AI For Business Research

AI For Business Research — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

• 

  Gapo

  Gapo is a Vietnamese social networking service based in Hanoi, Vietnam. Users are able to create a personal profile and share text, photos and videos with others on the platform. Users can also use Gapo for live streaming, instant messaging, blogging, and online payments. Gapo was launched in July 2019 by Hà Trung Kiên and Duong Vi Khoa. == History == Gapo was founded in response to calls for Vietnam's Communist-led government to produce a domestic alternative to social media giants like Facebook and Google. Gapo officially launched on July 23, 2019 at an event in Hanoi. The company received 500 billion đồng (US$22 million) in funding from technology corporation G-Group to be utilized in the first phase of development. They also partnered with Sony Music Entertainment to provide music content to its services. == Features == Gapo features a news feed for posting content, livestreaming, instant messaging, and blogging. It also allows users to pay online and access public services. == Reception == Within two days of launch, Gapo received about 200,000 registrations. By September 2019, the user base increased to one million. Upon launch, Gapo experienced significant technical difficulties. Users complained about the inability to sign up for a new account and said that certain functions were not available for use at launch. This issue caused Gapo to temporarily suspend their services in order to perform upgrades and bug fixes. Gapo relaunched the next day, though many users reported that the access speed decreased. The mobile app also received mixed reviews from users in both the App Store and the Google Play Store, with an average rating of 3.1 and 3.5, respectively. Most users found the app to be a knockoff of Facebook, although some users praised the app for being locally developed. === Expert opinions on platform viability === Le Hong Hiep of the ISEAS - Yusof Ishak Institute was doubtful that a Vietnamese-owned social network service could be as powerful as a foreign-based service, stating that Vietnam might not be able to develop a viable social media network to compete with the likes of Facebook or Google. Others, like blogger Ann Chi, said that, due to local players complying with local censorship policy, there is a chance that locals might not trust Gapo and other local services in light of possible surveillance. Regarding the targeted user base figure for the end of 2019 and 2021, experts cautioned that the company might need an additional trillion đồng of funding to reach its planned user base targets. In response, the company stated that Gapo was never meant to compete with Facebook, but instead noted that the main difference between Gapo and Facebook is that Gapo provides a personalized user experience through customization. == Censorship == Gapo has the right to censor posts and news that are deemed offensive and inaccurate by users or not approved by the censorship curators.

  Read more →
• 

  Spatial computing

  Spatial computing refers to 3D human–computer interaction techniques that are perceived by users as taking place in the real world, in and around their bodies and physical environments, instead of constrained to and perceptually behind computer screens or in purely virtual worlds. This concept inverts the long-standing practice of teaching people to interact with computers in digital environments, and instead teaches computers to better understand and interact with people more naturally in the human world. This concept overlaps with and encompasses others including extended reality, augmented reality, mixed reality, natural user interface, contextual computing, affective computing, and ubiquitous computing. The usage for labeling and discussing these adjacent technologies is imprecise. Spatial computing devices include sensors—such as RGB cameras, depth cameras, 3D trackers, inertial measurement units, or other tools—to sense and track nearby human bodies (including hands, arms, eyes, legs, mouths) during ordinary interactions with people and computers in a 3D space. They further use computer vision to attempt to understand real world scenes, such as rooms, streets or stores, to read labels, to recognize objects, create 3D maps, and more. Quite often they also use extended reality and mixed reality to superimpose virtual 3D graphics and virtual 3D audio onto the human visual and auditory system as a way of providing information more naturally and contextually than traditional 2D screens. Spatial computing often refers to personal computing devices like headsets and headphones, but other human-computer interactions that leverage real-time spatial positioning for displays, like projection mapping or cave automatic virtual environment displays, can also be considered spatial computing if they leverage human-computer input for the participants. == History == The term "spatial computing" apparently originated in the field of GIS around 1985 or earlier to describe computations on large-scale geospatial information. Early examples of spatial computing in GIS include ArcInfo and its iterations, initially released in 1981, a part of ArcGIS along with ArcEditor, which together provide mapping, analysis, editing, and geoprocessing for geodatabases. This is somewhat related to the modern use, but on the scale of continents, cities, and neighborhoods. Modern spatial computing is more centered on the human scale of interaction, around the size of a living room or smaller. But it is not limited to that scale in the aggregate. In the early 1990s, as field of virtual reality was beginning to be commercialized beyond academic and military labs, a startup called Worldesign in Seattle used the term Spatial Computing to describe the interaction between individual people and 3D spaces, operating more at the human end of the scale than previous GIS examples may have contemplated. The company built a CAVE-like environment it called the Virtual Environment Theater, whose 3D experience was of a virtual flyover of the Giza Plateau, circa 3000 BC. Robert Jacobson, CEO of Worldesign, attributes the origins of the term to experiments at the Human Interface Technology Lab, at the University of Washington, under the direction of Thomas A. Furness III. Jacobson was a co-founder of that lab before spinning off this early VR startup. In 1997, an academic publication by T. Caelli, Peng Lam, and H. Bunke called "Spatial Computing: Issues in Vision, Multimedia and Visualization Technologies" introduced the term more broadly for academic audiences, focusing on a variety of topics such as image processing, dead reckoning navigation, object recognition, and visualizing spatial data. The specific term "spatial computing" was later referenced again in 2003 by Simon Greenwold, as "human interaction with a machine in which the machine retains and manipulates referents to real objects and spaces". MIT Media Lab alumnus John Underkoffler gave a TED talk in 2010 giving a live demo of the multi-screen, multi-user spatial computing systems being developed by Oblong Industries, which sought to bring to life the futuristic interfaces conceptualized by Underkoffler in the films Minority Report and Iron Man. Google Earth, initially released by Keyhole Inc. in 2001 and re-released by Google in 2005 can be considered a capable GIS and includes advanced geospatial tools and capabilities. == Notable instances of the use of spatial computing == In 2019, Microsoft HoloLens released a video outlining Airbus' partnership with Microsoft Azure to utilize the latter's mixed reality services for streamlining and improving the aircraft design process, as well as reducing the error in development. Airbus utilized the HoloLens 2 to this end, and the executive vice president of engineering claimed that their design process' validation phases were "hugely accelerated by 80 percent", as well as "strongly believe[d]" that up to 30% improvements in their industrial tasks could be attained with the HoloLens 2. During the presentational video, Airbus cited the maturity of Microsoft Azure services as "key" for their usage of the HoloLens 2. Also in 2019, the U.S. army partnered with Microsoft to produce a HoloLens based Integrated Visual Augmentation System (IVAS) to enhance infantry members by giving troops various abilities, including but not limited to using holographs to train, projecting 3D maps into their vision, and seeing through smoke and corners. Microsoft received tens of thousands of hours of feedback for their systems by 2021. Sergeant Marc Krugh at the time claimed that Microsoft's partnership has already caused the army to rethink some of its troops' operation strategy. == Products == === Apple Vision Pro === Apple announced Apple Vision Pro, a device it markets as a "spatial computer", on June 5, 2023. It includes several features such as Spatial Audio, two 4K micro-OLED displays, the Apple R1 chip and eye tracking, and released in the United States on February 2, 2024. In announcing the platform, Apple invoked its history of popularizing 2D graphical user interfaces that supplanted prior human-computer interface mechanisms such as the command line. Apple suggests the introduction of spatial computing as a new category of interactive device, on the same level of importance as the introduction of the 2D GUI. Apple Vision Pro runs on a new operating system called visionOS, which combines eye tracking, gesture recognition, and voice input to enable immersive interaction without physical controllers. The platform is aimed at productivity, entertainment, collaboration, and enterprise use cases. === Magic Leap === Magic Leap had also previously used the term “spatial computing” to describe its own devices. Its first headset, the Magic Leap 1, was released on August 8, 2018. Magic Leap’s technology enables the display of content into the real world using an optical see-through head-mounted display, which projects an overlay of a virtual world into the user’s field of view. This allows for an experience where the physical and digital worlds are perceived simultaneously. === Microsoft Hololens === On February 24, 2019, Microsoft released the HoloLens 2, which includes mixed reality tools and can generate interactable, manipulatable holograms in 3D space. The holograms in question can be related to a physical object or completely independent and free-floating. The Azure Spatial Anchors cloud service was released simultaneously, which gives the holograms capability to persist across time and many individuals' devices. === Meta Quest === The Meta Quest 3, a mixed reality gaming headset that includes spatial audio, two color cameras, and grants the ability to interact with virtual characters released on October 9, 2023, at a notably cheaper price than the Apple Vision Pro, but with reduced capabilities. === Snap Spectacles === Spectacles (product) are augmented reality glasses developed by Snap Inc.. The latest generation includes a 46-degree stereoscopic display, adjustable tint, and Snapdragon processors. Spectacles allow users to interact with a collection of augmented reality experiences designed for education, entertainment, and utility. Currently, the device is in the hands of selected developers and creators, as part of an experimental AR ecosystem focused on creativity, use case exploration and expression.

