How Data Happened: A History from the Age of Reason to the Age of Algorithms is a 2023 non-fiction book written by Columbia University professors Chris Wiggins and Matthew L. Jones. The book explores the history of data and statistics from the end of the 18th century to the present day. == Content == The book starts at the end of the 18th century, when European states began tabulating physical resources, and ends at the present day, when algorithms manipulate our personal information as a commodity. It looks at the rise of data and statistics, and how early statistical methods were used to justify eugenics, quantify supposed racial differences, and develop military and industrial applications. The authors also discuss the impact of the internet and e-commerce on data collection, the rise of data science, and the consequences of government-run surveillance systems collecting vast amounts of personal data for customized, targeted advertising. They emphasize the importance of privacy and democracy and propose remedies to the problems caused by mass data collection, including stronger regulation of the tech industry and collective action by its employees. The book is a historical analysis that provides context for understanding the debates surrounding data and its control. The book has 336 pages and was published in 2023 by W. W. Norton & Company.
Tiimo
Tiimo is an app designed to help neurodivergent individuals with planning their life. In August 2024 the company raised €1.4 million, bringing their total funding to €4.3 million. At that point they had over 500,000 users, including 50,000 paid users. The app has Apple Watch support and a learning platform that includes courses on well-being and neurodiversity. The app was founded by Helene Lassen Nørlem and Melissa Würtz Azari in 2015. After being a finalist in 2024, in December 2025 Tiimo was won Apple’s iPhone App of the Year. The premium version is $10/mo and features an AI chatbot alongside the daily planner.
Umbrella review
In medical research, an umbrella review is a review of systematic reviews or meta-analyses. They may also be called overviews of reviews, reviews of reviews, summaries of systematic reviews, or syntheses of reviews. Umbrella reviews are among the highest levels of evidence currently available in medicine. By summarizing information from multiple overview articles, umbrella reviews make it easier to review the evidence and allow for comparison of results between each of the individual reviews. Umbrella reviews may address a broader question than a typical review, such as discussing multiple different treatment comparisons instead of only one. They are especially useful for developing guidelines and clinical practice, and when comparing competing interventions.
Single-source publishing
Single-source publishing, also known as single-sourcing publishing, is a content management method which allows the same source content to be used across different forms of media and more than one time. The labor-intensive and expensive work of editing need only be carried out once, on only one document; that source document (the single source of truth) can then be stored in one place and reused. This reduces the potential for error, as corrections are only made one time in the source document. The benefits of single-source publishing primarily relate to the editor rather than the user. The user benefits from the consistency that single-sourcing brings to terminology and information. This assumes the content manager has applied an organized conceptualization to the underlying content (A poor conceptualization can make single-source publishing less useful). Single-source publishing is sometimes used synonymously with multi-channel publishing though whether or not the two terms are synonymous is a matter of discussion. == Definition == While there is a general definition of single-source publishing, there is no single official delineation between single-source publishing and multi-channel publishing, nor are there any official governing bodies to provide such a delineation. Single-source publishing is most often understood as the creation of one source document in an authoring tool and converting that document into different file formats or human languages (or both) multiple times with minimal effort. Multi-channel publishing can either be seen as synonymous with single-source publishing, or similar in that there is one source document but the process itself results in more than a mere reproduction of that source. == History == The origins of single-source publishing lie, indirectly, with the release of Windows 3.0 in 1990. With the eclipsing of MS-DOS by graphical user interfaces, help files went from being unreadable text along the bottom of the screen to hypertext systems such as WinHelp. On-screen help interfaces