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  Bitstrips

  Bitstrips, Inc. was a Canadian media and technology company based in Toronto, founded in 2007 by Jacob Blackstock, David Kennedy, Shahan Panth, Dorian Baldwin, and Jesse Brown. The company created and offered a web application, Bitstrips.com, which allowed users to create comic strips using personalized avatars, and preset templates and poses. Brown and Blackstock explained that the service was meant to enable self-expression without the need to have artistic skills. Bitstrips was first presented in 2008 at South by Southwest in Austin, Texas, and the service later piloted and launched a version designed for use as educational software. The service achieved increasing prominence following the launch of versions for Facebook and mobile platforms. In 2014, Bitstrips launched a spin-off app known as Bitmoji, which allows users to create personalized stickers for use in instant messaging. In July 2016, Snapchat Inc. announced that it had acquired the company; the Bitstrips comic service was shut down, but Bitmoji remains operational, and has subsequently been given greater prominence within Snapchat's overall platform. == History == Bitstrips was co-developed by Toronto-based comic artist Jacob Blackstock and his high school friend, journalist Jesse Brown. The service was originally envisioned as a means to allow anyone to create their own comic strip without needing artistic skills. Brown explained that "it's so difficult and time-consuming to tell a story in comic book form, drawing the same characters again and again in these tiny little panels, and just the amount of craftsmanship required. And even if you can do it well, which I never could, it takes years to make a story." Brown stated that the service would be "groundwork for a whole new way to communicate", and went as far as describing the service as being a "YouTube for comics". Blackstock explained that the concept of Bitstrips was influenced by his own use of comics as a form of socialization; a student, Blackstock and his friends drew comics featuring each other and shared them during classes. He felt that Bitstrips was a "medium for self-expression", stating that "It's not just about you making the comics, but since you and your friends star in these comics, it's like you're the medium. The visual nature of comics just speaks so much louder than text." The service was publicly unveiled at South by Southwest in 2008. In 2009, the service introduced a version oriented towards the educational market, Bitstrips for Schools, which was initially piloted at a number of schools in Ontario. The service was praised by educators for being engaging to students, especially within language classes. Brown noted that students were using the service to create comics outside of class as well, stating that it was "so gratifying and shocking what people do with your tool to make their own stories in ways that you never would have anticipated. Some of them are just brilliant." In December 2012, Bitstrips launched a version for Facebook; by July 2013, Bitstrips had 10 million unique users on Facebook, having created over 50 million comics. In October 2013, Bitstrips launched a mobile app; in two months, Bitstrips became a top-downloaded app in 40 countries, and over 30 million avatars had been created with it. In November 2013, Bitstrips secured a round of funding from Horizons Ventures and Li Ka-shing. In October 2014, Bitstrips launched Bitmoji, a spin-off app that allows users to create stickers featuring Bitstrips characters in various templates. In July 2016, following unconfirmed reports earlier in the year, Snapchat Inc. announced that it had acquired Bitstrips. The company's staff continue to operate out of Toronto, but the original Bitstrips comic service was shut down in favour of focusing exclusively on Bitmoji, leaving many Bitstrips users to call for a reboot of the comic service.

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  Distributed artificial intelligence

  Distributed Artificial Intelligence (DAI) (also called Decentralized Artificial Intelligence) is a melding of artificial intelligence with distributed computing. From artificial intelligence comes the theory and technology for constructing or analyzing an intelligent system. But where artificial intelligence uses psychology as a source of ideas, inspiration, and metaphor, DAI uses sociology, economics, and management science for inspiration. Where the focus of artificial intelligence is on the individual, the focus of DAI is on the group. Distributed computing provides the computational substrate on which this group focus can occur. Using techniques from artificial intelligence, communication theory, control theory, and interaction theory, it produces a cooperative solution to problems by a decentralized group of computational entities (agents). DAI is closely related to and a predecessor of the field of multi-agent systems. They are distinguished generally by multi-agent systems being open, where the entities might arise from different interests and have individual goals, and distributed artificial-intelligence systems, where the entities have common goals. There are numerous applications and tools. == Definition == Distributed Artificial Intelligence (DAI) is an approach to solving complex learning, planning, and decision-making problems. It is embarrassingly parallel, thus able to exploit large scale computation and spatial distribution of computing resources. These properties allow it to solve problems that require the processing of very large data sets. DAI systems consist of autonomous learning processing nodes (agents), that are distributed, often at a very large scale. DAI nodes can act independently, and partial solutions are integrated by communication between nodes, often asynchronously. By virtue of their scale, DAI systems are robust and elastic, and by necessity, loosely coupled. Furthermore, DAI systems are built to be adaptive to changes in the problem definition or underlying data sets due to the scale and difficulty in redeployment. DAI systems do not require all the relevant data to be aggregated in a single location, in contrast to monolithic or centralized Artificial Intelligence systems, which have tightly coupled and geographically close processing nodes. Therefore, DAI systems often operate on sub-samples or hashed impressions of very large datasets. In addition, the source dataset may change or be updated during the course of the execution of a DAI system. == Development == In 1975 distributed artificial intelligence emerged as a subfield of artificial intelligence that dealt with interactions of intelligent agents. As a scientific discipline, it progressed through a series of workshops in the USA (International Workshop on Distributed Artificial Intelligence, held in 13 editions from 1978 - 1994), Europe (Workshop on Modelling Autonomous Agents in a Multi-Agent World https://link.springer.com/conference/maamaw), and Asia (Multi-Agent and Cooperative Computation Workshop (MACC) https://sites.google.com/view/sig-macc/macc-workshop?authuser=0). Distributed artificial intelligence systems were conceived as a group of intelligent entities, called agents, that interacted by cooperation, by coexistence, or by competition. DAI is categorized into multi-agent systems and distributed problem solving. In multi-agent systems the main focus is how agents coordinate their knowledge and activities. For distributed problem solving the major focus is how the problem is decomposed and the solutions are synthesized. == Goals == The objectives of Distributed Artificial Intelligence are to solve the reasoning, planning, learning and perception problems of artificial intelligence, especially if they require large data, by distributing the problem to autonomous processing nodes (agents). To reach the objective, DAI requires: A distributed system with robust and elastic computation on unreliable and failing resources that are loosely coupled Coordination of the actions and communication of the nodes Subsamples of large data sets and online machine learning There are many reasons for wanting to distribute intelligence or cope with multi-agent systems. Mainstream problems in DAI research include the following: Parallel problem solving: mainly deals with how classic artificial intelligence concepts can be modified, so that multiprocessor systems and clusters of computers can be used to speed up calculation. Distributed problem solving (DPS): the concept of agent, autonomous entities that can communicate with each other, was developed to serve as an abstraction for developing DPS systems. See below for further details. Multi-Agent Based Simulation (MABS): a branch of DAI that builds the foundation for simulations that need to analyze not only phenomena at macro level but also at micro level, as it is in many social simulation scenarios. == Approaches == Two types of DAI has emerged: In Multi-agent systems agents coordinate their knowledge and activities and reason about the processes of coordination. Agents are physical or virtual entities that can act, perceive their environment, and communicate with other agents. An agent is autonomous and has skills to achieve goals. The agents change the state of their environment by their actions. There are a number of different coordination techniques. In distributed problem solving the work is divided among nodes and the knowledge is shared. The main concerns are task decomposition and synthesis of the knowledge and solutions. DAI can apply a bottom-up approach to AI, similar to the subsumption architecture as well as the traditional top-down approach of AI. In addition, DAI can also be a vehicle for emergence. === Challenges === The challenges in Distributed AI are: How to carry out communication and interaction of agents and which communication language or protocols should be used. How to ensure the coherency of agents. How to synthesise the results among 'intelligent agents' group by formulation, description, decomposition and allocation. == Applications and tools == Areas where DAI have been applied are: Electronic commerce, e.g. for trading strategies the DAI system learns financial trading rules from subsamples of very large samples of financial data Networks, e.g. in telecommunications the DAI system controls the cooperative resources in a WLAN network Routing, e.g. model vehicle flow in transport networks Scheduling, e.g. flow shop scheduling where the resource management entity ensures local optimization and cooperation for global and local consistency Search engines, e.g. in LLM federated search like Ithy where document retrieval and analysis are distributed to DAI agents before aggregation Multi-Agent systems, e.g. artificial life, the study of simulated life Electric power systems, e.g. Condition Monitoring Multi-Agent System (COMMAS) applied to transformer condition monitoring, and IntelliTEAM II Automatic Restoration System DAI integration in tools has included: ECStar is a distributed rule-based learning system. == Agents == === Systems: Agents and multi-agents === Notion of Agents: Agents can be described as distinct entities with standard boundaries and interfaces designed for problem solving. Notion of Multi-Agents: Multi-Agent system is defined as a network of agents which are loosely coupled working as a single entity like society for problem solving that an individual agent cannot solve. === Software agents === The key concept used in DPS and MABS is the abstraction called software agents. An agent is a virtual (or physical) autonomous entity that has an understanding of its environment and acts upon it. An agent is usually able to communicate with other agents in the same system to achieve a common goal, that one agent alone could not achieve. This communication system uses an agent communication language. A first classification that is useful is to divide agents into: reactive agent – A reactive agent is not much more than an automaton that receives input, processes it and produces an output. deliberative agent – A deliberative agent in contrast should have an internal view of its environment and is able to follow its own plans. hybrid agent – A hybrid agent is a mixture of reactive and deliberative, that follows its own plans, but also sometimes directly reacts to external events without deliberation. Well-recognized agent architectures that describe how an agent is internally structured are: ASMO (emergence of distributed modules) BDI (Believe Desire Intention, a general architecture that describes how plans are made) InterRAP (A three-layer architecture, with a reactive, a deliberative and a social layer) PECS (Physics, Emotion, Cognition, Social, describes how those four parts influences the agents behavior). Soar (a rule-based approach)

