Image destriping is the process of removing stripes or streaks from images and videos without disrupting the original image/video. These artifacts plague a range of fields in scientific imaging including atomic force microscopy, light sheet fluorescence microscopy, and planetary satellite imaging. The most common image processing techniques to reduce stripe artifacts is with Fourier filtering. Unfortunately, filtering methods risk altering or suppressing useful image data. Methods developed for multiple-sensor imaging systems in planetary satellites use statistical-based methods to match signal distribution across multiple sensors. More recently, a new class of approaches leverage compressed sensing, to regularize an optimization problem, and recover stripe free images. In many cases, these destriped images have little to no artifacts, even at low signal to noise ratios.
Mark V. Shaney
Mark V. Shaney is a synthetic Usenet user whose postings in the net.singles newsgroups were generated by Markov chain techniques, based on text from other postings. The username is a play on the words "Markov chain". Many readers were fooled into thinking that the quirky, sometimes uncannily topical posts were written by a real person. The system was designed by Rob Pike with coding by Bruce Ellis. Don P. Mitchell wrote the Markov chain code, initially demonstrating it to Pike and Ellis using the Tao Te Ching as a basis. They chose to apply it to the net.singles netnews group. The program is fairly simple. It ingests the sample text (the Tao Te Ching, or the posts of a Usenet group) and creates a massive list of every sequence of three successive words (triplet) which occurs in the text. It then chooses two words at random, and looks for a word which follows those two in one of the triplets in its massive list. If there is more than one, it picks at random (identical triplets count separately, so a sequence which occurs twice is twice as likely to be picked as one which only occurs once). It then adds that word to the generated text. Then, in the same way, it picks a triplet that starts with the second and third words in the generated text, and that gives a fourth word. It adds the fourth word, then repeats with the third and fourth words, and so on. This algorithm is called a third-order Markov chain (because it uses sequences of three words). == Examples == A classic example, from 1984, originally sent as a mail message, later posted to net.singles is reproduced here: >From mvs Fri Nov 16 17:11 EST 1984 remote from alice It looks like Reagan is going to say? Ummm... Oh yes, I was looking for. I'm so glad I remembered it. Yeah, what I have wondered if I had committed a crime. Don't eat with your assessment of Reagon and Mondale. Up your nose with a guy from a firm that specifically researches the teen-age market. As a friend of mine would say, "It really doesn't matter"... It looks like Reagan is holding back the arms of the American eating public have changed dramatically, and it got pretty boring after about 300 games. People, having a much larger number of varieties, and are very different from what one can find in Chinatowns across the country (things like pork buns, steamed dumplings, etc.) They can be cheap, being sold for around 30 to 75 cents apiece (depending on size), are generally not greasy, can be adequately explained by stupidity. Singles have felt insecure since we came down from the Conservative world at large. But Chuqui is the way it happened and the prices are VERY reasonable. Can anyone think of myself as a third sex. Yes, I am expected to have. People often get used to me knowing these things and then a cover is placed over all of them. Along the side of the $$ are spent by (or at least for ) the girls. You can't settle the issue. It seems I've forgotten what it is, but I don't. I know about violence against women, and I really doubt they will ever join together into a large number of jokes. It showed Adam, just after being created. He has a modem and an autodial routine. He calls my number 1440 times a day. So I will conclude by saying that I can well understand that she might soon have the time, it makes sense, again, to get the gist of my argument, I was in that (though it's a Republican administration). _-_-_-_-Mark Other quotations from Mark's Usenet posts are: "I spent an interesting evening recently with a grain of salt." (Alternatively reported as "While at a conference a few weeks back, I spent an interesting evening with a grain of salt.") "I hope that there are sour apples in every bushel." (see also sour grapes) == History == In The Usenet Handbook Mark Harrison writes that after September 1981, students joined Usenet en masse, "creating the USENET we know today: endless dumb questions, endless idiots posing as savants, and (of course) endless victims for practical jokes." In December, Rob Pike created the netnews group net.suicide as prank, "a forum for bad jokes". Some users thought it was a legitimate forum, some discussed "riding motorcycles without helmets". At first, most posters were "real people", but soon "characters" began posting. Pike created a "vicious" character named Bimmler. At its peak, net.suicide had ten frequent posters; nine were "known to be characters." But ultimately, Pike deleted the newsgroup because it was too much work to maintain; Bimmler messages were created "by hand". The "obvious alternative" was software, running on a Bell Labs computer created by Bruce Ellis, based on the Markov code by Don Mitchell, which became the online character Mark V. Shaney. Kernighan and Pike listed Mark V. Shaney