  Read more →
• 

  Upper ontology

  In information science, an upper ontology (also known as a top-level ontology, upper model, or foundation ontology) is an ontology (in the sense used in information science) that consists of very general terms (such as "object", "property", "relation") that are common across all domains. An important function of an upper ontology is to support broad semantic interoperability among a large number of domain-specific ontologies by providing a common starting point for the formulation of definitions. Terms in the domain ontology are ranked under the terms in the upper ontology, e.g., the upper ontology classes are superclasses or supersets of all the classes in the domain ontologies. A number of upper ontologies have been proposed, each with its own proponents. Library classification systems predate upper ontology systems. Though library classifications organize and categorize knowledge using general concepts that are the same across all knowledge domains, neither system is a replacement for the other. == Development == Any standard foundational ontology is likely to be contested among different groups, each with its own idea of "what exists". One factor exacerbating the failure to arrive at a common approach has been the lack of open-source applications that would permit the testing of different ontologies in the same computational environment. The differences have thus been debated largely on theoretical grounds, or are merely the result of personal preferences. Foundational ontologies can however be compared on the basis of adoption for the purposes of supporting interoperability across domain ontologies. No particular upper ontology has yet gained widespread acceptance as a de facto standard. Different organizations have attempted to define standards for specific domains. The 'Process Specification Language' (PSL) created by the National Institute of Standards and Technology (NIST) is one example. Another important factor leading to the absence of wide adoption of any existing upper ontology is the complexity. Some upper ontologies—Cyc is often cited as an example in this regard—are very large, ranging up to thousands of elements (classes, relations), with complex interactions among them and with a complexity similar to that of a human natural language, and the learning process can be even longer than for a natural language because of the unfamiliar format and logical rules. The motivation to overcome this learning barrier is largely absent because of the paucity of publicly accessible examples of use. As a result, those building domain ontologies for local applications tend to create the simplest possible domain-specific ontology, not related to any upper ontology. Such domain ontologies may function adequately for the local purpose, but they are very time-consuming to relate accurately to other domain ontologies. To solve this problem, some genuinely top level ontologies have been developed, which are deliberately designed to have minimal overlap with any domain ontologies. Examples are Basic Formal Ontology and the DOLCE (see below). === Arguments for the infeasibility of an upper ontology === Historically, many attempts in many societies have been made to impose or define a single set of concepts as more primal, basic, foundational, authoritative, true or rational than all others. A common objection to such attempts points out that humans lack the sort of transcendent perspective — or God's eye view — that would be required to achieve this goal. Humans are bound by language or culture, and so lack the sort of objective perspective from which to observe the whole terrain of concepts and derive any one standard. Thomasson, under the headline "1.5 Skepticism about Category Systems", wrote: "category systems, at least as traditionally presented, seem to presuppose that there is a unique true answer to the question of what categories of entity there are – indeed the discovery of this answer is the goal of most such inquiries into ontological categories. [...] But actual category systems offered vary so much that even a short survey of past category systems like that above can undermine the belief that such a unique, true and complete system of categories may be found. Given such a diversity of answers to the question of what the ontological categories are, by what criteria could we possibly choose among them to determine which is uniquely correct?" Another objection is the problem of formulating definitions. Top level ontologies are designed to maximize support for interoperability across a large number of terms. Such ontologies must therefore consist of terms expressing very general concepts, but such concepts are so basic to our understanding that there is no way in which they can be defined, since the very process of definition implies that a less basic (and less well understood) concept is defined in terms of concepts that are more basic and so (ideally) more well understood. Very general concepts can often only be elucidated, for example by means of examples, or paraphrase. There is no self-evident way of dividing the world up into concepts, and certainly no non-controversial one There is no neutral ground that can serve as a means of translating between specialized (or "lower" or "application-specific") ontologies Human language itself is already an arbitrary approximation of just one among many possible conceptual maps. To draw any necessary correlation between English words and any number of intellectual concepts, that we might like to represent in our ontologies, is just asking for trouble. (WordNet, for instance, is successful and useful, precisely because it does not pretend to be a general-purpose upper ontology; rather, it is a tool for semantic / syntactic / linguistic disambiguation, which is richly embedded in the particulars and peculiarities of the English language.) Any hierarchical or topological representation of concepts must begin from some ontological, epistemological, linguistic, cultural, and ultimately pragmatic perspective. Such pragmatism does not allow for the exclusion of politics between persons or groups, indeed it requires they be considered as perhaps more basic primitives than any that are represented. Those who doubt the feasibility of general purpose ontologies are more inclined to ask "what specific purpose do we have in mind for this conceptual map of entities and what practical difference will this ontology make?" This pragmatic philosophical position surrenders all hope of devising the encoded ontology version of "The world is everything that is the case." (Wittgenstein, Tractatus Logico-Philosophicus). Finally, there are objections similar to those against artificial intelligence. Technically, the complex concept acquisition and the social / linguistic interactions of human beings suggest any axiomatic foundation of "most basic" concepts must be cognitive biological or otherwise difficult to characterize since we don't have axioms for such systems. Ethically, any general-purpose ontology could quickly become an actual tyranny by recruiting adherents into a political program designed to propagate it and its funding means, and possibly defend it by violence. Historically, inconsistent and irrational belief systems have proven capable of commanding obedience to the detriment or harm of persons both inside and outside a society that accepts them. How much more harmful would a consistent rational one be, were it to contain even one or two basic assumptions incompatible with human life? === Arguments for the feasibility of an upper ontology === Many of those who doubt the possibility of developing wide agreement on a common upper ontology fall into one of two traps: they assert that there is no possibility of universal agreement on any conceptual scheme; but they argue that a practical common ontology does not need to have universal agreement, it only needs a large enough user community (as is the case for human languages) to make it profitable for developers to use it as a means to general interoperability, and for third-party developer to develop utilities to make it easier to use; and they point out that developers of data schemes find different representations congenial for their local purposes; but they do not demonstrate that these different representations are in fact logically inconsistent. In fact, different representations of assertions about the real world (though not philosophical models), if they accurately reflect the world, must be logically consistent, even if they focus on different aspects of the same physical object or phenomenon. If any two assertions about the real world are logically inconsistent, one or both must be wrong, and that is a topic for experimental investigation, not for ontological representation. In practice, representations of the real world are created as and known to be approximations to the basic reality, and their use is circumscribed by the limits of e

  Read more →
• 

  Higuchi dimension

  In fractal geometry, the Higuchi dimension (or Higuchi fractal dimension (HFD)) is an approximate value for the box-counting dimension of the graph of a real-valued function or time series. This value is obtained via an algorithmic approximation so one also talks about the Higuchi method. It has many applications in science and engineering and has been applied to subjects like characterizing primary waves in seismograms, clinical neurophysiology and analyzing changes in the electroencephalogram in Alzheimer's disease. == Formulation of the method == The original formulation of the method is due to T. Higuchi. Given a time series X : { 1 , … , N } → R {\displaystyle X:\{1,\dots ,N\}\to \mathbb {R} } consisting of N {\displaystyle N} data points and a parameter k m a x ≥ 2 {\displaystyle k_{\mathrm {max} }\geq 2} the Higuchi Fractal dimension (HFD) of X {\displaystyle X} is calculated in the following way: For each k ∈ { 1 , … , k m a x } {\displaystyle k\in \{1,\dots ,k_{\mathrm {max} }}\} and m ∈ { 1 , … , k } {\displaystyle m\in \{1,\dots ,k}\} define the length L m ( k ) {\displaystyle L_{m}(k)} by L m ( k ) = N − 1 ⌊ N − m k ⌋ k 2 ∑ i = 1 ⌊ N − m k ⌋ | X N ( m + i k ) − X N ( m + ( i − 1 ) k ) | . {\displaystyle L_{m}(k)={\frac {N-1}{\lfloor {\frac {N-m}{k}}\rfloor k^{2}}}\sum _{i=1}^{\lfloor {\frac {N-m}{k}}\rfloor }|X_{N}(m+ik)-X_{N}(m+(i-1)k)|.} The length L ( k ) {\displaystyle L(k)} is defined by the average value of the k {\displaystyle k} lengths L 1 ( k ) , … , L k ( k ) {\displaystyle L_{1}(k),\dots ,L_{k}(k)} , L ( k ) = 1 k ∑ m = 1 k L m ( k ) . {\displaystyle L(k)={\frac {1}{k}}\sum _{m=1}^{k}L_{m}(k).} The slope of the best-fitting linear function through the data points { ( log ⁡ 1 k , log ⁡ L ( k ) ) } {\displaystyle \left\{\left(\log {\frac {1}{k}},\log L(k)\right)\right\}} is defined to be the Higuchi fractal dimension of the time-series X {\displaystyle X} . == Application to functions == For a real-valued function f : [ 0 , 1 ] → R {\displaystyle f:[0,1]\to \mathbb {R} } one can partition the unit interval [ 0 , 1 ] {\displaystyle [0,1]} into N {\displaystyle N} equidistantly intervals [ t j , t j + 1 ) {\displaystyle [t_{j},t_{j+1})} and apply the Higuchi algorithm to the times series X ( j ) = f ( t j ) {\displaystyle X(j)=f(t_{j})} . This results into the Higuchi fractal dimension of the function f {\displaystyle f} . It was shown that in this case the Higuchi method yields an approximation for the box-counting dimension of the graph of f {\displaystyle f} as it follows a geometrical approach (see Liehr & Massopust 2020). == Robustness and stability == Applications to fractional Brownian functions and the Weierstrass function reveal that the Higuchi fractal dimension can be close to the box-dimension. On the other hand, the method can be unstable in the case where the data X ( 1 ) , … , X ( N ) {\displaystyle X(1),\dots ,X(N)} are periodic or if subsets of it lie on a horizontal line (see Liehr & Massopust 2020).

