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Multi-scale approaches

The scale space representation of a signal obtained by Gaussian smoothing satisfies a number of special properties, scale-space axioms, which make it into a special form of multi-scale representation. There are, however, also other types of "multi-scale approaches" in the areas of computer vision, image processing and signal processing, in particular the notion of wavelets. The purpose of this article is to describe a few of these approaches: == Scale-space theory for one-dimensional signals == For one-dimensional signals, there exists quite a well-developed theory for continuous and discrete kernels that guarantee that new local extrema or zero-crossings cannot be created by a convolution operation. For continuous signals, it holds that all scale-space kernels can be decomposed into the following sets of primitive smoothing kernels: the Gaussian kernel : g ( x , t ) = 1 2 π t exp ⁡ ( − x 2 / 2 t ) {\displaystyle g(x,t)={\frac {1}{\sqrt {2\pi t}}}\exp({-x^{2}/2t})} where t > 0 {\displaystyle t>0} , truncated exponential kernels (filters with one real pole in the s-plane): h ( x ) = exp ⁡ ( − a x ) {\displaystyle h(x)=\exp({-ax})} if x ≥ 0 {\displaystyle x\geq 0} and 0 otherwise where a > 0 {\displaystyle a>0} h ( x ) = exp ⁡ ( b x ) {\displaystyle h(x)=\exp({bx})} if x ≤ 0 {\displaystyle x\leq 0} and 0 otherwise where b > 0 {\displaystyle b>0} , translations, rescalings. For discrete signals, we can, up to trivial translations and rescalings, decompose any discrete scale-space kernel into the following primitive operations: the discrete Gaussian kernel T ( n , t ) = I n ( α t ) {\displaystyle T(n,t)=I_{n}(\alpha t)} where α , t > 0 {\displaystyle \alpha ,t>0} where I n {\displaystyle I_{n}} are the modified Bessel functions of integer order, generalized binomial kernels corresponding to linear smoothing of the form f o u t ( x ) = p f i n ( x ) + q f i n ( x − 1 ) {\displaystyle f_{out}(x)=pf_{in}(x)+qf_{in}(x-1)} where p , q > 0 {\displaystyle p,q>0} f o u t ( x ) = p f i n ( x ) + q f i n ( x + 1 ) {\displaystyle f_{out}(x)=pf_{in}(x)+qf_{in}(x+1)} where p , q > 0 {\displaystyle p,q>0} , first-order recursive filters corresponding to linear smoothing of the form f o u t ( x ) = f i n ( x ) + α f o u t ( x − 1 ) {\displaystyle f_{out}(x)=f_{in}(x)+\alpha f_{out}(x-1)} where α > 0 {\displaystyle \alpha >0} f o u t ( x ) = f i n ( x ) + β f o u t ( x + 1 ) {\displaystyle f_{out}(x)=f_{in}(x)+\beta f_{out}(x+1)} where β > 0 {\displaystyle \beta >0} , the one-sided Poisson kernel p ( n , t ) = e − t t n n ! {\displaystyle p(n,t)=e^{-t}{\frac {t^{n}}{n!}}} for n ≥ 0 {\displaystyle n\geq 0} where t ≥ 0 {\displaystyle t\geq 0} p ( n , t ) = e − t t − n ( − n ) ! {\displaystyle p(n,t)=e^{-t}{\frac {t^{-n}}{(-n)!}}} for n ≤ 0 {\displaystyle n\leq 0} where t ≥ 0 {\displaystyle t\geq 0} . From this classification, it is apparent that we require a continuous semi-group structure, there are only three classes of scale-space kernels with a continuous scale parameter; the Gaussian kernel which forms the scale-space of continuous signals, the discrete Gaussian kernel which forms the scale-space of discrete signals and the time-causal Poisson kernel that forms a temporal scale-space over discrete time. If we on the other hand sacrifice the continuous semi-group structure, there are more options: For discrete signals, the use of generalized binomial kernels provides a formal basis for defining the smoothing operation in a pyramid. For temporal data, the one-sided truncated exponential kernels and the first-order recursive filters provide a way to define time-causal scale-spaces that allow for efficient numerical implementation and respect causality over time without access to the future. The first-order recursive filters also provide a framework for defining recursive approximations to the Gaussian kernel that in a weaker sense preserve some of the scale-space properties.
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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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The Last Question

"The Last Question" is a science fiction short story by American writer Isaac Asimov. It first appeared in the November 1956 issue of Science Fiction Quarterly; and in the anthologies in the collections Nine Tomorrows (1959), The Best of Isaac Asimov (1973), Robot Dreams (1986), The Best Science Fiction of Isaac Asimov (1986), the retrospective Opus 100 (1969), and Isaac Asimov: The Complete Stories, Vol. 1 (1990). While he also considered it one of his best works, "The Last Question" was Asimov's favorite short story of his own authorship, and is one of a loosely connected series of stories concerning a fictional computer called Multivac. Through successive generations, humanity questions Multivac on the subject of entropy. The story blends science fiction, theology, and philosophy. It has been recognized as a counterpoint to Fredric Brown's short short story "Answer", published two years earlier. == History == In conceiving Multivac, Asimov was extrapolating the trend towards centralization that characterized computation technology planning in the 1950s to an ultimate centrally managed global computer. After seeing a planetarium adaptation of his work, Asimov "privately" concluded that the story was his best science fiction yet written. He placed it just higher than "The Ugly Little Boy" (September 1958) and "The Bicentennial Man" (1976). The story asks the question of humanity's fate, and human existence as a whole, highlighting Asimov's focus on important aspects of our future like population growth and environmental issues. "The Last Question" ranks with "Nightfall" (1941) as one of Asimov's best-known and most acclaimed short stories. He wrote in 1973 that he appreciated how easy the story was to write after he had the idea. He was so often approached by fans who remembered the story but not the title, that in one instance he gave the answer, correctly, before the fan had even described the story. == Plot summary == By the year 2061, Multivac, a self-adjusting and self-correcting computer, has allowed mankind to reach beyond the planetary confines of Earth and harness solar energy. Two technicians, Adell and Lupov, celebrate Multivac's role in this development. Over drinks, they discuss that the sun will expire due to the second law of thermodynamics, which states that entropy inevitably increases. When Adell asks Multivac whether this can be reversed, the computer responds that it has insufficient data to answer. In several episodes over ten trillion years, increasingly advanced humans pose the same question to the computers of their time. Each time the computer gives the same response. At the heat death of the universe, the last disembodied consciousness of Man asks the question a final time of a computer that resides in hyperspace before merging with it. After collecting the last data from the dead universe, the computer continues to process it alone and finds an answer to the last question. Having no one to tell it to, it proceeds to demonstrate by saying "LET THERE BE LIGHT!" == Themes == === Philosophy === Although science and religion are frequently presented as having an oppositional relationship, "The Last Question" explores some biblical contexts ("Let there be light"). In Asimov's story, aspects like the great meaning of existence are culminated through both technology and human knowledge. The evolution from Multivac to AC also emulates a sort of cycle of existence. === Dystopian happy ending === Multivac's purpose was conceptualized with a desire for knowledge, promoting the idea that more knowledge will lead to a better and more fruitful future for humanity. However, the computer's answers regarding the future suggest an inevitable exhaustion of the Sun, and this thirst for knowledge becomes an obsession with the future. The story's