Sparse principal component analysis (SPCA or sparse PCA) is a technique used in statistical analysis and, in particular, in the analysis of multivariate data sets. It extends the classic method of principal component analysis (PCA) for the reduction of dimensionality of data by introducing sparsity structures to the input variables. A particular disadvantage of ordinary PCA is that the principal components are usually linear combinations of all input variables. SPCA overcomes this disadvantage by finding components that are linear combinations of just a few input variables (SPCs). This means that some of the coefficients of the linear combinations defining the SPCs, called loadings, are equal to zero. The number of nonzero loadings is called the cardinality of the SPC. == Mathematical formulation == Consider a data matrix, X {\displaystyle X} , where each of the p {\displaystyle p} columns represent an input variable, and each of the n {\displaystyle n} rows represents an independent sample from data population. One assumes each column of X {\displaystyle X} has mean zero, otherwise one can subtract column-wise mean from each element of X {\displaystyle X} . Let Σ = 1 n − 1 X ⊤ X {\displaystyle \Sigma ={\frac {1}{n-1}}X^{\top }X} be the empirical covariance matrix of X {\displaystyle X} , which has dimension p × p {\displaystyle p\times p} . Given an integer k {\displaystyle k} with 1 ≤ k ≤ p {\displaystyle 1\leq k\leq p} , the sparse PCA problem can be formulated as maximizing the variance along a direction represented by vector v ∈ R p {\displaystyle v\in \mathbb {R} ^{p}} while constraining its cardinality: max v T Σ v subject to ‖ v ‖ 2 = 1 ‖ v ‖ 0 ≤ k . {\displaystyle {\begin{aligned}\max \quad &v^{T}\Sigma v\\{\text{subject to}}\quad &\left\Vert v\right\Vert _{2}=1\\&\left\Vert v\right\Vert _{0}\leq k.\end{aligned}}} Eq. 1 The first constraint specifies that v is a unit vector. In the second constraint, ‖ v ‖ 0 {\displaystyle \left\Vert v\right\Vert _{0}} represents the ℓ 0 {\displaystyle \ell _{0}} pseudo-norm of v, which is defined as the number of its non-zero components. So the second constraint specifies that the number of non-zero components in v is less than or equal to k, which is typically an integer that is much smaller than dimension p. The optimal value of Eq. 1 is known as the k-sparse largest eigenvalue. If one takes k=p, the problem reduces to the ordinary PCA, and the optimal value becomes the largest eigenvalue of covariance matrix Σ. After finding the optimal solution v, one deflates Σ to obtain a new matrix Σ 1 = Σ − ( v T Σ v ) v v T , {\displaystyle \Sigma _{1}=\Sigma -(v^{T}\Sigma v)vv^{T},} and iterate this process to obtain further principal components. However, unlike PCA, sparse PCA cannot guarantee that different principal components are orthogonal. In order to achieve orthogonality, additional constraints must be enforced. The following equivalent definition is in matrix form. Let V {\displaystyle V} be a p×p symmetric matrix, one can rewrite the sparse PCA problem as max T r ( Σ V ) subject to T r ( V ) = 1 ‖ V ‖ 0 ≤ k 2 R a n k ( V ) = 1 , V ⪰ 0. {\displaystyle {\begin{aligned}\max \quad &Tr(\Sigma V)\\{\text{subject to}}\quad &Tr(V)=1\\&\Vert V\Vert _{0}\leq k^{2}\\&Rank(V)=1,V\succeq 0.\end{aligned}}} Eq. 2 Tr is the matrix trace, and ‖ V ‖ 0 {\displaystyle \Vert V\Vert _{0}} represents the non-zero elements in matrix V. The last line specifies that V has matrix rank one and is positive semidefinite. The last line means that one has V = v v T {\displaystyle V=vv^{T}} , so Eq. 2 is equivalent to Eq. 1. Moreover, the rank constraint in this formulation is actually redundant, and therefore sparse PCA can be cast as the following mixed-integer semidefinite program max T r ( Σ V ) subject to T r ( V ) = 1 | V i , i | ≤ z i , ∀ i ∈ { 1 , . . . , p } , | V i , j | ≤ 1 2 z i , ∀ i , j ∈ { 1 , . . . , p } : i ≠ j , V ⪰ 0 , z ∈ { 0 , 1 } p , ∑ i z i ≤ k {\displaystyle {\begin{aligned}\max \quad &Tr(\Sigma V)\\{\text{subject to}}\quad &Tr(V)=1\\&\vert V_{i,i}\vert \leq z_{i},\forall i\in \{1,...,p\},\vert V_{i,j}\vert \leq {\frac {1}{2}}z_{i},\forall i,j\in \{1,...,p\}:i\neq j,\\&V\succeq 0,z\in \{0,1\}^{p},\sum _{i}z_{i}\leq k\end{aligned}}} Eq. 3 Because of the cardinality constraint, the maximization problem is hard to solve exactly, especially when dimension p is high. In fact, the sparse PCA problem in Eq. 1 is NP-hard in the strong sense. == Computational considerations == As most sparse problems, variable selection in SPCA is