In computer science and machine learning, Cellular Neural Networks (CNN) or Cellular Nonlinear Networks (CNN) are a parallel computing paradigm similar to neural networks, with the difference that communication is allowed between neighbouring units only. Typical applications include image processing, analyzing 3D surfaces, solving partial differential equations, reducing non-visual problems to geometric maps, modelling biological vision and other sensory-motor organs. CNN is not to be confused with convolutional neural networks (also colloquially called CNN). == CNN architecture == Due to their number and variety of architectures, it is difficult to give a precise definition for a CNN processor. From an architecture standpoint, CNN processors are a system of finite, fixed-number, fixed-location, fixed-topology, locally interconnected, multiple-input, single-output, nonlinear processing units. The nonlinear processing units are often referred to as neurons or cells. Mathematically, each cell can be modeled as a dissipative, nonlinear dynamical system where information is encoded via its initial state, inputs and variables used to define its behavior. Dynamics are usually continuous, as in the case of Continuous-Time CNN (CT-CNN) processors, but can be discrete, as in the case of Discrete-Time CNN (DT-CNN) processors. Each cell has one output, by which it communicates its state with both other cells and external devices. Output is typically real-valued, but can be complex or even quaternion, i.e. a Multi-Valued CNN (MV-CNN). Most CNN processors, processing units are identical, but there are applications that require non-identical units, which are called Non-Uniform Processor CNN (NUP-CNN) processors, and consist of different types of cells. === Chua-Yang CNN === In the original Chua-Yang CNN (CY-CNN) processor, the state of the cell was a weighted sum of the inputs and the output was a piecewise linear function. However, like the original perceptron-based neural networks, the functions it could perform were limited: specifically, it was incapable of modeling non-linear functions, such as XOR. More complex functions are realizable via Non-Linear CNN (NL-CNN) processors. Cells are defined in a normed gridded space like two-dimensional Euclidean geometry. However, the cells are not limited to two-dimensional spaces; they can be defined in an arbitrary number of dimensions and can be square, triangle, hexagonal, or any other spatially invariant arrangement. Topologically, cells can be arranged on an infinite plane or on a toroidal space. Cell interconnect is local, meaning that all connections between cells are within a specified radius (with distance measured topologically). Connections can also be time-delayed to allow for processing in the temporal domain. Most CNN architectures have cells with the same relative interconnects, but there are applications that require a spatially variant topology, i.e. Multiple-Neighborhood-Size CNN (MNS-CNN) processors. Also, Multiple-Layer CNN (ML-CNN) processors, where all cells on the same layer are identical, can be used to extend the capability of CNN processors. The definition of a system is a collection of independent, interacting entities forming an integrated whole, whose behavior is distinct and qualitatively greater than its entities. Although connections are local, information exchange can happen globally through diffusion. In this sense, CNN processors are systems because their dynamics are derived from the interaction between the processing units and not within processing units. As a result, they exhibit emergent and collective behavior. Mathematically, the relationship between a cell and its neighbors, located within an area of influence, can be defined by a coupling law, and this is what primarily determines the behavior of the processor. When the coupling laws are modeled by fuzzy logic, it is a fuzzy CNN. When these laws are modeled by computational verb logic, it becomes a computational verb CNN. Both fuzzy and verb CNNs are useful for modelling social networks when the local couplings are achieved by linguistic terms. == History == The idea of CNN processors was introduced by Leon Chua and Lin Yang in 1988. In these articles, Chua and Yang outline the underlying mathematics behind CNN processors. They use this mathematical model to demonstrate, for a specific CNN implementation, that if the inputs are static, the processing units will converge, and can be used to perform useful calculations. They then suggest one of the first applications of CNN processors: image processing and pattern recognition (which is still the largest application to date). Leon Chua is still active in CNN research and publishes many of his articles in the International Journal of Bifurcation and Chaos, of which he is an editor. Both IEEE Transactions on Circuits and Systems and the International Journal of Bifurcation also contain a variety of useful articles on CNN