Rakuten Viber, commonly known as Viber, is a cross-platform voice over IP (VoIP) and instant messaging (IM) software application owned by the Japanese technology company Rakuten Group. The service is available as freeware for Android, iOS, Microsoft Windows, macOS and Linux. Users are registered and identified through a mobile phone number, although the service can also be accessed on desktop platforms without mobile connectivity. In addition to instant messaging, the platform allows users to exchange media such as images, videos and files, and provides a paid international calling service called Viber Out. The software was launched in 2010 by the company Viber Media, founded by Talmon Marco and Igor Magazinnik. Rakuten acquired Viber Media in 2014 and later renamed the company Rakuten Viber. The company is headquartered in Cyprus and maintains offices in London, Manila, Paris, San Francisco, Singapore, Tokyo and Beijing. == History == === Founding (2010) === Viber Media was founded in Tel Aviv, Israel, in 2010 by Talmon Marco and Igor Magazinnik. Marco and Magazinnik are also co-founders of the peer-to-peer media and file-sharing client iMesh. The company was run from Israel and was registered in Cyprus. Sani Maroli and Ofer Smocha soon joined the company as well. Marco said Viber allows instant calling and synchronization with contacts because the ID is the user's cell number. In its early days, Viber relied on a patchwork of outsourcing partners from different countries, commissioning specific solutions from external vendors — including teams based in Cyprus and Belarus. According to the company's statements, development of Viber's core functionality historically originated from its Tel Aviv office — a testament to its roots — even though the legal entity was registered elsewhere. === Early monetisation (2011) === In its first two years of availability, Viber did not generate revenues. It began doing so in 2013, via user payments for Viber Out voice calling and the Viber graphical messaging "sticker market". The company was originally funded by individual investors, described by Marco as "friends and family". They invested $20 million in the company, which had 120 employees as of May 2013. On 24 July 2013, Viber's support system was defaced by the Syrian Electronic Army. According to Viber, no sensitive user information was accessed. By the time Rakuten came forward with its acquisition deal in 2014, Viber had already stopped working with external vendors, choosing instead to consolidate development under its own offices. === Rakuten acquires Viber (2014) === On 13 February 2014, Rakuten announced they had acquired Viber Media for $900 million, and since then Viber has been owned by Rakuten, Inc., an e-commerce conglomerate headquartered in Tokyo. The sale of Viber earned the Shabtai family (Benny, his brother Gilad, and Gilad's son Ofer) some $500 million from their 55.2% stake in the company. At that sale price, the founders each realized over 30 times return on their investments. Later that year, the company established a UK presence with the incorporation of Viber UK Limited in London. Djamel Agaoua became Viber Media CEO in February 2017, replacing co-founder Marco who left in 2015. In July 2017 the corporate name of Viber Media was changed to Rakuten Viber and a new wordmark logo was introduced. Its legal name remains Viber Media, S.à r.l. based in Luxembourg. === Post-acquisition === In August 2015 Viber opened a regional office for Central and Eastern Europe in Sofia to support growth in the region. In 2017, Rakuten Viber and the World Wildlife Fund engaged in a commercial transaction aimed at raising awareness and protecting wildlife. After first using Viber to spread its message in June 2020, the International Federation of the Red Cross launched an official chatbot and community on the messaging app to combat the spread of false information, which they termed an infodemic, about COVID-19. The chatbot is still active as of June 2022, with over 1.4 million subscribers. In 2020, Rakuten Viber and the World Health Organization (the WHO) engaged in a commercial transaction for a chatbot to inform users of issues such as women's health. and an anti-smoking campaign. In the wake of the July–August 2020 Belarusian election protests, to avoid sanctions and harassment from monopolies the company closed its office in Minsk. In 2022, Ofir Eyal became Viber CEO, replacing Djamel Agaoua. Eyal is a Viber veteran; he worked as Vice President of Product in 2014 before his promotion to Chief Operating Officer in 2019. Shortly after the appointment of a new CEO, Viber continued its international expansion. In March 2022, Rakuten announced the opening of a development center in Tbilisi, Georgia, intended to support work on mobile applications and technology projects in the region. In July 2022, Rakuten Viber partnered with Rapyd to launch instant cross-border P2P payments. The company launched payments on the Viber app first in Greece and Germany, and then in other countries. In August, Mineski teamed up with Viber to develop a social minigame platform that can play off Viber's application. In May 2022, Rakuten Viber launched the premium chat service Viber Plus that offers exclusive features, including sticker market privileges, ad-free use, priority Viber support, exclusive badge, unique Viber icon, large file sharing, and more. In 2022, Viber joined the European Union’s Code of Conduct on countering illegal hate speech online. As part of this framework, the company undertook to review reported content and remove material identified as hate speech in accordance with the Code and its platform rules. In January 2024 Rakuten (the company behind Viber) established an office in Kyiv to bring together engineering and marketing departments. Alongside launching its Kyiv office the company joined Diia.City as a resident. Subsequently in October 2024 Rakuten Viber inaugurated an office in Manila to broaden its operations, in the Philippines. The company’s legal entity remains Viber Media S.