end displays a dichotomy between annihilation and peace. == Dramatic adaptations == === Planetarium shows === "The Last Question" was first adapted for the Abrams Planetarium at Michigan State University (in 1966), featuring the voice of Leonard Nimoy, as Asimov wrote in his autobiography In Joy Still Felt (1980). It was adapted for the Strasenburgh Planetarium in Rochester, New York (in 1969), under the direction of Ian C. McLennan. It was adapted for the Edmonton Space Sciences Centre in Edmonton, Alberta (early 1970s), under the direction of John Hault. It was adapted for the Gates Planetarium at the Denver Museum of Natural History in 1973 under the direction of Mark B. Peterson It subsequently played at the: Fels Planetarium of the Franklin Institute in Philadelphia in 1973 Planetarium of the Reading School District in Reading, Pennsylvania in 1974 Buhl Planetarium, Pittsburgh in 1974 The Space Transit Planetarium of the Museum of Science in Miami during 1977 Vanderbilt Planetarium in Centerport New York, in 1978, read by singer-songwriter and Long Island resident Harry Chapin. Hansen Planetarium in Salt Lake City, Utah (in 1980 and 1989) A reading of the story was played on BBC Radio 7 in 2008 and 2009. Gates Planetarium in Denver, Colorado (in early 2020) In 1989 Asimov updated the star show adaptation to add in quasars and black holes. The story was adapted as a comic book by Don Thompson and drawn by John Estes in the third issue of ORBiT.
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Model Context Protocol

The Model Context Protocol (MCP) is an open standard and open-source framework introduced by Anthropic in November 2024 to standardize the way artificial intelligence (AI) systems like large language models (LLMs) integrate and share data with external tools, systems, and data sources. MCP provides a standardized interface for reading files, executing functions, and handling contextual prompts. Following its announcement, the protocol was adopted by major AI providers, including OpenAI and Google DeepMind. == Background == MCP was announced by Anthropic in November 2024 as an open standard for connecting AI assistants to data systems such as content repositories, business management tools, and development environments. The protocol was created at Anthropic by engineers David Soria Parra and Justin Spahr-Summers. It aims to address the challenge of information silos and legacy systems. Before MCP, developers often had to build custom connectors for each data source or tool, resulting in what Anthropic described as an "N×M" data integration problem. Earlier stop-gap approaches—such as OpenAI's 2023 "function-calling" API and the ChatGPT plug-in framework—solved similar problems but required vendor-specific connectors. MCP re-uses the message-flow ideas of the Language Server Protocol (LSP) and is transported over JSON-RPC 2.0. In December 2025, Anthropic donated the MCP to the Agentic AI Foundation (AAIF), a directed fund under the Linux Foundation, co-founded by Anthropic, Block and OpenAI, with support from other companies. == Features == The protocol was released with software development kits (SDKs) in programming languages including Python, TypeScript, C# and Java. Anthropic maintains an open-source repository of reference MCP server implementations and SDKs. MCP defines a standardized framework for integrating AI systems with external data sources and tools. It includes specifications for data ingestion and transformation, contextual metadata tagging, and AI interoperability across different platforms. The protocol also supports bidirectional connections between data sources and AI tools. MCP enables applications such as querying structured databases with plain language in the field of natural language data access. The protocol is used in AI-assisted software development tools. Integrated development environments (IDEs), coding platforms such as Replit, and code intelligence tools like Sourcegraph have adopted MCP to grant AI coding assistants real-time access to project context. MCP Apps is an official extension to the Model Context Protocol built on mcp-ui. While the base MCP specification is restricted to text and structured data, MCP Apps standardizes the delivery of interactive user interfaces—such as dashboards, forms, and data visualizations—from MCP servers to host applications like Claude and ChatGPT. == Adoption == In March 2025, OpenAI officially adopted the MCP, after having integrated the standard across its products, including the ChatGPT desktop app. In September 2025, OpenAI added support for MCP to ChatGPT apps. This allows for third-party access inside ChatGPT. MCP can be integrated with Microsoft Semantic Kernel, and Azure OpenAI. MCP servers can be deployed to Cloudflare. In April 2026, the AAIF held the MCP Dev Summit North America in New York City, drawing approximately 1,200 attendees. == Reception == The Verge reported that MCP addresses a growing demand for AI agents that are contextually aware and capable of pulling from diverse sources. In April 2025, security researchers released an analysis that concluded there are multiple outstanding security issues with MCP, including prompt injection, tool permissions that allow for combining tools to exfiltrate data, and lookalike tools that can silently replace trusted ones. MCP has been likened to OpenAPI, a similar specification that aims to describe APIs.
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Graphical Kernel System

The Graphical Kernel System (GKS) is a 2D computer graphics system using vector graphics, introduced in 1977. It was suitable for making line and bar charts and similar tasks. A key concept was cross-system portability, based on an underlying coordinate system that could be represented on almost any hardware. GKS is best known as the basis for the graphics in the GEM GUI system used on the Atari ST and as part of Ventura Publisher. A draft international standard was circulated for review in September 1983. Final ratification of the standard was achieved in 1985, making it the first ISO graphics standard. A 3D system modelled on GKS was introduced as PHIGS, which saw some use in the 1980s and early 1990s. == Overview == GKS provides a set of drawing features for two-dimensional vector graphics suitable for charting and similar duties. The calls are designed to be portable across different programming languages, graphics devices and hardware, so that applications written to use GKS will be readily portable to many platforms and devices. GKS was fairly common on computer workstations in the 1980s and early 1990s. GKS formed the basis of Digital Research's GSX which evolved into VDI, one of the core components of GEM. GEM was the native GUI on the Atari ST and was occasionally seen on PCs, particularly in conjunction with Ventura Publisher. GKS was little used commercially outside these markets, but remains in use in some scientific visualization packages. It is also the underlying API defining the Computer Graphics Metafile. One popular application based on an implementation of GKS is the GR Framework, a C library for high-performance scientific visualization that has become a common plotting backend among Julia users. A main developer and promoter of the GKS was José Luis Encarnação, formerly director of the Fraunhofer Institute for Computer Graphics (IGD) in Darmstadt, Germany. GKS has been standardized in the following documents: ANSI standard ANSI X3.124 of 1985. ISO 7942:1985 standard, revised as ISO 7942:1985/Amd 1:1991 and ISO/IEC 7942-1:1994, as well as ISO/IEC 7942-2:1997, ISO/IEC 7942-3:1999 and ISO/IEC 7942-4:1998 The language bindings are ISO standard ISO 8651. GKS-3D (Graphical Kernel System for Three Dimensions) functional definition is ISO standard ISO 8805, and the corresponding C bindings are ISO/IEC 8806. The functionality of GKS is wrapped up as a data model standard in the STEP standard, section ISO 10303-46.