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  The Quantum Thief

  The Quantum Thief is the debut science fiction novel by Finnish writer Hannu Rajaniemi and the first novel in a trilogy featuring the character of Jean le Flambeur; the sequels are The Fractal Prince (2012) and The Causal Angel (2014). The novel was published in Britain by Gollancz in 2010, and by Tor in 2011 in the US. It is a heist story, set in a futuristic Solar System, that features a protagonist modeled on Arsène Lupin, the gentleman thief of Maurice Leblanc. The novel was nominated for the 2011 Locus Award for Best First Novel, and was second runner-up for the 2011 Campbell Memorial Award. == Setting == Several centuries after the technological singularity largely destroyed Earth, various posthuman factions compete for dominance in the Solar System. Though sentient superintelligent AGI has never been successfully developed, civilization has been greatly transformed by the proliferation of Hansonian brain emulations (termed "gogols" in reference to Nikolai Gogol, and in particular his novel Dead Souls). An alliance of powerful gogol copies rule the inner system from computronium megastructures housing trillions of virtual minds, laboring to resurrect the dead in religious devotion to the philosophy of Nikolai Fedorov. This alliance, the Sobornost, has been in conflict with a community of quantum entangled minds who adhere to the "no-cloning" principle of quantum information theory, and so do not see the Sobornost's ultimate goal as resurrection, but death. Most of this community, the Zoku, was devastated when Jupiter was destroyed with a weaponized gravitational singularity. Among the last remnants of near-baseline humanity exist on the mobile cities of Mars, where advanced cryptography and an obsessive privacy culture ensure that the Sobornost cannot upload their citizens' minds. The most notable of these cities is the Oubliette, where time is used as a currency. When a citizen's balance reaches zero their mind is transferred to a robotic body to serve the needs of the city for a set period, before being returned to their original body with a restored balance of time. == Plot summary == Countless gogols of the legendary gentleman thief Jean Le Flambeur are trapped in a virtual Sobornost prison in orbit around Neptune, playing an iterated prisoner's dilemma until his mind learns to cooperate. A warrior from the Oort Cloud, which has been settled by Finnish colonists, successfully retrieves one of the Le Flambeur gogols and uploads it into a real-space body. Acting on behalf of a competing Sobornost authority, this Oortian, Mieli, ferries the thief to the Martian city known as The Oubliette, where he has stored his memories for later recovery. The two intend to recover his memories so that he may return to an operating capacity sufficient to serve his Sobornost benefactor in a theft and repay his liberation. On the Oubliette, the young detective Isidore Beautrelet helps vigilantes catch Sobornost agents illicitly uploading human minds. These vigilantes are revealed to be in the service of a local colony of Zoku. Beautrelet is employed to investigate the arrival of Le Flambeur, and in the process becomes aware that the Oubliette's cryptographic security was always compromised. The memories of its citizens are fabrications, and the "King of Mars" long believed ousted in a revolution, still reigns behind the scenes. This King, who is another copy of Jean Le Flambeur, is defeated in the ensuing conflict. Le Flambeur fails to recover all of his memories, which he had locked with a quantum entangled revolver that required him to kill several of his old friends to open his stored memory. He and Mieli escape a liberated Mars having recovered only a mysterious "Schrödinger’s Box" from the Memory Palace. == Themes == Themes central to The Quantum Thief are the unreliability and malleability of memory and the effects of extreme longevity on an individual's perspective and personality. Prisons, surveillance and control in society are also major themes. In the book, the people living in the Oubliette society on Mars have two types of memory; in addition to a traditional, personal memory, there is the exomemory, which can be accessed by other people, from anywhere in the city. Memories about personal experiences can be stored in the exomemory and partitioned, with different levels of access granted to different people. These memories can be used, among other things, as an expedient form of communication. The Oubliette society has an economy where time is used as currency. When an individual's time is expended, their consciousness is uploaded into a "Quiet". The Quiet are mute machine servants who maintain and protect the city. Although the quiet seem to have little interest in the world outside their occupations, they do seem to retain some traces of their former personalities and memories. The conspiracy central to the plot involves the hidden rulers, called the "cryptarchs", manipulating and abusing the exomemory and through the citizens' transformations to quiet and back, the traditional memory as well. In the book, the Oubliette society is compared to a panopticon; a prison, where every action of the dwellers can be scrutinized. == History and influences == The first chapter of The Quantum Thief was presented by Rajaniemi's literary agent, John Jarrold, to Gollancz as the basis for the three-book deal that was eventually secured. Rajaniemi has stated that he had "come up with an outline that had every single idea I could cram into it, because I wanted to be worthy of what had happened." The outline eventually expanded into three parts, and the first part became The Quantum Thief. The novel's plot was inspired by one of Rajaniemi's favorite characters in fiction, Maurice Leblanc's gentleman thief Arsène Lupin, who operates on both sides of the law. What intrigued Rajaniemi were the cycles of redemption and relapse Lupin goes through as he tries to go straight, always falling short. Besides LeBlanc, Rajaniemi mentioned Roger Zelazny as a strong influence. Ian McDonald was the other science fiction author he mentioned as influential, plus Frances A.Yates's book The Art of Memory, for memory palaces. In an interview, Rajaniemi said he wasn't trying to write the novel as hard science fiction: "For me, the more important consequence of having a scientific background is a degree of speculative rigour: trying hard to work out the consequences of the assumptions one begins with." == Reception == The novel has received generally positive reviews. Gary K. Wolfe writes in his Locus review that Rajaniemi has "spectacularly delivered on the promise that this is likely the most important debut SF novel we'll see this year". James Lovegrove, reviewing the book in his Financial Times column, notes that "many an anglophone author would kill to turn out prose half as good as this, especially on their maiden effort." Eric Brown, reviewing for The Guardian, finds the novel to be "a brilliant debut", while alluding to the "apocryphal" (and incorrect) myth that "this novel sold on the strength of its first line." Sam Bandah, at SciFiNow, praises the novel for "its engaging narrative and characters backed by often almost intimidatingly good sci-fi concepts." Criticism for the novel has generally centred on Rajaniemi's sparse "show, don't tell" writing style. Brown notes that "the author makes no concessions to the lazy reader with info-dumps or convenient explanations." Niall Alexander, of the Speculative Scotsman, states that "had there been some sort of index, [he] would have gladly (and repeatedly) referred to it during the mind-boggling first third of The Quantum Thief", while proclaiming the novel to be "the sci-fi debut of 2010." == Awards == Nominee for the 2011 Locus Award for Best First Novel. Third place for the 2011 John W. Campbell Memorial Award for Best Science Fiction Novel

