In pure and applied mathematics, particularly quantum mechanics and computer graphics and their applications, a spherical basis is the basis used to express spherical tensors. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. While spherical polar coordinates are one orthogonal coordinate system for expressing vectors and tensors using polar and azimuthal angles and radial distance, the spherical basis are constructed from the standard basis and use complex numbers. == In three dimensions == A vector A in 3D Euclidean space R3 can be expressed in the familiar Cartesian coordinate system in the standard basis ex, ey, ez, and coordinates Ax, Ay, Az: or any other coordinate system with associated basis set of vectors. From this extend the scalars to allow multiplication by complex numbers, so that we are now working in C 3 {\displaystyle \mathbb {C} ^{3}} rather than R 3 {\displaystyle \mathbb {R} ^{3}} . === Basis definition === In the spherical bases denoted e+, e−, e0, and associated coordinates with respect to this basis, denoted A+, A−, A0, the vector A is: where the spherical basis vectors can be defined in terms of the Cartesian basis using complex-valued coefficients in the xy plane: in which i {\displaystyle i} denotes the imaginary unit, and one normal to the plane in the z direction: e 0 = e z {\displaystyle \mathbf {e} _{0}=\mathbf {e} _{z}} The inverse relations are: === Commutator definition === While giving a basis in a 3-dimensional space is a valid definition for a spherical tensor, it only covers the case for when the rank k {\displaystyle k} is 1. For higher ranks, one may use either the commutator, or rotation definition of a spherical tensor. The commutator definition is given below, any operator T q ( k ) {\displaystyle T_{q}^{(k)}} that satisfies the following relations is a spherical tensor: [ J ± , T q ( k ) ] = ℏ ( k ∓ q ) ( k ± q + 1 ) T q ± 1 ( k ) {\displaystyle [J_{\pm },T_{q}^{(k)}]=\hbar {\sqrt {(k\mp q)(k\pm q+1)}}T_{q\pm 1}^{(k)}} [ J z , T q ( k ) ] = ℏ q T q ( k ) {\displaystyle [J_{z},T_{q}^{(k)}]=\hbar qT_{q}^{(k)}} === Rotation definition === Analogously to how the spherical harmonics transform under a rotation, a general spherical tensor transforms as follows, when the states transform under the unitary Wigner D-matrix D ( R ) {\displaystyle {\mathcal {D}}(R)} , where R is a (3×3 rotation) group element in SO(3). That is, these matrices represent the rotation group elements. With the help of its Lie algebra, one can show these two definitions are equivalent. D ( R ) T q ( k ) D † ( R ) = ∑ q ′ = − k k T q ′ ( k ) D q ′ q ( k ) {\displaystyle {\mathcal {D}}(R)T_{q}^{(k)}{\mathcal {D}}^{\dagger }(R)=\sum _{q'=-k}^{k}T_{q'}^{(k)}{\mathcal {D}}_{q'q}^{(k)}} === Coordinate vectors === For the spherical basis, the coordinates are complex-valued numbers A+, A0, A−, and can be found by substitution of (3B) into (1), or directly calculated from the inner product ⟨, ⟩ (5): A 0 = ⟨ e 0 , A ⟩ = ⟨ e z , A ⟩ = A z {\displaystyle A_{0}=\left\langle \mathbf {e} _{0},\mathbf {A} \right\rangle =\left\langle \mathbf {e} _{z},\mathbf {A} \right\rangle =A_{z}} with inverse relations: In general, for two vectors with complex coefficients in the same real-valued orthonormal basis ei, with the property ei·ej = δij, the inner product is: where · is the usual dot product and the complex conjugate must be used to keep the magnitude (or "norm") of the vector positive definite. == Properties (three dimensions) == === Orthonormality === The spherical basis is an orthonormal basis, since the inner product ⟨, ⟩ (5) of every pair vanishes meaning the basis vectors are all mutually orthogonal: ⟨ e + , e − ⟩ = ⟨ e − , e 0 ⟩ = ⟨ e 0 , e + ⟩ = 0 {\displaystyle \left\langle \mathbf {e} _{+},\mathbf {e} _{-}\right\rangle =\left\langle \mathbf {e} _{-},\mathbf {e} _{0}\right\rangle =\left\langle \mathbf {e} _{0},\mathbf {e} _{+}\right\rangle =0} and each basis vector is a unit vector: ⟨ e + , e + ⟩ = ⟨ e − , e − ⟩ = ⟨ e 0 , e 0 ⟩ = 1 {\displaystyle \left\langle \mathbf {e} _{+},\mathbf {e} _{+}\right\rangle =\left\langle \mathbf {e} _{-},\mathbf {e} _{-}\right\rangle =\left\langle \mathbf {e} _{0},\mathbf {e} _{0}\right\rangle =1} hence the need for the normalizing factors of 1 / 2 {\displaystyle 1/\!