à r.l., registered in Luxembourg. Viber’s engineering work has been carried out across multiple countries and through external partners, including outsourcing and near-shore vendors. As a result, its development operations are distributed internationally rather than concentrated in a single location. In December 2024, Viber was blocked in Russia. Roskomnadzor announced the nationwide blocking of the messaging app due to non-compliance with local legal requirements. == Security audit == On 4 November 2014, Viber scored 1 out of 7 points on the Electronic Frontier Foundation's "Secure Messaging Scorecard". Viber received a point for encryption during transit but lost points because communications were not encrypted with keys that the provider did not have access to (i.e. the communications were not end-to-end encrypted), users could not verify contacts' identities, past messages were not secure if the encryption keys were stolen (i.e. the service did not provide forward secrecy), the code was not open to independent review (i.e. the code was not open-source), the security design was not properly documented, and there had not been a recent independent security audit. On 14 November 2014, the EFF changed Viber's score to 2 out of 7 after it had received an external security audit from Ernst & Young's Advanced Security Centre. On 19 April 2016, with the announcement of Viber version 6.0, Rakuten added end-to-end encryption to their service. The company said that the encryption protocol had only been audited internally, and promised to commission external audits "in the coming weeks". In May 2016, Viber published an overview of their encryption protocol, saying that it is a custom implementation that "uses the same concepts" as the Signal Protocol. In 2022, Rakuten Viber won a Security Award, by test.de, a tech firm based in Germany where there are over 3 million Viber users. In 2024, Rakuten Viber received SOC certification following an audit conducted by Ernst & Young. The certification relates to the company’s controls for data protection and information security. == Market share == As of December 2016, Viber had 800 million registered users. According to Statista, there are 260 million monthly active users as of January 2019. The Viber messenger is very popular in the Philippines, Greece, Eastern Europe, Russia, the Middle East, and some Asian markets. India was the largest market for Viber as of December 2014 with 33 million registered users, the fifth most popular instant messenger in the country. At the same time there were 30 million users in the United States, 28 million in Russia and 18 million in Brazil. Viber is particularly popular in Eastern Europe, being the most downloaded messaging app on Android in Belarus, Moldova and Ukraine as of 2016. It is also popular in Iraq, Libya and Nepal. Viber is translated in 44 languages and used in more than 190 co
Digital on-screen graphic
A digital on-screen graphic, digitally originated graphic (DOG, bug, network bug, on-screen bug or screenbug) is a watermark-like station logo that most television broadcasters overlay over a portion of the screen area of their programs to identify the channel. They are thus a form of permanent visual station identification, increasing brand recognition and asserting ownership of the video signal. The graphic identifies the source of programming, even if it has been time-shifted or recorded. Many of these technologies allow viewers to skip or omit traditional between-programming station identification; thus the use of a DOG enables the station or network to enforce brand identification even when standard commercials are skipped. DOG watermarking helps to reduce off-the-air copyright infringement—for example, the distribution of a current series' episodes on DVD: the watermarked content is easily differentiated from "official" DVD releases, and can help identify not only the station from which the broadcast was captured, but usually the actual date of the broadcast as well. Graphics may be used to identify if the correct subscription is being used for a type of venue. For example, showing Sky Sports within a pub in the United Kingdom requires a more expensive subscription; a channel authorized under this subscription adds a pint glass graphic to the bottom of the screen for inspectors to see. The graphic changes at certain times, making it harder to counterfeit. On the other hand, watermarks pollute the picture, distract viewers' attention and may cover an important piece of information presented in the television program. Extremely bright watermarks may cause screen burn-in or image persistence on some types of television sets such as the now mostly discontinued and rarely used plasma and CRT displays, and currently commonly used OLED and LCD displays. Usage of visually perceptible embedded watermarks requires the program author to have a separate clean copy for archival purposes, but this practice was not common decades ago when watermarking became popular among broadcasters. Watermarks present an issue when archival videos are used for a documentary that strives to create a coherent story. In some cases, watermarks are blurred or digitally removed if possible to clean up the picture. In the absence of visually perceptible watermarks, content control can be ensured with visually imperceptible digital