Kubity is a cloud-based 3D communication tool that works on desktop computers, the web, smartphones, tablets, augmented reality gear, and virtual reality glasses. Kubity is powered by several proprietary 3D processing engines including "Paragone" and "Etna" that prepare the 3D file for transfer over mobile devices. Kubity has practical applications for architecture, interior design, engineering, product design, film, and video games among others. The majority of its users create 3D models using SketchUp or Autodesk Revit software. Kubity products include the Kubity web app and Kubity Go (a mobile application for iOS and Android). Kubity is compatible across many platforms, devices and operating systems including: iOS, Android, Firefox, Chrome, Windows, MacOS, and Linux. == History == Kubity was created by SPK Technology (ex Kubity S.A.S.), a Paris-based software company specializing in automatic 3D data optimization and visualization. Founded in 2012 by a group of software engineers and an urban projects developer, they united around a simple idea: create a way for anyone, anywhere to simply and intuitively explore 3D models on smartphones and computers. In order to bring architects, engineers and designers together with their clients around a 3D model, it was essential to develop an interactive platform that supported multiple desktop and mobile devices for instantaneous and fluid 3D navigation. With specifications in place, 15 engineers fused together several technologies: 3D design, data compression, decimation and rendering optimization, web and mobile transfer, and virtual reality headset integration. In January 2014, the first public Kubity prototype (1.0 Amethyst) was launched to a small group of beta testers with a plug-in that allowed users to import 3D models from SketchUp to their browser. A global release was announced in April 2014 at the SketchUp Basecamp in Vail, Colorado. In May 2015, Kubity launched a web application that worked using WebGL technology (2.0 Citrine). For the first time, users were able to drag and drop any SketchUp file in a web browser without having to install a plug-in. In December 2015, Kubity launched a mobile application on the App Store for iPhone, iPod, and iPad as well as on Google Play for Android devices (3.0 Druzy). In November 2016, Kubity launched support for Oculus Rift and HTC Vive (4.0 Emerald). Beginning in November 2017, Kubity launched a full suite rollout of mobile applications over six months that included Kubity AR for augmented reality, Kubity VR for virtual reality, and Kubity Mirror for remote presentations and screen mirroring (5.0 Feldspar). In September 2018, a one-click plugin for SketchUp and Revit (Kubity PRO), along with a mobile-first revamp of Kubity Go was launched, allowing PRO-to-Go device pairing for automatic mobile sync (6.0 Gypsum). In early 2019, the Kubity Go application was updated to include fully integrated AR, VR, and screen mirroring functionalities, killing off the dedicated companion apps Kubity AR, Kubity VR and Kubity Mirror in the process (7.0 Heliotrope). In January 2020, support for the Kubity PRO plugin for SketchUp and Revit was migrated to a SketchUp-only web app. == Technology == Kubity is powered by a proprietary 3D crystallization engine known as "Paragone"; a technology developed by SPK Technology. Paragone takes constrained information from a 3D file and runs it through the "BlockWave" algorithm (US Patent 10,482.629), also developed by SPK Technology. BlockWave is a multiphase optimization algorithm that combines 3D design, data compression, decimation and rendering optimization, web and mobile transfer, and mixed reality headset integration to create a crystallized universal format of the original file. One phase of the BlockWave algorithm is based on the quadric-based polygonal surface simplification algorithm, performed using predefined heuristics, and is associated with a plurality of simplified versions of the 3D model, each version being associated with a predefined level of detail adapted to the user specific end device. BlockWave extracts data content, geometry and textures, then sets quadrics for each top of the original 