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The Froissart–Stora equation describes the change in polarization which a high energy charged particle beam in a storage ring will undergo as it passes through a resonance in the spin tune. It is named after the French physicists Marcel Froissart and Raymond Stora. The polarization following passage through the resonance is given by P y = P y 0 [ 2 exp ( − π | ϵ | 2 2 α 0 ) − 1 ] {\displaystyle P_{y}=P_{y0}\left[2\exp \left({-{\frac {\pi |\epsilon |^{2}}{2\alpha _{0}}}}\right)-1\right]} where ϵ {\displaystyle \epsilon } is the resonance strength and α 0 {\displaystyle \alpha _{0}} is the speed at which the resonance is crossed. P y 0 {\displaystyle P_{y0}} is the initial polarization before resonance crossing. The resonance may be crossed by raising the energy so that the spin tune passes through a resonance, or driven with a transverse magnetic field at a frequency that is in resonance with the spin oscillations. The Froissart–Stora equation has a direct analogy in condensed matter physics in the Landau–Zener effect. == Other spin-dynamics effects == The original Froissart–Stora equation was derived for polarized protons. It may also be applied to polarized electrons in storage rings. In this case, there are additional polarization effects resulting from the synchrotron radiation. In particular, the Sokolov–Ternov effect describes the polarization due to spin flip radiation. In the case of a non-planar ring, this must be generalized as was done by Derbenev and Kondratenko. == Notes ==
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{
"page_id": 38470594,
"source": null,
"title": "Froissart–Stora equation"
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In molecular biology mir-275 microRNA is a short RNA molecule. MicroRNAs function to regulate the expression levels of other genes by several mechanisms. == See also == MicroRNA == References == == Further reading == == External links == Page for mir-275 microRNA precursor family at Rfam
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{
"page_id": 36373443,
"source": null,
"title": "Mir-275 microRNA precursor family"
}
|
Tetra-amido macrocyclic ligands (TAMLs) constitute a class of macrocyclic ligands. When complexed to metals, TAMLs are proposed as environmentally friendly catalysts. Although never commercialized, iron-TAML complexes catalyze the degradation of pesticides, effluent streams from paper mills, dibenzothiophenes from diesel fuels, and anthrax spores. == References ==
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{
"page_id": 4260804,
"source": null,
"title": "Tetra-amido macrocyclic ligand"
}
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The necrobiome has been defined as the community of species associated with decaying remains after the death of an organism. The process of decomposition is complex. Microbes decompose cadavers, but other organisms including fungi, nematodes, insects, and larger scavenger animals also contribute. Once the immune system is no longer active, microbes colonizing the intestines and lungs decompose their respective tissues and then travel throughout the body via the circulatory and lymphatic systems to break down other tissue and bone. During this process, gases are released as a by-product and accumulate, causing bloating. Eventually, the gases seep through the body's wounds and natural openings, providing a way for some microbes to exit from the inside of the cadaver and inhabit the outside. The microbial communities colonizing the internal organs of a cadaver are referred to as the thanatomicrobiome. The region outside of the cadaver that is exposed to the external environment is referred to as the epinecrotic microbial communities of the necrobiome, and is especially important when determining the time and location of death for an individual. Different microbes play specific roles during each stage of the decomposition process. The microbes that colonize the cadaver and the rate of their activity are determined by the cadaver itself and the cadaver's surrounding environmental conditions. == History == There is textual evidence that human cadavers were first studied around the third century BC to gain an understanding of human anatomy. Many of the first human cadaver studies took place in Italy, where the earliest record of determining the cause of death from a human corpse dates back to 1286. However, understanding of the human body progressed slowly, in part because the spread of Christianity and other religious beliefs resulted in human dissection becoming illegal. Non-human animals only were dissected for anatomical understanding until
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"page_id": 56951751,
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the 13th century when officials realized human cadavers were necessary for a better understanding of the human body. It was not until 1676 that Antonie van Leeuwenhoek designed a lens that made it possible to visualize microbes, and not until the late 18th century when microbes were considered useful in understanding the body after death. In modern times, human cadavers are used for research, but other animal models can provide larger sample sizes and produce more controlled studies. Microbial colonization between humans and some non-human animals is so similar that those models can be used to understand the decomposition process for humans. Swine have been used repeatedly to understand the human decomposition process in terrestrial environments. Pigs are suitable for studying human decomposition because of their size, sparse hairs, and similar bacteria found in their GI tracts. Using nonhuman carcasses as study subjects also offers the benefit of minimizing variation in the sample population. Sophisticed molecular techniques have made it possible to identify the microbial communities that inhabit and decompose cadavers; however, this research is fairly new. Studying the necrobiome has become increasingly useful in determining the time and cause of death, which is useful in crime scene investigations. == Applications in forensics == === Microbial forensics === As the necrobiome deals with the various communities of bacteria and other organisms that catalyze the decomposition of plants and animals, this particular biome is an increasingly vital part of forensic science. The microbes occupying the space underneath and around a decomposing body are unique to it—similar to how fingerprints are exclusively unique to only one person. Using this differentiation, forensic investigators at a crime scene are able to distinguish between burial sites, as well as gain concrete factual information about how long the body has been there and the predicted area
|
{
"page_id": 56951751,
"source": null,
"title": "Necrobiome"
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in which the death possibly occurred. Forensic microbiologists investigate ways to determine time and place of death by analyzing the microbes present on the corpse. The microbial timeline of how a body decays is known as the microbial clock. It estimates how long a body has been in a certain place based on microbes present or missing. The succession of bacterial species populating the body after a period of four days is an indicator of minimum time since death. Recent studies have taken place to determine if bacteria alone can inform the post-mortem interval. Bacteria responsible for decomposing cadavers can be difficult to study because the bacteria found on a cadaver vary and change quickly. Bacteria can be brought to a cadaver by scavengers, air, or water. Other environmental factors like temperature and soil can impact the microbes found on a cadaver. The time of death can be estimated not only by the type and amount of bacteria on a cadaver, but also by the chemical compounds produced by those bacteria. Forensic anthropologist Arpad Vass determined, from research he undertook in the 1990s, that three types of fatty acids, produced when bacteria break down fat tissues, muscles, and food remnants in the stomach are useful in predicting the time since death during forensic investigations. === Forensic entomology === Forensic entomology, the study of insects (arthropods) found in decomposing humans, is useful in determining the post-mortem interval after 3–4 days have passed since the death. Various types of flies are usually drawn to a cadaver and typically lay their eggs there. Therefore, both the developmental stages of one species of fly and the succession of different species can give an estimate of how long the person has been deceased. Since the presence and life cycle of insects varies by temperature and
|
{
"page_id": 56951751,
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environmental conditions, this type of analysis cannot give the actual time of death, but results only in a minimum time since death. The deceased could not have been dead longer than the oldest maggot found. Insect activity can also indicate the cause of death. Blowflies typically lay their eggs in natural body cavities that are easily assessible, yet also sheltered. If the pattern of maggot activity appears elsewhere, that could indicate an injury, such as a stab wound, even if the surrounding tissue has decomposed. In the event of a death caused by poison, traces of the toxin may have been consumed by the maggots, without harming them. Since insect species tend to have certain geographic ranges and known habitat preferences, forensic entomologists can determine if a body has been moved after death. Analysis of the insects in the necrobiome can indicate if the death occurred in a different ecological or geographical environment than where the cadaver was found. == Research == === Human cadavers === The decomposition of human bodies is studied at research facilities known as body farms. Seven educational institution house such facilities in the United States: University of Tennessee in Knoxville, Western Carolina University, Texas State University, Sam Houston State University, Southern Illinois University, Colorado Mesa University, and University of South Florida. These facilities study the decomposition of cadavers in all possible manners of decay, including in open or frozen environments, buried underground, or within cars. Through the study of the cadavers, experts examine the microbial timeline and document what is typical in each stage in the various locations that each body is placed. In 2013, at the Southeast Texas Applied Forensics Science facility at Sam Houston State University, researchers documented the bacteria growing in two decomposing cadavers placed in a natural outdoor environment. Their focus
|
{
"page_id": 56951751,
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"title": "Necrobiome"
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was on the bloat stage, when hydrogen sulfide and methane produced by bacteria build up and inflate the cadaver. They found that "by the end of the bloat period...anaerobic bacteria such as Clostridia had become dominant" and swaps of the oral cavity "showed a shift toward Firmicutes, a group of bacteria that includes Clostridia." By 2019, Jennifer Pechal, a forensic science researcher at Michigan State University, had worked with microbes on almost 2,000 human remains in a spectrum of conditions. She proposed a pattern in the necrobiome that concurs with data from scientists in Italy, Austria, and France. They found that a "large, consistent shift in the microbial community" occurs about 48 hours after death, making it "fairly easy to tell if a body has been dead for more or less than 2 days." Pechal also hopes that microbial tests can be used in the future to help pathologists determine undiagnosed medical conditions that were the cause of death. === Non-human remains === A 2019 study at the University of Huddersfield in West Yorkshire, United Kingdom sought to investigate the influence fur has on the necrobiome of rabbits. The experiment involved six dead rabbits purchased from the pet food company, Kiezebrink. The fur was removed from the torsos of three of the test subjects. All six samples were placed on "sterile sand in clean plastic containers." Lids covering the containers prevented birds and other scavengers from accessing the carcasses, while small holes drilled into the sides of the containers allowed air flow and insect activity while the containers were exposed on the roof of a university building. Samples were collected from inside of the mouth, the upper skin of the torso exposed to the air environment, and the bottom skin of the torso in contact with the sand. Proteobacteria were
|
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the most abundant present, followed by Firmicutes, Bacteroidetes, and Actinobacteria during the active stage of decomposition. During the advanced stage of decomposition, Proteobacteria decreased from 99.4% to 81.6% in the oral cavity but were most abundant in the non-fur samples. Firmicutes were the most abundant for the skin samples in both fur and non-fur samples. Finally, Proteobacteria was most abundant in the soil interface during the beginning of decomposition in both fur and non-fur samples. The researchers also noted that Actinobacteria was the least abundant in the active stage and decreased even more during the dry stage. The conclusion of the experiment was that while bacterial communities changed over the course of decomposition, the most significant variation is attributed to different anatomical regions "but independently of the presence of the fur." == Technology and techniques == Techniques for analyzing the necrobiome involve phospholipid fatty acid (PLFA) analysis, total soil fatty acid methyl esters, and DNA profiling. This technology is used to simplify the sample collection into sequences that scientists can read. The simplified sequence of the necrobiome is run through a data bank to match the name of it. Due to the lack of universal algorithm technology, there is a knowledge gap in various platforms across different regions of the world. In order to close that gap, there needs to be an expansion of the technology. However, there are a few obstacles, including identifying needs, research, prototype development, acceptance, and adoption. Researchers are working on an algorithm to predict time since death with an accuracy of within two days, which would be an improvement over time frames given by forensic entomology. Jennifer Pechal states that those computer models must "be tested on bodies with a known time of death to ensure they are accurate." As of 2020, that technology is
|
{
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still 5 to 10 years away from becoming available. == See also == Microbiology of decomposition Biome Human microbiome == References ==
|
{
"page_id": 56951751,
"source": null,
"title": "Necrobiome"
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In molecular biology mir-277 microRNA is a short RNA molecule. MicroRNAs function to regulate the expression levels of other genes by several mechanisms. == See also == MicroRNA == References == == Further reading == == External links == Page for mir-277 microRNA precursor family at Rfam
|
{
"page_id": 36373455,
"source": null,
"title": "Mir-277 microRNA precursor family"
}
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A methylene group is any part of a molecule that consists of two hydrogen atoms bound to a carbon atom, which is connected to the remainder of the molecule by two single bonds. The group may be represented as −CH2− or >CH2, where the '>' denotes the two bonds. This stands in contrast to a situation where the carbon atom is bound to the rest of the molecule by a double bond, which is preferably called a methylidene group, represented =CH2. Formerly the methylene name was used for both isomers. The name “methylene bridge“ can be used for the single-bonded isomer, to emphatically exclude methylidene. The distinction is often important, because the double bond is chemically different from two single bonds. The methylene group should be distinguished from the CH2 molecule called carbene. This was also formerly called methylene. == Activated methylene == The central carbon in 1,3-dicarbonyl compound is known as an activated methylene group. This is because, owing to the structure, the carbon is especially acidic and can easily be deprotonated to form a methylene group. == See also == Carbene Methyl group Methine == References ==
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{
"page_id": 38339537,
"source": null,
"title": "Methylene group"
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In particle physics the Froissart bound, or Froissart limit, is a generic constraint that the total scattering cross section of two colliding high-energy particles cannot increase faster than c ln 2 ( s ) {\displaystyle c\ln ^{2}(s)} , with c a normalization constant and s the square of the center-of-mass energy (s is one of the three Mandelstam variables). == See also == Unitarity (physics) § Unitarity bounds S-matrix theory Regge theory == Further reading == The Froissart bound on scholarpedia, by M. Froissart == References ==
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{
"page_id": 65471441,
"source": null,
"title": "Froissart bound"
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The Creighton process involves the hydrogenation of a 6 carbon chain aldehyde. The reactant is 2,3,4,5,6-pentahydroxyhexanal (an aldehyde) and the product is 1,2,3,4,5,6-hexanehexol (an alcohol). The product thus has two more hydrogen atoms than the reactant: -CHO is replaced by -CH2OH. The Creighton process was patented in the 1920s. == References ==
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{
"page_id": 13698005,
"source": null,
"title": "Creighton process"
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In mathematics, the cobordism hypothesis, due to John C. Baez and James Dolan, concerns the classification of extended topological quantum field theories (TQFTs). In 2008, Jacob Lurie outlined a proof of the cobordism hypothesis, though the details of his approach have yet to appear in the literature as of 2022. In 2021, Daniel Grady and Dmitri Pavlov claimed a complete proof of the cobordism hypothesis, as well as a generalization to bordisms with arbitrary geometric structures. == Formulation == For a symmetric monoidal ( ∞ , n ) {\displaystyle (\infty ,n)} -category C {\displaystyle {\mathcal {C}}} which is fully dualizable and every k {\displaystyle k} -morphism of which is adjointable, for 1 ≤ k ≤ n − 1 {\displaystyle 1\leq k\leq n-1} , there is a bijection between the C {\displaystyle {\mathcal {C}}} -valued symmetric monoidal functors of the cobordism category and the objects of C {\displaystyle {\mathcal {C}}} . == Motivation == Symmetric monoidal functors from the cobordism category correspond to topological quantum field theories. The cobordism hypothesis for topological quantum field theories is the analogue of the Eilenberg–Steenrod axioms for homology theories. The Eilenberg–Steenrod axioms state that a homology theory is uniquely determined by its value for the point, so analogously what the cobordism hypothesis states is that a topological quantum field theory is uniquely determined by its value for the point. In other words, the bijection between C {\displaystyle {\mathcal {C}}} -valued symmetric monoidal functors and the objects of C {\displaystyle {\mathcal {C}}} is uniquely defined by its value for the point. == See also == Cobordism == References == == Further reading == Freed, Daniel S. (11 October 2012). "The Cobordism hypothesis". Bulletin of the American Mathematical Society. 50 (1). American Mathematical Society (AMS): 57–92. doi:10.1090/s0273-0979-2012-01393-9. ISSN 0273-0979. Seminar on the Cobordism Hypothesis and (Infinity,n)-Categories, 2013-04-22
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{