{\sqrt {2}}} . === Change of basis matrix === The defining relations (3A) can be summarized by a transformation matrix U: ( e + e − e 0 ) = U ( e x e y e z ) , U = ( − 1 2 − i 2 0 + 1 2 − i 2 0 0 0 1 ) , {\displaystyle {\begin{pmatrix}\mathbf {e} _{+}\\\mathbf {e} _{-}\\\mathbf {e} _{0}\end{pmatrix}}=\mathbf {U} {\begin{pmatrix}\mathbf {e} _{x}\\\mathbf {e} _{y}\\\mathbf {e} _{z}\end{pmatrix}}\,,\quad \mathbf {U} ={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&-{\frac {i}{\sqrt {2}}}&0\\+{\frac {1}{\sqrt {2}}}&-{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,,} with inverse: ( e x e y e z ) = U − 1 ( e + e − e 0 ) , U − 1 = ( − 1 2 + 1 2 0 + i 2 + i 2 0 0 0 1 ) . {\displaystyle {\begin{pmatrix}\mathbf {e} _{x}\\\mathbf {e} _{y}\\\mathbf {e} _{z}\end{pmatrix}}=\mathbf {U} ^{-1}{\begin{pmatrix}\mathbf {e} _{+}\\\mathbf {e} _{-}\\\mathbf {e} _{0}\end{pmatrix}}\,,\quad \mathbf {U} ^{-1}={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&+{\frac {1}{\sqrt {2}}}&0\\+{\frac {i}{\sqrt {2}}}&+{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,.} It can be seen that U is a unitary matrix, in other words its Hermitian conjugate U† (complex conjugate and matrix transpose) is also the inverse matrix U−1. For the coordinates: ( A + A − A 0 ) = U ∗ ( A x A y A z ) , U ∗ = ( − 1 2 + i 2 0 + 1 2 + i 2 0 0 0 1 ) , {\displaystyle {\begin{pmatrix}A_{+}\\A_{-}\\A_{0}\end{pmatrix}}=\mathbf {U} ^{\mathrm {} }{\begin{pmatrix}A_{x}\\A_{y}\\A_{z}\end{pmatrix}}\,,\quad \mathbf {U} ^{\mathrm {} }={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&+{\frac {i}{\sqrt {2}}}&0\\+{\frac {1}{\sqrt {2}}}&+{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,,} and inverse: ( A x A y A z ) = ( U ∗ ) − 1 ( A + A − A 0 ) , ( U ∗ ) − 1 = ( − 1 2 + 1 2 0 − i 2 − i 2 0 0 0 1 ) . {\displaystyle {\begin{pmatrix}A_{x}\\A_{y}\\A_{z}\end{pmatrix}}=(\mathbf {U} ^{\mathrm {} })^{-1}{\begin{pmatrix}A_{+}\\A_{-}\\A_{0}\end{pmatrix}}\,,\quad (\mathbf {U} ^{\mathrm {} })^{-1}={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&+{\frac {1}{\sqrt {2}}}&0\\-{\frac {i}{\sqrt {2}}}&-{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,.} === Cross products === Taking cross products of the spherical basis vectors, we find an obvious relation: e q × e q = 0 {\displaystyle \mathbf {e} _{q}\times \mathbf {e} _{q}={\boldsymbol {0}}} where q is a placeholder for +, −, 0, and two less obvious relations: e ± × e ∓ = ± i e 0 {\displaystyle \mathbf {e} _{\pm }\times \mathbf {e} _{\mp }=\pm i\mathbf {e} _{0}} e ± × e 0 = ± i e ± {\displaystyle \mathbf {e} _{\pm }\times \mathbf {e} _{0}=\pm i\mathbf {e} _{\pm }} === Inner product in the spherical basis === The inner product between two vectors A and B in the spherical basis follows from the above definition of the inner product: ⟨ A , B ⟩ = A + B + ⋆ + A − B − ⋆ + A 0 B 0 ⋆ {\displaystyle \left\langle \mathbf {A} ,\mathbf {B} \right\rangle =A_{+}B_{+}^{\star }+A_{-}B_{-}^{\star }+A_{0}B_{0}^{\star }}
Crucible (software)
Crucible is a collaborative code review application by Australian software company Atlassian. Like other Atlassian products, Crucible is a Web-based application primarily aimed at enterprise, and certain features that enable peer review of a codebase may be considered enterprise social software. Crucible is particularly tailored to remote workers, and facilitates asynchronous review and commenting on code. Crucible also integrates with popular source control tools, such as Git and Subversion. Crucible is not open source, but customers are allowed to view and modify the code for their own use.
