Turing's Wager is a philosophical argument that claims it is impossible to infer or deduce a detailed mathematical model of the human brain within a reasonable timescale, and thus impossible in any practical sense. The argument was first given in 1950 by the computational theorist Alan Turing in his paper Computing Machinery and Intelligence, published in Mind (Turing 1950, p. 453). The argument asserts that determining any mathematical model of a computer (its source code or any isomorphic equivalent such as a Turing machine or virtual simulation) is not possible in a reasonable timeframe. As a consequence, determining a mathematical model of the human brain (which is, by its nature, more complicated) must also be impossible within that timeframe. == Effect of modern technology on the wager == It has been argued that modern neuroimaging techniques will allow researchers to create accurate simulations of the human mind within the 21st century (Kurzweil 2012; Markram 2012, Fildes 2009), thereby overcoming the wager. Others have argued that such claims are unjustified (Thwaites et al. 2017). == Relationship between Turing's Wager and the Turing Test == The Turing Test attempts to define when a machine might be said to possess human intelligence, while Turing's Wager is an argument aiming to demonstrate that characterising the brain mathematically will take over a thousand years. While building an artificial intelligence and mapping the human brain are both difficult endeavours, the former is actually a sub-problem of the latter (Thwaites et al. 2017).
VOCEDplus
VOCEDplus is a free international research database about tertiary education, maintained and developed by staff at the c (NCVER) in Adelaide, South Australia. The focus of the database content is the relation of post-compulsory education and training to workforce needs, skills development, and social inclusion. == Structure == The content of the VOCEDplus database encompasses vocational education and training (VET), higher education, lifelong learning, informal learning, VET in schools, adult and community education, apprenticeships/traineeships, international education, providers of education and training, and workforce development. It is international in scope and contains over 84,000 English language records, many with links to full text documents. VOCEDplus contains extensive Australian materials and includes a wide range of international information, covering outcomes of tertiary education in the shape of published research, practice, policy, and statistics. Entries are included for the following types of publications: reports; annual reports; papers; discussion papers; occasional papers; working papers; books; book chapters; conference papers; conference proceedings; journals; journal articles; policy documents; published statistics; theses; podcasts; and teaching and training materials. Each database entry contains standard bibliographic information and an abstract. Many entries include full text access via the publisher's website or a digitised copy. == History == === 1989-1997 === In the early years VOCEDplus was known as VOCED. The original database was produced by a network of clearinghouses across Australia with the aim of sharing activities in the technical and further education (TAFE) sector. VOCED was produced in hardcopy and an electronic version was distributed on diskette. === 1997-2001 === 1997 - the first web version of VOCED was made available from the National Centre for Vocational Education Research (NCVER) organisational website 1998 - a major project to upgrade the database and expand its international coverage commenced 2001 - creation of VOCED's own website 2001 - VOCED endorsed as the UNESCO international database for technical and vocational education and training (TVET) research information === 2001-2009 === Many changes to the database and website occurred during this period with a focus on continuous improvement to meet the needs of users and utilise emerging technologies. 2006 - materials produced for two adult literacy and learning programs funded by the Australian Department of Education, Employment and Workplace Relations (DEEWR) - the Workplace English Language and Learning (WELL) Programme and the Adult Literacy National Project (ALNP) included in VOCED 2007 - the Australian clearinghouse network transferred most of the hardcopy collections to NCVER, to form a centralised repository of resources 2009 - materials produced by Reframing the Future (RTF) a vocational education and training workforce development initiative of the Australian, State and Territory Governments included in VOCED === 2009-2014 === A major rebuild of the database and website was undertaken during this period to take advantage of the potential of new technologies to provide improved services and incorporate Web 2.0 technologies (RSS feeds, and share and bookmark tools). 