  Read more →
• 

  Energy-based model

  An energy-based model (EBM), also called Canonical Ensemble Learning (CEL) or Learning via Canonical Ensemble (LCE), is an application of canonical ensemble formulation from statistical physics for learning from data. The approach prominently appears in generative artificial intelligence. EBMs provide a unified framework for many probabilistic and non-probabilistic approaches to such learning, particularly for training graphical and other structured models. An EBM learns the characteristics of a target dataset and generates a similar but larger dataset. EBMs detect the latent variables of a dataset and generate new datasets with a similar distribution. Energy-based generative neural networks is a class of generative models, which aim to learn explicit probability distributions of data in the form of energy-based models, the energy functions of which are parameterized by modern deep neural networks. Boltzmann machines are a special form of energy-based models with a specific parametrization of the energy. == Description == For a given input x {\displaystyle x} , the model describes an energy E θ ( x ) {\displaystyle E_{\theta }(x)} such that the Boltzmann distribution P θ ( x ) = e − β E θ ( x ) Z ( θ ) {\displaystyle P_{\theta }(x)={e^{-\beta E_{\theta }(x)} \over Z(\theta )}} is a probability (density), and typically β = 1 {\displaystyle \beta =1} . Since the normalization constant: Z ( θ ) := ∫ x ∈ X e − β E θ ( x ) d x {\displaystyle Z(\theta ):=\int _{x\in X}e^{-\beta E_{\theta }(x)}dx} (also known as the partition function) depends on all the Boltzmann factors of all possible inputs x {\displaystyle x} , it cannot be easily computed or reliably estimated during training simply using standard maximum likelihood estimation. However, for maximizing the likelihood during training, the gradient of the log-likelihood of a single training example x {\displaystyle x} is given by using the chain rule: ∂ θ log ⁡ ( P θ ( x ) ) = E x ′ ∼ P θ [ ∂ θ E θ ( x ′ ) ] − ∂ θ E θ ( x ) ( ∗ ) {\displaystyle \partial _{\theta }\log \left(P_{\theta }(x)\right)=\mathbb {E} _{x'\sim P_{\theta }}[\partial _{\theta }E_{\theta }(x')]-\partial _{\theta }E_{\theta }(x)\,()} The expectation in the above formula for the gradient can be approximately estimated by drawing samples x ′ {\displaystyle x'} from the distribution P θ {\displaystyle P_{\theta }} using Markov chain Monte Carlo (MCMC). Early energy-based models, such as the 2003 Boltzmann machine by Hinton, estimated this expectation via blocked Gibbs sampling. Newer approaches make use of more efficient Stochastic Gradient Langevin Dynamics (LD), drawing samples using: x 0 ′ ∼ P 0 , x i + 1 ′ = x i ′ − α 2 ∂ E θ ( x i ′ ) ∂ x i ′ + ϵ {\displaystyle x_{0}'\sim P_{0},x_{i+1}'=x_{i}'-{\frac {\alpha }{2}}{\frac {\partial E_{\theta }(x_{i}')}{\partial x_{i}'}}+\epsilon } , where ϵ ∼ N ( 0 , α ) {\displaystyle \epsilon \sim {\mathcal {N}}(0,\alpha )} . A replay buffer of past values x i ′ {\displaystyle x_{i}'} is used with LD to initialize the optimization module. The parameters θ {\displaystyle \theta } of the neural network are therefore trained in a generative manner via MCMC-based maximum likelihood estimation: the learning process follows an "analysis by synthesis" scheme, where within each learning iteration, the algorithm samples the synthesized examples from the current model by a gradient-based MCMC method (e.g., Langevin dynamics or Hybrid Monte Carlo), and then updates the parameters θ {\displaystyle \theta } based on the difference between the training examples and the synthesized ones – see equation ( ∗ ) {\displaystyle ()} . This process can be interpreted as an alternating mode seeking and mode shifting process, and also has an adversarial interpretation. Essentially, the model learns a function E θ {\displaystyle E_{\theta }} that associates low energies to correct values, and higher energies to incorrect values. After training, given a converged energy model E θ {\displaystyle E_{\theta }} , the Metropolis–Hastings algorithm can be used to draw new samples. The acceptance probability is given by: P a c c ( x i → x ∗ ) = min ( 1 , P θ ( x ∗ ) P θ ( x i ) ) . {\displaystyle P_{acc}(x_{i}\to x^{})=\min \left(1,{\frac {P_{\theta }(x^{})}{P_{\theta }(x_{i})}}\right).} == History == The term "energy-based models" was first coined in a 2003 JMLR paper where the authors defined a generalisation of independent components analysis to the overcomplete setting using EBMs. Other early work on EBMs proposed models that represented energy as a composition of latent and observable variables. == Characteristics == EBMs demonstrate useful properties: Simplicity and stability. The EBM is the only object that needs to be designed and trained. Separate networks need not be trained to ensure balance. Adaptive computation time. An EBM can generate sharp, diverse samples or (more quickly) coarse, less diverse samples. Given infinite time, this procedure produces true samples. Flexibility. In Variational Autoencoders (VAE) and flow-based models, the generator learns a map from a continuous space to a (possibly) discontinuous space containing different data modes. EBMs can learn to assign low energies to disjoint regions (multiple modes). Adaptive generation. EBM generators are implicitly defined by the probability distribution, and automatically adapt as the distribution changes (without training), allowing EBMs to address domains where generator training is impractical, as well as minimizing mode collapse and avoiding spurious modes from out-of-distribution samples. Compositionality. Individual models are unnormalized probability distributions, allowing models to be combined through product of experts or other hierarchical techniques. == Experimental results == On image datasets such as CIFAR-10 and ImageNet 32x32, an EBM model generated high-quality images relatively quickly. It supported combining features learned from one type of image for generating other types of images. It was able to generalize using out-of-distribution datasets, outperforming flow-based and autoregressive models. EBM was relatively resistant to adversarial perturbations, behaving better than models explicitly trained against them with training for classification. == Applications == Target applications include natural language processing, robotics and computer vision. The first energy-based generative neural network is the generative ConvNet proposed in 2016 for image patterns, where the neural network is a convolutional neural network. The model has been generalized to various domains to learn distributions of videos, and 3D voxels. They are made more effective in their variants. They have proven useful for data generation (e.g., image synthesis, video synthesis, 3D shape synthesis, etc.), data recovery (e.g., recovering videos with missing pixels or image frames, 3D super-resolution, etc), data reconstruction (e.g., image reconstruction and linear interpolation ). == Alternatives == EBMs compete with techniques such as variational autoencoders (VAEs), generative adversarial networks (GANs) or normalizing flows. == Extensions == === Joint energy-based models === Joint energy-based models (JEM), proposed in 2020 by Grathwohl et al., allow any classifier with softmax output to be interpreted as energy-based model. The key observation is that such a classifier is trained to predict the conditional probability p θ ( y | x ) = e f → θ ( x ) [ y ] ∑ j = 1 K e f → θ ( x ) [ j ] for y = 1 , … , K and f → θ = ( f 1 , … , f K ) ∈ R K , {\displaystyle p_{\theta }(y|x)={\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{\sum _{j=1}^{K}e^{{\vec {f}}_{\theta }(x)[j]}}}\ \ {\text{ for }}y=1,\dotsc ,K{\text{ and }}{\vec {f}}_{\theta }=(f_{1},\dotsc ,f_{K})\in \mathbb {R} ^{K},} where f → θ ( x ) [ y ] {\displaystyle {\vec {f}}_{\theta }(x)[y]} is the y-th index of the logits f → {\displaystyle {\vec {f}}} corresponding to class y. Without any change to the logits it was proposed to reinterpret the logits to describe a joint probability density: p θ ( y , x ) = e f → θ ( x ) [ y ] Z ( θ ) , {\displaystyle p_{\theta }(y,x)={\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}},} with unknown partition function Z ( θ ) {\displaystyle Z(\theta )} and energy E θ ( x , y ) = − f θ ( x ) [ y ] {\displaystyle E_{\theta }(x,y)=-f_{\theta }(x)[y]} . By marginalization, we obtain the unnormalized density p θ ( x ) = ∑ y p θ ( y , x ) = ∑ y e f → θ ( x ) [ y ] Z ( θ ) =: e − E θ ( x ) , {\displaystyle p_{\theta }(x)=\sum _{y}p_{\theta }(y,x)=\sum _{y}{\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}}=:e^{-E_{\theta }(x)},} therefore, E θ ( x ) = − log ⁡ ( ∑ y e f → θ ( x ) [ y ] Z ( θ ) ) , {\displaystyle E_{\theta }(x)=-\log \left(\sum _{y}{\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}}\right),} so that any classifier can be used to define an energy function E θ ( x ) {\displaystyle E_{\theta }(x)} .

