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  Legendre moment

  In mathematics, Legendre moments are a type of image moment and are achieved by using the Legendre polynomial. Legendre moments are used in areas of image processing including: pattern and object recognition, image indexing, line fitting, feature extraction, edge detection, and texture analysis. Legendre moments have been studied as a means to reduce image moment calculation complexity by limiting the amount of information redundancy through approximation. == Legendre moments == Source: With order of m + n, and object intensity function f(x,y): L m n = ( 2 m + 1 ) ( 2 n + 1 ) 4 ∫ − 1 1 ∫ − 1 1 P m ( x ) P n ( y ) f ( x , y ) d x d y {\displaystyle L_{mn}={\frac {(2m+1)(2n+1)}{4}}\int \limits _{-1}^{1}\int \limits _{-1}^{1}P_{m}(x)P_{n}(y)f(x,y)\,dx\,dy} where m,n = 1, 2, 3, ...∞ with the nth-order Legendre polynomials being: P n ( x ) = ∑ k = 0 n a k , n x k = ( − 1 ) n 2 n n ! ( d d x ) [ ( 1 − x 2 ) n ] {\displaystyle P_{n}(x)=\sum _{k=0}^{n}a_{k,n}x^{k}={\frac {(-1)^{n}}{2^{n}n!}}\left({\frac {d}{dx}}\right)[(1-x^{2})^{n}]} which can also be written: P n ( x ) = ∑ k = 0 D ( n ) ( − 1 ) k ( 2 n − 2 k ) ! 2 n k ! ( n − k ) ! ( n − 2 k ) ! x n − 2 k = ( 2 n ) ! 2 n ( n ! ) 2 x n − ( 2 n − 2 ) ! 2 n 1 ! ( n − 1 ) ! ( n − 2 ) ! x n − 2 + ⋯ {\displaystyle {\begin{aligned}P_{n}(x)&=\sum _{k=0}^{D(n)}(-1)^{k}{\frac {(2n-2k)!}{2^{n}k!(n-k)!(n-2k)!}}x^{n-2k}\\[5pt]&={\frac {(2n)!}{2^{n}(n!)^{2}}}x^{n}-{\frac {(2n-2)!}{2^{n}1!(n-1)!(n-2)!}}x^{n-2}+\cdots \end{aligned}}} where D(n) = floor(n/2). The set of Legendre polynomials {Pn(x)} form an orthogonal set on the interval [−1,1]: ∫ − 1 1 P n ( x ) P m ( x ) d x = 2 2 n + 1 δ n m {\displaystyle \int _{-1}^{1}P_{n}(x)P_{m}(x)\,dx={\frac {2}{2n+1}}\delta _{nm}} A recurrence relation can be used to compute the Legendre polynomial: ( n + 1 ) P n + 1 ( x ) − ( 2 n + 1 ) x P n ( x ) + n P n − 1 ( x ) = 0 {\displaystyle (n+1)P_{n+1}(x)-(2n+1)xP_{n}(x)+nP_{n-1}(x)=0} f(x,y) can be written as an infinite series expansion in terms of Legendre polynomials [−1 ≤ x,y ≤ 1.]: f ( x , y ) = ∑ m = 0 ∞ ∑ n = 0 ∞ λ m n P m ( x ) P n ( y ) {\displaystyle f(x,y)=\sum _{m=0}^{\infty }\sum _{n=0}^{\infty }\lambda _{mn}P_{m}(x)P_{n}(y)}

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  A.I.s

  A.I.s is a themed anthology of science fiction short works edited by American writers Jack Dann and Gardner Dozois. It was first published in paperback by Ace Books in December 2004. It was reissued as an ebook by Baen Books in June 2013. The book collects ten novelettes and short stories by various science fiction authors, together with a preface by the editors. == Contents == "Preface" (Jack Dann and Gardner Dozois) "Antibodies" (Charles Stross) "Trojan Horse" (Michael Swanwick) "Birth Day" (Robert Reed) "The Hydrogen Wall" (Gregory Benford) "The Turing Test" (Chris Beckett) "Dante Dreams" (Stephen Baxter) "The Names of All the Spirits" (J. R. Dunn) "From the Corner of My Eye" (Alexander Glass) "Halfjack" (Roger Zelazny) "Computer Virus" (Nancy Kress)

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  The Way (novel series)