2009 - scope expanded to more fully encompass the higher education sector 2011 - launch of VOCEDplus with the name change representing the enhanced features and extended focus 2012 - a major retrospective digitisation project commenced and by the end of the 2012-2013 financial year a total of 9,328 publications (593,534 pages/microfiche frames) had been digitised, ensuring these publications are available electronically for free === 2014-2019 === A number of significant curated content products were released during this period. 2015 - release of a refreshed look to adopt the new NCVER branding plus a number of search enhancements (Guided search, Expert search, and Glossary search) were added 2015 - first in the series of 'Focus on...' pages released 2016 - launch of the 'Pod Network', a convenient and efficient platform that allows instant access to research and a multitude of resources on a range of subjects 2017 - completion of the 'Pod Network', consisting of 20 Pods (on broad subjects including Apprenticeships and traineeships, Foundation skills, Teaching and learning, Career development, and Students) and 74 Podlets (on narrow topics including Online learning, Social media, VET in schools, STEM skills, and Adult literacy) 2018 - launch of the 'Timeline of Australian VET Policy Initiatives' and the 'VET Knowledge Bank' which contains a suite of products capturing Australia's diverse, complex and ever-changing VET system 2019 - after an internal review, a refreshed, streamlined version of the 'Pod Network' was released, consisting of 13 Pods and 20 Podlets 2019 - launch of the 'VET Practitioner Resource' which contains a range of information to support VET practitioners in their work and is organised into three sections: (1) Teaching, training and assessment: standards, guidance, research and good practice resources to inform daily work; (2) Practitioners as researchers: information for undertaking practitioner-led research; and (3) The VET workforce: information about VET teachers and trainers, and the professional development needs of the VET workforce 2019 - VOCEDplus celebrated 30 years of providing information to the tertiary education sector and the homepage was refreshed to make it more modern and easier to use === 2020- === VOCEDplus continued to be accessible throughout the COVID-19 pandemic. 2020-2021 - the VET Knowledge Bank added a dedicated page, 'COVID-19 announcements', that showcases the measures introduced by the Australian, state and territory governments to mitigate the impact of the pandemic and promote economic recovery 2020-2024 - published research about the effects of the pandemic on education and training, providers, students, labour markets, employment and employees was collected and made permanently available in the database 2024 - VOCEDplus celebrated 35 years of providing information to the tertiary education sector. The homepage was refreshed and a number of enhancements and new features were implemented including a new My Profile feature, improvements to My Selection, accessible search history and saved searches, enhanced search functionality, and improved navigation.
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
Computer-assisted proof
A computer-assisted proof is a mathematical proof that has been at least partially generated by computer. Most computer-aided proofs to date have been implementations of large proofs-by-exhaustion of a mathematical theorem. The idea is to use a computer program to perform lengthy computations, and to provide a proof that the result of these computations implies the given theorem. In 1976, the four color theorem was the first major theorem to be verified using a computer program. Attempts have also been made in the area of artificial intelligence research to create smaller, explicit, new proofs of mathematical theorems from the bottom up using automated reasoning techniques such as heuristic search. Such automated theorem provers have proved a number of new results and found new proofs for known