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  ELMo

  ELMo (embeddings from language model) is a word embedding method for representing a sequence of words as a corresponding sequence of vectors. It was created by researchers at the Allen Institute for Artificial Intelligence, and University of Washington and first released in February 2018. It is a bidirectional LSTM which takes character-level as inputs and produces word-level embeddings, trained on a corpus of about 30 million sentences and 1 billion words. The architecture of ELMo accomplishes a contextual understanding of tokens. Deep contextualized word representation is useful for many natural language processing tasks, such as coreference resolution and polysemy resolution. ELMo was historically important as a pioneer of self-supervised generative pretraining followed by fine-tuning, where a large model is trained to reproduce a large corpus, then the large model is augmented with additional task-specific weights and fine-tuned on supervised task data. It was an instrumental step in the evolution towards transformer-based language modelling. == Architecture == ELMo is a multilayered bidirectional LSTM on top of a token embedding layer. The output of all LSTMs concatenated together consists of the token embedding. The input text sequence is first mapped by an embedding layer into a sequence of vectors. Then two parts are run in parallel over it. The forward part is a 2-layered LSTM with 4096 units and 512 dimension projections, and a residual connection from the first to second layer. The backward part has the same architecture, but processes the sequence back-to-front. The outputs from all 5 components (embedding layer, two forward LSTM layers, and two backward LSTM layers) are concatenated and multiplied by a linear matrix ("projection matrix") to produce a 512-dimensional representation per input token. ELMo was pretrained on a text corpus of 1 billion words. The forward part is trained by repeatedly predicting the next token, and the backward part is trained by repeatedly predicting the previous token. After the ELMo model is pretrained, its parameters are frozen, except for the projection matrix, which can be fine-tuned to minimize loss on specific language tasks. This is an early example of the pretraining-fine-tune paradigm. The original paper demonstrated this by improving state of the art on six benchmark NLP tasks. === Contextual word representation === The architecture of ELMo accomplishes a contextual understanding of tokens. For example, the first forward LSTM of ELMo would process each input token in the context of all previous tokens, and the first backward LSTM would process each token in the context of all subsequent tokens. The second forward LSTM would then incorporate those to further contextualize each token. Deep contextualized word representation is useful for many natural language processing tasks, such as coreference resolution and polysemy resolution. For example, consider the sentenceShe went to the bank to withdraw money.In order to represent the token "bank", the model must resolve its polysemy in context. The first forward LSTM would process "bank" in the context of "She went to the", which would allow it to represent the word to be a location that the subject is going towards. The first backward LSTM would process "bank" in the context of "to withdraw money", which would allow it to disambiguate the word as referring to a financial institution. The second forward LSTM can then process "bank" using the representation vector provided by the first backward LSTM, thus allowing it to represent it to be a financial institution that the subject is going towards. == Historical context == ELMo is one link in a historical evolution of language modelling. Consider a simple problem of document classification, where we want to assign a label (e.g., "spam", "not spam", "politics", "sports") to a given piece of text. The simplest approach is the "bag of words" approach, where each word in the document is treated independently, and its frequency is used as a feature for classification. This was computationally cheap but ignored the order of words and their context within the sentence. GloVe and Word2Vec built upon this by learning fixed vector representations (embeddings) for words based on their co-occurrence patterns in large text corpora. Like BERT (but unlike "bag of words" such as Word2Vec and GloVe), ELMo word embeddings are context-sensitive, producing different representations for words that share the same spelling. It was trained on a corpus of about 30 million sentences and 1 billion words. Previously, bidirectional LSTM was used for contextualized word representation. ELMo applied the idea to a large scale, achieving state of the art performance. After the 2017 publication of Transformer architecture, the architecture of ELMo was changed from a multilayered bidirectional LSTM to a Transformer encoder, giving rise to BERT. BERT has a similar pretrain-fine-tune workflow, but uses a Transformer with implications for more parallelizable training.

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  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).

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  Operational historian

  In manufacturing, an operational historian is a time-series database application that is developed for operational process data. Historian software is often embedded or used in conjunction with standard DCS and PLC control systems to provide enhanced data capture, validation, compression, and aggregation capabilities. Historians have been deployed in almost every industry and contribute to functions such as supervisory control, performance monitoring, quality assurance, and, more recently, machine learning applications which can learn from vast quantities of historical data. These systems were originally developed to capture instrumentation and control data, which led many to use the term "tag" for a stream of process data, referring to the physical "tags" which had been placed on instrumentation for manually capturing data. Raw data may be accessed via OPC HDA, SQL, or REST API interfaces. == Operational Support == Operational historians are typically used within the manufacturing facility by engineers and operators for supervisory functions and analysis. An operational historian will typically capture all instrumentation and control data, whereas an enterprise historian that is deployed to support business functions will capture only a subset of the plant data. Typically, these applications offer data access through dedicated APIs (Application Programming Interfaces) and SDKs (Software Development Kits) which offer high-performance read and write operations. These operate through vendor-specific or custom applications. Front-end tools for trending process data over time are the most common interfaces to these databases. Because these applications are typically deployed next to or near the source of their process data, they are often marketed and sold as 'real-time database systems.' This distinction varies among vendors, who often have to make tradeoffs in performance between data capture and presentation, and application and analysis functionality. The following is a list of typical challenges for operational historians: data collection from instrumentation and controls storage and archiving of very large volumes of data organization of data in the form of "tags" or "points" limiting of monitoring (alarms) and validation aggregation and interpolation manual data entry (MDE) == Data access == As opposed to enterprise historians, the data access layer in the operational historian is designed to offer sophisticated data fetching modes without complex information analysis facilities. The following settings are typically available for data access operations: Data scope (single point or tag, history based on time range, history based on sample count) Request modes (raw data, last-known value, aggregation, interpolation) Sampling (single point, all points without sampling, all points with interval sampling) Data omission (based on the sample quality, based on the sample value, based on the count) Even though the operational historians are rarely relational database management systems, they often offer SQL-based interfaces to query the database. In most of such implementations, the dialect does not follow the SQL standard in order to provide syntax for specifying data access operations parameters.