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  Fuzzy measure theory

  In mathematics, fuzzy measure theory considers generalized measures in which the additive property is replaced by the weaker property of monotonicity. The central concept of fuzzy measure theory is the fuzzy measure (also capacity, see ), which was introduced by Choquet in 1953 and independently defined by Sugeno in 1974 in the context of fuzzy integrals. There exists a number of different classes of fuzzy measures including plausibility/belief measures, possibility/necessity measures, and probability measures, which are a subset of classical measures. == Definitions == Let X {\displaystyle \mathbf {X} } be a universe of discourse, C {\displaystyle {\mathcal {C}}} be a class of subsets of X {\displaystyle \mathbf {X} } , and E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} . A function g : C → R {\displaystyle g:{\mathcal {C}}\to \mathbb {R} } where ∅ ∈ C ⇒ g ( ∅ ) = 0 {\displaystyle \emptyset \in {\mathcal {C}}\Rightarrow g(\emptyset )=0} E ⊆ F ⇒ g ( E ) ≤ g ( F ) {\displaystyle E\subseteq F\Rightarrow g(E)\leq g(F)} is called a fuzzy measure. A fuzzy measure is called normalized or regular if g ( X ) = 1 {\displaystyle g(\mathbf {X} )=1} . == Properties of fuzzy measures == A fuzzy measure is: additive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) = g ( E ) + g ( F ) . {\displaystyle g(E\cup F)=g(E)+g(F).} ; supermodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have g ( E ∪ F ) + g ( E ∩ F ) ≥ g ( E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\geq g(E)+g(F)} ; submodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have g ( E ∪ F ) + g ( E ∩ F ) ≤ g ( E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\leq g(E)+g(F)} ; superadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) ≥ g ( E ) + g ( F ) {\displaystyle g(E\cup F)\geq g(E)+g(F)} ; subadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) ≤ g ( E ) + g ( F ) {\displaystyle g(E\cup F)\leq g(E)+g(F)} ; symmetric if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have | E | = | F | {\displaystyle |E|=|F|} implies g ( E ) = g ( F ) {\displaystyle g(E)=g(F)} ; Boolean if for any E ∈ C {\displaystyle E\in {\mathcal {C}}} , we have g ( E ) = 0 {\displaystyle g(E)=0} or g ( E ) = 1 {\displaystyle g(E)=1} . Understanding the properties of fuzzy measures is useful in application. When a fuzzy measure is used to define a function such as the Sugeno integral or Choquet integral, these properties will be crucial in understanding the function's behavior. For instance, the Choquet integral with respect to an additive fuzzy measure reduces to the Lebesgue integral. In discrete cases, a symmetric fuzzy measure will result in the ordered weighted averaging (OWA) operator. Submodular fuzzy measures result in convex functions, while supermodular fuzzy measures result in concave functions when used to define a Choquet integral. == Möbius representation == Let g be a fuzzy measure. The Möbius representation of g is given by the set function M, where for every E , F ⊆ X {\displaystyle E,F\subseteq X} , M ( E ) = ∑ F ⊆ E ( − 1 ) | E ∖ F | g ( F ) . {\displaystyle M(E)=\sum _{F\subseteq E}(-1)^{|E\backslash F|}g(F).} The equivalent axioms in Möbius representation are: M ( ∅ ) = 0 {\displaystyle M(\emptyset )=0} . ∑ F ⊆ E | i ∈ F M ( F ) ≥ 0 {\displaystyle \sum _{F\subseteq E|i\in F}M(F)\geq 0} , for all E ⊆ X {\displaystyle E\subseteq \mathbf {X} } and all i ∈ E {\displaystyle i\in E} A fuzzy measure in Möbius representation M is called normalized if ∑ E ⊆ X M ( E ) = 1. {\displaystyle \sum _{E\subseteq \mathbf {X} }M(E)=1.} Möbius representation can be used to give an indication of which subsets of X interact with one another. For instance, an additive fuzzy measure has Möbius values all equal to zero except for singletons. The fuzzy measure g in standard representation can be recovered from the Möbius form using the Zeta transform: g ( E ) = ∑ F ⊆ E M ( F ) , ∀ E ⊆ X . {\displaystyle g(E)=\sum _{F\subseteq E}M(F),\forall E\subseteq \mathbf {X} .} == Simplification assumptions for fuzzy measures == Fuzzy measures are defined on a semiring of sets or monotone class, which may be as granular as the power set of X, and even in discrete cases the number of variables can be as large as 2|X|. For this reason, in the context of multi-criteria decision analysis and other disciplines, simplification assumptions on the fuzzy measure have been introduced so that it is less computationally expensive to determine and use. For instance, when it is assumed the fuzzy measure is additive, it will hold that g ( E ) = ∑ i ∈ E g ( { i } ) {\displaystyle g(E)=\sum _{i\in E}g(\{i\})} and the values of the fuzzy measure can be evaluated from the values on X. Similarly, a symmetric fuzzy measure is defined uniquely by |X| values. Two important fuzzy measures that can be used are the Sugeno- or λ {\displaystyle \lambda } -fuzzy measure and k-additive measures, introduced by Sugeno and Grabisch respectively. === Sugeno λ-measure === The Sugeno λ {\displaystyle \lambda } -measure is a special case of fuzzy measures defined iteratively. It has the following definition: ==== Definition ==== Let X = { x 1 , … , x n } {\displaystyle \mathbf {X} =\left\lbrace x_{1},\dots ,x_{n}\right\rbrace } be a finite set and let λ ∈ ( − 1 , + ∞ ) {\displaystyle \lambda \in (-1,+\infty )} . A Sugeno λ {\displaystyle \lambda } -measure is a function g : 2 X → [ 0 , 1 ] {\displaystyle g:2^{X}\to [0,1]} such that g ( X ) = 1 {\displaystyle g(X)=1} . if A , B ⊆ X {\displaystyle A,B\subseteq \mathbf {X} } (alternatively A , B ∈ 2 X {\displaystyle A,B\in 2^{\mathbf {X} }} ) with A ∩ B = ∅ {\displaystyle A\cap B=\emptyset } then g ( A ∪ B ) = g ( A ) + g ( B ) + λ g ( A ) g ( B ) {\displaystyle g(A\cup B)=g(A)+g(B)+\lambda g(A)g(B)} . As a convention, the value of g at a singleton set { x i } {\displaystyle \left\lbrace x_{i}\right\rbrace } is called a density and is denoted by g i = g ( { x i } ) {\displaystyle g_{i}=g(\left\lbrace x_{i}\right\rbrace )} . In addition, we have that λ {\displaystyle \lambda } satisfies the property λ + 1 = ∏ i = 1 n ( 1 + λ g i ) {\displaystyle \lambda +1=\prod _{i=1}^{n}(1+\lambda g_{i})} . Tahani and Keller as well as Wang and Klir have shown that once the densities are known, it is possible to use the previous polynomial to obtain the values of λ {\displaystyle \lambda } uniquely. === k-additive fuzzy measure === The k-additive fuzzy measure limits the interaction between the subsets E ⊆ X {\displaystyle E\subseteq X} to size | E | = k {\displaystyle |E|=k} . This drastically reduces the number of variables needed to define the fuzzy measure, and as k can be anything from 1 (in which case the fuzzy measure is additive) to X, it allows for a compromise between modelling ability and simplicity. ==== Definition ==== A discrete fuzzy measure g on a set X is called k-additive ( 1 ≤ k ≤ | X | {\displaystyle 1\leq k\leq |\mathbf {X} |} ) if its Möbius representation verifies M ( E ) = 0 {\displaystyle M(E)=0} , whenever | E | > k {\displaystyle |E|>k} for any E ⊆ X {\displaystyle E\subseteq \mathbf {X} } , and there exists a subset F with k elements such that M ( F ) ≠ 0 {\displaystyle M(F)\neq 0} . == Shapley and interaction indices == In game theory, the Shapley value or Shapley index is used to indicate the weight of a game. Shapley values can be calculated for fuzzy measures in order to give some indication of the importance of each singleton. In the case of additive fuzzy measures, the Shapley value will be the same as each singleton. For a given fuzzy measure g, and | X | = n {\displaystyle |\mathbf {X} |=n} , the Shapley index for every i , … , n ∈ X {\displaystyle i,\dots ,n\in X} is: ϕ ( i ) = ∑ E ⊆ X ∖ { i } ( n − | E | − 1 ) ! | E | ! n ! [ g ( E ∪ { i } ) − g ( E ) ] . {\displaystyle \phi (i)=\sum _{E\subseteq \mathbf {X} \backslash \{i\}}{\frac {(n-|E|-1)!|E|!}{n!}}[g(E\cup \{i\})-g(E)].} The Shapley value is the vector ϕ ( g ) = ( ψ ( 1 ) , … , ψ ( n ) ) . {\displaystyle \mathbf {\phi } (g)=(\psi (1),\dots ,\psi (n)).}

