Buzsáki György
- Published in print:
- 2006
- Published Online:
- May 2009
- ISBN:
- 9780195301069
- eISBN:
- 9780199863716
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195301069.003.0007
- Subject:
- Neuroscience, Neuroendocrine and Autonomic, Techniques
In the absence of environmental inputs, such as during sleep, the brain engages in self-organized activity. The isolated neocortex, or small pieces of it, can sustain self-organized patterns. Neurons ...
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In the absence of environmental inputs, such as during sleep, the brain engages in self-organized activity. The isolated neocortex, or small pieces of it, can sustain self-organized patterns. Neurons in local or global regions of the cerebral cortex swing between excitable and less excitable (up and down) states. In the intact brain, properly timed exogenous influences can trigger upswing changes, if the cortical network has already spent a sufficient amount of time in the down state. Parallel with the increasing probability of cortical up-down state shifts, the membrane potential of thalamocortical neurons progressively polarizes. Cholinergic activity during REM sleep and in the waking brain is mainly responsible for the lack of down states in cortical neurons. The most prominent oscillation of the waking brain is the family of alpha rhythms that occur selectively in every sensory and motor thalamocortical system in the absence of sensory inputs.Less
In the absence of environmental inputs, such as during sleep, the brain engages in self-organized activity. The isolated neocortex, or small pieces of it, can sustain self-organized patterns. Neurons in local or global regions of the cerebral cortex swing between excitable and less excitable (up and down) states. In the intact brain, properly timed exogenous influences can trigger upswing changes, if the cortical network has already spent a sufficient amount of time in the down state. Parallel with the increasing probability of cortical up-down state shifts, the membrane potential of thalamocortical neurons progressively polarizes. Cholinergic activity during REM sleep and in the waking brain is mainly responsible for the lack of down states in cortical neurons. The most prominent oscillation of the waking brain is the family of alpha rhythms that occur selectively in every sensory and motor thalamocortical system in the absence of sensory inputs.
Jorge Busciglio and Atul Deshpande
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780195369007
- eISBN:
- 9780199865253
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195369007.003.0010
- Subject:
- Neuroscience, Molecular and Cellular Systems, Development
This chapter reviews recent work illustrating the utilization of human cortical neurons for the study of molecular mechanisms of β-amyloid (Aβ) and tau-related neuronal degeneration relevant to ...
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This chapter reviews recent work illustrating the utilization of human cortical neurons for the study of molecular mechanisms of β-amyloid (Aβ) and tau-related neuronal degeneration relevant to Alzheimer's disease (AD). It shows that the emerging view of multiple Aβ species capable of deleterious effects at multiple levels co-existing in AD will require a refined therapeutic strategy to address Aβ-mediated neurotoxicity. A specific and complex pattern of tau isoform expression has been observed in human cortical neurons (HCN), which may play a critical role in the development of human tauopathies.Less
This chapter reviews recent work illustrating the utilization of human cortical neurons for the study of molecular mechanisms of β-amyloid (Aβ) and tau-related neuronal degeneration relevant to Alzheimer's disease (AD). It shows that the emerging view of multiple Aβ species capable of deleterious effects at multiple levels co-existing in AD will require a refined therapeutic strategy to address Aβ-mediated neurotoxicity. A specific and complex pattern of tau isoform expression has been observed in human cortical neurons (HCN), which may play a critical role in the development of human tauopathies.
Christian Humpel
- Published in print:
- 2009
- Published Online:
- January 2010
- ISBN:
- 9780195326697
- eISBN:
- 9780199864874
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195326697.003.0015
- Subject:
- Neuroscience, Molecular and Cellular Systems
Alzheimer's disease (AD) is a progressive chronic disorder characterized by β-amyloid plaques, tau pathology, cell death of cholinergic neurons, and inflammatory responses. The reasons for this ...