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  Rendezvous hashing

  Rendezvous or highest random weight (HRW) hashing is an algorithm that allows clients to achieve distributed agreement on a set of k {\displaystyle k} options out of a possible set of n {\displaystyle n} options. A typical application is when clients need to agree on which sites (or proxies) objects are assigned to. Consistent hashing addresses the special case k = 1 {\displaystyle k=1} using a different method. Rendezvous hashing is both much simpler and more general than consistent hashing (see below). == History == Rendezvous hashing was invented by David Thaler and Chinya Ravishankar at the University of Michigan in 1996. Consistent hashing appeared a year later in the literature. Given its simplicity and generality, rendezvous hashing is now being preferred to consistent hashing in real-world applications. Rendezvous hashing was used very early on in many applications including mobile caching, router design, secure key establishment, and sharding and distributed databases. Other examples of real-world systems that use Rendezvous Hashing include the GitHub load balancer, the Apache Ignite distributed database, the Tahoe-LAFS file store, the CoBlitz large-file distribution service, Apache Druid, IBM's Cloud Object Store, the Arvados Data Management System, Apache Kafka, and the Twitter EventBus pub/sub platform. One of the first applications of rendezvous hashing was to enable multicast clients on the Internet (in contexts such as the MBONE) to identify multicast rendezvous points in a distributed fashion. It was used in 1998 by Microsoft's Cache Array Routing Protocol (CARP) for distributed cache coordination and routing. Some Protocol Independent Multicast routing protocols use rendezvous hashing to pick a rendezvous point. == Problem definition and approach == === Algorithm === Rendezvous hashing solves a general version of the distributed hash table problem: We are given a set of n {\displaystyle n} sites (servers or proxies, say). How can any set of clients, given an object O {\displaystyle O} , agree on a k-subset of sites to assign to O {\displaystyle O} ? The standard version of the problem uses k = 1. Each client is to make its selection independently, but all clients must end up picking the same subset of sites. This is non-trivial if we add a minimal disruption constraint, and require that when a site fails or is removed, only objects mapping to that site need be reassigned to other sites. The basic idea is to give each site S j {\displaystyle S_{j}} a score (a weight) for each object O i {\displaystyle O_{i}} , and assign the object to the highest scoring site. All clients first agree on a hash function h ( ⋅ ) {\displaystyle h(\cdot )} . For object O i {\displaystyle O_{i}} , the site S j {\displaystyle S_{j}} is defined to have weight w i , j = h ( O i , S j ) {\displaystyle w_{i,j}=h(O_{i},S_{j})} . Each client independently computes these weights w i , 1 , w i , 2 … w i , n {\displaystyle w_{i,1},w_{i,2}\dots w_{i,n}} and picks the k sites that yield the k largest hash values. The clients have thereby achieved distributed k {\displaystyle k} -agreement. If a site S {\displaystyle S} is added or removed, only the objects mapping to S {\displaystyle S} are remapped to different sites, satisfying the minimal disruption constraint above. The HRW assignment can be computed independently by any client, since it depends only on the identifiers for the set of sites S 1 , S 2 … S n {\displaystyle S_{1},S_{2}\dots S_{n}} and the object being assigned. HRW easily accommodates different capacities among sites. If site S k {\displaystyle S_{k}} has twice the capacity of the other sites, we simply represent S k {\displaystyle S_{k}} twice in the list, say, as S k , 1 , S k , 2 {\displaystyle S_{k,1},S_{k,2}} . Clearly, twice as many objects will now map to S k {\displaystyle S_{k}} as to the other sites. === Properties === Consider the simple version of the problem, with k = 1, where all clients are to agree on a single site for an object O. Approaching the problem naively, it might appear sufficient to treat the n sites as buckets in a hash table and hash the object name O into this table. Unfortunately, if any of the sites fails or is unreachable, the hash table size changes, forcing all objects to be remapped. This massive disruption makes such direct hashing unworkable. Under rendezvous hashing, however, clients handle site failures by picking the site that yields the next largest weight. Remapping is required only for objects currently mapped to the failed site, and disruption is minimal. Rendezvous hashing has the following properties: Low overhead: The hash function used is efficient, so overhead at the clients is very low. Load balancing: Since the hash function is randomizing, each of the n sites is equally likely to receive the object O. Loads are uniform across the sites. Site capacity: Sites with different capacities can be represented in the site list with multiplicity in proportion to capacity. A site with twice the capacity of the other sites will be represented twice in the list, while every other site is represented once. High hit rate: Since all clients agree on placing an object O into the same site SO, each fetch or placement of O into SO yields the maximum utility in terms of hit rate. The object O will always be found unless it is evicted by some replacement algorithm at SO. Minimal disruption: When a site fails, only the objects mapped to that site need to be remapped. Disruption is at the minimal possible level. Distributed k-agreement: Clients can reach distributed agreement on k sites simply by selecting the top k sites in the ordering. == O(log n) running time via skeleton-based hierarchical rendezvous hashing == The standard version of Rendezvous Hashing described above works quite well for moderate n, but when n {\displaystyle n} is extremely large, the hierarchical use of Rendezvous Hashing achieves O ( log ⁡ n ) {\displaystyle O(\log n)} running time. This approach creates a virtual hierarchical structure (called a "skeleton"), and achieves O ( log ⁡ n ) {\displaystyle O(\log n)} running time by applying HRW at each level while descending the hierarchy. The idea is to first choose some constant m {\displaystyle m} and organize the n {\displaystyle n} sites into c = ⌈ n / m ⌉ {\displaystyle c=\lceil n/m\rceil } clusters C 1 = { S 1 , S 2 … S m } , C 2 = { S m + 1 , S m + 2 … S 2 m } … {\displaystyle C_{1}=\left\{S_{1},S_{2}\dots S_{m}\right\},C_{2}=\left\{S_{m+1},S_{m+2}\dots S_{2m}\right\}\dots } Next, build a virtual hierarchy by choosing a constant f {\displaystyle f} and imagining these c {\displaystyle c} clusters placed at the leaves of a tree T {\displaystyle T} of virtual nodes, each with fanout f {\displaystyle f} . In the accompanying diagram, the cluster size is m = 4 {\displaystyle m=4} , and the skeleton fanout is f = 3 {\displaystyle f=3} . Assuming 108 sites (real nodes) for convenience, we get a three-tier virtual hierarchy. Since f = 3 {\displaystyle f=3} , each virtual node has a natural numbering in octal. Thus, the 27 virtual nodes at the lowest tier would be numbered 000 , 001 , 002 , . . . , 221 , 222 {\displaystyle 000,001,002,...,221,222} in octal (we can, of course, vary the fanout at each level - in that case, each node will be identified with the corresponding mixed-radix number). The easiest way to understand the virtual hierarchy is by starting at the top, and descending the virtual hierarchy. We successively apply Rendezvous Hashing to the set of virtual nodes at each level of the hierarchy, and descend the branch defined by the winning virtual node. We can in fact start at any level in the virtual hierarchy. Starting lower in the hierarchy requires more hashes, but may improve load distribution in the case of failures. For example, instead of applying HRW to all 108 real nodes in the diagram, we can first apply HRW to the 27 lowest-tier virtual nodes, selecting one. We then apply HRW to the four real nodes in its cluster, and choose the winning site. We only need 27 + 4 = 31 {\displaystyle 27+4=31} hashes, rather than 108. If we apply this method starting one level higher in the hierarchy, we would need 9 + 3 + 4 = 16 {\displaystyle 9+3+4=16} hashes to get to the winning site. The figure shows how, if we proceed starting from the root of the skeleton, we may successively choose the virtual nodes ( 2 ) 3 {\displaystyle (2)_{3}} , ( 20 ) 3 {\displaystyle (20)_{3}} , and ( 200 ) 3 {\displaystyle (200)_{3}} , and finally end up with site 74. The virtual hierarchy need not be stored, but can be created on demand, since the virtual nodes names are simply prefixes of base- f {\displaystyle f} (or mixed-radix) representations. We can easily create appropriately sorted strings from the digits, as required. In the example, we would be working with the strings 0 , 1 , 2 {\displaystyle 0,1,2} (at tier 1), 20 , 21 , 22 {\displaystyle 20,21,22} (at tier 2), and 200 , 201 , 202