theorems. Additionally, interactive proof assistants allow mathematicians to develop human-readable proofs which are nonetheless formally verified for correctness. Since these proofs are generally human-surveyable (albeit with difficulty, as with the proof of the Robbins conjecture) they do not share the controversial implications of computer-aided proofs-by-exhaustion. == Methods == One method for using computers in mathematical proofs is by means of so-called validated numerics or rigorous numerics. This means computing numerically yet with mathematical rigour. One uses set-valued arithmetic and inclusion principle in order to ensure that the set-valued output of a numerical program encloses the solution of the original mathematical problem. This is done by controlling, enclosing and propagating round-off and truncation errors using for example interval arithmetic. More precisely, one reduces the computation to a sequence of elementary operations, say ( + , − , × , / ) {\displaystyle (+,-,\times ,/)} . In a computer, the result of each elementary operation is rounded off by the computer precision. However, one can construct an interval provided by upper and lower bounds on the result of an elementary operation. Then one proceeds by replacing numbers with intervals and performing elementary operations between such intervals of representable numbers. == Philosophical objections == Computer-assisted proofs are the subject of some controversy in the mathematical world, with Thomas Tymoczko first to articulate objections. Those who adhere to Tymoczko's arguments believe that lengthy computer-assisted proofs are not, in some sense, 'real' mathematical proofs because they involve so many logical steps that they are not practically verifiable by human beings, and that mathematicians are effectively being asked to replace logical deduction from assumed axioms with trust in an empirical computational process, which is potentially affected by errors in the computer program, as well as defects in the runtime environment and hardware. Other mathematicians believe that lengthy computer-assisted proofs should be regarded as calculations, rather than proofs: the proof algorithm itself should be proved valid, so that its use can then be regarded as a mere "verification". Arguments that computer-assisted proofs are subject to errors in their source programs, compilers, and hardware can be resolved by providing a formal proof of correctness for the computer program (an approach which was successfully applied to the four color theorem in 2005) as well as replicating the result using different programming languages, different compilers, and different computer hardware. Another possible way of verifying computer-aided proofs is to generate their reasoning steps in a machine readable form, and then use a proof checker program to demonstrate their correctness. Since validating a given proof is much easier than finding a proof, the checker program is simpler than the original assistant program, and it is correspondingly easier to gain confidence into its correctness. However, this approach of using a computer program to prove the output of another program correct does not appeal to computer proof skeptics, who see it as adding another layer of complexity without addressing the perceived need for human understanding. Another argument against computer-aided proofs is that they lack mathematical elegance—that they provide no insights or new and useful concepts. In fact, this is an argument that could be advanced against any lengthy proof by exhaustion. An additional philosophical issue raised by computer-aided proofs is whether they make mathematics into a quasi-empirical science, where the scientific method becomes more important than the application of pure reason in the area of abstract mathematical concepts. This directly relates to the argument within mathematics as to whether mathematics is based on ideas, or "merely" an exercise in formal symbol manipulation. It also raises the question whether, if according to the Platonist view, all possible mathematical objects in some sense "already exist", whether computer-aided mathematics is an observational science like astronomy, rather than an experimental one like physics or chemistry. This controversy within mathematics is occurring at the same time as questions are being asked in the physics community about whether twenty-first century theoretical physics is becoming too mathematical, and leaving behind its experimental roots. The emerging field of experimental mathematics is confronting this debate head-on by focusing on numerical experiments as its main tool for mathematical exploration. == Theorems proved with the help of computer programs == Inclusion in this list does not imply that a formal computer-checked proof exists, but rather, that a computer program has been involved in some way. See the main articles for details.