"page_id": 41419738,
"source": null,
"title": "Cobordism hypothesis"
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Jacob Lurie (4 May 2009). On the Classification of Topological Field Theories == External links == cobordism hypothesis at the nLab
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"page_id": 41419738,
"source": null,
"title": "Cobordism hypothesis"
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5-Nitro-2-propoxyaniline, also known as P-4000 and Ultrasüss, is about 4,000 times the intensity of sucrose (hence its alternate name, P-4000). It is an orange solid that is only slightly soluble in water. It is stable in boiling water and dilute acids. 5-Nitro-2-propoxyaniline was once used as an artificial sweetener but has been banned in the United States because of its possible toxicity. In the US, food containing any added or detectable level of 5-nitro-2-propoxyaniline is deemed to be adulterated in violation of the act based upon an order published in the Federal Register of January 19, 1950 (15 FR 321). == References == == External links == Media related to 5-Nitro-2-propoxyaniline at Wikimedia Commons
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{
"page_id": 1967067,
"source": null,
"title": "5-Nitro-2-propoxyaniline"
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Lists of human genes are as follows: == By chromosome == Human chromosomes, each of which contains an incomplete list of genes located on that chromosome, are as follows: == Protein-coding genes == The lists below constitute a complete list of all known human protein-coding genes: == Transcription factors == 1639 genes which encode proteins that are known or expected to function as human transcription factors: List of human transcription factors == See also == List of enzymes List of proteins List of disabled human pseudogenes == External links == iHOP-Protein Information Database NextBio-Life Science Search Engine Entrez-Cross Database Query Search System TranscriptomeBrowser
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{
"page_id": 1639390,
"source": null,
"title": "Lists of human genes"
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In the field of obstetrics, lochia is the vaginal discharge after giving birth, containing blood, mucus, and uterine tissue. Lochia discharge typically continues for four to eight weeks after childbirth, a time known as the postpartum period or puerperium. A 2016 review ties this "lochial period" to worldwide customs of postpartum confinement, a time for the new mother and baby to bond. Lochia is sterile for the first two days, but not so by the third or fourth day, as the uterus begins to be colonized by vaginal commensals such as non-hemolytic streptococci and E. coli. The Cleveland Clinic recommends that pads be used instead of tampons to absorb the fluid as materials should not be inserted in the vagina soon after childbirth. == Stages == It progresses through three stages: Lochia rubra (or cruenta) is the first discharge, composed of blood, shreds of fetal membranes, decidua, vernix caseosa, lanugo and membranes. It is red in color because of the large amount of blood it contains. It lasts 1 to 4 days after birth, before easing to light "spotting". Lochia serosa is the term for lochia that has thinned and turned brownish or pink in color. It contains serous exudate, erythrocytes, leukocytes, cervical mucus and microorganisms. This stage continues until around the tenth day after delivery. Lochia serosa which persists to some weeks after birth can indicate late postpartum hemorrhaging, and should be reported to a physician. Lochia alba (or purulenta) is the name for lochia once it has turned whitish or yellowish-white. It typically lasts from the second through the third to sixth weeks after delivery. It contains fewer red blood cells and is mainly made up of leukocytes, epithelial cells, cholesterol, fat, mucus and microorganisms. Continuation beyond a few weeks can indicate a genital lesion, which should be
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{
"page_id": 1377246,
"source": null,
"title": "Lochia"
}
|
reported to a physician. == Complications == In general, lochia has an odor similar to that of normal menstrual fluid. Any offensive odor or change to a greenish color indicates contamination by organisms such as chlamydia or staph saprophyticus. Lochia that is retained within the uterus is known as lochiostasis or lochioschesis, and can result in lochiometra (distention of the uterus - pushing it out of shape). Lochiorrhea describes an excessive flow of lochia and can indicate infection. == References ==
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{
"page_id": 1377246,
"source": null,
"title": "Lochia"
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Belgian Scientific Expedition was a scientific survey of the Great Barrier Reef, conducted in 1967–1968. The Belgian Scientific Expedition to the Great Barrier Reef was a seven month expedition beginning in 1967, sponsored by the University of Liege, Belgium, the Belgium Ministry of Education and the National Foundation for Scientific Research. It indirectly honoured the Great Barrier Reef Expedition of 1928–1929, which was led by Maurice Yonge and a large group of researchers from Europe. This earlier expedition had studied the northern Great Barrier Reef primarily around Low Isles Reef. The 1967 expedition, led by Professor Albert Distèche took place between Lady Musgrave Island and Lizard Island off the coast of Queensland on the Great Barrier Reef. Seventy-five ship's crew, many researchers and guests were involved in the expedition. Its primary objective was to make scientific marine biology films. Ron Taylor, who would become famous for his films and diving work with sharks was one of the cinematographers hired to undertake the underwater filming using a 35mm motion picture camera. The former British warship, the De Moor was utilised for the study by the Belgian Navy. Captain Wally Muller was contracted to guide the De Moor through the Swain Reefs and remain with the expedition, on his charter vessel, the Careelah. Coral reef scientists participated in the study as time permitted. The ship would return to shore every 10 days. Among these scientists were David Barnes from the Townsville area and Robert Endean from the University of Queensland. Sir Maurice Yonge would also visit during this expedition, in recognition of his earlier work in 1928. Later studies of the Reef would be conducted and published as part of Project Stellaroid, which surveyed coral reefs in the North Pacific Ocean and their damage by the Crown of Thorns starfish. == References
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"page_id": 57738208,
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==
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"page_id": 57738208,
"source": null,
"title": "Belgian Scientific Expedition"
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Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable). It can be regarded as a stochastic approximation of gradient descent optimization, since it replaces the actual gradient (calculated from the entire data set) by an estimate thereof (calculated from a randomly selected subset of the data). Especially in high-dimensional optimization problems this reduces the very high computational burden, achieving faster iterations in exchange for a lower convergence rate. The basic idea behind stochastic approximation can be traced back to the Robbins–Monro algorithm of the 1950s. Today, stochastic gradient descent has become an important optimization method in machine learning. == Background == Both statistical estimation and machine learning consider the problem of minimizing an objective function that has the form of a sum: Q ( w ) = 1 n ∑ i = 1 n Q i ( w ) , {\displaystyle Q(w)={\frac {1}{n}}\sum _{i=1}^{n}Q_{i}(w),} where the parameter w {\displaystyle w} that minimizes Q ( w ) {\displaystyle Q(w)} is to be estimated. Each summand function Q i {\displaystyle Q_{i}} is typically associated with the i {\displaystyle i} -th observation in the data set (used for training). In classical statistics, sum-minimization problems arise in least squares and in maximum-likelihood estimation (for independent observations). The general class of estimators that arise as minimizers of sums are called M-estimators. However, in statistics, it has been long recognized that requiring even local minimization is too restrictive for some problems of maximum-likelihood estimation. Therefore, contemporary statistical theorists often consider stationary points of the likelihood function (or zeros of its derivative, the score function, and other estimating equations). The sum-minimization problem also arises for empirical risk minimization. There, Q i ( w ) {\displaystyle Q_{i}(w)} is the value of the loss function
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at i {\displaystyle i} -th example, and Q ( w ) {\displaystyle Q(w)} is the empirical risk. When used to minimize the above function, a standard (or "batch") gradient descent method would perform the following iterations: w := w − η ∇ Q ( w ) = w − η n ∑ i = 1 n ∇ Q i ( w ) . {\displaystyle w:=w-\eta \,\nabla Q(w)=w-{\frac {\eta }{n}}\sum _{i=1}^{n}\nabla Q_{i}(w).} The step size is denoted by η {\displaystyle \eta } (sometimes called the learning rate in machine learning) and here " := {\displaystyle :=} " denotes the update of a variable in the algorithm. In many cases, the summand functions have a simple form that enables inexpensive evaluations of the sum-function and the sum gradient. For example, in statistics, one-parameter exponential families allow economical function-evaluations and gradient-evaluations. However, in other cases, evaluating the sum-gradient may require expensive evaluations of the gradients from all summand functions. When the training set is enormous and no simple formulas exist, evaluating the sums of gradients becomes very expensive, because evaluating the gradient requires evaluating all the summand functions' gradients. To economize on the computational cost at every iteration, stochastic gradient descent samples a subset of summand functions at every step. This is very effective in the case of large-scale machine learning problems. == Iterative method == In stochastic (or "on-line") gradient descent, the true gradient of Q ( w ) {\displaystyle Q(w)} is approximated by a gradient at a single sample: w := w − η ∇ Q i ( w ) . {\displaystyle w:=w-\eta \,\nabla Q_{i}(w).} As the algorithm sweeps through the training set, it performs the above update for each training sample. Several passes can be made over the training set until the algorithm converges. If this is done, the data
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can be shuffled for each pass to prevent cycles. Typical implementations may use an adaptive learning rate so that the algorithm converges. In pseudocode, stochastic gradient descent can be presented as : A compromise between computing the true gradient and the gradient at a single sample is to compute the gradient against more than one training sample (called a "mini-batch") at each step. This can perform significantly better than "true" stochastic gradient descent described, because the code can make use of vectorization libraries rather than computing each step separately as was first shown in where it was called "the bunch-mode back-propagation algorithm". It may also result in smoother convergence, as the gradient computed at each step is averaged over more training samples. The convergence of stochastic gradient descent has been analyzed using the theories of convex minimization and of stochastic approximation. Briefly, when the learning rates η {\displaystyle \eta } decrease with an appropriate rate, and subject to relatively mild assumptions, stochastic gradient descent converges almost surely to a global minimum when the objective function is convex or pseudoconvex, and otherwise converges almost surely to a local minimum. This is in fact a consequence of the Robbins–Siegmund theorem. == Linear regression == Suppose we want to fit a straight line y ^ = w 1 + w 2 x {\displaystyle {\hat {y}}=w_{1}+w_{2}x} to a training set with observations ( ( x 1 , y 1 ) , ( x 2 , y 2 ) … , ( x n , y n ) ) {\displaystyle ((x_{1},y_{1}),(x_{2},y_{2})\ldots ,(x_{n},y_{n}))} and corresponding estimated responses ( y ^ 1 , y ^ 2 , … , y ^ n ) {\displaystyle ({\hat {y}}_{1},{\hat {y}}_{2},\ldots ,{\hat {y}}_{n})} using least squares. The objective function to be minimized is Q ( w ) = ∑ i =
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1 n Q i ( w ) = ∑ i = 1 n ( y ^ i − y i ) 2 = ∑ i = 1 n ( w 1 + w 2 x i − y i ) 2 . {\displaystyle Q(w)=\sum _{i=1}^{n}Q_{i}(w)=\sum _{i=1}^{n}\left({\hat {y}}_{i}-y_{i}\right)^{2}=\sum _{i=1}^{n}\left(w_{1}+w_{2}x_{i}-y_{i}\right)^{2}.} The last line in the above pseudocode for this specific problem will become: [ w 1 w 2 ] ← [ w 1 w 2 ] − η [ ∂ ∂ w 1 ( w 1 + w 2 x i − y i ) 2 ∂ ∂ w 2 ( w 1 + w 2 x i − y i ) 2 ] = [ w 1 w 2 ] − η [ 2 ( w 1 + w 2 x i − y i ) 2 x i ( w 1 + w 2 x i − y i ) ] . {\displaystyle {\begin{bmatrix}w_{1}\\w_{2}\end{bmatrix}}\leftarrow {\begin{bmatrix}w_{1}\\w_{2}\end{bmatrix}}-\eta {\begin{bmatrix}{\frac {\partial }{\partial w_{1}}}(w_{1}+w_{2}x_{i}-y_{i})^{2}\\{\frac {\partial }{\partial w_{2}}}(w_{1}+w_{2}x_{i}-y_{i})^{2}\end{bmatrix}}={\begin{bmatrix}w_{1}\\w_{2}\end{bmatrix}}-\eta {\begin{bmatrix}2(w_{1}+w_{2}x_{i}-y_{i})\\2x_{i}(w_{1}+w_{2}x_{i}-y_{i})\end{bmatrix}}.} Note that in each iteration or update step, the gradient is only evaluated at a single x i {\displaystyle x_{i}} . This is the key difference between stochastic gradient descent and batched gradient descent. In general, given a linear regression y ^ = ∑ k ∈ 1 : m w k x k {\displaystyle {\hat {y}}=\sum _{k\in 1:m}w_{k}x_{k}} problem, stochastic gradient descent behaves differently when m < n {\displaystyle m<n} (underparameterized) and m ≥ n {\displaystyle m\geq n} (overparameterized). In the overparameterized case, stochastic gradient descent converges to arg min w : w T x k = y k ∀ k ∈ 1 : n ‖ w − w 0 ‖ {\displaystyle \arg \min _{w:w^{T}x_{k}=y_{k}\forall k\in 1:n}\|w-w_{0}\|} . That is, SGD converges to the interpolation solution with minimum distance from the starting w 0 {\displaystyle w_{0}}
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"page_id": 1180641,
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"title": "Stochastic gradient descent"
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. This is true even when the learning rate remains constant. In the underparameterized case, SGD does not converge if learning rate remains constant. == History == In 1951, Herbert Robbins and Sutton Monro introduced the earliest stochastic approximation methods, preceding stochastic gradient descent. Building on this work one year later, Jack Kiefer and Jacob Wolfowitz published an optimization algorithm very close to stochastic gradient descent, using central differences as an approximation of the gradient. Later in the 1950s, Frank Rosenblatt used SGD to optimize his perceptron model, demonstrating the first applicability of stochastic gradient descent to neural networks. Backpropagation was first described in 1986, with stochastic gradient descent being used to efficiently optimize parameters across neural networks with multiple hidden layers. Soon after, another improvement was developed: mini-batch gradient descent, where small batches of data are substituted for single samples. In 1997, the practical performance benefits from vectorization achievable with such small batches were first explored, paving the way for efficient optimization in machine learning. As of 2023, this mini-batch approach remains the norm for training neural networks, balancing the benefits of stochastic gradient descent with gradient descent. By the 1980s, momentum had already been introduced, and was added to SGD optimization techniques in 1986. However, these optimization techniques assumed constant hyperparameters, i.e. a fixed learning rate and momentum parameter. In the 2010s, adaptive approaches to applying SGD with a per-parameter learning rate were introduced with AdaGrad (for "Adaptive Gradient") in 2011 and RMSprop (for "Root Mean Square Propagation") in 2012. In 2014, Adam (for "Adaptive Moment Estimation") was published, applying the adaptive approaches of RMSprop to momentum; many improvements and branches of Adam were then developed such as Adadelta, Adagrad, AdamW, and Adamax. Within machine learning, approaches to optimization in 2023 are dominated by Adam-derived optimizers. TensorFlow and
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PyTorch, by far the most popular machine learning libraries, as of 2023 largely only include Adam-derived optimizers, as well as predecessors to Adam such as RMSprop and classic SGD. PyTorch also partially supports Limited-memory BFGS, a line-search method, but only for single-device setups without parameter groups. == Notable applications == Stochastic gradient descent is a popular algorithm for training a wide range of models in machine learning, including (linear) support vector machines, logistic regression (see, e.g., Vowpal Wabbit) and graphical models. When combined with the back propagation algorithm, it is the de facto standard algorithm for training artificial neural networks. Its use has been also reported in the Geophysics community, specifically to applications of Full Waveform Inversion (FWI). Stochastic gradient descent competes with the L-BFGS algorithm, which is also widely used. Stochastic gradient descent has been used since at least 1960 for training linear regression models, originally under the name ADALINE. Another stochastic gradient descent algorithm is the least mean squares (LMS) adaptive filter. == Extensions and variants == Many improvements on the basic stochastic gradient descent algorithm have been proposed and used. In particular, in machine learning, the need to set a learning rate (step size) has been recognized as problematic. Setting this parameter too high can cause the algorithm to diverge; setting it too low makes it slow to converge. A conceptually simple extension of stochastic gradient descent makes the learning rate a decreasing function ηt of the iteration number t, giving a learning rate schedule, so that the first iterations cause large changes in the parameters, while the later ones do only fine-tuning. Such schedules have been known since the work of MacQueen on k-means clustering. Practical guidance on choosing the step size in several variants of SGD is given by Spall. === Implicit updates (ISGD) ===
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As mentioned earlier, classical stochastic gradient descent is generally sensitive to learning rate η. Fast convergence requires large learning rates but this may induce numerical instability. The problem can be largely solved by considering implicit updates whereby the stochastic gradient is evaluated at the next iterate rather than the current one: w new := w old − η ∇ Q i ( w new ) . {\displaystyle w^{\text{new}}:=w^{\text{old}}-\eta \,\nabla Q_{i}(w^{\text{new}}).} This equation is implicit since w new {\displaystyle w^{\text{new}}} appears on both sides of the equation. It is a stochastic form of the proximal gradient method since the update can also be written as: w new := arg min w { Q i ( w ) + 1 2 η ‖ w − w old ‖ 2 } . {\displaystyle w^{\text{new}}:=\arg \min _{w}\left\{Q_{i}(w)+{\frac {1}{2\eta }}\left\|w-w^{\text{old}}\right\|^{2}\right\}.} As an example, consider least squares with features x 1 , … , x n ∈ R p {\displaystyle x_{1},\ldots ,x_{n}\in \mathbb {R} ^{p}} and observations y 1 , … , y n ∈ R {\displaystyle y_{1},\ldots ,y_{n}\in \mathbb {R} } . We wish to solve: min w ∑ j = 1 n ( y j − x j ′ w ) 2 , {\displaystyle \min _{w}\sum _{j=1}^{n}\left(y_{j}-x_{j}'w\right)^{2},} where x j ′ w = x j 1 w 1 + x j , 2 w 2 + . . . + x j , p w p {\displaystyle x_{j}'w=x_{j1}w_{1}+x_{j,2}w_{2}+...+x_{j,p}w_{p}} indicates the inner product. Note that x {\displaystyle x} could have "1" as the first element to include an intercept. Classical stochastic gradient descent proceeds as follows: w new = w old + η ( y i − x i ′ w old ) x i {\displaystyle w^{\text{new}}=w^{\text{old}}+\eta \left(y_{i}-x_{i}'w^{\text{old}}\right)x_{i}} where i {\displaystyle i} is uniformly sampled between 1 and n {\displaystyle n} . Although theoretical