  The Way series is a trilogy of science fiction novels and one short story by American author Greg Bear published from 1985 to 1999. The first novel was Eon (1985), followed by a sequel, Eternity and a prequel, Legacy. It also includes The Way of All Ghosts, a short story that falls between Legacy and Eon. == Novels == === Eon === Eon chronicles the appearance and discovery of the Thistledown, and its subsequent effect on humanity. In the early 21st century, the United States and the USSR are on the verge of nuclear war. In that tense political climate, an asteroid appears out of near space after an unusual supernova and settles into an extremely elliptical orbit near Earth orbit. The two nations each try to claim this mysterious object, which appears to be a virtual duplicate of Juno. It is hollow and contains seven vast terraformed chambers. Two of the chambers contain cities long abandoned by human beings who seemed to come from Earth's future. The asteroid is called the Thistledown by its builders. A startling discovery is that it is bigger inside than outside. The seventh chamber appears to stretch into infinity. The human inhabitants of the Thistledown come from an alternate timeline, approximately 1000 years in the future. In their timeline, human civilization was nearly destroyed by the "Death", a calamitous World War involving nuclear weapons. The Death occurred at approximately the same time as the appearance of the Thistledown in the present time. Its presence threatens to cause the Death to occur on the current timeline as well. An expedition is sent down the seemingly infinite seventh chamber (The "Way", as it is known) where it encounters the descendants of humanity. The high technology of this civilization, known as the Hexamon, has control over genetic engineering, human augmentation, and matter itself. The Hexamon includes several alien species who have come to live with humanity's descendants. The Hexamon itself is at war with an alien race known as the Jarts from further down the corridor still. In 2007, CGSociety organised a "CG Challenge" based upon Eon === Eternity === Jarts, politics, and technology make up the second book in the series: Eternity. The Jart religion is based on the preservation of all data, which encompasses all life forms, past and present, and sending that data to the Jarts' future masters, their descendants. === Legacy === In the third book (a prequel, set in the time before Eon), Legacy, soldier Olmy ap Sennon is sent to spy on a group of dissidents who have used the spacetime tunnel of "the Way" (introduced in Eon) to colonize the alien world of Lamarckia, a planet with an ecosystem that learns from its changed environment in a way that resembles Lamarckian evolution. Its plants and animals turn out to actually be parts of continent-sized organisms. === "The Way of All Ghosts" === In the short story "The Way of All Ghosts" soldier Olmy ap Sennon is sent to close a lesion that formed out of a wayward gate into perfection. This story was published in 1999 in Far Horizons. == Fictional history of the Thistledown == Within the universe of The Way, the Thistledown is an asteroid starship built by hollowing out Juno and fitting it with mass-driver (rail gun) engines and thermonuclear drives. Inside the asteroid, seven giant "Chambers" are built, of which two host cities for the inhabitants, while others host machinery and recreation areas. The asteroid is prepared 500 years in the future, as told in Bear's novel Eon, and is engaged on a multi-generational journey to Epsilon Eridani, around which a habitable planet is known to circle. The journey is meant to take 60 years, as the ship can only maintain a velocity of 20% the speed of light. This limitation is removed after the technology of the Thistledown was improved to include inertial dampeners, allowing higher accelerations. Inhabiting the Thistledown are the best and brightest of Earth, who are quite diverse both culturally and politically. The Thistledown's society includes one transcendent genius, Konrad Korzenowski, whose preference for living in the Thistledown as compared with an outer universe, causes him to experiment with closed-geodesic space time in the Seventh Chamber, 20 years into the Thistledown's voyage. The results of his experiments are shattering in the extreme: He creates a unique pocket universe: The Way. == The Way == === Origin === The eponymous Way is an extension of the 7th Chamber, and was formed in the novels using the machinery of the 6th Chamber. This machinery is a selective inertial damper, developed by engineers within the Thistledown with twofold purpose—to permit the Thistledown to accelerate to the limit of its engines (up to 99% the speed of light) and to selectively dampen inertia within the vessel, e.g., water within waterways, high velocity train systems. The inertial dampening machinery within the 6th Chamber is anchored to the structure of the Thistledown, equally spaced around the chamber at the vertices of a regular heptagon. === Creation === At the creation, and rejoining of the Way to the Thistledown, the character Konrad Korzenowski and his engineers designed and 'built' the Way out of the in-folded geodesics of the inertial dampening field of the 6th Chamber machinery. This is described in the books by first considering the inertial dampening field: Within the Thistledown, the field envelops the asteroid, effectively isolating it from the Einsteinian Metrical Frame, permitting relative inertia to be ignored. The Thistledown was, at the time of activation, isolated from its continuum, but only selectively. Its matter and energy anchored it to its continuum and relative time, but its geometry and quantum entanglement had been strained by the inertial dampener, thus making it susceptible to superspace distortions, and therefore it could be affected by them negatively. Korzenowski, having been influenced by the earlier work of Vazquez on Earth, and in developing her work within the Thistledown, planned a radical extension of the inertial field of the 6th Chamber - effectively extending the field away to an infinite extent within the 7th Chamber. In order to do this effectively, he and his engineers modified a set of semi-sentient field calibration tools to build the first Clavicles. Unlike the field calibration tools from which they were descended, the Clavicles possessed the ability not only to manipulate the field, but extend it as an extension of the will of the operator. Already radical enough, Korzenowski and his team went further. By extending the field of the 6th Chamber from within the 7th Chamber of the Thistledown, they could then directly access what Vasquez had calculated within her own work—alternate world lines as non-gravity bent geodesics of superspace. Korzenowski thus 'felt' superspace within the 7th Chamber, selecting the infinite selection of possible alternate pocket universes accessible by the Clavicle to form, as a sheer act of will, the Way from his designs and his vision. The resulting structure was constructed, not of matter, but of previously in-folded superspace vectors now infinitely extended. (in the manner of Schwarzschild folded geometry, or of an asymptotic curve.) The Way was thus opened. The Way's geometry also gave rise to the Flaw - as superspace geometry of the field boundary was extended infinitely, so the folded geodesics of the field unfold in the geometric centre of the Way to form a singularity. This singularity, the Flaw, rests within the Way's plasma tube (which in turn is sustained by the Flaw). The Flaw 'produces' gravity by actively repulsing matter away from itself in an acceleration at the square of the distance away from itself. In addition, any object encircling the Flaw, and then exerting pressure against it, experiences this pressure as a translation force along the Flaw's length perpendicular to the direction of force. The motion thus induced is controllable by the angle at which an annular ring enclosure is pressed against the Flaw. The same spatial transform also can be used to turn tip turbines in order to generate electricity. The Flaw permits a violation of the First Law of Thermodynamics, therefore defining the Way as a perpetual motion machine of the First Order, making energy out of nothing. === Early history === The Way, as formed, was described by Bear as being in vacuum and did not consist of matter within its infinite length. Due to extremely slight ambiguity involved in its creation, the synchronicity between time within the Way, and within the Thistledown, was not exact. Thus, the Engineers spend two decades working to correct these faults using the Clavicles to manipulate the junction between Way and Thistledown. During this period, ambition led Korzenowksi to use the clavicle to open the first exploratory gate within the way, leading to the universe of the Jarts. Though the gate to Jart world was closed, the advanced Jarts neve

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  Emma Hart (computer scientist)

  Professor Emma Hart, FRSE (born 1967) is an English computer scientist known for her work in artificial immune systems (AIS), evolutionary computation and optimisation. She is a professor of computational intelligence at Edinburgh Napier University, editor-in-chief of the Journal of Evolutionary Computation (MIT Press), and D. Coordinator of the Future & Emerging Technologies (FET) Proactive Initiative, Fundamentals of Collective Adaptive Systems. == Early life and education == Hart was born in Middlesbrough, England in 1967. In 1990 she graduated from the University of Oxford with a first class BA(Hons) in Chemistry. She then continued her studies at the University of Edinburgh, graduating with an MSc in Artificial Intelligence in 1994, followed by a PhD that explored the use of immunology as an inspiration for computing, examining a range of techniques applied to optimization and data classification problems. Her dissertation was titled Immunology as a metaphor for computational information processing: Fact or fiction?, and her doctoral advisor was Peter Ross. == Career == In 2000 Hart took a position as a lecturer at Edinburgh Napier University, and was promoted to a Reader, Professor, and in 2008 Chair in Natural Computation. She is now director of the Centre of Algorithms, Visualisation and Evolving Systems (CAVES) group in the School of Computing. She continues to research in the area of developing novel bio-inspired techniques for solving a range of real-world optimisation and classification problems, as well as exploring the fundamental properties of immune-inspired computing through modelling and simulation. She is also involved in editorial activity and currently occupies the position of Editor-in-Chief of the Journal of Evolutionary Computation (MIT Press). Her interests lie in the area of bio-inspired computing, in particular artificial immune systems (AIS). She also undertakes research in three main areas: optimisation, self-organising/self-adaptive systems, and artificial intelligence. Hart is D. Coordinator of Fundamentals of Collective Adaptive Systems (FoCAS), a Future and Emerging Technologies Proactive Initiative funded by the European Commission under FP7. == Selected works == === Conference talks === Hart, Emma. "Lifelong learning in optimization (video)". 28th European Conference on Operational Research. The Association of European Operational Research Societies. Hart, Emma (December 2021). "Self-assembling robots and the potential of artificial evolution". TED talk 2021. === Journal articles === "An immune system approach to scheduling in changing environments". E.Hart, P.Ross. 1999. Proceedings of the 1st Annual Conference on Genetic and Evolutionary Computation (2), 1559–1566. "Exploiting the analogy between immunology and sparse distributed memories: A system for clustering non-stationary data". E.Hart, P.Ross. 2002. 1st International Conference on Artificial Immune Systems. "Evolutionary scheduling: A review". E Hart, P Ross, D Corne. 2005. Genetic Programming and Evolvable Machines 6(2), 191–220. DOI: https://doi.org/10.1007/s10710-005-7580-7 "Application areas of AIS: The past, the present and the future". E.Hart, J.Timmis. 2008. Applied soft computing 8(1), 191–201. DOI: https://doi.org/10.1016/j.asoc.2006.12.004 "Structure versus function: a topological perspective on immune networks". E.Hart, H.Bersini, F.Santos. 2010. Natural computing 9(3), 603–624. DOI: https://doi.org/10.1007/s11047-009-9138-8 "On the life-long learning capabilities of a nelli: A hyper-heuristic optimisation system". E.Hart, K.Sim. 2014. International Conference on Parallel Problem Solving from Nature, 282–291. DOI: https://doi.org/10.1007/978-3-319-10762-2_28 "A hyper-heuristic ensemble method for static job-shop scheduling". E.Hart, K.Sim. 2016. Evolutionary computation 24(4), 609-635. DOI: https://dx.doi.org/10.1162/EVCO_a_00183 == Awards and recognition == 2016, Featured article on Lifelong Learning in Optimisation, IFORS newsletter 2016, "A Combined Generative and Selective Hyper-heuristic for the Vehicle Routing Problem" presented at GECCO 2016 (Denver, USA), ACM 2016, "A Hybrid Parameter Control Approach Applied to a Diversity-based Multi-objective Memetic Algorithm for Frequency Assignment Problems" presented at WCCI 2016 (Vancouver, Canada), IEEE 2017, Keynote Speaker, 2017 International Joint Conference on Computational Intelligence 2018, Bronze Award in International Human-Competitive Awards (Humies), International Conference on Genetic and Evolutionary Computation, Kyoto Japan 2018, Nomination for best paper award, GECCO 18, Kyoto, Japan 2022, Elected Fellow of the Royal Society of Edinburgh