Imix video cube
The Imix (also known as ImMix) Video Cube is one of the first computer non-linear editing systems that was a full broadcast quality online video finishing machine. After its release in 1994, Imix released a more advanced version, the Imix Turbo Cube, which boasted 4 channels of real time layered visual effects. It was a hardware computer system controlled by an Apple Macintosh computer.
Clef (app)
Clef was a San Francisco-based technology company, known for developing a mobile app that created a two-factor authentication for websites. It allowed users to access sites with a single login password management service which stores encrypted passwords in private accounts. It had a standard verification method that requires access to data on the mobile phone to confirm the user's identity. The application required a Wi-Fi or mobile network, and the user could log in by scanning the computer screen with their phone. == History == Clef was founded in 2013 by Mark Hudnall, B. Byrne and Jesse Pollak. It raised $1.6 million in seed funding in November 2014. Clef integrated with many websites and applications, including WordPress. On March 17, 2017, Clef announced they would no longer support the plugin after June 6, 2017; Clef was acquired by Authy, another 2FA service, which later got acquired by Twilio.
Haskins Laboratories
Haskins Laboratories, Inc. is an independent research laboratory, founded in 1935 and located in New Haven, Connecticut since 1970. Many current Haskins researchers are affiliated with Yale University's Child Study Center and/or the University of Connecticut. Haskins is a multidisciplinary and international community of researchers who conduct basic research on spoken and written language and global literacy. A guiding perspective of their research has been to view speech and language as emerging from biological processes, including those of adaptation, response to stimuli, and conspecific interaction. Haskins Laboratories has a long history of technological and theoretical innovation, from creating systems of rules for speech synthesis and development of an early working prototype of a reading machine for the blind to developing the landmark concept of phonemic awareness as the critical preparation for learning to read an alphabetic writing system. == Research tools and facilities == Haskins Laboratories is equipped, in-house, with a comprehensive suite of tools and capabilities to advance its mission of research into language and literacy. As of 2014, these included: Anechoic chamber Electroencephalography BioSemi 264 electrode, 24 bit Active Two System EGI 128 electrode, Geodesic EEG System 300 Electromagnetic articulography (EMMA) Carstens AG501 NDI WAVE Eye tracking: HL is equipped with 3 SR Research eye-trackers. 2 Model Eyelink 1000 systems. 1 Model Eyelink 1000plus system. Magnetic resonance imaging: Haskins has access to MRI scanners through agreements with the University of Connecticut and the Yale School of Medicine. On-site, HL has a Linux computer cluster dedicated to analysis of MRI data. Motion capture: HL is equipped with a Vicon motion capture system with one Basler high-speed digital camera, six Vicon MX T-20 cameras and a Vicon MX Giganet for synching camera data and connecting cameras to the data capture computer. Near infrared spectroscopy: HL has a TechEn CW6 8x8 system (four emitters; eight detectors). Ultrasound sonogram == History == Many researchers have contributed to scientific breakthroughs at Haskins Laboratories since its founding. All of them are indebted to the pioneering work and leadership of Caryl Parker Haskins, Franklin S. Cooper, Alvin Liberman, Seymour Hutner and Luigi Provasoli. The history presented here focuses on the research program of the division of Haskins Laboratories that, since the 1940s, has been most well known for its work in the areas of speech, language, and reading. === 1930s === Caryl Haskins and Franklin S. Cooper established Haskins Laboratories in 1935. It was originally affiliated with Harvard University, MIT, and Union College in Schenectady, NY. Caryl Haskins conducted research in microbiology, radiation physics, and other fields in Cambridge, MA and Schenectady. In 1939 Haskins Laboratories moved its center to New York City. Seymour Hutner joined the staff to set up a research program in microbiology, genetics, and nutrition. The descendant of the division led by Hutner program eventually became a department of Pace University in New York. The two identically named organizations are no longer formally affiliated. === 1940s === The U. S. Office of Scientific Research and Development, under Vannevar Bush asked Haskins Laboratories to evaluate and develop technologies for assisting blinded World War II veterans. Experimental psychologist Alvin Liberman joined Haskins Laboratories to assist in