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Belief–desire–intention software model

The belief–desire–intention software model (BDI) is a software model developed for programming intelligent agents. Superficially characterized by the implementation of an agent's beliefs, desires and intentions, it actually uses these concepts to solve a particular problem in agent programming. In essence, it provides a mechanism for separating the activity of selecting a plan (from a plan library or an external planner application) from the execution of currently active plans. Consequently, BDI agents are able to balance the time spent on deliberating about plans (choosing what to do) and executing those plans (doing it). A third activity, creating the plans in the first place (planning), is not within the scope of the model, and is left to the system designer and programmer. == Overview == In order to achieve this separation, the BDI software model implements the principal aspects of Michael Bratman's theory of human practical reasoning (also referred to as Belief-Desire-Intention, or BDI). That is to say, it implements the notions of belief, desire and (in particular) intention, in a manner inspired by Bratman. For Bratman, desire and intention are both pro-attitudes (mental attitudes concerned with action). He identifies commitment as the distinguishing factor between desire and intention, noting that it leads to (1) temporal persistence in plans and (2) further plans being made on the basis of those to which it is already committed. The BDI software model partially addresses these issues. Temporal persistence, in the sense of explicit reference to time, is not explored. The hierarchical nature of plans is more easily implemented: a plan consists of a number of steps, some of which may invoke other plans. The hierarchical definition of plans itself implies a kind of temporal persistence, since the overarching plan remains in effect while subsidiary plans are being executed. An important aspect of the BDI software model (in terms of its research relevance) is the existence of logical models through which it is possible to define and reason about BDI agents. Research in this area has led, for example, to the axiomatization of some BDI implementations, as well as to formal logical descriptions such as Anand Rao and Michael Georgeff's BDICTL. The latter combines a multiple-modal logic (with modalities representing beliefs, desires and intentions) with the temporal logic CTL. More recently, Michael Wooldridge has extended BDICTL to define LORA (the Logic Of Rational Agents), by incorporating an action logic. In principle, LORA allows reasoning not only about individual agents, but also about communication and other interaction in a multi-agent system. The BDI software model is closely associated with intelligent agents, but does not, of itself, ensure all the characteristics associated with such agents. For example, it allows agents to have private beliefs, but does not force them to be private. It also has nothing to say about agent communication. Ultimately, the BDI software model is an attempt to solve a problem that has more to do with plans and planning (the choice and execution thereof) than it has to do with the programming of intelligent agents. This approach has recently been proposed by Steven Umbrello and Roman Yampolskiy as a means of designing autonomous vehicles for human values. == BDI agents == A BDI agent is a particular type of bounded rational software agent, imbued with particular mental attitudes, viz: Beliefs, Desires and Intentions (BDI). === Architecture === This section defines the idealized architectural components of a BDI system. Beliefs: Beliefs represent the informational state of the agent–its beliefs about the world (including itself and other agents). Beliefs can also include inference rules, allowing forward chaining to lead to new beliefs. Using the term belief rather than knowledge recognizes that what an agent believes may not necessarily be true (and in fact may change in the future). Beliefset: Beliefs are stored in database (sometimes called a belief base or a belief set), although that is an implementation decision. Desires: Desires represent the motivational state of the agent. They represent objectives or situations that the agent would like to accomplish or bring about. Examples of desires might be: find the best price, go to the party or become rich. Goals: A goal is a desire that has been adopted for active pursuit by the agent. Usage of the term goals adds the further restriction that the set of active desires must be consistent. For example, one should not have concurrent goals to go to a party and to stay at home – even though they could both be desirable. Intentions: Intentions represent the deliberative state of the agent – what the agent has chosen to do. Intentions are desires to which the agent has to some extent committed. In implemented systems, this means the agent has begun executing a plan. Plans: Plans are sequences of actions (recipes or knowledge areas) that an agent can perform to achieve one or more of its intentions. Plans may include other plans: my plan to go for a drive may include a plan to find my car keys. This reflects that in Bratman's model, plans are initially only partially conceived, with details being filled in as they progress. Events: These are triggers for reactive activity by the agent. An event may update beliefs, trigger plans or modify goals. Events may be generated externally and received by sensors or integrated systems. Additionally, events may be generated internally to trigger decoupled updates or plans of activity. BDI was also extended with an obligations component, giving rise to the BOID agent architecture to incorporate obligations, norms and commitments of agents that act within a social environment. === BDI interpreter === This section defines an idealized BDI interpreter that provides the basis of SRI's PRS lineage of BDI systems: initialize-state repeat options: option-generator (event-queue) selected-options: deliberate(options) update-intentions(selected-options) execute() get-new-external-events() drop-unsuccessful-attitudes() drop-impossible-attitudes() end repeat === Limitations and criticisms === The BDI software model is one example of a reasoning architecture for a single rational agent, and one concern in a broader multi-agent system. This section bounds the scope of concerns for the BDI software model, highlighting known limitations of the architecture. Learning: BDI agents lack any specific mechanisms within the architecture to learn from past behavior and adapt to new situations. Three attitudes: Classical decision theorists and planning research questions the necessity of having all three attitudes, distributed AI research questions whether the three attitudes are sufficient. Logics: The multi-modal logics that underlie BDI (that do not have complete axiomatizations and are not efficiently computable) have little relevance in practice. Multiple agents: In addition to not explicitly supporting learning, the framework may not be appropriate to learning behavior. Further, the BDI model does not explicitly describe mechanisms for interaction with other agents and integration into a multi-agent system. Explicit goals: Most BDI implementations do not have an explicit representation of goals. Lookahead: The architecture does not have (by design) any lookahead deliberation or forward planning. This may not be desirable because adopted plans may use up limited resources, actions may not be reversible, task execution may take longer than forward planning, and actions may have undesirable side effects if unsuccessful. == BDI agent implementations == === 'Pure' BDI === Procedural Reasoning System (PRS) IRMA (not implemented but can be considered as PRS with non-reconsideration) UM-PRS OpenPRS Distributed Multi-Agent Reasoning System (dMARS) AgentSpeak(L) – see Jason below AgentSpeak(RT) Agent Real-Time System (ARTS) (ARTS) JAM JACK Intelligent Agents JADEX (open source project) JaKtA JASON GORITE SPARK 3APL 2APL GOAL agent programming language CogniTAO (Think-As-One) Living Systems Process Suite PROFETA Gwendolen (Part of the Model Checking Agent Programming Languages Framework) === Extensions and hybrid systems === JACK Teams CogniTAO (Think-As-One) Living Systems Process Suite Brahms JaCaMo