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  Cross-entropy method

  The cross-entropy (CE) method is a Monte Carlo method for importance sampling and optimization. It is applicable to both combinatorial and continuous problems, with either a static or noisy objective. The method approximates the optimal importance sampling estimator by repeating two phases: Draw a sample from a probability distribution. Minimize the cross-entropy between this distribution and a target distribution to produce a better sample in the next iteration. Reuven Rubinstein developed the method in the context of rare-event simulation, where tiny probabilities must be estimated, for example in network reliability analysis, queueing models, or performance analysis of telecommunication systems. The method has also been applied to the traveling salesman, quadratic assignment, DNA sequence alignment, max-cut and buffer allocation problems. == Estimation via importance sampling == Consider the general problem of estimating the quantity ℓ = E u [ H ( X ) ] = ∫ H ( x ) f ( x ; u ) d x {\displaystyle \ell =\mathbb {E} _{\mathbf {u} }[H(\mathbf {X} )]=\int H(\mathbf {x} )\,f(\mathbf {x} ;\mathbf {u} )\,{\textrm {d}}\mathbf {x} } , where H {\displaystyle H} is some performance function and f ( x ; u ) {\displaystyle f(\mathbf {x} ;\mathbf {u} )} is a member of some parametric family of distributions. Using importance sampling this quantity can be estimated as ℓ ^ = 1 N ∑ i = 1 N H ( X i ) f ( X i ; u ) g ( X i ) {\displaystyle {\hat {\ell }}={\frac {1}{N}}\sum _{i=1}^{N}H(\mathbf {X} _{i}){\frac {f(\mathbf {X} _{i};\mathbf {u} )}{g(\mathbf {X} _{i})}}} , where X 1 , … , X N {\displaystyle \mathbf {X} _{1},\dots ,\mathbf {X} _{N}} is a random sample from g {\displaystyle g\,} . For positive H {\displaystyle H} , the theoretically optimal importance sampling density (PDF) is given by g ∗ ( x ) = H ( x ) f ( x ; u ) / ℓ {\displaystyle g^{}(\mathbf {x} )=H(\mathbf {x} )f(\mathbf {x} ;\mathbf {u} )/\ell } . This, however, depends on the unknown ℓ {\displaystyle \ell } . The CE method aims to approximate the optimal PDF by adaptively selecting members of the parametric family that are closest (in the Kullback–Leibler sense) to the optimal PDF g ∗ {\displaystyle g^{}} . == Generic CE algorithm == Choose initial parameter vector v ( 0 ) {\displaystyle \mathbf {v} ^{(0)}} ; set t = 1. Generate a random sample X 1 , … , X N {\displaystyle \mathbf {X} _{1},\dots ,\mathbf {X} _{N}} from f ( ⋅ ; v ( t − 1 ) ) {\displaystyle f(\cdot ;\mathbf {v} ^{(t-1)})} Solve for v ( t ) {\displaystyle \mathbf {v} ^{(t)}} , where v ( t ) = argmax v ⁡ 1 N ∑ i = 1 N H ( X i ) f ( X i ; u ) f ( X i ; v ( t − 1 ) ) log ⁡ f ( X i ; v ) {\displaystyle \mathbf {v} ^{(t)}=\mathop {\textrm {argmax}} _{\mathbf {v} }{\frac {1}{N}}\sum _{i=1}^{N}H(\mathbf {X} _{i}){\frac {f(\mathbf {X} _{i};\mathbf {u} )}{f(\mathbf {X} _{i};\mathbf {v} ^{(t-1)})}}\log f(\mathbf {X} _{i};\mathbf {v} )} If convergence is reached then stop; otherwise, increase t by 1 and reiterate from step 2. In several cases, the solution to step 3 can be found analytically. Situations in which this occurs are When f {\displaystyle f\,} belongs to the natural exponential family When f {\displaystyle f\,} is discrete with finite support When H ( X ) = I { x ∈ A } {\displaystyle H(\mathbf {X} )=\mathrm {I} _{\{\mathbf {x} \in A\}}} and f ( X i ; u ) = f ( X i ; v ( t − 1 ) ) {\displaystyle f(\mathbf {X} _{i};\mathbf {u} )=f(\mathbf {X} _{i};\mathbf {v} ^{(t-1)})} , then v ( t ) {\displaystyle \mathbf {v} ^{(t)}} corresponds to the maximum likelihood estimator based on those X k ∈ A {\displaystyle \mathbf {X} _{k}\in A} . == Continuous optimization—example == The same CE algorithm can be used for optimization, rather than estimation. Suppose the problem is to maximize some function S {\displaystyle S} , for example, S ( x ) = e − ( x − 2 ) 2 + 0.8 e − ( x + 2 ) 2 {\displaystyle S(x)={\textrm {e}}^{-(x-2)^{2}}+0.8\,{\textrm {e}}^{-(x+2)^{2}}} . To apply CE, one considers first the associated stochastic problem of estimating P θ ( S ( X ) ≥ γ ) {\displaystyle \mathbb {P} _{\boldsymbol {\theta }}(S(X)\geq \gamma )} for a given level γ {\displaystyle \gamma \,} , and parametric family { f ( ⋅ ; θ ) } {\displaystyle \left\{f(\cdot ;{\boldsymbol {\theta }})\right\}} , for example the 1-dimensional Gaussian distribution, parameterized by its mean μ t {\displaystyle \mu _{t}\,} and variance σ t 2 {\displaystyle \sigma _{t}^{2}} (so θ = ( μ , σ 2 ) {\displaystyle {\boldsymbol {\theta }}=(\mu ,\sigma ^{2})} here). Hence, for a given γ {\displaystyle \gamma \,} , the goal is to find θ {\displaystyle {\boldsymbol {\theta }}} so that D K L ( I { S ( x ) ≥ γ } ‖ f θ ) {\displaystyle D_{\mathrm {KL} }({\textrm {I}}_{\{S(x)\geq \gamma \}}\|f_{\boldsymbol {\theta }})} is minimized. This is done by solving the sample version (stochastic counterpart) of the KL divergence minimization problem, as in step 3 above. It turns out that parameters that minimize the stochastic counterpart for this choice of target distribution and parametric family are the sample mean and sample variance corresponding to the elite samples, which are those samples that have objective function value ≥ γ {\displaystyle \geq \gamma } . The worst of the elite samples is then used as the level parameter for the next iteration. This yields the following randomized algorithm that happens to coincide with the so-called Estimation of Multivariate Normal Algorithm (EMNA), an estimation of distribution algorithm. === Pseudocode === // Initialize parameters μ := −6 σ2 := 100 t := 0 maxits := 100 N := 100 Ne := 10 // While maxits not exceeded and not converged while t < maxits and σ2 > ε do // Obtain N samples from current sampling distribution X := SampleGaussian(μ, σ2, N) // Evaluate objective function at sampled points S := exp(−(X − 2) ^ 2) + 0.8 exp(−(X + 2) ^ 2) // Sort X by objective function values in descending order X := sort(X, S) // Update parameters of sampling distribution via elite samples μ := mean(X(1:Ne)) σ2 := var(X(1:Ne)) t := t + 1 // Return mean of final sampling distribution as solution return μ == Related methods == Simulated annealing Genetic algorithms Harmony search Estimation of distribution algorithm Tabu search Natural Evolution Strategy Ant colony optimization algorithms