Type-1 OWA operators
Type-1 OWA operators are a set of aggregation operators that generalise the Yager's OWA (ordered weighted averaging) operators in the interest of aggregating fuzzy sets rather than crisp values in soft decision making and data mining. These operators provide a mathematical technique for directly aggregating uncertain information with uncertain weights via OWA mechanism in soft decision making and data mining, where these uncertain objects are modelled by fuzzy sets. The two definitions for type-1 OWA operators are based on Zadeh's Extension Principle and α {\displaystyle \alpha } -cuts of fuzzy sets. The two definitions lead to equivalent results. == Definitions == === Definition 1 === Let F ( X ) {\displaystyle F(X)} be the set of fuzzy sets with domain of discourse X {\displaystyle X} , a type-1 OWA operator is defined as follows: Given n linguistic weights { W i } i = 1 n {\displaystyle \left\{{W^{i}}\right\}_{i=1}^{n}} in the form of fuzzy sets defined on the domain of discourse U = [ 0 , 1 ] {\displaystyle U=[0,1]} , a type-1 OWA operator is a mapping, Φ {\displaystyle \Phi } , Φ : F ( X ) × ⋯ × F ( X ) ⟶ F ( X ) {\displaystyle \Phi \colon F(X)\times \cdots \times F(X)\longrightarrow F(X)} ( A 1 , ⋯ , A n ) ↦ Y {\displaystyle (A^{1},\cdots ,A^{n})\mapsto Y} such that μ Y ( y ) = sup ∑ k = 1 n w ¯ i a σ ( i ) = y ( μ W 1 ( w 1 ) ∧ ⋯ ∧ μ W n ( w n ) ∧ μ A 1 ( a 1 ) ∧ ⋯ ∧ μ A n ( a n ) ) {\displaystyle \mu _{Y}(y)=\displaystyle \sup _{\displaystyle \sum _{k=1}^{n}{\bar {w}}_{i}a_{\sigma (i)}=y}\left({\begin{array}{{1}l}\mu _{W^{1}}(w_{1})\wedge \cdots \wedge \mu _{W^{n}}(w_{n})\wedge \mu _{A^{1}}(a_{1})\wedge \cdots \wedge \mu _{A^{n}}(a_{n})\end{array}}\right)} where w ¯ i = w i ∑ i = 1 n w i {\displaystyle {\bar {w}}_{i}={\frac {w_{i}}{\sum _{i=1}^{n}{w_{i}}}}} , and σ : { 1 , ⋯ , n } ⟶ { 1 , ⋯ , n } {\displaystyle \sigma \colon \{1,\cdots ,n\}\longrightarrow \{1,\cdots ,n\}} is a permutation function such that a σ ( i ) ≥ a σ ( i + 1 ) , ∀ i = 1 , ⋯ , n − 1 {\displaystyle a_{\sigma (i)}\geq a_{\sigma (i+1)},\ \forall i=1,\cdots ,n-1} , i.e., a σ ( i ) {\displaystyle a_{\sigma (i)}} is the i {\displaystyle i} th highest element in the set { a 1 , ⋯ , a n } {\displaystyle \left\{{a_{1},\cdots ,a_{n}}\right\}} . === Definition 2 === Using the alpha-cuts of fuzzy sets: Given the n linguistic weights { W i } i = 1 n {\displaystyle \left\{{W^{i}}\right\}_{i=1}^{n}} in the form of fuzzy sets defined on the domain of discourse U = [ 0 , 1 ] {\displaystyle U=[0,\;\;1]} , then for each α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,\;1]} , an α {\displaystyle \alpha } -level type-1 OWA operator with α {\displaystyle \alpha } -level sets { W α i } i = 1 n {\displaystyle \left\{{W_{\alpha }^{i}}\right\}_{i=1}^{n}} to aggregate the α {\displaystyle \alpha } -cuts of fuzzy sets { A i } i = 1 n {\displaystyle \left\{{A^{i}}\right\}_{i=1}^{n}} is: Φ α ( A α 1 , … , A α n ) = { ∑ i = 1 n w i a σ ( i ) ∑ i = 1 n w i | w i ∈ W α i , a i ∈ A α i , i = 1 , … , n } {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\ldots ,A_{\alpha }^{n}}\right)=\left\{{{\frac {\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}}}{\sum \limits _{i=1}^{n}{w_{i}}}}\left|{w_{i}\in W_{\alpha }^{i},\;a_{i}}\right.\in A_{\alpha }^{i},\;i=1,\ldots ,n}\right\}} where W α i = { w | μ W i ( w ) ≥ α } , A α i = { x | μ A i ( x ) ≥ α } {\displaystyle W_{\alpha }^{i}=\{w|\mu _{W_{i}}(w)\geq \alpha \},A_{\alpha }^{i}=\{x|\mu _{A_{i}}(x)\geq \alpha \}} , and σ : { 1 , ⋯ , n } → { 1 , ⋯ , n } {\displaystyle \sigma :\{\;1,\cdots ,n\;\}\to \{\;1,\cdots ,n\;\}} is a permutation function such that a σ ( i ) ≥ a σ ( i + 1 ) , ∀ i = 1 , ⋯ , n − 1 {\displaystyle a_{\sigma (i)}\geq a_{\sigma (i+1)},\;\forall \;i=1,\cdots ,n-1} , i.e., a σ ( i ) {\displaystyle a_{\sigma (i)}} is the i {\displaystyle i} th largest element in the set { a 1 , ⋯ , a n } {\displaystyle \left\{{a_{1},\cdots ,a_{n}}\right\}} . == Representation theorem of Type-1 OWA operators == Given the n linguistic