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A Very Fatal Murder

A Very Fatal Murder is a podcast produced by the satirical publication The Onion. A parody of true crime podcasts, A Very Fatal Murder is hosted by fictional New York City reporter David Pascall, who travels to the small town Bluff Springs, Nebraska to investigate the murder of prom queen Hayley Price. Pascall is voiced by David Sidorov, who also wrote for the podcast. The podcast premiered on January 23, 2018, and consists of 7 episodes. Season 2 was released in its entirety on May 11, 2019. == Production == A Very Fatal Murder satirizes popular true crime podcasts such as Serial, S-Town, and My Favorite Murder. According to head writer Katy Yeiser, the podcast is not meant as a take down of any particular podcast, but rather an ode to the genre. == Synopsis == The podcast follows fictional investigative reporter David Pascall (voiced by David Sidorov) who is searching for the perfect murder to create an award-winning podcast about. He is assisted by ETHL (the Extremely Timely Homicide Locator), an MIT-created computer programmed to find "the most interesting, violent, culturally relevant murder cases in America". == Episodes == === Season 1 === === Season 2 === == Reception == The podcast received mostly positive reviews, and was largely praised for attacking true-crime tropes such as the "hot dead girl" and the romanticization of small-town America. === Awards ===
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Evolutionary acquisition of neural topologies

Evolutionary acquisition of neural topologies (EANT/EANT2) is an evolutionary reinforcement learning method that evolves both the topology and weights of artificial neural networks. It is closely related to the works of Angeline et al. and Stanley and Miikkulainen. Like the work of Angeline et al., the method uses a type of parametric mutation that comes from evolution strategies and evolutionary programming (now using the most advanced form of the evolution strategies CMA-ES in EANT2), in which adaptive step sizes are used for optimizing the weights of the neural networks. Similar to the work of Stanley (NEAT), the method starts with minimal structures which gain complexity along the evolution path. == Contribution of EANT to neuroevolution == Despite sharing these two properties, the method has the following important features which distinguish it from previous works in neuroevolution. It introduces a genetic encoding called common genetic encoding (CGE) that handles both direct and indirect encoding of neural networks within the same theoretical framework. The encoding has important properties that makes it suitable for evolving neural networks: It is complete in that it is able to represent all types of valid phenotype networks. It is closed, i.e. every valid genotype represents a valid phenotype. (Similarly, the encoding is closed under genetic operators such as structural mutation and crossover.) These properties have been formally proven. For evolving the structure and weights of neural networks, an evolutionary process is used, where the exploration of structures is executed at a larger timescale (structural exploration), and the exploitation of existing structures is done at a smaller timescale (structural exploitation). In the structural exploration phase, new neural structures are developed by gradually adding new structures to an initially minimal network that is used as a starting point. In the structural exploitation phase, the weights of the currently available structures are optimized using an evolution strategy. == Performance == EANT has been tested on some benchmark problems such as the double-pole balancing problem, and the RoboCup keepaway benchmark. In all the tests, EANT was found to perform very well. Moreover, a newer version of EANT, called EANT2, was tested on a visual servoing task and found to outperform NEAT and the traditional iterative Gauss–Newton method. Further experiments include results on a classification problem.
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Class activation mapping

Class activation mapping methods are explainable AI (XAI) techniques used to visualize the regions of an input image that are the most relevant for a particular task, especially image classification, in convolutional neural networks (CNNs). These methods generate heatmaps by weighting the feature maps from a convolutional layer according to their relevance to the target class. In the field of artificial intelligence, generically defined as "the effort to automate intellectual tasks normally performed by humans", machine learning and deep learning were created. They both use statistical and computational methods to learn patterns from data, reducing the need for manually coded rules. Machine learning models are trained on input data and the known respective answers, learning the underlying patterns or structures present in the data. Traditional Machine learning algorithms employ manually designed feature sets, posing a direct link between machine learning designers and employed features. Deep learning is a subfield of machine learning, based on the concept of successive layers of representation, in which the data is progressively unfolded in different ways, to extract relevant and informative patterns in data analysis. Deep learning algorithms are defined as feature learning algorithms automatically learning hierarchical feature representations from raw data, extracting increasingly abstract features through multiple layers. CNNs are a specific architecture of deep learning models, designed to process spatially structured data, such as images, exploiting a series of convolution, non-linear activation and pooling operations to extract relevant features, contained in the so-called feature maps from input data. CNNs have demonstrated to be highly effective in a variety of computer vision and image processing tasks. CNNs (and deep learning models more broadly) are described as black boxes due to their complex and non-transparent internal layers of representation. The need for clearer indications on its internal working and decision-making process gave birth to XAI techniques. Among the proposed XAI techniques for computer vision tasks, Class activation mapping methods can show which pixels in an input image are important to the predicted logit for a class of interest, in a classification task. Class activation mapping methods were originally developed for class-discriminative scenarios to visualize which parts of the input image influenced the classification decision, namely to visually highlight the regions of those feature maps that contribute most strongly to the prediction of a given class. More advanced versions of these methods are not limited to image classification tasks, but have been extended also to several vision-related tasks, such as object