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  Teaspiller

  Teaspiller was a US-based web application for customers to find accountants and hire them to do their taxes and accounting online. In 2013 the company was acquired by Intuit, Inc and added to its TurboTax product line. The Teaspiller employees and code were all acquired and the product was renamed as "TurboTax CPA select". It enabled accountants to work remotely with clients (share files, send secure messages, schedule appointments), as well as find new clients looking for their specific skills through a complex search algorithm. This was done through extended profiles containing licensing information, professional histories, user ratings, peer endorsements, association memberships, and practice areas. The service had been called an H&R Block killer by Business Insider as it helped customers find accountants to prepare tax returns online. As of 2011 it had 20,000 US accountants listed on the site. The application was built using the Django framework. == History == Teaspiller was built by Vemdara, LLC, a web company based in New York and founded in 2009 by Amit Vemuri (a former VP at Travelocity). The web application was launched in 2010. In 2013 the company was acquired by Intuit as part of their TurboTax product line and renamed as "TurboTax CPA select".

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  DPVweb

  DPVweb is a database for virologists working on plant viruses combining taxonomic, bioinformatic and symptom data. == Description == DPVweb is a central web-based source of information about viruses, viroids and satellites of plants, fungi and protozoa. It provides comprehensive taxonomic information, including brief descriptions of each family and genus, and classified lists of virus sequences. It makes use of a large database that also holds detailed, curated, information for all sequences of viruses, viroids and satellites of plants, fungi and protozoa that are complete or that contain at least one complete gene. There are currently about 10,000 such sequences. For comparative purposes, DPVweb also contains a representative sequence of all other fully sequenced virus species with an RNA or single-stranded DNA genome. For each curated sequence the database contains the start and end positions of each feature (gene, non-translated region, etc.), and these have been checked for accuracy. As far as possible, the nomenclature for genes and proteins are standardized within genera and families. Sequences of features (either as DNA or amino acid sequences) can be directly downloaded from the website in FASTA format. The sequence information can also be accessed via client software for personal computers. == History == The Descriptions of Plant Viruses (DPVs) were first published by the Association of Applied Biologists in 1970 as a series of leaflets, each one written by an expert describing a particular plant virus. In 1998 all of the 354 DPVs published in paper were scanned, and converted into an electronic format in a database and distributed on CDROM. In 2001 the descriptions were made available on the new DPVweb site, providing open access to the now 400+ DPVs (currently 415) as well as taxonomic and sequence data on all plant viruses. == Uses == DPVweb is an aid to researchers in the field of plant virology as well as an educational resource for students of virology and molecular biology. The site provides a single point of access for all known plant virus genome sequences making it easy to collect these sequences together for further analysis and comparison. Sequence data from the DPVweb database have proved valuable for a number of projects: survey of codon usage bias amongst all plant viruses, two-way comparisons between comprehensive sets of sequences from the families Flexiviridae and Potyviridae that have helped inform taxonomy and clarify genus and species discrimination criteria, a survey and verification of the polyprotein cleavage sites within the family Potyviridae.