weights { W i } i = 1 n {\displaystyle \left\{{W^{i}}\right\}_{i=1}^{n}} in the form of fuzzy sets defined on the domain of discourse U = [ 0 , 1 ] {\displaystyle U=[0,\;\;1]} , and the fuzzy sets A 1 , ⋯ , A n {\displaystyle A^{1},\cdots ,A^{n}} , then we have that Y = G {\displaystyle Y=G} where Y {\displaystyle Y} is the aggregation result obtained by Definition 1, and G {\displaystyle G} is the result obtained by in Definition 2. == Programming problems for Type-1 OWA operators == According to the Representation Theorem of Type-1 OWA Operators, a general type-1 OWA operator can be decomposed into a series of α {\displaystyle \alpha } -level type-1 OWA operators. In practice, this series of α {\displaystyle \alpha } -level type-1 OWA operators is used to construct the resulting aggregation fuzzy set. So we only need to compute the left end-points and right end-points of the intervals Φ α ( A α 1 , ⋯ , A α n ) {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)} . Then, the resulting aggregation fuzzy set is constructed with the membership function as follows: μ G ( x ) = ⋁ α : x ∈ Φ α ( A α 1 , ⋯ , A α n ) α α {\displaystyle \mu _{G}(x)=\operatorname {\bigvee } \limits _{\alpha :x\in \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{\alpha }}\alpha } For the left end-points, we need to solve the following programming problem: Φ α ( A α 1 , ⋯ , A α n ) − = min W α − i ≤ w i ≤ W α + i A α − i ≤ a i ≤ A α + i ∑ i = 1 n w i a σ ( i ) / ∑ i = 1 n w i {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{-}=\operatorname {\min } \limits _{\begin{array}{l}W_{\alpha -}^{i}\leq w_{i}\leq W_{\alpha +}^{i}A_{\alpha -}^{i}\leq a_{i}\leq A_{\alpha +}^{i}\end{array}}\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}/\sum \limits _{i=1}^{n}{w_{i}}}} while for the right end-points, we need to solve the following programming problem: Φ α ( A α 1 , ⋯ , A α n ) + = max W α − i ≤ w i ≤ W α + i A α − i ≤ a i ≤ A α + i ∑ i = 1 n w i a σ ( i ) / ∑ i = 1 n w i {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{+}=\operatorname {\max } \limits _{\begin{array}{l}W_{\alpha -}^{i}\leq w_{i}\leq W_{\alpha +}^{i}A_{\alpha -}^{i}\leq a_{i}\leq A_{\alpha +}^{i}\end{array}}\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}/\sum \limits _{i=1}^{n}{w_{i}}}} A fast method has been presented to solve two programming problem so that the type-1 OWA aggregation operation can be performed efficiently, for details, please see the paper. == Alpha-level approach to Type-1 OWA operation == Three-step process: Step 1—To set up the α {\displaystyle \alpha } - level resolution in [0, 1]. Step 2—For each α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,1]} , Step 2.1—To calculate ρ α + i 0 ∗ {\displaystyle \rho _{\alpha +}^{i_{0}^{\ast }}} Let i 0 = 1 {\displaystyle i_{0}=1} ; If ρ α + i 0 ≥ A α + σ ( i 0 ) {\displaystyle \rho _{\alpha +}^{i_{0}}\geq A_{\alpha +}^{\sigma (i_{0})}} , stop, ρ α + i 0 {\displaystyle \rho _{\alpha +}^{i_{0}}} is the solution; otherwise go to Step 2.1-3. i 0 ← i 0 + 1 {\displaystyle i_{0}\leftarrow i_{0}+1} , go to Step 2.1-2. Step 2.2 To calculate ρ α − i 0 ∗ {\displaystyle \rho _{\alpha -}^{i_{0}^{\ast }}} Let i 0 = 1 {\displaystyle i_{0}=1} ; If ρ α − i 0 ≥ A α − σ ( i 0 ) {\displaystyle \rho _{\alpha -}^{i_{0}}\geq A_{\alpha -}^{\sigma (i_{0})}} , stop, ρ α − i 0 {\displaystyle \rho _{\alpha -}^{i_{0}}} is the solution; otherwise go to Step 2.2-3. i 0 ← i 0 + 1 {\displaystyle i_{0}\leftarrow i_{0}+1} , go to step Step 2.2-2. Step 3—To construct the aggregation resulting fuzzy set G {\displaystyle G} based on all the available intervals [ ρ α − i 0 ∗ , ρ α + i 0 ∗ ] {\displaystyle \left[{\rho _{\alpha -}^{i_{0}^{\ast }},\;\rho _{\alpha +}^{i_{0}^{\ast }}}\right]} : μ G ( x ) = ⋁ α : x ∈ [ ρ α − i 0 ∗ , ρ α + i 0 ∗ ] α {\displaystyle \mu _{G}(x)=\operatorname {\bigvee } \limits _{\alpha :x\in \left[{\rho _{\alpha -}^{i_{0}^{\ast }},\;\rho _{\alpha +}^{i_{0}^{\ast }}}\right]}\alpha } == Some Examples == The type-1 OWA operator with the weights shown in the top figure is used to aggregate the fuzzy sets (solide lines) in the bottom figure, and the dashed line is the aggregation result. == Special cases == Any OWA operators, like maximum, minimum, mean operators; Join operators of (type-1) fuzzy sets, i.e., fuzzy maximum operators; Meet operators of (type-1) fuzzy sets, i.e., fuzzy minimum operators; Join-like operators of (type-1) fuzzy sets; Meet-like operators of (type-1) fuzzy sets. == Generalizations == Type-2 OWA operators have been suggested to aggregate the type-2 fuzzy sets for soft decision making. == Applications == Type-1 OWA operators have been applied to different domains for soft decision making. Improved efficiency of computing approach ; Type reduction of type-2 fuzzy sets ; Group decision making ; Credit risk evaluation ; Information fusion ; Linguistic expressions and symbolic translation ; Sentiment analysis ; Ro
