In computer graphics and digital imaging, image scaling is the resizing of a digital image. In video technology, the magnification of digital material is known as upscaling or resolution enhancement. When scaling a vector graphic image, the graphic primitives that make up the image can be rendered using geometric transformations at any resolution with no loss of image quality. When scaling a raster graphics image, a new image with a higher or lower number of pixels must be generated. In the case of decreasing the pixel number (scaling down), this usually results in a visible quality loss. From the standpoint of digital signal processing, the scaling of raster graphics is a two-dimensional example of sample-rate conversion, the conversion of a discrete signal from a sampling rate (in this case, the local sampling rate) to another. == Mathematical == Image scaling can be interpreted as a form of image resampling or image reconstruction from the view of the Nyquist sampling theorem. According to the theorem, downsampling to a smaller image from a higher-resolution original can only be carried out after applying a suitable 2D anti-aliasing filter to prevent aliasing artifacts. The image is reduced to the information that can be carried by the smaller image. In the case of up sampling, a reconstruction filter takes the place of the anti-aliasing filter. A more sophisticated approach to upscaling treats the problem as an inverse problem, solving the question of generating a plausible image that, when scaled down, would look like the input image. A variety of techniques have been applied for this, including optimization techniques with regularization terms and the use of machine learning from examples. == Algorithms == An image size can be changed in several ways. === Nearest-neighbor interpolation === One of the simpler ways of increasing image size is nearest-neighbor interpolation, replacing every pixel with the nearest pixel in the output; for upscaling, this means multiple pixels of the same color will be present. This can preserve sharp details but also introduce jaggedness in previously smooth images. 'Nearest' in nearest-neighbor does not have to be the mathematical nearest. One common implementation is to always round toward zero. Rounding this way produces fewer artifacts and is faster to calculate. This algorithm is often preferred for images which have little to no smooth edges. A common application of this can be found in pixel art. === Bilinear and bicubic interpolation === Bilinear interpolation works by interpolating pixel color values, introducing a continuous transition into the output even where the original material has discrete transitions. Although this is desirable for continuous-tone images, this algorithm reduces contrast (sharp edges) in a way that may be undesirable for line art. Bicubic interpolation yields substantially better results, with an increase in computational cost. === Sinc and Lanczos resampling === Sinc resampling, in theory, provides the best possible reconstruction for a perfectly bandlimited signal. In practice, the assumptions behind sinc resampling are not completely met by real-world digital images. Lanczos resampling, an approximation to the sinc method, yields better results. Bicubic interpolation can be regarded as a computationally efficient approximation to Lanczos resampling. === Box sampling === One weakness of bilinear, bicubic, and related algorithms is that they sample a specific number of pixels. When downscaling below a certain threshold, such as more than twice for all bi-sampling algorithms, the algorithms will sample non-adjacent pixels, which results in both losing data and rough results. The trivial solution to this issue is box sampling, which is to consider the target pixel a box on the original image and sample all pixels inside the box. This ensures that all input pixels contribute to the output. The major weakness of this algorithm is that it is hard to optimize. === Mipmap === Another solution to the downscale problem of bi-sampling scaling is mipmaps. A mipmap is a prescaled set of downscaled copies. When downscaling, the nearest larger mipmap is used as the origin to ensure no scaling below the useful threshold of bilinear scaling. This algorithm is fast and easy to optimize. It is standard in many frameworks, such as OpenGL. The cost is using more image memory, exactly one-third more in the standard implementation. === Fourier-transform methods === Simple interpolation based on the Fourier transform pads the frequency domain with zero components (a smooth window-based approach would reduce the ringing). Besides the good conservation (or recovery) of details, notable are the ringing and the circular bleeding of content from the left border to the right border (and the other way around). === Edge-directed interpolation === Edge-directed interpolation algorithms aim to preserve edges in the image after scaling, unlike other algorithms, which can introduce staircase artifacts. Examples of algorithms for this task include New Edge-Directed Interpolation (NEDI), Edge-Guided Image Interpolation (EGGI), Iterative Curvature-Based Interpolation (ICBI), and Directional Cubic Convolution Interpolation (DCCI). A 2013 analysis found that DCCI had the best scores in peak signal-to-noise ratio and structural similarity on a series of test images. === hqx === For magnifying computer graphics with low resolution and/or few colors (usually from 2 to 256 colors), better results can be achieved by hqx or other pixel-art scaling algorithms. These