3D model, and identifies pairs of adjacent tops linked by vertices. The algorithm uses a local collapsing operator and a top-plan error metric to obtain a fixed number of faces or a maximum defined error; 3D meshing is simplified by replacing two points with one, then deleting the degrading faces and updating adjacent relations. Once decimation is completed, texture optimization is set using texture target parameters allowing maximized GPU memory to improve computing time. With texture encoding completed, the crystallized universal 3D file can now be easily opened on any user-specific end device and played across most digital devices with real-time rendering. == Features == === 3D Crystallization === A user converts (or crystallizes) a 3D file by exporting it with the Kubity web app. Crystallization adds features like AR/VR and cinematic fly-through tour as well as assigns the model a dedicated QR code. === Automatic Mobile Sync === When a 3D model is exported, it is automatically synced to Kubity Go on the user's mobile device. From there, it can be accessed, explored, and shared with others with or without an internet connection. === Security and Management === User models can be managed all in one place on Kubity Go or in a browser from their account. Models can be renamed, password-protected, shared, and played. === Augmented Reality === Developed using Apple ARKit and Google ARCore technology, Kubity Go's augmented reality feature maps the environment in a room detecting horizontal planes like tables and floors to track and place 3D objects. By blending digital objects and information with the environment, Kubity allows users to interact with 3D models in true augmented reality. Built-in communication features allows users to instantly share 3D models with anyone over text, email, social media, or direct device-to-device with a QR Code. Platform Support AR supports devices running iOS11 including: iPhone SE, iPhone 6s, iPhone 6s Plus, iPhone 7, iPhone 7 Plus, iPhone 8, iPhone X, all iPad Pro models, and iPad (2017). AR for Android requires Android 7.0 or later and access to the Google Play Store. === Virtual Reality === VR allows users to explore SketchUp models and Revit projects on-the-go right from a mobile device using Oculus Go, Google Cardboard, Samsung Gear VR, or the glasses-free Magic Window feature. Kubity's virtual reality feature is compatible with Oculus Go, Google Cardboard viewers and other cardboard compatible devices including clip-on style VR glasses like Homido Mini, as well as the mobile virtual reality headset, Samsung Gear VR. Samsung Gear VR supports: Galaxy S6, Galaxy S6 Edge, Galaxy S6 Edge+, Samsung Galaxy Note 5, Galaxy S7, Galaxy S7 Edge, Galaxy S8, Galaxy S8+, Samsung Galaxy Note Fan Edition, Samsung Galaxy Note 8, Samsung Galaxy A8/A8+ (2018), and Samsung Galaxy S9/Galaxy S9+. === Screen Mirroring === Screen mirroring allows a user to sync the sender device to a receiver on a webpage, then control from the sender device to give a remote presentation of the 3D model. Devices are easily synced by entering a six-digit number displayed on the receiving computer. == Platform support == On iOS, the Kubity application is compatible with devices running on the version 9.0 or higher. On Android, Kubity is compatible with devices running on the version 4.4 “Kit Kat” or higher. The web version of Kubity applications currently support web browsers compatible with WebGL2 : Mozilla Firefox and Google Chrome. AR is compatible with devices running iOS11 including: iPhone SE, iPhone 6s, iPhone 6s Plus, iPhone 7, iPhone 7 Plus, iPhone 8, iPhone X, all iPad Pro models, and iPad (2017), and Android devices. Requires Android 7.0 or later and access to the Google Play Store. VR is compatible with Google Cardboard viewers and other cardboard compatible devices including clip-on style VR glasses like Homido Mini, as well as the Samsung Gear VR and Oculus Go. Samsung Gear VR supports: Galaxy S6, Galaxy S6 Edge, Galaxy S6 Edge+, Samsung Galaxy Note 5, Galaxy S7, Galaxy S7 Edge, Galaxy S8, Galaxy S8+, Samsung Galaxy Note Fan Edition, Samsung Galaxy Note 8, Samsung Galaxy A8/A8+ (2018) and Samsung Galaxy S9/Galaxy S9+.
