law by Governor Greg Abbott on June 20, 2025. It went into effect on September 1, 2025. It was authored by Pete Flores and co-sponsored by Brent Hagenbuch, Juan Hinojosa, Joan Huffman, Phil King, and Tan Parker, as part of a package of legislation in the Texas House and Senate about A.I. and child pornography. Some supporters called it "common-sense" legislation falling within the "proper role" of government, protecting children and the "common good" within the state, with Heidi Ruiz, a police sergeant in Houston, describing the bill as "fantastic" and "fabulous." The bill drew comparisons to language, within Texas state legislation, which aimed to institute state-level book bans. Critics described the law as unconstitutional, saying it violated the Free Speech Clause of the First Amendment which prohibits abridgement of freedom of speech and the press, including the legal precedent set in Ashcroft v. Free Speech Coalition. The Comic Book Legal Defense Fund vowed to support those wrongly accused under the law. Much of the controversy regarding S.B. 20 involves the broad language pertaining to "obscene" pornographic images as including A.I.-created, animated, and cartoon depictions, with some critics arguing it could have a chilling effect on anime, manga, graphic novels, and other media produced, distributed, or created within Texas. == Provisions == S.B. 20 gives Texas police more provisions to restrict artificial intelligence-created child pornography, creating new criminal charge for possessing material depicting an underage person, under age 18, whether this child is an actual person or not. Those charged with this felony offense could go to state jail, but this could be elevated if the person charged has a prior conviction, of a $10,000 fine and two years in prison. == Reactions == === Support === Lieutenant Governor Dan Patrick applauded the unanimous passage of the law in the Texas Senate and called it "a priority" to protect children in Texas, and Texas citizens and thanked Pete Flores for his work on "this important issue". He later described the bill as part of the "bold, conservative agenda" that the Texas legislature passed during the 2025 legislative session. Phil King, one of the bill's co-sponsors, said that issue of child pornography had "infiltrated" the state's schools and said he was proud that the Texas legislature had "taken decisive action to protect our vulnerable Texans". Another co-sponsor of the legislation, Tan Parker described the law as "decisive action" to protect the children within Texas, and said he looked "forward to advancing this critical legislation" onward from the Texas Senate Criminal Justice Committee. He also described the legislation as "critical" action to protect the state's children from A.I.-generated child pornography and an "effective tool for law enforcement" to crack down on child porn perpetrators. Other supporters, such as police, and prosecutors, called the legislation an "important step" to ensure that images generated with A.I., along with deepfakes, "can't be shared with impunity" and necessary to ensure children's protection. Flores told senators that technology which enabled the production of "offensive" material by child predators had "no redeeming value whatsoever" and asserted that the materials had often been "used to groom and abuse children". John Leigh, a co-founder of Anime Matsuri, one of the largest conventions for anime within Texas, reassured those who contacted him, saying that the law is not targeted at anime and manga fans, stated that he supported the legislation, describing it as a step "in the right direction," and said that he did not believe it would "negatively impact" anime or related art in the state. Also, State Representative Dade Phelan emphasized the legislation's urgency to deal with A.I. and child pornography, adding that they need to "put some guardrails on it to where the public is being taken care of". The Texas Policy Research Foundation supported the legislation, saying that although it may lead to increased demands on state and local governmental resources, higher costs for local governments, and possible "civil liberty concerns" around online censorship, it represents a "necessary legal update" to address exploitation of children online, while "modernizing enforcement mechanisms" and recommended that lawmakers vote in favor of the law. Additionally, the group Texans for Fiscal Responsibility supported the law, arguing that it strengthened state law, upheld public safety, protected minors, and called it a "common-sense bill" protecting and promoting the "common good", children, and fell within the "proper role" of government. The Texas Public Policy Foundation also expressed their support for the law. A policy director for aforementioned conservative think tank, Zach Whiting, told the Texas Senate Committee on Criminal Justice, on March 4, 2025, that the foundation would assist legislators ans staff to "advance any and all measures to protect kids online" and shared an excerpt from of research paper about threats posed by A.I. in creating "sexually explicit deepfakes of children". === Opposition === Although the bill passed both chambers unanimously, there were some reports that the bill stalled due to opposition from Democratic lawmakers. Additionally, some individuals expressed concerns about the broad nature of the law's provisions. Anime Matsuri co-founder Deneice Leigh called for the law's wording to be clarified because "artists are anxious about displaying or selling fan art" even if the intention is "not be to penalize creators". She also described the bill as "vague and open to interpretation" as to what would be considered obscene and offensive while noting that the bill is not aiming to "target artists". Benjamin Napier, owner of Mansfield Comics and Manga in Mansfield, Texas, said that at first he felt the law was "ridiculous" and "kind of frivolous" at first, part of a "misguided puritanical onslaught", and noted that he would not cow "to the puritanical regime" if it was enacted. Kirsten Cather, an Asian Studies scholar at University of Texas, expressed concern at the law's misinterpretation because "many anime characters appear youthful, regardless of their actual age", said that the law could "stifle creative expression", and noted that the law's scope is broad enough to have manga and anime under scrutiny, a "real slippery slope here that's being breached". Marcel Green of Screen Rant said that the law's ambiguity led to concerns from manga and anime fans, and theorized that the law's application to a fan within Texas, who downloaded the 368th chapter of My Hero Academia, which has a "sexualized depiction" of an "underage high school student", would result in a criminal offense of "180 days to two years in state jail, along with a fine of up to $10,000". Green also said the law is problematic because many anime and manga characters are young, with many protagonists as minors and argued that the law could apply in limited cases, if state officials deemed an anime or manga under scrutiny as lacking "artistic value". Evan D. Mullicane, on the same site, said the vague wording of the legislation made it "dangerous" for anime such as Dragon Ball and Naruto, and could impact more than hentai, predicting it will be used against more than its "intended target" and be used to censor stories with "young LGBTQIA characters". Another critic on the same site, Carlyle Edmundson, called for anime fans to step up and prevent the law's enactment "for the good of artists and fans everywhere", saying that the legislation was "draconian" and claimed it was the most extreme case of anime and manga censorship in U.S. history. Nick Valdez of ComicBook.com said that the legislation could lead to censorship of "many anime and manga projects," like Kill la Kill and The 100 Girlfriends Who Really, Really, Really, Really, Really Love You, becoming a crime, and said that even if the law is enforced in a case-by-case basis, it could lead to a "much larger ban of materials in the state" itself due to the content of certain manga and anime. Vanessa Esguerra of The Mary Sue argued that possession of manga like Berserk and Vagabond, or viewing Dandadan, could be deemed illegal under the law, due to various parts of each of these media, and asserted that viewing and owning certain anime and other media, falling under the law's provisions,