produce sharp edges and maintain a high level of detail. === Vectorization === Vector extraction, or vectorization, offers another approach. Vectorization first creates a resolution-independent vector representation of the graphic to be scaled. The resulting SVG vector file can then be exported and rendered at any required resolution without quality loss, serving directly as production-ready artwork for scalable display & printing. This technique is used by Adobe Illustrator, Live Trace, and Inkscape. Scalable Vector Graphics are well suited to simple geometric images, while photographs do not fare well with vectorization due to their complexity. === Deep convolutional neural networks === This method uses machine learning for more detailed images, such as photographs and complex artwork. Programs that use this method include waifu2x, Imglarger and Neural Enhance. Demonstration of conventional vs. waifu2x upscaling with noise reduction, using a detail of Phosphorus and Hesperus by Evelyn De Morgan. [Click image for full size] AI-driven upscaling software allows detail and sharpness to be added to historical photographs, where it is not present in the original. The availability of AI upscaling tools has led to confusion where a person believes that the upscaled version of a blurry image is genuinely showing them the subject of the original photograph. In 2025 a user of the social media site X posted an AI-upscaled version of a low resolution photo of Donald Trump that they had zoomed in on, and asked if anyone could "explain what the hell is happening to his forehead". Experts noted that the image had been distorted by the upscaling process, and that such tools "inevitably have to invent, or at least recreate, details that were or were not there". == Applications == === General === Image scaling is used in, among other applications, web browsers, image editors, image and file viewers, software magnifiers, digital zoom, the process of generating thumbnail images, and when outputting images through screens or printers. === Video === This application is the magnification of images for home theaters for HDTV-ready output devices from PAL-Resolution content, for example, from a DVD player. Upscaling is performed in real time, and the output signal is not saved. === Pixel-art scaling === As pixel-art graphics are usually low-resolution, they rely on careful placement of individual pixels, often with a limited palette of colors. This results in graphics that rely on stylized visual cues to define complex shapes with little resolution, down to individual pixels. This makes scaling pixel art a particularly difficult problem. Specialized algorithms were developed to handle pixel-art graphics, as the traditional scaling algorithms do not take perceptual cues into account. Since a typical application is to improve the appearance of fourth-generation and earlier video games on arcade and console emulators, many are designed to run in real time for small input images at 60 frames per second. On fast hardware, these algorithms are suitable for gaming and other real-time image processing. These algorithms provide sharp, crisp graphics, while minimizing blur. Scaling art algorithms have been implemented in a wide range of emulators such as HqMAME and DOSBox, as well as 2D game engines and game engine recreations such as ScummVM. They gained recognition with game
Mobile Passport Control
Mobile Passport Control (MPC) is a mobile app that enables eligible travelers entering the United States to submit their passport information and customs declaration form to Customs and Border Protection via smartphone or tablet and go through the inspections process using an expedited lane. It is available to "U.S. citizens, U.S. lawful permanent residents, Canadian B1/B2 citizen visitors and returning Visa Waiver Program travelers with approved ESTA". The app is available on iOS and Android devices and is operational at 34 US airports, 14 international airports offering preclearance facilities, and 4 seaports. The use of Mobile Passport Control operations have increased threefold from 2016 to 2017. == History == Mobile Passport Control operations were launched in Atlanta at the Hartsfield-Jackson International Airport in 2016 and is now available at 34 U.S. airports, 14 international airports that offer preclearance and 4 U.S. cruise ports. The Mobile Passport app is authorized by CBP and sponsored by the Airports Council International-North America, Boeing, and the Port of Everglades. Airside Mobile, Inc. secured a Series A funding of $6 million in the fall of 2017. == How it works == During the customs process at the Federal Inspection Service (FIS) area of a U.S. airport, travelers arriving from international locations typically wait in long lines before presenting passports and paperwork and verbally answering questions made by CBP officials. Eligible travelers who have downloaded the Mobile Passport app can expedite this process by submitting information regarding their passport and trip details, and a newly-taken selfie, via their mobile device to CBP officials, then access an expedited line. Mobile Passport Control users will be required to show their physical passport(s) and briefly talk to a CBP officer. == Locations == === US airports === Atlanta (ATL) Baltimore (BWI) Boston (BOS) Charlotte (CLT) Chicago (ORD) Dallas/Ft Worth (DFW) Denver (DEN) Detroit (DTW) as of 7/2024 Ft. Lauderdale (FLL) Honolulu (HNL) Houston (HOU and IAH) Kansas City (MCI) Las Vegas (LAS) Los Angeles (LAX) Miami (MIA) Minneapolis (MSP) New York (JFK) Newark (EWR) Oakland (OAK) Orlando (MCO) Palm Beach (PBI) Philadelphia (PHL) Phoenix (PHX) Pittsburgh (PIT) Portland (PDX) Sacramento (SMF) San Diego (SAN) San Francisco (SFO) San Jose (SJC) San Juan (SJU) Seattle (SEA) Tampa (TPA) Washington Dulles (IAD) === International Preclearance locations === Abu Dhabi (AUH) Aruba (AUA) Bermuda (BDA) Calgary (YYC) Dublin (DUB) Edmonton (YEG) Halifax (YHZ) Montreal (YUL) Nassau (NAS) Ottawa (YOW) Shannon (SNN) Toronto (YYZ) Vancouver (YVR) Winnipeg (YWG) Sepinggan (BPN) === Seaports === Fort Lauderdale (PEV) Miami (MSE) San Juan (PUE) West Palm Beach (WPB)