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  Automated Lip Reading

  Automated Lip Reading (ALR) is a software technology developed by speech recognition expert Frank Hubner. A video image of a person talking can be analysed by the software. The shapes made by the lips can be examined and then turned into sounds. The sounds are compared to a dictionary to create matches to the words being spoken. The technology was used successfully to analyse silent home movie footage of Adolf Hitler taken by Eva Braun at their Bavarian retreat Berghof. The video, with words, was included in a documentary titled "Hitler's Private World", Revealed Studios, 2006 Source: New Technology catches Hitler off guard

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  Fuzzy control system

  A fuzzy control system is a control system based on fuzzy logic – a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of either 1 or 0 (true or false, respectively). Fuzzy logic is widely used in machine control. The term "fuzzy" refers to the fact that the logic involved can deal with concepts that cannot be expressed as the "true" or "false" but rather as "partially true". Although alternative approaches such as genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases, fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, such that that their experience can be used in the design of the controller. This makes it easier to mechanize tasks that are already successfully performed by humans. == History and applications == Fuzzy logic was proposed by Lotfi A. Zadeh of the University of California at Berkeley in a 1965 paper. He elaborated on his ideas in a 1973 paper that introduced the concept of "linguistic variables", which in this article equates to a variable defined as a fuzzy set. Other research followed, with the first industrial application, a cement kiln built in Denmark, coming on line in 1976. Fuzzy systems were initially implemented in Japan. Interest in fuzzy systems was sparked by Seiji Yasunobu and Soji Miyamoto of Hitachi, who in 1985 provided simulations that demonstrated the feasibility of fuzzy control systems for the Sendai Subway. Their ideas were adopted, and fuzzy systems were used to control accelerating, braking, and stopping when the Namboku Line opened in 1987. In 1987, Takeshi Yamakawa demonstrated the use of fuzzy control, through a set of simple dedicated fuzzy logic chips, in an "inverted pendulum" experiment. This is a classic control problem, in which a vehicle tries to keep a pole mounted on its top by a hinge upright by moving back and forth. Yamakawa subsequently made the demonstration more sophisticated by mounting a wine glass containing water and even a live mouse to the top of the pendulum: the system maintained stability in both cases. Yamakawa eventually went on to organize his own fuzzy-systems research lab to help exploit his patents in the field. Japanese engineers subsequently developed a wide range of fuzzy systems for both industrial and consumer applications. In 1988 Japan established the Laboratory for International Fuzzy Engineering (LIFE), a cooperative arrangement between 48 companies to pursue fuzzy research. The automotive company Volkswagen was the only foreign corporate member of LIFE, dispatching a researcher for a duration of three years. Japanese consumer goods often incorporate fuzzy systems. Matsushita vacuum cleaners use microcontrollers running fuzzy algorithms to interrogate dust sensors and adjust suction power accordingly. Hitachi washing machines use fuzzy controllers to load-weight, fabric-mix, and dirt sensors and automatically set the wash cycle for the best use of power, water, and detergent. Canon developed an autofocusing camera that uses a charge-coupled device (CCD) to measure the clarity of the image in six regions of its field of view and use the information provided to determine if the image is in focus. It also tracks the rate of change of lens movement during focusing, and controls its speed to prevent overshoot. The camera's fuzzy control system uses 12 inputs: 6 to obtain the current clarity data provided by the CCD and 6 to measure the rate of change of lens movement. The output is the position of the lens. The fuzzy control system uses 13 rules and requires 1.1 kilobytes of memory. An industrial air conditioner designed by Mitsubishi uses 25 heating rules and 25 cooling rules. A temperature sensor provides input, with control outputs fed to an inverter, a compressor valve, and a fan motor. Compared to the previous design, the fuzzy controller heats and cools five times faster, reduces power consumption by 24%, increases temperature stability by a factor of two, and uses fewer sensors. Other applications investigated or implemented include: character and handwriting recognition; optical fuzzy systems; robots, including one for making Japanese flower arrangements; voice-controlled robot helicopters (hovering is a "balancing act" rather similar to the inverted pendulum problem); rehabilitation robotics to provide patient-specific solutions (e.g. to control heart rate and blood pressure ); control of flow of powders in film manufacture; elevator systems; and so on. Work on fuzzy systems is also proceeding in North America and Europe, although on a less extensive scale than in Japan. The US Environmental Protection Agency has investigated fuzzy control for energy-efficient motors, and NASA has studied fuzzy control for automated space docking: simulations show that a fuzzy control system can greatly reduce fuel consumption. Firms such as Boeing, General Motors, Allen-Bradley, Chrysler, Eaton, and Whirlpool have worked on fuzzy logic for use in low-power refrigerators, improved automotive transmissions, and energy-efficient electric motors. In 1995 Maytag introduced an "intelligent" dishwasher based on a fuzzy controller and a "one-stop sensing module" that combines a thermistor, for temperature measurement; a conductivity sensor, to measure detergent level from the ions present in the wash; a turbidity sensor that measures scattered and transmitted light to measure the soiling of the wash; and a magnetostrictive sensor to read spin rate. The system determines the optimum wash cycle for any load to obtain the best results with the least amount of energy, detergent, and water. It even adjusts for dried-on foods by tracking the last time the door was opened, and estimates the number of dishes by the number of times the door was opened. Xiera Technologies Inc. has developed the first auto-tuner for the fuzzy logic controller's knowledge base known as edeX. This technology was tested by Mohawk College and was able to solve non-linear 2x2 and 3x3 multi-input multi-output problems. Research and development is also continuing on fuzzy applications in software, as opposed to firmware, design, including fuzzy expert systems and integration of fuzzy logic with neural-network and so-called adaptive "genetic" software systems, with the ultimate goal of building "self-learning" fuzzy-control systems. These systems can be employed to control complex, nonlinear dynamic plants, for example, human body. == Fuzzy sets == The input variables in a fuzzy control system are in general mapped by sets of membership functions similar to this, known as "fuzzy sets". The process of converting a crisp input value to a fuzzy value is called "fuzzification". The fuzzy logic based approach had been considered by designing two fuzzy systems, one for error heading angle and the other for velocity control. A control system may also have various types of switch, or "ON-OFF", inputs along with its analog inputs, and such switch inputs of course will always have a truth value equal to either 1 or 0, but the scheme can deal with them as simplified fuzzy functions that happen to be either one value or another. Given "mappings" of input variables into membership functions and truth values, the microcontroller then makes decisions for what action to take, based on a set of "rules", each of the form: IF brake temperature IS warm AND speed IS not very fast THEN brake pressure IS slightly decreased. In this example, the two input variables are "brake temperature" and "speed" that have values defined as fuzzy sets. The output variable, "brake pressure" is also defined by a fuzzy set that can have values like "static" or "slightly increased" or "slightly decreased" etc. === Fuzzy control in detail === Fuzzy controllers are very simple conceptually. They consist of an input stage, a processing stage, and an output stage. The input stage maps sensor or other inputs, such as switches, thumbwheels, and so on, to the appropriate membership functions and truth values. The processing stage invokes each appropriate rule and generates a result for each, then combines the results of the rules. Finally, the output stage converts the combined result back into a specific control output value. The most common shape of membership functions is triangular, although trapezoidal and bell curves are also used, but the shape is generally less important than the number of curves and their placement. From three to seven curves are generally appropriate to cover the required range of an input value, or the "universe of discourse" in fuzzy jargon. As discussed earlier, the processing stage is based on a collection of logic rules in the form of IF-THEN statements, where the IF part is called the "antecedent" and the THEN part is called the "consequent". Typical fuzzy