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  Gundam Build Divers Re:Rise

  Gundam Build Divers Re:Rise (Japanese: ガンダムビルドダイバーズRe:RISE, Hepburn: Gandamu Birudo Daibāzu Re:Raizu) is a Japanese original net animation anime series produced by Sunrise Beyond, and the fourth series within the Gundam Build Series sub-series. A sequel to the 2018 anime Gundam Build Divers, it is the first Gundam anime series to be released in the Reiwa period, released to celebrate the franchise's 40th anniversary. The series is directed by Shinya Watada and written by Yasuyuki Muto. Initially announced at the Gundam 40th anniversary video, the series aired on its Gundam Channel YouTube channel from October 10 to December 26, 2019. A TV airing of the ONA began on BS11 on October 12, 2019, and on January 28, 2020, on Tokyo MX. A second season aired from April 9 to August 27, 2020. Two spinoffs of the series were later serialized in Kadokawa's Gundam Ace magazine and Hobby Japan. == Plot == Two years have passed since the EL-Diver Incident, an event that almost destroyed the Gunpla Battle Nexus Online (GBN) game until it was resolved by the force group known as "Build Divers", and soon after more EL-Divers were discovered. In order to make the game more secure, a newer version of the game was rolled out in order to prevent the same incident from happening again and with newer experiences that would make the gameplay more immersive to players. The story focuses on Hiroto Kuga, a high schooler who is a rogue mercenary Gunpla Diver in GBN, who goes in the game and wanders throughout its countless dimensions while helping out other Divers whether it is on insistence or by hire. Despite his selfless act, he chooses to remain unaffiliated with anyone and refuses rewards and Force (Diver parties) group invites, isolating himself from other people even in real life. His primary goal as a Diver is to be reunited with a mysterious girl from his past named Eve, who was in fact the very first EL-Diver to appear in the game. But after a special request mission, Hiroto is united with three other active Divers in a strange world named "Eldora" and forms the Force group "BUILD DiVERS" in what appears to be just another GBN gamespace event, until they learn the truth about Eldora and its consequences not only for GBN, but for the entire world. == Characters == === BUILD DiVERS === Hiroto Kuga (クガ・ヒロト, Kuga Hiroto) / Hiroto (ヒロト, Hiroto) Voiced by: Chiaki Kobayashi (Japanese); Billy Kametz (English) The main protagonist of the series and a high-school builder, veteran diver, and a former ace member of the Force group Avalon, who lives in Yokohama. He was one of the first minors to make it to the deep end of GBN, due to his conviction of being a person who does his best to help others. He was active prior and during the events of the previous series. Now working as a rogue diver for hire after leaving Avalon, he wanders the GBN gamespace alone, harboring regrets, resentments, and suffering from trauma after the death of his close friend and lover, the EL-Diver Eve. He is very calm and a man of few words, usually refusing others' reward and help, especially on joining other forces, but this stoic persona is a mental mask to hide his condition from everyone, including his parents. But when a special mission done by Freddie united him with Kazami, May and Parviz, they accidentally formed the force team named "BUILD DiVERS" to protect the Eldorans from the One-Eyes army. Currently he is the ace of his unit and the leader of the overall force. Hiroto uses the PFF-X7 Core Gundam as his main Gunpla, based on the RX-78-2 Gundam from the original Mobile Suit Gundam series. Its special armament system called the "core-change" gimmick and his first theme invented from that gimmick is the "Planets System". This allows the Core Gundam to be equipped with various types of armor and weapons, each for a different situation named after the eight planets. Hiroto later upgrades his Gunpla into the PFF-X7II Core Gundam II. This new Core Gundam can transform into the "Core Flyer", in a similar fashion to the original Gundam's FF-X7 Core Fighter for increased mobility and like its predecessor, it can also use the Planets System: Earth Armor (PFF-X7/E3 Earthree Gundam): Core Gundam's default blue armor, focused on traditional all-around combat. Mars Armor (PFF-X7/M4 Marsfour Gundam): A red armor whose focus is on fragments of four styles of close combat, hence "Cross-Combat". Venus Armor (PFF-X7/V2 Veetwo Gundam): A green armor whose focus is commando style ranged and bombardment combat, additionally with option works. Mercury Armor (PFF-X7/M1 Mercuone Gundam): A navy armor whose focus is underwater combat. Jupiter Armor (PFF-X7/J5 Jupitive Gundam): A white armor whose focus is fast orbital combat. Uranus Armor (PFF-X7II/U7 Uraven Gundam): An indigo armor focused on reconnaissance and high powered sniping. Saturn Armor (PFF-X7II/S6 Saturnix Gundam): An orange armor focused in demolition style close combat without beam weapons, originally developed to counter Gundam Frames. Neptune Armor (PFF-X7II/N8 Nepteight Gundam): An aqua-green armor equipped with a customized Volture Lumiere system similar to the one from Mobile Suit Gundam SEED C.E. 73: Stargazer, intended to be used for traveling through GBN's space in a short amount of time, but was used for launching into orbit instead of maneuvering in deep space. It is ultimately discarded in Eldora's orbit due to the strain of leaving Eldora's gravitational field. Pluto Armor (PFF-X7II+/P9 Plutine Gundam): Appearing only on Gundam Build Metaverse, the black colored armor is used for close combat and dueling purposes with its color scheme reminiscent of that of EcoPla. PFF-X7II/BUILD DiVERS Re:Rising Gundam: A special combination of the Core Gundam II with the WoDom Pod + and parts from the Gundam Aegis Knight and the EX Valkylander, armed with two giant beam sabers, eight miracle wings born from Eve's blessings, and the "Grand Cross Cannon", Hiroto's first special move, made with the help of his team. In one occasion, Hiroto changes his avatar to a Haro to pilot the Mobile Builder Haro Loader to help with the repairs on Cuadorn by making a prosthetic wing out of gunpla parts. During the Gunpla Battle Royal, he pilots an unmodified ASW-G-08 Gundam Barbatos Lupus Rex from Mobile Suit Gundam: Iron-Blooded Orphans. In Battlelogue, it is revealed that he has made a second Core Gundam II that he leaves on Eldora with the colors of the Gundam MK-II Titan. Another variant of this Gunpla sports the old "Gundam G3" colors with his team's personal crest, which is most likely to represent Sarah since the color of her hair, eyes, and dress embody Hiroto's time with Eve before they joined Avalon and to symbolize how he has officially befriended the original Build Divers. Each of the two units have unique advancements, the Titan color specializes in ground and underwater combat and the G3 color specializes in aerial and space combat. May (メイ, Mei) Voiced by: Mai Fuchigami (Japanese); Lauren Landa (English) A seemingly late teens female diver who prefers to play solo, she is a very calm and no-nonsense girl whose interest is in battles alone. However, she is not a fan of those who engage their opponents head on and prefers to implement a strategic approach. She is mature and has a strong sense of justice, and can be impulsive rushing into situations, especially for those in danger. Later in the series, she is revealed to be one of the 87 EL-Divers, however she was not one of those who were saved after the EL-Diver incident two years ago, she was born shortly after. After she was born she was given her own Mobile Doll body similar to Sarah, that is when she first met her, Koichi, Tsukasa, and Nanami. During the Lotus Challenge Eldoran style rehearsal battle it is revealed that she, as a new sister of Sarah, addresses the latter as the older since Sarah is chronologically older, regardless of her maturity. In the final episode, she is revealed to have been born with the remnant data originating from Eve, the first born EL-Diver who Hiroto befriended and fell in love with several years ago, and carries Eve's earring on her armband. In Battlelogue, it's implied that she is currently living with Hiroto IRL and in GBN is his attendant. May uses the JMA0530-MAY WoDom Pod as her main Gunpla, which is a customized JMA-0530 Walking Dome from Turn A Gundam. In the later episodes, the mobile suit is revealed to be a disguise for its true form, the HER-SELF Mobile Doll May. May later upgrades her WoDom Pod into the JMA0530-MAYBD WoDom Pod +. During the Gunpla Battle Royal, she uses her Mobile Doll (albeit with a new color scheme and the Gundam Base logo) along with an unmodified NZ-999 II Neo Zeong mobile armor from Mobile Suit Gundam Narrative. Kazami Torimachi (トリマチ・カザミ, Torimachi Kazami) / Kazami (カザミ, Kazami) Voiced by: Masaaki Mizunaka (Japanese); Ray Chase (English) A diver who was a former member of the diver group "Mu Dish". He is a very energet

