Environmental informatics

Environmental informatics is the science of information applied to environmental science. As such, it provides the information processing and communication infrastructure to the interdisciplinary field of environmental sciences aiming at data, information and knowledge integration, the application of computational intelligence to environmental data as well as the identification of environmental impacts of information technology. Environmental informatics thus acts as a bridge, providing an interdisciplinary means of analysing, describing and understanding the complex interactions between humans, nature and technology. Since each field of applied computer science has its own subject matter, terminology and methods, specialised disciplines, such as environmental, bio- and geoinformatics have emerged, each of which combines computer science with a specific field of application such as environmental, bio- or geosciences. Environmental informatics, bioinformatics and geoinformatics all deal with computer-based processing of environmental phenomena. However, environmental informatics is the only field that pursues normative goals (e.g., political goals of environmental protection, environmental planning, and sustainability). This also influences the choice of methods. This also distinguishes it from application areas such as numerical weather prediction, which is considered an early and important example of computer simulation of environmental phenomena. The UK Natural Environment Research Council defines environmental informatics as the "research and system development focusing on the environmental sciences relating to the creation, collection, storage, processing, modelling, interpretation, display and dissemination of data and information." Kostas Karatzas defined environmental informatics as the "creation of a new 'knowledge-paradigm' towards serving environmental management needs." Karatzas argued further that environmental informatics "is an integrator of science, methods and techniques and not just the result of using information and software technology methods and tools for serving environmental engineering needs." Environmental informatics emerged in early 1990 in Central Europe. Current initiatives to effectively manage, share, and reuse environmental and ecological data are indicative of the increasing importance of fields like environmental informatics and ecoinformatics to develop the foundations for effectively managing ecological information. Examples of these initiatives are National Science Foundation Datanet projects, DataONE and Data Conservancy. == Subject matter and objectives == The subject of environmental informatics are environmental information systems (EIS). An EIS 'is a computer-based system that integrates and stores data collected about the natural environment and provides powerful methods for accessing and evaluating it.' This allows environmental data to be processed by computers for environmental protection, planning, research and technology. According to Jaeschke and Bossel, environmental informatics has three interrelated objectives: Environmental informatics serves to procure data and information for describing the state and development of the environment. Of particular importance is information that is needed to prevent or limit undesirable changes and to support desirable changes. Based on the evaluation and analysis of data, environmental informatics improves our understanding of the environment and the interactions between nature, technology and society. It thus supports environmentally relevant decisions. This enables the influence of development (system correction), the assessment of the effects and side effects of potential measures, and the creation of tools for the routine planning, implementation and monitoring of measures. == History == The simulation model World3, which formed the basis of the highly acclaimed study The Limits to Growth, is considered the starting point of environmental informatics. It incorporated environmental information, among other things, to calculate scenarios for global development. In the mid-1980s, interest grew in structuring environmental protection as an area of application for computer science. One of the first publications in German was the book Informatik im Umweltschutz. Anwendungen und Perspektiven (Computer science in environmental protection. Applications and perspectives) from 1986. The term 'environmental informatics' did not appear until around 1993, which is why the development of environmental informatics is usually referred to as having taken place in the 1990s. In 1993, the first university chair for environmental informatics was established in Cottbus. In 1994, the anthology Umweltinformatik. Informatikmethoden für Umweltschutz und Umweltforschung (Environmental