allowed software companies to cease the printing of large, expensive help manuals with their products, reducing costs for both producer and consumer. This system raised opportunities as well, and many developers fundamentally changed the way they thought about publishing. Writers of software documentation did not simply move from being writers of traditional bound books to writers of electronic publishing, but rather they became authors of central documents which could be reused multiple times across multiple formats. The first single-source publishing project was started in 1993 by Cornelia Hofmann at Schneider Electric in Seligenstadt, using software based on Interleaf to automatically create paper documentation in multiple languages based on a single original source file. XML, developed during the mid- to late-1990s, was also significant to the development of single-source publishing as a method. XML, a markup language, allows developers to separate their documentation into two layers: a shell-like layer based on presentation and a core-like layer based on the actual written content. This method allows developers to write the content only one time while switching it in and out of multiple different formats and delivery methods. In the mid-1990s, several firms began creating and using single-source content for technical documentation (Boeing Helicopter, Sikorsky Aviation and Pratt & Whitney Canada) and user manuals (Ford owners manuals) based on tagged SGML and XML content generated using the Arbortext Epic editor with add-on functions developed by a contractor. The concept behind this usage was that complex, hierarchical content that did not lend itself to discrete componentization could be used across a variety of requirements by tagging the differences within a single document using the capabilities built into SGML and XML. Ford, for example, was able to tag its single owner's manual files so that 12 model years could be generated via a resolution script running on the single completed file. Pratt & Whitney, likewise, was able to tag up to 20 subsets of its jet engine manuals in single-source files, calling out the desired version at publication time. World Book Encyclopedia also used the concept to tag its articles for American and British versions of English. Starting from the early 2000s, single-source publishing was used with an increasing frequency in the field of technical translation. It is still regarded as the most efficient method of publishing the same material in different languages. Once a printed manual was translated, for example, the online help for the software program which the manual accompanies could be automatically generated using the method. Metadata could be created for an entire manual and individual pages or files could then be translated from that metadata with only one step, removing the need to recreate information or even database structures. Although single-source publishing is now decades old, its importance has increased urgently as of the 2010s. As consumption of information products rises and the number of target audiences expands, so does the work of developers and content creators. Within the industry of software and its documentation, there is a perception that the choice is to embrace single-source publishing or render one's operations obsolete. == Criticism == Editors using single-source publishing have been criticized for below-standard work quality, leading some critics to describe single-source publishing as the "conveyor belt assembly" of content creation. While heavily used in technical translation, there are risks of error in regard to indexing. While two words might be synonyms in English, they may not be synonyms in another language. In a document produced via single-sourcing, the index will be translated automatically and the two words will be rendered as synonyms. This is because they are synonyms in the source language, while in the target language they are not.
Tuple
In mathematics, a tuple is a finite sequence (or ordered list) of numbers. More generally, it is a sequence of mathematical objects, called the elements of the tuple. An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term "infinite tuple" is occasionally used for "infinite sequences". Tuples are usually written by listing the elements within parentheses "( )" and separated by commas; for example, (2, 7, 4, 1, 7) denotes a 5-tuple. Other types of brackets are sometimes used, although they may have a different meaning. An n-tuple can be formally defined as the image of a function that has the set of the first n natural numbers as its domain (1, 2, ..., n). Tuples may be also defined from ordered pairs by a recurrence starting from an ordered pair; indeed, an n-tuple can be identified with the ordered pair of its (n − 1) first elements