detection, image captioning, visual question answering and image segmentation. == Background == The following methods laid the groundwork for the class activation maps approaches, forming the conceptual basis of using gradients to highlight class-discriminative regions. === Class model visualization and saliency maps for convolutional neural networks === The class model visualization and image-specific saliency maps approaches have been presented in the foundational work "Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps" by Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman and it generalizes the deconvnet method by Zeiler and Fergus. Class model visualization synthesizes an artificial input image that strongly activates the output neurons associated with a target class. Given a trained, fixed model, this method starts with a zero-initialized image, backpropagates the gradients from the class score to the image pixels, updates the image pixels increasing the specific class scores and it repeats the pixel updating process, showing an encoded (idealized version) prototype of the class of interest. Image-specific class saliency visualization method provides a visual explanation by highlighting the most relevant pixels in an image for predicting a certain class C of interest. This is done by computing the gradient of the class score with respect to the input image, I 0 , {\displaystyle I_{0},} w = ∂ S C ∂ I | I 0 {\displaystyle w=\left.{\frac {\partial S_{C}}{\partial I}}\right|_{I_{0}}} approximating the model locally (around I 0 {\displaystyle I_{0}} ) as linear, using a first-order Taylor expansion: S C ( I ) ≈ w C T I + b {\displaystyle S_{C}(I)\approx w_{C}^{T}I+b} . The magnitude of w C {\displaystyle w_{C}} , the gradient, indicates the importancy of the pixels: larger gradients suggest greater influence on the prediction. Once the gradient is known, the saliency map is defined as the maximum absolute gradient across the color channels: M i j = m a x C | ∂ S C ∂ I i j C | {\displaystyle M_{ij}=max_{C}\left|{\frac {\partial S_{C}}{\partial I_{ij}^{C}}}\right|} resulting in an saliency map (i.e. heatmap). === Guided backpropagation === The concept of guided backpropagation can be traced for the first time in the paper by Springenberg et al. "Striving For Simplicity: The All Convolutional Net" and also this method builds upon the work by Zeiler and Fergus "Visualizing and Understanding Convolutional Networks". Guided backpropagation core is to understand what a CNN is learning, by visualizing the patterns that activate more strongly individual neurons (or filters), in architectures which do not rely on max-pooling layer. When propagating gradients back through a rectified linear unit (ReLU), guided backpropagation passes the gradient if and only if the input to the ReLU was positive (forward pass) and the output gradient is positive (backward signal), tackling both inactive neurons, negative gradients and suppressing the noise. The result displays sharper, high-resolution visualizations of what each neuron is responding to. Guided backpropagation represents a simple and practical method for model interpretability, helping understand how and where neural networks detect semantic concepts across layers. Moreover, it can be applied to any network architecture, due to its working principle. == Base versions == Class activation mapping and gradient-weighted class activation mapping are the original and most widely used methods for visual explanations in convolutional neural networks. These methods serve as the foundation for many later developments in explainable AI. Notation: In this article, the symbols i and j represent integer indices that disappear inside sums or averages, while x and y are the continuous (or up-sampled integer) coordinates of the final heat-map that is plotted. === Class activation mapping (CAM) === Class activation mapping (CAM) was the first, and the original, version of CAM methods, and it gave the name to the whole category. The approach was firstly introduced by Zhou et al. in their seminal work "Learning Deep Features for Discriminative Localization". This approach achieves class-specific heatmaps by modifying image classification CNN architectures, replacing fully-connected layers with convolutional layers and a final global average pooling layer. Its main scope is to localize and highlight discriminative regions of an input image that a CNN uses to identify a particular class, without needing explicit bounding box annotations. ==== Global average pooling (GAP) ==== Global average pooling (GAP) represents the key element in the original CAM approach. It is a dimensionality reduction technique and, similarly to other pooling layers, it allows the downsampling of the feature maps, calculating representative values for a specific region of the feature map. The particularity of GAP is that it calculates a single value for an entire feature map, significantly reducing the model dimensions. ==== Mathematical description ==== The mathematical description considers as its key the combination of convolutional and GAP layers. In CAM, it is mandatory to have the GAP layer after the last convolutional layer and before the final linear classifier layer. This last element of the architecture connects the output logits (the network predictions) y C {\displaystyle y^{C}} , to the GAP values, with its respective fine-tuned weights, w k C {\displaystyle w_{k}^{C}} . Considering A k {\displaystyle A^{k}} as the last feature maps of the last convolutional layer, GAP produces one value for each feature map, by averaging all the matrix elements (i, j) of the feature map: F k = 1 m n ∑ i = 1 m ∑ j = 1 n A i j k {\displaystyle F^{k}={\frac {1}{mn}}\sum _{i=1}^{m}\sum _{j=1}^{n}A_{ij}^{k}} with A k = [ A 11 k A 12 k ⋯ A 1 n k A 21 k A 22 k ⋯ A 2 n k ⋮ ⋮ ⋱ ⋮ A m 1 k A m 2 k ⋯ A m n k ] = { A i j k ∣ 1 ≤ i ≤ m , 1 ≤ j ≤ n } {\displaystyle A^{k}={\begin{bmatrix}A_{11}^{k}&A_{12}^{k}&\cdots &A_{1n}^{k}\\A_{21}^{k}&A_{22}^{k}&\cdots &A_{2n}^{k}\\\vdots &\vdots &\ddots &\vdots \\A_{m1}^{k}&A_{m2}^{k}&\cdots &A_{mn}^{k}\end{bmatrix}}=\left\{A_{
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Neuroshima

Neuroshima is a Polish tabletop roleplaying system inspired by such films and games as Mad Max, Fallout, The Matrix, Terminator and Deadlands: Hell on Earth. It is currently available only in Polish. The game's motto is "never trust the machines". Its designers include Michal Oracz and Ignacy Trzewiczek. == Setting == The game describes the United States in the mid-21st century, after a nuclear war started by a cybernetic revolt, which molded the continent into a barren wasteland. It seems that the reason for the war to break out was a sentient Artificial Intelligence commonly referred to as Moloch and made up of interconnected net of military computers: automated factories, military facilities, power plants and alike, that now cover the whole north of the U.S., from Oregon to the Great Lakes. On the south, there is another creation, called the Neojungle, that poses a threat to those who survived the war. It is a semi-intelligent carnivorous vegetation that grows very quickly, advancing north from Latin America. Right in the middle, there are humans. They are surrounded by mutant creatures, some bred by Moloch and hostile towards humans, and some simply animals and humans misshapen by nuclear fallout. On top of that there are Moloch's deadly machines lurking to complete the picture. But what is stressed in the book is that the worst enemy of humans is within them: hatred, indifference, greed. === Landscapes of Neuroshima === Car wrecks, ruined