Agentive logic
Agentive logic (also called the logic of action or logic of agency) is the field of philosophical logic and logic in computer science that studies formal representations of agents, their actions, and their abilities. An agentive logic in the narrower sense is a formal system whose primitive operators express that an agent does something, can do something, or sees to it that something is the case. Agentive logics generalise modal logic by adding modalities indexed to agents and to actions. Typical examples include: STIT logics (from sees to it that) with operators of the form [ i s t i t : φ ] {\displaystyle [i\ {\mathsf {stit}}:\varphi ]} meaning that agent i {\displaystyle i} sees to it that φ {\displaystyle \varphi } holds; dynamic logics of action with program-like modalities [ α ] φ {\displaystyle [\alpha ]\varphi } and ⟨ α ⟩ φ {\displaystyle \langle \alpha \rangle \varphi } meaning, roughly, that after every (respectively, some) execution(s) of action α {\displaystyle \alpha } , φ {\displaystyle \varphi } holds; logics with explicit agentive operators such as "can do", "brings about", or "is able to ensure". Agentive logics are used in action theory in philosophy, in the semantics of natural language, in the theory of program verification, and in artificial intelligence, where they underpin formalisms for reasoning about actions, planning, and intelligent agents. == Terminology and scope == The adjective agentive derives from the Latin agens ("one who acts") and originally referred to the grammatical agent of a verb. In logical contexts it designates operators or predicates whose primary argument position is an agent rather than a proposition alone, for example A i φ {\displaystyle A_{i}\varphi } ("agent i {\displaystyle i} does φ {\displaystyle \varphi } ") or C i φ {\displaystyle C_{i}\varphi } ("agent i {\displaystyle i} can bring about φ {\displaystyle \varphi } "). In contemporary literature, agentive logic is sometimes used narrowly for formal reconstructions of St. Anselm's modal account of facere ("to do"). More broadly, the term is used interchangeably with logic of action or logic of agency to cover a family of modal and dynamic logics designed to capture the structure of action and choice. == Historical background == === Medieval and early modern roots === Medieval logicians already explored analogies between modalities of action and alethic modalities such as possibility and necessity, for instance, in discussions of obligation and power. An influential early agentive analysis is due to St. Anselm (11th century), who treated "doing φ {\displaystyle \varphi } " as a kind of modal operator on propositions, anticipating later modal logics of agency. Modern reconstructions of Anselm's theory show that the resulting "agentive logic" can be modelled with neighbourhood semantics and satisfies a recognisable square of opposition. === Modern logic of action === Modern study of the logic of action began in the mid-20th century, parallel to developments in deontic logic and tense logic. Early systems were proposed by Georg Henrik von Wright, Stig Kanger, and others, often motivated by questions about norms and responsibility. From the 1960s onward, two largely independent but eventually converging traditions emerged: a branching-time tradition, culminating in STIT logics, emphasising agents' choices among possible futures; and dynamic logics of programs and actions, developed within computer science to reason about program execution. In the 1990s and 2000s, action logics were further developed in connection with knowledge representation, planning, and multi-agent systems in AI, and with dynamic and update semantics in linguistics. == Core ideas == Despite their diversity, most agentive logics share some general themes: Agents are treated as explicit indices of modal operators, as in [ i d o e s ] φ {\displaystyle [i\ {\mathsf {does}}]\varphi } or C i φ {\displaystyle C_{i}\varphi } . Actions are represented either implicitly, via changes between possible worlds along an accessibility relation, or explicitly, as terms denoting primitive and composite actions. Choice and ability are captured by modalities describing what an agent can ensure, usually relative to assumptions about the environment and other agents. Formal properties such as closure under composition, interaction between different agents, and connections to obligation (what an agent ought to do) and knowledge (what an agent knows how to do) are investigated. == STIT logics == STIT ("sees to it that") logics, originating in work by Nuel Belnap and collaborators, treat agency in a branching-time framework. A STIT model consists of a partially ordered set of moments with a tree-like structure, sets of histories (maximal branches through the tree), and for each agent at each moment, a partition of the histories through that moment representing the choices available to the agent. Intuitively, an agent's action at a moment determines which equivalence class (choice cell) of histories becomes actual; a formula [ i s t i t : φ ] {\displaystyle [i\ {\mathsf {stit}}:\varphi ]} is true at a history–moment pair if φ {\displaystyle \varphi } holds on all histories in the choice cell corresponding to the agent's current action. Different STIT operators have been distinguished, notably: the Chellas STIT operator, often written [ i c s t i t : φ ] {\displaystyle [i\ {\mathsf {cstit}}:\varphi ]} , which requires only that the agent's choice guarantees φ {\displaystyle \varphi } ; and the deliberative STIT operator, [ i d s t i t : φ ] {\displaystyle [i\ {\mathsf {dstit}}:\varphi ]} , which additionally requires that φ {\displaystyle \varphi } is not already historically necessary. STIT frameworks have been extended with group agency operators, temporal modalities, epistemic operators, and deontic operators to study responsibility, collective action, and obligations under indeterminism. == Dynamic logics of action == Dynamic logic was originally developed to reason about the behaviour of