in the acknowledgements in The Practice of Programming, noting its roots in Mitchell's markov, which, adapted as shaney, was used for "humorous deconstructionist activities" in the 1980s. Dewdney pointed out "perhaps Mark V. Shaney's magnum opus: a 20-page commentary on the deconstructionist philosophy of Jean Baudrillard" directed by Pike, with assistance from Henry S. Baird and Catherine Richards, to be distributed by email. The piece was based on Jean Baudrillard's "The Precession of Simulacra", published in Simulacra and Simulation (1981). == Reception == The program was discussed by A. K. Dewdney in the Scientific American "Computer Recreations" column in 1989, by Penn Jillette in his PC Computing column in 1991, and in several books, including the Usenet Handbook, Bots: the Origin of New Species, Hippo Eats Dwarf: A Field Guide to Hoaxes and Other B.S., and non-computer-related journals such as Texas Studies in Literature and Language. Dewdney wrote about the program's output, "The overall impression is not unlike what remains in the brain of an inattentive student after a late-night study session. Indeed, after reading the output of Mark V. Shaney, I find ordinary writing almost equally strange and incomprehensible!" He noted the reactions of newsgroup users, who have "shuddered at Mark V. Shaney's reflections, some with rage and others with laughter:" The opinions of the new net.singles correspondent drew mixed reviews. Serious users of the bulletin board's services sensed satire. Outraged, they urged that someone "pull the plug" on Mark V. Shaney's monstrous rantings. Others inquired almost admiringly whether the program was a secret artificial intelligence project that was being tested in a human conversational environment. A few may even have thought that Mark V. Shaney was a real person, a tortured schizophrenic desperately seeking a like-minded companion. Concluding, Dewdney wrote, "If the purpose of computer prose is to fool people into thinking that it was written by a sane person, Mark V. Shaney probably falls short." A 2012 article in Observer compared Mark V. Shaney's "strangely beautiful" postings to the Horse_ebooks account on Twitter and music reviews at Pitchfork, saying that "this mash-up of gibberish and human sentiment" is what "made Mark V. Shaney so endlessly fascinating".
Master data management
Master data management (MDM) is a discipline in which business and information technology collaborate to ensure the uniformity, accuracy, stewardship, semantic consistency, and accountability of the enterprise's official shared master data assets. == Reasons for master data management == Data consistency and accuracy: MDM ensures that the organization's critical data is consistent and accurate across all systems, reducing discrepancies and errors caused by multiple, siloed copies of the same data. Improved decision-making: By providing a single version of the truth (SVOT), MDM enables organizations to deliver the right data to decision makers, allowing them to clearly understand business performance and make informed, data-driven decisions. Operational efficiency: With the consistent and accurate data provided by an MDM, operational processes such as reporting and inventory management can be automated to improve efficiency. Employee learning, onboarding, and customer service also become more efficient, as MDM data facilitates rapid, accurate, and thorough information retrieval, permitting more employee time to be spent on work. Regulatory compliance: MDM tries to help organizations comply with industry standards and regulations by ensuring that master data is accurately recorded, maintained, and audited. However, issues with data quality, classification, and reconciliation may require data transformation. As with other Extract, Transform, Load-based data movements, these processes are expensive and inefficient, reducing return on investment for a project. == Business unit and product line segmentation == As a result of business unit and product line segmentation, the same entity (whether a customer, supplier, or product) will be included in different product lines. This leads to data redundancy and even confusion. For example, a customer takes out a mortgage at a bank. If the marketing and customer service departments have separate databases, advertisements might still be sent to the customer, even though they've already signed up. The two parts of the bank are unaware, and the customer is sent irrelevant communications. Record linkage can associate different records corresponding to the same entity, mitigating this issue. == Mergers and acquisitions == One of the most common problems for master data management is company growth through mergers or acquisitions. Reconciling these separate master data systems can present difficulties, as existing applications have dependencies on the master databases. Ideally, database administrators resolve this problem through deduplication of the master data as part of the merger. Over time, as further mergers and acquisitions occur, the problem can multiply. Data reconciliation processes can become extremely complex or even unreliable. Some organizations end up with 10, 15, or even 100 separate and poorly integrated master databases. This can cause serious problems in customer satisfaction, operational efficiency, decision support, and regulatory compliance. Another problem involves determining the proper degrees of detail and normalization to include in the master data schema. For example, in a federated Human Resources environment, the enterprise software may focus on storing