Dissociated press
Dissociated press is a parody generator (a computer program that generates nonsensical text). The generated text is based on another text using the Markov chain technique. The name is a play on "Associated Press" and the psychological term dissociation (although word salad is more typical of conditions like aphasia and schizophrenia – which is, however, frequently confused with dissociative identity disorder by laypeople). An implementation of the algorithm is available in Emacs. Another implementation is available as a Perl module in CPAN, Games::Dissociate. == The algorithm == The algorithm starts by printing a number of consecutive words (or letters) from the source text. Then it searches the source text for an occurrence of the few last words or letters printed out so far. If multiple occurrences are found, it picks a random one, and proceeds with printing the text following the chosen occurrence. After a predetermined length of text is printed out, the search procedure is repeated for the newly printed ending. Considering that words and phrases tend to appear in specific grammatical contexts, the resulting text usually seems correct grammatically, and if the source text is uniform in style, the result appears to be of similar style and subject, and takes some effort on the reader's side to recognize as not genuine. Still, the randomness of the assembly process deprives it of any logical flow - the loosely related parts are connected in a nonsensical way, creating a humorously abstract, random result. == Examples == Here is a short example of word-based Dissociated Press applied to the Jargon File: wart: n. A small, crocky feature that sticks out of an array (C has no checks for this). This is relatively benign and easy to spot if the phrase is bent so as to be not worth paying attention to the medium in question. Here is a short example of letter-based Dissociated Press applied to the same source: window sysIWYG: n. A bit was named aften /bee´t@/ prefer to use the other guy's re, especially in every cast a chuckle on neithout getting into useful informash speech makes removing a featuring a move or usage actual abstractionsidered interj. Indeed spectace logic or problem! == History == The dissociated press algorithm is described in HAKMEM (1972) Item #176. The name "dissociated press" is first known to have been associated with the Emacs implementation. Brian Hayes discussed a Travesty algorithm in Scientific American in November 1983. The article provided a garbled William Faulkner passage: When he got on the table, he come in. He never come out of my own pocket as a measure of protecting the company against riot and bloodshed. And when he said. "You tell me a bus ticket, let alone write out no case histories. Then the law come back with a knife!" Hugh Kenner and Joseph O'Rourke of Johns Hopkins University discussed their frequency table-based Travesty generator for microcomputers in BYTE in November 1984. The article included the Turbo Pascal source for two versions of the generator, one using Hayes' algorithm and another using Claude Shannon's Hellbat algorithm. Murray Lesser offered a compiled BASIC version in the magazine in July 1985, in September 1985 Peter Wayner offered a version that used tree data structures instead of frequency tables, and in December 1985 Neil J. Rubenking offered a version written in Turbo Pascal that stored frequency information in a B-tree.
Adam Tauman Kalai
Adam Tauman Kalai is an American computer scientist who specializes in artificial intelligence and works at OpenAI. == Education and career == Kalai graduated from Harvard University in 1996 with a BA in computer science and received a MA and PhD, both in computer science, from Carnegie Mellon University in 1999 and 2001, respectively. His doctoral advisor was Avrim Blum. After graduation, Kalai did his postdoctoral research at Massachusetts Institute of Technology under Santosh Vempala until 2003. Kalai became a faculty member at the Toyota Technological Institute at Chicago from 2003 to 2006, followed by a stint as an assistant professor at Georgia Institute of Technology from 2007 to 2008. He joined Microsoft Research in 2008 and subsequently moved to OpenAI in 2023. == Contributions == Kalai is known for his algorithm for generating random factored numbers (see Bach's algorithm), for co-inventing the cooperative-competitive value (coco value), for efficiently learning learning mixtures of Gaussians, for the Blum-Kalai-Wasserman algorithm for learning parity with noise, and for the intractability of the folk theorem in game theory. More recently, Kalai is known for identifying and reducing gender bias in word embeddings, which are a representation of words commonly used in AI systems. In 2026, he coauthored a Nature paper on hallucinations in large language models. == Personal life == Kalai is the son of game theorist Ehud Kalai and is married to cryptographer Yael Tauman Kalai.