developing a "sound alphabet" to represent the letters in a text for use in a reading machine for the blind. Luigi Provasoli joined Haskins Laboratories to set up a research program in marine biology. The program in marine biology moved to Yale University in 1970 and disbanded with Provasoli's retirement in 1978. === 1950s === Franklin S. Cooper invented the pattern playback, a machine that converts pictures of the acoustic patterns of speech back into sound. With this device, Alvin Liberman, Cooper, and Pierre Delattre (and later joined by Katherine Safford Harris, Leigh Lisker, Arthur Abramson, and others), discovered the acoustic cues for the perception of phonetic segments (consonants and vowels). Liberman and colleagues proposed a motor theory of speech perception to resolve the acoustic complexity: they hypothesized that we perceive speech by tapping into a biological specialization, a speech module, that contains knowledge of the acoustic consequences of articulation. Liberman, aided by Frances Ingemann and others, organized the results of the work on speech cues into a groundbreaking set of rules for speech synthesis by the Pattern Playback. === 1960s === Franklin S. Cooper and Katherine Safford Harris, working with Peter MacNeilage, were the first researchers in the U.S. to use electromyographic techniques, pioneered at the University of Tokyo, to study the neuromuscular organization of speech. Leigh Lisker and Arthur Abramson looked for simplification at the level of articulatory action in the voicing of certain contrasting consonants. They showed that many acoustic properties of voicing contrasts arise from variations in voice onset time, the relative phasing of the onset of vocal cord vibration and the end of a consonant. Their work has been widely replicated and elaborated, here and abroad, over the following decades. Donald Shankweiler and Michael Studdert-Kennedy used a dichotic listening technique (presenting different nonsense syllables simultaneously to opposite ears) to demonstrate the dissociation of phonetic (speech) and auditory (nonspeech) perception by finding that phonetic structure devoid of meaning is an integral part of language, typically processed in the left cerebral hemisphere. Liberman, Cooper, Shankweiler, and Studdert-Kennedy summarized and interpreted fifteen years of research in "Perception of the Speech Code", still among the most cited papers in the speech literature. It set the agenda for many years of research at Haskins and elsewhere by describing speech as a code in which speakers overlap (or coarticulate) segments to form syllables. Researchers at Haskins connected their first computer to a speech synthesizer designed by Haskins Laboratories' engineers. Ignatius Mattingly, with British collaborators, John N. Holmes and J.N. Shearme, adapted the Pattern playback rules to write the first computer program for synthesizing continuous speech from a phonetically spelled input. A further step toward a reading machine for the blind combined Mattingly's program with an automatic look-up procedure for converting alphabetic text into strings of phonetic symbols. === 1970s === In 1970, Haskins Laboratories moved to New Haven, Connecticut, and entered into affiliation agreements with Yale University and the University of Connecticut; Haskins remains fully independent of both Yale and UConn, administratively and financially. The lab's original location in New Haven, at 270 Crown Street (from 1970 to 2005), was leased from Yale University. Isabelle Liberman, Donald Shankweiler, and Alvin Liberman teamed up with Ignatius Mattingly to study the relationship between speech perception and reading, a topic implicit in Haskins Laboratories' research program since its inception. They developed the concept of phonemic awareness, the knowledge that would-be readers must be aware of the phonemic structure of their language in order to be able to read. Leonard Katz related the work to contemporary cognitive theory and provided expertise in experimental design and data analysis. Under the broad rubric of the "alphabetic principle", this is the core of the lab's present program of reading pedagogy. Patrick Nye joined Haskins Laboratories to lead a team working on the reading machine for the blind. The project culminated when the addition of an optical character recognizer allowed investigators to assemble the first automatic text-to-speech reading machine. By the end of the decade this technology had advanced to the point where commercial concerns assumed the task of designing and manufacturing reading machines for the blind. In 1973, Franklin S. Cooper was selected to form a panel of six experts charged with investigating the famous 18-minute gap in the White House office tapes of President Richard Nixon related to the Watergate scandal. Building on earlier work, Philip Rubin developed the sinewave synthesis program, which was then used by Robert Remez, Rubin, and colleagues to show that listeners can perceive continuous speech without traditional speech cues from a pattern of sinewaves that track the changing resonances of the vocal tract. This paved the way for a view of speech as a dynamic pattern of trajectories through articulatory-acoustic space. Philip Rubin and colleagues developed Paul Mermelstein's anatomically simplified vocal tract model, originally worked on at Bell Laboratories, into the first articulatory synthesizer that can be controlled in a phy