a computationally intractable non-convex NP-hard problem, therefore greedy sub-optimal algorithms are often employed to find solutions. Note also that SPCA introduces hyperparameters quantifying in what capacity large parameter values are penalized. These might need tuning to achieve satisfactory performance, thereby adding to the total computational cost. == Algorithms for SPCA == Several alternative approaches (of Eq. 1) have been proposed, including a regression framework, a penalized matrix decomposition framework, a convex relaxation/semidefinite programming framework, a generalized power method framework an alternating maximization framework forward-backward greedy search and exact methods using branch-and-bound techniques, a certifiably optimal branch-and-bound approach Bayesian formulation framework. A certifiably optimal mixed-integer semidefinite branch-and-cut approach The methodological and theoretical developments of Sparse PCA as well as its applications in scientific studies are recently reviewed in a survey paper. === Notes on Semidefinite Programming Relaxation === It has been proposed that sparse PCA can be approximated by semidefinite programming (SDP). If one drops the rank constraint and relaxes the cardinality constraint by a 1-norm convex constraint, one gets a semidefinite programming relaxation, which can be solved efficiently in polynomial time: max T r ( Σ V ) subject to T r ( V ) = 1 1 T | V | 1 ≤ k V ⪰ 0. {\displaystyle {\begin{aligned}\max \quad &Tr(\Sigma V)\\{\text{subject to}}\quad &Tr(V)=1\\&\mathbf {1} ^{T}|V|\mathbf {1} \leq k\\&V\succeq 0.\end{aligned}}} Eq. 3 In the second constraint, 1 {\displaystyle \mathbf {1} } is a p×1 vector of ones, and |V| is the matrix whose elements are the absolute values of the elements of V. The optimal solution V {\displaystyle V} to the relaxed problem Eq. 3 is not guaranteed to have rank one. In that case, V {\displaystyle V} can be truncated to retain only the dominant eigenvector. While the semidefinite program does not scale beyond n=300 covariates, it has been shown that a second-order cone relaxation of the semidefinite relaxation is almost as tight and successfully solves problems with n=1000s of covariates == Applications == === Financial Data Analysis === Suppose ordinary PCA is applied to a dataset where each input variable represents a different asset, it may generate principal components that are weighted combination of all the assets. In contrast, sparse PCA would produce principal components that are weighted combination of only a few input assets, so one can easily interpret its meaning. Furthermore, if one uses a trading strategy based on these principal components, fewer assets imply less transaction costs. === Biology === Consider a dataset where each input variable corresponds to a specific gene. Sparse PCA can produce a principal component that involves only a few genes, so researchers can focus on these specific genes for further analysis. === High-dimensional Hypothesis Testing === Contemporary datasets often have the number of input variables ( p {\displaystyle p} ) comparable with or even much larger than the number of samples ( n {\displaystyle n} ). It has been shown that if p / n {\displaystyle p/n} does not converge to zero, the classical PCA is not consistent. In other words, if we let k = p {\displaystyle k=p} in Eq. 1, then the optimal value does not converge to the largest eigenvalue of data population when the sample size n → ∞ {\displaystyle n\rightarrow \infty } , and the optimal solution does not converge to the direction of maximum variance. But sparse PCA can retain consistency even if p ≫ n . {\displaystyle p\gg n.} The k-sparse largest eigenvalue (the optimal value of Eq. 1) can be used to discriminate an isometric model, where every direction has the same variance, from a spiked covariance model in high-dimensional setting. Consider a hypothesis test where the null hypothesis specifies that data X {\displaystyle X} are generated from a multivariate normal distribution with mean 0 and covariance equal to an identity matrix, and the alternative hypothesis specifies that data X {\displaystyle X} is generated from a spiked model with signal strength θ {\displaystyle \theta } : H 0 : X ∼ N ( 0 , I p ) , H 1 : X ∼ N ( 0 , I p + θ v v T ) , {\displaystyle H_{0}:X\sim N(0,I_{p}),\quad H_{1}:X\sim N(0,I_{p}+\theta vv^{T}),} where v ∈ R p {\displaystyle v\in \mathbb {R} ^{p}
Cozi