people's data as current status, adding a few fields to identify the date of hire, date of last promotion, etc. However, this simplification can introduce business-impacting errors into dependent systems for planning and forecasting. The stakeholders of such systems may be forced to build a parallel network of new interfaces to track the onboarding of new hires, planned retirements, and divestment, which works against one of the aims of master data management. == People, processes and technology == Master data management is enabled by technology, but is more than the technologies that enable it. An organization's master data management capability will also include people and processes in its definition. === People === Several roles should be staffed within MDM. Most prominently, the Data Owner and the Data Steward. Several people would likely be allocated to each role and each person responsible for a subset of Master Data (e.g. one data owner for employee master data, another for customer master data). The Data Owner is responsible for the requirements for data definition, data quality, data security, etc. as well as for compliance with data governance and data management procedures. The Data Owner should also be funding improvement projects in case of deviations from the requirements. The Data Steward is running the master data management on behalf of the data owner and probably also being an advisor to the Data Owner. === Processes === Master data management can be viewed as a "discipline for specialized quality improvement" defined by the policies and procedures put in place by a data governance organization. It has the objective of providing processes for collecting, aggregating, matching, consolidating, quality-assuring, persisting and distributing master data throughout an organization to ensure a common understanding, consistency, accuracy and control, in the ongoing maintenance and application use of that data. Processes commonly seen in master data management include source identification, data collection, data transformation, normalization, rule administration, error detection and correction, data consolidation, data storage, data distribution, data classification, taxonomy services, item master creation, schema mapping, product codification, data enrichment, hierarchy management, business semantics management and data governance. === Technology === A master data management tool can be used to support master data management by removing duplicates, standardizing data (mass maintaining), and incorporating rules to eliminate incorrect data from entering the system to create an authoritative source of master data. Master data are the products, accounts, and parties for which the business transactions are completed. Where the technology approach produces a "golden record" or relies on a "source of record" or "system of record", it is common to talk of where the data is "mastered". This is accepted terminology in the information technology industry, but care should be taken, both with specialists and with the wider stakeholder community, to avoid confusing the concept of "master data" with that of "mastering data". ==== Implementation models ==== There are several models for implementing a technology solution for master data management. These depend on an organization's core business, its corporate structure, and its goals. These include: Source of record Registry Consolidation Coexistence Transaction/centralized ===== Source of record ===== This model identifies a single application, database, or simpler source (e.g. a spreadsheet) as being the "source of record" (or "system of record" where solely application databases are relied on). The benefit of this model is its conceptual simplicity, but it may not fit with the realities of complex master data distribution in large organizations. The source of record can be federated, for example by groups of attributes (so that different attributes of a master data entity may have different sources of record) or geographically (so that different parts of an organization may have different master sources). Federation is only applicable in certain use cases, where there is a clear delineation of which subsets of records will be found in which sources. The source of record model can be applied more widely than simply to master data, for example to reference data. ==== Transmission of master data ==== There are several ways in which master data may be collated and distributed to other systems. This includes: Data consolidation – The process of capturing master data from multiple sources and integrating it into a single hub (operational data store) for replication to other destination systems. Data federation – The process of providing a single virtual view of master data from one or more sources to one or more destination systems. Data propagation – The process of copying master data from one system to another, typically through point-to-point interfaces in legacy systems. == Change management in implementation == Challenges in adopting master data management within large organizations often arise when stakeholders disagree on a "single version of the truth" concept is not affirmed by stakeholders, who believe that their local definition of the master data is necessary. For example, the product hierarchy used to manage inventory may be entirely different from the product hierarchies used to support marketing efforts or pay sales representatives. It is above all necessary to identify if different master data is genuinely required. If it is required, then the solution implemented (technology and process) must be able to allow multiple versions of the truth to exist but will prov