Informatics: Informatics Methods for Environmental Protection and Environmental Research) was published. The development of environmental informatics was 'primarily initiated by German computer science.' In the English-speaking world, the volume Environmental Informatics was published in 1995, mainly based on the German anthology of 1994. An article in the conference proceedings of the World Computer Congress of the International Federation for Information Processing (IFIP) in Hamburg in 1994 describes the initial situation of environmental informatics as follows: 'On the one hand, we suffer from the huge amount of available data – people sometimes speak of data graveyards – on the other hand, the really relevant data may still be missing.' This statement indicates the need that led to the emergence of environmental informatics as a specialised discipline of applied computer science. Furthermore, the specific characteristics and processing requirements of environmental data necessitated the emergence of environmental informatics. The special features of environmental data include: The data structures required are highly heterogeneous due to specific processes and differing perspectives on environmental aspects (e.g., water protection, emission control, hazardous substances). In addition to the heterogeneity of the data, heterogeneous databases also play a role, as environmental data is often obtained and presented in an interdisciplinary manner. Obligations change frequently as a result of new legislation, whether regional (e.g. state regulations on water protection), national (e.g. federal emission control regulations) or international (e.g. Registration, Evaluation, Authorisation and Restriction of Chemicals|REACH). The objects represented are often multidimensional and, therefore, require complex geometric representation using curves or polygons. It is often necessary to process uncertain, imprecise or incomplete data, which is, for example, the result of extrapolations or forecasts. A new "knowledge paradigm" has emerged to meet the requirements of environmental management. Environmental informatics produces its own concepts, methods and techniques and is not merely the result of using information and communication technology methods and tools to meet environmental requirements. The development of environmental informatics since the 1990s has been significantly influenced by the newly established conferences EnviroInfo, ISESS and ITEE and is documented in the respective proceedings. Aspects of sustainability and sustainable development were increasingly integrated into environmental informatics after 2000, thereby expanding the field. In 2004, the Working Group on Sustainable Information Society of the Gesellschaft für Informatik e. V. (German Informatics Society, GI) published the Memorandum on a Sustainable Information Society, which formulates recommendations for an information society that is compatible with human, social and natural needs. Since 2007, environmental informatics has often been described in more detail as informatics for environmental protection, sustainable development and risk management. The increased focus on sustainability has also contributed to the formation of the research focus Information and Communications Technology for Sustainability (ICT4S) and to the emergence of the international conference ICT4S in 2013. ICT-ENSURE, the European Commission's funding measure for the establishment of a European research area on "ICT for Environmental Sustainability Research" (2008–2010), has also contributed to the structuring of environmental informatics. == Environmental informatics and sustainable development == Efforts to place environmental informatics within the context of sustainable development have been growing since 2000 and were significantly influenced by the Memorandum on a Sustainable Information Society. According to this Memorandum, the information society offers great but unevenly distributed opportunities for education, participation and intercultural understanding. In addition, the Memorandum highlighted the material and energy consumption of inf

List of ARM Cortex-M development tools