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"page_id": 1180641,
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convergence of this procedure happens under relatively mild assumptions, in practice the procedure can be quite unstable. In particular, when η {\displaystyle \eta } is misspecified so that I − η x i x i ′ {\displaystyle I-\eta x_{i}x_{i}'} has large absolute eigenvalues with high probability, the procedure may diverge numerically within a few iterations. In contrast, implicit stochastic gradient descent (shortened as ISGD) can be solved in closed-form as: w new = w old + η 1 + η ‖ x i ‖ 2 ( y i − x i ′ w old ) x i . {\displaystyle w^{\text{new}}=w^{\text{old}}+{\frac {\eta }{1+\eta \left\|x_{i}\right\|^{2}}}\left(y_{i}-x_{i}'w^{\text{old}}\right)x_{i}.} This procedure will remain numerically stable virtually for all η {\displaystyle \eta } as the learning rate is now normalized. Such comparison between classical and implicit stochastic gradient descent in the least squares problem is very similar to the comparison between least mean squares (LMS) and normalized least mean squares filter (NLMS). Even though a closed-form solution for ISGD is only possible in least squares, the procedure can be efficiently implemented in a wide range of models. Specifically, suppose that Q i ( w ) {\displaystyle Q_{i}(w)} depends on w {\displaystyle w} only through a linear combination with features x i {\displaystyle x_{i}} , so that we can write ∇ w Q i ( w ) = − q ( x i ′ w ) x i {\displaystyle \nabla _{w}Q_{i}(w)=-q(x_{i}'w)x_{i}} , where q ( ) ∈ R {\displaystyle q()\in \mathbb {R} } may depend on x i , y i {\displaystyle x_{i},y_{i}} as well but not on w {\displaystyle w} except through x i ′ w {\displaystyle x_{i}'w} . Least squares obeys this rule, and so does logistic regression, and most generalized linear models. For instance, in least squares, q ( x i ′ w ) =
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y i − x i ′ w {\displaystyle q(x_{i}'w)=y_{i}-x_{i}'w} , and in logistic regression q ( x i ′ w ) = y i − S ( x i ′ w ) {\displaystyle q(x_{i}'w)=y_{i}-S(x_{i}'w)} , where S ( u ) = e u / ( 1 + e u ) {\displaystyle S(u)=e^{u}/(1+e^{u})} is the logistic function. In Poisson regression, q ( x i ′ w ) = y i − e x i ′ w {\displaystyle q(x_{i}'w)=y_{i}-e^{x_{i}'w}} , and so on. In such settings, ISGD is simply implemented as follows. Let f ( ξ ) = η q ( x i ′ w old + ξ ‖ x i ‖ 2 ) {\displaystyle f(\xi )=\eta q(x_{i}'w^{\text{old}}+\xi \|x_{i}\|^{2})} , where ξ {\displaystyle \xi } is scalar. Then, ISGD is equivalent to: w new = w old + ξ ∗ x i , where ξ ∗ = f ( ξ ∗ ) . {\displaystyle w^{\text{new}}=w^{\text{old}}+\xi ^{\ast }x_{i},~{\text{where}}~\xi ^{\ast }=f(\xi ^{\ast }).} The scaling factor ξ ∗ ∈ R {\displaystyle \xi ^{\ast }\in \mathbb {R} } can be found through the bisection method since in most regular models, such as the aforementioned generalized linear models, function q ( ) {\displaystyle q()} is decreasing, and thus the search bounds for ξ ∗ {\displaystyle \xi ^{\ast }} are [ min ( 0 , f ( 0 ) ) , max ( 0 , f ( 0 ) ) ] {\displaystyle [\min(0,f(0)),\max(0,f(0))]} . === Momentum === Further proposals include the momentum method or the heavy ball method, which in ML context appeared in Rumelhart, Hinton and Williams' paper on backpropagation learning and borrowed the idea from Soviet mathematician Boris Polyak's 1964 article on solving functional equations. Stochastic gradient descent with momentum remembers the update Δw at each iteration, and determines the next update as a linear
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combination of the gradient and the previous update: Δ w := α Δ w − η ∇ Q i ( w ) {\displaystyle \Delta w:=\alpha \Delta w-\eta \,\nabla Q_{i}(w)} w := w + Δ w {\displaystyle w:=w+\Delta w} that leads to: w := w − η ∇ Q i ( w ) + α Δ w {\displaystyle w:=w-\eta \,\nabla Q_{i}(w)+\alpha \Delta w} where the parameter w {\displaystyle w} which minimizes Q ( w ) {\displaystyle Q(w)} is to be estimated, η {\displaystyle \eta } is a step size (sometimes called the learning rate in machine learning) and α {\displaystyle \alpha } is an exponential decay factor between 0 and 1 that determines the relative contribution of the current gradient and earlier gradients to the weight change. The name momentum stems from an analogy to momentum in physics: the weight vector w {\displaystyle w} , thought of as a particle traveling through parameter space, incurs acceleration from the gradient of the loss ("force"). Unlike in classical stochastic gradient descent, it tends to keep traveling in the same direction, preventing oscillations. Momentum has been used successfully by computer scientists in the training of artificial neural networks for several decades. The momentum method is closely related to underdamped Langevin dynamics, and may be combined with simulated annealing. In mid-1980s the method was modified by Yurii Nesterov to use the gradient predicted at the next point, and the resulting so-called Nesterov Accelerated Gradient was sometimes used in ML in the 2010s. === Averaging === Averaged stochastic gradient descent, invented independently by Ruppert and Polyak in the late 1980s, is ordinary stochastic gradient descent that records an average of its parameter vector over time. That is, the update is the same as for ordinary stochastic gradient descent, but the algorithm also keeps track of w
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"page_id": 1180641,
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¯ = 1 t ∑ i = 0 t − 1 w i . {\displaystyle {\bar {w}}={\frac {1}{t}}\sum _{i=0}^{t-1}w_{i}.} When optimization is done, this averaged parameter vector takes the place of w. === AdaGrad === AdaGrad (for adaptive gradient algorithm) is a modified stochastic gradient descent algorithm with per-parameter learning rate, first published in 2011. Informally, this increases the learning rate for sparser parameters and decreases the learning rate for ones that are less sparse. This strategy often improves convergence performance over standard stochastic gradient descent in settings where data is sparse and sparse parameters are more informative. Examples of such applications include natural language processing and image recognition. It still has a base learning rate η, but this is multiplied with the elements of a vector {Gj,j} which is the diagonal of the outer product matrix G = ∑ τ = 1 t g τ g τ T {\displaystyle G=\sum _{\tau =1}^{t}g_{\tau }g_{\tau }^{\mathsf {T}}} where g τ = ∇ Q i ( w ) {\displaystyle g_{\tau }=\nabla Q_{i}(w)} , the gradient, at iteration τ. The diagonal is given by G j , j = ∑ τ = 1 t g τ , j 2 . {\displaystyle G_{j,j}=\sum _{\tau =1}^{t}g_{\tau ,j}^{2}.} This vector essentially stores a historical sum of gradient squares by dimension and is updated after every iteration. The formula for an update is now w := w − η d i a g ( G ) − 1 2 ⊙ g {\displaystyle w:=w-\eta \,\mathrm {diag} (G)^{-{\frac {1}{2}}}\odot g} or, written as per-parameter updates, w j := w j − η G j , j g j . {\displaystyle w_{j}:=w_{j}-{\frac {\eta }{\sqrt {G_{j,j}}}}g_{j}.} Each {G(i,i)} gives rise to a scaling factor for the learning rate that applies to a single parameter wi. Since the denominator in this factor,
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"page_id": 1180641,
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G i = ∑ τ = 1 t g τ 2 {\textstyle {\sqrt {G_{i}}}={\sqrt {\sum _{\tau =1}^{t}g_{\tau }^{2}}}} is the ℓ2 norm of previous derivatives, extreme parameter updates get dampened, while parameters that get few or small updates receive higher learning rates. While designed for convex problems, AdaGrad has been successfully applied to non-convex optimization. === RMSProp === RMSProp (for Root Mean Square Propagation) is a method invented in 2012 by James Martens and Ilya Sutskever, at the time both PhD students in Geoffrey Hinton's group, in which the learning rate is, like in Adagrad, adapted for each of the parameters. The idea is to divide the learning rate for a weight by a running average of the magnitudes of recent gradients for that weight. Unusually, it was not published in an article but merely described in a Coursera lecture. Citation 1: https://deepai.org/machine-learning-glossary-and-terms/rmsprop#:~:text=The%20RMSProp%20algorithm%20was%20introduced,its%20effectiveness%20in%20various%20applications. Citation 2: this video at 36:37 https://www.youtube.com/watch?v=-eyhCTvrEtE&t=36m37s So, first the running average is calculated in terms of means square, v ( w , t ) := γ v ( w , t − 1 ) + ( 1 − γ ) ( ∇ Q i ( w ) ) 2 {\displaystyle v(w,t):=\gamma v(w,t-1)+\left(1-\gamma \right)\left(\nabla Q_{i}(w)\right)^{2}} where, γ {\displaystyle \gamma } is the forgetting factor. The concept of storing the historical gradient as sum of squares is borrowed from Adagrad, but "forgetting" is introduced to solve Adagrad's diminishing learning rates in non-convex problems by gradually decreasing the influence of old data. And the parameters are updated as, w := w − η v ( w , t ) ∇ Q i ( w ) {\displaystyle w:=w-{\frac {\eta }{\sqrt {v(w,t)}}}\nabla Q_{i}(w)} RMSProp has shown good adaptation of learning rate in different applications. RMSProp can be seen as a generalization of Rprop and is capable to work with mini-batches as
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"page_id": 1180641,
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well opposed to only full-batches. === Adam === Adam (short for Adaptive Moment Estimation) is a 2014 update to the RMSProp optimizer combining it with the main feature of the Momentum method. In this optimization algorithm, running averages with exponential forgetting of both the gradients and the second moments of the gradients are used. Given parameters w ( t ) {\displaystyle w^{(t)}} and a loss function L ( t ) {\displaystyle L^{(t)}} , where t {\displaystyle t} indexes the current training iteration (indexed at 1 {\displaystyle 1} ), Adam's parameter update is given by: m w ( t ) := β 1 m w ( t − 1 ) + ( 1 − β 1 ) ∇ w L ( t − 1 ) {\displaystyle m_{w}^{(t)}:=\beta _{1}m_{w}^{(t-1)}+\left(1-\beta _{1}\right)\nabla _{w}L^{(t-1)}} v w ( t ) := β 2 v w ( t − 1 ) + ( 1 − β 2 ) ( ∇ w L ( t − 1 ) ) 2 {\displaystyle v_{w}^{(t)}:=\beta _{2}v_{w}^{(t-1)}+\left(1-\beta _{2}\right)\left(\nabla _{w}L^{(t-1)}\right)^{2}} m ^ w ( t ) = m w ( t ) 1 − β 1 t {\displaystyle {\hat {m}}_{w}^{(t)}={\frac {m_{w}^{(t)}}{1-\beta _{1}^{t}}}} v ^ w ( t ) = v w ( t ) 1 − β 2 t {\displaystyle {\hat {v}}_{w}^{(t)}={\frac {v_{w}^{(t)}}{1-\beta _{2}^{t}}}} w ( t ) := w ( t − 1 ) − η m ^ w ( t ) v ^ w ( t ) + ε {\displaystyle w^{(t)}:=w^{(t-1)}-\eta {\frac {{\hat {m}}_{w}^{(t)}}{{\sqrt {{\hat {v}}_{w}^{(t)}}}+\varepsilon }}} where ε {\displaystyle \varepsilon } is a small scalar (e.g. 10 − 8 {\displaystyle 10^{-8}} ) used to prevent division by 0, and β 1 {\displaystyle \beta _{1}} (e.g. 0.9) and β 2 {\displaystyle \beta _{2}} (e.g. 0.999) are the forgetting factors for gradients and second moments of gradients, respectively. Squaring and square-rooting is
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"page_id": 1180641,
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done element-wise. As the exponential moving averages of the gradient m w ( t ) {\displaystyle m_{w}^{(t)}} and the squared gradient v w ( t ) {\displaystyle v_{w}^{(t)}} are initialized with a vector of 0's, there would be a bias towards zero in the first training iterations. A factor 1 1 − β 1 / 2 t {\displaystyle {\tfrac {1}{1-\beta _{1/2}^{t}}}} is introduced to compensate this bias and get better estimates m ^ w ( t ) {\displaystyle {\hat {m}}_{w}^{(t)}} and v ^ w ( t ) {\displaystyle {\hat {v}}_{w}^{(t)}} . The initial proof establishing the convergence of Adam was incomplete, and subsequent analysis has revealed that Adam does not converge for all convex objectives. Despite this, Adam continues to be used due to its strong performance in practice. ==== Variants ==== The popularity of Adam inspired many variants and enhancements. Some examples include: Nesterov-enhanced gradients: NAdam, FASFA varying interpretations of second-order information: Powerpropagation and AdaSqrt. Using infinity norm: AdaMax AMSGrad, which improves convergence over Adam by using maximum of past squared gradients instead of the exponential average. AdamX further improves convergence over AMSGrad. AdamW, which improves the weight decay. === Sign-based stochastic gradient descent === Even though sign-based optimization goes back to the aforementioned Rprop, in 2018 researchers tried to simplify Adam by removing the magnitude of the stochastic gradient from being taken into account and only considering its sign. === Backtracking line search === Backtracking line search is another variant of gradient descent. All of the below are sourced from the mentioned link. It is based on a condition known as the Armijo–Goldstein condition. Both methods allow learning rates to change at each iteration; however, the manner of the change is different. Backtracking line search uses function evaluations to check Armijo's condition, and in principle the loop in
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"page_id": 1180641,
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the algorithm for determining the learning rates can be long and unknown in advance. Adaptive SGD does not need a loop in determining learning rates. On the other hand, adaptive SGD does not guarantee the "descent property" – which Backtracking line search enjoys – which is that f ( x n + 1 ) ≤ f ( x n ) {\displaystyle f(x_{n+1})\leq f(x_{n})} for all n. If the gradient of the cost function is globally Lipschitz continuous, with Lipschitz constant L, and learning rate is chosen of the order 1/L, then the standard version of SGD is a special case of backtracking line search. === Second-order methods === A stochastic analogue of the standard (deterministic) Newton–Raphson algorithm (a "second-order" method) provides an asymptotically optimal or near-optimal form of iterative optimization in the setting of stochastic approximation. A method that uses direct measurements of the Hessian matrices of the summands in the empirical risk function was developed by Byrd, Hansen, Nocedal, and Singer. However, directly determining the required Hessian matrices for optimization may not be possible in practice. Practical and theoretically sound methods for second-order versions of SGD that do not require direct Hessian information are given by Spall and others. (A less efficient method based on finite differences, instead of simultaneous perturbations, is given by Ruppert.) Another approach to the approximation Hessian matrix is replacing it with the Fisher information matrix, which transforms usual gradient to natural. These methods not requiring direct Hessian information are based on either values of the summands in the above empirical risk function or values of the gradients of the summands (i.e., the SGD inputs). In particular, second-order optimality is asymptotically achievable without direct calculation of the Hessian matrices of the summands in the empirical risk function. When the objective is a nonlinear least-squres loss
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Q ( w ) = 1 n ∑ i = 1 n Q i ( w ) = 1 n ∑ i = 1 n ( m ( w ; x i ) − y i ) 2 , {\displaystyle Q(w)={\frac {1}{n}}\sum _{i=1}^{n}Q_{i}(w)={\frac {1}{n}}\sum _{i=1}^{n}(m(w;x_{i})-y_{i})^{2},} where m ( w ; x i ) {\displaystyle m(w;x_{i})} is the predictive model (e.g., a deep neural network) the objective's structure can be exploited to estimate 2nd order information using gradients only. The resulting methods are simple and often effective == Approximations in continuous time == For small learning rate η {\textstyle \eta } stochastic gradient descent ( w n ) n ∈ N 0 {\textstyle (w_{n})_{n\in \mathbb {N} _{0}}} can be viewed as a discretization of the gradient flow ODE d d t W t = − ∇ Q ( W t ) {\displaystyle {\frac {d}{dt}}W_{t}=-\nabla Q(W_{t})} subject to additional stochastic noise. This approximation is only valid on a finite time-horizon in the following sense: assume that all the coefficients Q i {\textstyle Q_{i}} are sufficiently smooth. Let T > 0 {\textstyle T>0} and g : R d → R {\textstyle g:\mathbb {R} ^{d}\to \mathbb {R} } be a sufficiently smooth test function. Then, there exists a constant C > 0 {\textstyle C>0} such that for all η > 0 {\textstyle \eta >0} max k = 0 , … , ⌊ T / η ⌋ | E [ g ( w k ) ] − g ( W k η ) | ≤ C η , {\displaystyle \max _{k=0,\dots ,\lfloor T/\eta \rfloor }\left|\mathbb {E} [g(w_{k})]-g(W_{k\eta })\right|\leq C\eta ,} where E {\textstyle \mathbb {E} } denotes taking the expectation with respect to the random choice of indices in the stochastic gradient descent scheme. Since this approximation does not capture the random fluctuations around the
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"page_id": 1180641,
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mean behavior of stochastic gradient descent solutions to stochastic differential equations (SDEs) have been proposed as limiting objects. More precisely, the solution to the SDE d W t = − ∇ ( Q ( W t ) + 1 4 η | ∇ Q ( W t ) | 2 ) d t + η Σ ( W t ) 1 / 2 d B t , {\displaystyle dW_{t}=-\nabla \left(Q(W_{t})+{\tfrac {1}{4}}\eta |\nabla Q(W_{t})|^{2}\right)dt+{\sqrt {\eta }}\Sigma (W_{t})^{1/2}dB_{t},} for Σ ( w ) = 1 n 2 ( ∑ i = 1 n Q i ( w ) − Q ( w ) ) ( ∑ i = 1 n Q i ( w ) − Q ( w ) ) T {\displaystyle \Sigma (w)={\frac {1}{n^{2}}}\left(\sum _{i=1}^{n}Q_{i}(w)-Q(w)\right)\left(\sum _{i=1}^{n}Q_{i}(w)-Q(w)\right)^{T}} where d B t {\textstyle dB_{t}} denotes the Ito-integral with respect to a Brownian motion is a more precise approximation in the sense that there exists a constant C > 0 {\textstyle C>0} such that max k = 0 , … , ⌊ T / η ⌋ | E [ g ( w k ) ] − E [ g ( W k η ) ] | ≤ C η 2 . {\displaystyle \max _{k=0,\dots ,\lfloor T/\eta \rfloor }\left|\mathbb {E} [g(w_{k})]-\mathbb {E} [g(W_{k\eta })]\right|\leq C\eta ^{2}.} However this SDE only approximates the one-point motion of stochastic gradient descent. For an approximation of the stochastic flow one has to consider SDEs with infinite-dimensional noise. == See also == Backtracking line search Broken Neural Scaling Law Coordinate descent – changes one coordinate at a time, rather than one example Linear classifier Online machine learning Stochastic hill climbing Stochastic variance reduction == Notes == == References == == Further reading == Bottou, Léon (2004), "Stochastic Learning", Advanced Lectures on Machine Learning, LNAI, vol. 3176, Springer, pp. 146–168,
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ISBN 978-3-540-23122-6 Buduma, Nikhil; Locascio, Nicholas (2017), "Beyond Gradient Descent", Fundamentals of Deep Learning : Designing Next-Generation Machine Intelligence Algorithms, O'Reilly, ISBN 9781491925584 LeCun, Yann A.; Bottou, Léon; Orr, Genevieve B.; Müller, Klaus-Robert (2012), "Efficient BackProp", Neural Networks: Tricks of the Trade, Springer, pp. 9–48, ISBN 978-3-642-35288-1 Spall, James C. (2003), Introduction to Stochastic Search and Optimization, Wiley, ISBN 978-0-471-33052-3 == External links == "Gradient Descent, How Neural Networks Learn". 3Blue1Brown. October 16, 2017. Archived from the original on 2021-12-22 – via YouTube. Goh (April 4, 2017). "Why Momentum Really Works". Distill. 2 (4). doi:10.23915/distill.00006. Interactive paper explaining momentum.