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  Gundam Build Metaverse

  Gundam Build Metaverse (Japanese: ガンダムビルドメタバース, Hepburn: Gandamu Birudo Metabāzu) is a Japanese original net animation anime mini-series produced by Sunrise Beyond, and the fifth series within the Gundam Build Series sub-series. The series celebrates the 10th anniversary of the Gundam Build franchise, including characters from the previous installments. == Plot == The story is set in the same universe of the Gundam Build series in an online metaverse space where users can use avatars to move around and interact with other users, including conducting Gunpla (Gundam plastic model) battles with them. The story centers on Rio Hōjō, a boy who lives in Hawaii, and who learns how to build Gunpla from a local hobbyist named Seria Urutsuki. In the metaverse, a figure known as Mask Lady teaches him the art of Gunpla battling, and he strives to get better at it every day. With his custom Lah Gundam, he seeks out ever stronger opponents. == Characters == === Main characters === Rio Hojo (ホウジョウ・リオ, Hōjō Rio) Voiced by: Chika Anzai A young boy from Hawaii who is an enthusiast of Gunpla Battle and is an apprentice of the mysterious Diver "Mask Lady". Rio's Gunpla is the Lah Gundam, modeled after an entry-grade RX-78-2 Gundam, from the original Mobile Suit Gundam anime series. Seria Urutsuki (ウルツキ・セリア, Urutsuki Seria) / Mask Lady (マスクレディー, Masuku Reidi) Voiced by: Rio Tsuchiya A clerk at a local hobby shop and the instructor at their Gunpla class, Seria becomes Rio's Gunpla mentor using the alias "Mask Lady". Seria's Gunpla is the ZGMF-X20A-PF Gundam Perfect Strike Freedom Rouge, based on both the MBF-02 Strike Rouge and the GAT-X105+AQM/E-YM1 Perfect Strike Gundam from Mobile Suit Gundam Seed and the ZGMF-X20A Strike Freedom Gundam from Mobile Suit Gundam Seed Destiny. === Returning characters === Fumina Hoshino (ホシノ・フミナ, Hoshino Fumina) Voiced by: Yui Makino A veteran Gunpla Battler from the early days of the sport and the Leader of "Team Try Fighters", she works as an advertiser and announcer within the Metaverse realm. Tatsuya Yuuki (ユウキ・タツヤ, Yūki Tatsuya) / Meijin Kawaguchi III (三代目メイジン・カワグチ, Sandaime Meijin Kawaguchi) Voiced by: Takuya Satō A builder and three-times Gunpla Battle world champion who inherited the name of the legendary Meijin Kawaguchi, known as "Meijin Kawaguchi III", and still the current title holder. His newest Gunpla is the Gundam Amazing Barbatos Lupus based on the ASW-G-08 Gundam Barbatos Lupus from Mobile Suit Gundam: Iron-Blooded Orphans. Riku Mikami (ミカミ・リク, Mikami Riku) / Riku (リク) Voiced by: Yūsuke Kobayashi The Founder and former leader of the legendary force, "Build Divers". His Gunpla is the Gundam 00 Diver Arc, the latest version of the original GN-0000DVR Gundam 00 Diver from Gundam Build Divers, incorporating elements from the 00 Gundam from Mobile Suit Gundam 00 and the Gundam AGE-FX from Mobile Suit Gundam AGE. Sarah (サラ, Sara) Voiced by: Haruka Terui An EL-Diver and member of the Build Divers. Momoka Yashiro (ヤシロ・モモカ, Yashiro Momoka) / Momo (モモ) Voiced by: Nene Hieda Member of Build Divers. Her gunpla is the MOMOKAPOOL (R×R), an upgraded version of her PEN-01M Momokapool from Gundam Build Divers Aya Fujisawa (フジサワ・アヤ, Fujisawa Aya) / Ayame (アヤメ) Voiced by: Manami Numakura Member of Build Divers. Her Gunpla is the F-Kunoichi Kai, an SD Gunpla based on the F91 Gundam F91 from Mobile Suit Gundam F91. Sei Iori (イオリ・セイ, Iori Sei) Voiced by: Mikako Komatsu A builder and one time Gunpla Battle World Champion. His current Gunpla is the GAT-X105B/EG Build Strike Exceed Galaxy, the latest version of the original GAT-X105B Build Strike Gundam from Gundam Build Fighters. Aria von Reiji Asuna (アリーア・フォン・レイジ・アスナ, Arīa fon Reiji Asuna) Voiced by: Sachi Kokuryu A prince from the country called Arian that exists within a space colony in another dimension, who became friends with Sei Iori and together won the Gunpla Battle World Championship. He somehow manages to log into the metaverse to reunite with his friend, piloting the SB-011 Star Burning Gundam. Sekai Kamiki (カミキ・セカイ, Kamiki Sekai) Voiced by: Kazumi Togashi A veteran builder and former member of Team Try Fighters. He is currently the Japanese National representative Champion. In the series he develops a rivalry relationship with Hiroto similar to that of Kyoya and Rommel. His current Gunpla is the Shin Burning Gundam, the latest version of the original KMK-B01 Kamiki Burning Gundam from Gundam Build Fighters Try which is based on the Burning Gundam and Master Gundam. Hiroto Kuga (クガ・ヒロト, Kuga Hiroto) / Hiroto (ヒロト, Hiroto) Voiced by: Chiaki Kobayashi A veteran diver, the one responsible for discovering more EL-Divers, and a former member of the legendary force "Avalon", who later joined the unofficial, "BUILD DiVERS" and eventually became the current Force Leader, and as well as the current title holder of "Hero of Gunpla". In the third episode he is the only Build Diver member who participates in the tournament, while his fellow force-mates are in the audience routing for him and Rio. His Gunpla is the Plutine Gundam, which is a combination of his Core Gundam II Plus, upgraded from the Core Gundam II featured in Gundam Build Divers Re:Rise equipped with the Pluto Armor. Magee (マギー, Magī) Voiced by: Taishi Murata A flamboyant veteran Diver who owns a shop in the metaverse and is an acquaintance of Seria's. Freddie (フレディ, Furedi) Voiced by: Ai Kakuma An alien anthropomorphic dog boy from planet Eldora, a support member to both Build Diver teams, who manages to access the metaverse from his home planet along his fellow Eldorans. Ogre (オーガ, Ōga) Voiced by: Wataru Hatano Kyoya Kisugi (キスギ・キョウヤ, Kisugi Kyōya) / Kyoya Kujo (クジョウ・キョウヤ, Kujō Kyōya) Voiced by: Jun Kasama Leader of the legendary force "Avalon" and the reigning and current title holder of "World Champion". He along with Hiroto Kuga, Maria Urutsuki, and Tatsuya Yuuki are currently at the top of the entire gunpla world community. His current gunpla is an recolored version of his AGE-TRYMAG Gundam TRY AGE Magnum from Gundam Build Divers Re:Rise. Susumu Sazaki (サザキ・ススム, Sazaki Susumu) Voiced by: Ryo Hirohashi Kaoruko Sazaki (サザキ・カオルコ, Sazaki Kaoruko) Voiced by: Ryo Hirohashi Mahiru Shigure (シグレ・マヒル, Shigure Mahiru) Voiced by: Rinko Natsuhi Keiko Sano (サノ・ケイコ, Sano Keiko) Voiced by: Ami Naito === Others === Maria Urutsuki (ウルツキ・マリア, Urutsuki Maria) / Mascarilla (マスカリージャ, Masukarīja) Voiced by: Ai Kakuma A mysterious masked woman with a harsh rivalry with Seria and a similar avatar as hers, she is later revealed as Seria's younger sister Maria, who began to loathe her sister after she quit on their dream to fight for the title of Lady Kawaguchi. She later obtains the title, becoming "Lady Kawaguchi VII". Jeff (ジェフさん, Jefu-san) Voiced by: Kenta Miyake A distant relative of Seria and Maria's and owner of the hobby shop where Seria lives. Mellow Neige (メロウ・ネージュ, Merō Nēju) Voiced by: Chikano Ibuki A sentient A.I. who is the current publicity face of the Gunpla Metaverse. == Episodes ==