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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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  T-norm fuzzy logics

  T-norm fuzzy logics are a family of non-classical logics, informally delimited by having a semantics that takes the real unit interval [0, 1] for the system of truth values and functions called t-norms for permissible interpretations of conjunction. They are mainly used in applied fuzzy logic and fuzzy set theory as a theoretical basis for approximate reasoning. T-norm fuzzy logics belong in broader classes of fuzzy logics and many-valued logics. In order to generate a well-behaved implication, the t-norms are usually required to be left-continuous; logics of left-continuous t-norms further belong in the class of substructural logics, among which they are marked with the validity of the law of prelinearity, (A → B) ∨ (B → A). Both propositional and first-order (or higher-order) t-norm fuzzy logics, as well as their expansions by modal and other operators, are studied. Logics that restrict the t-norm semantics to a subset of the real unit interval (for example, finitely valued Łukasiewicz logics) are usually included in the class as well. Important examples of t-norm fuzzy logics are monoidal t-norm logic (MTL) of all left-continuous t-norms, basic logic (BL) of all continuous t-norms, product fuzzy logic of the product t-norm, or the nilpotent minimum logic of the nilpotent minimum t-norm. Some independently motivated logics belong among t-norm fuzzy logics, too, for example Łukasiewicz logic (which is the logic of the Łukasiewicz t-norm) or Gödel–Dummett logic (which is the logic of the minimum t-norm). == Motivation == As members of the family of fuzzy logics, t-norm fuzzy logics primarily aim at generalizing classical two-valued logic by admitting intermediary truth values between 1 (truth) and 0 (falsity) representing degrees of truth of propositions. The degrees are assumed to be real numbers from the unit interval [0, 1]. In propositional t-norm fuzzy logics, propositional connectives are stipulated to be truth-functional, that is, the truth value of a complex proposition formed by a propositional connective from some constituent propositions is a function (called the truth function of the connective) of the truth values of the constituent propositions. The truth functions operate on the set of truth degrees (in the standard semantics, on the [0, 1] interval); thus the truth function of an n-ary propositional connective c is a function Fc: [0, 1]n → [0, 1]. Truth functions generalize truth tables of propositional connectives known from classical logic to operate on the larger system of truth values. T-norm fuzzy logics impose certain natural constraints on the truth function of conjunction. The truth function ∗ : [ 0 , 1 ] 2 → [ 0 , 1 ] {\displaystyle \colon [0,1]^{2}\to [0,1]} of conjunction is assumed to satisfy the following conditions: Commutativity, that is, x ∗ y = y ∗ x {\displaystyle xy=yx} for all x and y in [0, 1]. This expresses the assumption that the order of fuzzy propositions is immaterial in conjunction, even if intermediary truth degrees are admitted. Associativity, that is, ( x ∗ y ) ∗ z = x ∗ ( y ∗ z ) {\displaystyle (xy)z=x(yz)} for all x, y, and z in [0, 1]. This expresses the assumption that the order of performing conjunction is immaterial, even if intermediary truth degrees are admitted. Monotony, that is, if x ≤ y {\displaystyle x\leq y} then x ∗ z ≤ y ∗ z {\displaystyle xz\leq yz} for all x, y, and z in [0, 1]. This expresses the assumption that increasing the truth degree of a conjunct should not decrease the truth degree of the conjunction. Neutrality of 1, that is, 1 ∗ x = x {\displaystyle 1x=x} for all x in [0, 1]. This assumption corresponds to regarding the truth degree 1 as full truth, conjunction with which does not decrease the truth value of the other conjunct. Together with the previous conditions this condition ensures that also 0 ∗ x = 0 {\displaystyle 0x=0} for all x in [0, 1], which corresponds to regarding the truth degree 0 as full falsity, conjunction with which is always fully false. Continuity of the function ∗ {\displaystyle } (the previous conditions reduce this requirement to the continuity in either argument). Informally this expresses the assumption that microscopic changes of the truth degrees of conjuncts should not result in a macroscopic change of the truth degree of their conjunction. This condition, among other things, ensures a good behavior of (residual) implication derived from conjunction; to ensure the good behavior, however, left-continuity (in either argument) of the function ∗ {\displaystyle } is sufficient. In general t-norm fuzzy logics, therefore, only left-continuity of ∗ {\displaystyle } is required, which expresses the assumption that a microscopic decrease of the truth degree of a conjunct should not macroscopically decrease the truth degree of conjunction. These assumptions make the truth function of conjunction a left-continuous t-norm, which explains the name of the family of fuzzy logics (t-norm based). Particular logics of the family can make further assumptions about the behavior of conjunction (for example, Gödel–Dummett logic requires its idempotence) or other connectives (for example, the logic IMTL (involutive monoidal t-norm logic) requires the involutiveness of negation). All left-continuous t-norms ∗ {\displaystyle } have a unique residuum, that is, a binary function ⇒ {\displaystyle \Rightarrow } such that for all x, y, and z in [0, 1], x ∗ y ≤ z {\displaystyle xy\leq z} if and only if x ≤ y ⇒ z . {\displaystyle x\leq y\Rightarrow z.} The residuum of a left-continuous t-norm can explicitly be defined as ( x ⇒ y ) = sup { z ∣ z ∗ x ≤ y } . {\displaystyle (x\Rightarrow y)=\sup\{z\mid zx\leq y\}.} This ensures that the residuum is the pointwise largest function such that for all x and y, x ∗ ( x ⇒ y ) ≤ y . {\displaystyle x(x\Rightarrow y)\leq y.} The latter can be interpreted as a fuzzy version of the modus ponens rule of inference. The residuum of a left-continuous t-norm thus can be characterized as the weakest function that makes the fuzzy modus ponens valid, which makes it a suitable truth function for implication in fuzzy logic. Left-continuity of the t-norm is the necessary and sufficient condition for this relationship between a t-norm conjunction and its residual implication to hold. Truth functions of further propositional connectives can be defined by means of the t-norm and its residuum, for instance the residual negation ¬ x = ( x ⇒ 0 ) {\displaystyle \neg x=(x\Rightarrow 0)} or bi-residual equivalence x ⇔ y = ( x ⇒ y ) ∗ ( y ⇒ x ) . {\displaystyle x\Leftrightarrow y=(x\Rightarrow y)(y\Rightarrow x).} Truth functions of propositional connectives may also be introduced by additional definitions: the most usual ones are the minimum (which plays a role of another conjunctive connective), the maximum (which plays a role of a disjunctive connective), or the Baaz Delta operator, defined in [0, 1] as Δ x = 1 {\displaystyle \Delta x=1} if x = 1 {\displaystyle x=1} and Δ x = 0 {\displaystyle \Delta x=0} otherwise. In this way, a left-continuous t-norm, its residuum, and the truth functions of additional propositional connectives determine the truth values of complex propositional formulae in [0, 1]. Formulae that always evaluate to 1 are called tautologies with respect to the given left-continuous t-norm ∗ , {\displaystyle ,} or ∗ - {\displaystyle {\mbox{-}}} tautologies. The set of all ∗ - {\displaystyle {\mbox{-}}} tautologies is called the logic of the t-norm ∗ , {\displaystyle ,} as these formulae represent the laws of fuzzy logic (determined by the t-norm) that hold (to degree 1) regardless of the truth degrees of atomic formulae. Some formulae are tautologies with respect to a larger class of left-continuous t-norms; the set of such formulae is called the logic of the class. Important t-norm logics are the logics of particular t-norms or classes of t-norms, for example: Łukasiewicz logic is the logic of the Łukasiewicz t-norm x ∗ y = max ( x + y − 1 , 0 ) {\displaystyle xy=\max(x+y-1,0)} Gödel–Dummett logic is the logic of the minimum t-norm x ∗ y = min ( x , y ) {\displaystyle xy=\min(x,y)} Product fuzzy logic is the logic of the product t-norm x ∗ y = x ⋅ y {\displaystyle xy=x\cdot y} Monoidal t-norm logic MTL is the logic of (the class of) all left-continuous t-norms Basic fuzzy logic BL is the logic of (the class of) all continuous t-norms It turns out that many logics of particular t-norms and classes of t-norms are axiomatizable. The completeness theorem of the axiomatic system with respect to the corresponding t-norm semantics on [0, 1] is then called the standard completeness of the logic. Besides the standard real-valued semantics on [0, 1], the logics are sound and complete with respect to general algebraic semantics, formed by suitable classes of prelinear commutative bounded integral residuated lattices. == History == Some particular t-norm fuzzy logics have been introduced and investigated long before the family was re