and its nth element, for example, ( ( ( 1 , 2 ) , 3 ) , 4 ) = ( 1 , 2 , 3 , 4 ) {\displaystyle \left(\left(\left(1,2\right),3\right),4\right)=\left(1,2,3,4\right)} . In computer science, tuples come in many forms. Most typed functional programming languages implement tuples directly as product types, tightly associated with algebraic data types, pattern matching, and destructuring assignment. Many programming languages offer an alternative to tuples, known as record types, featuring unordered elements accessed by label. A few programming languages combine ordered tuple product types and unordered record types into a single construct, as in C structs and Haskell records. Relational databases may formally identify their rows (records) as tuples. Tuples also occur in relational algebra; when programming the semantic web with the Resource Description Framework (RDF); in linguistics; and in philosophy. == Etymology == The term originated as an abstraction of the sequence: single, couple/double, triple, quadruple, quintuple, sextuple, septuple, octuple, ..., n‑tuple, ..., where the prefixes are taken from the Latin names of the numerals. The unique 0-tuple is called the null tuple or empty tuple. A 1‑tuple is called a single (or singleton), a 2‑tuple is called an ordered pair or couple, and a 3‑tuple is called a triple (or triplet). The number n can be any nonnegative integer. For example, a complex number can be represented as a 2‑tuple of reals, a quaternion can be represented as a 4‑tuple, an octonion can be represented as an 8‑tuple, and a sedenion can be represented as a 16‑tuple. Although these uses treat ‑tuple as the suffix, the original suffix was ‑ple as in "triple" (three-fold) or "decuple" (ten‑fold). This originates from medieval Latin plus (meaning "more") related to Greek ‑πλοῦς, which replaced the classical and late antique ‑plex (meaning "folded"), as in "duplex". == Properties == The general rule for the identity of two n-tuples is ( a 1 , a 2 , … , a n ) = ( b 1 , b 2 , … , b n ) {\displaystyle (a_{1},a_{2},\ldots ,a_{n})=(b_{1},b_{2},\ldots ,b_{n})} if and only if a 1 = b 1 , a 2 = b 2 , … , a n = b n {\displaystyle a_{1}=b_{1},{\text{ }}a_{2}=b_{2},{\text{ }}\ldots ,{\text{ }}a_{n}=b_{n}} . Thus a tuple has properties that distinguish it from a set: A tuple may contain multiple instances of the same element, so tuple ( 1 , 2 , 2 , 3 ) ≠ ( 1 , 2 , 3 ) {\displaystyle (1,2,2,3)\neq (1,2,3)} ; but set { 1 , 2 , 2 , 3 } = { 1 , 2 , 3 } {\displaystyle \{1,2,2,3\}=\{1,2,3\}} . Tuple elements are ordered: tuple ( 1 , 2 , 3 ) ≠ ( 3 , 2 , 1 ) {\displaystyle (1,2,3)\neq (3,2,1)} , but set { 1 , 2 , 3 } = { 3 , 2 , 1 } {\displaystyle \{1,2,3\}=\{3,2,1\}} . A tuple has a finite number of elements, while a set or a multiset may have an infinite number of elements. == Definitions == There are several definitions of tuples that give them the properties described in the previous section. === Tuples as functions === The 0 {\displaystyle 0} -tuple may be identified as the empty function. For n ≥ 1 , {\displaystyle n\geq 1,} the n {\displaystyle n} -tuple ( a 1 , … , a n ) {\displaystyle \left(a_{1},\ldots ,a_{n}\right)} may be identified with the surjective function F : { 1 , … , n } → { a 1 , … , a n } {\displaystyle F~:~\left\{1,\ldots ,n\right\}~\to ~\left\{a_{1},\ldots ,a_{n}\right\}} with domain domain F = { 1 , … , n } = { i ∈ N : 1 ≤ i ≤ n } {\displaystyle \operatorname {domain} F=\left\{1,\ldots ,n\right\}=\left\{i\in \mathbb {N} :1\leq i\leq n\right\}} and with codomain codomain F = { a 1 , … , a n } , {\displaystyle \operatorname {codomain} F=\left\{a_{1},\ldots ,a_{n}\right\},} that is defined at i ∈ domain F = { 1 , … , n } {\displaystyle i\in \operatorname {domain} F=\left\{1,\ldots ,n\right\}} by F ( i ) := a i . {\displaystyle F(i):=a_{i}.} That is, F {\displaystyle F} is the function defined by 1 ↦ a 1 ⋮ n ↦ a n {\displaystyle {\begin{alignedat}{3}1\;&\mapsto &&\;a_{1}\\\;&\;\;\vdots &&\;\\n\;&\mapsto &&\;a_{n}\\\end{alignedat}}} in which case the equality ( a 1 , a 2 , … , a n ) = ( F ( 1 ) , F ( 2 ) , … , F ( n ) ) {\displaystyle \left(a_{1},a_{2},\dots ,a_{n}\right)=\left(F(1),F(2),\dots ,F(n)\right)} necessarily holds. Tuples as sets of ordered pairs Functions are commonly identified with their graphs, which is a certain set of ordered pairs. Indeed, many authors use graphs as the definition of a function. Using this definition of "function", the above function F {\displaystyle F} can be defined as: F := { ( 1 , a 1 ) , … , ( n , a n ) } . {\displaystyle F~:=~\left\{\left(1,a_{1}\right),\ldots ,\left(n,a_{n}\right)\right\}.