computer programs, treating program execution as a kind of action. In propositional dynamic logic (PDL), action terms α , β , … {\displaystyle \alpha ,\beta ,\dots } denote abstract programs or actions, and formulas of the form [ α ] φ {\displaystyle [\alpha ]\varphi } and ⟨ α ⟩ φ {\displaystyle \langle \alpha \rangle \varphi } express that all, respectively some, terminating executions of α {\displaystyle \alpha } lead to states where φ {\displaystyle \varphi } holds. From the standpoint of agentive logic, dynamic logic provides: a language for building complex actions from primitives via sequencing, choice, and iteration (e.g., α ; β {\displaystyle \alpha ;\beta } , α ∪ β {\displaystyle \alpha \cup \beta } , α ∗ {\displaystyle \alpha ^{}} ); a Kripke semantics in which actions correspond to labelled accessibility relations; and proof systems (such as Hoare logic and weakest precondition calculi) for reasoning about the correctness of action sequences. Extensions such as concurrent dynamic logic add operators for parallel composition, allowing reasoning about interacting processes and concurrent actions. John-Jules Ch. Meyer and others have argued that dynamic logic is a natural base for logics of agents, by adding modalities for knowledge, belief, and ability on top of the action modalities. Dynamic logics have also been applied to normative reasoning, yielding dynamic deontic logics where actions are related to obligations and permissions, and to dynamic epistemic logics in which information-changing actions such as announcements are modelled as programs. == Situation calculus and other action formalisms == In artificial intelligence, reasoning about action and change is often based on first-order languages that explicitly represent situations, events, and fluents (time-varying properties). The best known is situation calculus, introduced by John McCarthy and developed extensively by Raymond Reiter. In such formalisms: action terms name primitive actions; a function symbol (often d o {\displaystyle {\mathsf {do}}} ) maps an action and a situation to a successor situation; and axioms describe which fluents hold in which situations and how actions change them. Reiter's successor state axioms give compact specifications of how each fluent changes under all actions, and precondition axioms specify when actions are possible. Related formalisms include the event calculus and fluent calculus, which provide alternative ways of representing events and their effects. While these systems are often first-order rather than modal, they are closely related to agentive logics: their action terms and transition structures can be seen as providing models for dynamic or STIT-style modalities, and conversely, dynamic logics can be used as abstract specification languages for such AI formalisms. == Ability, agency, and related modalities == Many agentive logics introduce explicit operators for ability or "can-do"
Link-richness
Link-richness is the quality, possessed by some websites, of having many hyperlinks. Classified advertising sites like Craigslist tend to be very link-rich, sometimes with hundreds of links on their main page. They help users find the links they are looking for by grouping links into clusters. Inadequate link richness has been described as frustrating to readers, as it reduces transparency of site content from the main page. Students new to wiki collaboration were found to need guidance in how to take full advantage of the medium's potential for creating link-rich content. Link-richness in some contexts can be distracting, as when an article is surrounded by extraneous links. Indeed, it is becoming accepted as a best practice for universities to have link-rich home pages that do not rely on user categorisation and exploration of long sequences of links and are not constrained by traditional boundaries between departments. Tools are sometimes needed to make the publishing of link-rich web sites tractable, and many people may lack the technical skills, time, or inclination to engage in hand- crafting new digital document forms. A link-rich site that is low on content is sometimes referred to as a "gateway site." Link-rich portals were popular on the Web in 2000. Yahoo! and other sites featuring categories with many links were heavily used and often required fewer than three clicks to reach the content. Web designers were creating flat sites with content positioned close to the top of pages.
Artificial Intelligence for Digital Response
Artificial Intelligence for Digital Response (AIDR) is a free and open source platform to filter and classify social media messages related to emergencies, disasters, and humanitarian crises. It has been developed by the Qatar Computing Research Institute and awarded the Grand Prize for the 2015 Open Source Software World Challenge. Muhammad Imran stated that he and his team "have developed novel computational techniques and technologies, which can help gain insightful and actionable information from online sources to enable rapid decision-making" - according to him the system "combines human intelligence with machine learning techniques, to solve many real-world challenges during mass emergencies and health issues". == How to use == It can be used by logging in with ones Twitter credentials and by collecting tweets by specifying keywords or hashtags, like #ChileEarthquake, and possibly a geographical region as well. == Use == It has been deployed in conjunction with UNICEF in Zambia to classify short messages related to AIDS/HIV received through the U-Report platform. AIDR was used for the first time during the 2010 Pakistan floods. The first real test of AIDR took place during the 2014 Iquique earthquake in Chile. == Related talks and events == Muhammad Imran delivered a keynote talk on the science behind the AIDR system at the International Conference on Information Systems for Crisis Response And Management (ISCRAM). Abdelkader Lattab and Ji Lucas also presented the system at the 2016 QCRI-IBM Data Science Connect event.
