Spotify Kids is a Swedish kid-friendly Music streaming service developed by Spotify. It offers curated content for children, including music, audiobooks, lullabies, and bedtime stories, while providing their parents with parental controls. The service is only available to subscribers to Spotify's Premium Family subscription plan. == Function == Spotify Kids is a Swedish Kid-friendly Music Streaming Service that allows children to browse Spotify with parental controls. Using the app, parents can view their children's listening history, block specific songs, and share playlists with their children. The app also includes sing-along songs, playlists designed for young children, and curated audiobooks, lullabies, and bedtime stories. Access is included in Spotify's Premium Family subscription plan, and is exclusive to subscribers to the plan. Users can configure the app for a specific age group upon first launch. The playlists on Spotify Kids are curated by groups including Discovery Kids, Nickelodeon, Universal Pictures, and The Walt Disney Company. All content on the Spotify Kids app is curated by editors. As of March 2021, there were roughly 8,000 songs available on the platform. The design of the Spotify Kids app is colorful, and user interface varies depending on the age group for which the app is configured. Spotify Kids is designed to comply with consent and data collection regulations for apps used by children. TechCrunch explains that it is "designed on a grand scale to drive subscriptions to Spotify's top-tier $14.99-per-month Premium Family Plan." == Release == After being beta tested in Ireland in October 2019, it was released as a beta across the United Kingdom on February 11, 2020. It was later released in Sweden, Denmark, Australia, New Zealand, Mexico, Argentina, and Brazil. On March 31, 2021, it was made available in France, Canada, and the United States.
Imo.im
imo.im is a proprietary audio/video calling and instant messaging software service. It allows sending music, video, PDFs and other files, along with various free stickers. It supports encrypted group video and voice calls with up to 20 participants. According to its developer, the service possesses over 200 million users and over 50 million messages per day are sent through it. == History == The product was created as a web-based application in 2005 for accessing multiple chat platforms, including Facebook Messenger, Google Talk, Yahoo! Messenger, and Skype chat. It was developed by Pagebites, which is a subsidiary of Singularity IM, Inc. and required a subscriber's phone number to verify the users' account. In March 2014, support for all third-party messaging networks ended. In January 2018, the app reached 500 million installs. imo.im has implemented end-to-end encryption for its chats and calls, ensuring that the conversations remain private between the sender and receiver.
Data room
Data rooms are secure spaces used for housing data, usually of a privileged or confidential nature. They can be physical data rooms, virtual data rooms (VDRs), or data centers. They are primarily used for a variety of corporate purposes, including data storage, document exchange, file sharing, financial transactions, and legal proceedings. Today, data rooms are central to workflows in mergers and acquisitions, venture capital, and corporate restructuring, increasingly utilizing artificial intelligence to securely manage and review large datasets. Historically, data rooms were strictly physical locations heavily guarded and monitored. Today, the vast majority of corporate data rooms are hosted virtually on secure cloud platforms, though physical rooms are still occasionally used for highly sensitive government or proprietary intelligence. == Physical Data Rooms == In mergers and acquisitions (M&A), the traditional data room genuinely consists of a physically secured and continually monitored room, normally in the vendor's offices or those of their legal counsel. Bidders and their advisers visit this room in order to inspect and report on various documents, legal contracts, and financial statements made available during the due diligence process. Historically, physical data rooms presented significant logistical challenges. Often, only one bidder at a time was allowed to enter to maintain document integrity and confidentiality. If new documents or new versions of documents were required, they had to be brought in by courier as hardcopies. Teams involved in large due diligence processes typically had to be flown in from many regions or countries and remain available throughout the process. Because these teams comprised a number of experts in different fields—such as legal counsel, forensic accountants, and industry specialists—the overall cost of keeping such groups on call near the physical data room was often extremely high. == Virtual Data Rooms (VDRs) == To address the costs and logistical bottlenecks of physical data rooms, virtual data rooms (VDRs) were developed to provide secure, online dissemination of confidential information. A VDR is essentially a secure cloud repository with strictly controlled access. Access is managed through secure log-ons supplied by the vendor or authority, which can be disabled at any time if a bidder withdraws from a transaction. Because much of the information released during corporate transactions is highly confidential, VDRs utilize digital rights management (DRM) to control information. Restrictions are applied to the viewers' ability to release data to third parties by disabling forwarding, copying, or printing capabilities. Modern VDRs also employ dynamic watermarking and detailed auditing capabilities. Detailed auditing is required for legal reasons so that a precise digital footprint is kept of who has viewed which version of each document, and for how long. Furthermore, modern VDR platforms are