Query language
A query language, also known as data query language or database query language (DQL), is a computer language used to make queries in databases and information systems. In database systems, query languages rely on strict theory to retrieve information. A well known example is the Structured Query Language (SQL). == Types == Broadly, query languages can be classified according to whether they are database query languages or information retrieval query languages. The difference is that a database query language attempts to give factual answers to factual questions, while an information retrieval query language attempts to find documents containing information that is relevant to an area of inquiry. Other types of query languages include: Full-text. The simplest query language is treating all terms as bag of words that are to be matched with the postings in the inverted index and where subsequently ranking models are applied to retrieve the most relevant documents. Only tokens are defined in the CFG. Web search engines often use this approach. Boolean. A query language that also supports the use of the Boolean operators AND, OR, NOT. Structured. A language that supports searching within (a combination of) fields when a document is structured and has been indexed using its document structure. Natural language. A query language that supports natural language by parsing the natural language query to a form that can be best used to retrieve relevant documents, for example with Question answering systems or conversational search. == Examples == Attempto Controlled English is a query language that is also a controlled natural language. AQL is a query language for the ArangoDB native multi-model database system. .QL is a proprietary object-oriented query language for querying relational databases; successor of Datalog. CodeQL is the analysis engine used by developers to automate security checks, and by security researchers to perform variant analysis on GitHub. Contextual Query Language (CQL) a formal language for representing queries to information retrieval systems such as web indexes or bibliographic catalogues. Cypher is a query language for the Neo4j graph database. DMX is a query language for data mining models. Datalog is a query language for deductive databases. F-logic is a declarative object-oriented language for deductive databases and knowledge representation. FQL enables you to use a SQL-style interface to query the data exposed by the Graph API. It provides advanced features not available in the Graph API. Gellish English is a language that can be used for queries in Gellish English Databases, for dialogues (requests and responses) as well as for information modeling and knowledge modeling. Gremlin is an Apache Software Foundation graph traversal language for OLTP and OLAP graph systems. GraphQL is a data query language developed by Facebook as an alternate to REST and ad-hoc webservice architectures. HTSQL is a query language that translates HTTP queries to SQL. ISBL is a query language for PRTV, one of the earliest relational database management systems. Jaql is a functional data processing and query language most commonly used for JSON query processing. JPQL is a query language defined as part of Jakarta Persistence (used in Java applications to make queries to a relational DB using entity objects instead of DB tables). jq is a functional programming language often used for processing queries against one or more JSON documents, including very large ones. JSONiq is a declarative query language designed for collections of JSON documents. KQL (Kusto Query Language), a query language by Microsoft used in Azure Data Explorer LDAP is an application protocol for querying and modifying directory services running over TCP/IP. LogiQL is a variant of Datalog and is the query language for the LogicBlox system. M Formula language, a mashup query language used in Microsoft's Power Query. MQL is a cheminformatics query language for a substructure search allowing beside nominal properties also numerical properties. MDX is a query language for OLAP databases. N1QL is a Couchbase's query language finding data in Couchbase Servers. Object Query Language OCL (Object Constraint Language). Despite its name, OCL is also an object query language and an OMG standard. OPath, intended for use in querying WinFS Stores. Poliqarp Query Language is a special query language designed to analyze annotated text. Used in the Poliqarp search engine. PQL is a special-purpose programming language for managing process models based on information about scenarios that these models describe. PRQL PRQL (Pipelined Relational Query Language) is a modern language for transforming data. Consists of a curated set of orthogonal transformations, which are combined together to form a pipeline. PTQL based on relational queries over program traces, allowing programmers to write expressive, declarative queries about program behavior. QUEL is a relational database access language, similar in most ways to SQL. RDQL is a RDF query language. SMARTS is the cheminformatics standard for a substructure search. SPARQL is a query language for RDF graphs. SQL is a well-known query language and data manipulation language for relational databases. XQuery is a query language for XML data sources. XPath is a declarative language for navigating XML documents. YQL is an SQL-like query language created by Yahoo!. Search engine query languages, e.g., as used by Google. or Bing
Education by algorithm