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Crab cavities are a form of electromagnetic cavity used in particle accelerators to provide a transverse deflection to particle bunches. They can be used to provide rotation to a charged particle bunch by applying a time varying magnetic field. This rotation of the bunch can be used as a diagnostic tool to measure the length of a bunch (the longitudinal dimension is projected into the transverse plane, and imaged) or as a means of increasing the luminosity at an interaction point of a collider if the colliding beams cross each other at an angle (then called crab crossing). The KEKB accelerator introduced this technology in its last upgrade. == See also == Cavity resonator == References ==
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{
"page_id": 1770466,
"source": null,
"title": "Crab cavity"
}
|
A spur or track in radiation chemistry is a region of high concentration of chemical products after ionizing radiation passes through. The spur model, proposed by Samuel and Magee in 1953, describes the kinetic behavior of reaction spurs involving one type of radicals in a diffusion-driven environment. The spurs from gamma rays or X-rays are considered to be spherical, while those from alpha particles are cylindrical, also called tracks. == See also == Linear energy transfer Radiobiology == References ==
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{
"page_id": 70714339,
"source": null,
"title": "Spur (chemistry)"
}
|
Dilution is the process of decreasing the concentration of a solute in a solution, usually simply by mixing with more solvent like adding more water to the solution. To dilute a solution means to add more solvent without the addition of more solute. The resulting solution is thoroughly mixed so as to ensure that all parts of the solution are identical. The same direct relationship applies to gases and vapors diluted in air for example. Although, thorough mixing of gases and vapors may not be as easily accomplished. For example, if there are 10 grams of salt (the solute) dissolved in 1 litre of water (the solvent), this solution has a certain salt concentration (molarity). If one adds 1 litre of water to this solution, the salt concentration is reduced. The diluted solution still contains 10 grams of salt (0.171 moles of NaCl). Mathematically this relationship can be shown by equation: c 1 V 1 = c 2 V 2 {\displaystyle c_{1}V_{1}=c_{2}V_{2}} where c1 = initial concentration or molarity V1 = initial volume c2 = final concentration or molarity V2 = final volume .... == Basic room purge equation == The basic room purge equation is used in industrial hygiene. It determines the time required to reduce a known vapor concentration existing in a closed space to a lower vapor concentration. The equation can only be applied when the purged volume of vapor or gas is replaced with "clean" air or gas. For example, the equation can be used to calculate the time required at a certain ventilation rate to reduce a high carbon monoxide concentration in a room. D t = [ V Q ] ⋅ ln [ C initial C ending ] {\displaystyle D_{t}=\left[{\frac {V}{Q}}\right]\cdot \ln \left[{\frac {C_{\text{initial}}}{C_{\text{ending}}}}\right]} Sometimes the equation is also written as: ln
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"page_id": 3736547,
"source": null,
"title": "Dilution (equation)"
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[ C ending C initial ] = − Q V ⋅ ( t ending − t initial ) {\displaystyle \ln \left[{\frac {C_{\text{ending}}}{C_{\text{initial}}}}\right]\quad ={-}{\frac {Q}{V}}\cdot (t_{\text{ending}}-t_{\text{initial}})} where t initial = 0 {\displaystyle t_{\text{initial}}=0} Dt = time required; the unit of time used is the same as is used for Q V = air or gas volume of the closed space or room in cubic feet, cubic metres or litres Q = ventilation rate into or out of the room in cubic feet per minute, cubic metres per hour or litres per second Cinitial = initial concentration of a vapor inside the room measured in ppm Cfinal = final reduced concentration of the vapor inside the room in ppm == Dilution ventilation equation == The basic room purge equation can be used only for purge scenarios. In a scenario where a liquid continuously evaporates from a container in a ventilated room, a differential equation has to be used: d C d t = G − Q ′ C V {\displaystyle {\frac {dC}{dt}}={\frac {G-Q'C}{V}}} where the ventilation rate has been adjusted by a mixing factor K: Q ′ = Q K {\displaystyle Q'={\frac {Q}{K}}} C = concentration of a gas G = generation rate V = room volume Q′ = adjusted ventilation rate of the volume == Dilution in welding == The dilution in welding terms is defined as the weight of the base metal melted divided by the total weight of the weld metal. For example, if we have a dilution of 0.40, the fraction of the weld metal that came from the consumable electrode is 0.60. == See also == Displacement ventilation Reaction rate Partial molar quantities Apparent molar property Excess molar quantity Heat of dilution == References == == External links == http://pubs.acs.org/doi/abs/10.1021/ja01320a004 Easy dilution calculator
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"page_id": 3736547,
"source": null,
"title": "Dilution (equation)"
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Purushottam Chakraborty is an Indian physicist who is one of the renowned experts in materials analysis using ion beams and secondary ion mass spectrometry (SIMS). He is a former senior professor of Physics at Saha Institute of Nuclear Physics, Kolkata, India & former adjunct professor of Physics at University of Pretoria, South Africa. == Scientific career == Prof Chakraborty did his Ph.D. on the "Design and development of a radio-frequency (RF) quadrupole mass spectrometer (QMS) for the study of secondary-ions emitted from ion-bombarded metal surfaces". The QMS was initially fabricated by Profs S D Dey, S B Karmohapatro and B M Banerjee at Saha Institute of Nuclear Physics, Kolkata, India. Prof Chakraborty upgraded the equipment by appropriately lowering the frequency of the RF voltage so that the QMS could handle the masses above 200 amu and also by converting the system into a full-fledged UHV-based Secondary Ion Mass Spectrometry (SIMS) Setup at Saha Institute of Nuclear Physics, Kolkata. Making use of the indigenous SIMS instrument, he initiated the experimental research on Ion-Matter Interactions, for which he was awarded "Premchand Roychand Scholarship (PRS)" and conferred "Mouat Medal" by the University of Calcutta in 1986. Later, he pursued research on Atomic Collisions in Solids, Inelastic Ion-Surface Collisions and Ion-Beam Modifications & Analysis of Materials. His other research areas include Low-Dimensional Materials and Nanoscale Systems, X-UV Optics, Optoelectronics, Nonlinear Optics, Photonics, Plasmonics, etc. Prof Chakraborty's work on the fabrication of ‘layered Synthetic Microstructures (LSM)’, at the FOM-Institute for Atomic and Molecular Physics – Amsterdam (AMOLF), in collaboration with the Philips Research Laboratories Netherlands, was recognized as a pioneering contribution in the "realization of optical devices for the extreme ultraviolet to soft X-rays". The methodology of fabricating aspherically-curved mirrors for reflecting soft x-rays at near-normal incidence was employed to construct ‘Soft X-ray Telescopes’ for
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imaging Solar Corona and Solar Flakes in the X-UV domain of electromagnetic spectrum. The European Space Agency, Netherlands also used this technique for reflecting X-rays with wavelengths of 1.85 and 10 to 17 Angstroms. Prof. Chakraborty's "Alkali-element based MCsn+ Molecular-ion SIMS" approach has been used for the quantitative analysis of materials without calibration standards, in general and for the composition analysis of surfaces and interfaces of ultrathin films, superlattices and nanostructured materials, in particular. The technique has been recognized as an important contribution in the field of ion-beam analysis of materials. Prof Chakraborty's work on ‘Ion-beam Synthesis of Metal-Glass Nanocomposites’ has led to the development of novel photonic materials, thereby opening the way for advances in all-optical switching, coupled waveguides and optical computation. Professor Chakraborty visited and delivered invited lectures at various renowned universities and research institutes across the globe such as Imperial College London, UK; Vanderbilt University, USA; Yale University, USA; Asian Institute of Technology, Thailand; Kyoto University, Japan; and CERN (Geneva), Switzerland to name a few. Prof Chakraborty was the visiting professor of Pontifical Catholic University of Rio de Janeiro, Brazil; Osaka Electro-Communication University, Japan; Universite Laval, Quebec, Canada; Friedrich Schiller University, Jena, Germany; University of Padova, Italy; International Centre for Theoretical Physics (ICTP), Trieste, Italy; FOM - Institute for Atomic and Molecular Physics, The Netherlands to name a few. == Awards and recognition == Adjudged the "Most Eminent Mass Spectrometrist of India' by the Indian Society for Mass Spectrometry (ISMS) for his outstanding contributions in SIMS Conferred "Gold Medal" in 2003 by the Chairman, Atomic Energy Commission, Government of India Premchand Roychand Scholar of the University of Calcutta (1979) Mouat Silver Medal – Awarded by the University of Calcutta (1986) Fellow, West Bengal Academy of Science and Technology Fellow, Indian Chemical Society == Keynote speeches == Prof
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Chakraborty organized and delivered keynote address at various international conferences; to name a few: 16th International Workshop on Inelastic Ion-Surface Collisions (IISC-16) 17 - 22 Sep. 2006 Hernstein, A-2560 Hernstein, Austria 7th Asian International Seminar on Atomic and Molecular Physics, 4 – 7 December, IIT-Madras, India International Summit on Current Trends in Mass Spectrometry, 13 – 15 July 2015, New Orleans, USA 8th World Congress on Spectroscopy and Analytical Techniques, September (11 – 12), 2018, Stockholm, Sweden 9th World Congress on Spectroscopy and Analytical Techniques, March (06 – 07), 2019, Paris, France International Webinar on Mass Spectrometry and Separation Techniques, London, March (05 – 06), 2021 "Professor Hiralal Das Memorial Lecture", Physics Department, Rajiv Gandhi University, Arunachal Pradesh, India, 11 November 2021 4th Edition of World Nanotechnology Conference (World Nano 2021), Las Vegas, Nevada, USA, 25 – 27 April 2022 Global Conference on Nanotechnology, Madrid, Spain (NanoSeries 2022), 21 - 24 June 2022 30th National Conference on Condensed Matter Physics, National Institute of Technology (NIT) – Nagaland, 14 – 16 December 2022 (Plenary Speaker) 67th Annual Conference of the South African Institute of Physics, held at the University of Zululand, South Africa during July 3-7, 2023 == Publications == Purushottam Chakraborty has published more than 120 research papers in international journals that includes monographs, reviews and book-chapters. Purushottam Chakraborty, MCsn+-SIMS: An Innovative Approach for Direct Compositional Analysis of Materials without Standards, Energy Procedia, Volume 41, (2013), p. 80-109 M P Bruijn, Prof. Chakraborty, J. Verhoeven, H W van Essen, M. J. van der Wiel, Automatic electron-beam deposition of multilayer soft x-ray coatings with laterally graded d-spacing, Optical Engineering 25, 916 (1986) Purushottam Chakraborty, Layered synthetic microstructures as optical elements for the extreme ultraviolet and soft X-rays, Int. J. Mod. Phys B 5, (1991), p:2133-2228 Biswajit Saha, Purushottam Chakraborty, Hubert Gnaser,
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Manjula Sharma and Milan K Sanyal, Exact compositional analysis of SiGe alloys by matrix effect compensated MCs+-SIMS, Appl Phys A 108, 671 (2012) P. Chakraborty, Metal nanoclusters in glasses as non-linear photonic materials, Journal of Materials Science (Kluwer Academic Publishers) Volume 33, p: 2235-2249 (1998) Binita Ghosh and Purushottam Chakraborty, Optical Nonlinearities of Colloidal Metal Quantum Dot – Glass Composites for Nanophotonics (Book: Nanocomposites and Polymers with Analytical Methods) (Edited by John Cuppoletti, Intech Publishers) (2011) Journal of Physics: Conference Series (IOP Publications, UK), Volume 80 (Edited by Pranawa C Deshmukh, Purushottam Chakraborty and Jim F Williams), (2006) Binita Ghosh and Purushottam Chakraborty, Photonic Materials (Ed: Purushottam Chakraborty), Encyclopedia of Materials: Electronics, Volume 2 (Elsevier) == Books edited == "Ion Beam Analysis of Surfaces and Interfaces of Condensed Matter Systems" (Edited by Purushottam Chakraborty), Nova Science Publishers, New York, 2002, ISBN 1590335384 Photonic Materials (Volume 2; Encyclopaedia of Materials: Electronics), Elsevier Science USA, 1st Edition, 1 January 2023: ISBN 9780128197288 Nanoscale Matter and Principles for Sensing and Labeling Applications: 206 (Advanced Structured Materials), 1st Ed 2024 Edition, 21 January 2024: ISBN 9819978475 == References ==
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Rajeshwari Chatterjee (24 January 1922 – 3 September 2010) was an Indian scientist and an academic. She was the first woman engineer from Karnataka and described herself as an engineering-scientist. During her tenure at the Indian Institute of Science (IISc), Bangalore, Chatterjee was a professor and later chairperson of the department of Electrical Communication Engineering. == Early life and education == Rajeshwari Chatterjee was born on 24 January 1922 in Karnataka. She had her primary education in a "special English school" founded by her grandmother, Kamalamma Dasappa, one of the first women graduates from Mysore and who was very active in the field of education, especially for widows and deserted wives. After her school finals, Chatterjee was tempted to take up History but eventually chose physics and mathematics. She studied in Central College of Bangalore and earned B.Sc. (Hons) and M.Sc. degrees in mathematics. In both these exams she ranked first in Mysore University. She received the Mummadi Krishnaraja Wodeyar Award, the M.T. Narayana Iyengar Prize and the Walters Memorial Prize respectively for her performances in the B.Sc. and M.Sc. examinations. In 1943, after her M.Sc., Chatterjee joined the Indian Institute of Science (IISc), Bangalore as a Research Student in the then Electrical Technology Department in the area of Communication. She approached physicist C.V. Raman to work under him. Some sources say that Raman refused to take her, stating that Rajeshwari had no degrees in physics, while others say that he was averse to the idea of having women students. After the Second World War, an interim government was set up in India to transfer power from the British to Indians, which offered scholarships to bright young scientists to study abroad. Chatterjee applied for a scholarship in the field of electronics and its applications, and in 1946, she was selected
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as a "bright student" by the Government of Delhi and given a scholarship to go abroad to pursue higher studies. Chatterjee chose to study in University of Michigan, Ann Arbor in the United States. In the 1950s, it was very difficult for Indian women to go abroad to pursue higher education. But Chatterjee was determined to do so. In July 1947, one month before India's independence, she started her journey to the USA on a converted troop ship SS Marine Adder and reached there after 30 days. In the US, she was admitted to the University of Michigan and obtained her master's degree from the Department of Electrical Engineering. Then following the guidelines of the contract she had with the Government of India, she underwent an eight months' practical training in the Division of Radio Frequency Measurements at the National Bureau of Standards in Washington, D.C. After the completion of the training she went back to the University of Michigan in 1949 on a Barbour scholarship and resumed her studies. In early 1953, she obtained her Ph.D. degree under the guidance of Professor William Gould Dow and successfully completed her dissertation. == Career in India == In 1953, after obtaining her PhD degree, she returned to India and became a faculty member at the IISc Department of Electrical Communication Engineering, later saying that she taught "electromagnetic theory, electron tube circuits, microwave technology, and radio engineering". That same year, she married Sisir Kumar Chatterjee, who was a faculty member of the same college. After their marriage, she and her husband built a microwave research laboratory and began research in the field of Microwave Engineering, the first such research in India. In the same period, Chatterjee was selected for the position of chairman in the Department of Electrical Communication Engineering. Over her
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lifetime, she mentored 20 PhD students, wrote over 100 research papers, and authored seven books. She taught classes in electromagnetic theory, electron tube circuits, microwave technology and radio engineering. Following her retirement from the IISc in 1982, she worked on social programs, including the Indian Association for Women's Studies. She also preferred to call herself an "engineering-scientist", as she did not work in industry like most engineers. == Publications == Elements of Microwave Engineering Antenna Theory And Practice A Thousand Streams: A Personal History Dielectric And Dielectric Loaded Antennas Advanced Microwave Engineering: Special Advanced Topics Vasudhaiva Kutumbakam: The Whole World Is But One Family: Real Stories of Some Women and Men of India Antennas for Information Super Skyways: An Exposition on Outdoor and Indoor Wireless Antenna, co-authored by Perambur S. Neelakanta == Personal life == Rajeshwari's father, B.M. Shivaramajah, was an advocate in Nanjangud. Her grandmother, Kamalamma Dasappa, was one of the first women graduates in the erstwhile state of Mysore. Rajeswari married Sisir Kumar Chatterjee, a faculty of IISc in 1953. The couple had a daughter Indira Chatterjee, who is now a professor of electrical and biomedical engineering at the University of Nevada, Reno, U.S. == Awards == For her contribution and works in the field of Microwave engineering, she won many awards. Some of the notable awards and honours are— Mummadi Krishnaraja Wodeyar Award for first rank in the BSc (Hons) M T Narayana Iyengar prize and the Waters Memorial prize for the first rank in M.Sc. Mountbatten prize for the best paper from the Institute of Electrical and Radio Engineering (UK) J.C Bose Memorial prize for the best research paper from the Institution of Engineers Ramlal Wadhwa Award for the best research and teaching work from the Institute of Electronics and Telecommunication Engineers. Chatterjee received a posthumous
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award in 2017 from the Indian Ministry of Women and Child Development, when she was named as one of "the first women achievers of India" for her work in microwave engineering and antennae engineering. == References ==
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Alternation of generations (also known as metagenesis or heterogenesis) is the predominant type of life cycle in plants and algae. In plants both phases are multicellular: the haploid sexual phase – the gametophyte – alternates with a diploid asexual phase – the sporophyte. A mature sporophyte produces haploid spores by meiosis, a process which reduces the number of chromosomes to half, from two sets to one. The resulting haploid spores germinate and grow into multicellular haploid gametophytes. At maturity, a gametophyte produces gametes by mitosis, the normal process of cell division in eukaryotes, which maintains the original number of chromosomes. Two haploid gametes (originating from different organisms of the same species or from the same organism) fuse to produce a diploid zygote, which divides repeatedly by mitosis, developing into a multicellular diploid sporophyte. This cycle, from gametophyte to sporophyte (or equally from sporophyte to gametophyte), is the way in which all land plants and most algae undergo sexual reproduction. The relationship between the sporophyte and gametophyte phases varies among different groups of plants. In the majority of algae, the sporophyte and gametophyte are separate independent organisms, which may or may not have a similar appearance. In liverworts, mosses and hornworts, the sporophyte is less well developed than the gametophyte and is largely dependent on it. Although moss and hornwort sporophytes can photosynthesise, they require additional photosynthate from the gametophyte to sustain growth and spore development and depend on it for supply of water, mineral nutrients and nitrogen. By contrast, in all modern vascular plants the gametophyte is less well developed than the sporophyte, although their Devonian ancestors had gametophytes and sporophytes of approximately equivalent complexity. In ferns the gametophyte is a small flattened autotrophic prothallus on which the young sporophyte is briefly dependent for its nutrition. In flowering plants, the