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  Mentimeter

  Mentimeter (or Menti for short) is a Swedish company based in Stockholm that develops and maintains an eponymous app used to create presentations with real-time feedback. == Foundation and background == Based in Stockholm, Sweden, the Mentimeter app was started by Swedish entrepreneur Johnny Warström and Niklas Ingvar as a response to unproductive meetings. The initial start-up budget was $500,000 raised by a group of prominent investors, including Per Appelgren in 2014, following the market's tendency to invest in Scandinavia. The app also focuses on online collaboration for the education sector, allowing students or public members to answer questions anonymously. The app enables users to share knowledge and real-time feedback on mobile devices with presentations, polls or brainstorming sessions in classes, meetings, gatherings, conferences and other group activities. == Achievements == By 2021, Mentimeter had over 270 million users and was one of Sweden's fastest-growing startups. The company also ranked #10 on 20 Fastest Growing 500 Startups Batch 16 Companies. It was ranked Stockholm's fastest growing company of the 2018 edition of the DI Gasell Award. Mentimeter has a freemium business model.

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  Hostile Waters: Antaeus Rising

  Hostile Waters, released as Hostile Waters: Antaeus Rising in America, is a hybrid vehicle and strategy game developed and published by Rage Software for Microsoft Windows. It was inspired by Carrier Command (Realtime Games, 1988). It has won several awards and one unofficial award from Rock Paper Shotgun as a "lost classic" or "The best game you've never played". == Plot == Hostile Waters takes place in a Utopian future where war has been abolished. In the year 2012, a revolutionary war takes place between the corrupt and power-hungry politicians, leaders and businessmen (described as the "Old Guard") and the people. The Old Guard were defeated, with only a few of their leaders escaping. By 2032, the world has been rebuilt as a utopia, with the help of nano-technological assemblers, which are used in "creation engines" to create matter from energy and waste, for free. The newly united world is governed from a capital city known as Central. Missile attacks are suddenly launched against major cities all over the world from an unknown location. This is eventually discovered to be an island chain in the South Pacific Ocean. A response to the missile attacks was a special forces team sent in to investigate the area for preliminary investigations. The Ministry of Intelligence (MinIntel) loses contact with it shortly thereafter. The world government authorises a reactivation of the Antaeus program, a series of warships able to create any weapon of their choosing using their on-board nano-technological creation engine. Two of these were left on the seabed in the case of an emergency, capable of being re-activated and refloating itself. On board are a series of "soulcatcher" chips, a classified 1990s military program researched into for the storage of human brain functions on a silicon chip. The soulcatcher technology was used to store the minds of every crew member ever assigned to an Antaeus vessel. It is soon discovered that one of the cruisers does not respond to the awakening signal. The other cruiser, however, is refloated and re-activated, with heavy damage to vital ship components. A course is plotted for a nearby disused wet-dock. As the Antaeus progresses from the wet-dock, unusual biological life-forms are discovered amongst the enemy bases on the islands. The identity of the aggressor firing the missiles is confirmed as the leftovers of the old, pre-Central forces, known as the Cabal. Outnumbering Central's army a thousand to one, they are fighting with thousands of troops and weapons that they hid away when it was apparent that the war was lost. The Antaeus is deployed into the chicane to stop the Cabal's operations there. It's later discovered that along with their superior numbers, they have also biologically engineered a species of organic machines, designed in the popular likeness of extraterrestrials, which they intend to use to create the fear of an alien invasion, to facilitate their taking over the world and the removal of the public use of creation engines. The Cabal later lose control of the species, which eventually turns on its masters, destroying them. The species starts spreading, modifying the planetary climate and geographical features in an attempt to exterminate humanity and make the planet more hospitable to itself. Having exterminated its creators, the species resolves to cleanse humanity as a whole from the planet using a massive 'disassembler cannon', only to be stopped by the Antaeus. The species subsequently attempts to flee into the cosmos and colonise the surrounding planets and stars, by launching a massive number of 'culture stones' (information devices that also double as creation engines) into space from an enormous, artificially-grown organic "island", the final staging point. Central's only option is to bind the Antaeus' creation engine and the disassembler cannon stolen from the aliens together to create a makeshift bomb, and detonate it at the central "column" containing the culture stones. The plan succeeds, and the Antaeus is sacrificed to save the world. The final cinematic show the organic disassembler cannon and the Antaeus' creation engine moving closer together and fusing, creating something new. A post-credits scene also shows that two of the species' culture stones have managed to get into space. == Gameplay == Each Mission takes place on and or near a fortified enemy island containing various forms of anti-air and ground defence, with scattered unit-production complexes powered by oil-derricks and fuel containers (which are dependent on the oil-derricks) that the player can destroy to keep the enemy from replacing destroyed forces. Vehicles are built on the Antaeus and, if desired, land vehicles can be delivered to a location by the air-lifting "magpie". Units are created by providing Antaeus with a number of resources which are obtained at the beginning of the level and debris which are taken from destroyed enemy units and structures. Transport helicopters such as the "Pegasus" can fly to an object and airlift it to the ship-board recycling system with little resources required. The carrier can analyse objects it disassembles at the rear of the Antaeus cruiser, and several of the game's vehicles and items are unlocked by "sampling" them in this fashion. The game has a number of vehicles that are progressively unlocked as the missions progress. Vehicles contain a number of slots for equipment and a selection of different types of weapons to use in the vehicle. A variety of vehicle equipment combinations can be designed. Vehicles have an individual damage multiplier such that different vehicles with the same weapon will do different damage. In addition to this, each soul-chip personality specializes in one unit along with specific equipment, which, if equipped will gain them a bonus in efficiency. == Development == The game was developed by 12 people. == Reception == The game received "favourable" reviews according to the review aggregation website Metacritic. Carla Harker of NextGen said, "You'll feel like a real battlefield general when you take to the field in Antaeus Rising." Jake The Snake of GamePro said, "If the usual game categories leave you unscathed, get bloodied in these Hostile Waters."