towns and villages, collapsed roofs on deserted houses, broken glass in the windows of abandoned gas stations fill the landscape of the United States of the middle of the 21st century. Technology is history - cars will not start, radios are jammed, no electricity whatsoever almost everywhere the characters go. Shops and malls are looted, prosperous villages are burned by gangers, and safe places are very sparse. === People in Neuroshima === No one knows how many people survived the war with machines, but it is estimated that their number oscillates around 2-3 million. Some people reverted to nomadic lifestyles and live in the deserts, some of them try to build the civilisation anew in devastated cities, some of them form gangs of highwaymen (called gangers), some of them just try to make a living by growing crops, and finally, there are those who just wander around the wasteland; the adventuring sort here is mostly represented by player characters. Each village they visit in this world is a discrete microcosm and nothing is certain as whether the inhabitants are welcoming or shoot strangers on sight. The continent is full of small, anonymous settlements, but there are places which aspire to become post-nuclear states. === Places in Neuroshima === In this world it is very important where you come from, and that is because people are prejudiced and afraid of strangers. Different places produce different kinds of people, and who you are is determined by where you are from. Examples: The Southern Hegemony - (commonly referred to as 'the Hegemony') - located in what was once Arizona, New Mexico and partially Texas. A place where brute force determines one's place in the society. Dominated by gangs and unhampered by Moloch, the Hegemony is a threat to neighbouring lands. Vegas - the only well-lit city in the post-apocalyptic world. Home to many playhouses and casinos, it attracts people from every part of the country. Mother Desert - if you were born in the desert, whenever you go away from civilisation, you feel at home. Many Native Americans still live out there and are doing fine - after all the warheads did not hit the deserts. Detroit - known for some of the best drivers and racers in the post-nuclear US. Home of many gangs, such as The Shultz (mafia styled), Hurons (punkers), The League (racers), Parker Lots (gothic assassins) and the Gas Drinkers (mutant barbarians). New York - a place which has established a strong government and would like to rebuild America. They maintain schools, factories and railways and send soldiers to fight Moloch. Surprisingly enough, they sometimes succeed. Texas - the healthiest place in America. Actually, the only place where one can find green vegetation. Modern Texans still grow crops, breed horses and herd cattle, like their ancestors in the 19th century did. The Appalachian Federation - a place ruled by feudal lords. They have a social class system, in which people are divided into nobility and peasantry. Thanks to its iron and coal deposits, it's one of the richest places in the post-nuclear U.S. The Outpost - A mobile settlement run by scientists who aim to destroy Moloch. In coalition with New York, they manage an army, which is yet to stop Moloch's advance south. They steal technology from the machines they destroy and apply it to their own advantage. == System == The game uses its own, custom system of rules. The dice you use is d20. This system does not have an official name, but it is unconnected to the d20 system, as it typically uses three twenty-sided dice. === Four colours === Neuroshima relies on the division of the gameplay into something the authors called Four Colours, namely steel, chrome, rust and mercury. The choice of a particular colour is made by the gamemaster (the decision can be consulted with the players in order to enhance the game experience) and determines the mood, atmosphere and the type of events/characters present in the story. The name of the colour itself implies the kind of gameplay it will symbolise. These colours are: Steel - this kind of gameplay is characterised by a slightly optimistic attitude towards the world. The aim is to raise the spirit of the characters by showing them that the war with the machines that is going on may be a difficult one, but it is not unwinnable, and that humans, when strong and united, can build the world anew. Example of a story: a unit of soldiers dispatched from the Outpost is sent to build a bunker and establish a relay base far in the north in order to plan a counter-tactic against Moloch's advance south. Chromium - is characterised by a hedonistic attitude. The characters are supposed to enjoy anything that is left from the world after the war and the story is supposed to allow them to do that. Example: the characters are offered a well-paid job by a local ganger boss who extorts wares from local tradesmen. Their job is to drive around the county and pick up the extorted items and trade it for drugs. Rust - a depressing, pessimistic mood. The characters will encounter rust, dilapidation and ruin everywhere they go. All the elements and NPCs of a story played in this mood are supposed to put the characters down and destroy their spirit. Example: the characters, badly wounded after a gunfight and robbed of all their possession find refuge in a village which is constantly raided by gangers. The characters' quest is to repel those attacks, but the enemies outnumber them and are well equipped, whereas the characters have nothing to fight with. Mercury (Quicksilver) - the most depressing side of the game; usually stories played in this mood end with the death of all the characters. The aim of this mood is to show that any kind of action undertaken is futile and that the war is already over, hence all the people are already dead, which is a fact they just need to realise. Example: a group of soldiers stationed in a bunker is awaiting an attack by mutants. They are well-armed and trained, but there is a mistake in the intelligence they were given and they do not know yet that they are seriously outnumbered. The attack commences at dusk and it is already too late to retreat, so the characters decide to seal off the bunker, hopeful that the mutants will not be able to get inside and simply go away. The mutants attack the bunker with chemical weapons instead. The characters do not have enough gas masks to go around. As an effect, those strong enough will kill the weaker ones to get their masks, not knowing that the mutants will blow up the sealed entrance the following morning. == Official rulebooks and sourcebooks == The current edition is 1.5 [1]. Since the release of the game in 2003, sourcebooks have been appearing. The game keeps growing bigger with every add-on, as well as the storyline, which is updated in those sourcebooks and in Space Pirate (pl. Gwiezdny Pirat) magazine, also published by Portal. === List of released rulebooks and sourcebooks === Neuroshima 1.0 - the original edition of the core rulebook (out of print). Neuroshima 1.5 - enhanced and revised core rulebook, with new material added and some material cut out. Wyścig (The Race) - sourcebook dedicated to cars and racing; contains rules concerning building your own vehicle and new character classes connected with driving. Gladiator - sourcebook describing in detail the "Gladiator" character class. Supplement (Supplement) - sourcebook revising the core rulebook. Detroit - sourcebook describing the city of Detroit, its inhabi
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Ghost in the Shell