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reduction of the gametophyte is much more extreme; it consists of just a few cells which grow entirely inside the sporophyte. Animals develop differently. They directly produce haploid gametes. No haploid spores capable of dividing are produced, so generally there is no multicellular haploid phase. Some insects have a sex-determining system whereby haploid males are produced from unfertilized eggs; however females produced from fertilized eggs are diploid. Life cycles of plants and algae with alternating haploid and diploid multicellular stages are referred to as diplohaplontic. The equivalent terms haplodiplontic, diplobiontic and dibiontic are also in use, as is describing such an organism as having a diphasic ontogeny. Life cycles of animals, in which there is only a diploid multicellular stage, are referred to as diplontic. Life cycles in which there is only a haploid multicellular stage are referred to as haplontic. == Definition == Alternation of generations is defined as the alternation of multicellular diploid and haploid forms in the organism's life cycle, regardless of whether these forms are free-living. In some species, such as the alga Ulva lactuca, the diploid and haploid forms are indeed both free-living independent organisms, essentially identical in appearance and therefore said to be isomorphic. In many algae, the free-swimming, haploid gametes form a diploid zygote which germinates into a multicellular diploid sporophyte. The sporophyte produces free-swimming haploid spores by meiosis that germinate into haploid gametophytes. However, in land plants, either the sporophyte or the gametophyte is very much reduced and is incapable of free living. For example, in all bryophytes the gametophyte generation is dominant and the sporophyte is dependent on it. By contrast, in all seed plants the gametophytes are strongly reduced, although the fossil evidence indicates that they were derived from isomorphic ancestors. In seed plants, the female gametophyte develops totally within
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the sporophyte, which protects and nurtures it and the embryonic sporophyte that it produces. The pollen grains, which are the male gametophytes, are reduced to only a few cells (just three cells in many cases). Here the notion of two generations is less obvious; as Bateman & Dimichele say "sporophyte and gametophyte effectively function as a single organism". The alternative term 'alternation of phases' may then be more appropriate. == History == === In animals === Initially, Adelbert von Chamisso (studying salps, colonial marine animals between 1815 and 1818) and Japetus Steenstrup (studying the development of trematodes in 1842, and also tunicates and cnidarians) described the succession of differently organized generations (sexual and asexual) in animals as "alternation of generations". Later, the phenomenon in animals became known as heterogamy, while the term "alternation of generations" was restricted to the life cycles of plants, meaning specifically the alternation of haploid gametophytes and diploid sporophytes. === In plants === In 1851, Wilhelm Hofmeister demonstrated the morphological alternation of generations in plants, between a spore-bearing generation (sporophyte) and a gamete-bearing generation (gametophyte). By that time, a debate emerged focusing on the origin of the asexual generation of land plants (i.e., the sporophyte) and is conventionally characterized as a conflict between theories of antithetic (Ladislav Josef Čelakovský, 1874) and homologous (Nathanael Pringsheim, 1876) alternation of generations. In 1874, Eduard Strasburger discovered the alternation between diploid and haploid nuclear phases, also called cytological alternation of nuclear phases. Although most often coinciding, morphological alternation and nuclear phases alternation are sometimes independent of one another, e.g., in many red algae, the same nuclear phase may correspond to two diverse morphological generations. In some ferns which lost sexual reproduction, there is no change in nuclear phase, but the alternation of generations is maintained. == Alternation of generations in
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plants == === Fundamental elements === The diagram above shows the fundamental elements of the alternation of generations in plants. There are many variations in different groups of plants. The processes involved are as follows: Two single-celled haploid gametes, each containing n unpaired chromosomes, fuse to form a single-celled diploid zygote, which now contains n pairs of chromosomes, i.e. 2n chromosomes in total. The single-celled diploid zygote germinates, dividing by the normal process (mitosis), which maintains the number of chromosomes at 2n. The result is a multi-cellular diploid organism, called the sporophyte (because at maturity it produces spores). When it reaches maturity, the sporophyte produces one or more sporangia (singular: sporangium) which are the organs that produce diploid spore mother cells (sporocytes). These divide by a special process (meiosis) that reduces the number of chromosomes by a half. This initially results in four single-celled haploid spores, each containing n unpaired chromosomes. The single-celled haploid spore germinates, dividing by the normal process (mitosis), which maintains the number of chromosomes at n. The result is a multi-cellular haploid organism, called the gametophyte (because it produces gametes at maturity). When it reaches maturity, the gametophyte produces one or more gametangia (singular: gametangium) which are the organs that produce haploid gametes. At least one kind of gamete possesses some mechanism for reaching another gamete in order to fuse with it. The 'alternation of generations' in the life cycle is thus between a diploid (2n) generation of multicellular sporophytes and a haploid (n) generation of multicellular gametophytes. The situation is quite different from that in animals, where the fundamental process is that a multicellular diploid (2n) individual directly produces haploid (n) gametes by meiosis. In animals, spores (i.e. haploid cells which are able to undergo mitosis) are not produced, so there is no asexual multicellular
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generation. Some insects have haploid males that develop from unfertilized eggs, but the females are all diploid. === Variations === The diagram shown above is a good representation of the life cycle of some multi-cellular algae (e.g. the genus Cladophora) which have sporophytes and gametophytes of almost identical appearance and which do not have different kinds of spores or gametes. However, there are many possible variations on the fundamental elements of a life cycle which has alternation of generations. Each variation may occur separately or in combination, resulting in a bewildering variety of life cycles. The terms used by botanists in describing these life cycles can be equally bewildering. As Bateman and Dimichele say "[...] the alternation of generations has become a terminological morass; often, one term represents several concepts or one concept is represented by several terms." Possible variations are: Relative importance of the sporophyte and the gametophyte. Equal (homomorphy or isomorphy).Filamentous algae of the genus Cladophora, which are predominantly found in fresh water, have diploid sporophytes and haploid gametophytes which are externally indistinguishable. No living land plant has equally dominant sporophytes and gametophytes, although some theories of the evolution of alternation of generations suggest that ancestral land plants did. Unequal (heteromorphy or anisomorphy). Dominant gametophyte (gametophytic).In liverworts, mosses and hornworts, the dominant form is the haploid gametophyte. The diploid sporophyte is not capable of an independent existence, gaining most of its nutrition from the parent gametophyte, and having no chlorophyll when mature. Dominant sporophyte (sporophytic).In ferns, both the sporophyte and the gametophyte are capable of living independently, but the dominant form is the diploid sporophyte. The haploid gametophyte is much smaller and simpler in structure. In seed plants, the gametophyte is even more reduced (at the minimum to only three cells), gaining all its nutrition from the sporophyte.
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The extreme reduction in the size of the gametophyte and its retention within the sporophyte means that when applied to seed plants the term 'alternation of generations' is somewhat misleading: "[s]porophyte and gametophyte effectively function as a single organism". Some authors have preferred the term 'alternation of phases'. Differentiation of the gametes. Both gametes the same (isogamy).Like other species of Cladophora, C. callicoma has flagellated gametes which are identical in appearance and ability to move. Gametes of two distinct sizes (anisogamy). Both of similar motility.Species of Ulva, the sea lettuce, have gametes which all have two flagella and so are motile. However they are of two sizes: larger 'female' gametes and smaller 'male' gametes. One large and sessile, one small and motile (oogamy). The larger sessile megagametes are eggs (ova), and smaller motile microgametes are sperm (spermatozoa, spermatozoids). The degree of motility of the sperm may be very limited (as in the case of flowering plants) but all are able to move towards the sessile eggs. When (as is almost always the case) the sperm and eggs are produced in different kinds of gametangia, the sperm-producing ones are called antheridia (singular antheridium) and the egg-producing ones archegonia (singular archegonium). Antheridia and archegonia occur on the same gametophyte, which is then called monoicous. (Many sources, including those concerned with bryophytes, use the term 'monoecious' for this situation and 'dioecious' for the opposite. Here 'monoecious' and 'dioecious' are used only for sporophytes.)The liverwort Pellia epiphylla has the gametophyte as the dominant generation. It is monoicous: the small reddish sperm-producing antheridia are scattered along the midrib while the egg-producing archegonia grow nearer the tips of divisions of the plant. Antheridia and archegonia occur on different gametophytes, which are then called dioicous.The moss Mnium hornum has the gametophyte as the dominant generation. It is
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dioicous: male plants produce only antheridia in terminal rosettes, female plants produce only archegonia in the form of stalked capsules. Seed plant gametophytes are also dioicous. However, the parent sporophyte may be monoecious, producing both male and female gametophytes or dioecious, producing gametophytes of one gender only. Seed plant gametophytes are extremely reduced in size; the archegonium consists only of a small number of cells, and the entire male gametophyte may be represented by only two cells. Differentiation of the spores. All spores the same size (homospory or isospory).Horsetails (species of Equisetum) have spores which are all of the same size. Spores of two distinct sizes (heterospory or anisospory): larger megaspores and smaller microspores. When the two kinds of spore are produced in different kinds of sporangia, these are called megasporangia and microsporangia. A megaspore often (but not always) develops at the expense of the other three cells resulting from meiosis, which abort. Megasporangia and microsporangia occur on the same sporophyte, which is then called monoecious.Most flowering plants fall into this category. Thus the flower of a lily contains six stamens (the microsporangia) which produce microspores which develop into pollen grains (the microgametophytes), and three fused carpels which produce integumented megasporangia (ovules) each of which produces a megaspore which develops inside the megasporangium to produce the megagametophyte. In other plants, such as hazel, some flowers have only stamens, others only carpels, but the same plant (i.e. sporophyte) has both kinds of flower and so is monoecious. Megasporangia and microsporangia occur on different sporophytes, which are then called dioecious.An individual tree of the European holly (Ilex aquifolium) produces either 'male' flowers which have only functional stamens (microsporangia) producing microspores which develop into pollen grains (microgametophytes) or 'female' flowers which have only functional carpels producing integumented megasporangia (ovules) that contain a megaspore
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that develops into a multicellular megagametophyte. There are some correlations between these variations, but they are just that, correlations, and not absolute. For example, in flowering plants, microspores ultimately produce microgametes (sperm) and megaspores ultimately produce megagametes (eggs). However, in ferns and their allies there are groups with undifferentiated spores but differentiated gametophytes. For example, the fern Ceratopteris thalictrioides has spores of only one kind, which vary continuously in size. Smaller spores tend to germinate into gametophytes which produce only sperm-producing antheridia. === A complex life cycle === Plant life cycles can be complex. Alternation of generations can take place in plants which are at once heteromorphic, sporophytic, oogametic, dioicous, heterosporic and dioecious, such as in a willow tree (as most species of the genus Salix are dioecious). The processes involved are: An immobile egg, contained in the archegonium, fuses with a mobile sperm, released from an antheridium. The resulting zygote is either male or female. A male zygote develops by mitosis into a microsporophyte, which at maturity produces one or more microsporangia. Microspores develop within the microsporangium by meiosis.In a willow (like all seed plants) the zygote first develops into an embryo microsporophyte within the ovule (a megasporangium enclosed in one or more protective layers of tissue known as integument). At maturity, these structures become the seed. Later the seed is shed, germinates and grows into a mature tree. A male willow tree (a microsporophyte) produces flowers with only stamens, the anthers of which are the microsporangia. Microspores germinate producing microgametophytes; at maturity one or more antheridia are produced. Sperm develop within the antheridia.In a willow, microspores are not liberated from the anther (the microsporangium), but develop into pollen grains (microgametophytes) within it. The whole pollen grain is moved (e.g. by an insect or by the wind) to an
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ovule (megagametophyte), where a sperm is produced which moves down a pollen tube to reach the egg. A female zygote develops by mitosis into a megasporophyte, which at maturity produces one or more megasporangia. Megaspores develop within the megasporangium; typically one of the four spores produced by meiosis gains bulk at the expense of the remaining three, which disappear.Female willow trees (megasporophytes) produce flowers with only carpels (modified leaves that bear the megasporangia). Megaspores germinate producing megagametophytes; at maturity one or more archegonia are produced. Eggs develop within the archegonia. The carpels of a willow produce ovules, megasporangia enclosed in integuments. Within each ovule, a megaspore develops by mitosis into a megagametophyte. An archegonium develops within the megagametophyte and produces an egg. The whole of the gametophytic generation remains within the protection of the sporophyte except for pollen grains (which have been reduced to just three cells contained within the microspore wall). == Life cycles of different plant groups == The term "plants" is taken here to mean the Archaeplastida, i.e. the glaucophytes, red and green algae and land plants. Alternation of generations occurs in almost all multicellular red and green algae, both freshwater forms (such as Cladophora) and seaweeds (such as Ulva). In most, the generations are homomorphic (isomorphic) and free-living. Some species of red algae have a complex triphasic alternation of generations, in which there is a gametophyte phase and two distinct sporophyte phases. For further information, see Red algae: Reproduction. Land plants all have heteromorphic (anisomorphic) alternation of generations, in which the sporophyte and gametophyte are distinctly different. All bryophytes, i.e. liverworts, mosses and hornworts, have the gametophyte generation as the most conspicuous. As an illustration, consider a monoicous moss. Antheridia and archegonia develop on the mature plant (the gametophyte). In the presence of water, the biflagellate
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sperm from the antheridia swim to the archegonia and fertilisation occurs, leading to the production of a diploid sporophyte. The sporophyte grows up from the archegonium. Its body comprises a long stalk topped by a capsule within which spore-producing cells undergo meiosis to form haploid spores. Most mosses rely on the wind to disperse these spores, although Splachnum sphaericum is entomophilous, recruiting insects to disperse its spores. The life cycle of ferns and their allies, including clubmosses and horsetails, the conspicuous plant observed in the field is the diploid sporophyte. The haploid spores develop in sori on the underside of the fronds and are dispersed by the wind (or in some cases, by floating on water). If conditions are right, a spore will germinate and grow into a rather inconspicuous plant body called a prothallus. The haploid prothallus does not resemble the sporophyte, and as such ferns and their allies have a heteromorphic alternation of generations. The prothallus is short-lived, but carries out sexual reproduction, producing the diploid zygote that then grows out of the prothallus as the sporophyte. In the spermatophytes, the seed plants, the sporophyte is the dominant multicellular phase; the gametophytes are strongly reduced in size and very different in morphology. The entire gametophyte generation, with the sole exception of pollen grains (microgametophytes), is contained within the sporophyte. The life cycle of a dioecious flowering plant (angiosperm), the willow, has been outlined in some detail in an earlier section (A complex life cycle). The life cycle of a gymnosperm is similar. However, flowering plants have in addition a phenomenon called 'double fertilization'. In the process of double fertilization, two sperm nuclei from a pollen grain (the microgametophyte), rather than a single sperm, enter the archegonium of the megagametophyte; one fuses with the egg nucleus to form the
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zygote, the other fuses with two other nuclei of the gametophyte to form 'endosperm', which nourishes the developing embryo. == Evolution of the dominant diploid phase == It has been proposed that the basis for the emergence of the diploid phase of the life cycle (sporophyte) as the dominant phase (e.g. as in vascular plants) is that diploidy allows masking of the expression of deleterious mutations through genetic complementation. Thus if one of the parental genomes in the diploid cells contained mutations leading to defects in one or more gene products, these deficiencies could be compensated for by the other parental genome (which nevertheless may have its own defects in other genes). As the diploid phase was becoming predominant, the masking effect likely allowed genome size, and hence information content, to increase without the constraint of having to improve accuracy of DNA replication. The opportunity to increase information content at low cost was advantageous because it permitted new adaptations to be encoded. This view has been challenged, with evidence showing that selection is no more effective in the haploid than in the diploid phases of the lifecycle of mosses and angiosperms. == Similar processes in other organisms == === Rhizaria === Some organisms currently classified in the clade Rhizaria and thus not plants in the sense used here, exhibit alternation of generations. Most Foraminifera undergo a heteromorphic alternation of generations between haploid gamont and diploid agamont forms. The diploid form is typically much larger than the haploid form; these forms are known as the microsphere and megalosphere, respectively. === Fungi === Fungal mycelia are typically haploid. When mycelia of different mating types meet, they produce two multinucleate ball-shaped cells, which join via a "mating bridge". Nuclei move from one mycelium into the other, forming a heterokaryon (meaning "different nuclei"). This