  Read more →
• 

  Two-phase commit protocol

  In transaction processing, databases, and computer networking, the two-phase commit protocol (2PC, tupac) is a type of atomic commitment protocol (ACP). It is a distributed algorithm that coordinates all the processes that participate in a distributed atomic transaction on whether to commit or abort (roll back) the transaction. This protocol (a specialised type of consensus protocol) achieves its goal even in many cases of temporary system failure (involving either process, network node, communication, etc. failures), and is thus widely used. However, it is not resilient to all possible failure configurations, and in rare cases, manual intervention is needed to remedy an outcome. To accommodate recovery from failure (automatic in most cases) the protocol's participants use logging of the protocol's states. Log records, which are typically slow to generate but survive failures, are used by the protocol's recovery procedures. Many protocol variants exist that primarily differ in logging strategies and recovery mechanisms. Though usually intended to be used infrequently, recovery procedures compose a substantial portion of the protocol, due to many possible failure scenarios to be considered and supported by the protocol. In a "normal execution" of any single distributed transaction (i.e., when no failure occurs, which is typically the most frequent situation), the protocol consists of two phases: The commit-request phase (or voting phase), in which a coordinator process attempts to prepare all the transaction's participating processes (named participants, cohorts, or workers) to take the necessary steps for either committing or aborting the transaction and to vote, either "Yes": commit (if the transaction participant's local portion execution has ended properly), or "No": abort (if a problem has been detected with the local portion), and The commit phase, in which, based on voting of the participants, the coordinator decides whether to commit (only if all have voted "Yes") or abort the transaction (otherwise), and notifies the result to all the participants. The participants then follow with the needed actions (commit or abort) with their local transactional resources (also called recoverable resources; e.g., database data) and their respective portions in the transaction's other output (if applicable). The two-phase commit (2PC) protocol should not be confused with the two-phase locking (2PL) protocol, a concurrency control protocol. == Assumptions == The protocol works in the following manner: one node is a designated coordinator, which is the master site, and the rest of the nodes in the network are designated the participants. The protocol assumes that: there is stable storage at each node with a write-ahead log, no node crashes forever, the data in the write-ahead log is never lost or corrupted in a crash, and any two nodes can communicate with each other. The last assumption is not too restrictive, as network communication can typically be rerouted. The first two assumptions are much stronger; if a node is totally destroyed then data can be lost. The protocol is initiated by the coordinator after the last step of the transaction has been reached. The participants then respond with an agreement message or an abort message depending on whether the transaction has been processed successfully at the participant. == Basic algorithm == === Commit request (or voting) phase === The coordinator sends a query to commit message to all participants and waits until it has received a reply from all participants. The participants execute the transaction up to the point where they will be asked to commit. They each write an entry to their undo log and an entry to their redo log. Each participant replies with: either an agreement message (participant votes Yes to commit), if the participant's actions succeeded; or an abort message (participant votes No to commit), if the participant experiences a failure that will make it impossible to commit. === Commit (or completion) phase === ==== Success ==== If the coordinator received an agreement message from all participants during the commit-request phase: The coordinator sends a commit message to all the participants. Each participant completes the operation, and releases all the locks and resources held during the transaction. Each participant sends an acknowledgement to the coordinator. The coordinator completes the transaction when all acknowledgements have been received. ==== Failure ==== If any participant votes No during the commit-request phase (or the coordinator's timeout expires): The coordinator sends a rollback message to all the participants. Each participant undoes the transaction using the undo log, and releases the resources and locks held during the transaction. Each participant sends an acknowledgement to the coordinator. The coordinator undoes the transaction when all acknowledgements have been received. ==== Message flow ==== Coordinator Participant QUERY TO COMMIT --------------------------------> VOTE YES/NO prepare/abort <------------------------------- commit/abort COMMIT/ROLLBACK --------------------------------> ACKNOWLEDGEMENT commit/abort <-------------------------------- end An next to the record type means that the record is forced to stable storage. == Disadvantages == The greatest disadvantage of the two-phase commit protocol is that it is a blocking protocol. If the coordinator fails permanently, some participants will never resolve their transactions: After a participant has sent an agreement message as a response to the commit-request message from the coordinator, it will block until a commit or rollback is received. A two-phase commit protocol cannot dependably recover from a failure of both the coordinator and a cohort member during the commit phase. If only the coordinator had failed, and no cohort members had received a commit message, it could safely be inferred that no commit had happened. If, however, both the coordinator and a cohort member failed, it is possible that the failed cohort member was the first to be notified, and had actually done the commit. Even if a new coordinator is selected, it cannot confidently proceed with the operation until it has received an agreement from all cohort members, and hence must block until all cohort members respond. == Implementing the two-phase commit protocol == === Common architecture === In many cases the 2PC protocol is distributed in a computer network. It is easily distributed by implementing multiple dedicated 2PC components similar to each other, typically named transaction managers (TMs; also referred to as 2PC agents or Transaction Processing Monitors), that carry out the protocol's execution for each transaction (e.g., The Open Group's X/Open XA). The databases involved with a distributed transaction, the participants, both the coordinator and participants, register to close TMs (typically residing on respective same network nodes as the participants) for terminating that transaction using 2PC. Each distributed transaction has an ad hoc set of TMs, the TMs to which the transaction participants register. A leader, the coordinator TM, exists for each transaction to coordinate 2PC for it, typically the TM of the coordinator database. However, the coordinator role can be transferred to another TM for performance or reliability reasons. Rather than exchanging 2PC messages among themselves, the participants exchange the messages with their respective TMs. The relevant TMs communicate among themselves to execute the 2PC protocol schema above, "representing" the respective participants, for terminating that transaction. With this architecture the protocol is fully distributed (does not need any central processing component or data structure), and scales up with number of network nodes (network size) effectively. This common architecture is also effective for the distribution of other atomic commitment protocols besides 2PC, since all such protocols use the same voting mechanism and outcome propagation to protocol participants. === Protocol optimizations === Database research has been done on ways to get most of the benefits of the two-phase commit protocol while reducing costs by protocol optimizations and protocol operations saving under certain system's behavior assumptions. ==== Presumed abort and presumed commit ==== Presumed abort or Presumed commit are common such optimizations. An assumption about the outcome of transactions, either commit, or abort, can save both messages and logging operations by the participants during the 2PC protocol's execution. For example, when presumed abort, if during system recovery from failure no logged evidence for commit of some transaction is found by the recovery procedure, then it assumes that the transaction has been aborted, and acts accordingly. This means that it does not matter if aborts are logged at all, and such logging can be saved under this assumption. Typical

  Read more →
• 

  Gen (software)

  Gen is a Computer Aided Software Engineering (CASE) application development environment marketed by Broadcom Inc. Gen was previously known as CA Gen, IEF (Information Engineering Facility), Composer by IEF, Composer, COOL:Gen, Advantage:Gen and AllFusion Gen. The toolset originally supported the information technology engineering methodology developed by Clive Finkelstein, James Martin and others in the early 1980s. Early versions supported IBM's DB2 database, 3270 'block mode' screens and generated COBOL code. In the intervening years the toolset has been expanded to support additional development techniques such as component-based development; creation of client/server and web applications and generation of C, Java and C#. In addition, other platforms are now supported such as many variants of Unix-like Operating Systems (AIX, HP-UX, Solaris, Linux) as well as Windows. Its range of supported database technologies have widened to include ORACLE, Microsoft SQL Server, ODBC, JDBC as well as the original DB2. The toolset is fully integrated - objects identified during analysis carry forward into design without redefinition. All information is stored in a repository (central encyclopedia). The encyclopedia allows for large team development - controlling access so that multiple developers may not change the same object simultaneously. == History == === 1985-1997: Texas Instruments === It was initially produced by Texas Instruments, with input from James Martin and his consultancy firm James Martin Associates, and was based on the Information Engineering Methodology (IEM). The first version was launched in 1985. IEF (Information Engineering Facility) became popular among large government departments and public utilities. It initially supported a CICS/COBOL/DB2 target environment. However, it now supports a wider range of relational databases and operating systems. IEF was intended to shield the developer from the complexities of building complete multi-tier cross-platform applications. In 1995, Texas Instruments decided to change their marketing focus for the product. Part of this change included a new name - "Composer". By 1996, IEF had become a popular tool. However, it was criticized by some IT professionals for being too restrictive, as well as for having a high per-workstation cost ($15K USD). But it is claimed that IEF reduces development time and costs by removing complexity and allowing rapid development of large scale enterprise transaction processing systems. === 1997-2000: Sterling Software === In 1997, Composer had another change of branding, Texas Instruments sold the Texas Instruments Software division, including the Composer rights, to Sterling Software. Sterling software changed the well known name "Information Engineering Facility" to "COOL:Gen". COOL was an acronym for "Common Object Oriented Language" - despite the fact that there was little object orientation in the product. === 2000-2018: Computer Associates === In 2000, Sterling Software was acquired by Computer Associates (now CA). CA has rebranded the product three times to date and the product is still used widely today. Under CA, recent releases of the tool added support for the CA-Datacom DBMS, the Linux operating system, C# code generation and ASP.NET web clients. The current version is known as CA Gen - version 8 being released in May 2010, with support for customised web services, and more of the toolset being based around the Eclipse framework. === 2018-current: Broadcom === As of 2020, CA Gen is owned and marketed by Broadcom Inc., which rebranded the product to Gen to avoid confusion with the former owner of the product. There are a variety of "add-on" tools available for Gen, including GuardIEn - a Configuration Management and Developer Productivity Suite, QAT Wizard, an interview style wizard that takes advantage of the meta model in Gen, products for multi-platform application reporting and XML/SOAP enabling of Gen applications., and developer productivity tools such as Access Gen, APMConnect, QA Console and Upgrade Console from Response Systems Version 8.6 of CA Gen came to market in June 2016. Version 8.6.3 of CA Gen was released in 2021. Following this release, Broadcom have switched to a continuous delivery model with new features to be delivered as patches.