watermarks. In some cases, the graphic also shows the name of the current program. Some television networks may place additional logos or text alongside their DOG to advertise significant upcoming programs. For example, broadcasters of the Olympic Games (most notably United States broadcaster NBC) often add the Olympic rings to their DOG for a period of time leading up to and during the Games. == Usage == == Connections with sponsor tags == Another graphic on television usually connected with sports (particularly in North America, though not in Europe) is the sponsor tag. It shows the logos of certain sponsors, accompanied by some background relevant to the game, the network logo, announcement and music of some kind. == Usage in ham radio and television == In most countries, the ham station is required to periodically identify their amateur-television transmission. Such stations frequently overlay their callsign on the signal instead of placing a card in the background. Most hams use homebuilt devices or old consumer character generators to generate such identifications rather than using graphical superimposes of high cost to do so. Only rarely one can see real graphics, as the callsign is usually written in the "OSD font". == Live DOGs by hobbyists == One of the easiest and most sought-after devices used to generate DOGs by hobbyists is the 1980s vintage Sony XV-T500 video superimposer. This device can luma-key a signal, capture a still frame into memory and then overlay the keyed graphic in one of eight colors onto any CVBS signal. Another method commonly used by hobbyists and even low-budgeted television stations was Amiga computers with genlock interfaces.
Artificial intelligence systems integration
The core idea of artificial intelligence systems integration is making individual software components, such as speech synthesizers, interoperable with other components, such as common sense knowledgebases, in order to create larger, broader and more capable A.I. systems. The main methods that have been proposed for integration are message routing, or communication protocols that the software components use to communicate with each other, often through a middleware blackboard system. Most artificial intelligence systems involve some sort of integrated technologies, for example, the integration of speech synthesis technologies with that of speech recognition. However, in recent years, there has been an increasing discussion on the importance of systems integration as a field in its own right. Proponents of this approach are researchers such as Marvin Minsky, Aaron Sloman, Deb Roy, Kristinn R. Thórisson and Michael A. Arbib. A reason for the recent attention A.I. integration is attracting is that there have already been created a number of (relatively) simple A.I. systems for specific problem domains (such as computer vision, speech synthesis, etc.), and that integrating what's already available is a more logical approach to broader A.I. than building monolithic systems from scratch. == Integration focus == The focus on systems' integration, especially with regard to modular approaches, derive from the fact that most intelligences of significant scales are composed of a multitude of processes and/or utilize multi-modal input and output. For example, a humanoid-type of intelligence would preferably have to be able to talk using speech synthesis, hear using speech recognition, understand using a logical (or some other undefined) mechanism, and so forth. In order to produce artificially intelligent software of broader intelligence, integration of these modalities is necessary. == Challenges and solutions == Collaboration is an integral part of software development as evidenced by the size of software companies and the size of their software departments. Among the tools to ease software collaboration are various procedures and standards that developers can follow to ensure quality, reliability and that their software is compatible with software created by others (such as W3C standards for webpage development). However, collaboration in fields of A.I. has been lacking, for the most part not seen outside the respected schools, departments or research institutes (and sometimes not within them either). This presents practitioners of A.I. systems integration with a substantial problem and often causes A.I. researchers to have to 're-invent the wheel' each time they want a specific functionality to work with their software. Even more damaging is the "not invented here" syndrome, which manifests itself in a strong reluctance of A.I. researchers to build on the work of others. The outcome of this in A.I. is a large set of "solution islands": A.I. research has produced numerous isolated software components and mechanisms that deal with various parts of intelligence separately. To take some examples: Speech synthesis FreeTTS from CMU Speech recognition Sphinx from CMU Logical reasoning OpenCyc from Cycorp Open Mind Common Sense Net from MIT With the increased popularity of the free software movement, a lot of the software being created, including A.I. systems, is available for public exploit. The next natural step is to merge these individual software components into coherent, intelligent systems of a broader nature. As a multitude of components (that often serve the same purpose) have already been created by the community, the most accessible way of integration is giving each of these components an easy way to communicate with each other. By doing so, each component by itself becomes a module, which can then be tried in various settings and configurations of larger architectures. Some challenging and limitations of using A.I. software is the uncontrolled