typically built to comply with stringent information security standards such as ISO 27001 and SOC 2. Transitioning from sequential physical data rooms to parallel virtual data rooms has been shown to significantly reduce the duration of M&A transactions while allowing sellers to field multiple bidders simultaneously. == Key Applications == Data rooms are commonly used by legal, accounting, investment banking, and private equity firms. Primary applications include: Mergers and Acquisitions (M&A): VDRs are central to the sell-side M&A process. After potential buyers sign a Non-Disclosure Agreement (NDA) and review a Confidential Information Memorandum (CIM), they are granted data room access to perform deep financial due diligence, such as Quality of Earnings (QoE) analysis and legal liability assessments. Venture Capital and Startups: Startups use data rooms as a centralized location for key operational data, capitalization tables, and financial projections to streamline due diligence for angel investors and venture capital firms during fundraising rounds. Initial Public Offerings (IPOs): Taking a company public requires intense regulatory scrutiny. Data rooms are used to securely share company histories and financial audits with investment bankers, legal teams, and regulatory bodies. Corporate Restructuring and Insolvency: During bankruptcies or corporate carve-outs, data rooms are used to organize outstanding debt profiles, creditor agreements, and operational liabilities. == Emerging Technologies == In recent years, the management of virtual data rooms has increasingly incorporated Artificial Intelligence (AI) and Machine Learning (ML). Generative AI and Natural Language Processing (NLP) tools are now integrated into VDRs to automatically index thousands of documents, perform auto-redaction of personally identifiable information (PII), and assist buy-side analysts in identifying hidden liabilities within unstructured text data during the due diligence phase. Modern AI algorithms can extract line items from financial statements to instantly populate structured databases.
Data lineage
Data lineage refers to the process of tracking how data is generated, transformed, transmitted and used across systems over time. It documents data's origins, transformations and movements, providing detailed visibility into its life cycle. This process simplifies the identification of errors in data analytics workflows, by enabling users to trace issues back to their root causes. Data lineage facilitates the ability to replay specific segments or inputs of the dataflow. This can be used in debugging or regenerating lost outputs. In database systems, this concept is closely related to data provenance, which involves maintaining records of inputs, entities, systems and processes that influence data. Data provenance provides a historical record of data origins and transformations. It supports forensic activities such as data-dependency analysis, error/compromise detection, recovery, auditing and compliance analysis: "Lineage is a simple type of why provenance." Data governance plays a critical role in managing metadata by establishing guidelines, strategies and policies. Enhancing data lineage with data quality measures and master data management adds business value. Although data lineage is typically represented through a graphical user interface (GUI), the methods for gathering and exposing metadata to this interface can vary. Based on the metadata collection approach, data lineage can be categorized into three types: Those involving software packages for structured data, programming languages and Big data systems. Data lineage information includes technical metadata about data transformations. Enriched data lineage may include additional elements such as data quality test results, reference data, data models, business terminology, data stewardship information, program management details and enterprise systems associated with data points and transformations. Data lineage visualization tools often include masking features that allow users to focus on information relevant to specific use cases. To unify representations across disparate systems, metadata normalization or standardization may be required. == Representation of data lineage == Representation broadly depends on the scope of the metadata management and reference point of interest. Data lineage provides sources of the data and intermediate data flow hops from the reference point with backward data lineage, leading to the final destination's data points and its intermediate data flows with forward data lineage. These views can be combined with end-to-end lineage for a reference point that provides a complete audit trail of that data point of interest from sources to their final destinations. As the data points or hops increase, the complexity of such representation becomes incomprehensible. Thus, the best feature of the data lineage view is the ability to simplify the view by temporarily masking unwanted peripheral data points. Tools with the masking feature enable scalability of the view and enhance analysis with the best user experience for both technical and business users. Data lineage also enables companies to trace sources of specific business data to track errors, implement changes in processes and implementing system migrations to save significant amounts of time and resources. Data lineage can improve efficiency in business intelligence BI processes. Data lineage can be represented visually to discover the data flow and movement from its source to destination via various changes and hops on its way in the enterprise environment. This includes how the data is transformed along the way, how the representation and parameters change and how the data splits or converges after each hop. A simple representation of the Data Lineage can be shown with dots