  Read more →
• 

  Documentation

  Documentation is any communicable material that is used to describe, explain, or instruct regarding some attributes of an object, system, or procedure, such as its parts, assembly, installation, maintenance, and use. As a form of knowledge management and knowledge organization, documentation can be provided on paper, online, or on digital or analog media, such as audio tape or CDs. Examples of such resources include user guides, white papers, online help, and quick-reference guides. Paper or hard-copy documentation has become less common. Contemporary documentation is often distributed through websites, software products, and other online applications. Documentation, understood as a set of instructional materials, should not be confused with documentation science, which is the study of the recording and retrieval of information. == Principles for producing documentation == While associated International Organization for Standardization (ISO) standards are not easily available publicly, a guide from other sources for this topic may serve the purpose. Documentation development may involve document drafting, formatting, submitting, reviewing, approving, distributing, reposting and tracking, etc., and are convened by associated standard operating procedure in a regulatory industry. It could also involve creating content from scratch. Documentation should be easy to read and understand. If it is too long and too wordy, it may be misunderstood or ignored. Clear, concise words should be used, and sentences should be limited to a maximum of 15 words. Documentation intended for a general audience should avoid gender-specific terms and cultural biases. In a series of procedures, steps should be clearly numbered. == Producing documentation == Technical writers and corporate communicators are professionals whose field and work is documentation. Ideally, technical writers have a background in both the subject matter and also in writing, managing content, and information architecture. Technical writers more commonly collaborate with subject-matter experts, such as engineers, technical experts, medical professionals, etc. to define and then create documentation to meet the user's needs. Corporate communications includes other types of written documentation, for example: Market communications (MarCom): MarCom writers endeavor to convey the company's value proposition through a variety of print, electronic, and social media. This area of corporate writing is often engaged in responding to proposals. Technical communication (TechCom): Technical writers document a company's product or service. Technical publications can include user guides, installation and configuration manuals, and troubleshooting and repair procedures. Legal writing: This type of documentation is often prepared by attorneys or paralegals. Compliance documentation: This type of documentation codifies standard operating procedures, for any regulatory compliance needs, as for safety approval, taxation, financing, and technical approval. Healthcare documentation: This field of documentation encompasses the timely recording and validation of events that have occurred during the course of providing health care. == Documentation in computer science == === Types === The following are typical software documentation types: Request for proposal Requirements/statement of work/scope of work Software design and functional specification System design and functional specifications Change management, error and enhancement tracking User acceptance testing Manpages The following are typical hardware and service documentation types: Network diagrams Network maps Datasheet for IT systems (server, switch, e.g.) Service catalog and service portfolio (Information Technology Infrastructure Library) === Software Documentation Folder (SDF) tool === A common type of software document written in the simulation industry is the SDF. When developing software for a simulator, which can range from embedded avionics devices to 3D terrain databases by way of full motion control systems, the engineer keeps a notebook detailing the development "the build" of the project or module. The document can be a wiki page, Microsoft Word document or other environment. They should contain a requirements section, an interface section to detail the communication interface of the software. Often a notes section is used to detail the proof of concept, and then track errors and enhancements. Finally, a testing section to document how the software was tested. This documents conformance to the client's requirements. The result is a detailed description of how the software is designed, how to build and install the software on the target device, and any known defects and workarounds. This build document enables future developers and maintainers to come up to speed on the software in a timely manner, and also provides a roadmap to modifying code or searching for bugs. === Software tools for network inventory and configuration === These software tools can automatically collect data of your network equipment. The data could be for inventory and for configuration information. The Information Technology Infrastructure Library requests to create such a database as a basis for all information for the IT responsible. It is also the basis for IT documentation. Examples include XIA Configuration. == Documentation in criminal justice == "Documentation" is the preferred term for the process of populating criminal databases. Examples include the National Counterterrorism Center's Terrorist Identities Datamart Environment, sex offender registries, and gang databases. == Documentation in early childhood education == Documentation, as it pertains to the early childhood education field, is "when we notice and value children's ideas, thinking, questions, and theories about the world and then collect traces of their work (drawings, photographs of the children in action, and transcripts of their words) to share with a wider community". Thus, documentation is a process, used to link the educator's knowledge and learning of the child/children with the families, other collaborators, and even to the children themselves. Documentation is an integral part of the cycle of inquiry - observing, reflecting, documenting, sharing and responding. Pedagogical documentation, in terms of the teacher documentation, is the "teacher's story of the movement in children's understanding". According to Stephanie Cox Suarez in "Documentation - Transforming our Perspectives", "teachers are considered researchers, and documentation is a research tool to support knowledge building among children and adults". Documentation can take many different styles in the classroom. The following exemplifies ways in which documentation can make the research, or learning, visible: Documentation panels (bulletin-board-like presentation with multiple pictures and descriptions about the project or event). Daily log (a log kept every day that records the play and learning in the classroom) Documentation developed by or with the children (when observing children during documentation, the child's lens of the observation is used in the actual documentation) Individual portfolios (documentation used to track and highlight the development of each child) Electronic documentation (using apps and devices to share documentation with families and collaborators) Transcripts or recordings of conversations (using recording in documentation can bring about deeper reflections for both the educator and the child) Learning stories (a narrative used to "describe learning and help children see themselves as powerful learners") The classroom as documentation (reflections and documentation of the physical environment of a classroom). Documentation is certainly a process in and of itself, and it is also a process within the educator. The following is the development of documentation as it progresses for and in the educator themselves: Develop(s) habits of documentation Become(s) comfortable with going public with recounting of activities Develop(s) visual literacy skills Conceptualize(s) the purpose of documentation as making learning styles visible, and Share(s) visible theories for interpretation purposes and further design of curriculum.

  Read more →
• 

  GeneTalk

  GeneTalk is a web-based platform, tool, and database for filtering, reduction and prioritization of human sequence variants from next-generation sequencing (NGS) data. GeneTalk allows editing annotation about sequence variants and build up a crowd sourced database with clinically relevant information for diagnostics of genetic disorders. GeneTalk allows searching for information about specific sequence variants and connects to experts on variants that are potentially disease-relevant. == Application to diagnostics == Users can upload NGS data in Variant Call Format (VCF) onto the GeneTalk server into their accounts. All entries of the file are preprocessed and shown in the integrated VCF viewer. Filtering tools are set by the user to reduce the number of clinically non-relevant variants. After filtering and prioritization users can interpret relevant variants by retrieving information (annotations) about variants from the GeneTalk database. The communication platform allow users to contact experts about specific variants, genes, or genetic disorders, to exchange knowledge and expertise. === Analysis procedure === Steps required to analyze VCF files Upload VCF file Edit pedigree and phenotype information for segregation filtering Filter VCF file by editing the filtering options View results and annotations Add annotations === Filtering tools === The following filtering options may be used to reduce the non-relevant sequence variants in VCF files. Functional – filter out variants that have effects on protein level Linkage – filter out variants that are on specified chromosomes Gene panel – filter variants by genes or gene panels, subscribe to publicly available gene panels or create own ones Frequency – show only variants with a genotype frequency lower than specified Inheritance – filter out variants by presumed mode of inheritance Annotation – show only variants with a score for medical relevance and scientific evidence == Communication platform and expert network == Users can share VCF files with colleagues and coworkers. The integrated mailing systems allows users to contact experts easily. Users can create annotations and comments and rate annotations regarding medical relevance and scientific evidence, that is helpful for the community of users for diagnosis of genetic disorders. Registered users provide information about their field of knowledge in their profile and can be contacted by other users. == Potential applications == Developing diagnostics Genetic analysis Capturing data generated by community Communication and exchange of knowledge and expertise

  Read more →
• 

  Cancer Likelihood in Plasma

  Cancer Likelihood in Plasma (CLiP) refers to a set of ensemble learning methods for integrating various genomic features useful for the noninvasive detection of early cancers from blood plasma. An application of this technique for early detection of lung cancer (Lung-CLiP) was originally described by Chabon et al. (2020) from the labs of Ash Alizadeh and Max Diehn at Stanford. This method relies on several improvements to cancer personalized profiling by deep sequencing (CAPP-Seq) for analysis of circulating tumor DNA (ctDNA). The CLiP technique integrates multiple distinctive genomic features of a cancer of interest findings within a machine-learning framework for cancer detection. For example, studies have shown that the majority of somatic mutations found in cell-free DNA (cfDNA) are not tumor derived, but instead reflect clonal hematopoeisis (also known as CHIP). Even though CHIP tends to target specific genes, it also involves many generally non-recurrent mutations that can be shed from leukocytes and detected in cfDNA, regardless of whether profiling patients with cancer and healthy adults. However, genuine tumor derived ctDNA mutations can be distinguished from CHIP-derived mutations. This is because unlike tumor-derived mutations, CHIP-derived mutations that are shed from leukocytes into plasma tend to occur on longer cfDNA fragments, and to lack specific mutational signatures such as those associated with tobacco smoking in lung cancer that are also found in tumor derived ctDNA molecules. CLiP integrates these features within hierarchical ensemble machine learning models that consider somatic mutations and copy number alternations, among other features. While the CLiP method is unique in relying exclusively on mutations and copy number alterations, it is related to a variety of other liquid biopsy methods being commercially developed for early cancer detection using ctDNA and proteins (e.g., CancerSEEK / DETECT-A ), cfDNA fragmentation patterns (e.g., DELFI), and DNA methylation (e.g., cfMeDIP-Seq, Grail). While the CLiP method has not yet been broadly applied for population-based cancer screening, it has been shown to distinguish discriminate early-stage lung cancers from risk-matched controls across multiple cohorts of patients enrolled across the US.