fatal errors. For example, serious and fatal errors have been discovered in very precise fields such as human oncology, as in an article published in the journal Oral Oncology Reports entitled "When AI goes wrong: Fatal errors in oncological research reviewing assistance". The article pointed out a grave error in artificial intelligence based on GBT in the field of biophysics. Many online communities for A.I. developers exist where tutorials, examples, and forums aim at helping both beginners and experts build intelligent systems. However, few communities have succeeded in making a certain standard, or a code of conduct popular to allow the large collection of miscellaneous systems to be integrated with ease. == Methodologies == === Constructionist design methodology === The constructionist design methodology (CDM, or 'Constructionist A.I.') is a formal methodology proposed in 2004, for use in the development of cognitive robotics, communicative humanoids and broad AI systems. The creation of such systems requires the integration of a large number of functionalities that must be carefully coordinated to achieve coherent system behavior. CDM is based on iterative design steps that lead to the creation of a network of named interacting modules, communicating via explicitly typed streams and discrete messages. The OpenAIR message protocol (see below) was inspired by the CDM and has frequently been used to aid in the development of intelligent systems using CDM. == Examples == ASIMO, Honda's humanoid robot, and QRIO, Sony's version of a humanoid robot. Cog, M.I.T. humanoid robot project under the direction of Rodney Brooks. AIBO, Sony's robot dog, integrates vision, hearing and motorskills. TOPIO, TOSY's humanoid robot can play ping-pong with human
Issue tree
An issue tree, also called logic tree, is a graphical breakdown of a question that dissects it into its different components vertically and that progresses into details as it reads to the right. Issue trees are useful in problem solving to identify the root causes of a problem as well as to identify its potential solutions. They also provide a reference point to see how each piece fits into the whole picture of a problem. == Types == According to professor of strategy Arnaud Chevallier, elaborating an approach used at McKinsey & Company, there are two types of issue trees: diagnostic ones and solution ones. Diagnostic trees break down a "why" key question, identifying all the possible root causes for the problem. Solution trees break down a "how" key question, identifying all the possible alternatives to fix the problem. == Rules == Four basic rules can help ensure that issue trees are optimal, according to Chevallier: Consistently answer a "why" or a "how" question Progress from the key question to the analysis as it moves to the right Have branches that are mutually exclusive and collectively exhaustive (MECE) Use an insightful breakdown The requirement for issue trees to be collectively exhaustive implies that divergent thinking is a critical skill. == Applications == === In management interviews === Issue trees are used to answer questions in case interviews for management consulting positions. A quantitative type of question, the market sizing question, requires the interviewee to estimate the size of a data group such as a specific segment of a population, an amount of objects, a company's revenues, or similar. The candidates are expected to use a structured and logical method of arriving at their answer, and using an issue tree provides a diagram to aid the candidate's logical reasoning. Issue trees are used for other types of case interview questions as well.
Production Rule Representation
The Production Rule Representation (PRR) is a proposed standard of the Object Management Group (OMG) that aims to define a vendor-neutral model for representing production rules within the Unified Modeling Language (UML), specifically for use in forward-chaining rule engines. == History == The OMG set up a Business Rules Working Group in 2002 as the first standards body to recognize the importance of the "Business Rules Approach". It issued 2 main RFPs in 2003 – a standard for modeling production rules (PRR), and a standard for modeling business rules as business documentation (BSBR, now SBVR). PRR was mostly defined by and for vendors of Business Rule Engines (BREs) (sometimes termed Business Rules Engine(s), like in Wikipedia). Contributors have included all the major BRE vendors, members of RuleML, and leading UML vendors. == Evolution == The PRR RFP originally suggested that PRR use a combination of UML OCL and Action Semantics for rule conditions and actions. However, expecting modellers to learn 2 relatively obscure UML languages in order to define a production rule proved unpalatable. Therefore, PRR OCL was defined that included OCL extensions for simple rule actions (as well as external functions). PRR OCL is currently considered "non-normative" i.e. is not part of the PRR standard per se. PRR beta applies just to a PRR Core that excludes an explicit expression language. The PRR RFP envisaged covering both forward and backward chaining rule engines. However, the lack of vendor support for / interest in backward chaining caused this to be revise to forward chaining and "sequential" semantics. The latter is simply the scripting mode provided by many BPM tools, where rules are listed and executed sequentially as if programmed. This provides PRR with better compatibility with typical BPM scripting engines (and acknowledges the fact that most BREs today support a "sequential" mode of operation, improving performance in some circumstances). == Status == PRR is currently at version 1.0.