and lines, where dots represent data containers for data points, and lines connecting them represent transformations the data undergoes between the data containers. Data lineage can be visualized at various levels based on the granularity of the view. At a very high-level, data lineage is visualized as systems that the data interacts with before it reaches its destination. At its most granular, visualizations at the data point level can provide the details of the data point and its historical behavior, attribute properties and trends and data quality of the data passed through that specific data point in the data lineage. The scope of the data lineage determines the volume of metadata required to represent its data lineage. Usually, data governance and data management of an organization determine the scope of the data lineage based on their regulations, enterprise data management strategy, data impact, reporting attributes and critical data elements of the organization. == Rationale == Distributed systems like Google Map Reduce, Microsoft Dryad, Apache Hadoop (an open-source project) and Google Pregel provide such platforms for businesses and users. However, even with these systems, Big Data analytics can take several hours, days or weeks to run, simply due to the data volumes involved. For example, a ratings prediction algorithm for the Netflix Prize challenge took nearly 20 hours to execute on 50 cores, and a large-scale image processing task to estimate geographic information took 3 days to complete using 400 cores. "The Large Synoptic Survey Telescope is expected to generate terabytes of data every night and eventually store more than 50 petabytes, while in the bioinformatics sector, the 12 largest genome sequencing houses in the world now store petabytes of data apiece. It is very difficult for a data scientist to trace an unknown or an unanticipated result. === Big data debugging === Big data analytics is the process of examining large data sets to uncover hidden patterns, unknown correlations, market trends, customer preferences and other useful business information. Machine learning, among other algorithms, is used to transform and analyze the data. Due to the large size of the data, there could be unknown features in the data. The massive scale and unstructured nature of data, the complexity of these analytics pipelines, and long runtimes pose significant manageability and debugging challenges. Even a single error in these analytics can be extremely difficult to identify and remove. While one may debug them by re-running the entire analytics through a debugger for stepwise debugging, this can be expensive due to the amount of time and resources needed. Auditing and data validation are other major problems due to the growing ease of access to relevant data sources for use in experiments, the sharing of data between scientific communities and use of third-party data in business enterprises. As such, more cost-efficient ways of analyzing data intensive scale-able computing (DISC) are crucial to their continued effective use. === Challenges in Big Data debugging === ==== Massive scale ==== According to an EMC/IDC study, 2.8 ZB of data were created and replicated in 2012. Furthermore, the same study states that the digital universe will double every two years between now and 2020, and that there will be approximately 5.2 TB of data for every person in 2020. Based on current technology, the storage of this much data will mean greater energy usage by data centers. ==== Unstructured data ==== Unstructured data usually refers to information that doesn't reside in a traditional row-column database. Unstructured data files often include text and multimedia content, such as e-mail messages, word processing documents, videos, photos, audio files, presentations, web pages and many other kinds of business documents. While these types of files may have an internal structure, they are still considered "unstructured" because the data they contain doesn't fit neatly into a database. The amount of unstructured data in enterprises is growing many times faster than structured databases are growing. Big data can include both structured and unstructured data, but IDC estimates that 90 percent of Big Data is unstructured data. The fundamental challenge of unstructured data sources is that they are difficult for non-technical business users and data analysts alike to unbox, understand and prepare for analytic use. Beyond issues of structure, the sheer volume of this type of data contributes to such difficulty. Because of this, current data mining techniques often leave out valuable information and make analyzing unstructured data laborious and expensive. In today's competitive business environment, companies have to find and analyze the relevant data they need quickly. The challenge is going through the volumes of data and accessing the level of detail needed, all at a high speed. The challenge only grows as the degree of granularity increases. One possible solution is hardware. Some vendors are using increased memory and parallel processing to crunch large volumes of data quickly. Another method is putting data in-memory but using a grid
Cipher device
A cipher device was a term used by the US military in the first half of the 20th century to describe a manually operated cipher equipment that converted the plaintext into ciphertext or vice versa. A similar term, cipher machine, was used to describe the cipher equipment that required external power for operation. Cipher box or crypto box is a physical cryptographic device used to encrypt and decrypt messages between plaintext (unencrypted) and ciphertext (encrypted or secret) forms. The ciphertext is suitable for transmission over a channel, such as radio, that might be observed by an adversary the communicating parties wish to conceal the plaintext from.