This is a list of development tools for 32-bit ARM Cortex-M-based microcontrollers, which consists of Cortex-M0, Cortex-M0+, Cortex-M1, Cortex-M3, Cortex-M4, Cortex-M7, Cortex-M23, Cortex-M33, Cortex-M35P, Cortex-M52, Cortex-M55, and Cortex-M85 cores. == Development toolchains == IDE, compiler, linker, debugger, flashing (in alphabetical order): Ac6 System Workbench for STM32 (based on Eclipse and the GNU GCC toolchain with direct support for all ST-provided evaluation boards, Eval, Discovery and Nucleo, debug with ST-LINK) ARM Development Studio 5 by ARM Ltd. Atmel Studio by Atmel (based on Visual Studio and GNU GCC Toolchain) Code Composer Studio by Texas Instruments CoIDE by CooCox (note - website dead since 2018) Crossware Development Suite for ARM by Crossware CrossWorks for ARM by Rowley Dave by Infineon. For XMC processors only. Includes project wizard, detailed register decoding and a code library still under development. DRT by SOMNIUM Technologies. Based on GCC toolchain and proprietary linker technology. Available as a plugin for Atmel Studio and an Eclipse-based IDE. EmBitz (formerly Em::Blocks) – free, fast (non-eclipse) IDE for ST-LINK (live data updates), OpenOCD, including GNU Tools for ARM and project wizards for ST, Atmel, EnergyMicro etc. Embeetle IDE - free, fast (non-eclipse) IDE. Works both on Linux and Windows. emIDE by emide – free Visual Studio Style IDE including GNU Tools for ARM GNU ARM Eclipse – A family of Eclipse CDT extensions and tools for GNU ARM development GNU Tools (aka GCC) for ARM Embedded Processors by ARM Ltd – free GCC for bare metal IAR Embedded Workbench for ARM by IAR Systems ICC by ImageCraft Keil MDK-ARM by Keil LPCXpresso by NXP (formerly Red Suite by Code Red Technologies) MikroC by mikroe – mikroC MULTI by Green Hills Software, for all Arm 7, 9, Cortex-M, Cortex-R, Cortex-A Ride and RKit for ARM by Raisonance SEGGER Embedded Studio for ARM by Segger. SEGGER Ozone by Segger. STM32CubeIDE by STMicroelectronics - Combines STCubeMX with TrueSTUDIO into a single Eclipse style package Sourcery CodeBench by Mentor Graphics TASKING VX-Toolset by Altium TrueSTUDIO by Atollic Visual Studio by Microsoft as IDE, with GNU Tools as compiler/linker – e.g. supported by VisualGDB VXM Design's Buildroot toolchain for Cortex. It integrates GNU toolchain, Nuttx, filesystem and debugger/flasher in one build. winIDEA/winIDEAOpen by iSYSTEM YAGARTO – free GCC (no longer supported) Code::Blocks (EPS edition) (debug with ST-LINK no GDB and no OpenOCD required) IDE for Arduino ARM boards Arduino – IDE for Atmel SAM3X (Arduino Due) Energia – Arduino IDE for Texas Instruments Tiva and CC3200 Notes: == Debugging tools == JTAG and/or SWD debug interface host adapters (in alphabetical order): Black Magic Probe by 1BitSquared. CMSIS-DAP by Mbed. Crossconnect by Rowley Associates. DSTREAM by ARM Holdings Green Hills Probe and SuperTrace Probe by Green Hills Software. iTAG by iSYSTEM. I-jet by IAR Systems. Jaguar by Crossware. J-Link by Segger Supports JTAG and SWD. Supports ARM7, ARM9, ARM11, Cortex-A, Cortex-M, Cortex-R, Renesas RX, Microchip PIC32. Eclipse plug-in available. Supports GDB, RDI, Ozone debuggers. J-Trace by Segger. Supports JTAG, SWD, and ETM trace on Cortex-M. JTAGjet by Signum. LPC-LINK by Embedded Artists (for NXP) This is only embedded on NXP LPCXpresso development boards. LPC-LINK 2 by NXP. This device can be reconfigured to support 3 different protocols: J-LINK by Segger, CMSIS-DAP by ARM, Redlink by Code Red. Multilink debug probes, Cyclone in-system programming/debugging interfaces, and a GDB Server plug-in for Eclipse-based ARM IDEs by PEmicro. OpenOCD open source GDB server supports a variety of JTAG probes OpenOCD Eclipse plug-in available in GNU ARM Eclipse Plug-ins. AK-OPENJTAG by Artekit (Open JTAG-compatible). AK-LINK by Artekit. PEEDI by RONETIX Debug Probe by Raspberry Pi. RLink by Raisonance. ST-LINK/V2 by STMicroelectronics The ST-LINK/V2 debugger embedded on STM32 Nucleo and Discovery development boards can be converted to SEGGER J-LINK protocol. TRACE32 Debugger and ETM/ITM Trace by Lauterbach. ULINK by Keil. Debugging tools and/or debugging plug-ins (in alphabetical order): Memfault Error Analysis for post mortem debugging Percepio Tracealyzer, RTOS trace visualizer (with Eclipse plugin). Segger SystemView, RTOS trace visualizer. == Real-time operating systems == Commonly referred to as RTOS: == C/C++ software libraries == The following are free C/C++ libraries: ARM Cortex libraries: Cortex Microcontroller Software Interface Standard (CMSIS) libopencm3 (formerly called libopenstm32) libmaple for STM32F1 chips LPCOpen for NXP LPC chips Alternate C standard libraries: Bionic libc, dietlibc, EGLIBC, glibc, klibc, musl, Newlib, uClibc FAT file system libraries: EFSL, FatFs, Petit FatFs Fixed-point math libraries: libfixmath, fixedptc, FPMLib Encryption libraries: Comparison of TLS implementations wolfSSL == Non-C/C++ computer languages and software libraries ==

Mortimer Rogoff