Collocation extraction
Collocation extraction is the task of using a computer to extract collocations automatically from a corpus. The traditional method of performing collocation extraction is to find a formula based on the statistical quantities of those words to calculate a score associated to every word pairs. Proposed formulas are mutual information, t-test, z test, chi-squared test and likelihood ratio. Within the area of corpus linguistics, collocation is defined as a sequence of words or terms which co-occur more often than would be expected by chance. 'Crystal clear', 'middle management', 'nuclear family', and 'cosmetic surgery' are examples of collocated pairs of words. Some words are often found together because they make up a compound noun, for example 'riding boots' or 'motor cyclist' or ‘collocation extraction’ its very self.
Shearlet
In applied mathematical analysis, shearlets are a multiscale framework which allows efficient encoding of anisotropic features in multivariate problem classes. Originally, shearlets were introduced in 2006 for the analysis and sparse approximation of functions f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} . They are a natural extension of wavelets, to accommodate the fact that multivariate functions are typically governed by anisotropic features such as edges in images, since wavelets, as isotropic objects, are not capable of capturing such phenomena. Shearlets are constructed by parabolic scaling, shearing, and translation applied to a few generating functions. At fine scales, they are essentially supported within skinny and directional ridges following the parabolic scaling law, which reads length² ≈ width. Similar to wavelets, shearlets arise from the affine group and allow a unified treatment of the continuum and digital situation leading to faithful implementations. Although they do not constitute an orthonormal basis for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} , they still form a frame allowing stable expansions of arbitrary functions f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} . One of the most important properties of shearlets is their ability to provide optimally sparse approximations (in the sense of optimality in ) for cartoon-like functions f {\displaystyle f} . In imaging sciences, cartoon-like functions serve as a model for anisotropic features and are compactly supported in [ 0 , 1 ] 2 {\displaystyle [0,1]^{2}} while being C 2 {\displaystyle C^{2}} apart from a closed piecewise C 2 {\displaystyle C^{2}} singularity curve with bounded curvature. The decay rate of the L 2 {\displaystyle L^{2}} -error of the N {\displaystyle N} -term shearlet approximation obtained by taking the N {\displaystyle N} largest coefficients from the shearlet expansion is in fact optimal up to a log-factor: ‖ f − f N ‖ L 2 2 ≤ C N − 2 ( log N ) 3 , N → ∞ , {\displaystyle \|f-f_{N}\|_{L^{2}}^{2}\leq CN^{-2}(\log N)^{3},\quad N\to \infty ,} where the constant C {\displaystyle C} depends only on the maximum curvature of the singularity curve and the maximum magnitudes of f {\displaystyle f} , f ′ {\displaystyle f'} and f ″ . {\displaystyle f''.} This approximation rate significantly improves the best N {\displaystyle N} -term approximation rate of wavelets providing only O ( N − 1 ) {\displaystyle O(N^{-1})} for such class of functions. Shearlets are to date the only directional representation system that provides sparse approximation of anisotropic features while providing a unified treatment of the continuum and digital realm that allows faithful implementation. Extensions of shearlet systems to L 2 ( R d ) , d ≥ 2 {\displaystyle L^{2}(\mathbb {R} ^{d}),d\geq 2} are also available. A comprehensive presentation of the theory and applications of shearlets can be found in. == Definition == === Continuous shearlet systems === The construction of continuous shearlet systems is based on parabolic scaling matrices A a = [ a 0 0 a 1 / 2 ] , a > 0 {\displaystyle A_{a}={\begin{bmatrix}a&0\\0&a^{1/2}\end{bmatrix}},\quad a>0} as a means to change the resolution, on shear matrices S s = [ 1 s 0 1 ] , s ∈ R {\displaystyle S_{s}={\begin{bmatrix}1&s\\0&1\end{bmatrix}},\quad s\in \mathbb {R} } as a means to change the orientation, and finally on translations to change the positioning. In comparison to curvelets, shearlets use shearings instead of rotations, the advantage being that the shear operator S s {\displaystyle S_{s}} leaves the integer lattice invariant in case s ∈ Z {\displaystyle s\in \mathbb {Z} } , i.e., S s Z 2 ⊆ Z 2 . {\displaystyle S_{s}\mathbb {Z} ^{2}\subseteq \mathbb {Z} ^{2}.} This indeed allows a unified treatment of the continuum and digital realm, thereby guaranteeing a faithful digital implementation. For ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} the continuous shearlet system generated by ψ {\displaystyle \psi } is then defined as SH c o n t ( ψ ) = { ψ a , s , t = a 3 / 4 ψ ( S s A a ( ⋅ − t ) ) ∣ a > 0 , s ∈ R , t ∈ R 2 } , {\displaystyle \operatorname {SH} _{\mathrm {cont} }(\psi )=\{\psi _{a,s,t}=a^{3/4}\psi (S_{s}A_{a}(\cdot -t))\mid a>0,s\in \mathbb {R} ,t\in \mathbb {R} ^{2}\},} and the corresponding continuous shearlet transform is given by the map f ↦ S H ψ f ( a , s , t ) = ⟨ f , ψ a , s , t ⟩ , f ∈ L 2 ( R 2 ) , ( a , s , t ) ∈ R > 0 × R × R 2 . {\displaystyle f\mapsto {\mathcal {SH}}_{\psi }f(a,s,t)=\langle f,\psi _{a,s,t}\rangle ,\quad f\in L^{2}(\mathbb {R} ^{2}),\quad (a,s,t)\in \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} === Discrete shearlet systems === A discrete version of shearlet systems can be directly obtained from SH c o n t ( ψ ) {\displaystyle \operatorname {SH} _{\mathrm {cont} }(\psi )} by discretizing the parameter set R > 0 × R × R 2 . {\displaystyle \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} There are numerous approaches for this but the most popular one is given by { ( 2 j , k , A 2 j − 1 S k − 1 m ) ∣ j ∈ Z , k ∈ Z , m ∈ Z 2 } ⊆ R > 0 × R × R 2 . {\displaystyle \{(2^{j},k,A_{2^{j}}^{-1}S_{k}^{-1}m)\mid j\in \mathbb {Z} ,k\in \mathbb {Z} ,m\in \mathbb {Z} ^{2}\}\subseteq \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} From this, the discrete shearlet system associated with the shearlet generator ψ {\displaystyle \psi } is defined by SH ( ψ ) = { ψ j , k , m = 2 3 j / 4 ψ ( S k A 2 j ⋅ − m ) ∣ j ∈ Z , k ∈ Z , m ∈ Z 2 } , {\displaystyle \operatorname {SH} (\psi )=\{\psi _{j,k,m}=2^{3j/4}\psi (S_{k}A_{2^{j}}\cdot {}-m)\mid j\in \mathbb {Z} ,k\in \mathbb {Z} ,m\in \mathbb {Z} ^{2}\},} and the associated discrete shearlet transform is defined by f ↦ S H ψ f ( j , k , m ) = ⟨ f , ψ j , k , m ⟩ , f ∈ L 2 ( R 2 ) , ( j , k , m ) ∈ Z × Z × Z 2 . {\displaystyle f\mapsto {\mathcal {SH}}_{\psi }f(j,k,m)=\langle f,\psi _{j,k,m}\rangle ,\quad f\in L^{2}(\mathbb {R} ^{2}),\quad (j,k,m)\in \mathbb {Z} \times \mathbb {Z} \times \mathbb {Z} ^{2}.} == Examples == Let ψ 1 ∈ L 2 ( R ) {\displaystyle \psi _{1}\in L^{2}(\mathbb {R} )} be a function satisfying the discrete Calderón condition, i.e., ∑ j ∈ Z | ψ ^ 1 ( 2 − j ξ ) | 2 = 1 , for a.e. ξ ∈ R , {\displaystyle \sum _{j\in \mathbb {Z} }|{\hat {\psi }}_{1}(2^{-j}\xi )|^{2}=1,{\text{for a.e. }}\xi \in \mathbb {R} ,} with ψ ^ 1 ∈ C ∞ ( R ) {\displaystyle {\hat {\psi }}_{1}\in C^{\infty }(\mathbb {R} )} and supp ψ ^ 1 ⊆ [ − 1 2 , − 1 16 ] ∪ [ 1 16 , 1 2 ] , {\displaystyle \operatorname {supp} {\hat {\psi }}_{1}\subseteq [-{\tfrac {1}{2}},-{\tfrac {1}{16}}]\cup [{\tfrac {1}{16}},{\tfrac {1}{2}}],} where ψ ^ 1 {\displaystyle {\hat {\psi }}_{1}} denotes the Fourier transform of ψ 1 . {\displaystyle \psi _{1}.} For instance, one can choose ψ 1 {\displaystyle \psi _{1}} to be a Meyer wavelet. Furthermore, let ψ 2 ∈ L 2 ( R ) {\displaystyle \psi _{2}\in L^{2}(\mathbb {R} )} be such that ψ ^ 2 ∈ C ∞ ( R ) , {\displaystyle {\hat {\psi }}_{2}\in C^{\infty }(\mathbb {R} ),} supp ψ ^ 2 ⊆ [ − 1 , 1 ] {\displaystyle \operatorname {supp} {\hat {\psi }}_{2}\subseteq [-1,1]} and ∑ k = − 1 1 | ψ ^ 2 ( ξ + k ) | 2 = 1 , for a.e. ξ ∈ [ − 1 , 1 ] . {\displaystyle \sum _{k=-1}^{1}|{\hat {\psi }}_{2}(\xi +k)|^{2}=1,{\text{for a.e. }}\xi \in \left[-1,1\right].