} === Tuples as nested ordered pairs === Another way of modeling tuples in set theory is as nested ordered pairs. This approach assumes that the notion of ordered pair has already been defined. The 0-tuple (i.e. the empty tuple) is represented by the empty set ∅ {\displaystyle \emptyset } . An n-tuple, with n > 0, can be defined as an ordered pair of its first entry and an (n − 1)-tuple (which contains the remaining entries when n > 1): ( a 1 , a 2 , a 3 , … , a n ) = ( a 1 , ( a 2 , a 3 , … , a n ) ) {\displaystyle (a_{1},a_{2},a_{3},\ldots ,a_{n})=(a_{1},(a_{2},a_{3},\ldots ,a_{n}))} This definition can be applied recursively to the (n − 1)-tuple: ( a 1 , a 2 , a 3 , … , a n ) = ( a 1 , ( a 2 , ( a 3 , ( … , ( a n , ∅ ) … ) ) ) ) {\displaystyle (a_{1},a_{2},a_{3},\ldots ,a_{n})=(a_{1},(a_{2},(a_{3},(\ldots ,(a_{n},\emptyset )\ldots ))))} Thus, for example: ( 1 , 2 , 3 ) = ( 1 , ( 2 , ( 3 , ∅ ) ) ) ( 1 , 2 , 3 , 4 ) = ( 1 , ( 2 , ( 3 , ( 4 , ∅ ) ) ) ) {\displaystyle {\begin{aligned}(1,2,3)&=(1,(2,(3,\emptyset )))\\(1,2,3,4)&=(1,(2,(3,(4,\emptyset ))))\\\end{aligned}}} A variant of this definition starts "peeling off" elements from the other end: The 0-tuple is the empty set ∅ {\displaystyle \emptyset } . For n > 0: ( a 1 , a 2 , a 3 , … , a n ) = ( ( a 1 , a 2 , a 3 , … , a n − 1 ) , a n ) {\displaystyle (a_{1},a_{2},a_{3},\ldots ,a_{n})=((a_{1},a_{2},a_{3},\ldots ,a_{n-1}),a_{n})} This definition can be applied recursively: ( a 1 , a 2 , a 3 , … , a n ) = ( ( … ( ( ( ∅ , a 1 ) , a 2 ) , a 3 ) , … ) , a n ) {\displaystyle (a_{1},a_{2},a_{3},\ldots ,a_{n})=((\ldots (((\emptyset ,a_{1}),a_{2}),a_{3}),\ldots ),a_{n})} Thus, for example: ( 1 , 2 , 3 ) = ( ( ( ∅ , 1 ) , 2 ) , 3 ) ( 1 , 2 , 3 , 4 ) = ( ( ( ( ∅ , 1 ) , 2 ) , 3 ) , 4 ) {\displaystyle {\begin{aligned}(1,2,3)&=(((\emptyset ,1),2),3)\\(1,2,3,4)&=((((\emptyset ,1),2),3),4)\\\end{aligned}}} === Tuples as nested sets === Using Kuratowski's representation for an ordered pair, the second definition above can be reformulated in terms of pure set theory: The 0-tuple (i.e. the empty tuple) is represented by the empty set ∅ {\displaystyle \emptyset } ; Let x {\displaystyle x} be an n-tuple ( a 1 , a 2 , … , a n ) {\displaystyle (a_{1},a_{2},\ldots ,a_{n})} , and let x → b ≡ ( a 1 , a 2 , … , a n , b ) {\displaystyle x\rightarrow b\equiv (a_{1},a_{2},\ldots ,a_{n},b)} . Then, x → b ≡ { { x } , { x , b } } {\displaystyle x\rightarrow b\equiv \{\{x\},\{x,b\}\}} . (The right arrow, → {\displaystyle \rightarrow } , could be read as "adjoined with".) In this formulation: ( ) = ∅ ( 1 ) = ( ) → 1 = { { ( ) } , { ( ) , 1 } } = { { ∅ } , { ∅ , 1 } } ( 1 , 2 ) = ( 1 ) → 2 = { { ( 1 ) } , { ( 1 ) , 2 } } = { { { { ∅ } , { ∅ , 1 } } } , { { { ∅ } , { ∅ , 1 } } , 2 } } ( 1 , 2 , 3 ) = ( 1 , 2 ) → 3 = { { ( 1 , 2 ) } , { ( 1 , 2 ) , 3 } } = { { { { { { ∅ } , { ∅ , 1 } } } , { { { ∅ } , { ∅ , 1 } } , 2 } } } , { { { { { ∅ } , { ∅ , 1 } } } , { { { ∅ } , { ∅ , 1 } } , 2 } } , 3 } } {\displaystyle {\begin{array}{lclcl}()&&&=&\emptyset \\&&&&\\(1)&=&()\rightarrow 1&=&\{\{()\},\{(),1\}\}\\&&&=&\{\{\emptyset \},\{\emptyset ,1\}\}\\&&&&\\(1,2)&=&(1)\rightarrow 2&=&\{\{(1)\},\{(1),2\}\}\\&&&=&\{\{\{\{\emptyset \},\{\emptyset ,1\}\}\},\\&&&&\{\{\{\emptyset \},\{\emptyset ,1\}\},2\}\}\\&&&&\\(1,2,3)&=&(1,2)\rightarrow 3&=&\{\{(1,2)\},\{(1,2),3\}\}\\&&&=&\{\{\{\{\{\{\empty
Self-supervised learning
Self-supervised learning (SSL) is a paradigm in machine learning where a model is trained on a task using the data itself to generate supervisory signals, rather than relying on externally-provided labels. In the context of neural networks, self-supervised learning aims to leverage inherent structures or relationships within the input data to create meaningful training signals. SSL tasks are designed so that solving them requires capturing essential features or relationships in the data. The input data is typically augmented or transformed in a way that creates pairs of related samples, where one sample serves as the input, and the other is used to formulate the supervisory signal. This augmentation can involve introducing noise, cropping, rotation, or other transformations. Self-supervised learning more closely imitates the way humans learn to classify objects. During SSL, the model learns in two steps. First, the task is solved based on an auxiliary or pretext classification task using pseudo-labels, which help to initialize the model parameters. Next, the actual task is performed with supervised or unsupervised learning. Self-supervised learning has produced promising results in recent years, and has found practical application in fields such as audio processing, and is being used by Facebook and others for speech recognition. == Pseudo-labels == Pseudo-labels are automatically generated labels that a model assigns to unlabeled data based on its own predictions. They are widely used in self-supervised and semi-supervised learning, where ground-truth annotations are limited or unavailable. By treating predicted labels as surrogate ground truth, learning algorithms