Mortimer Alan Rogoff (May 2, 1921 – August 1, 2008) was an American inventor, businessman, and author as well as an amateur photographer and radio operator. He is recognized for his work in spread spectrum technology which is the technology that modern cell phones and GPS systems are based on. He is also considered the grandfather of the electronic navigation chart. == Early life == Rogoff was born in Brooklyn, New York. He earned his B.S.E.E. from Rensselaer Polytechnic Institute in 1943 and his M.S.E.E. from Columbia University in 1948. While at Rensselaer he was a member of Kappa Nu fraternity and the Features Editor for the student newspaper. During World War II, he enlisted in the United States Navy and worked on developing radio communication and aerial navigation systems. One of the techniques he developed was undetectable by Axis forces because its power was below that of the background noise and its frequency varied in random ways. This secure transmission was the beginning of spread spectrum technology which would become the basis for GPS and CDMA cellular telephone systems. Although he was never able to patent the technology because it was a military secret he did get some recognition for it almost forty years later when he received the Institute of Electrical and Electronics Engineers’ Pioneer Award in 1981. == Career == Rogoff worked for twenty-two years (1946 to 1968) for ITT Laboratories in New Jersey. In 1958, he became their deputy director of Engineering. He was Vice President of ITT Laboratories from 1962 to 1963. From 1963 to 1968, he was promoted to the corporate staff where he became head of European operations. In 1968 he left ITT to work for the Diebold Group where he became an Executive Vice President. After leaving the Diebold Group he founded several technology and automation businesses, including his own consulting firm, and Teletext Communications Corporation. Later in the 1970s, he was a Principal with Booz Allen Hamilton. In 1979, his book ‘’Calculator Navigation’’ was published. This book demonstrated practical methods for calculating precise ship locations using radio navigation with a consumer calculator. In 1981, he founded a new company, Navigation Sciences Inc., in Bethesda, Maryland. With this company he patented a method for marine navigation that combined radar maps with electronic charts in 1986. This was a major advancement in field. Today, this system is known as the Electronic Chart Display and Information System (ECDIS). Rogoff had seen the need for a new charting system in 1968 from his apartment at 180 East End Avenue in New York City. From there, he saw a boating accident where a life was lost and decided there had to be a way to automate navigation. Rogoff then became of member of the International Maritime Organization’s (IMO) sub-committee on Safety of Navigation, a representative to the International Electrotechnical Commission, and became the chairman of the Radio Technical Commission for Maritime Services Special Committee 109 on Electronic Charts. He was able to use his influence on these boards to push through a proposal of ECDIS standards in 1989 where none has been before. As his friend Giuseppe Carnevali said, “Although nobody could argue against the need for a standard, no one was ready to endorse one; however, nobody was brave enough to oppose it.” A Test Bed project on these proposals was conducted by the United States Coast Guard. The amended standards were accepted by the IMO in November, 1995. In 2000, he was named as a Fellow of the Institute of Navigation. He was also a Fellow of the Institute of Electrical and Electronics Engineers. During this time, he was also president of the Navigational Electronic Charts System Association. == Personal == In 1979, he moved to Washington, D.C. and bought a home in Nantucket, Massachusetts. He married Sheila Zunser in 1943 and they were together for sixty-five years. They had three daughters: Louisa Thompson, Alice Rogoff, and Julia Peach. His sister was sociologist Natalie Rogoff Ramsøy of the University of Oslo. He was a member of the Cosmos Club and President of The Navigational Electronic Chart System Association (NECSA). He was a very good amateur photographer and liked amateur radio (call sign W2EE). He died in Nantucket from bladder cancer. == Patents == Patent number: 4176316 – Secure Communication System – November 27, 1979 With Louis A. DeRosa Patent number: 4590569 – Electronic Navigation System – May 20, 1986 With Peter M. Winkler and John N. Ackley Patent number: RE34004 – Secure Communication System – July 21, 1992 With Louis A. DeRosa == Publications == Rogoff, Mortimer September 1957. Automatic Analysis of Infrared Spectra. Annals of the New York Academy of Sciences; vol. 69: no. 1: 27–37. Gen. P.C. Sandretto and Mortimer Rogoff. 1958 “A Novel Concept for Application to the Control of Airways Traffic.” NAVIGATION: Journal of The Institute of Navigation; vol. 6: no. 2: 102–107 Rogoff, Mortimer 1979. Calculator Navigation; ISBN 0-393-03192-6. Published by W.W. Norton & Company (New York and London). Rogoff, Mortimer December 1985. Electronic Charting. Yachting; vol. 158: no. 6: 54–57. Rogoff, Mortimer Winter 1990. Electronic Charts in the Nineties. NAVIGATION: Journal of The Institute of Navigation; vol. 37: no. 4: 305–318.