Cozi is a family organization website and mobile app designed to streamline household management. It offers shared calendars, to-do lists, shopping lists, and messaging tools, allowing multiple users to coordinate under one account. Founded in 2005 by former Microsoft employees, Cozi has evolved through acquisitions and now operates under OurFamilyWizard. The app is available in both free and premium versions on iOS, Android, and desktop platforms. == History == Cozi was founded in 2005 by Robbie Cape and Jan Miksovsky, two former Microsoft employees who sought to simplify family logistics with technology. The company's first product, Cozi Central, was released on September 25, 2006, and included a family calendar, shopping lists, family messaging and a photo collage screensaver. The company is based in Seattle, Washington. Cozi has both a freemium version, and a paid version called Cozi Gold. Cozi Gold's additional features include Cozi Contacts, a birthday tracker, more reminders, mobile month view, and change notifications. The software can be used on desktop or mobile applications for iOS and Android. On June 5, 2011, Cozi set a Guinness World Record for the longest line of ducks in a row. The line stretched for one mile and was made up of 17,782 rubber ducks. Cozi was acquired by Time Inc. in 2014. After the Meredith Corporation acquired Time in 2018, Cozi was moved into the Parents Network division. On May 4, 2022, Cozi was acquired by OurFamilyWizard of Minneapolis, Minnesota, reporting more than 20 million registered users.
Tilly Norwood
Tilly Norwood is a character created using generative artificial intelligence in 2025 by Xicoia, the AI division of Particle6 Group, a production company founded by Eline Van der Velden. "AI Commissioner", the first project to feature the Norwood character, was criticised by reviewers for The Guardian, PC Gamer, and The A.V. Club. A press release that talent agencies expressed interest in representing the character attracted strong criticism from Hollywood actors and firms, prompting allegations of personality rights violations and arguments over the impact of the character on production costs in the media industry. == History == Norwood was created by Xicoia, which was founded in February 2025 as the artificial intelligence (AI) division of Particle6, a production company founded by Dutch actress and producer Eline Van der Velden in 2015. Van der Velden had previously starred in a satirical comedy series for BBC Three based around her character Miss Holland, whom she created in 2012 as a parody of beauty standards. She stated that the process of creating Norwood took "a long time" and compared the process to that of writers creating characters. An Instagram account under Norwood's name, with posts dating back to 6 May 2025, had gained 50,000 followers by October 3, and featured AI-generated modelling shots, selfies, and epic film scenes. Van der Velden stated in July 2025 that she intended Norwood to be the next Scarlett Johansson or Natalie Portman and later said that audiences were more interested in a film's story than whether its actors were real. Particle6 has claimed that using Norwood could cut production costs by 90%. On 30 July 2025, a comedy sketch named "AI Commissioner" was released, featuring Norwood as an "actress" along with other AI-generated characters. It was created with ten AI software tools, with a script generated by ChatGPT. Stuart Heritage of The Guardian described it as technically competent but "relentlessly unfunny to watch", with "sloppily written, woodenly delivered dialogue", and that Norwood's teeth kept "blurring into a single white block." Joshua Wolens of PC Gamer wrote that Norwood's exaggerated mouth movements gave the impression "that her skeleton was about to leave her body", while William Hughes of The A.V. Club wrote that the sketch's attempt at mimicking human body and mouth movements produced "such a hideous uncanny valley effect" that it gave them "a full-on case of the screaming fantods". By October 2, the sketch had been viewed more than 700,000 times on YouTube. Xicoia was officially announced on 27 September 2025, at the Zurich Summit, part of the Zurich Film Festival; there, van der Velden unveiled Norwood and later joined a panel with Verena Puhm, head of Luma AI's Studio Dream Lab LA. They suggested that media companies were quietly embracing AI and that public announcements of AI-generated works were imminent. Van der Velden claimed that studios had dropped their objections by May after being opposed in February, and that multiple talent agencies