can make use of large quantities of unlabeled data in the training process. Pseudo-labeling also plays an important role in systems that must adapt to concept drift, where the statistical properties of the data change over time. In these scenarios, the model may detect that an incoming instance deviates from previously learned behavior. The system then generates a classification result for that instance, and this predicted class is used as a pseudo-label for updating or retraining model components that are becoming outdated. This approach enables continuous adaptation in dynamic environments without requiring manual annotation. In many adaptive learning pipelines, pseudo-labels are chosen when the classifier produces sufficiently confident predictions, reducing the risk of propagating errors. These pseudo-labeled instances are then incorporated into training to refresh or evolve the model's understanding of emerging data patterns, particularly when existing components show signs of “aging” due to drift or distributional shifts. This strategy reduces reliance on manual labeling while helping maintain long-term model performance. == Types == === Autoassociative self-supervised learning === Autoassociative self-supervised learning is a specific category of self-supervised learning where a neural network is trained to reproduce or reconstruct its own input data. In other words, the model is tasked with learning a representation of the data that captures its essential features or structure, allowing it to regenerate the original input. The term "autoassociative" comes from the fact that the model is essentially associating the input data with itself. This is often achieved using autoencoders, which are a type of neural network architecture used for representation learning. Autoencoders consist of an encoder network that maps the input data to a lower-dimensional representation (latent space), and a decoder network that reconstructs the input from this representation. The training process involves presenting the model with input data and requiring it to reconstruct the same data as closely as possible. The loss function used during training typically penalizes the difference between the original input and the reconstructed output (e.g. mean squared error). By minimizing this reconstruction error, the autoencoder learns a meaningful representation of the data in its latent space. === Contrastive self-supervised learning === For a binary classification task, training data can be divided into positive examples and negative examples. Positive examples are those that match the target. For example, if training a classifier to identify birds, the positive training data would include images that contain birds. Negative examples would be images that do not. Contrastive self-supervised learning uses both positive and negative examples. The loss function in contrastive learning is used to minimize the distance between positive sample pairs, while maximizing the distance between negative sample pairs. An early example uses a pair of 1-dimensional convolutional neural networks to process a pair of images and maximize their agreement. Contrastive Language-Image Pre-training (CLIP) allows joint pretraining of a text encoder and an image encoder, such that a matching image-text pair have image encoding vector and text encoding vector that span a small angle (having a large cosine similarity). InfoNCE (Noise-Contrastive Estimation) is a method to optimize two models jointly, based on Noise Contrastive Estimation (NCE). Given a set X = { x 1 , … x N } {\displaystyle X=\left\{x_{1},\ldots x_{N}\right\}} of N {\displaystyle N} random samples containing one positive sample from p ( x t + k ∣ c t ) {\displaystyle p\left(x_{t+k}\mid c_{t}\right)} and N − 1 {\displaystyle N-1} negative samples from the 'proposal' distribution p ( x t + k ) {\displaystyle p\left(x_{t+k}\right)} , it minimizes the following loss function: L N = − E X [ log f k ( x t + k , c t ) ∑ x j ∈ X f k ( x j , c t ) ] {\displaystyle {\mathcal {L}}_{\mathrm {N} }=-\mathbb {E} _{X}\left[\log {\frac {f_{k}\left(x_{t+k},c_{t}\right)}{\sum _{x_{j}\in X}f_{k}\left(x_{j},c_{t}\right)}}\right]} === Non-contrastive self-supervised learning === Non-contrastive self-supervised learning (NCSSL) uses only positive examples. Counterintuitively, NCSSL converges on a useful local minimum rather than reaching a trivial solution, with zero loss. For the example of binary classification, it would trivially learn to classify each example as positive. Effective NCSSL requires an extra predictor on the online side that does not back-propagate on the target side. === Joint-Embedding and Predictive Architectures === A major class of self-supervised learning moves beyond contrastive pairs, instead maximizing the agreement between views while