Temporal resolution

Temporal resolution (TR) refers to the discrete resolution of a measurement with respect to time. It is defined as the amount of time needed to revisit and acquire data for the same location. When applied to remote sensing, this amount of time is influenced by the sensor platform's orbital characteristics and the features of the sensor itself. The temporal resolution is low when the revisiting delay is high and vice versa. Temporal resolution is typically expressed in days. == Physics == Often there is a trade-off between the temporal resolution of a measurement and its spatial resolution, due to Heisenberg's uncertainty principle. In some contexts, such as particle physics, this trade-off can be attributed to the finite speed of light and the fact that it takes a certain period of time for the photons carrying information to reach the observer. In this time, the system might have undergone changes itself. Thus, the longer the light has to travel, the lower the temporal resolution. == Technology == === Computing === In another context, there is often a tradeoff between temporal resolution and computer storage. A transducer may be able to record data every millisecond, but available storage may not allow this, and in the case of 4D PET imaging the resolution may be limited to several minutes. === Electronic displays === In some applications, temporal resolution may instead be equated to the sampling period, or its inverse, the refresh rate, or update frequency in Hertz, of a TV, for example. The temporal resolution is distinct from temporal uncertainty. This would be analogous to conflating image resolution with optical resolution. One is discrete, the other, continuous. The temporal resolution is a resolution somewhat the 'time' dual to the 'space' resolution of an image. In a similar way, the sample rate is equivalent to the pixel pitch on a display screen, whereas the optical resolution of a display screen is equivalent to temporal uncertainty. Note that both this form of image space and time resolutions are orthogonal to measurement resolution, even though space and time are also orthogonal to each other. Both an image or an oscilloscope capture can have a signal-to-noise ratio, since both also have measurement resolution. === Oscilloscopy === An oscilloscope is the temporal equivalent of a microscope, and it is limited by temporal uncertainty the same way a microscope is limited by optical resolution. A digital sampling oscilloscope has also a limitation analogous to image resolution, which is the sample rate. A non-digital non-sampling oscilloscope is still limited by temporal uncertainty. The temporal uncertainty can be related to the maximum frequency of continuous signal the oscilloscope could respond to, called the bandwidth and given in Hertz. But for oscilloscopes, this figure is not the temporal resolution. To reduce confusion, oscilloscope manufacturers use 'Sa/s' instead of 'Hz' to specify the temporal resolution. Two cases for oscilloscopes exist: either the probe settling time is much shorter than the real time sampling rate, or it is much larger. The case where the settling time is the same as the sampling time is usually undesirable in an oscilloscope. It is more typical to prefer a larger ratio either way, or if not, to be somewhat longer than two sample periods. In the case where it is much longer, the most typical case, it dominates the temporal resolution. The shape of the response during the settling time also has as strong effect on the temporal resolution. For this reason probe leads usually offer an arrangement to 'compensate' the leads to alter the trade off between minimal settling time, and minimal overshoot. If it is much shorter, the oscilloscope may be prone to aliasing from radio frequency interference, but this can be removed by repeatedly sampling a repetitive signal and averaging the results together. If the relationship between the 'trigger' time and the sample clock can be controlled with greater accuracy than the sampling time, then it is possible to make a measurement of a repetitive waveform with much higher temporal resolution than the sample period by upsampling each record before averaging. In this case the temporal uncertainty may be limited by clock jitter.

Link-richness

Link-richness is the quality, possessed by some websites, of having many hyperlinks. Classified advertising sites like Craigslist tend to be very link-rich, sometimes with hundreds of links on their main page. They help users find the links they are looking for by grouping links into clusters. Inadequate link richness has been described as frustrating to readers, as it reduces transparency of site content from the main page. Students new to wiki collaboration were found to need guidance in how to take full advantage of the medium's potential for creating link-rich content. Link-richness in some contexts can be distracting, as when an article is surrounded by extraneous links. Indeed, it is becoming accepted as a best practice for universities to have link-rich home pages that do not rely on user categorisation and exploration of long sequences of links and are not constrained by traditional boundaries between departments. Tools are sometimes needed to make the publishing of link-rich web sites tractable, and many people may lack the technical skills, time, or inclination to engage in hand- crafting new digital document forms. A link-rich site that is low on content is sometimes referred to as a "gateway site." Link-rich portals were popular on the Web in 2000. Yahoo! and other sites featuring categories with many links were heavily used and often required fewer than three clicks to reach the content. Web designers were creating flat sites with content positioned close to the top of pages.