processors authored by other knowledgeable researchers. The former tends to focus on new CNN architectures and the latter more on the dynamical aspects of CNN processors. In 1993, Tamas Roska and Leon Chua introduced the first algorithmically programmable analog CNN processor in the world. The multi-national effort was funded by the Office of Naval Research, the National Science Foundation, and the Hungarian Academy of Sciences, and researched by the Hungarian Academy of Sciences and the University of California. This article proved that CNN processors were producible and provided researchers a physical platform to test their CNN theories. After this article, companies started to invest into larger, more capable processors, based on the same basic architecture as the CNN Universal Processor. Tamas Roska is another key contributor to CNNs. His name is often associated with biologically inspired information processing platforms and algorithms, and he has published numerous key articles and has been involved with companies and research institutions developing CNN technology. === Literature === Two references are considered invaluable since they manage to organize the vast amount of CNN literature into a coherent framework: An overview by Valerio Cimagalli and Marco Balsi. The paper provides a concise intro to definitions, CNN types, dynamics, implementations, and applications. "Cellular Neural Networks and Visual Computing Foundations and Applications", written by Leon Chua and Tamas Roska, which provides examples and exercises. The book covers many different aspects of CNN processors and can serve as a textbook for a Masters or Ph.D. course. Other resources include The proceedings of "The International Workshop on Cellular Neural Networks and Their Applications" provide much CNN literature. The proceedings are available online, via IEEE Xplore, for conferences held in 1990, 1992, 1994, 1996, 1998, 2000, 2002, 2005 and 2006. There was also a workshop held in Santiago de Composetela, Spain. Topics included theory, design, applications, algorithms, physical implementations and programming and training methods. For an understanding of the analog semiconductor based CNN technology, AnaLogic Computers has their product line, in addition to the published articles available on their homepage and their publication list. They also have information on other CNN technologies such as optical computing. Many of the commonly used functions have already been implemented using CNN processors. A good reference point for some of these can be found in image processing libraries for CNN based visual computers such as Analogic’s CNN-based systems. == Related processing architectures == CNN processors could be thought of as a hybrid between artificial neural network (ANN) and Continuous Automata (CA). === Artificial Neural Networks === The processing units of CNN and NN are similar. In both cases, the processor units are multi-input, dynamical systems, and the behavior of the overall systems is driven primarily through the weights of the processing unit’s linear interconnect. However, in CNN processors, connections are made locally, whereas in ANN, connections are global. For example, neurons in one layer are fully connected to another layer in a feed-forward NN and all the neurons are fully interconnected in Hopfield networks. In ANNs, the weights of interconnections contain information on the processing system’s previous state or feedback. But in CNN processors, the weights are used to determine the dynamics of the system. Furthermore, due to the high inter-connectivity of ANNs, they tend not exploit locality in either the data set or the processing and as a result, they usually are highly redundant systems that allow for robust, fault-tolerant behavior without catastrophic errors. A cross between an ANN and a CNN processor is a Ratio Memory CNN (RMCNN). In RMCNN processors, the cell interconnect is local and topologically invariant, but the weights are used to store
Pulse-coupled networks
Pulse-coupled networks or pulse-coupled neural networks (PCNNs) are neural models proposed by modeling a cat's visual cortex, and developed for high-performance biomimetic image processing. In 1989, Eckhorn introduced a neural model to emulate the mechanism of cat's visual cortex. The Eckhorn model provided a simple and effective tool for studying small mammal’s visual cortex, and was soon recognized as having significant application potential in image processing. In 1994, Johnson adapted the Eckhorn model to an image processing algorithm, calling this algorithm a pulse-coupled neural network. The basic property of the Eckhorn's linking-field model (LFM) is the coupling term. LFM is a modulation of the primary input by a biased offset factor driven by the linking input. These drive a threshold variable that decays from an initial high value. When the threshold drops below zero it is reset to a high value and the process starts