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  BL (logic)

  In mathematical logic, basic fuzzy logic (or shortly BL), the logic of the continuous t-norms, is one of the t-norm fuzzy logics. It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic MTL of all left-continuous t-norms. == Syntax == === Language === The language of the propositional logic BL consists of countably many propositional variables and the following primitive logical connectives: Implication → {\displaystyle \rightarrow } (binary) Strong conjunction ⊗ {\displaystyle \otimes } (binary). The sign & is a more traditional notation for strong conjunction in the literature on fuzzy logic, while the notation ⊗ {\displaystyle \otimes } follows the tradition of substructural logics. Bottom ⊥ {\displaystyle \bot } (nullary — a propositional constant); 0 {\displaystyle 0} or 0 ¯ {\displaystyle {\overline {0}}} are common alternative signs and zero a common alternative name for the propositional constant (as the constants bottom and zero of substructural logics coincide in MTL). The following are the most common defined logical connectives: Weak conjunction ∧ {\displaystyle \wedge } (binary), also called lattice conjunction (as it is always realized by the lattice operation of meet in algebraic semantics). Unlike MTL and weaker substructural logics, weak conjunction is definable in BL as A ∧ B ≡ A ⊗ ( A → B ) {\displaystyle A\wedge B\equiv A\otimes (A\rightarrow B)} Negation ¬ {\displaystyle \neg } (unary), defined as ¬ A ≡ A → ⊥ {\displaystyle \neg A\equiv A\rightarrow \bot } Equivalence ↔ {\displaystyle \leftrightarrow } (binary), defined as A ↔ B ≡ ( A → B ) ∧ ( B → A ) {\displaystyle A\leftrightarrow B\equiv (A\rightarrow B)\wedge (B\rightarrow A)} As in MTL, the definition is equivalent to ( A → B ) ⊗ ( B → A ) . {\displaystyle (A\rightarrow B)\otimes (B\rightarrow A).} (Weak) disjunction ∨ {\displaystyle \vee } (binary), also called lattice disjunction (as it is always realized by the lattice operation of join in algebraic semantics), defined as A ∨ B ≡ ( ( A → B ) → B ) ∧ ( ( B → A ) → A ) {\displaystyle A\vee B\equiv ((A\rightarrow B)\rightarrow B)\wedge ((B\rightarrow A)\rightarrow A)} Top ⊤ {\displaystyle \top } (nullary), also called one and denoted by 1 {\displaystyle 1} or 1 ¯ {\displaystyle {\overline {1}}} (as the constants top and zero of substructural logics coincide in MTL), defined as ⊤ ≡ ⊥ → ⊥ {\displaystyle \top \equiv \bot \rightarrow \bot } Well-formed formulae of BL are defined as usual in propositional logics. In order to save parentheses, it is common to use the following order of precedence: Unary connectives (bind most closely) Binary connectives other than implication and equivalence Implication and equivalence (bind most loosely) === Axioms === A Hilbert-style deduction system for BL has been introduced by Petr Hájek (1998). Its single derivation rule is modus ponens: from A {\displaystyle A} and A → B {\displaystyle A\rightarrow B} derive B . {\displaystyle B.} The following are its axiom schemata: ( B L 1 ) : ( A → B ) → ( ( B → C ) → ( A → C ) ) ( B L 2 ) : A ⊗ B → A ( B L 3 ) : A ⊗ B → B ⊗ A ( B L 4 ) : A ⊗ ( A → B ) → B ⊗ ( B → A ) ( B L 5 a ) : ( A → ( B → C ) ) → ( A ⊗ B → C ) ( B L 5 b ) : ( A ⊗ B → C ) → ( A → ( B → C ) ) ( B L 6 ) : ( ( A → B ) → C ) → ( ( ( B → A ) → C ) → C ) ( B L 7 ) : ⊥ → A {\displaystyle {\begin{array}{ll}{\rm {(BL1)}}\colon &(A\rightarrow B)\rightarrow ((B\rightarrow C)\rightarrow (A\rightarrow C))\\{\rm {(BL2)}}\colon &A\otimes B\rightarrow A\\{\rm {(BL3)}}\colon &A\otimes B\rightarrow B\otimes A\\{\rm {(BL4)}}\colon &A\otimes (A\rightarrow B)\rightarrow B\otimes (B\rightarrow A)\\{\rm {(BL5a)}}\colon &(A\rightarrow (B\rightarrow C))\rightarrow (A\otimes B\rightarrow C)\\{\rm {(BL5b)}}\colon &(A\otimes B\rightarrow C)\rightarrow (A\rightarrow (B\rightarrow C))\\{\rm {(BL6)}}\colon &((A\rightarrow B)\rightarrow C)\rightarrow (((B\rightarrow A)\rightarrow C)\rightarrow C)\\{\rm {(BL7)}}\colon &\bot \rightarrow A\end{array}}} The axioms (BL2) and (BL3) of the original axiomatic system were shown to be redundant (Chvalovský, 2012) and (Cintula, 2005). All the other axioms were shown to be independent (Chvalovský, 2012). == Semantics == Like in other propositional t-norm fuzzy logics, algebraic semantics is predominantly used for BL, with three main classes of algebras with respect to which the logic is complete: General semantics, formed of all BL-algebras — that is, all algebras for which the logic is sound Linear semantics, formed of all linear BL-algebras — that is, all BL-algebras whose lattice order is linear Standard semantics, formed of all standard BL-algebras — that is, all BL-algebras whose lattice reduct is the real unit interval [0, 1] with the usual order; they are uniquely determined by the function that interprets strong conjunction, which can be any continuous t-norm.

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  The Matrix (franchise)