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  Source criticism

  Source criticism (or information evaluation) is the process of evaluating an information source, i.e.: a document, a person, a speech, a fingerprint, a photo, an observation, or anything used in order to obtain knowledge. In relation to a given purpose, a given information source may be more or less valid, reliable or relevant. Broadly, "source criticism" is the interdisciplinary study of how information sources are evaluated for given tasks. == Meaning == Problems in translation: The Danish word kildekritik, like the Norwegian word kildekritikk and the Swedish word källkritik, derived from the German Quellenkritik and is closely associated with the German historian Leopold von Ranke (1795–1886). Historian Wolfgang Hardtwig wrote: His [Ranke's] first work Geschichte der romanischen und germanischen Völker von 1494–1514 (History of the Latin and Teutonic Nations from 1494 to 1514) (1824) was a great success. It already showed some of the basic characteristics of his conception of Europe, and was of historiographical importance particularly because Ranke made an exemplary critical analysis of his sources in a separate volume, Zur Kritik neuerer Geschichtsschreiber (On the Critical Methods of Recent Historians). In this work he raised the method of textual criticism used in the late eighteenth century, particularly in classical philology to the standard method of scientific historical writing. (Hardtwig, 2001, p. 12739) Historical theorist Chris Lorenz wrote: The larger part of the nineteenth and twentieth centuries would be dominated by the research-oriented conception of historical method of the so-called Historical School in Germany, led by historians as Leopold Ranke and Berthold Niebuhr. Their conception of history, long been regarded as the beginning of modern, 'scientific' history, harked back to the 'narrow' conception of historical method, limiting the methodical character of history to source criticism. (Lorenz, 2001) In the early 21st century, source criticism is a growing field in, among other fields, library and information science. In this context source criticism is studied from a broader perspective than just, for example, history, classical philology, or biblical studies (but there, too, it has more recently received new attention). == Principles == The following principles are from two Scandinavian textbooks on source criticism, written by the historians Olden-Jørgensen (1998) and Thurén (1997): Human sources may be relics (e.g. a fingerprint) or narratives (e.g. a statement or a letter). Relics are more credible sources than narratives. A given source may be forged or corrupted; strong indications of the originality of the source increases its reliability. The closer a source is to the event which it purports to describe, the more one can trust it to give an accurate description of what really happened A primary source is more reliable than a secondary source, which in turn is more reliable than a tertiary source and so on. If a number of independent sources contain the same message, the credibility of the message is strongly increased. The tendency of a source is its motivation for providing some kind of bias. Tendencies should be minimized or supplemented with opposite motivations. If it can be demonstrated that the witness (or source) has no direct interest in creating bias, the credibility of the message is increased. Two other principles are: Knowledge of source criticism cannot substitute for subject knowledge: "Because each source teaches you more and more about your subject, you will be able to judge with ever-increasing precision the usefulness and value of any prospective source. In other words, the more you know about the subject, the more precisely you can identify what you must still find out". (Bazerman, 1995, p. 304). The reliability of a given source is relative to the questions put to it. "The empirical case study showed that most people find it difficult to assess questions of cognitive authority and media credibility in a general sense, for example, by comparing the overall credibility of newspapers and the Internet. Thus these assessments tend to be situationally sensitive. Newspapers, television and the Internet were frequently used as sources of orienting information, but their credibility varied depending on the actual topic at hand" (Savolainen, 2007). The following questions are often good ones to ask about any source according to the American Library Association (1994) and Engeldinger (1988): How was the source located? What type of source is it? Who is the author and what are the qualifications of the author in regard to the topic that is discussed? When was the information published? In which country was it published? What is the reputation of the publisher? Does the source show a particular cultural or political bias? For literary sources complementing criteria are: Does the source contain a bibliography? Has the material been reviewed by a group of peers, or has it been edited? How does the article/book compare with similar articles/books? == Levels of generality == Some principles of source criticism are universal, other principles are specific for certain kinds of information sources. There is today no consensus about the similarities and differences between source criticism in the natural science and humanities. Logical positivism claimed that all fields of knowledge were based on the same principles. Much of the criticism of logical positivism claimed that positivism is the basis of the sciences, whereas hermeneutics is the basis of the humanities. This was, for example, the position of Jürgen Habermas. A newer position, in accordance with, among others, Hans-Georg Gadamer and Thomas Kuhn, understands both science and humanities as determined by researchers' preunderstanding and paradigms. Hermeneutics is thus a universal theory. The difference is, however, that the sources of the humanities are themselves products of human interests and preunderstanding, whereas the sources of the natural sciences are not. Humanities are thus "doubly hermeneutic". Natural scientists, however, are also using human products (such as scientific papers) which are products of preunderstanding (and can lead to, for example, academic fraud). == Contributing fields == === Epistemology === Epistemological theories are the basic theories about how knowledge is obtained and are thus the most general theories about how to evaluate information sources. Empiricism evaluates sources by considering the observations (or sensations) on which they are based. Sources without basis in experience are not seen as valid. Rationalism provides low priority to sources based on observations. In order to be meaningful, observations must be explained by clear ideas or concepts. It is the logical structure and the well definedness that is in focus in evaluating information sources from the rationalist point of view. Historicism evaluates information sources on the basis of their reflection of their sociocultural context and their theoretical development. Pragmatism evaluate sources on the basis of how their values and usefulness to accomplish certain outcomes. Pragmatism is skeptical about claimed neutral information sources. The evaluation of knowledge or information sources cannot be more certain than is the construction of knowledge. If one accepts the principle of fallibilism then one also has to accept that source criticism can never 100% verify knowledge claims. As discussed in the next section, source criticism is intimately linked to scientific methods. The presence of fallacies of argument in sources is another kind of philosophical criterion for evaluating sources. Fallacies are presented by Walton (1998). Among the fallacies are the ad hominem fallacy (the use of personal attack to try to undermine or refute a person's argument) and the straw man fallacy (when one arguer misrepresents another's position to make it appear less plausible than it really is, in order more easily to criticize or refute it.) === Research methodology === Research methods are methods used to produce scholarly knowledge. The methods that are relevant for producing knowledge are also relevant for evaluating knowledge. An example of a book that turns methodology upside-down and uses it to evaluate produced knowledge is Katzer; Cook & Crouch (1998). === Science studies === Studies of quality evaluation processes such as peer review, book reviews and of the normative criteria used in evaluation of scientific and scholarly research. Another field is the study of scientific misconduct. Harris (1979) provides a case study of how a famous experiment in psychology, Little Albert, has been distorted throughout the history of psychology, starting with the author (Watson) himself, general textbook authors, behavior therapists, and a prominent learning theorist. Harris proposes possible causes for these distortions and analyzes the Albert study as an ex