  Read more →
• 

  Controlled vocabulary

  A controlled vocabulary provides a way to organize knowledge for subsequent retrieval. Controlled vocabularies are used in subject indexing schemes, subject headings, thesauri, taxonomies and other knowledge organization systems. Controlled vocabulary schemes mandate the use of predefined, preferred terms that have been preselected by the designers of the schemes, in contrast to natural language vocabularies, which have no such restriction. == In library and information science == In library and information science, controlled vocabulary is a carefully selected list of words and phrases, which are used to tag units of information (document or work) so that they may be more easily retrieved by a search. Controlled vocabularies solve the problems of homographs, synonyms and polysemes by a bijection between concepts and preferred terms. In short, controlled vocabularies reduce unwanted ambiguity inherent in normal human languages where the same concept can be given different names and ensure consistency. For example, in the Library of Congress Subject Headings (a subject heading system that uses a controlled vocabulary), preferred terms—subject headings in this case—have to be chosen to handle choices between variant spellings of the same word (American versus British), choice among scientific and popular terms (cockroach versus Periplaneta americana), and choices between synonyms (automobile versus car), among other difficult issues. Choices of preferred terms are based on the principles of user warrant (what terms users are likely to use), literary warrant (what terms are generally used in the literature and documents), and structural warrant (terms chosen by considering the structure, scope of the controlled vocabulary). Controlled vocabularies also typically handle the problem of homographs with qualifiers. For example, the term pool has to be qualified to refer to either swimming pool or the game pool to ensure that each preferred term or heading refers to only one concept. === Types used in libraries === There are two main kinds of controlled vocabulary tools used in libraries: subject headings and thesauri. While the differences between the two are diminishing, there are still some minor differences: Historically, subject headings were designed to describe books in library catalogs by catalogers while thesauri were used by indexers to apply index terms to documents and articles. Subject headings tend to be broader in scope describing whole books, while thesauri tend to be more specialized covering very specific disciplines. Because of the card catalog system, subject headings tend to have terms that are in indirect order (though with the rise of automated systems this is being removed), while thesaurus terms are always in direct order. Subject headings tend to use more pre-coordination of terms such that the designer of the controlled vocabulary will combine various concepts together to form one preferred subject heading. (e.g., children and terrorism) while thesauri tend to use singular direct terms. Thesauri list not only equivalent terms but also narrower, broader terms and related terms among various preferred and non-preferred (but potentially synonymous) terms, while historically most subject headings did not. For example, the Library of Congress Subject Heading itself did not have much syndetic structure until 1943, and it was not until 1985 when it began to adopt the thesauri type term "Broader term" and "Narrow term". The terms are chosen and organized by trained professionals (including librarians and information scientists) who possess expertise in the subject area. Controlled vocabulary terms can accurately describe what a given document is actually about, even if the terms themselves do not occur within the document's text. Well known subject heading systems include the Library of Congress system, Medical Subject Headings (MeSH) created by the United States National Library of Medicine, and Sears. Well known thesauri include the Art and Architecture Thesaurus and the ERIC Thesaurus. When selecting terms for a controlled vocabulary, the designer has to consider the specificity of the term chosen, whether to use direct entry, inter consistency and stability of the language. Lastly the amount of pre-coordination (in which case the degree of enumeration versus synthesis becomes an issue) and post-coordination in the system is another important issue. Controlled vocabulary elements (terms/phrases) employed as tags, to aid in the content identification process of documents, or other information system entities (e.g. DBMS, Web Services) qualifies as metadata. == Indexing languages == There are three main types of indexing languages. Controlled indexing language – only approved terms can be used by the indexer to describe the document Natural language indexing language – any term from the document in question can be used to describe the document Free indexing language – any term (not only from the document) can be used to describe the document When indexing a document, the indexer also has to choose the level of indexing exhaustivity, the level of detail in which the document is described. For example, using low indexing exhaustivity, minor aspects of the work will not be described with index terms. In general the higher the indexing exhaustivity, the more terms indexed for each document. In recent years free text search as a means of access to documents has become popular. This involves using natural language indexing with an indexing exhaustively set to maximum (every word in the text is indexed). These methods have been compared in some studies, such as the 2007 article, "A Comparative Evaluation of Full-text, Concept-based, and Context-sensitive Search". === Advantages === Controlled vocabularies are often claimed to improve the accuracy of free text searching, such as to reduce irrelevant items in the retrieval list. These irrelevant items (false positives) are often caused by the inherent ambiguity of natural language. Take the English word football for example. Football is the name given to a number of different team sports. Worldwide the most popular of these team sports is association football, which also happens to be called soccer in several countries. The word football is also applied to rugby football (rugby union and rugby league), American football, Australian rules football, Gaelic football, and Canadian football. A search for football therefore will retrieve documents that are about several completely different sports. Controlled vocabulary solves this problem by tagging the documents in such a way that the ambiguities are eliminated. Compared to free text searching, the use of a controlled vocabulary can dramatically increase the performance of an information retrieval system, if performance is measured by precision (the percentage of documents in the retrieval list that are actually relevant to the search topic). In some cases controlled vocabulary can enhance recall as well, because unlike natural language schemes, once the correct preferred term is searched, there is no need to search for other terms that might be synonyms of that term. === Disadvantages === A controlled vocabulary search may lead to unsatisfactory recall, in that it will fail to retrieve some documents that are actually relevant to the search question. This is particularly problematic when the search question involves terms that are sufficiently tangential to the subject area such that the indexer might have decided to tag it using a different term (but the searcher might consider the same). Essentially, this can be avoided only by an experienced user of controlled vocabulary whose understanding of the vocabulary coincides with that of the indexer. Another possibility is that the article is just not tagged by the indexer because indexing exhaustivity is low. For example, an article might mention football as a secondary focus, and the indexer might decide not to tag it with "football" because it is not important enough compared to the main focus. But it turns out that for the searcher that article is relevant and hence recall fails. A free text search would automatically pick up that article regardless. On the other hand, free text searches have high exhaustivity (every word is searched) so although it has much lower precision, it has potential for high recall as long as the searcher overcome the problem of synonyms by entering every combination. Controlled vocabularies may become outdated rapidly in fast developing fields of knowledge, unless the preferred terms are updated regularly. Even in an ideal scenario, a controlled vocabulary is often less specific than the words of the text itself. Indexers trying to choose the appropriate index terms might misinterpret the author, while this precise problem is not a factor in a free text, as it uses the author's own words. The use of controlled vocabularies can be costly compared to free

  Read more →
• 

  List of library and information science journals

  This list covers the journals, magazines, periodicals already published and continuing in the discipline of library and information science (LIS). It doesn't include ceased titles or predatory journals. Titles listed were taken from various scholarly sources, UGC Care and Wikipedia articles. == LIS journal prestige as assessed by LIS faculty == In a 2013 article by Laura Manzari, 232 LIS faculty members from ALA-accredited information science programs ranked the most prestigious journals in library and information science. The following journals were ranked in the top ten most prestigious: Journal of the Association for Information Science and Technology The Library Quarterly Annual Review of Information Science and Technology Journal of Documentation Library Trends Library and Information Science Research Information Processing and Management Journal of Education for Library and Information Science Education College & Research Libraries First Monday (journal) A subsequent study by Safón and Docampo in 2023 identified impactful LIS journals based on their influence on papers published in other LIS publications. Journals listed in the top ten in this study that did not appear in Manzari's list include: Scientometrics International Journal of Information Management Quantitative Science Studies MIS Quarterly Information and Management Journal of the Association for Information Systems Journal of Informetrics The Journal of Academic Librarianship == India == Annals of Library and Information Studies. (Pub: CSIR-NIScPR ), Formerly: Annals of Library Science. ISSN 0003-4835. (1954-) OPEN ACCESS Collnet Journal of Scientrometrics and Information Management (Pub: Taru Publications, Online through Taylor and Francis) ISSN: 0973-7766 Online 2168-930X. College Libraries (Pub: West Bengal College Librarians’ Association (WBCLA) ISSN 0972-1975, Quarterly DESIDOC Journal of Library and Information Technology (DJLIT) (Formerly: DESIDOC Bulletin 0970-8154, DESIDOC Bulletin of Information Technology. 0971-4383/0974-0643) (Pub: Defence Scientific Information & Documentation Centre) ISSN: 0974-0643, ISSN: 0976-4658 (O), Bi-monthly, OPEN ACCESS. Grandhalaya Sarvaswam (Bilingual: Telugu & English) [Pub: Andhra Pradesh Library Association, Vijayawada, Andhra Pradesh, India] (1915–) Gyankosh: Journal of Library and Information Management. (Pub: Integrated Academy Of Management And Technology. Through: Indian Journals.Com). ISSN: 2229-4023 (P), 2249-3182. Half yearly. IASLIC Bulletin (Pub: Indian Association of Special Libraries and Information Centres) ISSN: 0018-8411. Quarterly (1956-) IASLIC Newsletter (Pub: Indian Association of Special Libraries and Information Centres. (Pub: Indian Association of Special Libraries and Information Centres) ISSN 0018-845X. Monthly. (1966-) INFLIBNET Newsletter. (Pub: INFLIBNET). Monthly. Informatics Studies. (Pub: Centre For Informatics Research And Development). Quarterly. Through: Indian journals.com. ISSN: 2583-8994 (Online), 2320-530X (Print) ISST Journal of Advances in Librarianship (Pub:Intellectuals Society for Socio-Techno Welfare) ISSN: 0976-9021. Semiannual. Journal of Advanced Research in Library and Information Science. (JALIS Publishers). 4/year. ISSN 2277-2219. Journal of Indian Library Association (Pub: Indian Library Association). ISSN (P) 2277-5145 O) 2456-513X. Quarterly. (1965-). Journal of Scientometric Research. (Pub: Phcog.Net). ISSN (P) 2321-6654, (O) 2320-0057]; Frequency : Triannual. KELPRO Bulletin (Pub: Kerala Library Professionals' Organisation - KELPRO). ISSN 0975-4911( Print),2582-497X (O).(1993-) KIIT Journal of Library and Information Management (Pub: KIIT University, online through Indian Journals.com) Half yearly. ISSN: 2348-0858. Library Herald. (Pub: Delhi Library Association - DLA). Quarterly. ISSN: 0024-2292. Library Progress (International). (Pub: Bpas Publications, Through: ). Half yearly. ISSN: 0970-1052. (O) ISSN: 2320-317X. (1981-) Pearl: A Journal of Library and Information Science. (Pub: University Library Teacher's Association of Andhra Pradesh, Hyderabad), ISSN: 0973-7081 (print), 0975-6922 (online). Quarterly. RBU Journal of Library and Information Science. (Pub: Rabindra Bharati University).ISSN: 0972-2750. Annual. SALIS Journal of Information Management and Technology - SJIMT. (Pub: Society for the Advancement of Library and Information Science). Half-yearly. ISSN 0975-4105. SALIS Journal of Library and Information Science - SJLIS: an International Journal. (Pub: Society for the Advancement of Library and Information Science). Half-yearly. ISSN: 0973-3108. SRELS journal of Information and Knowledge (Formerly: Library Science with a Slant to Documentation, ISSN: 0024-2543; Library Science with a Slant to Documentation and Information Studies ISSN: 0970-6089; SRELS Journal of Information Management ISSN: ). Quarterly. ISSN: 2583-9314 (O) World Digital Libraries. Half yearly. ISSN: 0974-567X (P), 0975-7597 (O). == Other countries == African Journal of Library, Archives and Information Science Art Libraries Journal (Cambridge University Press) Bibliothèque de l'École des Chartes Canadian Journal of Information and Library Science Cataloging & Classification Quarterly Communications in Information Literacy Cataloging & Classification Quarterly Catholic Library Association Children and Libraries Code4Lib Journal College & Research Libraries Communications in Information Literacy Disability in Library and Information Studies Electronic Journal of Academic and Special Librarianship El Profesional de la Información (es) (EPI) (Formerly Information World en Español) Evidence Based Library and Information Practice (journal) Faslname-ye Ketab Florida Libraries. Florida Library Association. Georgia Library Quarterly. Quarterly. (Pub: Georgia Library Association). Hipertext.net IFLA Journal In the Library with the Lead Pipe Information & Culture International Journal of Information Retrieval Research (IJIRR) Information Processing and Management Information Research Information Sciences (journal) Information Visualization (journal) Information, Communication & Society International Journal of Geographical Information Science Information Research: An International Electronic Journal (IR) Internet Research (journal) Issues in Science and Technology Librarianship Italian Journal of Library and Information Studies (JLIS.it) JLIS.it Journal of Documentation (JDoc) Journal of Information Ethics Journal of Information Science (JIS) Journal of Information Technology Journal of Informetrics Journal of Librarianship and Information Science Journal of Library & Information Studies - JLIS. (Pub: National Taiwan University) Journal of Library Administration Journal of Religious & Theological Information Journal of the Association for Information Science and Technology (Formerly Journal of the American Society for Information Science and Technology) (JASIST) Journal of the Medical Library Association Journal of the Canadian Health Libraries Association (Pub: Canadian Health Libraries Association). Knowledge Organization (journal) Knowledge Quest. (Pub: American Association of School Librarians) Library and Information Science Abstracts Library Literature and Information Science Library, Information Science & Technology Abstracts Library Literature and Information Science Retrospective Library Review (journal) Library Trends Libri (journal) Malaysian Journal of Library and Information Science MLA Forum New Century Library New Review of Children's Literature and Librarianship Notes (journal) Portal – Libraries and the Academy Progressive Librarian, Progressive Librarians Guild Reference and User Services Quarterly Reference Services Review Research Evaluation (journal) Scientometrics (journal) Serials Review South African Journal of Libraries and Information Science The Charleston Advisor The Christian Librarian, from the Association of Christian Librarians The Journal of Academic Librarianship The Library Quarterly (LQ) The Public-Access Computer Systems Review TripleC Webolog