Molecular graphics
Molecular graphics is the discipline and philosophy of studying molecules and their properties through graphical representation. IUPAC limits the definition to representations on a "graphical display device". Ever since Dalton's atoms and Kekulé's benzene, there has been a rich history of hand-drawn atoms and molecules, and these representations have had an important influence on modern molecular graphics. Colour molecular graphics are often used on chemistry journal covers artistically. == History == Prior to the use of computer graphics in representing molecular structure, Robert Corey and Linus Pauling developed a system for representing atoms or groups of atoms from hard wood on a scale of 1 inch = 1 angstrom connected by a clamping device to maintain the molecular configuration. These early models also established the CPK coloring scheme that is still used today to differentiate the different types of atoms in molecular models (e.g. carbon = black, oxygen = red, nitrogen = blue, etc). This early model was improved upon in 1966 by W.L. Koltun and are now known as Corey-Pauling-Koltun (CPK) models. The earliest efforts to produce models of molecular structure was done by Project MAC using wire-frame models displayed on a cathode ray tube in the mid 1960s. In 1965, Carroll Johnson distributed the Oak Ridge thermal ellipsoid plot (ORTEP) that visualized molecules as a ball-and-stick model with lines representing the bonds between atoms and ellipsoids to represent the probability of thermal motion. Thermal ellipsoid plots quickly became the de facto standard used in the display of X-ray crystallography data, and are still in wide use today. The first practical use of molecular graphics was a simple display of the protein myoglobin using a wireframe representation in 1966 by Cyrus Levinthal and Robert Langridge working at Project MAC. Among the milestones in high-performance molecular graphics was the work of Nelson Max in "realistic" rendering of macromolecules using reflecting spheres. Initially much of the technology concentrated on high-performance 3D graphics. During the 1970s, methods for displaying 3D graphics using cathode ray tubes were developed using continuous tone computer graphics in combination with electro-optic shutter viewing devices. The first devices used an active shutter 3D system, generating different perspective views for the left and right channel to provide the illusion of three-dimensional viewing. Stereoscopic viewing glasses were designed using lead lanthanum zirconate titanate (PLZT) ceramics as electronically controlled shutter elements. Active 3D glasses require batteries and work in concert with the display to actively change the presentation by the lenses to the wearer's eyes. Many modern 3D glasses use a passive, polarized 3D system that enables the wearer to visualize 3D effects based on their own perception. Passive 3D glasses are more common today since they are less expensive. The requirements of macromolecular crystallography also drove molecular graphics because the traditional techniques of physical model-building could not scale. The first two protein structures solved by molecular graphics without the aid of the Richards' Box were built with Stan Swanson's program FIT on the Vector General graphics display in the laboratory of Edgar Meyer at Texas A&M University: First Marge Legg in Al Cotton's lab at A&M solved a second, higher-resolution structure of staph. nuclease (1975) and then Jim Hogle solved the structure of monoclinic lysozyme in 1976. A full year passed before other graphics systems were used to replace the Richards' Box for modelling into density in 3-D. Alwyn Jones' FRODO program (and later "O") were developed to overlay the molecular electron density determined from X-ray crystallography and the hypothetical molecular structure. === Timeline === == Types == === Ball-and-stick models === In the ball-and-stick model, atoms are drawn as small sphered connected by rods representing the chemical bonds between them. === Space-filling models === In the space-filling model, atoms are drawn as solid spheres to suggest the space they occupy, in proportion to their van der Waals radii. Atoms that share a bond overlap with each other. === Surfaces === In some models, the surface of the molecule is approximated and shaded to represent a physical property of the molecule, such as electronic charge density. === Ribbon diagrams === Ribbon diagrams are schematic representations of protein structure and are one of the most common methods of protein depiction used today. The ribbon shows the overall path and organization of the protein backbone in 3D, and serves as a visual framework on which to hang details of the full atomic structure, such as the balls for the oxygen atoms bound to the active site of myoglobin in the adjacent image. Ribbon diagrams are generated by interpolating a smooth curve through the polypeptide backbone. α-helices are shown as coiled ribbons or thick tubes, β-strands as arrows, and non-repetitive coils or loops as lines or thin tubes. The direction of the polypeptide chain is shown locally by the arrows, and may be indicated overall by a colour ramp along the length of the ribbon.