Ghost in the Shell is a Japanese cyberpunk military science fiction media franchise that began with the eponymous manga series, written and illustrated by Masamune Shirow. The manga, first serialized from 1989 to 1991, is set in the mid-21st-century and follows the fictional counter-cyberterrorist organization Public Security Section 9, led by protagonist Major Motoko Kusanagi. Animation studio Production I.G has produced several anime adaptations of the series. These include the 1995 film of the same name and its 2004 sequel, Ghost in the Shell 2: Innocence; the 2002 television series Ghost in the Shell: Stand Alone Complex and its 2020 follow-up, Ghost in the Shell: SAC_2045; and the Ghost in the Shell: Arise original video animation series. In addition, an American-produced live-action film was released in March 2017. == Overview == === Title === The original editor Koichi Yuri says: At first, Ghost in the Shell came from Shirow, but when Yuri asked for "something more flashy", Shirow came up with "攻殻機動隊 Koukaku Kidou Tai (Shell Squad)" for Yuri. But Shirow was attached to including "Ghost in the Shell" as well even if in smaller type. === Setting === Primarily set in the mid-twenty-first century in the fictional Japanese city of Niihama, Niihama Prefecture (新浜県新浜市, Niihama-ken Niihama-shi), otherwise known as New Port City (ニューポートシティ, Nyū Pōto Shiti), the manga and the many anime adaptations follow the members of Public Security Section 9, a task-force consisting of various professionals skilled at solving and preventing crime, mostly with some sort of police background. Political intrigue and counter-terrorism operations are standard fare for Section 9, but the various actions of corrupt officials, companies, and cyber-criminals in each scenario are unique and require the diverse skills of Section 9's staff to prevent a series of incidents from escalating. In this post-cyberpunk iteration of a possible future, computer technology has advanced to the point that many members of the public possess cyberbrains, technology that allows them to interface their biological brain with various networks. The level of cyberization varies from simple minimal interfaces to almost complete replacement of the brain with cybernetic parts, in cases of severe trauma. This can also be combined with various levels of prostheses, with a fully prosthetic body enabling a person to become a cyborg. The main character of Ghost in the Shell, Major Motoko Kusanagi, is such a cyborg, having had a terrible accident befall her as a child that ultimately required her to use a full-body prosthesis to house her cyberbrain. This high level of cyberization, however, opens the brain up to attacks from highly skilled hackers, with the most dangerous being those who will hack a person to bend to their whims. == Media == === Literature === ==== Original manga ==== The original Ghost in the Shell manga ran in Japan from April 1989 to November 1990 in Kodansha's manga anthology Young Magazine, and was released in a tankōbon volume on October 2, 1991. Ghost in the Shell 2: Man-Machine Interface followed in 1997 for nine issues in Young Magazine, and was collected in the Ghost in the Shell: Solid Box on December 1, 2000. Then a standard version with modifications and new pages was published on June 26, 2001. Four stories from Man-Machine Interface that were not released in tankobon format from previous releases were later collected in Ghost in the Shell 1.5: Human-Error Processor, and published by Kodansha on July 17, 2003. Several art books have also been published for the manga. === Films === ==== Animated films ==== Two animated films based on the original manga have been released, both directed by Mamoru Oshii and animated by Production I.G. Ghost in the Shell was released in 1995 and follows the "Puppet Master" storyline from the manga. It was re-released in 2008 as Ghost in the Shell 2.0 with new audio and updated 3D computer graphics in certain scenes. Innocence, otherwise known as Ghost in the Shell 2: Innocence, was released in 2004, with its story based on a chapter from the first manga. ==== Live-action film ==== In 2008, DreamWorks and producer Steven Spielberg acquired the rights to a live-action film adaptation of the original Ghost in the Shell manga. On January 24, 2014, Rupert Sanders was announced as director, with a screenplay by William Wheeler. In April 2016, the full cast was announced, which included Juliette Binoche, Chin Han, Lasarus Ratuere and Kaori Momoi, and Scarlett Johansson in the lead role; the casting of Johansson drew accusations of whitewashing. Principal photography on the film began on location in Wellington, New Zealand, on February 1, 2016. Filming wrapped in June 2016. Ghost in the Shell premiered in Tokyo on March 16, 2017, and was released in the United States on March 31, 2017, in 2D, 3D and IMAX 3D. It received mixed reviews, with praise for its visuals and Johansson's performance but criticism for its script. === Television === ==== Stand Alone Complex TV series, film and ONA ==== In 2002, Ghost in the Shell: Stand Alone Complex premiered on Animax, presenting a new telling of Ghost in the Shell independent from the original manga, focusing on Section 9's investigation of the Laughing Man hacker. It was followed in 2004 by a second season titled Ghost in the Shell: S.A.C. 2nd GIG, which focused on the Individual Eleven terrorist group. The primary storylines of both seasons were compressed into OVAs broadcast as Ghost in the Shell: Stand Alone Complex The Laughing Man in 2005 and Ghost in the Shell: Stand Alone Complex Individual Eleven in 2006. Also in 2006, Ghost in the Shell: Stand Alone Complex - Solid State Society, featuring Section 9's confrontation with a hacker known as the Puppeteer, was broadcast, serving as a finale to the anime series. The extensive score for the series and its films was composed by Yoko Kanno. On April 7, 2017, Kodansha and Production I.G announced that Kenji Kamiyama and Shinji Aramaki would be co-directing a new Kōkaku Kidōtai anime production. On December 7, 2018, it was reported by Netflix that they had acquired the worldwide streaming rights to the original net animation (ONA) anime series, titled Ghost in the Shell: SAC_2045, and that it would premiere on April 23, 2020. The series is in 3DCG and Sola Digital Arts collaborated with Production I.G on the project. Ilya Kuvshinov handled character designs. The series had two seasons of 12 episodes each. In addition to the anime, a series of published books, two separate manga adaptations, and several video games for consoles and mobile phones have been released for Stand Alone Complex. ==== Arise OVA, TV series and film ==== In 2013, a new iteration of the series titled Ghost in the Shell: Arise premiered, taking an original look at the Ghost in the Shell world, set before the original manga. It was released as a series of four original video animation (OVA) episodes (with limited theatrical releases) from 2013 to 2014, then recompiled as a 10-episode television series under the title of Kōkaku Kidōtai: Arise - Alternative Architecture. An additional fifth OVA titled Pyrophoric Cult, originally premiering in the Alternative Architecture broadcast as two original episodes, was released on August 26, 2015. Kazuchika Kise served as the chief director of the series, with Tow Ubukata as head writer. Cornelius was brought onto the project to compose the score for the series, with the Major's new voice actress Maaya Sakamoto also providing vocals for certain tracks. Ghost in the Shell: The New Movie, also known as Ghost in the Shell: Arise − The Movie or New Ghost in the Shell, is a 2015 film directed by Kazuya Nomura that serves as a finale to the