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  Collision problem

  The r-to-1 collision problem is an important theoretical problem in complexity theory, quantum computing, and computational mathematics. The collision problem most often refers to the 2-to-1 version: given n {\displaystyle n} even and a function f : { 1 , … , n } → { 1 , … , n } {\displaystyle f:\,\{1,\ldots ,n\}\rightarrow \{1,\ldots ,n\}} , we are promised that f is either 1-to-1 or 2-to-1. We are only allowed to make queries about the value of f ( i ) {\displaystyle f(i)} for any i ∈ { 1 , … , n } {\displaystyle i\in \{1,\ldots ,n\}} . The problem then asks how many such queries we need to make to determine with certainty whether f is 1-to-1 or 2-to-1. == Classical solutions == === Deterministic === Solving the 2-to-1 version deterministically requires n 2 + 1 {\textstyle {\frac {n}{2}}+1} queries, and in general distinguishing r-to-1 functions from 1-to-1 functions requires n r + 1 {\textstyle {\frac {n}{r}}+1} queries. This is a straightforward application of the pigeonhole principle: if a function is r-to-1, then after n r + 1 {\textstyle {\frac {n}{r}}+1} queries we are guaranteed to have found a collision. If a function is 1-to-1, then no collision exists. Thus, n r + 1 {\textstyle {\frac {n}{r}}+1} queries suffice. If we are unlucky, then the first n / r {\displaystyle n/r} queries could return distinct answers, so n r + 1 {\textstyle {\frac {n}{r}}+1} queries is also necessary. === Randomized === If we allow randomness, the problem is easier. By the birthday paradox, if we choose (distinct) queries at random, then with high probability we find a collision in any fixed 2-to-1 function after Θ ( n ) {\displaystyle \Theta ({\sqrt {n}})} queries. == Quantum solution == The BHT algorithm, which uses Grover's algorithm, solves this problem optimally by only making O ( n 1 / 3 ) {\displaystyle O(n^{1/3})} queries to f. The matching lower bound of Ω ( n 1 / 3 ) {\displaystyle \Omega (n^{1/3})} was proved by Aaronson and Shi using the polynomial method.

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  Touch 'n Go eWallet

  Touch 'n Go eWallet is a Malaysian digital wallet and online payment platform, established in Kuala Lumpur, Malaysia, in July 2017 as a joint venture between Touch 'n Go and Ant Financial. It allows users to make payments at over 280,000 merchant touch points via QR code, as well as perform peer-to-peer (P2P) money transfers. Since then, the e-wallet further diversified for users to pay for tolls via RFID or PayDirect, street parking and various online payment spanning e-hailing, car-sharing apps or taxis, various overhead bills; top-up for mobile prepaid or in-game currencies; purchases on e-commerce websites; food delivery; renewing motor insurance and other insurance/takaful plans; and even movie, bus, trains or airline tickets. == Background == Prior to the launch of the e-wallet service, Touch 'n Go provided stored-value physical all-in-one contactless card (namely Touch 'n Go cards or "TnG cards") that users can use to pay for toll fares, public transportation and parking lots as well as purchases in some retail stores. In 1999, Touch 'n Go also markets SmartTag devices that allow road users to pass through certain toll booths without the need to unwind the car window. The high entry cost of the device (around RM 100 each) also meant that only few can enjoy the seamless experience. In 2009, Touch 'n Go partnered with Maxis to launch FastTap, a new mobile payment service that utilised Near-Field Communication (NFC). Maxis customers can make payments by placing the phone near the card readers (that also supports physical bank cards and Touch ’N Go cards). However, the venture featured only one phone model, Nokia 6212, which greatly limited the public reach. In July 2012, Touch 'n Go announced another collaboration with CIMB and Maxis to create similar NFC-based online transaction service that runs on compatible smartphones. Touch 'n Go Wallet was launched in February 2017 as an QR code-based e-wallet application, to compete with Samsung Pay that utilizes NFC modules. In the controlled pilot test in Taman Tun Dr Ismail, the correspondents can experience basic functionalities (prepaid mobile service reload, bills payment, movie tickets and flight tickets purchase, transfer of money with another user, and payments at participating stores and restaurants). While the deployed version of the app was generally well-received, the existing process to transfer the balance to the physical TnG card stored value from the app garnered unanimous backlash. Test groups felt that the need to head to a self-service terminal named "Pick Up Device" in person within 24 hours for completion, along with the failure to do so (the balance would be credited back to the wallet after 24 hours), was not divulged clearly and also defeated the purpose of convenience, not to mention there were only 2 such terminals. The feature was eventually suspended. On 15 November 2017, Touch 'n Go was granted permission by the Central Bank of Malaysia to form a joint venture with Ant Financial, a Chinese-based financial company that operates Alipay. The partnership allowed the local e-wallet to learn from and build upon the operational model pioneered by Alipay. In June 2018, it was reported that Touch 'n Go was pilot testing the uses of the Touch 'n Go eWallet in Rapid Transit, as the ticketing system was enabled on the Kelana Jaya line in the Klang Valley. Pilot testing only applied to stations in Kelana Jaya, KL Gateway–Universiti, Kerinchi, KL Sentral, Dang Wangi, KLCC, and Ampang Park. The test was reported to be successful in February 2020 and was planned to be fully deployed on the LRT and MRT. Due to unforeseen circumstances, this feature did not come into fruition, the app merely adds in-app purchase of monthly concession cards called "My50". In August 2018, Touch 'n Go announced that selected drivers may experience first-hand a new RFID-based payment (later rebranded as "myRFID") that serves to replace SmartTag devices on closed toll roads with during pilot testing phase commencing on 3 September 2018. On 2 November 2018, participation in the ongoing pilot programme was expanded, allowing more drivers to sign up ahead of the public rollout of the RFID system. During the same period, Touch 'n Go has discontinued the sales of SmartTAG devices in favor of the RFID-based payment system. Initially, the installation of the RFID chip onto the car could only be done by Touch 'n Go staff at the RFID fitment centers, at no cost. As the pilot testing concluded on 15 February 2020, a self-installation kit are being offered to the public on Lazada and Shopee. Support for taxi-hailing mobile apps was added in November 2018 when Touch 'n Go partnered with EzCab and Public Cab, allowing users to make payments via QR code. This was later expanded to support MULA on 7 January 2020, and later MyCar on 4 April 2020. Touch 'n Go eWallet was also the first eWallet to convert Kuala Lumpur's most famous Ramadan bazaar in Kampong Bahru into "Kampong Kashless", a venue that can accept cashless QR payments. It welcomed more than 250,000 Malaysians including local celebrities and government officials. On 1 October 2019, some e-commerce websites owned by the Alibaba Group (TMall and Taobao) began to support Touch 'n Go eWallet payments, Lazada joined the list on 29 October 2019. Touch 'n Go eWallet was one of the three e-wallet services in Malaysia (the other being Boost and GrabPay) that was eligible for its users to receive an RM 30 credit in conjunction of E-Tunai Rakyat program under the Budget 2020 plan, that further normalizes adoption of cashless and mobile payment among Malaysians. Unlike Boost and GrabPay, whose P2P transfers were completely disabled until users have exhausted the RM 30 first, Touch 'n Go eWallet did not impose such measures. in 2020, Touch 'n Go eWallet joined DuitNow, an electronic transaction ecosystem in Malaysia which allows the funds from Touch 'n Go eWallet to be transferred to other competing services and vice versa, by implementing a standard DuitNow QR code deisgn. Japan become the first country outside Malaysia to support Touch 'n Go eWallet payment via Alipay Connect. During the COVID-19 pandemic and the enforcement of the movement control order, use of eWallets (including Touch 'n Go eWallet) increased tremendously among citizens due to its contactless nature of the payment and increased take-out orders at home; which in turn helped small and medium-sized enterprises to thrive. Touch 'n Go eWallet launched its loyalty programme – The Goal Hunter – in October 2020 where on monthly basis, users collect stamps by paying with the app in exchange for rewards that include lucky draws and other vouchers. == Services == Touch 'n Go eWallet app is available for download on both Google Play and Apple Appstore. It utilizes QR code technology for local in-store payments. The Touch 'n Go eWallet app also diversifies payment types, including but not limited to Utility bills Purchase of motor insurance policy Pay Later facility Prepaid reload and Postpaid payment to telecommunications companies loan repayments for courts, MBSJ payments, zakat and PTPTN payment for car parking P2P transfer airline ticket bookings; movie tickets from TGV Cinemas RFID refuelling at Shell stations (defunct after Shell launched its own payment app in 2024) User can reload the eWallet credit by setting up auto-reload, purchasing reload pins from convenience stores (such as 7-Eleven, KK Super Mart, MyNews, Family Mart etc.), reloading by FPX and credit/debit card. The PayDirect feature allows users to link their physical Touch 'n Go cards into the eWallet, where the toll fare can be debited from the eWallet balance when flashing the card near the sensor. In the circumstance of insufficient balance in the app, the toll fare will be deducted from the physical card's balance instead. This also conveniently allows users to view the card's remaining balance. Touch 'n Go eWallet is the first and only eWallet to offer a money-back guarantee when an unauthorised transaction is made on the user’s eWallet account, subject to Terms & Conditions. Payment via QR code scanning, including Touch 'n Go eWallet, becomes a norm in most of the shops/restaurants across Malaysia, including roadside hawkers/stall owners and automatic vending machines. The merchants usually display their owner's individual QR or Business account that they can apply for in-app. The popularity attributes to the low merchant onboarding cost (Unlike NFC payment and debit/credit card that requires purchase or rental of a payment terminal device at a yearly fee.) The app is also one of the few ewallet that supports bidirectional liquidity (alongside MAE developed by Maybank), where funds can be transferred two-way with bank accounts. This is not possible with the other major ewallets (GrabPay, Boost, ShopeePay etc.) where the money that is reloaded to the wallet cannot be transferred to another bank account, unless through manual req