Hyper basis function network
In machine learning, a Hyper basis function network, or HyperBF network, is a generalization of radial basis function (RBF) networks concept, where the Mahalanobis-like distance is used instead of the Euclidean distance measure. Hyper basis function networks were first introduced by Poggio and Girosi in the 1990 paper “Networks for Approximation and Learning”. == Network Architecture == The typical HyperBF network structure consists of a real input vector x ∈ R n {\displaystyle x\in \mathbb {R} ^{n}} , a hidden layer of activation functions and a linear output layer. The output of the network is a scalar function of the input vector, ϕ : R n → R {\displaystyle \phi :\mathbb {R} ^{n}\to \mathbb {R} } , is given by where N {\displaystyle N} is a number of neurons in the hidden layer, μ j {\displaystyle \mu _{j}} and a j {\displaystyle a_{j}} are the center and weight of neuron j {\displaystyle j} . The activation function ρ j ( | | x − μ j | | ) {\displaystyle \rho _{j}(||x-\mu _{j}||)} at the HyperBF network takes the following form where R j {\displaystyle R_{j}} is a positive definite d × d {\displaystyle d\times d} matrix. Depending on the application, the following types of matrices R j {\displaystyle R_{j}} are usually considered R j = 1 2 σ 2 I d × d {\displaystyle R_{j}={\frac {1}{2\sigma ^{2}}}\mathbb {I} _{d\times d}} , where σ > 0 {\displaystyle \sigma >0} . This case corresponds to the regular RBF network. R j = 1 2 σ j 2 I d × d {\displaystyle R_{j}={\frac {1}{2\sigma _{j}^{2}}}\mathbb {I} _{d\times d}} , where σ j > 0 {\displaystyle \sigma _{j}>0} . In this case, the basis functions are radially symmetric, but are scaled with different width. R j = d i a g ( 1 2 σ j 1 2 , . . . , 1 2 σ j z 2 ) I d × d {\displaystyle R_{j}=diag\left({\frac {1}{2\sigma _{j1}^{2}}},...,{\frac {1}{2\sigma _{jz}^{2}}}\right)\mathbb {I} _{d\times d}} , where σ j i > 0 {\displaystyle \sigma _{ji}>0} . Every neuron has an elliptic shape with a varying size. Positive definite matrix, but not diagonal. == Training == Training HyperBF networks involves estimation of weights a j {\displaystyle a_{j}} , shape and centers of neurons R j {\displaystyle R_{j}} and μ j {\displaystyle \mu _{j}} . Poggio and Girosi (1990) describe the training method with moving centers and adaptable neuron shapes. The outline of the method is provided below. Consider the quadratic loss of the network H [ ϕ ∗ ] = ∑ i = 1 N ( y i − ϕ ∗ ( x i ) ) 2 {\displaystyle H[\phi ^{}]=\sum _{i=1}^{N}(y_{i}-\phi ^{}(x_{i}))^{2}} . The following conditions must be satisfied at the optimum: where R j = W T W {\displaystyle R_{j}=W^{T}W} . Then in the gradient descent method the values of a j , μ j , W {\displaystyle a_{j},\mu _{j},W} that minimize H [ ϕ ∗ ] {\displaystyle H[\phi ^{}]} can be found as a stable fixed point of the following dynamic system: where ω {\displaystyle \omega } determines the rate of convergence. Overall, training HyperBF networks can be computationally challenging. Moreover, the high degree of freedom of HyperBF leads to overfitting and poor generalization. However, HyperBF networks have an important advantage that a small number of neurons is enough for learning complex functions.