preventing collapse through statistical constraints. Rooted in Deep Canonical Correlation Analysis (Deep CCA), this approach includes Joint-Embedding Architectures (JEA) like Barlow Twins and VICReg, which enforce covariance constraints to learn invariant representations without negative sampling. Deep Latent Variable Path Modelling (DLVPM) generalizes this to multimodal systems, using path models to enforce correlation and orthogonality across diverse data types. In 2022 Yann LeCun introduced Joint-Embedding Predictive Architectures (JEPA) as a step towards decision making, reasoning, and autonomous human intelligence in machines, including self-improvement through autonomous learning. Founded in representation learning, LeCun included the concept of a “world model” in JEPA which aims to enable machines to replicate human intellect by providing machines with a concept for the world in which they exist. Unlike autoencoders, JEPAs operate entirely in latent space, avoiding pixel-level noise to focus on semantic structure. Rather than just learning invariance, JEPAs learn by predicting masked latent representations from visible context. JEPA has been applied to domains such as image analysis, audio processing, and motion in images and video. == Comparison with other forms of machine learning == SSL belongs to supervised learning methods insofar as the goal is to generate a classified output from the input. At the same time, however, it does not require the explicit use of labeled input-output pairs. Instead, correlations, metadata embedded in the data, or domain knowledge present in the input are implicitly and autonomously extracted from the data. These supervisory signals, extracted from the data, can then be used for training. SSL is similar to unsupervised learning in that it does not require labels in the sample data. Unlike unsupervised learning, however, learning is not done using inherent data structures. Semi-supervised learning combines supervised and unsupervised learning, requiring only a small portion of the learning data be labeled. In transfer learning, a model designed for one task is reused on a different task. Training an autoencoder intrinsically constitutes a self-supervised process, because the output pattern needs to become an optimal reconstruction of the input pattern itself. However, in current jargon, the term 'self-supervised' often refers to tasks based on a pretext-task training setup
Reverse data management
Reverse data management describes a branch and set of research questions in relational database theory that aim to reverse the common focus of standard data management. Instead of focusing on the "forward" transformation of an input databases (a set of relational tables) to an output table, which is the main focus of standard query evaluation, reverse data management reverses that focus and studies the possible input database transformations that would achieve a desired output. Usually the objective is to find an intervention (a deletion, addition, or change of tuples) of minimal size, in order to achieve a particular change in the output. The problem has been studied at least since the 1980s, but has received renewed attention due to an influential paper in the early 2000s that made a connection between provenance and view propagation. The term was coined in a VLDB 2011 vision paper. The problem has been receiving significant attention in recent years due to its connection to computational fairness. == Topics in reverse data management problems == Example topics in reverse data management include: Deletion propagation with source side-effects: Find a minimal number of tuples to delete in the database in order to delete a particular tuple in the output. Deletion propagation with view side-effects: Find a set of tuples to delete in the database in order to delete a particular tuple in the output, while removing the minimal number of other output tuples. Causal responsibility: Find a minimal number of tuples to delete in the database in order to make a particular input tuple counterfactual. This notion is inspired by the notions of actual cause and causal responsibility from the work of Halpern and Pearl. Resilience: Find a minimal number of tuples to delete in the database in order to make a Boolean query false. The complexity of this problem is identical to the problem of deletion propagation with source-side effects over a different database. Smallest witness problem: Find a minimal number of tuples to keep in the a database (or equivalently, delete a maximal number of tuples) while keeping a particular tuple in the output. Minimum repair: Given a database that violates certain integrity constraints, find a minimal number of tuples to delete in the database in order to fulfill all constraints (also called to "repair" the database).