over. This is different than the standard integrate-and-fire neural model, which accumulates the input until it passes an upper limit and effectively "shorts out" to cause the pulse. LFM uses this difference to sustain pulse bursts, something the standard model does not do on a single neuron level. It is valuable to understand, however, that a detailed analysis of the standard model must include a shunting term, due to the floating voltages level in the dendritic compartment(s), and in turn this causes an elegant multiple modulation effect that enables a true higher-order network (HON). A PCNN is a two-dimensional neural network. Each neuron in the network corresponds to one pixel in an input image, receiving its corresponding pixel's color information (e.g. intensity) as an external stimulus. Each neuron also connects with its neighboring neurons, receiving local stimuli from them. The external and local stimuli are combined in an internal activation system, which accumulates the stimuli until it exceeds a dynamic threshold, resulting in a pulse output. Through iterative computation, PCNN neurons produce temporal series of pulse outputs. The temporal series of pulse outputs contain information of input images and can be used for various image processing applications, such as image segmentation and feature generation. Compared with conventional image processing means, PCNNs have several significant merits, including robustness against noise, independence of geometric variations in input patterns, capability of bridging minor intensity variations in input patterns, etc. A simplified PCNN called a spiking cortical model was developed in 2009. == Applications == PCNNs are useful for image processing, as discussed in a book by Thomas Lindblad and Jason M. Kinser. PCNNs have been used in a variety of image processing applications, including: image segmentation, pattern recognition, feature generation, face extraction, motion detection, region growing, image denoising and image enhancement Multidimensional pulse image processing of chemical structure data using PCNN has been discussed by Kinser, et al. They have also been applied to an all pairs shortest path problem.
Dry Drowning
Dry Drowning is a cyberpunk mystery visual novel developed by Studio V and published by VLG Publishing and WhisperGames for Microsoft Windows on August 2, 2019. It was released on the Nintendo Switch on February 22, 2021. == Gameplay == The player takes control of Mordred Foley and has to read through the story, while making decisions at certain points. Depending on the choices, the player can influence the relationship to other characters as well as the course of the game, discovering more than 150 story branches, and eventually reach one out of three different endings with variations. The game also includes passages where the player has to find clues or items on the screen by clicking on them. These can be used in interrogation scenes with certain characters in order to unmask them and discover their lies. Throughout the game, the player has access to an in-game operating system called AquaOS. With that, they can re-read their conversations, look at their found items, and read biographies of the characters encountered. == Plot == The game is set in the fictional and totalitarian city Nova Polemos in Europa in 2066. Mordred Foley and Hera Kairis are private investigators and before the events of the game, they sent two of the most dangerous serial killers ever, Jennifer Kingston and Robert Herrington, to the electric chair. However, after their execution, their agency underwent an investigation for falsifying the evidence presented during the case, which completely destroyed its reputation. Now they want to restart their careers and lives, while dealing with their past traumas. Soon, Mordred is caught up in several cases that all led him to believe that the dreaded serial killer named Pandora has returned. In order to solve these cases, both Mordred and Hera have to face their pasts and fears, all while a racist political party is about to make the lives of refugees in Nova Polemos even worse. == Development == The game was initially conceived by Giacomo Masi and Samuele Zolfanelli, then developed by Studio V and directed and written by Giacomo Masi. It was originally written in Italian and translated into English, Chinese, Japanese, Korean, and German. The soundtrack was composed, written, and performed by Giorgio Maioli. The ending theme and Hera's pieces, performed on piano, were created by Alessandro Masi. The background and character artworks were made by Giulia Carli, other graphic elements such as the UI were created by Samuele Zolfanelli. The developers cited L.A. Noire, Ace Attorney, Blade Runner and Heavy Rain as some of their inspirations for the game. === Releases === Dry Drowning was originally released on Microsoft Windows through Steam, GOG, Itch.io, and Utomik in August 2019. In July 2019, Giacomo Masi announced the game would be released for Xbox One in 2020, though it was not released that year. A Nintendo Switch port was released on February 22, 2021, and a version for PlayStation 4 is set to release in 2021. == Reception == According to review aggregator platform Metacritic, Dry Drowning received "mixed or average reviews" for PC based on 11 reviews and "generally favorable reviews" for Nintendo Switch based on 6 reviews. Fellow review aggregator OpenCritic assessed that the game received fair approval, being recommended by 55% of critics. 