Education by algorithm refers to automated solutions that algorithmic agents or social bots offer to education, to assist with mundane educational tasks. These are often instrumentalist “educational reforms” or “curriculum transformations”, which have been implemented by policy makers and are supported by proprietary education technologies. New educational policies, mandated by transnational governance forums (like the OECD), have manufactured a connection between economies and education. Governments, schools and universities are expected to introduce or prepare students for an “unknown future”, to “future proof” them against an identified issue or to mitigate a national crisis. Technologies are seen as a catalyst to effect these changes. However, these policies mask a deeper problem, which include the assetization of education and the use of technologies as a means for surveillance and behavior modification. The traces that students and leave, through cookies, logins learning activities, assignments and tests, are collected, facetted, and shared with commercial organizations by these agents, to both predict future behavior and shape it. Techno solutionist thinking has led to managers adopting educational policies and reforms, and looking towards technologies to act as disrupters, liberators or agents to improve efficiency. During the COVID-19 pandemic, many more students had to modify their learning and working circumstances to protect themselves. Academics shifted their assessment practices from the dominant assessment of learning paradigm to an orientation that saw value in "assessment for learning". Big tech assisted, and teaching infrastructure became further privatized, and unbundling of education provision went a step further. Following the return to class, this assessment paradigm became rationalised in education. Leaving the space for algorithmic agents to step in. Academics work was increasingly driven by learning experience platforms and student understanding was extended through interleaving, behavior modification nudges and rewards and scheduled high stakes assessments. This data collection may also be construed as surveillance., or perceived as evidence of a Fourth Industrial Revolution
WeChat or Weixin in Chinese (Chinese: 微信; pinyin: Wēixìn ; lit. 'micro-message') is an instant messaging, social media, and mobile payment app developed by Tencent. First released in 2011, it became the world's largest standalone mobile app in 2018 with over 1 billion monthly active users. The Chinese version of WeChat, Weixin, has been described as China's "app for everything" and a super-app because of its wide range of functions. WeChat provides text messaging, hold-to-talk voice messaging, broadcast (one-to-many) messaging, video conferencing, video games, mobile payment, sharing of photographs and videos and location sharing. It has been described as having "an almost indispensable part of life in China". Accounts registered using Chinese phone numbers are managed under the Weixin brand, and their data is stored in mainland China and subject to Weixin's terms of service and privacy policy. Non-Chinese numbers are registered under WeChat, and WeChat users are subject to a more liberal terms of service and better privacy policy, and their data is stored in the Netherlands for users in the European Union, and in Singapore for other users. User activity on Weixin, the Chinese version of the app, is analyzed, tracked and shared with Chinese authorities upon request as part of the mass surveillance network in China. Chinese-registered Weixin accounts censor politically sensitive topics, and the software license agreement for Weixin (but not WeChat) explicitly forbids content which "[en]danger[s] national security, divulge[s] state secrets, subvert[s] state power and undermine[s] national unity", as well as other types of content such as content that "[u]ndermine[s] national religious policies" and content that is "[i]nciting illegal assembly, association, procession, demonstrations and gatherings disrupting the social order". Due to its central part of Chinese life, a Chinese person having their WeChat account banned can cause a significant disruption to their life. Any interactions between Weixin and WeChat users are subject to the terms of service and privacy policies of both services. == History == By 2010, Tencent had already attained a massive user base with their desktop messenger app QQ. Recognizing smart phones were likely to disrupt this status quo, CEO Pony Ma sought to proactively invest in alternatives to their own QQ messenger app. WeChat began as a project at Tencent Guangzhou Research and Project center in October 2010. The original version of the app was created by Allen Zhang, named "Weixin" (微信) by Pony Ma, and launched in 2011. The user adoption of WeChat was initially very slow, with users wondering why key features were missing; however, after the release of the Walkie-talkie-like voice messaging feature in May of that year, growth surged. By 2012, when the number of users reached 100 million, Weixin was re-branded "WeChat" by President Martin Lau for the international market. During a period of government support of e-commerce development—for example in the 12th five-year plan (2011–2015)—WeChat also saw new features enabling payments and commerce in 2013, which saw massive adoption after their virtual Red envelope promotion for Chinese New Year 2014. WeChat had over 889 million monthly active users by 2016, and as of 2019 WeChat's monthly active users had risen to an estimate of one billion. As of January 2022, it was reported