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process is called plasmogamy. Actual fusion to form diploid nuclei is called karyogamy, and may not occur until sporangia are formed. Karogamy produces a diploid zygote, which is a short-lived sporophyte that soon undergoes meiosis to form haploid spores. When the spores germinate, they develop into new mycelia. === Slime moulds === The life cycle of slime moulds is very similar to that of fungi. Haploid spores germinate to form swarm cells or myxamoebae. These fuse in a process referred to as plasmogamy and karyogamy to form a diploid zygote. The zygote develops into a plasmodium, and the mature plasmodium produces, depending on the species, one to many fruiting bodies containing haploid spores. === Animals === Alternation between a multicellular diploid and a multicellular haploid generation is never encountered in animals. In some animals, there is an alternation between parthenogenic and sexually reproductive phases (heterogamy), for instance in salps and doliolids (class Thaliacea). Both phases are diploid. This has sometimes been called "alternation of generations", but is quite different. In some other animals, such as hymenopterans, males are haploid and females diploid, but this is always the case rather than there being an alternation between distinct generations. == See also == Apomixis – Replacement of the normal sexual reproduction by asexual reproduction, without fertilization Evolutionary history of plants#life cycles: Evolutionary origin of the alternation of phases Ploidy – Number of sets of chromosomes of a cell == Notes and references == == Bibliography == Barnes, R.S.K.; Calow, P.; Olive, P.J.W.; Golding, D.W. & Spicer, J.I. (2001), The Invertebrates: a synthesis, Oxford; Malden, MA: Blackwell, ISBN 978-0-632-04761-1 Bateman, R.M. & Dimichele, W.A. (1994), "Heterospory – the most iterative key innovation in the evolutionary history of the plant kingdom" (PDF), Biological Reviews of the Cambridge Philosophical Society, 69 (3): 345–417, doi:10.1111/j.1469-185x.1994.tb01276.x, S2CID
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29709953, archived from the original (PDF) on 2012-04-15, retrieved 2010-12-30 Bell, P.R. & Hemsley, A.R. (2000), Green Plants: their Origin and Diversity (2nd ed.), Cambridge, etc.: Cambridge University Press, ISBN 978-0-521-64109-8 Foster, A.S. & Gifford, E.M. (1974), Comparative Morphology of Vascular Plants (2nd ed.), San Francisco: W.H. Freeman, ISBN 978-0-7167-0712-7 Guiry, M.D.; Guiry, G.M. (2008), "Cladophora", AlgaeBase, World-wide electronic publication, National University of Ireland, Galway, retrieved 2011-07-21 Kirby, A. (2001), Ulva, the sea lettuce, Monterey Bay Aquarium Research Institute, archived from the original on 2011-05-16, retrieved 2011-01-01 Scott, Thomas (1996), Concise Encyclopedia Biology, Berlin: Walter de Gruyter, ISBN 978-3-11-010661-9 Shyam, R. (1980), "On the life-cycle, cytology and taxonomy of Cladophora callicoma from India", American Journal of Botany, 67 (5): 619–24, doi:10.2307/2442655, JSTOR 2442655 Sporne, K.R. (1974a), The Morphology of Angiosperms, London: Hutchinson, ISBN 978-0-09-120611-6 Sporne, K.R. (1974b), The Morphology of Gymnosperms (2nd ed.), London: Hutchinson, ISBN 978-0-09-077152-3 Stewart, W.N. & Rothwell, G.W. (1993), Paleobotany and the Evolution of Plants (2nd ed.), Cambridge, UK: Cambridge University Press, ISBN 978-0-521-38294-6 Watson, E.V. (1981), British Mosses and Liverworts (3rd ed.), Cambridge, UK: Cambridge University Press, ISBN 978-0-521-28536-0 Taylor, T.N.; Kerp, H. & Hass, H. (2005), "Life history biology of early land plants: Deciphering the gametophyte phase", Proceedings of the National Academy of Sciences of the United States of America, 102 (16): 5892–5897, Bibcode:2005PNAS..102.5892T, doi:10.1073/pnas.0501985102, PMC 556298, PMID 15809414
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Cuminaldehyde (4-isopropylbenzaldehyde) is a natural organic compound with the molecular formula C10H12O. It is a benzaldehyde with an isopropyl group substituted in the 4-position. Cuminaldehyde is a constituent of the essential oils of eucalyptus, myrrh, cassia, cumin, and others. It has a pleasant smell and contributes to the aroma of these oils. It is used commercially in perfumes and other cosmetics. It has been shown that cuminaldehyde, as a small molecule, inhibits the fibrillation of alpha-synuclein, which, if aggregated, forms insoluble fibrils in pathological conditions characterized by Lewy bodies, such as Parkinson's disease, dementia with Lewy bodies and multiple system atrophy. Cuminaldehyde can be prepared synthetically by the reduction of 4-isopropylbenzoyl chloride or by the formylation of cumene. The thiosemicarbazone of cuminaldehyde has antiviral properties. == References ==
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"title": "Cuminaldehyde"
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Frame Arms Girl (Japanese: フレームアームズ・ガール, Hepburn: Furēmu Āmuzu Gāru) is a series of heavily customizable model kit girls produced by Kotobukiya, originally released in 2015 as a moé reimagining of the more traditional, equally customizable Frame Arms mecha line and acts as a sister series to the Megami Device line of more traditional, non-derivative mecha musume kits, of which the line has regularly crossed over with. A prequel manga for the anime by Tsuneo Tsuneishi began serialization in Kadokawa Shoten's Comp Ace magazine in December 2016. An anime television series inspired by the line aired from April 3, 2017, to June 19, 2017. A recap film Frame Arms Girl: Kyakkyau Fufu na Wonderland was released on June 29, 2019. == Summary == Based on the original Frame Arms line, Frame Arms Girl features the robots from that line re-portrayed as anthropomorphic mecha musume, known as F.A. Girls for short, who can be equipped with various armor and weapon parts, including mixing and matching those from other original Kotobukiya kit lines, Frame Arms and the M.S.G accessory series included. The end result resembles a doll or figure with accessories attached, ranging from heavy armaments to articles of clothing, sold at the size of 1/1 scale for lore purposes, but translate to 1/10 by default and 1/24 scale for handscale versions when compared to the human body. The line's initial character design was illustrated by Fumikane Shimada, loosely inspired by Takayuki Yanase original Frame Arms mecha designs, but has since expanded to commission other artists to help on new F.A. Girls. == Multimedia Storyline == === Characters === The following is a description of characters and their personalities that appeared in the anime and manga as opposed to their respective real life kits' instruction manuals. Gennai Ao (源内 あお) Voiced by: Yoko
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Hikasa A human girl who is given the job of providing data for the F.A. Girls by Factory Advance. Because her parents have business overseas, she lives alone in her apartment. As more F.A. Girls are sent to her, she slowly begins accepting them as a family. Gourai (轟雷, Gōrai) Voiced by: Narumi Kaho An F.A. Girl who is sent to Ao to gather emotion data. She is a ground-based fighter who can move quickly with tank-style treads, but has a disadvantage over aerial types. It is revealed that there are many copies of her sent out to different people around the city, but Ao's is the only one that is active. She is the first F.A. Girl that Ao receives. Stylet (スティレット, Suteiretto) Voiced by: Yu Ayase A bossy F.A. Girl who gets flustered easily. Equipped with wings, she specializes in aerial combat. Ao nicknames her Sty-ko. She and Baselard are sent to Ao's apartment shortly after Gourai. Baselard (バーゼラルド, Bāzerarudo) Voiced by: Rika Nagae An energetic and childish F.A. Girl who likes to cause mischief. Like Stylet, she is an aerial type who focuses on guided laser weapons. She and Stylet are sent to Ao's apartment shortly after Gourai. Materia Sisters (マテリア姉妹, Materia Shimai) Voiced by: Erii Yamazaki A pair of F.A. Girls who have the same model and can be considered as sisters, given the names White (シロ, Shiro) and Black (クロ, Kuro) to distinguish from each other. They are oddly affectionate towards each other and take pleasure in torturing others, often omitting the use of armor in favor of powerful weaponry. Ao receives them sometime after getting Gourai, Stylet, and Baselard. Architect (アーキテクト, Ākitekuto) Voiced by: Hibiku Yamamura An F.A. girl who, along with the Materia Sisters, is the basis of every other F.A. Girl and,
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according to Stylet, has no physical body and only manifests herself during certain battles to carry out her programming. She was given a physical body after Gourai and Jinrai defeated her, loaded with the data generated during their battle. She shows very little emotion compared to the other F.A. Girls, and has the ability to alter her appearance in battle. She is the seventh F.A. Girl that Ao receives. Jinrai (迅雷, Jinrai) Voiced by: Minami Kabayama A proud and traditionalist F.A. Girl who has a particularly obsession with the Sengoku period and specializes in ninja techniques. She is the sixth F.A. Girl that Ao receives. Hresvelgr (フレズヴェルク, Furezuveruku) Voiced by: Rika Abe A powerful F.A. Girl who gave Gourai her first defeat, causing Gourai to improve further. Ao nicknames her Hres. She is arrogant, a little antagonistic, and loves to battle. Factory Advance later provides her with an upgrade that alters her appearance, but this unintentionally corrupts her. After Gourai defeats her, she is freed from her corruptive state and is allowed to stay with Ao, developing a much nicer personality afterwards. She is the last F.A. Girl that Ao receives. Kotobuki Bukiko (寿 武希子) Voiced by: Kanomi Izawa Ao's best friend, who is obsessed with model kits and often provides Ao with the latest parts after finding out about the F.A. Girls. She is also a moé reimagining of Kotobukiya, the real-life company behind Frame Arms Girls. Guriko A mysterious girl that Ao meets at the park that she used to visit when she was a child, who guides Ao to a time capsule that she buried there. She disappears afterwards. A doll version of her is found inside of the time capsule, which implies that she is a vision from Ao's past. Jyuden-kun Every F.A. Girl is accompanied
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by these small robots who are tasked with recharging them and preparing them for battles. They can also act as a chair or as a bed for them, and can serve as a communication device. Sleipni-taro It was originally a cleaning robot that experiences malfunctions. After it was repaired, the robot was also given an upgrade as well as artificial intelligence. It usually serves as a means of transportation for the F.A. Girls and as a rideable toy by Baselard. Nipako Godhand's mascot. In the show, she cameos as a nipper tsukumogami who haunts Ao's school after a girl misused a pair of plastic cutting nippers on metal, being the GodHand SPN-120 Ultimate, a nipper regarded as a glass cannon for its highest quality cuts in the plamo hobby and highest level of fragility on misuse. Nipako haunts the school at night, possessing the very same nippers that broke. After cutting off an unneeded fragment that was to be cleaned from Gourai's armor, the nippers return to normal and is taken back to Ao's place as a souvenir while Nipako watches them with happiness, implying that she is now at peace knowing that she will be handled with care in the future. Innocentia A newly developed F.A. Girl who was teased at the end of the final episode. Her abilities and future remain unknown and she is unvoiced within the anime. === Manga === A manga prequel written by Kotobukiya and illustrated by Tsuneo Tsuneishi, titled Frame Arms Girl: Lab Days (フレームアームズ・ガール ラボ・デイズ, Frēmu Āmuzu Gāru: Rabo Deizu), began serialization in Kadokawa Shoten's Comp Ace magazine from December 26, 2016. === Anime === A 12-episode anime television adaption aired on Tokyo MX between April 3, 2017, and June 19, 2017, also airing on BS11 and AT-X. The anime was directed
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by Keiichiro Kawaguchi at studios Zexcs and Studio A-Cat with scripts written by Deko Akao and the music is produced by Keigo Hoashi and Kakeru Ishihama. Sentai Filmworks have licensed it for home video and digital release. The series was streamed by the Anime Network. The opening theme is "Tiny Tiny" by Rie Murakawa while the ending theme is "Fullscratch Love", performed by the series' voice actresses. The anime follows a girl named Ao who is sent a prototype F.A. Girl known as Gourai and is tasked with helping her gather data on both battle and emotions. The two soon encounter more F.A. Girls sent by Factory Advance, the company who created them, who Gourai battles against while also having various adventures alongside. Any F.A. Girls that Gourai defeats are allowed to stay with her and Ao. A film titled Frame Arms Girl: Kyakkyau Fufu na Wonderland has been announced. It was revealed that the film will be a compilation film with new added footage. The film premiered on June 29, 2019. == Note == == See also == Alice Gear Aegis Arcanadea, another plastic model series created by Kotobukiya Busou Shinki Hundred Infinite Stratos Little Battlers Experience Symphogear == References == == External links == Official anime website (in Japanese) Official website (in Japanese) Frame Arms Girl Official on YouTube Frame Arms Girl (anime) at Anime News Network's encyclopedia
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Thomas Hertog is a Belgian cosmologist at KU Leuven university and was a key collaborator of Professor Stephen Hawking. == Early life == Thomas Hertog was born on 27 May 1975. He graduated Summa cum laude from KU Leuven in 1997 with an MSc degree in physics. He obtained his Master's degree at the University of Cambridge in Part III of the Mathematical Tripos and obtained a Ph.D. degree at Cambridge with a thesis on the origins of cosmic expansion under the supervision of Stephen Hawking. == Career == Hertog had the opportunity to conduct research with Stephen Hawking in the field of cosmic inflation, a branch of the Big Bang theory. He then worked as a researcher at the University of California - Santa Barbara in the United States and the Université de Paris VII in France. He became a fellow at CERN in Geneva in 2005. In October 2011, Hertog was appointed professor at the Institute for Theoretical Physics at KU Leuven through the Odysseus program of the Flemish government. He leads a research group studying the relationship between the Big Bang and string theory, with the idea that concepts like space and time lose their meaning. He also emphasizes Georges Lemaître's insight that the Big Bang is central to Einstein's gravitational waves. Hertog worked in the field of quantum cosmology and string theory with James Hartle and Stephen Hawking. In 2011, after years of research, they came to a new insight by combining the mathematics of quantum cosmology and that of string theory. In 2018, he published 'A smooth exit from eternal inflation?' with Stephen Hawking. Hertog was an important contributor to the development of top-down cosmology. He explains the theory in his 2023 book On the Origin of Time, which Hawking asked him to write just
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before his death. == Selected publications == === Books === Hertog, Thomas; Baert, Barbara; Van de Stock, Jan (2021). Big Bang: Imagining the Universe. Translated by Simpson, Helen; Logan, Sandy. Hannibal Books. ISBN 9789463887878. Hertog, Thomas (2023). On the Origin of Time: Stephen Hawking's Final Theory. Random House. ISBN 9780593128442. === Journal articles === Binétruy, P.; Bohé, A.; Hertog, T.; Steer, D. A. (9 December 2009). "Gravitational wave bursts from cosmic superstrings with Y-junctions". Physical Review D. 80 (12). American Physical Society (APS): 123510. arXiv:0907.4522. Bibcode:2009PhRvD..80l3510B. doi:10.1103/physrevd.80.123510. ISSN 1550-7998. S2CID 7271201. Hertog, Thomas; Horowitz, Gary T (30 July 2004). "Towards a Big Crunch Dual". Journal of High Energy Physics. 2004 (7). Springer Science and Business Media LLC: 073. arXiv:hep-th/0406134. Bibcode:2004JHEP...07..073H. doi:10.1088/1126-6708/2004/07/073. ISSN 1029-8479. S2CID 16255740. Hawking, S. W.; Hertog, T.; Reall, H. S. (29 June 2000). "Brane new world". Physical Review D. 62 (4). American Physical Society (APS): 043501. arXiv:hep-th/0003052. Bibcode:2000PhRvD..62d3501H. doi:10.1103/physrevd.62.043501. ISSN 0556-2821. S2CID 7180487. Hawking, S. W.; Hertog, Thomas (2018). "A smooth exit from eternal inflation?". Journal of High Energy Physics. 2018 (4). Springer Science and Business Media LLC: 147. arXiv:1707.07702. Bibcode:2018JHEP...04..147H. doi:10.1007/jhep04(2018)147. ISSN 1029-8479. S2CID 13745992. == See also == On the Origin of Time Christophe Galfard == References == == External links == https://orcid.org/0000-0002-9021-5966 https://www.researchgate.net/profile/Thomas_Hertog
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This is a categorized list of physics mnemonics. == Mechanics == === Work: formula === "Lots of Work makes me Mad!": Work = Mad: M=Mass a=acceleration d=distance == Thermodynamics == === Ideal gas law === "Pure Virgins Never Really Tire": PV=nRT The equation PV = nRT represents the ideal gas law, where P is the pressure of the gas, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature. === Gibbs's free energy formula === "Good Honey Tastes Sweet": (delta)G = H - T(delta)S. Gibbs free energy is a thermodynamic state function that measures the energy available for a system to do work, and is given by the formula G = H – TS, where H is enthalpy, T is temperature, and S is entropy. == Electrodynamics == === Ohm's Law === "Virgins Are Rare": Volts = Amps x Resistance === Relation between Resistance and Resistivity === REPLAY Resistance = ρ (Length/Area) === Inductive and Capacitive circuits === Once upon a time, the symbol E (for electromotive force) was used to designate voltages. Then, every student learned the phrase ELI the ICE man as a reminder that: For an inductive (L) circuit, the EMF (E) is ahead of the current (I) While for a capactive circuit (C), the current (I) is ahead of the EMF (E). And then they all lived happily ever after. === Open and Short circuits === "There are zero COVS grazing in the field!" This is a mnemonic to remember the useful fact that: The Current through an Open circuit is always zero The Voltage across a Short circuit is always zero === Order of rainbow colors === ROYGBIV (in reverse VIBGYOR) is commonly used to remember the order of colors in the visible light
|
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"page_id": 45417452,
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spectrum, as seen in a rainbow. Richard of York gave battle in vain" (red, orange, yellow, green, blue, indigo, violet). Additionally, the fictitious name Roy G. Biv can be used as well. (red, orange, yellow, green, blue, indigo, violet). === Speed of light === The phrase "We guarantee certainty, clearly referring to this light mnemonic." represents the speed of light in meters per second through the number of letters in each word: 299,792,458. === Electromagnetic spectrum === In the order of increasing frequency or decreasing wavelength of electromagnetic waves; Road Men Invented Very Unique Xtra Gums Ronald McDonald Invented Very Unusual & eXcellent Gherkins. Remember My Instructions Visible Under X-Ray Glasses Raging (or Red) Martians Invaded Venus Using X-ray Guns. Rahul's Mother Is Visiting Uncle Xavier's Garden. Ryann May I Visit YoUr eX-Girlfriend? Rich Men In Vegas Use eXpensive Gadgets Rich Men In Vegas Use X-ray Glasses Royal Magicians Interested Viewing Untied X-mas Gifts In the order of increasing wavelength; Good Xylophones Use Very Interesting Musical Rhythms. Godzilla-X Using Violence In Meeting Room. Granddad Xavier Unfortunately Vomited In My Room. Grandma's X-Large Underwear Visible In My Room. === Microwave frequency bands === Microwave frequency bands ordered by increasing wavelengths (decreasing frequencies): King Xerxes Can Seduce Lovely (princesses) == Other == === Radium series (or uranium series) === To remember the decay chain of 238U, commonly called the "radium series" (sometimes "uranium series"). Beginning with naturally occurring uranium-238; A Bitty Bitty Ant Asked Another Ant About Bitty Bitty Ants' Bitty Bitty Aunts A = alpha decay B = beta decay == See also == List of electronic color code mnemonics List of chemistry mnemonics == References ==