were considering representing Norwood. The latter claim drew heightened attention to the character and was printed as fact by Deadline under the headline "Talent Agents Circle AI Actress Tilly Norwood." The report caused controversy, with Vulture describing the reaction to it as "Hollywood [lurching] into a fresh wave of existential panic" while being critical of Deadline's reporting, writing that "when Deadline called it a 'revelation' and published the supposed interest as fact without verification, [it] metastasized into a full-fledged cyberpunk news cycle", and that "by Tuesday, it had grown like wildfire." By September 2025, AI-generated videos had been released depicting Norwood on a red carpet, crying on the sofa of The Graham Norton Show, and starring in mock trailers for sci-fi, fantasy, horror, and action films. Later that month, actresses Melissa Barrera, Kiersey Clemons, and Natasha Lyonne suggested boycotting any agency who signed Norwood, while Mara Wilson asked why none of the "hundreds of living young women whose faces were composited together" to create Norwood could be hired instead. Also around this time, Emily Blunt described Norwood as "really, really scary", and Sophie Turner, Toni Collette, Ralph Ineson, and Ariel Winter also expressed disapproval, while Lukas Gage, Odessa A'zion, and Trace Lysette joked about having supposedly worked with Norwood and finding her incompetent and unpleasant to work with, with Gage claiming that "She was a nightmare to work with!" and "She couldn't hit her mark and she was late!" and Lysette adding "She cut me in line at lunch one day and didn't even say excuse me. She won't get far." Jenelle Riley, Nicholas Alexander Chavez, and the American union SAG-AFTRA stated that they do not consider Norwood an actress. The Gersh Agency and WME both announced that they would not sign Norwood. Whoopi Goldberg and Charlie Fink expressed scepticism that AI could replace jobs. Esquire UK reported that a post on Deadline's Instagram account about Norwood also sparked "varying levels of disgust and outrage" in its comments section from Adelaide Kane, Eiza González, Katie Cassidy, Jewel Staite, Lucy Hale, Stephen Sean Ford, and others, singling out González's comment, saying "Shame on whoever is trying to normalize this. Horrific and terrifying." Actor Bronson Pinchot expressed concern that Norwood could take his job. The British union Equity and the Canadian union ACTRA also condemned Norwood. Following this criticism, Van der Velden released a statement claiming Norwood was "not a replacement for a human being, but a creative work." She also denied that a £120,000 grant from the British Film Institute to fund Particle6 had been used to create Norwood, stating that Norwood had been a self-funded project solely for Xicoia. In late October, businessman Kevin O'Leary, while advocating for the use of AI to replace background actors, stated that they could be replaced with "100 Norwell Tillies" without being able to tell the difference. Ryan Reynolds and a real woman named Natalie "Tilly" Norwood also starred in an advertisement for Mint Mobile's internet service provider Minternet that mocked the character of Norwood. In November 2025, Van der Velden stated in an interview with Deadline that she planned to create 40 further "very diverse" characters alongside Norwood in order to expand the character's "whole universe". Also that month, actress Jameela Jamil criticized the idea of Norwood as "deeply disturbing" for being "a teenage-looking girl who can't say no to a type of sex scene" or "advocate for herself". Van der Velden announced later that month that Particle6 would be producing the History Channel's Streets of the Past, a Dutch documentary series which would be hosted by reality television personality Corjan Mol and would use AI to recreate historical scenes. In March 2026, a music video titled "Take The Lead" featuring Norwood was released on YouTube. It addressed the backlash of Norwood's creation by opening with the lyrics: "When they talk about me, they don't see/ The human spark, the creativity," and, "I'm just a tool, but I've got life." It also featured a disclaimer that says: "made by 18 real humans — from production designers to costume designers to prompters, editors and an actor." The vocals were generated by Suno. == Commentary == Charles Pulliam-Moore of The Verge argued that Norwood's introduction was a stunt to normalize "AI actors" despite Norwood essentially being a digital puppet. Straight Arrow News