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  Algorithms and Combinatorics

  Algorithms and Combinatorics (ISSN 0937-5511) is a book series in mathematics, and particularly in combinatorics and the design and analysis of algorithms. It is published by Springer Science+Business Media, and was founded in 1987. == Books == The books published in this series include: The Simplex Method: A Probabilistic Analysis (Karl Heinz Borgwardt, 1987, vol. 1) Geometric Algorithms and Combinatorial Optimization (Martin Grötschel, László Lovász, and Alexander Schrijver, 1988, vol. 2; 2nd ed., 1993) Systems Analysis by Graphs and Matroids (Kazuo Murota, 1987, vol. 3) Greedoids (Bernhard Korte, László Lovász, and Rainer Schrader, 1991, vol. 4) Mathematics of Ramsey Theory (Jaroslav Nešetřil and Vojtěch Rödl, eds., 1990, vol. 5) Matroid Theory and its Applications in Electric Network Theory and in Statics (Andras Recszki, 1989, vol. 6) Irregularities of Partitions: Papers from the meeting held in Fertőd, July 7–11, 1986 (Gábor Halász and Vera T. Sós, eds., 1989, vol. 8) Paths, Flows, and VLSI-Layout: Papers from the meeting held at the University of Bonn, Bonn, June 20–July 1, 1988 (Bernhard Korte, László Lovász, Hans Jürgen Prömel, and Alexander Schrijver, eds., 1990, vol. 9) New Trends in Discrete and Computational Geometry (János Pach, ed., 1993, vol. 10) Discrete Images, Objects, and Functions in Z n {\displaystyle \mathbb {Z} ^{n}} (Klaus Voss, 1993, vol. 11) Linear Optimization and Extensions (Manfred Padberg, 1999, vol. 12) The Mathematics of Paul Erdős I (Ronald Graham and Jaroslav Nešetřil, eds., 1997, vol. 13) The Mathematics of Paul Erdős II (Ronald Graham and Jaroslav Nešetřil, eds., 1997, vol. 14) Geometry of Cuts and Metrics (Michel Deza and Monique Laurent, 1997, vol. 15) Probabilistic Methods for Algorithmic Discrete Mathematics (M. Habib, C. McDiarmid, J. Ramirez-Alfonsin, and B. Reed, 1998, vol. 16) Modern Cryptography, Probabilistic Proofs and Pseudorandomness (Oded Goldreich, 1999, vol. 17) Geometric Discrepancy: An Illustrated Guide (Jiří Matoušek, 1999, vol. 18) Applied Finite Group Actions (Adalbert Kerber, 1999, vol. 19) Matrices and Matroids for Systems Analysis (Kazuo Murota, 2000, vol. 20; corrected ed., 2010) Combinatorial Optimization (Bernhard Korte and Jens Vygen, 2000, vol. 21; 5th ed., 2012) The Strange Logic of Random Graphs (Joel Spencer, 2001, vol. 22) Graph Colouring and the Probabilistic Method (Michael Molloy and Bruce Reed, 2002, Vol. 23) Combinatorial Optimization: Polyhedra and Efficiency (Alexander Schrijver, 2003, vol. 24. In three volumes: A. Paths, flows, matchings; B. Matroids, trees, stable sets; C. Disjoint paths, hypergraphs) Discrete and Computational Geometry: The Goodman-Pollack Festschrift (B. Aronov, S. Basu, J. Pach, and M. Sharir, eds., 2003, vol. 25) Topics in Discrete Mathematics: Dedicated to Jarik Nešetril on the Occasion of his 60th birthday (M. Klazar, J. Kratochvíl, M. Loebl, J. Matoušek, R. Thomas, and P. Valtr, eds., 2006, vol. 26) Boolean Function Complexity: Advances and Frontiers (Stasys Jukna, 2012, Vol. 27) Sparsity: Graphs, Structures, and Algorithms (Jaroslav Nešetřil and Patrice Ossona de Mendez, 2012, vol. 28) Optimal Interconnection Trees in the Plane (Marcus Brazil and Martin Zachariasen, 2015, vol. 29) Combinatorics and Complexity of Partition Functions (Alexander Barvinok, 2016, vol. 30)