  Read more →
• 

  Artificial intelligence of things

  Artificial Intelligence of Things (AIoT) is the combination of artificial intelligence (AI) technologies with the Internet of things (IoT) infrastructure to create systems capable of sensing, learning, and acting on data without continuous human intervention. While IoT focuses on connectivity and sensor data collection, AI enables IoT devices to analyse data in real time and produce actionable outputs, including automated decisions at the edge. == Applications == === Manufacturing and predictive maintenance === Manufacturing accounts for the largest share of AIoT adoption by industry vertical. A common application is predictive maintenance, where sensors measuring vibration, temperature, current draw, and acoustic emissions feed machine learning models trained to detect signatures that precede equipment failure. These systems can flag developing faults weeks or months in advance, and in more advanced deployments can autonomously adjust machine parameters such as motor speed or cooling cycles to delay or prevent failure. === Other industries === In healthcare, AIoT enables remote patient monitoring through wearable devices that collect vital signs and apply AI models to detect anomalies or predict deterioration. In logistics, GPS and telematics sensors combined with AI models support real-time route optimisation, vehicle maintenance prediction, and fuel cost forecasting. Smart building systems use occupancy, temperature, and energy sensors with AI to dynamically adjust HVAC and lighting, reducing energy consumption. == Architecture == AIoT systems typically operate across three layers: a device layer of sensors and actuators that collect data, a connectivity layer that transmits data via protocols such as MQTT or HTTP, and a compute layer where AI models process the data either in the cloud or at the edge. The trend toward edge-based processing, where inference runs on low-cost processors near the data source rather than in a centralised cloud, has accelerated as hardware costs have fallen and applications increasingly require sub-second response times. == Market == Market sizing estimates for AIoT vary significantly depending on scope and definition. Fortune Business Insights valued the AIoT market at USD 35.65 billion in 2023, projecting growth to USD 253.86 billion by 2030 at a compound annual growth rate of 32.4%. Grand View Research estimated the broader market at USD 171.4 billion in 2024 with a CAGR of 31.7% through 2030, reflecting a wider definition that includes AI-integrated hardware components. North America accounted for approximately 40% of global market share in 2024, with the Asia-Pacific region projected as the fastest-growing market.

  Read more →
• 

  Five safes

  The Five Safes is a framework for helping make decisions about making effective use of data which is confidential or sensitive. It is mainly used to describe or design research access to statistical data held by government and health agencies, and by data archives such as the UK Data Service. It is not an internationally accepted standard. Two of the Five Safes refer to statistical disclosure control, and so the Five Safes is usually used to contrast statistical and non-statistical controls when comparing data management options. == Concept == The Five Safes proposes that data management decisions be considered as solving problems in five 'dimensions': projects, people, settings, data and outputs. The combination of the controls leads to 'safe use'. These are most commonly expressed as questions, for example: These dimensions are scales, not limits. That is, solutions can have a mix of more or fewer controls in each dimension, but the overall aim of 'safe use' independent of the particular mix. For example, a public use file available for open download cannot control who uses it, where or for what purpose, and so all the control (protection) must be in the data itself. In contrast, a file which is only accessed through a secure environment with certified users can contain very sensitive information: the non-statistical controls allow the data to be 'unsafe'. One academic likened the process to a graphic equalizer, where bass and treble can be combined independently to produce a sound the listener likes, which has proven to be a very useful metaphor. This 2023 Data Foundation webinar is an expert discussion of how the elements interact, including an excellent introductory representation. There is no 'order' to the Five Safes, in that one is necessarily more important than the others. However, Ritchie argued that the 'managerial' controls (projects, people, setting) should be addressed before the 'statistical' controls (data, output). The Five Safes concept is associated with other topics which developed from the same programme at ONS, although these are not necessarily implemented. Safe people is associated with 'active researcher management', while safe outputs is linked with principles-based output statistical disclosure control. The Five Safes is a positive framework, describing what is and is not. The EDRU ('evidence-based, default-open, risk-managed, user-centred') attitudinal model is sometimes used to give a normative context == The 'data access spectrum' == From 2003 the Five Safes was also represented in a simpler form as a 'Data Access Spectrum'. The non-data controls (project, people, setting, outputs) tend to work together, in that organisations often see these as a complementary set of restrictions on access. These can then be contrasted with choices about data anonymisation to present a linear representation of data access options. This presentation is consistent with the idea of 'data as a residual', as well as data protection laws of the time which often characterised data simply as anonymous or not anonymous. A similar idea had already been developed independently in 2001 by Chuck Humphrey of the Canadian RDC network, the 'continuum of access'. More recently, The Open Data Institute has developed a 'Data Spectrum toolkit' which includes industry-specific examples. == History and terminology == The Five Safes was devised in the winter of 2002/2003 by Felix Ritchie at the UK Office for National Statistics (ONS) to describe its secure remote-access Virtual Microdata Laboratory (VML). It was described at this time as the 'VML Security Model'. This was adopted by the NORC data enclave, and more widely in the US, as the 'portfolio model' (although this is now also used to refer to a slightly different legal/statistical/educational breakdown). In 2012 the framework as was still being referred to as the 'VML security model', but its increasing use among non-UK organisations led to the adoption of the more general and informative phrase 'Five Safes'. The original framework only had four safes (projects, people, settings and outputs): the framework was used to describe highly detailed data access through a secure environment, and so the 'data' dimension was irrelevant. From 2007 onwards, 'safe data' was included as the framework was used to a describe a wider range of ONS activities. As the US version was based upon the 2005 specification, some US iterations uses have the original four dimensions (eg). Some discussions, such as the OECD, use the term 'secure' instead 'safe'. However, the use of both these terms can cause presentational problems: less control in a particular dimension could be seen to imply 'unsafe users' or 'insecure settings', for example, which distracts from the main message. Hence, the Australian government uses the term "five data sharing principles". The 'Anonymisation Decision-Making Framework' uses a framework based on the Five Safes but relabelling "projects", "people", and "settings" as "governance", "agency" and "infrastructure", respectively; "Output" is omitted, and "safe use" becomes "functional anonymisation". There is no reference to the Five Safes or any associated literature. The Australian version was required to include references to the Five Safes, and presented it as an alternative without comment. == Application == The framework has had three uses: pedagogical, descriptive, and design. Since 2016, it has also been used, directly and indirectly in legislation. See for more detailed examples. === Pedagogy === The first significant use of the framework, other than internal administrative use, was to structure researcher training courses at the UK Office for National Statistics from 2003. UK Data Archive, Administrative Data Research Network, Eurostat, Statistics New Zealand, the Mexican National Institute of Statistics and Geography, NORC, Statistics Canada and the Australian Bureau of Statistics, amongst others, have also used this framework. Most of these courses are for researchers using restricted-access facilities; the Eurostat courses are unusual in that they are designed for all users of sensitive data. === Description === The framework is often used to describe existing data access solutions (e.g. UK HMRC Data Lab, UK Data Service, Statistics New Zealand) or planned/conceptualised ones (e.g. Eurostat in 2011). An early use was to help identify areas where ONS' still had 'irreducible risks' in its provision of secure remote access. The framework is mostly used for confidential social science data. To date it appears to have made little impact on medical research planning, although it is now included in the revised guidelines on implementing HIPAA regulations in the US, and by Cancer Research UK and the Health Foundation in the UK. It has also been used to describe a security model for the Scottish Health Informatics Programme. === Design === In general the Five Safes has been used to describe solutions post-factum, and to explain/justify choices made, but an increasing number of organisations have used the framework to design data access solutions. For example, the Hellenic Statistical Agency developed a data strategy built around the Five Safes in 2016; the UK Health Foundation used the Five Safes to design its data management and training programmes. Use in the private sector is less common but some organisations have incorporated the Five Safes into consulting services. In 2015 the UK Data Service organized a workshop to encourage data users from the academic and private sectors to think about how to manage confidential research data, using the Five Safes to demonstrate alternative options and best practice. Early adopters for strategic design use were in Australia: both the Australian Bureau of Statistics and the Australian Department of Social Service used the Five Safes as an ex ante design tool. In 2017 the Australian Productivity Commission recommended adopting a version of the framework to support cross-government data sharing and re-use. This underwent extensive consultation and culminated in the DAT Act 2022. Since 2020 the Five Safes has been the overriding framework for the design of new secure facilities and data sharing arrangements in the UK for public health and social sciences. This has been promoted by the Office for Statistics Regulation, the UK Statistics Authority, NHS DIgital, and the research funding bodies Administrative Data Research UK and DARE UK. === Regulation and legislation === Three laws have incorporated the Fives Safes. They are explicit in the South Australian Public Sector (Data Sharing) Act 2016, and implicit in the research provisions of the UK Digital Economy Act 2017. The Australian Data Availability and Transparency Act 2022 renames the Five Safes as the Five Data Sharing Principles.A 2025 statutory review of the DAT Act 2022 found "that the DAT Act has not been effective in achieving its objectives.". The review includes specific referen