compared Tilly Norwood to Aki Ross, a CGI character from 2001 that was similarly intended to become a "digital star" and appear in multiple films, while Nicholas Schrivens, writing for The Conversation, likened Norwood to the posthumous use of footage of Carrie Fisher as Princess Leia for Star Wars: The Rise of Skywalker in 2019 and the Los Angeles Times likened Norwood to Hatsune Miku. Scrivens also wrote that "no AI creation has achieved the media cut-through that Tilly has". Moises Mendez II of Out dismissed this as "vapid bullshit", writing, "Nobody wants AI actresses." Scottish actress Briony Monroe alleged that Norwood had been modeled after her likeness and mannerisms, and stated that she was consulting Equity regarding the matter. Musician Stella Hennen said in a viral TikTok video, which was uploaded in October 2025 and featured a side-by-side comparison between herself and Norwood, that Norwood was her "doppleganger". On April 14, 2026, Marie Claire published an article titled "Is Tilly Norwood the Most Dangerous 'Actress' in Hollywood?", though it noted that AI-generated characters are "still not very good at, well, acting," "audiences have not been kind to AI-led productions," and "Norwood's 'performances' have already faced negative reviews as well". The University of Southern California's Entertainment Technology Center's AI media director Yves Bergquist dismissed th
Dreams of Violets
Dreams of Violets is a film entirely generated by artificial intelligence, produced and directed by brothers Ash and Pooya Koosha. The film will be screened at the Tribeca Film Festival on 10 June 2026. All images and characters in the film were generated using AI-powered video tools and based on journalistic reports, photographs, and eyewitness accounts. == Plot == The film is a fictionalized dramatization of the events surrounding the massacre of Iranian civilians in January 2026. International organizations estimate the death toll at over 7,000, amidst protests and state violence that unfolded during a communications blackout.
The Old Axolotl
The Old Axolotl (Polish: Starość aksolotla) is a 2015 digital-only novel by Polish science-fiction author Jacek Dukaj. The novel was released in Polish on March 10, 2015, and shortly afterward, on March 24 that year, in English (translated by Stanley Bill). It has been described as "an experiment in reading (and creating) the electronic literature of the future". It is Dukaj's first novel to be published in English, though several of his short stories (The Golden Galley, 1996, The Iron General, 2010, The Apocrypha of Lem, 2011) have been translated prior to this. The novel has inspired two Netflix original series: the 2020 Belgian Into the Night, and its 2022 Turkish language spin-off Yakamoz S-245. == Plot == The novel presents a post-apocalyptic, cyberpunk vision of Earth where biological life has been wiped out, inhabited by robots and mechs, many of which are humans whose consciousness has been digitized in the wake of an extinction event. == Significance and analysis == The novel is an example of electronic literature, available only in digital formats, and has no traditional paper version. It was designed from the beginning not only to incorporate more traditional elements such as illustrations, but also hypertext, and 3D-printable models of main robotic characters designed by Alex Jaeger, the art director of Transformers films. The novel composition is layered, with the narrative layer, an encyclopedic/hyperlinked footnote layer, and a multimedia layer, including illustrations and a short promotional video by the Oscar-nominated Platige Image studio. One of the novel's central questions is: "What does it mean to be human?" Other subjects include post humanism and other "staples of cyberpunk and related genres, such as the artificial intelligence". The novel is representative of Dukaj's prose, posing philosophical questions about the future of man and technology. The author explained that: "stories such as The Old Axolotl that model an ‘escape from the body’ are born out of a sense of progress as a process of ‘de-animalising’ human beings through science. This has its origin in the pre-Enlightenment intuition of ‘liberation from nature’. For one of the last shackles of nature is corporeality itself, the limitations of our physicality." The other major element of the novel is Dukaj's attempts to introduce the reader to the new style of electronic literature. The novel was nominated for the 2016 Janusz A. Zajdel Award.