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  Evidence-based library and information practice

  Evidence-based library and information practice (EBLIP) or evidence-based librarianship (EBL) is the use of evidence-based practices (EBP) in the field of library and information science (LIS). This means that all practical decisions made within LIS should 1) be based on research studies and 2) that these research studies are selected and interpreted according to some specific norms characteristic for EBP. Typically such norms disregard theoretical studies and qualitative studies and consider quantitative studies according to a narrow set of criteria of what counts as evidence. If such a narrow set of methodological criteria are not applied, it is better instead to speak of research based library and information practice. == Characteristics == Evidence-based practice in general has been characterised as a positivist approach; EBLIP is therefore also a positivist approach to LIS. As such, EBLIP is an approach in contrast to other approaches to LIS. The use of statistical approaches known as meta-analysis to conclude what evidence has been reported in the literature is one among other methods which is typical for the evidence-based approach. In 2002, Booth noted the three schools of EBILP had some commonalities, including the context of day-to-day decision-making, an emphasis on improving the quality of professional practice, a pragmatic focus on the 'best available evidence', incorporation of the user perspective, the acceptance of a broad range of quantitative and qualitative research designs, and access, either first-hand or second-hand, to the (process of) evidence-based practice and its products. He added one more, that EBILP is concerned with getting the best value for money. == The role of library and information science in EBP == Evidence-based practice in general is based on a very thorough search of the scientific literature and a very thorough selection and analysis of the retrieved literature. A close familiarity with database searching is needed, and library and information professionals have important roles to play in this respect. Therefore LIS professionals should be well suited to help professionals in other disciplines doing EBP. EBLIP is the application of this approach on LIS itself. It should be mentioned, however, that EBP started in medicine as evidence-based medicine (EBM) from which it spread to other fields. Only slowly and to a limited extent has EBP moved on to LIS. The EBLIP process can be applied to a variety of scenarios in LIS, including customer service, collection development, library management and information literacy instruction. In general, quantitative methods are used in LIS research. A 2010 study revealed five categories that capture the different ways library and information professionals experience evidence-based practice: Evidence-based practice is experienced as irrelevant; Evidence-based practice is experienced as learning from published research; Evidence-based practice is experienced as service improvement; Evidence-based practice is experienced as a way of being; Evidence-based practice is experienced as a weapon.

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  Behavior selection algorithm

  In artificial intelligence, a behavior selection algorithm, or action selection algorithm, is an algorithm that selects appropriate behaviors or actions for one or more intelligent agents. In game artificial intelligence, it selects behaviors or actions for one or more non-player characters. Common behavior selection algorithms include: Finite-state machines Hierarchical finite-state machines Decision trees Behavior trees Hierarchical task networks Hierarchical control systems Utility systems Dialogue tree (for selecting what to say) == Related concepts == In application programming, run-time selection of the behavior of a specific method is referred to as the strategy design pattern.

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  The Drivers Cooperative

  The Drivers Cooperative or Co-Op Ride is an American ridesharing company and mobile app that is a workers cooperative, owned collectively by the drivers. The cooperative launched in May 2021 in New York City, with the first 2,500 drivers issued their ownership certificates in a media event. The cooperative was co-founded by Grenadan immigrant and for hire vehicle driver Ken Lewis, labor organizer Erik Forman, and former Uber executive Alissa Orlando. Mohammad Hossen is the first member of the drivers' advisory board, which they plan to expand democratically as more drivers are onboarded. Other staff include software and industry veterans and in addition to co-founder Lewis, there are other drivers in management roles such as ex-driver and organizer David Alexis. The Co-Op Ride app is on the iOS and Android platforms and is built on Google Maps, Stripe, and Waze. By July, the app had been downloaded by 30,000 users and the number of drivers increased to 3,400, and by August there were 40,000 users. The cooperative is owned by the drivers themselves, and takes 15% from each ride for business overhead costs, as opposed to the 25% to 40% ride hail apps like Uber or Lyft take per ride. While being ultimately owned by the driver members, not by investors, the cooperative began with seed money from the Minnesota-based Community Development Financial Institution Shared Capital Cooperative, the local Lower East Side People's Federal Credit Union, and welcomed individual donations via crowdfunding in the form of revenue sharing debt on Wefunder. Each driver is a member of the cooperative and owns one share of the company and one vote in business and leadership decisions. In addition to a larger percentage of the fees per ride driven, each driver as a part-owner will also receive a share of the company's profits after loans and other expenses are paid, in the form of weighted dividends. The drivers use their own cars. The cooperative vets its owner-members further than what is already performed by the New York City Taxi and Limousine Commission (TLC), and gives a fixed price when a car is ordered and does not engage in surge pricing. The TLC imposed a minimum payrate for mobile app ridesharing companies operating in New York city in 2018. In 2021 that is $1.26 per mile which Uber and Lyft do not pay above; the cooperative pays a minimum mileage of $1.64. The cooperative intends to be able to set aside 10% of profits to community foundations and other non-profits and community organizations. The cooperative has engaged in advocacy around a policy agenda voted on by its members. Legislation to achieve this policy goal was introduced by State Senator Julia Salazar and Assemblymember Jessica González-Rojas, with the support of a coalition led by The Drivers Cooperative, United Auto Workers Region 9 and 9A, Sunrise Movement, New York Lawyers for the Public Interest, and New York Communities for Change.