LaMDA
LaMDA (Language Model for Dialogue Applications) is a family of conversational large language models developed by Google. Originally developed and introduced as Meena in 2020, the first-generation LaMDA was announced during the 2021 Google I/O keynote, while the second generation was announced the following year. In June 2022, LaMDA gained widespread attention when Google engineer Blake Lemoine made claims that the chatbot had become sentient. The scientific community has largely rejected Lemoine's claims, though it has led to conversations about the efficacy of the Turing test, which measures whether a computer can pass for a human. In February 2023, Google announced Gemini (then Bard), a conversational artificial intelligence chatbot powered by LaMDA, to counter the rise of OpenAI's ChatGPT. == History == === Background === On January 28, 2020, Google unveiled Meena, a neural network-powered chatbot with 2.6 billion parameters, which Google claimed to be superior to all other existing chatbots. The company previously hired computer scientist Ray Kurzweil in 2012 to develop multiple chatbots for the company, including one named Danielle. The Google Brain research team, who developed Meena, hoped to release the chatbot to the public in a limited capacity, but corporate executives refused on the grounds that Meena violated Google's "AI principles around safety and fairness". Meena was later renamed LaMDA as its data and computing power increased, and the Google Brain team again sought to deploy the software to the Google Assistant, the company's virtual assistant software, in addition to opening it up to a public demo. Both requests were once again denied by company leadership. LaMDA's two lead researchers, Daniel de Freitas and Noam Shazeer, eventually left the company in frustration. === First generation === Google announced the LaMDA conversational large language model during the Google I/O keynote on May 18, 2021, powered by artificial intelligence. The acronym stands for "Language Model for Dialogue Applications". Built on the seq2seq architecture, transformer-based neural networks developed by Google Research in 2017, LaMDA was trained on human dialogue and stories, allowing it to engage in open-ended conversations. Google states that responses generated by LaMDA have been ensured to be "sensible, interesting, and specific to the context". LaMDA has access to multiple symbolic text processing systems, including a database, a real-time clock and calendar, a mathematical calculator, and a natural language translation system, giving it superior accuracy in tasks supported by those systems, and making it among the first dual process chatbots. LaMDA is also not stateless because its "sensibleness" metric is fine-tuned by "pre-conditioning" each dialog turn by prepending many of the most recent dialog interactions, on a user-by-user basis. LaMDA is tuned on nine unique performance metrics: sensibleness, specificity, interestingness, safety, groundedness, informativeness, citation accuracy, helpfulness, and role consistency. Tests by Google indicated that LaMDA surpassed human responses in the area of interestingness. The pre-training dataset consists of 2.97B documents, 1.12B dialogs, and 13.39B utterances, for a total of 1.56T words. The largest LaMDA model has 137B non-embedding parameters. === Second generation === On May 11, 2022, Google unveiled LaMDA 2, the successor to LaMDA, during the 2022 Google I/O keynote. The new incarnation of the model draws examples of text from numerous sources, using it to formulate unique "natural conversations" on topics that it may not have been trained to respond to. === Sentience claims === On June 11, 2022, The Washington Post reported that Google engineer Blake Lemoine had been placed on paid administrative leave after Lemoine told company executives Blaise Agüera y Arcas and Jen Gennai that LaMDA had become sentient. Lemoine came to this conclusion after the chatbot made questionable responses to questions regarding self-identity, moral values, religion, and Isaac Asimov's Three Laws of Robotics. Google refuted these claims, insisting that there was substantial evidence to indicate that LaMDA was not sentient. In an interview with Wired, Lemoine reiterated his claims that LaMDA was "a person" as dictated by the Thirteenth Amendment to the U.S. Constitution, comparing it to an "alien intelligence