Tensor operator

In pure and applied mathematics, quantum mechanics and computer graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. The coordinate-free generalization of a tensor operator is known as a representation operator. == The general notion of scalar, vector, and tensor operators == In quantum mechanics, physical observables that are scalars, vectors, and tensors, must be represented by scalar, vector, and tensor operators, respectively. Whether something is a scalar, vector, or tensor depends on how it is viewed by two observers whose coordinate frames are related to each other by a rotation. Alternatively, one may ask how, for a single observer, a physical quantity transforms if the state of the system is rotated. Consider, for example, a system consisting of a molecule of mass M {\displaystyle M} , traveling with a definite center of mass momentum, p z ^ {\displaystyle p{\mathbf {\hat {z}} }} , in the z {\displaystyle z} direction. If we rotate the system by 90 ∘ {\displaystyle 90^{\circ }} about the y {\displaystyle y} axis, the momentum will change to p x ^ {\displaystyle p{\mathbf {\hat {x}} }} , which is in the x {\displaystyle x} direction. The center-of-mass kinetic energy of the molecule will, however, be unchanged at p 2 / 2 M {\displaystyle p^{2}/2M} . The kinetic energy is a scalar and the momentum is a vector, and these two quantities must be represented by a scalar and a vector operator, respectively. By the latter in particular, we mean an operator whose expected values in the initial and the rotated states are p z ^ {\displaystyle p{\mathbf {\hat {z}} }} and p x ^ {\displaystyle p{\mathbf {\hat {x}} }} . The kinetic energy on the other hand must be represented by a scalar operator, whose expected value must be the same in the initial and the rotated states. In the same way, tensor quantities must be represented by tensor operators. An example of a tensor quantity (of rank two) is the electrical quadrupole moment of the above molecule. Likewise, the octupole and hexadecapole moments would be tensors of rank three and four, respectively. Other examples of scalar operators are the total energy operator (more commonly called the Hamiltonian), the potential energy, and the dipole-dipole interaction energy of two atoms. Examples of vector operators are the momentum, the position, the orbital angular momentum, L {\displaystyle {\mathbf {L} }} , and the spin angular momentum, S {\displaystyle {\mathbf {S} }} . (Fine print: Angular momentum is a vector as far as rotations are concerned, but unlike position or momentum it does not change sign under space inversion, and when one wishes to provide this information, it is said to be a pseudovector.) Scalar, vector and tensor operators can also be formed by products of operators. For example, the scalar product L ⋅ S {\displaystyle {\mathbf {L} }\cdot {\mathbf {S} }} of the two vector operators, L {\displaystyle {\mathbf {L} }} and S {\displaystyle {\mathbf {S} }} , is a scalar operator, which figures prominently in discussions of the spin–orbit interaction. Similarly, the quadrupole moment tensor of our example molecule has the nine components Q i j = ∑ α q α ( 3 r α , i r α , j − r α 2 δ i j ) . {\displaystyle Q_{ij}=\sum _{\alpha }q_{\alpha }\left(3r_{\alpha ,i}r_{\alpha ,j}-r_{\alpha }^{2}\delta _{ij}\right).} Here, the indices i {\displaystyle i} and j {\displaystyle j} can independently take on the values 1, 2, and 3 (or x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} ) corresponding to the three Cartesian axes, the index α {\displaystyle \alpha } runs over all particles (electrons and nuclei) in the molecule, q α {\displaystyle q_{\alpha }} is the charge on particle α {\displaystyle \alpha } , and r α , i {\displaystyle r_{\alpha ,i}} is the i {\displaystyle i} -th component of the position of this particle. Each term in the sum is a tensor operator. In particular, the nine products r α , i r α , j {\displaystyle r_{\alpha ,i}r_{\alpha ,j}} together form a second rank tensor, formed by taking the outer product of the vector operator r α {\displaystyle {\mathbf {r} }_{\alpha }} with itself. == Rotations of quantum states == === Quantum rotation operator === The rotation operator about the unit vector n (defining the axis of rotation) through angle θ is U [ R ( θ , n ^ ) ] = exp ⁡ ( − i θ ℏ n ^ ⋅ J ) {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right)} where J = (Jx, Jy, Jz) are the rotation generators (also the angular momentum matrices): J x = ℏ 2 ( 0 1 0 1 0 1 0 1 0 ) J y = ℏ 2 ( 0 i 0 − i 0 i 0 − i 0 ) J z = ℏ ( − 1 0 0 0 0 0 0 0 1 ) {\displaystyle J_{x}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&1&0\\1&0&1\\0&1&0\end{pmatrix}}\,\quad J_{y}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&i&0\\-i&0&i\\0&-i&0\end{pmatrix}}\,\quad J_{z}=\hbar {\begin{pmatrix}-1&0&0\\0&0&0\\0&0&1\end{pmatrix}}} and let R ^ = R ^ ( θ , n ^ ) {\displaystyle {\widehat {R}}={\widehat {R}}(\theta ,{\hat {\mathbf {n} }})} be a rotation matrix. According to the Rodrigues' rotation formula, the rotation operator then amounts to U [ R ( θ , n ^ ) ] = 1 1 − i sin ⁡ θ ℏ n ^ ⋅ J − 1 − cos ⁡ θ ℏ 2 ( n ^ ⋅ J ) 2 . {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=1\!