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  Ensemble averaging (machine learning)

  In machine learning, ensemble averaging is the process of creating multiple models (typically artificial neural networks) and combining them to produce a desired output, as opposed to creating just one model. Ensembles of models often outperform individual models, as the various errors of the ensemble constituents "average out". == Overview == Ensemble averaging is one of the simplest types of committee machines. Along with boosting, it is one of the two major types of static committee machines. In contrast to standard neural network design, in which many networks are generated but only one is kept, ensemble averaging keeps the less satisfactory networks, but with less weight assigned to their outputs. The theory of ensemble averaging relies on two properties of artificial neural networks: In any network, the bias can be reduced at the cost of increased variance In a group of networks, the variance can be reduced at no cost to the bias. This is known as the bias–variance tradeoff. Ensemble averaging creates a group of networks, each with low bias and high variance, and combines them to form a new network which should theoretically exhibit low bias and low variance. Hence, this can be thought of as a resolution of the bias–variance tradeoff. The idea of combining experts can be traced back to Pierre-Simon Laplace. == Method == The theory mentioned above gives an obvious strategy: create a set of experts with low bias and high variance, and average them. Generally, what this means is to create a set of experts with varying parameters; frequently, these are the initial synaptic weights of a neural network, although other factors (such as learning rate, momentum, etc.) may also be varied. Some authors recommend against varying weight decay and early stopping. The steps are therefore: Generate N experts, each with their own initial parameters (these values are usually sampled randomly from a distribution) Train each expert separately Combine the experts and average their values. Alternatively, domain knowledge may be used to generate several classes of experts. An expert from each class is trained, and then combined. A more complex version of ensemble average views the final result not as a mere average of all the experts, but rather as a weighted sum. If each expert is y i {\displaystyle y_{i}} , then the overall result y ~ {\displaystyle {\tilde {y}}} can be defined as: y ~ ( x ; α ) = ∑ j = 1 p α j y j ( x ) {\displaystyle {\tilde {y}}(\mathbf {x} ;\mathbf {\alpha } )=\sum _{j=1}^{p}\alpha _{j}y_{j}(\mathbf {x} )} where α {\displaystyle \mathbf {\alpha } } is a set of weights. The optimization problem of finding alpha is readily solved through neural networks, hence a "meta-network" where each "neuron" is in fact an entire neural network can be trained, and the synaptic weights of the final network is the weight applied to each expert. This is known as a linear combination of experts. It can be seen that most forms of neural network are some subset of a linear combination: the standard neural net (where only one expert is used) is simply a linear combination with all α j = 0 {\displaystyle \alpha _{j}=0} and one α k = 1 {\displaystyle \alpha _{k}=1} . A raw average is where all α j {\displaystyle \alpha _{j}} are equal to some constant value, namely one over the total number of experts. A more recent ensemble averaging method is negative correlation learning, proposed by Y. Liu and X. Yao. This method has been widely used in evolutionary computing. == Benefits == The resulting committee is almost always less complex than a single network that would achieve the same level of performance The resulting committee can be trained more easily on smaller datasets The resulting committee often has improved performance over any single model The risk of overfitting is lessened, as there are fewer parameters (e.g. neural network weights) which need to be set.

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  Load file

  A load file in the litigation community is commonly referred to as the file used to import data (coded, captured or extracted data from ESI processing) into a database; or the file used to link images. These load files carry commands, commanding the software to carry out certain functions with the data found in them. Load files are usually ASCII text files that have delimited fields of information. Such load files may have data about documents to be imported into a document management software such as Concordance or Summation. Or they may have the path or directory where images may reside so that the software can link such images to their corresponding records. Some database programs take one load file for importing images and another for importing data while others take only one load file for both pieces of information. OCR or Search-able Text which is considered "data" is also imported into most database programs via the same load files. Though some people prefer to load the OCR into their databases by running a separate command to search and find the desired text. Commonly used databases and their corresponding file extensions are: Summation (DII , CSV), Concordance (OPT, DAT), Sanction (SDT), IPRO (LFP), Ringtail (MDB) and DB/TextWorks (TXT).

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  Degree of truth

  In classical logic, propositions are typically unambiguously considered as being true or false. For instance, the proposition one is both equal and not equal to itself is regarded as simply false, being contrary to the Law of Noncontradiction; while the proposition one is equal to one is regarded as simply true, by the Law of Identity. However, some mathematicians, computer scientists, and philosophers have been attracted to the idea that a proposition might be more or less true, rather than wholly true or wholly false. Consider this pizza is hot. In mathematics, this idea can be developed in terms of fuzzy logic. In computer science, it has found application in artificial intelligence. In philosophy, the idea has proved particularly appealing in the case of vagueness. Degrees of truth is an important concept in law. The term is an older concept than conditional probability. Instead of determining the objective probability, only a subjective assessment is defined. In adjudicative processes, 'substantive truth' is distinct from 'formal legal truth' which comes in four degrees: hearsay, balance of probabilities, proven beyond reasonable doubt and absolute truth (knowledge reserved unto God).

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  Fuzzy electronics

  Fuzzy electronics is an electronic technology that uses fuzzy logic, instead of the two-state Boolean logic more commonly used in digital electronics. Fuzzy electronics is fuzzy logic implemented on dedicated hardware. This is to be compared with fuzzy logic implemented in software running on a conventional processor. Fuzzy electronics has a wide range of applications, including control systems and artificial intelligence. == History == The first fuzzy electronic circuit was built by Takeshi Yamakawa et al. in 1980 using discrete bipolar transistors. The first industrial fuzzy application was in a cement kiln in Denmark in 1982. The first VLSI fuzzy electronics was by Masaki Togai and Hiroyuki Watanabe in 1984. In 1987, Yamakawa built the first analog fuzzy controller. The first digital fuzzy processors came in 1988 by Togai (Russo, pp. 2–6). In the early 1990s, the first fuzzy logic chips were presented to the public. Two companies which are Omron and NEC have announced the development of dedicated fuzzy electronic hardware in the year 1991. Two years later, the Japanese Omron Cooperation has shown a working fuzzy chip during a technical fair.