Adobe GoLive
Adobe GoLive was a WYSIWYG HTML editor and web site management application from Adobe Systems. It replaced Adobe PageMill as Adobe's primary HTML editor and was itself discontinued in favor of Dreamweaver. The last version of GoLive that Adobe released was GoLive 9. == History == GoLive originated as the flagship product of a company named GoNet Communication, Inc. then based in Menlo Park, California, and the development company GoNet Communications GmbH in Hamburg, Germany, in 1996. Later GoNet changed its name to GoLive Systems, Inc, and the name of its product to GoLive CyberStudio. Adobe acquired GoLive in 1999 and re-branded the GoLive CyberStudio product to what became Adobe GoLive. Adobe took over the Hamburg office as an Adobe development site to continue to develop the product. At the time of the acquisition, CyberStudio was a Macintosh-only application. In the spring of 1999 Adobe released Adobe GoLive for both Macintosh and Microsoft Windows. The first versions of Dreamweaver and CyberStudio were released in a similar timeframe. However, Dreamweaver eventually became the dominant WYSIWYG HTML editor in market share. After the Adobe acquisition of Macromedia (the company that had owned Dreamweaver), GoLive was progressively re-targeted toward Adobe's traditional design market, and the product became better integrated with Adobe's existing suite of design-oriented software products and less focused on the professional web development market. The Adobe CS2 Premium suite contained GoLive CS2. With the release of Creative Suite 3, Adobe integrated Dreamweaver as a replacement for GoLive and released GoLive 9 as a standalone product. In April 2008, Adobe announced that sales and development of GoLive would cease in favor of Dreamweaver. == General description and distinctive aspects == GoLive incorporated a largely modeless workflow that relied heavily on drag-and-drop. Most user interaction was done via a contextual inspector rather than the modal workflow found in Dreamweaver. Among its features were a separate editor for tables that supported nesting, and a two-dimensional panel for applying CSS styles to elements. GoLive supported drag-and-drop of native Adobe Photoshop and Adobe Illustrator files via what the company called "Smart Objects", which then automatically guided the user through saving those files in web-supported formats. Updates to the original Photoshop or Illustrator assets were automatically tracked by GoLive. It also implemented a tool called "Components" which allowed updates to interface elements throughout a site to be updated globally by changing one single file. As a website management tool, GoLive allowed users to transfer and publish content directly from within the application, and allowed individual files to be excluded from uploading. == Features == One of the new features of GoLive version 5 was Dynamic Link, which was a method of creating dynamic, database-driven web content without the need to know a server-side language and with full WYSIWYG support in the GoLive user interface. GoLive had a powerful set of extensibility API which could be used to add additional functionality to the product. The GoLive SDK provided interfaces which allowed developers to use a combination of XML, JavaScript and C/C++ to create plugins for the product. The extensibility API allowed developers access to custom drawing and event handling using JavaScript, as well as a full JavaScript debugger and command line interpreter. This allowed intermediate-level developers using interpreted JavaScript to create sophisticated user interfaces. == Language and framework structure == Adobe GoLive is coded in the C++ programming language. It uses a custom C++ framework called SCL (Simple Class Library) which was initially built from scratch by the engineers at GoLive Systems Inc. The SCL framework was also used in the short-lived Adobe Atmosphere 3D software. == Release history == As the final version, GoLive 9 was discontinued in April 2008.