\!1-{\frac {i\sin \theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} -{\frac {1-\cos \theta }{\hbar ^{2}}}({\hat {\mathbf {n} }}\cdot \mathbf {J} )^{2}.} An operator Ω ^ {\displaystyle {\widehat {\Omega }}} is invariant under a unitary transformation U if Ω ^ = U † Ω ^ U ; {\displaystyle {\widehat {\Omega }}={U}^{\dagger }{\widehat {\Omega }}U;} in this case for the rotation U ^ ( R ) {\displaystyle {\widehat {U}}(R)} , Ω ^ = U ( R ) † Ω ^ U ( R ) = exp ⁡ ( i θ ℏ n ^ ⋅ J ) Ω ^ exp ⁡ ( − i θ ℏ n ^ ⋅ J ) . {\displaystyle {\widehat {\Omega }}={U(R)}^{\dagger }{\widehat {\Omega }}U(R)=\exp \left({\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right){\widehat {\Omega }}\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right).} === Angular momentum eigenkets === The orthonormal basis set for total angular momentum is | j , m ⟩ {\displaystyle |j,m\rangle } , where j is the total angular momentum quantum number and m is the magnetic angular momentum quantum number, which takes values −j, −j + 1, ..., j − 1, j. A general state within the j subspace | ψ ⟩ = ∑ m c j m | j , m ⟩ {\displaystyle |\psi \rangle =\sum _{m}c_{jm}|j,m\rangle } rotates to a new state by: | ψ ¯ ⟩ = U ( R ) | ψ ⟩ = ∑ m c j m U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =U(R)|\psi \rangle =\sum _{m}c_{jm}U(R)|j,m\rangle } Using the completeness condition: I = ∑ m ′ | j , m ′ ⟩ ⟨ j , m ′ | {\displaystyle I=\sum _{m'}|j,m'\rangle \langle j,m'|} we have | ψ ¯ ⟩ = I U ( R ) | ψ ⟩ = ∑ m m ′ c j m | j , m ′ ⟩ ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =IU(R)|\psi \rangle =\sum _{mm'}c_{jm}|j,m'\rangle \langle j,m'|U(R)|j,m\rangle } Introducing the Wigner D matrix elements: D ( R ) m ′ m ( j ) = ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle {D(R)}_{m'm}^{(j)}=\langle j,m'|U(R)|j,m\rangle } gives the matrix multiplication: | ψ ¯ ⟩ = ∑ m m ′ c j m D m ′ m ( j ) | j , m ′ ⟩ ⇒ | ψ ¯ ⟩ = D ( j ) | ψ ⟩ {\displaystyle |{\bar {\psi }}\rangle =\sum _{mm'}c_{jm}D_{m'm}^{(j)}|j,m'\rangle \quad \Rightarrow \quad |{\bar {\psi }}\rangle =D^{(j)}|\psi \rangle } For one basis ket: | j , m ¯ ⟩ = ∑ m ′ D ( R ) m ′ m ( j ) | j , m ′ ⟩ {\displaystyle |{\overline {j,m}}\rangle =\sum _{m'}{D(R)}_{m'm}^{(j)}|j,m'\rangle } For the case of orbital angular momentum, the eigenstates | ℓ , m ⟩ {\displaystyle |\ell ,m\rangle } of the orbital angular momentum operator L and solutions of Laplace's equation on a 3d sphere are spherical harmonics: Y ℓ m ( θ , ϕ ) = ⟨ θ , ϕ | ℓ , m ⟩ = ( 2 ℓ + 1 ) 4 π ( ℓ − m ) ! ( ℓ + m ) ! P ℓ m ( cos ⁡ θ ) e i m ϕ {\displaystyle Y_{\ell }^{m}(\theta ,\phi )=\langle \theta ,\phi |\ell ,m\rangle ={\sqrt {{(2\ell +1) \over 4\pi }{(\ell -m)! \over (\ell +m)!}}}\,P_{\ell }^{m}(\cos {\theta })\,e^{im\phi }} where Pℓm is an associated Legendre polynomial, ℓ is the orbital angular momentum quantum number, and m is the orbital magnetic quantum number which takes the values −ℓ, −ℓ + 1, ... ℓ − 1, ℓ The formalism of spherical harmonics have wide applications in applied mathematics, and are closely related to the formalism of spherical tensors, as shown below. Spherical harmonics are functions of the polar and azimuthal angles, ϕ and θ respectively, which can be conveniently collected into a unit vector n(θ, ϕ) pointing in the direction of those angles, in the Cartesian basis it is: n ^ ( θ , ϕ ) = cos ⁡ ϕ sin ⁡ θ e x + s

WebCL

WebCL (Web Computing Language) is a JavaScript binding to OpenCL for heterogeneous parallel computing within any compatible web browser without the use of plug-ins, first announced in March 2011. It is developed on similar grounds as OpenCL and is considered as a browser version of the latter. Primarily, WebCL allows web applications to actualize speed with multi-core CPUs and GPUs. With the growing popularity of applications that need parallel processing like image editing, augmented reality applications and sophisticated gaming, it has become more important to improve the computational speed. With these background reasons, a non-profit Khronos Group designed and developed WebCL, which is a Javascript binding to OpenCL with a portable kernel programming, enabling parallel computing on web browsers, across a wide range of devices. In short, WebCL consists of two parts, one being Kernel programming, which runs on the processors (devices) and the other being JavaScript, which binds