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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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  G'MIC

  G'MIC (GREYC's Magic for Image Computing) is a free and open-source framework for image processing. It defines a script language that allows the creation of complex macros. Originally usable only through a command line interface, it is currently mostly popular as a GIMP plugin, and is also included in Krita. G'MIC is dual-licensed under CECILL-2.1 or CECILL-C. == Features == G'MIC's graphical interface is notable for its noise removal filters, which came from an earlier project called GREYCstoration by the same authors. G'MIC offers many built-in commands for image processing, including basic mathematical manipulations, look up tables, and filtering operations. More complex macros and pipelines built out of those commands are defined in its library files. == Interpreters == === Command line === G'MIC is primarily a script language callable from a shell. For example, to display an image: This command displays the image contained in the file image.jpg and allows zooming in to examine values. Several filters can be applied in succession. For example, to crop and resize an image: === Graphical interface === G'MIC comes with a Qt-based graphical interface, which may be integrated as a Gimp or Krita plugin. It contains several hundred filters written in the G'MIC language, dynamically updated through an internet feed. The interface provides a preview and setting sliders for each filter. G'MIC is one of the most popular Gimp plugins. === G'MIC Online === Most of the filters available for the graphical interface are also available online. === ZArt === ZArt is a graphical interface for real-time manipulation of webcam images. === libgmic === Libgmic is a C++ library that can be linked to third-party applications. It sees integration in Flowblade and Veejay.

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  Computer-automated design

  Design Automation usually refers to electronic design automation, or Design Automation which is a Product Configurator. Extending Computer-Aided Design (CAD), automated design and Computer-Automated Design (CAutoD) are more concerned with a broader range of applications, such as automotive engineering, civil engineering, composite material design, control engineering, dynamic system identification and optimization, financial systems, industrial equipment, mechatronic systems, steel construction, structural optimisation, and the invention of novel systems. The concept of CAutoD perhaps first appeared in 1963, in the IBM Journal of Research and Development, where a computer program was written. to search for logic circuits having certain constraints on hardware design to evaluate these logics in terms of their discriminating ability over samples of the character set they are expected to recognize. More recently, traditional CAD simulation is seen to be transformed to CAutoD by biologically-inspired machine learning, including heuristic search techniques such as evolutionary computation, and swarm intelligence algorithms. == Guiding designs by performance improvements == To meet the ever-growing demand of quality and competitiveness, iterative physical prototyping is now often replaced by 'digital prototyping' of a 'good design', which aims to meet multiple objectives such as maximised output, energy efficiency, highest speed and cost-effectiveness. The design problem concerns both finding the best design within a known range (i.e., through 'learning' or 'optimisation') and finding a new and better design beyond the existing ones (i.e., through creation and invention). This is equivalent to a search problem in an almost certainly, multidimensional (multivariate), multi-modal space with a single (or weighted) objective or multiple objectives. == Normalized objective function: cost vs. fitness == Using single-objective CAutoD as an example, if the objective function, either as a cost function J ∈ [ 0 , ∞ ) {\displaystyle J\in [0,\infty )} , or inversely, as a fitness function f ∈ ( 0 , 1 ] {\displaystyle f\in (0,1]} , where f = J 1 + J {\displaystyle f={\tfrac {J}{1+J}}} , is differentiable under practical constraints in the multidimensional space, the design problem may be solved analytically. Finding the parameter sets that result in a zero first-order derivative and that satisfy the second-order derivative conditions would reveal all local optima. Then comparing the values of the performance index of all the local optima, together with those of all boundary parameter sets, would lead to the global optimum, whose corresponding 'parameter' set will thus represent the best design. However, in practice, the optimization usually involves multiple objectives and the matters involving derivatives are a lot more complex. == Dealing with practical objectives == In practice, the objective value may be noisy or even non-numerical, and hence its gradient information may be unreliable or unavailable. This is particularly true when the problem is multi-objective. At present, many designs and refinements are mainly made through a manual trial-and-error process with the help of a CAD simulation package. Usually, such a posteriori learning or adjustments need to be repeated many times until a ‘satisfactory’ or ‘optimal’ design emerges. == Exhaustive search == In theory, this adjustment process can be automated by computerised search, such as exhaustive search. As this is an exponential algorithm, it may not deliver solutions in practice within a limited period of time. == Search in polynomial time == One approach to virtual engineering and automated design is evolutionary computation such as evolutionary algorithms. === Evolutionary algorithms === To reduce the search time, the biologically-inspired evolutionary algorithm (EA) can be used instead, which is a (non-deterministic) polynomial algorithm. The EA based multi-objective "search team" can be interfaced with an existing CAD simulation package in a batch mode. The EA encodes the design parameters (encoding being necessary if some parameters are non-numerical) to refine multiple candidates through parallel and interactive search. In the search process, 'selection' is performed using 'survival of the fittest' a posteriori learning. To obtain the next 'generation' of possible solutions, some parameter values are exchanged between two candidates (by an operation called 'crossover') and new values introduced (by an operation called 'mutation'). This way, the evolutionary technique makes use of past trial information in a similarly intelligent manner to the human designer. The EA based optimal designs can start from the designer's existing design database, or from an initial generation of candidate designs obtained randomly. A number of finely evolved top-performing candidates will represent several automatically optimized digital prototypes. There are websites that demonstrate interactive evolutionary algorithms for design. allows you to evolve 3D objects online and have them 3D printed. allows you to do the same for 2D images.