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George Crawford Hyndman (1796–1867) was an Irish auctioneer and amateur biologist. He was the son of Cherry Crawford Hyndman (1766-1845) and James Hyndman (1761?–1825), a Belfast Woollen merchant. Both parents, in the 1790s, were active in the republican Society of United Irishmen. In heavily garrisoned Belfast, neither appear to have been implicated in the 1798 rebellion, but, for whatever reason, James Hyndman did not join other merchants and local dignitaries in signing a proclamation published just before the risings to the north and south of the town in June, which expressed support for the government. George was educated at the Belfast Academy until apprenticed to his father’s business at age 14. After his father died in 1825, he took the business over while devoting his leisure time to Irish natural history. He was particularly interested in the study of marine zoology and marine botany, especially molluscs and algae. His specimens of both groups may now be found in the Ulster Museum. Hyndman was a member of the Belfast Dredging Committee (other members were George Dickie, Edward Waller and John Gwyn Jeffreys). This operated from 1857 to 1859, under grants from the British Association for the Advancement of Science. William Thompson described Panningia hyndmani, a hermit crab for him as the discoverer in Belfast Lough. He was also a founder member of the Belfast Natural History Society and contributed to S.A.Stewart and T.H.Corry's Flora of the North-east. Anapagurus hyndmanni (Bell, 1845) as well as A. laevis and Pagurus cuanensis were also discovered by Hyndman at Portaferry (and Bangor) and named by Thompson (q.v.) without formal descriptions. Other hermit crab species named for Hyndman were: Escharina hyndmanni (Johnson, 1847) Iophon hyndmani (Bowerbank, 1858) Pseudione hyndmanni (Bate & Westwood, 1868). The Ulster Museum has an 1854-62 archive of George Crawford Hyndman containing 20
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letters from Francis Archer, Edward Benn, J. Bristow, Edward Charlesworth(1813–93) an English naturalist and palaeontologist), A. Crawford, Robert Damon (1814-1889) Dorset geologist and dealer in fossils), George Dickie, Edmund Getty, John Gwyn Jeffreys, William Molony, R. W. Hincks, J. Morpan, Robert Patterson, Edward Waller (1803-1873) Irish land owner owner of a yacht used for dredgings) and Charles Ward. == Works == 1853 Notes on the natural history of Tory Island. Ulster Journal of Archaeology 1: 34–37. 1857 Note on a curious monstrosity of the common shell (Fusus antiquus). Nat. Hist. : 250. 1858 Report of the Proceedings of the Belfast Dredging Committee. Report for the British Association for the Advancement of Science : 220-237 [1] 1859 Report of the Belfast Dredging Committee. Report for the British Association for the Advancement of Science : 282-293 [2] 1860 Report of the Belfast Dredging Committee for 1859. Report for the British Association for the Advancement of Science : 116-119 [3] (Committee joined by Charles Wyville Thomson. Most of Hyndman's discoveries are published with attribution in Thompson, William (edited by Patterson, R.) The Natural History of Ireland Volume 4: Mammalia, reptiles and fishes. Also, invertebrata. London: Henry G. Bohn, 1856 == References == Chesney, H.C.G. 1995 Ireland's pioneering malacologists - from dredging to drummondi. Arch. Nat. Hist. 22: 229-239 Foster, J. W. and Chesney, H. C. G (eds.), 1977: Nature in Ireland: A Scientific and Cultural History. Lilliput Press. ISBN 0-7735-1817-7. == External links == About Ireland pdfs of The Natural History of Ireland
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The olive branch, a ramus of Olea europaea, is a symbol of peace. It is generally associated with the customs of ancient Greece and ancient Rome, and is connected with supplication to divine beings and persons in power. Likewise, it is found in most cultures of the Mediterranean Basin and thence expanded to become an almost universally recognized peace symbol in the modern world. == In the Greco-Roman world == In Greek tradition, a hiketeria (ἱκετηρία) was an olive branch held by supplicants to show their status as such when approaching persons of power or in temples when supplicating the gods. In Greek mythology, Athena competed with Poseidon for possession of Athens. Poseidon claimed possession by thrusting his trident into the Acropolis, where a well of sea-water gushed out. Athena took possession by planting the first olive tree beside the well. The court of gods and goddesses ruled that Athena had the better right to the land because she had given it the better gift. Olive wreaths were worn by brides and awarded to olympic victors. The olive branch was one of the attributes of Eirene on Roman Imperial coins. For example, the reverse of a tetradrachm of Vespasian from Alexandria, 70-71 AD, shows Eirene standing holding a branch upward in her right hand. The Roman poet Virgil (70–19 BC) associated "the plump olive" with the goddess Pax (the Roman Eirene) and he used the olive branch as a symbol of peace in his Aeneid: For the Romans, there was an intimate relationship between war and peace, and Mars, the god of war, had another aspect, Mars Pacifer, Mars the bringer of Peace, who is shown on coins of the later Roman Empire bearing an olive branch. Appian describes the use of the olive-branch as a gesture of peace by
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"title": "Olive branch"
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the enemies of the Roman general Scipio Aemilianus in the Numantine War and by Hasdrubal the Boeotarch of Carthage. Although peace was associated with the olive branch during the time of the Greeks, the symbolism became even stronger under the Pax Romana when envoys used olive branches as tokens of peace. == Early Christianity == The olive branch appears with a dove in early Christian art. The dove derives from the simile of the Holy Spirit in the Gospels and the olive branch from classical symbolism. The early Christians, according to Winckelmann, often allegorized peace on their sepulchers by the figure of a dove bearing an olive branch in its beak. For example, in the Catacomb of Priscilla in Rome (2nd – 5th centuries AD) there is a depiction of three men (traditionally taken to be Shadrach, Meshach, and Abednego of the Book of Daniel) over whom hovers a dove with a branch; and in another of the Roman catacombs there is a shallow relief sculpture showing a dove with a branch flying to a figure marked in Greek ΕΙΡΗΝΗ (Eirene, or Peace). Tertullian (c. 160 – c. 220) compared Noah's dove in the Hebrew Bible, who "announced to the world the assuagement of divine wrath, when she had been sent out of the ark and returned with the olive branch" with the Holy Spirit in baptism "bringing us the peace of God, sent out from the heavens". In his 4th-century Latin translation of the story of Noah, St Jerome rendered "leaf of olive" (Hebrew alé zayit) in Genesis 8:11 as "branch of olive" (Latin ramum olivae). In the 5th century, by which time a dove with an olive branch had become established as a Christian symbol of peace, St Augustine wrote in On Christian Doctrine that, "perpetual peace is
|
{
"page_id": 1704944,
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|
indicated by the olive branch (oleae ramusculo) which the dove brought with it when it returned to the ark." However, in Jewish tradition, there is no association of the olive leaf with peace in the story of the flood. == Modern usage == An olive branch, sometimes held by a dove, was used as a peace symbol in 18th-century Britain, France and America. A 1729 portrait of Louis XV by François Lemoyne portrays him offering Europe an olive branch. A £2 note of North Carolina (1771) depicted the dove and olive with a motto meaning: "Peace restored". Georgia's $40 note of 1778 portrayed the dove and olive and a hand holding a dagger, with a motto meaning "Either war or peace, prepared for both." The olive branch appeared as a peace symbol in other 18th century prints. In January 1775, the frontispiece of the London Magazine published an engraving: "Peace descends on a cloud from the Temple of Commerce," in which the Goddess of Peace brings an olive branch to America and Britannia. A petition adopted by the American Continental Congress in July 1775 in the hope of avoiding a full-blown war with Great Britain was called the Olive Branch Petition. On July 4, 1776, a resolution was passed that allowed the creation of the Great Seal of the United States. On the Great Seal, there is an eagle grasping an olive branch in its right talon. The olive branch traditionally has been recognized as a symbol for peace. It was added to the seal in March 1780 by the second committee appointed by Congress to design the seal. The olive branch has thirteen olives and thirteen olive leaves to represent the thirteen original colonies. Later on, the bald eagle and bundle of thirteen arrows were added. The idea of
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{
"page_id": 1704944,
"source": null,
"title": "Olive branch"
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|
the olive branch opposing the bundle of thirteen arrows was to "denote the power of peace & war which is exclusively vested in Congress." The flag of Cyprus and coat of arms of Cyprus both use olive branches as symbols of peace between the communities of the country; it also appears on the flag of Eritrea. Olive branches can be found in many police patches and badges across the world to signify peace. The emblem and flag of the United Nations bear a pair of stylized olive branches surrounding a world map. The olive branch is a symbol of peace in Arab folk traditions. In 1974, Palestinian leader Yasser Arafat brought an olive branch to the UN General Assembly and said, "Today I have come bearing an olive branch and a freedom-fighter's gun. Do not let the olive branch fall from my hand." Several towns have been named Olive Branch as a symbol of peaceful living, such as Olive Branch, Mississippi. Some Western given names and surnames, such as "Oliver", "Olivier" and "Olifant" allude to an olive branch. == Gallery == == See also == == References == == External links == What does the olive branch symbolize?, Reference.com
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{
"page_id": 1704944,
"source": null,
"title": "Olive branch"
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|
The Cell Ontology is an ontology that aims at capturing the diversity of cell types in animals. It is part of the Open Biomedical and Biological Ontologies (OBO) Foundry. The Cell Ontology identifiers and organizational structure are used to annotate data at the level of cell types, for example in single-cell RNA-seq studies. It is one important resource in the construction of the Human Cell Atlas. The Cell Ontology was first described in an academic article in 2005. == See also == Gene ontology OBO Foundry == References == == External links == Cell Ontology GitHub page
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{
"page_id": 68682738,
"source": null,
"title": "Cell Ontology"
}
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In artificial intelligence, a differentiable neural computer (DNC) is a memory augmented neural network architecture (MANN), which is typically (but not by definition) recurrent in its implementation. The model was published in 2016 by Alex Graves et al. of DeepMind. == Applications == DNC indirectly takes inspiration from Von-Neumann architecture, making it likely to outperform conventional architectures in tasks that are fundamentally algorithmic that cannot be learned by finding a decision boundary. So far, DNCs have been demonstrated to handle only relatively simple tasks, which can be solved using conventional programming. But DNCs don't need to be programmed for each problem, but can instead be trained. This attention span allows the user to feed complex data structures such as graphs sequentially, and recall them for later use. Furthermore, they can learn aspects of symbolic reasoning and apply it to working memory. The researchers who published the method see promise that DNCs can be trained to perform complex, structured tasks and address big-data applications that require some sort of reasoning, such as generating video commentaries or semantic text analysis. DNC can be trained to navigate rapid transit systems, and apply that network to a different system. A neural network without memory would typically have to learn about each transit system from scratch. On graph traversal and sequence-processing tasks with supervised learning, DNCs performed better than alternatives such as long short-term memory or a neural turing machine. With a reinforcement learning approach to a block puzzle problem inspired by SHRDLU, DNC was trained via curriculum learning, and learned to make a plan. It performed better than a traditional recurrent neural network. == Architecture == DNC networks were introduced as an extension of the Neural Turing Machine (NTM), with the addition of memory attention mechanisms that control where the memory is stored, and
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{
"page_id": 52036598,
"source": null,
"title": "Differentiable neural computer"
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temporal attention that records the order of events. This structure allows DNCs to be more robust and abstract than a NTM, and still perform tasks that have longer-term dependencies than some predecessors such as Long Short Term Memory (LSTM). The memory, which is simply a matrix, can be allocated dynamically and accessed indefinitely. The DNC is differentiable end-to-end (each subcomponent of the model is differentiable, therefore so is the whole model). This makes it possible to optimize them efficiently using gradient descent. The DNC model is similar to the Von Neumann architecture, and because of the resizability of memory, it is Turing complete. === Traditional DNC === DNC, as originally published === Extensions === Refinements include sparse memory addressing, which reduces time and space complexity by thousands of times. This can be achieved by using an approximate nearest neighbor algorithm, such as Locality-sensitive hashing, or a random k-d tree like Fast Library for Approximate Nearest Neighbors from UBC. Adding Adaptive Computation Time (ACT) separates computation time from data time, which uses the fact that problem length and problem difficulty are not always the same. Training using synthetic gradients performs considerably better than Backpropagation through time (BPTT). Robustness can be improved with use of layer normalization and Bypass Dropout as regularization. == See also == Differentiable programming == References == == External links == A bit-by-bit guide to the equations governing differentiable neural computers DeepMind's Differentiable Neural Network Thinks Deeply
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{
"page_id": 52036598,
"source": null,
"title": "Differentiable neural computer"
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In chemistry, an alcohol (from Arabic al-kuḥl 'the kohl'), is a type of organic compound that carries at least one hydroxyl (−OH) functional group bound to a saturated carbon atom. Alcohols range from the simple, like methanol and ethanol, to complex, like sugar alcohols and cholesterol. The presence of an OH group strongly modifies the properties of hydrocarbons, conferring hydrophilic (water-loving) properties. The OH group provides a site at which many reactions can occur. == History == The flammable nature of the exhalations of wine was already known to ancient natural philosophers such as Aristotle (384–322 BCE), Theophrastus (c. 371–287 BCE), and Pliny the Elder (23/24–79 CE). However, this did not immediately lead to the isolation of alcohol, even despite the development of more advanced distillation techniques in second- and third-century Roman Egypt. An important recognition, first found in one of the writings attributed to Jābir ibn Ḥayyān (ninth century CE), was that by adding salt to boiling wine, which increases the wine's relative volatility, the flammability of the resulting vapors may be enhanced. The distillation of wine is attested in Arabic works attributed to al-Kindī (c. 801–873 CE) and to al-Fārābī (c. 872–950), and in the 28th book of al-Zahrāwī's (Latin: Abulcasis, 936–1013) Kitāb al-Taṣrīf (later translated into Latin as Liber servatoris). In the twelfth century, recipes for the production of aqua ardens ("burning water", i.e., alcohol) by distilling wine with salt started to appear in a number of Latin works, and by the end of the thirteenth century, it had become a widely known substance among Western European chemists. The works of Taddeo Alderotti (1223–1296) describe a method for concentrating alcohol involving repeated fractional distillation through a water-cooled still, by which an alcohol purity of 90% could be obtained. The medicinal properties of ethanol were studied by Arnald
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{
"page_id": 1014,
"source": null,
"title": "Alcohol (chemistry)"
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|
of Villanova (1240–1311 CE) and John of Rupescissa (c. 1310–1366), the latter of whom regarded it as a life-preserving substance able to prevent all diseases (the aqua vitae or "water of life", also called by John the quintessence of wine). == Nomenclature == === Etymology === The word "alcohol" derives from the Arabic kohl (Arabic: الكحل, romanized: al-kuḥl), a powder used as an eyeliner. The first part of the word (al-) is the Arabic definite article, equivalent to the in English. The second part of the word (kuḥl) has several antecedents in Semitic languages, ultimately deriving from the Akkadian 𒎎𒋆𒁉𒍣𒁕 (guḫlum), meaning stibnite or antimony. Like its antecedents in Arabic and older languages, the term alcohol was originally used for the very fine powder produced by the sublimation of the natural mineral stibnite to form antimony trisulfide Sb2S3. It was considered to be the essence or "spirit" of this mineral. It was used as an antiseptic, eyeliner, and cosmetic. Later the meaning of alcohol was extended to distilled substances in general, and then narrowed again to ethanol, when "spirits" was a synonym for hard liquor. Paracelsus and Libavius both used the term alcohol to denote a fine powder, the latter speaking of an alcohol derived from antimony. At the same time Paracelsus uses the word for a volatile liquid; alcool or alcool vini occurs often in his writings. Bartholomew Traheron, in his 1543 translation of John of Vigo, introduces the word as a term used by "barbarous" authors for "fine powder." Vigo wrote: "the barbarous auctours use alcohol, or (as I fynde it sometymes wryten) alcofoll, for moost fine poudre." The 1657 Lexicon Chymicum, by William Johnson glosses the word as "antimonium sive stibium." By extension, the word came to refer to any fluid obtained by distillation, including "alcohol of
|
{
"page_id": 1014,
"source": null,
"title": "Alcohol (chemistry)"