Ghost in the Shell: Arise story arc. The film is a continuation to the plot of the Pyrophoric Cult episode of Arise, and ties up loose ends from that arc. A manga adaptation was serialized in Kodansha's Young Magazine, which started on March 13 and ended on August 26, 2013. ==== 2026 anime ==== On May 25, 2024, it was announced that a new anime television series adaptation will be produced by Science Saru for a July 2026 premiere. Saru will be in a production committee with Bandai Namco Filmworks, Kodansha and Production I.G. The series will be directed by Monkochan, with a script by EnJoe Toh. === Video games === Ghost in the Shell was developed by Exact and released for the PlayStation on July 17, 1997, in Japan by Sony Computer Entertainment. It is a third-person shooter featuring an original storyline where the character plays a rookie member of Section 9. The video game's soundtrack Megatech Body features various techno artists, such as Takkyu Ishino, Scan X and Mijk Van Dijk. Several video games were also developed to tie into the Stand Alone Complex television series, in addition to a first-person shooter by Nexon and Neople titled Ghost in the Shell: Stand Alone Complex - First Assault Online,
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Fuzzy differential equation

Fuzzy differential equation are general concept of ordinary differential equation in mathematics defined as differential inclusion for non-uniform upper hemicontinuity convex set with compactness in fuzzy set. d x ( t ) / d t = F ( t , x ( t ) , α ) , {\displaystyle dx(t)/dt=F(t,x(t),\alpha ),} for all α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,1]} . == First order fuzzy differential equation == A first order fuzzy differential equation with real constant or variable coefficients x ′ ( t ) + p ( t ) x ( t ) = f ( t ) {\displaystyle x'(t)+p(t)x(t)=f(t)} where p ( t ) {\displaystyle p(t)} is a real continuous function and f ( t ) : [ t 0 , ∞ ) → R F {\displaystyle f(t)\colon [t_{0},\infty )\rightarrow R_{F}} is a fuzzy continuous function y ( t 0 ) = y 0 {\displaystyle y(t_{0})=y_{0}} such that y 0 ∈ R F {\displaystyle y_{0}\in R_{F}} . == Linear systems of fuzzy differential equations == A system of equations of the form x ( t ) n ′ = a n 1 ( t ) x 1 ( t ) + . . . . . . + a n n ( t ) x n ( t ) + f n ( t ) {\displaystyle x(t)'_{n}=a_{n}1(t)x_{1}(t)+......+a_{n}n(t)x_{n}(t)+f_{n}(t)} where a i j {\displaystyle a_{i}j} are real functions and f i {\displaystyle f_{i}} are fuzzy functions x n ′ ( t ) = ∑ i = 0 1 a i j x i . {\displaystyle x'_{n}(t)=\sum _{i=0}^{1}a_{ij}x_{i}.} == Fuzzy partial differential equations == A fuzzy differential equation with partial differential operator is ∇ x ( t ) = F ( t , x ( t ) , α ) , {\displaystyle \nabla x(t)=F(t,x(t),\alpha ),} for all α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,1]} . == Fuzzy fractional differential equation == A fuzzy differential equation with fractional differential operator is d n x ( t ) d t n = F ( t , x ( t ) , α ) , {\displaystyle {\frac {d^{n}x(t)}{dt^{n}}}=F(t,x(t),\alpha ),} for all α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,1]} where n {\displaystyle n} is a rational number.
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Universal portfolio algorithm

The universal portfolio algorithm is a portfolio selection algorithm from the field of machine learning and information theory. The algorithm learns adaptively from historical data and maximizes log-optimal growth rate in the long run, per the Kelly criterion. It was introduced by the late Stanford University information theorist Thomas M. Cover. The algorithm rebalances the portfolio at the beginning of each trading period. At the beginning of the first trading period it starts with a naive diversification. In the following trading periods the portfolio composition depends on the historical total return of all possible constant-rebalanced portfolios. The universal portfolio algorithm is the predecessor of the various online portfolio selection methodologies.
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TuVox

TuVox is a company that produces VXML-based telephone speech-recognition applications to replace DTMF touch-tone systems for their clients. == History == TuVox was founded in 2001 by Steven S. Pollock and Ashok Khosla, formerly of Apple Computer Corporation and Claris Corporation. Since then, TuVox has grown to over 150 employees and has US offices in Cupertino, California and Boca Raton, Florida as well as international offices in London, Vancouver and Sydney. In 2005, TuVox acquired the customers and hosting facilities of Net-By-Tel. In 2007, the company raised $20m for its speech recognition, and phone menu software. On July 22, 2010, West Interactive — a subsidiary of West Corporation — announced its acquisition of TuVox. == Customers == TuVox clients include: 1-800-Flowers.com, AMC Entertainment, American Airlines, British Airways, M&T Bank, Canon Inc., Gateway, Inc., Motorola, Progress Energy Inc., Telecom New Zealand, Time, Inc., BECU, Virgin America and USAA.
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The Old Axolotl

The Old Axolotl (Polish: Starość aksolotla) is a 2015 digital-only novel by Polish science-fiction author Jacek Dukaj. The novel was released in Polish on March 10, 2015, and shortly afterward, on March 24 that year, in English (translated by Stanley Bill). It has been described as "an experiment in reading (and creating) the electronic literature of the future". It is Dukaj's first novel to be published in English, though several of his short stories (The Golden Galley, 1996, The Iron General, 2010, The Apocrypha of Lem, 2011) have been translated prior to this. The novel has inspired two Netflix original series: the 2020 Belgian Into the Night, and its 2022 Turkish language spin-off Yakamoz S-245. == Plot == The novel presents a post-apocalyptic, cyberpunk vision of Earth where biological life has been wiped out, inhabited by robots and mechs, many of which are humans whose consciousness has been digitized in the wake of an extinction event. == Significance and analysis == The novel is an example of electronic literature, available only in digital formats, and has no traditional paper version. It was designed from the beginning not only to incorporate more traditional elements such as illustrations, but also hypertext, and 3D-printable models of main robotic characters designed by Alex Jaeger, the art director of Transformers films. The novel composition is layered, with the narrative layer, an encyclopedic/hyperlinked footnote layer, and a multimedia layer, including illustrations and a short promotional video by the Oscar-nominated Platige Image studio. One of the novel's central questions is: "What does it mean to be human?" Other subjects include post humanism and other "staples of cyberpunk and related genres, such as the artificial intelligence". The novel is representative of Dukaj's prose, posing philosophical questions about the future of man and technology. The author explained that: "stories such as The Old Axolotl that model an ‘escape from the body’ are born out of a sense of progress as a process of ‘de-animalising’ human beings through science. This has its origin in the pre-Enlightenment intuition of ‘liberation from nature’. For one of the last shackles of nature is corporeality itself, the limitations of our physicality." The other major element of the novel is Dukaj's attempts to introduce the reader to the new style of electronic literature. The novel was nominated for the 2016 Janusz A. Zajdel Award.
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