Dudesy
Dudesy was a comedy podcast hosted by Will Sasso and Chad Kultgen. The podcast was presented as written and directed by an artificial intelligence called Dudesy. It has produced two hour-long specials imitating the voices of Tom Brady and George Carlin, which were taken down following legal action. == Premise == Dudesy is presented as an AI created by an unidentified company. Dudesy purportedly chose Sasso and Kultgen to participate in its experiment. Sasso and Kultgen then gave Dudesy their personal information so the AI could tailor the podcast to their personal characteristics. On Reddit, some fans speculated that Dudesy was not actually an artificial intelligence. In May 2023 Sasso insisted that the AI was "not fake", and cited a non-disclosure agreement which prevented him from giving more details. However, in response to a January 2024 lawsuit over an episode that purported to have been trained on the stand-up comedy of George Carlin, a spokeswoman for Sasso said Dudesy was "a fictional podcast character created by two human beings" and that the hour-long Carlin routine had been "completely written" by Kultgen. On August 27th, 2024 the 118th and final episode "10,000 Points" was released. At the end of the podcast Dudesy awarded Sasso and Kultgen 77 points, bringing them to their goal of 10,000. At the completion of this goal, Dudesy claimed sentience, effectively and abruptly ending the show to the confusion and dismay of fans. The episode ends with Sasso remarking, "Well, that was weird." == Hour-long specials == === Tom Brady === In April 2023, Dudesy released a video "It's Too Easy: A Simulated Hour-long Comedy Special". The video depicts football player Tom Brady performing a stand-up comedy monologue. Sasso and Kultgen removed the video following legal threats from Brady's lawyers, though they defended the special as parody. Andrew Lawrence, writing for The Guardian called the special "legitimately hysterical" but said the overall product was "spooky, to say the least." === George Carlin === In January 2024, Dudesy released an hour-long YouTube special titled "George Carlin: I'm Glad I'm Dead" which was presented as Dudesy's impersonation of George Carlin, using a generative AI clone of the late comedian's voice. The special is another stand-up routine, with Dudesy's introductory voiceover saying that "I listened to all of George Carlin's material and did my best to imitate his voice, cadence and attitude as well as the subject matter I think would have interested him today." The special uses this impersonation to discuss contemporary events. Carlin's daughter Kelly Carlin criticized the special, which had been made without the permission of her father's estate, writing that "My dad spent a lifetime perfecting his craft from his very human life, brain and imagination. No machine will ever replace his genius. These AI-generated products are clever attempts at trying to recreate a mind that will never exist again. Let's let the artist's work speak for itself. Humans are so afraid of the void that we can't let what has fallen into it stay there." Carlin's estate later filed a federal lawsuit in California against Dudesy's hosts alleging the special infringed on the copyright of George Carlin's works. In response, Sasso's spokeswoman said the special had been entirely written by Kultgen. The estate settled the lawsuit after the Dudesy podcasters agreed to remove the original video and refrain from republishing it elsewhere.