} One typically chooses ψ ^ 2 {\displaystyle {\hat {\psi }}_{2}} to be a smooth bump function. Then ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} given by ψ ^ ( ξ ) = ψ ^ 1 ( ξ 1 ) ψ ^ 2 ( ξ 2 ξ 1 ) , ξ = ( ξ 1 , ξ 2 ) ∈ R 2 , {\displaystyle {\hat {\psi }}(\xi )={\hat {\psi }}_{1}(\xi _{1}){\hat {\psi }}_{2}\left({\tfrac {\xi _{2}}{\xi _{1}}}\right),\quad \xi =(\xi _{1},\xi _{2})\in \mathbb {R} ^{2},} is called a classical shearlet. It can be shown that the corresponding discrete shearlet system SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} constitutes a Parseval frame for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} consisting of bandlimited functions. Another example are compactly supported shearlet systems, where a compactly supported function ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} can be chosen so that SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} forms a frame for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} . In this case, all shearlet elements in SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} are compactly supported providing superior spatial localization compared to the classical shearlets, which are bandlimited. Although a compactly supported shearlet system does not generally form a Parseval frame, any function f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} can be represented by the shearlet expansion due to its frame property. == Cone-adapted shearlets == One drawback of shearlets defined as above is the directional bias of shearlet elements associated with large shearing parameters. This effect is already r
Mark Keane (cognitive scientist)
Mark Thomas Gerard Keane (Irish: Marcus Ó Cathain, born 3 July 1961, Dublin, Ireland) is a cognitive scientist and author of several books on human cognition and artificial intelligence, including Cognitive Psychology: A Student's Handbook (8 editions, with Michael Eysenck), Advances in the Psychology of Thinking (1992, with Ken Gilhooly), Novice Programming Environments (1992/2018, with Marc Eisenstadt and Tim Rajan), Advances in Case-Based Reasoning (1995, with J-P Haton and Michel Manago)., Case-Based Reasoning: Research & Development (2022, with N Wiratunga). == Education == Keane received a B.A. in Psychology from University College Dublin in 1982. He then received a Ph.D. from Trinity College Dublin in 1987. He then moved to postdoctoral positions in Queen Mary University of London and the Open University. == Academic career == He was a Lecturer in Psychology at Cardiff University. He became a lecturer in Computer Science at Trinity College Dublin in 1990, and became a fellow in 1994. Keane moved to become Chair of Computer Science at University College Dublin in 1998. In 2006, he was seconded to Science Foundation Ireland as Director of ICT, overseeing on a $700m research investment. He advised the Irish Government on its 3.7B euro Strategy for Science, Technology & Innovation (SSTI). From 2006 to 2007, he was Director General of Science Foundation Ireland before returning to University College Dublin where he was appointed VP of Innovation & Partnerships (2007-2009). Keane's research has been split between cognitive science and computer science. His cognitive science research has been in analogy, metaphor, conceptual combination and similarity. His computer science research has been in natural language processing, machine learning, case-based reasoning, text analytics and explainable artificial intelligence. He has been a PI in the Science Foundation Ireland funded Insight Centre for Data Analytics working on digital journalism and digital humanities. More recently, he was deputy director of the VistaMilk SFI Research Centre that is exploring precision agriculture in the dairy sector.