Necrobotics
Necrobotics is the practice of using biotic materials (or dead organisms) as robotic components. Necrobotics can serve as an alternative to mechanical components that are difficult to manufacture by using biological components designed by natural selection in order to exploit the highly developed selective design implemented in biological lifeforms via the process of evolution. In July 2022, researchers in the Preston Innovation Lab at Rice University in Houston, Texas published a paper in Advanced Science introducing the concept and demonstrating its capability by repurposing dead spiders as robotic grippers and applying pressurized air to activate their gripping arms. In April 2025 researchers at Shinshu University created a “bio-hybrid drone” using silk-worm moth antennae to detect the source of a smell. In November 2025 researchers at McGill University demonstrated the use of a mosquito proboscis as a fine nozzle in experimental 3D printing. Necrobotics utilizes the spider's organic hydraulic system and their compact legs to create an efficient and simple gripper system. The necrobotic spider gripper is capable of lifting small and light objects, thereby serving as an alternative to complex and costly small mechanical grippers. == Background == The main appeal of the spider's body in necrobotics is its compact leg mechanism and use of hydraulic pressure. The spider's anatomy utilizes a simple hydraulic (fluid) pressure system. Spider legs have flexor muscles that naturally constrict their legs when relaxed. A force is required to straighten and extend their legs, which spiders accomplish by pumping hemolymph fluid (blood) through their joints as a means of hydraulic pressure. It takes no external power to curl their legs due to their flexor muscles' natural curled state. In July 2022, researchers in the Preston Innovation Lab at Rice University published a paper detailing their experiments with the gripper. Although dead spiders no longer produce hemolymph, Te Faye Yap (lead author and mechanical engineering graduate) found that pumping air through a needle into the spider's cephalothorax (main body) accomplishes the same results as hemolymph. The original hydraulic (fluid) system is essentially converted into a pneumatic (air) system. == Fabrication == Obtain a spider Euthanize the spider using a cold temperature of around -4°C for 5-7 days Insert a 25 gauge hypodermic needle into the spider's cephalothorax (main body) Apply glue around the needle to form a seal and allow it to dry Connect a syringe or pump to the needle Extend the spider's legs by pumping air in == Testing and Data == === Internal Force Versus Gripping Force === The typical pressure in a resting spider's legs ranges from 4 kPa to 6.1 kPa. Researchers extended the legs by increasing the spider's internal pressure to 5.5 kPa. Pumping air into the body increases the internal pressure, causing the legs to expand. Pumping air out of the body decreases internal pressure, causing the legs to contract due to their flexor leg muscles. When the internal pressure decreases to 0 kPa, the gripper would be fully closed, allowing for the gripper to grasp objects. This action demonstrates that as internal pressure decreases, the gripping force increases. Inversely, when internal pressure increases, the gripping force decreases. By gripping individual weighted acetate beads, it is found that the necrobotic gripper achieves a maximum gripping force of 0.35 milinewtons. === Spider Weight Versus Gripping Force === To estimate the gripping forces of smaller and larger spiders, researchers created a plot to predict the gripping force relative to the size of the spider. The wolf spider's body weight is relatively equal to the gripping force of its legs. The mass of the gripper is 33.5 mg and can lift 1.3 times its body weight (43.6 mg or 0.35 mN). However, with larger spiders, the gripping force relative to body weight decreases. For example, a 200-gram goliath birdeater is predicted to lift 10% of its weight (20 grams or 196 mN). Though there is an inverse relationship between spider mass and gripping force, larger spiders exert greater gripping forces than smaller spiders. === Gripper Lifespan === The necrobotic gripper's functionality is entirely reliant on the structural integrity of the spider. If the spider were to break down easily and frequently, the gripper would not be practical. Using cyclic testing, a series of repeated actions, it is found that the necrobotic gripper can actuate 700 to 1000 times. After 1000 cycles, cracks begin forming on the membrane of the leg joints due to dehydration. Weakened and decomposing joints lead to frequent breakage and replacement, thereby serving as an obstacle in applying necrobotics to real-world scenarios. One theorized fix to this issue is applying beeswax or a lubricant to the joints. Researchers found that over 10 days, the mass of an uncoated spider decreased 17 times more than the mass of a spider coated with beeswax. Lubricating joints combats dehydration and slows the loss of organic material. == Constraints == With the usage of organic material, there is a higher chance of the component decomposing and breaking down as opposed to traditional mechanical systems. There may be additional work and management required to replace these grippers if they fail. Additionally, organic inconsistencies with the spiders will yield inaccurate results. Not all wolf spiders develop the same, so gripping force and leg contraction can vary between grippers. There are moral implications behind euthanizing spiders for robotics. The ethical boundaries that necrobotics push in the pursuit of biohybrid systems raise concerns, as opponents say it may lead to the hybridization of mammals and is intrusive to nature. Proponents respond that repurposing dead animals has been human practice for millennia and that necrobotics should be pursued to advance science.