Groundswell (book)
Groundswell is a book by Forrester Research executives Charlene Li and Josh Bernoff that focuses on how companies can take advantage of emerging social technologies. It was published in 2008 by Harvard Business Press. A revised edition was published in 2011. The book attempts to explain a shift in the relationship between customers and companies, in which companies are no longer able to control customers' attitudes through market research, customer service, and advertising. Instead, customers are controlling the conversation by using new media to communicate about products and companies. == Synopsis == The groundswell is characterized by several tactics that guide companies into using social technologies strategically and effectively. Listening: Businesses should listen to their customers to understand what the market is looking for in their products. In order to do this, a company needs to find out if their customers are using social technologies and how they are using them. Talking: Instead of advertising to customers, marketing departments should find creative ways to connect with users about their experience with a product and their feelings about the brand. One common method is participation in social networks. Energizing: Enthusiastic customers are part of the groundswell, and companies can recognize and appreciate these customers by creating online communities and social platforms where they can connect with the brand and provide reviews. Supporting: Businesses can harness the support of their own employees by creating internal social applications for them to connect with the brand, also known as enterprise social software. == Groundswell in action == === Examples === Some companies distinguish their product through the use of social technologies. Tom Dickson successfully marketed his Blendtec line of blenders through the viral marketing campaign Will It Blend? The groundswell spread marketing messages through Digg and YouTube with a small budget and little marketing experience. Other companies have been able to listen to and talk with the groundswell by building their own online communities. Procter & Gamble created beinggirl.com Archived 2016-04-10 at the Wayback Machine to introduce girls to P&G feminine care products. The community approach worked because the company could reach girls with information that might seem embarrassing or sensitive in a traditional marketing campaign. === Risks === Features of particular industries or companies can make direct customer engagement more difficult. For instance, some companies must work within industry regulations, national or multinational corporations must balance corporate and local engagement, and other companies must find ways to engage with customers on time-sensitive issues. == Reception == Kevin Allison of the Financial Times praised the book for its focus on Web analytics: "[Groundswell] is not so much a manifesto or a dissection of online culture as it is a how-to manual for executives and mid-level managers trying to navigate this fast-changing and often confusing environment." The book won the American Marketing Association Foundation’s Berry-AMA Book Prize for best marketing book of 2009. It was also listed by: Amazon, as one of the Top 10 Business & Investing Books of 2008 CIO Insight, as one of the Top 10 Business-Tech Books of 2008 and one of 10 Insightful Web 2.0 Books Fortune as Magazine as one of the 3 best Web books of 2008 Advertising Age as number 3 of 10 Books You Should Have Read BusinessWeek as one of the Best Innovation & Design Books of 2008 "strategy+business" as one of the Best Business Books 2008 and “Top Shelf” in Marketing
Kernel density estimation
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy. == Definition == Let x = ( x 1 , x 2 , x 3 , . . . ) {\displaystyle \mathbf {x} =\left(x_{1},x_{2},x_{3},...\right)} be independent and identically distributed samples drawn from some univariate distribution with an unknown density f at any given point x. We are interested in estimating the shape of this function f. Its kernel density estimator is f ^ h ( x ) = 1 n ∑ i = 1 n K h ( x − x i ) = 1 n h ∑ i = 1 n K ( x − x i h ) , {\displaystyle {\hat {f}}_{h}(x)={\frac {1}{n}}\sum _{i=1}^{n}K_{h}(x-x_{i})={\frac {1}{nh}}\sum _{i=1}^{n}K{\left({\frac {x-x_{i}}{h}}\right)},} where K is the kernel — a non-negative function — and h > 0 is a smoothing parameter called the bandwidth or simply width. A kernel with subscript h is called the scaled kernel and defined as Kh(x) = 1/h K(x/h). Intuitively one wants to choose h as small as the data will allow; however, there is always a trade-off between the bias of the estimator and its variance. The choice of bandwidth is discussed in more detail below. A range of kernel functions are commonly used: uniform, triangular, biweight, triweight, Epanechnikov (parabolic), normal, and others. The Epanechnikov kernel is optimal in a mean square error sense, though the loss of efficiency is small for the kernels listed previously. Due to its convenient mathematical properties, the normal kernel is often used, which means K(x) = ϕ(x), where ϕ is the standard normal density function. The kernel density estimator then