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wine," the distilled essence of wine. Libavius in Alchymia (1594) refers to "vini alcohol vel vinum alcalisatum". Johnson (1657) glosses alcohol vini as "quando omnis superfluitas vini a vino separatur, ita ut accensum ardeat donec totum consumatur, nihilque fæcum aut phlegmatis in fundo remaneat." The word's meaning became restricted to "spirit of wine" (the chemical known today as ethanol) in the 18th century and was extended to the class of substances so-called as "alcohols" in modern chemistry after 1850. The term ethanol was invented in 1892, blending "ethane" with the "-ol" ending of "alcohol", which was generalized as a libfix. The term alcohol originally referred to the primary alcohol ethanol (ethyl alcohol), which is used as a drug and is the main alcohol present in alcoholic drinks. The suffix -ol appears in the International Union of Pure and Applied Chemistry (IUPAC) chemical name of all substances where the hydroxyl group is the functional group with the highest priority. When a higher priority group is present in the compound, the prefix hydroxy- is used in its IUPAC name. The suffix -ol in non-IUPAC names (such as paracetamol or cholesterol) also typically indicates that the substance is an alcohol. However, some compounds that contain hydroxyl functional groups have trivial names that do not include the suffix -ol or the prefix hydroxy-, e.g. the sugars glucose and sucrose. === Systematic names === IUPAC nomenclature is used in scientific publications, and in writings where precise identification of the substance is important. In naming simple alcohols, the name of the alkane chain loses the terminal e and adds the suffix -ol, e.g., as in "ethanol" from the alkane chain name "ethane". When necessary, the position of the hydroxyl group is indicated by a number between the alkane name and the -ol: propan-1-ol for CH3CH2CH2OH, propan-2-ol
|
{
"page_id": 1014,
"source": null,
"title": "Alcohol (chemistry)"
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for CH3CH(OH)CH3. If a higher priority group is present (such as an aldehyde, ketone, or carboxylic acid), then the prefix hydroxy-is used, e.g., as in 1-hydroxy-2-propanone (CH3C(O)CH2OH). Compounds having more than one hydroxy group are called polyols. They are named using suffixes -diol, -triol, etc., following a list of the position numbers of the hydroxyl groups, as in propane-1,2-diol for CH3CH(OH)CH2OH (propylene glycol). In cases where the hydroxy group is bonded to an sp2 carbon on an aromatic ring, the molecule is classified separately as a phenol and is named using the IUPAC rules for naming phenols. Phenols have distinct properties and are not classified as alcohols. === Common names === In other less formal contexts, an alcohol is often called with the name of the corresponding alkyl group followed by the word "alcohol", e.g., methyl alcohol, ethyl alcohol. Propyl alcohol may be n-propyl alcohol or isopropyl alcohol, depending on whether the hydroxyl group is bonded to the end or middle carbon on the straight propane chain. As described under systematic naming, if another group on the molecule takes priority, the alcohol moiety is often indicated using the "hydroxy-" prefix. In archaic nomenclature, alcohols can be named as derivatives of methanol using "-carbinol" as the ending. For instance, (CH3)3COH can be named trimethylcarbinol. ==== Primary, secondary, and tertiary ==== Alcohols are then classified into primary, secondary (sec-, s-), and tertiary (tert-, t-), based upon the number of carbon atoms connected to the carbon atom that bears the hydroxyl functional group. The respective numeric shorthands 1°, 2°, and 3° are sometimes used in informal settings. The primary alcohols have general formulas RCH2OH. The simplest primary alcohol is methanol (CH3OH), for which R = H, and the next is ethanol, for which R = CH3, the methyl group. Secondary alcohols are those
|
{
"page_id": 1014,
"source": null,
"title": "Alcohol (chemistry)"
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|
of the form RR'CHOH, the simplest of which is 2-propanol (R = R' = CH3). For the tertiary alcohols, the general form is RR'R"COH. The simplest example is tert-butanol (2-methylpropan-2-ol), for which each of R, R', and R" is CH3. In these shorthands, R, R', and R" represent substituents, alkyl or other attached, generally organic groups. == Examples == == Applications == Alcohols have a long history of myriad uses. For simple mono-alcohols, which is the focus on this article, the following are most important industrial alcohols: methanol, mainly for the production of formaldehyde and as a fuel additive ethanol, mainly for alcoholic beverages, fuel additive, solvent, and to sterilize hospital instruments. 1-propanol, 1-butanol, and isobutyl alcohol for use as a solvent and precursor to solvents C6–C11 alcohols used for plasticizers, e.g. in polyvinylchloride fatty alcohol (C12–C18), precursors to detergents Methanol is the most common industrial alcohol, with about 12 million tons/y produced in 1980. The combined capacity of the other alcohols is about the same, distributed roughly equally. == Toxicity == With respect to acute toxicity, simple alcohols have low acute toxicities. Doses of several milliliters are tolerated. For pentanols, hexanols, octanols, and longer alcohols, LD50 range from 2–5 g/kg (rats, oral). Ethanol is less acutely toxic. All alcohols are mild skin irritants. Methanol and ethylene glycol are more toxic than other simple alcohols. Their metabolism is affected by the presence of ethanol, which has a higher affinity for liver alcohol dehydrogenase. In this way, methanol will be excreted intact in urine. == Physical properties == In general, the hydroxyl group makes alcohols polar. Those groups can form hydrogen bonds to one another and to most other compounds. Owing to the presence of the polar OH alcohols are more water-soluble than simple hydrocarbons. Methanol, ethanol, and propanol are miscible
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{
"page_id": 1014,
"source": null,
"title": "Alcohol (chemistry)"
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in water. 1-Butanol, with a four-carbon chain, is moderately soluble. Because of hydrogen bonding, alcohols tend to have higher boiling points than comparable hydrocarbons and ethers. The boiling point of the alcohol ethanol is 78.29 °C, compared to 69 °C for the hydrocarbon hexane, and 34.6 °C for diethyl ether. == Occurrence in nature == Alcohols occur widely in nature, as derivatives of glucose such as cellulose and hemicellulose, and in phenols and their derivatives such as lignin. Starting from biomass, 180 billion tons/y of complex carbohydrates (sugar polymers) are produced commercially (as of 2014). Many other alcohols are pervasive in organisms, as manifested in other sugars such as fructose and sucrose, in polyols such as glycerol, and in some amino acids such as serine. Simple alcohols like methanol, ethanol, and propanol occur in modest quantities in nature, and are industrially synthesized in large quantities for use as chemical precursors, fuels, and solvents. == Production == === Hydroxylation === Many alcohols are produced by hydroxylation, i.e., the installation of a hydroxy group using oxygen or a related oxidant. Hydroxylation is the means by which the body processes many poisons, converting lipophilic compounds into hydrophilic derivatives that are more readily excreted. Enzymes called hydroxylases and oxidases facilitate these conversions. Many industrial alcohols, such as cyclohexanol for the production of nylon, are produced by hydroxylation. === Ziegler and oxo processes === In the Ziegler process, linear alcohols are produced from ethylene and triethylaluminium followed by oxidation and hydrolysis. An idealized synthesis of 1-octanol is shown: Al(C2H5)3 + 9 C2H4 → Al(C8H17)3 Al(C8H17)3 + 3O + 3 H2O → 3 HOC8H17 + Al(OH)3 The process generates a range of alcohols that are separated by distillation. Many higher alcohols are produced by hydroformylation of alkenes followed by hydrogenation. When applied to a terminal alkene,
|
{
"page_id": 1014,
"source": null,
"title": "Alcohol (chemistry)"
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|
as is common, one typically obtains a linear alcohol: RCH=CH2 + H2 + CO → RCH2CH2CHO RCH2CH2CHO + 3 H2 → RCH2CH2CH2OH Such processes give fatty alcohols, which are useful for detergents. === Hydration reactions === Some low molecular weight alcohols of industrial importance are produced by the addition of water to alkenes. Ethanol, isopropanol, 2-butanol, and tert-butanol are produced by this general method. Two implementations are employed, the direct and indirect methods. The direct method avoids the formation of stable intermediates, typically using acid catalysts. In the indirect method, the alkene is converted to the sulfate ester, which is subsequently hydrolyzed. The direct hydration uses ethylene (ethylene hydration) or other alkenes from cracking of fractions of distilled crude oil. Hydration is also used industrially to produce the diol ethylene glycol from ethylene oxide. === Fermentation === Ethanol is obtained by fermentation of glucose (which is often obtained from starch) in the presence of yeast. Carbon dioxide is cogenerated. Like ethanol, butanol can be produced by fermentation processes. Saccharomyces yeast are known to produce these higher alcohols at temperatures above 75 °F (24 °C). The bacterium Clostridium acetobutylicum can feed on cellulose (also an alcohol) to produce butanol on an industrial scale. === Substitution === Primary alkyl halides react with aqueous NaOH or KOH to give alcohols in nucleophilic aliphatic substitution. Secondary and especially tertiary alkyl halides will give the elimination (alkene) product instead. Grignard reagents react with carbonyl groups to give secondary and tertiary alcohols. Related reactions are the Barbier reaction and the Nozaki–Hiyama–Kishi reaction. === Reduction === Aldehydes or ketones are reduced with sodium borohydride or lithium aluminium hydride (after an acidic workup). Another reduction using aluminium isopropoxide is the Meerwein–Ponndorf–Verley reduction. Noyori asymmetric hydrogenation is the asymmetric reduction of β-keto-esters. === Hydrolysis === Alkenes engage in an
|
{
"page_id": 1014,
"source": null,
"title": "Alcohol (chemistry)"
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acid catalyzed hydration reaction using concentrated sulfuric acid as a catalyst that gives usually secondary or tertiary alcohols. Formation of a secondary alcohol via alkene reduction and hydration is shown: The hydroboration-oxidation and oxymercuration-reduction of alkenes are more reliable in organic synthesis. Alkenes react with N-bromosuccinimide and water in halohydrin formation reaction. Amines can be converted to diazonium salts, which are then hydrolyzed. == Reactions == === Deprotonation === With aqueous pKa values of around 16–19, alcohols are, in general, slightly weaker acids than water. With strong bases such as sodium hydride or sodium they form salts called alkoxides, with the general formula RO−M+ (where R is an alkyl and M is a metal). R−OH + NaH → R−O−Na+ + H2 2 R−OH + 2 Na → 2 R−O−Na+ + H2 The acidity of alcohols is strongly affected by solvation. In the gas phase, alcohols are more acidic than in water. In DMSO, alcohols (and water) have a pKa of around 29–32. As a consequence, alkoxides (and hydroxide) are powerful bases and nucleophiles (e.g., for the Williamson ether synthesis) in this solvent. In particular, RO− or HO− in DMSO can be used to generate significant equilibrium concentrations of acetylide ions through the deprotonation of alkynes (see Favorskii reaction). === Nucleophilic substitution === Tertiary alcohols react with hydrochloric acid to produce tertiary alkyl chloride. Primary and secondary alcohols are converted to the corresponding chlorides using thionyl chloride and various phosphorus chloride reagents. Primary and secondary alcohols, likewise, convert to alkyl bromides using phosphorus tribromide, for example: 3 R−OH + PBr3 → 3 RBr + H3PO3 In the Barton–McCombie deoxygenation an alcohol is deoxygenated to an alkane with tributyltin hydride or a trimethylborane-water complex in a radical substitution reaction. === Dehydration === Meanwhile, the oxygen atom has lone pairs of nonbonded electrons
|
{
"page_id": 1014,
"source": null,
"title": "Alcohol (chemistry)"
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that render it weakly basic in the presence of strong acids such as sulfuric acid. For example, with methanol: Upon treatment with strong acids, alcohols undergo the E1 elimination reaction to produce alkenes. The reaction, in general, obeys Zaytsev's rule, which states that the most stable (usually the most substituted) alkene is formed. Tertiary alcohols are eliminated easily at just above room temperature, but primary alcohols require a higher temperature. This is a diagram of acid catalyzed dehydration of ethanol to produce ethylene: A more controlled elimination reaction requires the formation of the xanthate ester. === Protonolysis === Tertiary alcohols react with strong acids to generate carbocations. The reaction is related to their dehydration, e.g. isobutylene from tert-butyl alcohol. A special kind of dehydration reaction involves triphenylmethanol and especially its amine-substituted derivatives. When treated with acid, these alcohols lose water to give stable carbocations, which are commercial dyes. === Esterification === Alcohol and carboxylic acids react in the so-called Fischer esterification. The reaction usually requires a catalyst, such as concentrated sulfuric acid: R−OH + R'−CO2H → R'−CO2R + H2O Other types of ester are prepared in a similar manner−for example, tosyl (tosylate) esters are made by reaction of the alcohol with 4-toluenesulfonyl chloride in pyridine. === Oxidation === Primary alcohols (R−CH2OH) can be oxidized either to aldehydes (R−CHO) or to carboxylic acids (R−CO2H). The oxidation of secondary alcohols (R1R2CH−OH) normally terminates at the ketone (R1R2C=O) stage. Tertiary alcohols (R1R2R3C−OH) are resistant to oxidation. The direct oxidation of primary alcohols to carboxylic acids normally proceeds via the corresponding aldehyde, which is transformed via an aldehyde hydrate (R−CH(OH)2) by reaction with water before it can be further oxidized to the carboxylic acid. Reagents useful for the transformation of primary alcohols to aldehydes are normally also suitable for the oxidation of secondary alcohols
|
{
"page_id": 1014,
"source": null,
"title": "Alcohol (chemistry)"
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|
to ketones. These include Collins reagent and Dess–Martin periodinane. The direct oxidation of primary alcohols to carboxylic acids can be carried out using potassium permanganate or the Jones reagent. == See also == == Notes == == Citations == == General references == Metcalf AA (1999). The World in So Many Words. Houghton Mifflin. ISBN 0-395-95920-9.
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{
"page_id": 1014,
"source": null,
"title": "Alcohol (chemistry)"
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The molecular formula C12H15ClN2 (molar mass: 222.72 g/mol) may refer to: 5-Chloro-DMT 5-Chloro-αET
|
{
"page_id": 78906362,
"source": null,
"title": "C12H15ClN2"
}
|
In molecular biology mir-278 microRNA is a short RNA molecule belonging to a class of molecules referred to as microRNAs. These function to regulate the expression levels of other genes by several mechanisms, primarily binding to their target at its 3'UTR. == Mis- and altered expression in Drosophila == miR-278 affects energy metabolism in the Drosophila melanogaster species. Elevated insulin production has been observed in miR-278 mutants, due to insulin resistance in the absence of this microRNA. miR-278 is now known to act through regulation of the expanded gene transcript, and most likely through further miR-278 targets as well. Misexpression in the developing eye has been found to result in overgrowth, partially through apoptotic inhibition. There is a single base substitution which blocks the gain-of-function phenotype, indicating the acquisition of novel functions by misexpressed miRNAs which bring about unscheduled cell proliferation in vivo. This is reflective of a microRNA potential in the promotion of tumour formation. == See also == MicroRNA == References == == Further reading == Yu, J. -Y.; Reynolds, S. H.; Hatfield, S. D.; Shcherbata, H. R.; Fischer, K. A.; Ward, E. J.; Long, D.; Ding, Y.; Ruohola-Baker, H. (2009). "Dicer-1-dependent Dacapo suppression acts downstream of Insulin receptor in regulating cell division of Drosophila germline stem cells". Development. 136 (9): 1497–1507. doi:10.1242/dev.025999. PMC 2674257. PMID 19336466. == External links == Page for mir-278 microRNA precursor family at Rfam
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{
"page_id": 36373499,
"source": null,
"title": "Mir-278 microRNA precursor family"
}
|
Thioglycolate broth is a multipurpose, enrichment, differential medium used primarily to determine the oxygen requirements of microorganisms. Sodium thioglycolate in the medium consumes oxygen and permits the growth of obligate anaerobes. This, combined with the diffusion of oxygen from the top of the broth, produces a range of oxygen concentrations in the medium along its depth. The oxygen concentration at a given level is indicated by a redox-sensitive dye such as resazurin that turns pink in the presence of oxygen. This allows the differentiation of obligate aerobes, obligate anaerobes, facultative anaerobes, microaerophiles, and aerotolerant organisms. For example, obligately anaerobic Clostridium species will be seen growing only in the bottom of the test tube. Thioglycolate broth is also used to recruit macrophages to the peritoneal cavity of mice when injected intraperitoneally. It recruits numerous macrophages, but does not activate them. == References ==
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{
"page_id": 19661820,
"source": null,
"title": "Thioglycolate broth"
}
|
The Gewald reaction (or the Gewald aminothiophene synthesis) is an organic reaction involving the condensation of a ketone (or aldehyde when R2 = H) with a α-cyanoester in the presence of elemental sulfur and base to give a poly-substituted 2-amino-thiophene. The reaction is named after the German chemist Karl Gewald. == Reaction mechanism == The reaction mechanism of the Gewald reaction was elucidated 30 years after the reaction was discovered. The first step is a Knoevenagel condensation between the ketone (1) and the α-cyanoester (2) to produce the stable intermediate 3. The mechanism of the addition of the elemental sulfur is unknown. It is postulated to proceed through intermediate 4. Cyclization and tautomerization will produce the desired product (6). Microwave irradiation has been shown beneficial to reaction yields and times. == Variations == In one variation of the Gewald reaction a 3-acetyl-2-aminothiophene is synthesized starting from a dithiane (an adduct of sulfur and acetone if R = CH3 or acetaldehyde if R = H) and the sodium salt of cyanoacetone which in itself is very unstable: == References == == External links == Media related to Gewald reaction at Wikimedia Commons
|
{
"page_id": 2032636,
"source": null,
"title": "Gewald reaction"
}
|
The middle finger, long finger, second finger, third finger, toll finger or tall man is the third digit of the human hand, typically located between the index finger and the ring finger. It is typically the longest digit. In anatomy, it is also called the third finger, digitus medius, digitus tertius or digitus III. == Overview == In Western countries, extending the middle finger (either by itself, or along with the index finger in the United Kingdom: see V sign) is an offensive and obscene gesture, widely recognized as a form of insult, due to its resemblance of an erect penis. It is known, colloquially, as "flipping the bird", "flipping (someone) off", or "giving (someone) the finger". The middle finger is often used for finger snapping together with the thumb. == See also == Finger numbering Galileo's middle finger == References == == External links == Media related to Middle fingers at Wikimedia Commons
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{
"page_id": 525310,
"source": null,
"title": "Middle finger"
}
|
The Prévost reaction is a chemical reaction in which an alkene is converted by iodine and the silver salt of benzoic acid to a vicinal diol with anti stereochemistry. The reaction was discovered by the French chemist Charles Prévost (1899–1983). == Reaction mechanism == The reaction between silver benzoate (1) and iodine is very fast and produces a very reactive iodinium benzoate intermediate (2). The reaction of the iodinium salt (2) with an alkene gives another short-lived iodinium salt (3). Nucleophilic substitution (SN2) by the benzoate salt gives the ester (4). Another silver ion causes the neighboring group substitution of the benzoate ester to give the oxonium salt (5). A second SN2 substitution by the benzoate anion gives the desired diester (6). In the final step hydrolysis of the ester groups gives the anti-diol. This outcome is the opposite of that of the related Woodward cis-hydroxylation which gives syn addition. == References == == See also == Woodward cis-hydroxylation
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{
"page_id": 14091260,
"source": null,
"title": "Prévost reaction"
}
|
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