Qlone
Qlone is a 3D scanning app based on photogrammetry for creation of 3D models on mobile devices. The resultant 3D models can be exported for external use. Qlone was featured at the Apple Worldwide Developers Conference in 2021. It was also featured on BBC Click. == Qlone features == === 3D scanning === 3D scanning with Qlone requires the use of an included mat design. The user prints the mat onto a sheet of paper, then places the object to be scanned in the centre of the mat. An augmented reality dome within the Qlone app guides the user through the subsequent scanning process. The iOS version of Qlone allows scanning without the mat. === 3D editing === Qlone's editing features allow users to adjust 3D scanned models using texture mapping, polygon mesh size simplification, digital sculpting, cleaning and smoothing, and artistic effects. === File export === Qlone exports directly to multiple 3D platforms including SketchFab, i.materialise, Lens Studio for Snapchat, Shapeways and CGTrader. Models can also be exported in different 3D formats for use in other 3D tools – OBJ, STL, FBX, USDZ, GLB (Binary gLTF), PLY, and X3D. == Use in Science, Education and Academia == Due to its inexpensive, simple and accessible nature for creating 3D models, Qlone was used in many academically educational and scientific research projects. The European Space Agency used Qlone to scan rocks in a Tele-Robotic rock collection experiment. Neurosurgeons from the University of Southern California and surgeons from Tulane University School of Medicine used Qlone to create 3D models of cadaveric specimens and anatomical models with the aim of increasing access to such components for enhancing anatomy training and allowing realistic surgical simulations for neurosurgeons and practitioners worldwide. Archaeologists from Texas A&M University used Qlone to create 3D replicas of artifacts and models and students from Vancouver iTech Preparatory Middle School used Qlone to create 3D scans of more than 100 artifacts from Fort Vancouver National Historic Site.
Frankenstein complex
The Frankenstein complex is a term coined by Isaac Asimov in his robot series, referring to the fear of mechanical men. == History == Some of Asimov's science fiction short stories and novels predict that this suspicion will become strongest and most widespread in respect of "mechanical men" that most-closely resemble human beings (see android), but it is also present on a lower level against robots that are plainly electromechanical automatons. The "Frankenstein complex" is similar in many respects to Masahiro Mori's uncanny valley hypothesis. The name, "Frankenstein complex", is derived from the name of Victor Frankenstein in the 1818 novel Frankenstein; or, The Modern Prometheus by Mary Shelley. In Shelley's story, Frankenstein created an intelligent, somewhat superhuman being, but he finds that his creation is horrifying to behold and abandons it. This ultimately leads to Victor's death at the conclusion of a vendetta between himself and his creation. In much of his fiction, Asimov depicts the general attitude of the public towards robots as negative, with ordinary people fearing that robots will either replace them or dominate them, although dominance would not be allowed under the specifications of the Three Laws of Robotics, the first of which is: "A robot may not harm a human being or, through inaction, allow a human being to come to harm." However, Asimov's fictitious earthly public is not fully persuaded by this, and remains largely suspicious and fearful of robots. I, Robot's short story "Little Lost Robot" is about this "fear of robots". In Asimov's robot novels, the Frankenstein complex is a major problem for roboticists and robot manufacturers. They do all they can to reassure the public that robots are harmless, even though this sometimes involves hiding the truth because they think that the public would misunderstand it. The fear by the public and the response of the manufacturers is an example of the theme of paternalism, the dread of paternalism, and the conflicts that arise from it in Asimov's fiction. The same theme occurs in many later works of fiction featuring robots, although it is rarely referred to as such.