4players.de gave a positive rating of 80% and wrote: "Stylish noir thriller with an interesting story, but mechanical limitations – despite a variety of possible interactions." Screen Rant gave a mixed rating of 3 out of 5 stars and wrote, "Dry Drowning may be a fair bit messy, but there's charm here. Players who are willing to embrace the cheesier elements will find some joy in its well-crafted setting and a decent murder mystery plot. The game is constrictive and lacks the genuine shock and engagement of top tier visual novels like Doki Doki Literature Club!, but there are some moments of clever world building and a strong enough mystery propelling it." The Italian review site SpazioGames gave a positive rating of 8.5 out of 10 points and wrote: "Dry Drowning is a very good game with great narrative experience. Every relationship between the characters is layered to increase player involvement, and each choice has different consequences. A thriller game that deserves to be played." === Awards === The game won Best of EGS 2019 and Best of JOIN 2019 awards, an honorable mention at GAMEROME and was nominated as "Best Italian Debut Game" at the Italian Video Game Awards 2020. It was also declared Best Game at Join The Indie 2019.
Mars Plus
Mars Plus is a 1994 science fiction novel by American writer Frederik Pohl and Thomas T. Thomas. It is the sequel to Pohl's 1976 novel Man Plus, which is about a cyborg, Roger Torraway, who is designed to operate in the harsh Martian environment, so that humans can start to colonize Mars. Mars Plus is set fifty years after the first novel. Young Demeter Coghlan travels to Mars, now settled by humans and cyborgs, and finds herself amidst a rebellion by the colonists. == Plot == In Man Plus, set in the not-too-distant future, with threat of the Cold War becoming a fighting war, people plan for the colonization of Mars to escape the seemingly-inevitable Armageddon. The American government begins a cyborg program to create a being capable of surviving the harsh Martian environment: a "Man Plus" called Roger Torraway who is converted from man to cyborg. While his cyborg body is adapted to Mars, he feels strange at first. As more nations develop cyborgs, the computer networks of Earth become sentient. Mars Plus is set fifty years after the first novel, when Mars is settled by humans and cyborgs. The cyborg Torroway is in the novel, but he is not the main character. The protagonist is Demeter Coghlan, a young woman from Earth who travels to Mars. Demeter is seeking information about a canyon that she believes may be significant if the colonists begin to convert Mars to an Earth-like planet. Amidst a backdrop of spies and newly dispatched Earth diplomats, the inexperienced Demeter senses that tensions are rising on the planet. She is further disoriented due to recovering from an accident. Despite the risks in the region, Demeter has intense sexual encounters with some of the local colonists. When the locals rebel against the surveillance set up by the computer network, Demeter is kidnapped by the computer network. == Reception == The reviewer from SFBook Reviews criticizes the book, saying "nothing really happens" and stating that there is no linkage to Man Plus apart from the presence of the cyborg Torraway; moreover, the reviewer states that the questions posed in the first novel are not answered. SF Reviews calls Mars Plus "...not as good as Man Plus but...not bad", and it is praised for "...some nice touches: Demeter continuously forgetting to think about geology; her careless dictation to the computer and her irresistible urges for wild sex." SF Reviews criticizes the writing in Mars Plus for being "...a little careless in places" and in need of more "...more crafting and pruning."
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
Sample (graphics)
In computer graphics, a sample is an intersection of a channel and a pixel. The diagram below depicts a 24-bit pixel, consisting of 3 samples for Red, Green, and Blue. In this particular diagram, the Red sample occupies 9 bits, the Green sample occupies 7 bits and the Blue sample occupies 8 bits, totaling 24 bits per pixel. Note that the samples do not have to be equal size and not all samples are mandatory in a pixel. Also, a pixel can consist of more than 3 samples (e.g. 4 samples of the RGBA color space). A sample is related to a subpixel on a physical display.