  Read more →
• 

  Randomized rounding

  In computer science and operations research, randomized rounding is a widely used approach for designing and analyzing approximation algorithms. Many combinatorial optimization problems are computationally intractable to solve exactly (to optimality). For such problems, randomized rounding can be used to design fast (polynomial time) approximation algorithms—that is, algorithms that are guaranteed to return an approximately optimal solution given any input. The basic idea of randomized rounding is to convert an optimal solution of a relaxation of the problem into an approximately-optimal solution to the original problem. The resulting algorithm is usually analyzed using the probabilistic method. == Overview == The basic approach has three steps: Formulate the problem to be solved as an integer linear program (ILP). Compute an optimal fractional solution x {\displaystyle x} to the linear programming relaxation (LP) of the ILP. Round the fractional solution x {\displaystyle x} of the LP to an integer solution x ′ {\displaystyle x'} of the ILP. (Although the approach is most commonly applied with linear programs, other kinds of relaxations are sometimes used. For example, see Goemans' and Williamson's semidefinite programming-based Max-Cut approximation algorithm.) In the first step, the challenge is to choose a suitable integer linear program. Familiarity with linear programming, in particular modelling using linear programs and integer linear programs, is required. For many problems, there is a natural integer linear program that works well, such as in the Set Cover example below. (The integer linear program should have a small integrality gap; indeed randomized rounding is often used to prove bounds on integrality gaps.) In the second step, the optimal fractional solution can typically be computed in polynomial time using any standard linear programming algorithm. In the third step, the fractional solution must be converted into an integer solution (and thus a solution to the original problem). This is called rounding the fractional solution. The resulting integer solution should (provably) have cost not much larger than the cost of the fractional solution. This will ensure that the cost of the integer solution is not much larger than the cost of the optimal integer solution. The main technique used to do the third step (rounding) is to use randomization, and then to use probabilistic arguments to bound the increase in cost due to the rounding (following the probabilistic method from combinatorics). Therein, probabilistic arguments are used to show the existence of discrete structures with desired properties. In this context, one uses such arguments to show the following: Given any fractional solution x {\displaystyle x} of the LP, with positive probability the randomized rounding process produces an integer solution x ′ {\displaystyle x'} that approximates x {\displaystyle x} according to some desired criterion. Finally, to make the third step computationally efficient, one either shows that x ′ {\displaystyle x'} approximates x {\displaystyle x} with high probability (so that the step can remain randomized) or one derandomizes the rounding step, typically using the method of conditional probabilities. The latter method converts the randomized rounding process into an efficient deterministic process that is guaranteed to reach a good outcome. == Example: the set cover problem == The following example illustrates how randomized rounding can be used to design an approximation algorithm for the set cover problem. Fix any instance ⟨ c , S ⟩ {\displaystyle \langle c,{\mathcal {S}}\rangle } of set cover over a universe U {\displaystyle {\mathcal {U}}} . === Computing the fractional solution === For step 1, let IP be the standard integer linear program for set cover for this instance. For step 2, let LP be the linear programming relaxation of IP, and compute an optimal solution x ∗ {\displaystyle x^{}} to LP using any standard linear programming algorithm. This takes time polynomial in the input size. The feasible solutions to LP are the vectors x {\displaystyle x} that assign each set s ∈ S {\displaystyle s\in {\mathcal {S}}} a non-negative weight x s {\displaystyle x_{s}} , such that, for each element e ∈ U {\displaystyle e\in {\mathcal {U}}} , x ′ {\displaystyle x'} covers e {\displaystyle e} —the total weight assigned to the sets containing e {\displaystyle e} is at least 1, that is, ∑ s ∋ e x s ≥ 1. {\displaystyle \sum _{s\ni e}x_{s}\geq 1.} The optimal solution x ∗ {\displaystyle x^{}} is a feasible solution whose cost ∑ s ∈ S c ( S ) x s ∗ {\displaystyle \sum _{s\in {\mathcal {S}}}c(S)x_{s}^{}} is as small as possible. Note that any set cover C {\displaystyle {\mathcal {C}}} for S {\displaystyle {\mathcal {S}}} gives a feasible solution x {\displaystyle x} (where x s = 1 {\displaystyle x_{s}=1} for s ∈ C {\displaystyle s\in {\mathcal {C}}} , x s = 0 {\displaystyle x_{s}=0} otherwise). The cost of this C {\displaystyle {\mathcal {C}}} equals the cost of x {\displaystyle x} , that is, ∑ s ∈ C c ( s ) = ∑ s ∈ S c ( s ) x s . {\displaystyle \sum _{s\in {\mathcal {C}}}c(s)=\sum _{s\in {\mathcal {S}}}c(s)x_{s}.} In other words, the linear program LP is a relaxation of the given set-cover problem. Since x ∗ {\displaystyle x^{}} has minimum cost among feasible solutions to the LP, the cost of x ∗ {\displaystyle x^{}} is a lower bound on the cost of the optimal set cover. === Randomized rounding step === In step 3, we must convert the minimum-cost fractional set cover x ∗ {\displaystyle x^{}} into a feasible integer solution x ′ {\displaystyle x'} (corresponding to a true set cover). The rounding step should produce an x ′ {\displaystyle x'} that, with positive probability, has cost within a small factor of the cost of x ∗ {\displaystyle x^{}} .Then (since the cost of x ∗ {\displaystyle x^{}} is a lower bound on the cost of the optimal set cover), the cost of x ′ {\displaystyle x'} will be within a small factor of the optimal cost. As a starting point, consider the most natural rounding scheme: For each set s ∈ S {\displaystyle s\in {\mathcal {S}}} in turn, take x s ′ = 1 {\displaystyle x'_{s}=1} with probability min ( 1 , x s ∗ ) {\displaystyle \min(1,x_{s}^{})} , otherwise take x s ′ = 0 {\displaystyle x'_{s}=0} . With this rounding scheme, the expected cost of the chosen sets is at most ∑ s c ( s ) x s ∗ {\displaystyle \sum _{s}c(s)x_{s}^{}} , the cost of the fractional cover. This is good. Unfortunately the coverage is not good. When the variables x s ∗ {\displaystyle x_{s}^{}} are small, the probability that an element e {\displaystyle e} is not covered is about ∏ s ∋ e 1 − x s ∗ ≈ ∏ s ∋ e exp ⁡ ( − x s ∗ ) = exp ⁡ ( − ∑ s ∋ e x s ∗ ) ≈ exp ⁡ ( − 1 ) . {\displaystyle \prod _{s\ni e}1-x_{s}^{}\approx \prod _{s\ni e}\exp(-x_{s}^{})=\exp {\Big (}-\sum _{s\ni e}x_{s}^{}{\Big )}\approx \exp(-1).} So only a constant fraction of the elements will be covered in expectation. To make x ′ {\displaystyle x'} cover every element with high probability, the standard rounding scheme first scales up the rounding probabilities by an appropriate factor λ > 1 {\displaystyle \lambda >1} . Here is the standard rounding scheme: Fix a parameter λ ≥ 1 {\displaystyle \lambda \geq 1} . For each set s ∈ S {\displaystyle s\in {\mathcal {S}}} in turn, take x s ′ = 1 {\displaystyle x'_{s}=1} with probability min ( λ x s ∗ , 1 ) {\displaystyle \min(\lambda x_{s}^{},1)} , otherwise take x s ′ = 0 {\displaystyle x'_{s}=0} . Scaling the probabilities up by λ {\displaystyle \lambda } increases the expected cost by λ {\displaystyle \lambda } , but makes coverage of all elements likely. The idea is to choose λ {\displaystyle \lambda } as small as possible so that all elements are provably covered with non-zero probability. Here is a detailed analysis. ==== Lemma (approximation guarantee for rounding scheme) ==== Fix λ = ln ⁡ ( 2 | U | ) {\displaystyle \lambda =\ln(2|{\mathcal {U}}|)} . With positive probability, the rounding scheme returns a set cover x ′ {\displaystyle x'} of cost at most 2 ln ⁡ ( 2 | U | ) c ⋅ x ∗ {\displaystyle 2\ln(2|{\mathcal {U}}|)c\cdot x^{}} (and thus of cost O ( log ⁡ | U | ) {\displaystyle O(\log |{\mathcal {U}}|)} times the cost of the optimal set cover). (Note: with care the O ( log ⁡ | U | ) {\displaystyle O(\log |{\mathcal {U}}|)} can be reduced to ln ⁡ ( | U | ) + O ( log ⁡ log ⁡ | U | ) {\displaystyle \ln(|{\mathcal {U}}|)+O(\log \log |{\mathcal {U}}|)} .) ==== Proof ==== The output x ′ {\displaystyle x'} of the random rounding scheme has the desired properties as long as none of the following "bad" events occur: the cost c ⋅ x ′ {\displaystyle c\cdot x'} of x ′ {\displaystyle x'} exceeds 2 λ c ⋅ x ∗ {\displaystyle 2\lambda c\cdot x^{}} , or for some element e {\displaystyle e} , x ′ {\displaystyle x'} fails to cover e {\displaystyle e} . The expectation of each x s ′ {\displaystyle x'_{s}} is at most λ x s ∗ {\displaystyle \lambda x_{s

  Read more →