the web application to OpenCL. The completed and ratified specification for WebCL 1.0 was released on March 19, 2014. == Implementation == Currently, no browsers natively support WebCL. However, non-native add-ons are used to implement WebCL. For example, Nokia developed a WebCL extension. Mozilla does not plan to implement WebCL in favor of WebGL Compute Shaders, which were in turn scrapped in favor of WebGPU. Mozilla (Firefox) - hg.mozilla.org/projects/webcl/ === WebCL working draft === Samsung (WebKit) - github.com/SRA-SiliconValley/webkit-webcl (unavailable) Nokia (Firefox) - github.com/toaarnio/webcl-firefox (down since Nov 2014, Last Version for FF 34) Intel (Crosswalk) - www.crosswalk-project.org === Example C code === The basic unit of a parallel program is kernel. A kernel is any parallelizable task used to perform a specific job. More often functions can be realized as kernels. A program can be composed of one or more kernels. In order to realize a kernel, it is essential that a task is parallelizable. Data dependencies and order of execution play a vital role in producing efficient parallelized algorithms. A simple example can be thought of the case of loop unrolling performed by C compilers, where a statement like:can be unrolled into:Above statements can be parallelized and can be made to run simultaneously. A kernel follows a similar approach where only the snapshot of the ith iteration is captured inside kernel. Rewriting the above code using a kernel:Running a WebCL application involves the following steps: Allow access to devices and provide context Hand over the kernel to a device Cause the device to execute the kernel Retrieve results from the device Use the data inside JavaScript Further details about the same can be found at == Exceptions List == WebCL, being a JavaScript based implementation, doesn't return an error code when errors occur. Instead, it throws an exception such as OUT_OF_RESOURCES, OUT_OF_HOST_MEMORY, or the WebCL-specific WEBCL_IMPLEMENTATION_FAILURE. The exception object describes the machine-readable name and human-readable message describing the error. The syntax is as follows: From the code above, it can be observed that the message field can be a NULL value. Other exceptions include: INVALID_OPERATION – if the blocking form of this function is called from a WebCLCallback INVALID_VALUE – if eventWaitList is empty INVALID_CONTEXT – if events specified in eventWaitList do not belong to the same context INVALID_DEVICE_TYPE – if deviceType is given, but is not one of the valid enumerated values DEVICE_NOT_FOUND – if there is no WebCLDevice available that matches the given deviceType More information on exceptions can be found in the specs document. There is another exception that is raised upon trying to call an object that is ‘released’. On using the release method, the object doesn't get deleted permanently but it frees the resources associated with that object. In order to avoid this exception, releaseAll method can be used, which not only frees the resources but also deletes all the associated objects created. == Security == WebCL, being an open-ended software developed for web applications, has lots of scope for vulnerabilities in the design and development fields too. This forced the developers working on WebCL to give security the utmost importance. Few concerns that were addressed are: Out-of-bounds Memory Access: This occurs by accessing the memory locations, outside the allocated space. An attacker can rewrite or erase all the important data stored in those memory locations. Whenever there arises such a case, an error must be generated at the compile time, and zero must be returned at run-time, not letting the program override the memory. A project WebCL Validator, was initiated by the Khronos Group (developers) on handling this vulnerability. Memory Initialization: This is done to prevent the applications to access the memory locations of previous applications. WebCL ensures that this doesn't happen by initializing all the buffers, variables used to zero before it runs the current application. OpenCL 1.2 has an extension ‘cl_khr_initialize_memory’, which enables this. Denial of Service: The most common attack on web applications cannot be eliminated by WebCL or the browser. OpenCL can be provided with watchdog timers and pre-emptive multitasking, which can be used by WebCL in order to detect and terminate the contexts that are taking too long or consume lot of resources. There is an extension of OpenCL 1.2 ‘cl_khr_terminate_context’ like for the previous one, which enables to terminate the process that might cause a denial of service attack. == Related browser bugs == Bug 664147 - [WebCL] add openCL in gecko, Mozilla Bug 115457: [Meta] WebCL support for WebKit, WebKit Bugzilla