Clanker
Clanker is a derogatory term for robots and artificial intelligence (AI) software. The term has been used in Star Wars media, first appearing in the franchise's 2005 video game Star Wars: Republic Commando. In 2025, the term became widely used to express hatred or distaste for machines ranging from delivery robots to large language models. This trend has been attributed to anxiety around the negative societal effects of AI. == In science fiction == The term has been previously used in science fiction literature, first appearing in a 1958 article by William Tenn in which he uses it to describe robots from science fiction films like Metropolis. The Star Wars franchise began using the term as a slur against droids in the 2005 video game Star Wars: Republic Commando before being prominently used in the animated series Star Wars: The Clone Wars, which follows a galaxy-wide war between the Galactic Republic's clone troopers and the Confederacy of Independent Systems' battle droids. In Star Wars media, robots—more commonly known as droids—are routinely depicted as the subjects of discrimination. For example, in the original Star Wars film, C-3PO and R2-D2 are abducted by Jawas and sold to the family of Luke Skywalker. When visiting a cantina in Mos Eisley, both droids are refused service by the bartender, who remarks that "We don't serve their kind." In Star Wars lore, the term clanker had entered use by the time of the franchise's High Republic Era and became prominent during the Clone Wars, in which clone troopers regularly use the phrase against battle droids. == AI backlash == The growing popularity of the term clanker reflects an increase in direct contact between people and AI systems. On sidewalks, delivery robots impede mobility and cause safety issues. In digital spaces, cybersecurity experts have raised concerns about the rising number of bots online, which now make up a large portion of internet traffic. A 2025 report estimated that about one in five social media accounts are automated. The term is also a reaction to AI advocacy from industrialists like Elon Musk and Sam Altman, who have championed the integration of AI into nearly every aspect of modern life. This includes efforts by major companies and startups alike, such as Amazon's development of humanoid robots to replace human workers in service industries. Such initiatives have further fueled public skepticism, reinforcing the association of clanker with unease over automation and the displacement of human roles. A global survey conducted by the research firm Gartner in December 2023 found that 64% of customers would prefer companies to avoid using AI in customer service, with another 53% stating they would consider switching to a different company if they discovered AI was handling their service interactions. Another report by Ernst & Young, published in July 2025, found that 42% of employees across Europe are worried that the use of AI in the workplace may threaten their employment. Criticism has also been directed at the technology itself. Some of the backlash stems from concerns about the resource consumption of AI systems, their frequent reliance on copyrighted material without consent, and questions about the intentions of the corporations behind them. There are also concerns about the potential cognitive effects of relying heavily on AI. A study, authored by researchers at Microsoft and Carnegie Mellon University, warns that regular dependence on AI may leave users mentally unprepared for real-world problem solving, likening the effect to cognitive atrophy. In June 2025, United States Senator Ruben Gallego tweeted that his "new bill makes sure you don't have to talk to a clanker if you don't want to", referring to proposed legislation that would require call centers to disclose their use of automated customer service agents to callers in the United States and offer the option to switch to a human representative. == Analysis == Linguist Adam Aleksic has described clanker as an evolution of racial slurs that anthropomorphize robotic systems. Internet memes incorporating the term often reference historical discrimination against marginalized groups such as African Americans. Based on the work of linguist Geoffrey Nunberg, American news website Axios has argued that clanker is merely a derogatory word, rather than a slur, because it does not perpetuate social inequities. NPR has noted the irony that the word robot was coined by Karel Čapek for his 1920 science-fiction play R.U.R. as a similar criticism of industrialization forcing workers to become devoid of their humanity. Aleksic has observed that robot can be further traced to the Proto-Slavic noun orbъ, which means 'slave'. While other science fiction media include pejoratives for androids and robots, such as skinjob and toaster from the Blade Runner and Battlestar Galactica franchises, respectively, clanker is believed to have gained popularity because its usage is intuitive and flexible. Whereas AI slop describes low-quality output from artificial intelligence, clanker belittles the underlying computer systems.