becomes f ^ h ( x ) = 1 n ∑ i = 1 n 1 h 2 π exp ( − ( x − x i ) 2 2 h 2 ) , {\displaystyle {\hat {f}}_{h}(x)={\frac {1}{n}}\sum _{i=1}^{n}{\frac {1}{h{\sqrt {2\pi }}}}\exp \left({\frac {-(x-x_{i})^{2}}{2h^{2}}}\right),} where h {\displaystyle h} is the standard deviation of the sample x {\displaystyle \mathbf {x} } . The construction of a kernel density estimate finds interpretations in fields outside of density estimation. For example, in thermodynamics, this is equivalent to the amount of heat generated when heat kernels (the fundamental solution to the heat equation) are placed at each data point locations xi. Similar methods are used to construct discrete Laplace operators on point clouds for manifold learning (e.g. diffusion map). == Example == Kernel density estimates are closely related to histograms, but can be endowed with properties such as smoothness or continuity by using a suitable kernel. The diagram below based on these 6 data points illustrates this relationship: For the histogram, first, the horizontal axis is divided into sub-intervals or bins which cover the range of the data: In this case, six bins each of width 2. Whenever a data point falls inside this interval, a box of height 1/12 is placed there. If more than one data point falls inside the same bin, the boxes are stacked on top of each other. For the kernel density estimate, normal kernels with a standard deviation of 1.5 (indicated by the red dashed lines) are placed on each of the data points xi. The kernels are summed to make the kernel density estimate (solid blue curve). The smoothness of the kernel density estimate (compared to the discreteness of the histogram) illustrates how kernel density estimates converge faster to the true underlying density for continuous random variables. == Bandwidth selection == The bandwidth of the kernel is a free parameter which exhibits a strong influence on the resulting estimate. To illustrate its effect, we take a simulated random sample from the standard normal distribution (plotted at the blue spikes in the rug plot on the horizontal axis). The grey curve is the true density (a normal density with mean 0 and variance 1). In comparison, the red curve is undersmoothed since it contains too many spurious data artifacts arising from using a bandwidth h = 0.05, which is too small. The green curve is oversmoothed since using the bandwidth h = 2 obscures much of the underlying structure. The black curve with a bandwidth of h = 0.337 is considered to be optimally smoothed since its density estimate is close to the true density. An extreme situation is encountered in the limit h → 0 {\displaystyle h\to 0} (no smoothing), where the estimate is a sum of n delta functions centered at the coordinates of analyzed samples. In the other extreme limit h → ∞ {\displaystyle h\to \infty } the estimate retains the shape of the used kernel, centered on the mean of the samples (completely smooth). The most common optimality criterion used to select this parameter is the expected L2 risk function, also termed the mean integrated squared error: MISE ( h ) = E [ ∫ ( f ^ h ( x ) − f ( x ) ) 2 d x ] {\displaystyle \operatorname {MISE} (h)=\operatorname {E} \!\left[\int \!{\left({\hat {f}}\!_{h}(x)-f(x)\right)}^{2}dx\right]} Under weak assumptions on f and K, (f is the, generally unknown, real density function), MISE ( h ) = AMISE ( h ) + o ( ( n h ) − 1 + h 4 ) {\displaystyle \operatorname {MISE} (h)=\operatorname {AMISE} (h)+{\mathcal {o}}{\left((nh)^{-1}+h^{4}\right)}} where o is the little o notation, and n the sample size (as above). The AMISE is the asymptotic MISE, i. e. the two leading terms, AMISE ( h ) = R ( K ) n h + 1 4 m 2 ( K ) 2 h 4 R ( f ″ ) {\displaystyle \operatorname {AMISE} (h)={\frac {R(K)}{nh}}+{\frac {1}{4}}m_{2}(K)^{2}h^{4}R(f'')} where R ( g ) = ∫ g ( x ) 2 d x {\textstyle R(g)=\int g(x)^{2}\,dx} for a function g, m 2 ( K ) = ∫ x 2 K ( x ) d x {\textstyle m_{2}(K)=\int x^{2}K(x)\,dx} and f ″ {\displaystyle f''} is the second derivative of f {\displaystyle f} and K {\displaystyle K} is the kernel. The minimum of this AMISE is the solution to this differential equation ∂ ∂ h AMISE ( h ) = − R ( K ) n h 2 + m 2 ( K ) 2 h 3 R ( f ″ ) = 0 {\displaystyle {\frac {\partial }{\partial h}}\operatorname {AMISE} (h)=-{\frac {R(K)}{nh^{2}}}+m_{2}(K)^{2}h^{3}R(f'')=0} or h AMISE = R ( K ) 1 / 5 m 2 ( K ) 2 / 5 R ( f ″ ) 1 / 5 n − 1 / 5 = C n − 1 / 5 {\displaystyle h_{\operatorname {AMISE} }={\frac {R(K)^{1/5}}{m_{2}(K)^{2/5}R(f'')^{1/5}}}n^{-1/5}=Cn^{-1/5}} Neither the AMISE nor the hAMISE formulas can be used directly since they involve the unknown density function f {\displaystyle f} or its second derivative f ″ {\displaystyle f''} . To overcome that difficulty, a variety of automatic, data-based methods have been developed to select the bandwidth. Several review studies have been undertaken to compare their efficacies, with the general consensus that the plug-in selectors and cross validation selectors are the most useful over a wide range of data sets. Substituting any bandwidth h which has the same asymptotic order n−1/5 as hAMISE into the AMISE gives that AMISE(h) = O(n−4/5), where O is the big O notation. It can be shown that, under weak