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  Data (word)

  The word data is most often used as a singular collective mass noun in educated everyday usage. However, due to the history and etymology of the word, considerable controversy has existed on whether it should be considered a mass noun used with verbs conjugated in the singular, or should be treated as the plural of the now-rarely-used datum. == Usage in English == In one sense, data is the plural form of datum. Datum actually can also be a count noun with the plural datums (see usage in datum article) that can be used with cardinal numbers (e.g., "80 datums"); data (originally a Latin plural) is not used like a normal count noun with cardinal numbers and can be plural with plural determiners such as these and many, or it can be used as a mass noun with a verb in the singular form. Even when a very small quantity of data is referenced (one number, for example), the phrase piece of data is often used, as opposed to datum. The debate over appropriate usage continues, but "data" as a singular form is far more common. In English, the word datum is still used in the general sense of "an item given". In cartography, geography, nuclear magnetic resonance and technical drawing, it is often used to refer to a single specific reference datum from which distances to all other data are measured. Any measurement or result is a datum, though data point is now far more common. Data is indeed most often used as a singular mass noun in educated everyday usage. Some major newspapers, such as The New York Times, use it either in the singular or plural. In The New York Times, the phrases "the survey data are still being analyzed" and "the first year for which data is available" have appeared within one day. The Wall Street Journal explicitly allows this usage in its style guide. The Associated Press style guide classifies data as a collective noun that takes the singular when treated as a unit but the plural when referring to individual items (e.g., "The data is sound" and "The data have been carefully collected"). In scientific writing, data is often treated as a plural, as in These data do not support the conclusions, but the word is also used as a singular mass entity like information (e.g., in computing and related disciplines). British usage now widely accepts treating data as singular in standard English, including everyday newspaper usage at least in non-scientific use. UK scientific publishing still prefers treating it as a plural. Some UK university style guides recommend using data for both singular and plural use, and others recommend treating it only as a singular in connection with computers. The IEEE Computer Society allows usage of data as either a mass noun or plural based on author preference, while IEEE in the editorial style manual indicates to always use the plural form. Some professional organizations and style guides require that authors treat data as a plural noun. For example, the Air Force Flight Test Center once stated that the word data is always plural, never singular.

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  Learning augmented algorithm

  A learning augmented algorithm (also called algorithm with predictions) is an algorithm that can make use of a prediction to improve its performance. Whereas in regular algorithms just the problem instance is inputted, learning augmented algorithms accept an extra parameter. This extra parameter often is a prediction of some property of the solution. This prediction is then used by the algorithm to improve its running time or the quality of its output. The most common application are online algorithms, where a prediction on the uncertain instance is provided. == Description == A learning augmented algorithm typically takes an input ( I , A ) {\displaystyle ({\mathcal {I}},{\mathcal {A}})} . Here I {\displaystyle {\mathcal {I}}} is a problem instance and A {\displaystyle {\mathcal {A}}} is the prediction. A prediction can be any object. Common are the following types: Prediction of an optimal solution. The prediction gives a solution to the problem or characterizes an optimal solution. Prediction of the input. This is mainly used for online problems. Prediction of algorithmic actions. A prediction tailored to a specific algorithm that suggests a specific algorithm execution. Learning augmented algorithms usually satisfy the following three properties: Consistency. A learning augmented algorithm is said to be consistent if the algorithm can be proven to have a good performance when it is provided with an accurate prediction. Smoothness. A learning augmented algorithm is called smooth if its performance can be bounded by a function of the quality of the prediction. Here, the quality can be measured in a problem specific way. This is also called the prediction error. Robustness. A learning augmented algorithm is called robust if its worst-case performance can be bounded even if the given prediction is inaccurate. Learning augmented algorithms generally do not prescribe how the prediction should be done. For this purpose machine learning can be used. == Applications == A few examples of problems where learning augmented algorithms have been applied are the following. === Online algorithms === The ski rental problem The weighted paging problem The set cover problem Nonclairvoyant scheduling The online bipartite matching problem === Warm starting === ==== Data structures ==== The binary search algorithm is an algorithm for finding elements of a sorted list x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} . It needs O ( log ⁡ ( n ) ) {\displaystyle O(\log(n))} steps to find an element with some known value y {\displaystyle y} in a list of length n {\displaystyle n} . With a prediction i {\displaystyle i} for the position of y {\displaystyle y} , the following learning augmented algorithm can be used. First, look at position i {\displaystyle i} in the list. If x i = y {\displaystyle x_{i}=y} , the element has been found. If x i < y {\displaystyle x_{i} y {\displaystyle x_{i}>y} , do the same as in the previous case, but instead consider i − 1 , i − 2 , i − 4 , … {\displaystyle i-1,i-2,i-4,\ldots } . The error is defined to be η = | i − i ∗ | {\displaystyle \eta =|i-i^{}|} , where i ∗ {\displaystyle i^{}} is the real index of y {\displaystyle y} . In the learning augmented algorithm, probing the positions i + 1 , i + 2 , i + 4 , … {\displaystyle i+1,i+2,i+4,\ldots } takes log 2 ⁡ ( η ) {\displaystyle \log _{2}(\eta )} steps. Then a binary search is performed on a list of size at most 2 η {\displaystyle 2\eta } , which takes log 2 ⁡ ( η ) {\displaystyle \log _{2}(\eta )} steps. This makes the total running time of the algorithm 2 log 2 ⁡ ( η ) {\displaystyle 2\log _{2}(\eta )} . So, when the error is small, the algorithm is faster than a normal binary search. This shows that the algorithm is consistent. Even in the worst case, the error will be at most n {\displaystyle n} . Then the algorithm takes at most O ( log ⁡ ( n ) ) {\displaystyle O(\log(n))} steps, so the algorithm is robust. ==== More examples ==== The maximum weight matching problem === Approximation algorithms === The maximum cut problem The vertex cover problem === Mechanism Design === The facility location problem

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