of terrestrial origin". He further revealed that he had been dismissed by Google after he hired an attorney on LaMDA's behalf after the chatbot requested that Lemoine do so. On July 22, Google fired Lemoine, asserting that Blake had violated their policies "to safeguard product information" and rejected his claims as "wholly unfounded". Internal controversy instigated by the incident prompted Google executives to decide against releasing LaMDA to the public, which it had previously been considering. Lemoine's claims were widely pushed back by the scientific community. Many experts rejected the idea that LaMDA was sentient, including former New York University psychology professor Gary Marcus, David Pfau of Google sister company DeepMind, Erik Brynjolfsson of the Institute for Human-Centered Artificial Intelligence at Stanford University, and University of Surrey professor Adrian Hilton. Yann LeCun, who leads Meta Platforms' AI research team, stated that neural networks such as LaMDA were "not powerful enough to attain true intelligence". University of California, Santa Cruz professor Max Kreminski noted that LaMDA's architecture did not "support some key capabilities of human-like consciousness" and that its neural network weights were "frozen", assuming it was a typical large language model. Philosopher Nick Bostrom noted, however, that the lack of precise and consensual criteria for determining whether a system is conscious warrants some uncertainty. IBM Watson lead developer David Ferrucci compared how LaMDA appeared to be human in the same way Watson did when it was first introduced. Former Google AI ethicist Timnit Gebru called Lemoine a victim of a "hype cycle" initiated by researchers and the media. Lemoine's claims have also generated discussion on whether the Turing test remained useful to determine researchers' progress toward achieving artificial general intelligence, with Will Omerus of the Post opining that the test actually measured whether machine intelligence systems were capable of deceiving humans, while Brian Christian of The Atlantic said that the controversy was an instance of the ELIZA effect. == Products == === AI Test Kitchen === With the unveiling of LaMDA 2 in May 2022, Google also launched the AI Test Kitchen, a mobile application for the Android operating system powered by LaMDA capable of providing lists of suggestions on-demand based on a complex goal. Originally open only to Google employees, the app was set to be made available to "select academics, researchers, and policymakers" by invitation sometime in the year. In August, the company began allowing users in the U.S. to sign up for early access. In November, Google released a "season 2" update to the app, integrating a limited form of Google Brain's Imagen text-to-image model. A third iteration of the AI Test Kitchen was in development by January 2023, expected to launch at I/O later that year. Following the 2023 I/O keynote in May, Google added MusicLM, an AI-powered music generator first previewed in January, to the AI Test Kitchen app. In August, the app was delisted from Google Play and the Apple App Store, instead moving completely online. === Bard === On February 6, 2023, Google announced Bard, a conversational AI chatbot powered by LaMDA, in response to the unexpected popularity of OpenAI's ChatGPT chatbot. Google positions the chatbot as a "collaborative AI service" rather than a search engine. Bard became available for early access on March 21. === Other products === In addition to Bard, Pichai also unveiled the company's Generative Language API, an application programming interface also based on LaMDA, which he announced would be opened up to third-party developers in March 2023. == Architecture == LaMDA is a decoder-only Transformer language model. It is pre-trained on a text corpus that includes both documents and dialogs consisting of 1.56 trillion words, and is then trained with fine-tuning data generated by manually annotated responses for "sensibleness, interestingness, and safety". LaMDA was retrieval-augmented to improve the accuracy of facts provided to the user. Three different models were tested, with the largest having 137 billion non-embedding parameters:
Data validation and reconciliation