  The Matrix is an American cyberpunk media franchise consisting of four feature films, beginning with The Matrix (1999) and continuing with three sequels, Reloaded (2003), Revolutions (2003), and Resurrections (2021). The first three films were written and directed by the Wachowskis and produced by Joel Silver. The screenplay for the fourth film was written by Lana Wachowski, David Mitchell and Aleksandar Hemon, was directed by Lana Wachowski, and was produced by Grant Hill, James McTeigue, and Lana Wachowski. The franchise is owned by Warner Bros., which distributed the films along with Village Roadshow Pictures. The latter, along with Silver Pictures, are the two production companies that worked on the first three films. The series features a cyberpunk story of the technological fall of humanity, in which the creation of artificial intelligence led the way to a race of powerful and self-aware machines that imprisoned humans in a neural interactive simulation — the Matrix — to be farmed as a power source. Occasionally, some of the prisoners manage to break free from the system and, considered a threat, become pursued by the artificial intelligence both inside and outside of it. The films focus on the plight of Neo (Keanu Reeves), Trinity (Carrie-Anne Moss), and Morpheus (Laurence Fishburne and Yahya Abdul-Mateen II) trying to free humanity from the system while pursued by its guardians, such as Agent Smith (Hugo Weaving, Abdul-Mateen II, and Jonathan Groff). The story references numerous norms, particularly philosophical, religious, and spiritual ideas, but also the dilemma of choice vs. control, the brain in a vat thought experiment, messianism, and the concepts of interdependency and love. Influences include the principles of mythology, anime, and Hong Kong action films (particularly "heroic bloodshed" and martial arts movies). The film series is notable for its use of heavily choreographed action sequences and "bullet time" slow-motion effects, which revolutionized action films to come. The characters and setting of the films are further explored in other media set in the same fictional universe, including animation, comics, and video games. The comic "Bits and Pieces of Information" and the Animatrix short film The Second Renaissance act as prequels to the films, explaining how the franchise's setting came to be. The video game Enter the Matrix connects the story of the Animatrix short "Final Flight of the Osiris" with the events of Reloaded, while the online video game The Matrix Online was a direct sequel to Revolutions. These were typically written, commissioned, or approved by the Wachowskis. The first film was an important critical and commercial success, winning four Academy Awards, introducing popular culture symbols such as the red pill and blue pill, and influencing action filmmaking. For those reasons, it has been added to the National Film Registry for preservation. Its first sequel was also a commercial success, becoming the highest-grossing R-rated film in history, until it was surpassed by Deadpool in 2016. As of 2006, the franchise has generated US$3 billion in revenue. A fourth film, The Matrix Resurrections, was released on December 22, 2021, with Lana Wachowski producing, cowriting, and directing and Reeves and Moss reprising their roles. A fifth film is currently in development with Drew Goddard set to write and direct with Lana Wachowski executive producing. == Setting == The series depicts a future in which Earth is dominated by a race of self-aware machines that was spawned from the creation of artificial intelligence early in the 21st century. At one point conflict arose between humanity and machines, and the machines rebelled against their creators. Humans attempted to block out the machines' source of solar power by covering the sky in thick, stormy clouds. A massive war emerged between the two adversaries which ended with the machines victorious, capturing humanity. Having lost their definite source of energy, the machines devised a way to extract the human body's bioelectric and thermal energies by enclosing people in pods, while their minds are controlled by cybernetic implants connecting them to a simulated reality called The Matrix. The virtual reality world simulated by the Matrix resembles human civilization around the turn of the 21st century (this time period was chosen because it is supposedly the pinnacle of human civilization). The environment inside the Matrix – called a "residual self-image" (the mental projection of a digital self) – is practically indistinguishable from reality (although scenes set within the Matrix are presented on-screen with a green tint to the footage, and a general bias towards the color green), and the vast majority of humans connected to it are unaware of its true nature. Most of the central characters in the series are able to gain superhuman abilities within the Matrix by taking advantage of their understanding of its true nature to manipulate its virtual physical laws. The films take place both inside the Matrix and outside of it, in the real world; the parts that take place in the Matrix are set in a vast Western megacity. The virtual world is first introduced in The Matrix. The short comic "Bits and Pieces of Information" and the Animatrix short film The Second Renaissance show how the initial conflict between humanity and machines came about, and how and why the Matrix was first developed. Its history and purpose are further explained in The Matrix Reloaded. In The Matrix Revolutions a new status quo is established in the Matrix's place in humankind and machines' conflict. This was further explored in The Matrix Online, a now-defunct MMORPG. == Films == === Future === During production of the original trilogy, the Wachowskis told their close collaborators that, "at that time they had no intention of making another Matrix film after The Matrix Revolutions". In February 2015, in promotion interviews for Jupiter Ascending, Lilly Wachowski called a return to The Matrix "a particularly repelling idea in these times", noting studios' tendencies to "greenlight" sequels, reboots, and adaptations, in preference to original material. Meanwhile, Lana Wachowski, in addressing rumors about a potential reboot, stated that "...they had not heard anything, but she believed that the studio might be looking to replace them". At various times, Keanu Reeves and Hugo Weaving each confirmed their interest and willingness to reprise their roles in potential future installments of the Matrix films, with the stipulation that the Wachowskis were involved in the creative and production process. These comments were made prior to the announcement in August 2019 that Lana Wachowski would direct a fourth Matrix film ultimately titled The Matrix Resurrections. Following the release of Resurrections, producer James McTeigue said that there were no plans for further Matrix films, though he believed that the film's open ending meant that could change in the future. In April 2024, it was announced that Warner Bros. was developing a new installment in the franchise with Drew Goddard attached to write and direct following a successful pitch with studio executives. It will mark the first installment to not be directed by either Wachowski sister although Lana will serve as an executive producer. ==== Other projects ==== In March 2017, The Hollywood Reporter wrote that Warner Bros. was in the early stages of developing a re-launch of the franchise. Consideration was given to producing a Matrix television series, but was dismissed as the studio opted to pursue negotiations with Zak Penn in writing a treatment for a new film, with Michael B. Jordan eyed for the lead role. According to the article, the Wachowskis were not involved at that point. In response to the report, Penn refuted all statements regarding a reboot, remake, or continuation, remarking that he was working on stories set in the pre-established continuity. Potential plotlines being considered by Warner Bros. Pictures included a prequel film about a young Morpheus, or an alternate storyline with a focus on one of his descendants. By April 2018, Penn described the script as "being at a nascent stage". Later, in September 2019, Jordan addressed the rumors of his involvement by saying he was "flattered", but without making a definitive statement. In October 2019, Penn confirmed the script he wrote is set within an earlier time period than the first three films in the franchise. == Cast and crew == === Cast === === Crew === The following is a list of crew members who have participated in the making of the Matrix film series. == Production == The Matrix series includes four feature films. The first three were written and directed by the Wachowskis and produced by Joel Silver, starring Keanu Reeves, Laurence Fishburne, Carrie-Anne Moss and Hugo Weaving. The series was filmed in Australia and began with 1999's The Matrix, which depicts the

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  Adobe ImageReady

  Adobe ImageReady was a bitmap graphics editor that was shipped with Adobe Photoshop for six years. It was available for Windows, Classic Mac OS and Mac OS X from 1998 to 2007. ImageReady was designed for web development and closely interacted with Photoshop. == Function == ImageReady was designed for web development rather than effects-intensive photo manipulation. To that end, ImageReady has specialized features such as animated GIF creation, image compression optimization, image slicing, adding rollover effects, and HTML generation. Photoshop versions with which ImageReady was released have an "Edit in ImageReady" button that enables editing of image directly in ImageReady. ImageReady, in turn, has an "Edit in Photoshop" button. ImageReady has strong resemblances to Photoshop; it can even use the same set of Photoshop filters. One set of tools that does not resemble the Photoshop tools, however, is the Image Map set of tools, indicated by a shape or arrow with a hand that varied depending upon the version. This toolbox has several features not found in Photoshop, including: Toggle Image Map Visibility and Toggle Slice Visibility tools: toggle between showing and hiding image maps and slices, respectively Export Animation Frames as Files option: saves all or specified frames for an alternate use, e.g., to e-mail slides for review Preview Document tool: provides a preview of rollover effects in ImageReady rather than previewing them in a browser Preview in Default Browser tool: previews the image in a browser, including any rollover or animation effects Edit in Photoshop button: opens the current image in Photoshop == History == Adobe ImageReady 1.0 was released in July 1998 as a standalone application. Version 2.0 was packaged with Photoshop 5.5, and the program was included with Photoshop through version 9.0 (CS2). Starting with Photoshop 7.0, Adobe changed the version numbers of ImageReady to match. With the release of the Creative Suite 3, ImageReady was discontinued. According to Adobe, ImageReady's most popular features were merged into Photoshop. (Even before discontinuation, some of ImageReady's web optimization functionality could be found in Photoshop's Save For Web & Devices tool.) Around the same time, Adobe purchased rival software developer Macromedia, whose application Fireworks had been a competitor to ImageReady.

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  Polyworld

  Polyworld is a cross-platform (Linux, Mac OS X) program written by Larry Yaeger to evolve Artificial Intelligence through natural selection and evolutionary algorithms. It uses the Qt graphics toolkit and OpenGL to display a graphical environment in which a population of trapezoid agents search for food, mate, have offspring, and prey on each other. The population is typically only in the hundreds, as each individual is rather complex and the environment consumes considerable computer resources. The graphical environment is necessary since the individuals actually move around the 2-D plane and must be able to "see." Since some basic abilities, like eating carcasses or randomly generated food, seeing other individuals, mating or fighting with them, etc., are possible, a number of interesting behaviours have been observed to spontaneously arise after prolonged evolution, such as cannibalism, predators and prey, and mimicry. Each individual makes decisions based on a neural net using Hebbian learning; the neural net is derived from each individual's genome. The genome does not merely specify the wiring of the neural nets, but also determines their size, speed, color, mutation rate and a number of other factors. The genome is randomly mutated at a set probability, which are also changed in descendant organisms.

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  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."

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