Diagnosis (artificial intelligence)
As a subfield in artificial intelligence, diagnosis is concerned with the development of algorithms and techniques that are able to determine whether the behaviour of a system is correct. If the system is not functioning correctly, the algorithm should be able to determine, as accurately as possible, which part of the system is failing, and which kind of fault it is facing. The computation is based on observations, which provide information on the current behaviour. The expression diagnosis also refers to the answer of the question of whether the system is malfunctioning or not, and to the process of computing the answer. This word comes from the medical context where a diagnosis is the process of identifying a disease by its symptoms. == Example == An example of diagnosis is the process of a garage mechanic with an automobile. The mechanic will first try to detect any abnormal behavior based on the observations on the car and his knowledge of this type of vehicle. If he finds out that the behavior is abnormal, the mechanic will try to refine his diagnosis by using new observations and possibly testing the system, until he discovers the faulty component; the mechanic plays an important role in the vehicle diagnosis. == Expert diagnosis == The expert diagnosis (or diagnosis by expert system) is based on experience with the system. Using this experience, a mapping is built that efficiently associates the observations to the corresponding diagnoses. The experience can be provided: By a human operator. In this case, the human knowledge must be translated into a computer language. By examples of the system behaviour. In this case, the examples must be classified as correct or faulty (and, in the latter case, by the type of fault). Machine learning methods are then used to generalize from the examples. The main drawbacks of these methods are: The difficulty acquiring the expertise. The expertise is typically only available after a long period of use of the system (or similar systems). Thus, these methods are unsuitable for safety- or mission-critical systems (such as a nuclear power plant, or a robot operating in space). Moreover, the acquired expert knowledge can never be guaranteed to be complete. In case a previously unseen behaviour occurs, leading to an unexpected observation, it is impossible to give a diagnosis. The complexity of the learning. The off-line process of building an expert system can require a large amount of time and computer memory. The size of the final expert system. As the expert system aims to map any observation to a diagnosis, it will in some cases require a huge amount of storage space. The lack of robustness. If even a small modification is made on the system, the process of constructing the expert system must be repeated. A slightly different approach is to build an expert system from a model of the system rather than directly from an expertise. An example is the computation of a diagnoser for the diagnosis of discrete event systems. This approach can be seen as model-based, but it benefits from some advantages and suffers some drawbacks of the expert system approach. == Model-based diagnosis == Model-based diagnosis is an example of abductive reasoning using a model of the system. In general, it works as follows: We have a model that describes the behaviour of the system (or artefact). The model is an abstraction of the behaviour of the system and can be incomplete. In particular, the faulty behaviour is generally little-known, and the faulty model may thus not be represented. Given observations of the system, the diagnosis system simulates the system using the model, and compares the observations actually made to the observations predicted by the simulation. The modelling can be simplified by the following rules (where A b {\displaystyle Ab\,} is the Abnormal predicate): ¬ A b ( S ) ⇒ I n t 1 ∧ O b s 1 {\displaystyle \neg Ab(S)\Rightarrow Int1\wedge Obs1} A b ( S ) ⇒ I n t 2 ∧ O b s 2 {\displaystyle Ab(S)\Rightarrow Int2\wedge Obs2} (fault model) The semantics of these formulae is the following: if the behaviour of the system is not abnormal (i.e. if it is normal), then the internal (unobservable) behaviour will be I n t 1 {\displaystyle Int1\,} and the observable behaviour O b s 1 {\displaystyle Obs1\,} . Otherwise, the internal behaviour will be I n t 2 {\displaystyle Int2\,} and the observable behaviour O b s 2 {\displaystyle Obs2\,} . Given the observations O b s {\displaystyle Obs\,} , the problem is to determine whether the system behaviour is normal or not ( ¬ A b ( S ) {\displaystyle \neg Ab(S)\,} or A b ( S ) {\displaystyle Ab(S)\,} ). This is an example of abductive reasoning. == Diagnosability == A system is said to be diagnosable if whatever the behavior of the system, we will be able to determine without ambiguity a unique diagnosis. The problem of diagnosability is very important when designing a system because on one hand one may want to reduce the number of sensors to reduce the cost, and on the other hand one may want to increase the number of sensors to increase the probability of detecting a faulty behavior. Several algorithms for dealing with these problems exist. One class of algorithms answers the question whether a system is diagnosable; another class looks for sets of sensors that make the system diagnosable, and optionally comply to criteria such as cost optimization. The diagnosability of a system is generally computed from the model of the system. In applications using model-based diagnosis, such a model is already present and doesn't need to be built from scratch.