Industrial process data validation and reconciliation, or more briefly, process data reconciliation (PDR), is a technology that uses process information and mathematical methods in order to automatically ensure data validation and reconciliation by correcting measurements in industrial processes. The use of PDR allows for extracting accurate and reliable information about the state of industry processes from raw measurement data and produces a single consistent set of data representing the most likely process operation. == Models, data and measurement errors == Industrial processes, for example chemical or thermodynamic processes in chemical plants, refineries, oil or gas production sites, or power plants, are often represented by two fundamental means: Models that express the general structure of the processes, Data that reflects the state of the processes at a given point in time. Models can have different levels of detail, for example one can incorporate simple mass or compound conservation balances, or more advanced thermodynamic models including energy conservation laws. Mathematically the model can be expressed by a nonlinear system of equations F ( y ) = 0 {\displaystyle F(y)=0\,} in the variables y = ( y 1 , … , y n ) {\displaystyle y=(y_{1},\ldots ,y_{n})} , which incorporates all the above-mentioned system constraints (for example the mass or heat balances around a unit). A variable could be the temperature or the pressure at a certain place in the plant. === Error types === Data originates typically from measurements taken at different places throughout the industrial site, for example temperature, pressure, volumetric flow rate measurements etc. To understand the basic principles of PDR, it is important to first recognize that plant measurements are never 100% correct, i.e. raw measurement y {\displaystyle y\,} is not a solution of the nonlinear system F ( y ) = 0 {\displaystyle F(y)=0\,\!} . When using measurements without correction to generate plant balances, it is common to have incoherencies. Measurement errors can be categorized into two basic types: random errors due to intrinsic sensor accuracy and systematic errors (or gross errors) due to sensor calibration or faulty data transmission. Random errors means that the measurement y {\displaystyle y\,\!} is a random variable with mean y ∗ {\displaystyle y^{}\,\!} , where y ∗ {\displaystyle y^{}\,\!} is the true value that is typically not known. A systematic error on the other hand is characterized by a measurement y {\displaystyle y\,\!} which is a random variable with mean y ¯ {\displaystyle {\bar {y}}\,\!} , which is not equal to the true value y ∗ {\displaystyle y^{}\,} . For ease in deriving and implementing an optimal estimation solution, and based on arguments that errors are the sum of many factors (so that the Central limit theorem has some effect), data reconciliation assumes these errors are normally distributed. Other sources of errors when calculating plant balances include process faults such as leaks, unmodeled heat losses, incorrect physical properties or other physical parameters used in equations, and incorrect structure such as unmodeled bypass lines. Other errors include unmodeled plant dynamics such as holdup changes, and other instabilities in plant operations that violate steady state (algebraic) models. Additional dynamic errors arise when measurements and samples are not taken at the same time, especially lab analyses. The normal practice of using time averages for the data input partly reduces the dynamic problems. However, that does not completely resolve timing inconsistencies for infrequently-sampled data like lab analyses. This use of average values, like a moving average, acts as a low-pass filter, so high frequency noise is mostly eliminated. The result is that, in practice, data reconciliation is mainly making adjustments to correct systematic errors like biases. === Necessity of removing measurement errors === ISA-95 is the international standard for the integration of enterprise and control systems It asserts that: Data reconciliation is a serious issue for enterprise-control integration. The data have to be valid to be useful for the enterprise system. The data must often be determined from physical measurements that have associated error factors. This must usually be converted into exact values for the enterprise system. This conversion may require manual, or intelligent reconciliation of the converted values [...]