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  Construction of t-norms

  In mathematics, t-norms are a special kind of binary operations on the real unit interval [0, 1]. Various constructions of t-norms, either by explicit definition or by transformation from previously known functions, provide a plenitude of examples and classes of t-norms. This is important, e.g., for finding counter-examples or supplying t-norms with particular properties for use in engineering applications of fuzzy logic. The main ways of construction of t-norms include using generators, defining parametric classes of t-norms, rotations, or ordinal sums of t-norms. Relevant background can be found in the article on t-norms. == Generators of t-norms == The method of constructing t-norms by generators consists in using a unary function (generator) to transform some known binary function (most often, addition or multiplication) into a t-norm. In order to allow using non-bijective generators, which do not have the inverse function, the following notion of pseudo-inverse function is employed: Let f: [a, b] → [c, d] be a monotone function between two closed subintervals of extended real line. The pseudo-inverse function to f is the function f (−1): [c, d] → [a, b] defined as f ( − 1 ) ( y ) = { sup { x ∈ [ a , b ] ∣ f ( x ) < y } for f non-decreasing sup { x ∈ [ a , b ] ∣ f ( x ) > y } for f non-increasing. {\displaystyle f^{(-1)}(y)={\begin{cases}\sup\{x\in [a,b]\mid f(x)y\}&{\text{for }}f{\text{ non-increasing.}}\end{cases}}} === Additive generators === The construction of t-norms by additive generators is based on the following theorem: Let f: [0, 1] → [0, +∞] be a strictly decreasing function such that f(1) = 0 and f(x) + f(y) is in the range of f or in [f(0+), +∞] for all x, y in [0, 1]. Then the function T: [0, 1]2 → [0, 1] defined as T(x, y) = f (-1)(f(x) + f(y)) is a t-norm. Alternatively, one may avoid using the notion of pseudo-inverse function by having T ( x , y ) = f − 1 ( min ( f ( 0 + ) , f ( x ) + f ( y ) ) ) {\displaystyle T(x,y)=f^{-1}\left(\min \left(f(0^{+}),f(x)+f(y)\right)\right)} . The corresponding residuum can then be expressed as ( x ⇒ y ) = f − 1 ( max ( 0 , f ( y ) − f ( x ) ) ) {\displaystyle (x\Rightarrow y)=f^{-1}\left(\max \left(0,f(y)-f(x)\right)\right)} . And the biresiduum as ( x ⇔ y ) = f − 1 ( | f ( x ) − f ( y ) | ) {\displaystyle (x\Leftrightarrow y)=f^{-1}\left(\left|f(x)-f(y)\right|\right)} . If a t-norm T results from the latter construction by a function f which is right-continuous in 0, then f is called an additive generator of T. Examples: The function f(x) = 1 – x for x in [0, 1] is an additive generator of the Łukasiewicz t-norm. The function f defined as f(x) = –log(x) if 0 < x ≤ 1 and f(0) = +∞ is an additive generator of the product t-norm. The function f defined as f(x) = 2 – x if 0 ≤ x < 1 and f(1) = 0 is an additive generator of the drastic t-norm. Basic properties of additive generators are summarized by the following theorem: Let f: [0, 1] → [0, +∞] be an additive generator of a t-norm T. Then: T is an Archimedean t-norm. T is continuous if and only if f is continuous. T is strictly monotone if and only if f(0) = +∞. Each element of (0, 1) is a nilpotent element of T if and only if f(0) < +∞. The multiple of f by a positive constant is also an additive generator of T. T has no non-trivial idempotents. (Consequently, e.g., the minimum t-norm has no additive generator.) === Multiplicative generators === The isomorphism between addition on [0, +∞] and multiplication on [0, 1] by the logarithm and the exponential function allow two-way transformations between additive and multiplicative generators of a t-norm. If f is an additive generator of a t-norm T, then the function h: [0, 1] → [0, 1] defined as h(x) = e−f (x) is a multiplicative generator of T, that is, a function h such that h is strictly increasing h(1) = 1 h(x) · h(y) is in the range of h or equal to 0 or h(0+) for all x, y in [0, 1] h is right-continuous in 0 T(x, y) = h (−1)(h(x) · h(y)). Vice versa, if h is a multiplicative generator of T, then f: [0, 1] → [0, +∞] defined by f(x) = −log(h(x)) is an additive generator of T. == Parametric classes of t-norms == Many families of related t-norms can be defined by an explicit formula depending on a parameter p. This section lists the best known parameterized families of t-norms. The following definitions will be used in the list: A family of t-norms Tp parameterized by p is increasing if Tp(x, y) ≤ Tq(x, y) for all x, y in [0, 1] whenever p ≤ q (similarly for decreasing and strictly increasing or decreasing). A family of t-norms Tp is continuous with respect to the parameter p if lim p → p 0 T p = T p 0 {\displaystyle \lim _{p\to p_{0}}T_{p}=T_{p_{0}}} for all values p0 of the parameter. === Schweizer–Sklar t-norms === The family of Schweizer–Sklar t-norms, introduced by Berthold Schweizer and Abe Sklar in the early 1960s, is given by the parametric definition T p S S ( x , y ) = { T min ( x , y ) if p = − ∞ ( x p + y p − 1 ) 1 / p if − ∞ < p < 0 T p r o d ( x , y ) if p = 0 ( max ( 0 , x p + y p − 1 ) ) 1 / p if 0 < p < + ∞ T D ( x , y ) if p = + ∞ . {\displaystyle T_{p}^{\mathrm {SS} }(x,y)={\begin{cases}T_{\min }(x,y)&{\text{if }}p=-\infty \\(x^{p}+y^{p}-1)^{1/p}&{\text{if }}-\infty −∞ Continuous if and only if p < +∞ Strict if and only if −∞ < p ≤ 0 (for p = −1 it is the Hamacher product) Nilpotent if and only if 0 < p < +∞ (for p = 1 it is the Łukasiewicz t-norm). The family is strictly decreasing for p ≥ 0 and continuous with respect to p in [−∞, +∞]. An additive generator for T p S S {\displaystyle T_{p}^{\mathrm {SS} }} for −∞ < p < +∞ is f p S S ( x ) = { − log ⁡ x if p = 0 1 − x p p otherwise. {\displaystyle f_{p}^{\mathrm {SS} }(x)={\begin{cases}-\log x&{\text{if }}p=0\\{\frac {1-x^{p}}{p}}&{\text{otherwise.}}\end{cases}}} === Hamacher t-norms === The family of Hamacher t-norms, introduced by Horst Hamacher in the late 1970s, is given by the following parametric definition for 0 ≤ p ≤ +∞: T p H ( x , y ) = { T D ( x , y ) if p = + ∞ 0 if p = x = y = 0 x y p + ( 1 − p ) ( x + y − x y ) otherwise. {\displaystyle T_{p}^{\mathrm {H} }(x,y)={\begin{cases}T_{\mathrm {D} }(x,y)&{\text{if }}p=+\infty \\0&{\text{if }}p=x=y=0\\{\frac {xy}{p+(1-p)(x+y-xy)}}&{\text{otherwise.}}\end{cases}}} The t-norm T 0 H {\displaystyle T_{0}^{\mathrm {H} }} is called the Hamacher product. Hamacher t-norms are the only t-norms which are rational functions. The Hamacher t-norm T p H {\displaystyle T_{p}^{\mathrm {H} }} is strict if and only if p < +∞ (for p = 1 it is the product t-norm). The family is strictly decreasing and continuous with respect to p. An additive generator of T p H {\displaystyle T_{p}^{\mathrm {H} }} for p < +∞ is f p H ( x ) = { 1 − x x if p = 0 log ⁡ p + ( 1 − p ) x x otherwise. {\displaystyle f_{p}^{\mathrm {H} }(x)={\begin{cases}{\frac {1-x}{x}}&{\text{if }}p=0\\\log {\frac {p+(1-p)x}{x}}&{\text{otherwise.}}\end{cases}}} === Frank t-norms === The family of Frank t-norms, introduced by M.J. Frank in the late 1970s, is given by the parametric definition for 0 ≤ p ≤ +∞ as follows: T p F ( x , y ) = { T m i n ( x , y ) if p = 0 T p r o d ( x , y ) if p = 1 T L u k ( x , y ) if p = + ∞ log p ⁡ ( 1 + ( p x − 1 ) ( p y − 1 ) p − 1 ) otherwise. {\displaystyle T_{p}^{\mathrm {F} }(x,y)={\begin{cases}T_{\mathrm {min} }(x,y)&{\text{if }}p=0\\T_{\mathrm {prod} }(x,y)&{\text{if }}p=1\\T_{\mathrm {Luk} }(x,y)&{\text{if }}p=+\infty \\\log _{p}\left(1+{\frac {(p^{x}-1)(p^{y}-1)}{p-1}}\right)&{\text{otherwise.}}\end{cases}}} The Frank t-norm T p F {\displaystyle T_{p}^{\mathrm {F} }} is strict if p < +∞. The family is strictly decreasing and continuous with respect to p. An additive generator for T p F {\displaystyle T_{p}^{\mathrm {F} }} is f p F ( x ) = { − log ⁡ x if p = 1 1 − x if p = + ∞ log ⁡ p − 1 p x − 1 otherwise. {\displaystyle f_{p}^{\mathrm {F} }(x)={\begin{cases}-\log x&{\text{if }}p=1\\1-x&{\text{if }}p=+\infty \\\log {\frac {p-1}{p^{x}-1}}&{\text{otherwise.}}\end{cases}}} === Yager t-norms === The family of Yager t-norms, introduced in the early 1980s by Ronald R. Yager, is given for 0 ≤ p ≤ +∞ by T p Y ( x , y ) = { T D ( x , y ) if p = 0 max ( 0 , 1 − ( ( 1 − x ) p + ( 1 − y ) p ) 1 / p ) if 0 < p < + ∞ T m i n ( x , y ) if p = + ∞ {\displaystyle T_{p}^{\mathrm {Y} }(x,y)={\begin{cases}T_{\mathrm {D} }(x,y)&{\text{if }}p=0\\\max \left(0,1-((1-x)^{p}+(1-y)^{p})^{1/p}\right)&{\text{if }}0 Read more →