assumptions, there cannot exist a non-parametric estimator that converges at a faster rate than the kernel estimator. Note that the n−4/5 rate is slower than the typical n−1 convergence rate of parametric methods. If the bandwidth is not held fixed, but is varied depending upon the location of either the estimate (balloon estimator) or the samples (pointwise estimator), this produces a particularly powerful method termed adaptive or variable bandwidth kernel density estimation. Bandwidth selection for kernel density estimation of heavy-tailed distributions is relatively difficult. === A rule-of-thumb bandwidth estimator === If Gaussian basis functions are used to approximate univariate data, and the underlying density being estimated is Gaussian, the optimal choice for h (that is, the bandwidth that minimises the mean integrated squared error) is: h = ( 4 σ ^ 5 3 n ) 1 / 5 ≈ 1.06 σ ^ n − 1 / 5 , {\displaystyle h={\left({\frac {4{\hat {\sigma }}^{5}}{3n}}\right)}^{1/5}\approx 1.06\,{\hat {\sigma }}\,n^{-1/5},} An h {\displaystyle h} value is considered more robust when it improves the fit for long-tailed and skewed distributions or for bimodal mixture distributions. This is often done empirically by replacing the standard deviation σ ^ {\displaystyle {\hat {\sigma }}} by the parameter A {\displaystyle A} below: A = min ( σ ^ , I Q R 1.34 ) {\displaystyle A=\min \left({\hat {\sigma }},{\frac {\mathrm {IQR} }{1.34}}\right)} where IQR is the
Global digital divide
The global digital divide describes global disparities, primarily between developed and developing countries, in regards to access to computing and information resources such as the Internet and the opportunities derived from such access. The Internet is expanding very quickly, and not all countries—especially developing countries—can keep up with the constant changes. The term "digital divide" does not necessarily mean that someone does not have technology; it could mean that there is simply a difference in technology. These differences can refer to, for example, high-quality computers, fast Internet, technical assistance, or telephone services. == Statistics == There is a large inequality worldwide in terms of the distribution of installed telecommunication bandwidth. In 2014 only three countries (China, US, Japan) host 50% of the globally installed bandwidth potential (see pie-chart Figure on the right). This concentration is not new, as historically only ten countries have hosted 70–75% of the global telecommunication capacity (see Figure). The U.S. lost its global leadership in terms of installed bandwidth in 2011, being replaced by China, which hosts more than twice as much national bandwidth potential in 2014 (29% versus 13% of the global total). == Versus the digital divide == The global digital divide is a special case of the digital divide; the focus is set on the fact that "Internet has developed unevenly throughout the world" causing some countries to fall behind in technology, education, labor, democracy, and tourism. The concept of the digital divide was originally popularized regarding the disparity in Internet access between rural and urban areas of the United States of America; the global digital divide mirrors this disparity on an international scale. The global digital divide also contributes to the inequality of access to goods and services available through technology. Computers and the Internet provide users with improved education, which can lead to higher wages; the people living in nations with limited access are therefore disadvantaged. This global divide is often characterized as falling along what is sometimes called the North–South divide of "northern" wealthier nations and "southern" poorer ones. == Obstacles to a solution == Some people argue that necessities need to be considered before achieving digital inclusion, such as an ample food supply and quality health care. Minimizing the global digital divide requires considering and addressing the following types of access: === Physical access === Involves "the distribution of ICT devices per capita…and land lines per thousands". Individuals need to obtain access to computers, landlines, and networks in order to access the Internet. This access barrier is also addressed in Article 21 of the convention on the Rights of Persons with Disabilities by the United Nations. === Financial access === The cost of ICT devices, traffic, applications, technician and educator training, software, maintenance, and infrastructures require ongoing financial means. Financial access and "the levels of household income play a significant role in widening the gap". === Socio-demographic access === Empirical tests have identified that several socio-demographic characteristics foster or limit ICT access and usage. Among different countries, educational levels and income are the most powerful explanatory variables, with age being a third one. While a Global Gender Gap in access and usage of ICT's exist, empirical evidence shows that this is due to unfavorable conditions concerning employment, education and income and not to technophobia or lower ability. In the contexts understudy, women with the prerequisites for access and usage turned