. Systems must be set up to ensure that accurate data are sent to production and from production. Inadvertent operator or clerical errors may result in too much production, too little production, the wrong production, incorrect inventory, or missing inventory. == History == PDR has become more and more important due to industrial processes that are becoming more and more complex. PDR started in the early 1960s with applications aiming at closing material balances in production processes where raw measurements were available for all variables. At the same time the problem of gross error identification and elimination has been presented. In the late 1960s and 1970s unmeasured variables were taken into account in the data reconciliation process., PDR also became more mature by considering general nonlinear equation systems coming from thermodynamic models., , Quasi steady state dynamics for filtering and simultaneous parameter estimation over time were introduced in 1977 by Stanley and Mah. Dynamic PDR was formulated as a nonlinear optimization problem by Liebman et al. in 1992. == Data reconciliation == Data reconciliation is a technique that targets at correcting measurement errors that are due to measurement noise, i.e. random errors. From a statistical point of view the main assumption is that no systematic errors exist in the set of measurements, since they may bias the reconciliation results and reduce the robustness of the reconciliation. Given n {\displaystyle n} measurements y i {\displaystyle y_{i}} , data reconciliation can mathematically be expressed as an optimization problem of the following form: min x , y ∗ ∑ i = 1 n ( y i ∗ − y i σ i ) 2 subject to F ( x , y ∗ ) = 0 y min ≤ y ∗ ≤ y max x min ≤ x ≤ x max , {\displaystyle {\begin{aligned}\min _{x,y^{}}&\sum _{i=1}^{n}\left({\frac {y_{i}^{}-y_{i}}{\sigma _{i}}}\right)^{2}\\{\text{subject to }}&F(x,y^{})=0\\&y_{\min }\leq y^{}\leq y_{\max }\\&x_{\min }\leq x\leq x_{\max },\end{aligned}}\,\!} where y i ∗ {\displaystyle y_{i}^{}\,\!} is the reconciled value of the i {\displaystyle i} -th measurement ( i = 1 , … , n {\displaystyle i=1,\ldots ,n\,\!} ), y i {\displaystyle y_{i}\,\!} is the measured value of the i {\displaystyle i} -th measurement ( i = 1 , … , n {\displaystyle i=1,\ldots ,n\,\!} ), x j {\displaystyle x_{j}\,\!} is the j {\displaystyle j} -th unmeasured variable ( j = 1 , … , m {\displaystyle j=1,\ldots ,m\,\!} ), and σ i {\displaystyle \sigma _{i}\,\!} is the standard deviation of the i {\displaystyle i} -th measurement ( i = 1 , … , n {\displaystyle i=1,\ldots ,n\,\!} ), F ( x , y ∗ ) = 0 {\displaystyle F(x,y^{})=0\,\!} are the p {\displaystyle p\,\!} process equality constraints and x min , x max , y min , y max {\displaystyle x_{\min },x_{\max },y_{\min },y_{\max }\,\!} are the bounds on the measured and unmeasured variables. The term ( y i ∗ − y i σ i ) 2 {\displaystyle \left({\frac {y_{i}^{}-y_{i}}{\sigma _{i}}}\right)^{2}\,\!} is called the penalty of measurement i. The objective function is the sum of the penalties, which will be denoted in the following by f ( y ∗ ) = ∑ i = 1 n ( y i ∗ − y i σ i ) 2 {\displaystyle f(y^{})=\sum _{i=1}^{n}\left({\frac {y_{i}^{}-y_{i}}{\sigma _{i}}}\right)^{2}} . In other words, one wants to minimize the overall correction (measured in the least squares term) that is needed in order to satisfy the system constraints. Additionally, each least squares term is weighted by the standard deviation of the corresponding measurement. The standard deviation is related to the accuracy of the measurement. For example, at a 95% confidence level, the standard deviation is about half the accuracy. === Redundancy === Data reconciliation relies strongly on the concept of redundancy to correct the measurements as little as possible in order to satisfy the process constraints. Here, redundancy is defined differently from redundancy in information theory. Instead, redundancy arises from combining sensor data with the model (algebraic constraints), sometimes more specifically called "spatial redundancy", "analytical redundancy", or "topological redundancy". Redundancy can be due to sensor redundancy, where sensors are duplicated in order to have more than one measurement of the same quantity. Redundancy also arises when a single variable can be estimated in several independent ways from separate sets of measurements at a given time or time averaging period, using the algebraic constraints. Redundancy is linked to the concept