that WeChat has more than 1.2 billion users. After the launch of WeChat payment in 2013, its users reached 400 million the next year, 90 percent of whom were in China. By comparison, Facebook Messenger and WhatsApp had about one billion monthly active users in 2016 but did not offer most of the other services available on WeChat. For example, in Q2 2017, WeChat's revenues from social media advertising were about US$0.9 billion (RMB6 billion) compared with Facebook's total revenues of US$9.3 billion, 98% of which were from social media advertising. WeChat's revenues from its value-added services were US$5.5 billion. By 2018, WeChat had been used by 93.5% of Chinese internet users. In that year, it became the world's largest standalone mobile app in 2018 with over 1 billion monthly active users. In response to a border dispute between India and China, WeChat was banned in India in June 2020 along with several other Chinese apps, including TikTok. U.S. president Donald Trump sought to ban U.S. "transactions" with WeChat through an executive order but was blocked by a preliminary injunction issued in the United States District Court for the Northern District of California in September 2020. Joe Biden officially dropped Trump's efforts to ban WeChat in the U.S. in June 2021. == Features == WeChat, has been described as China's "app for everything" and a super-app because of its wide range of functions. WeChat provides text messaging, hold-to-talk voice messaging, broadcast (one-to-many) messaging, video conferencing, video games, mobile payment, sharing of photographs and videos and location sharing. It has been described as having "an almost indispensable part of life in China". Due to its central part of Chinese life, a Chinese person having their WeChat account banned can cause a significant disruption to their life. === Messaging === WeChat provides a variety of features including text messaging, hold-to-talk voice messaging, broadcast (one-to-many) messaging, video calls and conferencing, video games, photograph and video sharing, as well as location sharing. WeChat also allows users to exchange contacts with people nearby via Bluetooth, as well as providing various features for contacting people at random if desired (if people are open to it). It can also integrate with other social networking services such as Facebook and Tencent QQ. Photographs may also be embellished with filters and captions, and automatic translation service is available and could also translate the conversation during messaging. WeChat supports different instant messaging methods, including text messages, voice messages, walkie talkie, and stickers. Users can send previously saved or live pictures and videos, profiles of other users, coupons, lucky money packages, or current GPS locations with friends either individually or in a group chat. WeChat also provides a message recall feature to allow users to recall and withdraw information (e.g. images, documents) that are sent within 2 minutes in a conversation. WeChat also provides a voice-to-text feature that brings convenience when it is not convenient to listen to voice messages, as well as the basic ability to recognize emojis based on different tones of voice. A distance sensing feature is implemented in WeChat. It has the ability to activate the receivers' hold-to-talk function when the phone was brought in close proximity to the ear. After the receiver was held at a certain distance from the ear, the sensor would then proceed to automatically disable the phone speakers. This feature eliminates the risk of the user's voice messages being inadvertently broadcast to the general public. === Public accounts === WeChat users can register as a public account (公众号), which enables them to push feeds to subscribers, interact with subscribers, and provide subscribers with services. Users can also create an official account, which fall under service, subscription, or enterprise accounts. Once users as individuals or organizations set up a type of account, they cannot change it to another type. By the end of 2014, the number of WeChat official accounts had reached 8 million. Official accounts of organizations can apply to be verified (cost 300 RMB or about US$45). Official accounts can be used as a platform for services such as hospital pre-registrations, or credit card service. To create an official account, the applicant must register with Chinese authorities, which discourages "foreign companies". In April 2022, WeChat announced that it will start displaying the location of users in China every time they post on a public account. Meanwhile, overseas users on public accounts will also display the country based on their IP address. === Moments === "Moments" (朋友圈) is WeChat's brand name for its social feed of friends' updates. "Moments" is an interactive platform that allows users to post images, text, and short videos taken by users. It also allows users to share articles and music (associated with QQ Music or other web-based music services). Friends in the contact list can like the content and leave comments, functioning similarly to a private social network. In 2017 WeChat had a policy of a maximum of two advertisements per day per Moments user. Privacy in WeChat works by groups of friends: only the friends from the user's contact are able to view their Moments' contents and comments. The friends of the user will only be able to see the likes and comments from other users only if they are in a mutual friend group. For example, friends from high school are not able to
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).