out to be more active users of digital tools than men. In the US, for example, the figures for 2018 show 89% of men and 88% of women use the Internet. === Cognitive access === In order to use computer technology, a certain level of information literacy is needed. Further challenges include information overload and the ability to find and use reliable information. === Design access === Computers need to be accessible to individuals with different learning and physical abilities including complying with Section 508 of the Rehabilitation Act as amended by the Workforce Investment Act of 1998 in the United States. === Institutional access === In illustrating institutional access, Wilson states "the numbers of users are greatly affected by whether access is offered only through individual homes or whether it is offered through schools, community centers, religious institutions, cybercafés, or post offices, especially in poor countries where computer access at work or home is highly limited". === Political access === Guillen & Suarez argue that "democratic political regimes enable faster growth of the Internet than authoritarian or totalitarian regimes." The Internet is considered a form of e-democracy, and attempting to control what citizens can or cannot view is in contradiction to this. Recently situations in Iran and China have denied people the ability to access certain websites and disseminate information. Iran has prohibited the use of high-speed Internet in the country and has removed many satellite dishes in order to prevent the influence of Western culture, such as music and television. === Cultural access === Many experts claim that bridging the digital divide is not sufficient and that the images and language needed to be conveyed in a language and images that can be read across different cultural lines. A 2013 study conducted by Pew Research Center noted how participants taking the survey in Spanish were nearly twice as likely not to use the internet. == Examples == In the early 21st century, residents of developed countries enjoy many Internet services which are not yet widely available in developing countries, including: Mobile phones and small electronic communication devices; E-communities and social-networking; Fast broadband Internet connections, enabling advanced Internet applications; Affordable and widespread Internet access, either through personal computers at home or work, through public terminals in public libraries and Internet cafes, and through wireless access points; E-commerce enabled by efficient electronic payment networks like credit cards and reliable shipping services; Virtual globes featuring street maps searchable down to individual street addresses and detailed satellite and aerial photography; Online research systems which enable users to peruse newspaper and magazine articles that may be centuries old, without having to leave home; Electronic readers such as Kindle, Sony Reader, Samsung Papyrus and Iliad by iRex Technologies; Price engines which help consumers find the best possible online prices and similar services which find the best possible prices at local retailers; Electronic services delivery of government services, such as the ability to pay taxes, fees, and fines online. Further civic engagement through e-government and other sources such as finding information about candidates regarding political situations. == Proposed remedies == There are four specific arguments why it is important to "bridge the gap": Economic equality – For example, the telephone is often seen as one of the most important components, because having access to a working telephone can lead to higher safety. If there were to be an emergency, one could easily call for help if one could use a nearby phone. In another example, many work-related tasks are online, and people without access to the Internet may not be able to complete work up to company standards. The Internet is regarded by some as a basic component of civic life that developed countries ought to guarantee for their citizens. Additionally, welfare services, for example, are sometimes offered via the Internet. Social mobility – Computer and Internet use is regarded as being very important to development and success. However, some children are not getting as much technical education as others, because lower socioeconomic areas cannot afford to provide schools with computer facilities. For this reason, some kids are being separated and not receiving the same chance as others to be successful. Democracy – Some people believe that eliminating the digital divide would help countries become healthier democracies. They argue that communities would become much more involved in events such as elections or decision making. Economic growth – It is believed that less-developed nations could gain quick access to economic growth if the information infrastructure were to be developed and well used. By improving the latest technologies, certain countries and industries can gain a competitive advantage. While these four arguments are meant to lead to a solution to the digital divide, there are a couple of other components that need to be considered. The first one is rural living versus s