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Alzheimer's disease (AD) is a progressive chronic disorder characterized by β-amyloid plaques, tau pathology, cell death of cholinergic neurons, and inflammatory responses. The reasons for this disease are unknown, but damage of the cerebrovascular system are thought to play an important role. This chapter summarizes the most important hypotheses: the role of the β-amyloid cascade, tau pathology, cerebrovascular damage, glutamate-induced cell death, silent stroke and acidosis, the cell death of cholinergic neurons, the neurovascular unit, growth factor effects, and inflammation. Vascular risk factors are discussed by focusing on the idea that the cerebrovascular dysfunction triggers the development of the disease. A common hypothesis tries to link the different pathologies of the disease. Different forms of dementia, such as mild cognitive impairment, vascular dementia, and finally AD may overlap at certain stages.Less
Alzheimer's disease (AD) is a progressive chronic disorder characterized by β-amyloid plaques, tau pathology, cell death of cholinergic neurons, and inflammatory responses. The reasons for this disease are unknown, but damage of the cerebrovascular system are thought to play an important role. This chapter summarizes the most important hypotheses: the role of the β-amyloid cascade, tau pathology, cerebrovascular damage, glutamate-induced cell death, silent stroke and acidosis, the cell death of cholinergic neurons, the neurovascular unit, growth factor effects, and inflammation. Vascular risk factors are discussed by focusing on the idea that the cerebrovascular dysfunction triggers the development of the disease. A common hypothesis tries to link the different pathologies of the disease. Different forms of dementia, such as mild cognitive impairment, vascular dementia, and finally AD may overlap at certain stages.
Bas Edixhoven and Jean-Marc Couveignes (eds)
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691142012
- eISBN:
- 9781400839001
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691142012.001.0001
- Subject:
- Mathematics, Number Theory
Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's ...
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Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program. The book begins with a concise and concrete introduction that makes it accessible to readers without an extensive background in arithmetic geometry, and it includes a chapter that describes actual computations.Less
Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program. The book begins with a concise and concrete introduction that makes it accessible to readers without an extensive background in arithmetic geometry, and it includes a chapter that describes actual computations.
F. Richard Stephenson and David A. Green
- Published in print:
- 2002
- Published Online:
- January 2010
- ISBN:
- 9780198507666
- eISBN:
- 9780191709876
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507666.003.0008
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
The remnant of this SN — known as the Crab Nebula (G184.6-5.8) — has attracted more attention among radio and X-ray astronomers than any other SNR. Not only is the remnant, which contains a pulsar, ...
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The remnant of this SN — known as the Crab Nebula (G184.6-5.8) — has attracted more attention among radio and X-ray astronomers than any other SNR. Not only is the remnant, which contains a pulsar, fairly bright at optical wavelengths, it is a powerful emitter of both radio waves and X-rays. The SN, which occurred in Taurus, was extensively recorded in both China and Japan. It was also briefly mentioned in a Constantinople source. Following a brief period of daylight visibility, the star was only lost to view after twenty-one months. Both Chinese and Japanese records assert that the SN was within about 1 deg of zeta Tau. The only nearby SNR is the Crab Nebula itself. Although several records state that the SN was a little to the SE of zeta Tau, the Crab Nebula lies to the NW of this star. However, these records share a common source and the directional problems are not insurmountable.Less
The remnant of this SN — known as the Crab Nebula (G184.6-5.8) — has attracted more attention among radio and X-ray astronomers than any other SNR. Not only is the remnant, which contains a pulsar, fairly bright at optical wavelengths, it is a powerful emitter of both radio waves and X-rays. The SN, which occurred in Taurus, was extensively recorded in both China and Japan. It was also briefly mentioned in a Constantinople source. Following a brief period of daylight visibility, the star was only lost to view after twenty-one months. Both Chinese and Japanese records assert that the SN was within about 1 deg of zeta Tau. The only nearby SNR is the Crab Nebula itself. Although several records state that the SN was a little to the SE of zeta Tau, the Crab Nebula lies to the NW of this star. However, these records share a common source and the directional problems are not insurmountable.
Carlo Giunti and Chung W. Kim
- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780198508717
- eISBN:
- 9780191708862
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508717.003.0014
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter discusses the physics of direct measurements of neutrino mass with detailed treatment of beta decay, pion and tau decays, and neutrinoless double-beta decay.
This chapter discusses the physics of direct measurements of neutrino mass with detailed treatment of beta decay, pion and tau decays, and neutrinoless double-beta decay.
Ivan Gaskell
- Published in print:
- 2019
- Published Online:
- May 2019
- ISBN:
- 9781526118196
- eISBN:
- 9781526142016
- Item type:
- chapter
- Publisher:
- Manchester University Press
- DOI:
- 10.7228/manchester/9781526118196.003.0012
- Subject:
- Anthropology, Anthropology, Global
This chapter examines the place of Oceanic clubs in New England collections. During the nineteenth century, they occupied an equivocal position in the New England mental repertory as indices of ...
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This chapter examines the place of Oceanic clubs in New England collections. During the nineteenth century, they occupied an equivocal position in the New England mental repertory as indices of savage sophistication, and as souvenirs of colonial childhood or travel. Focusing on a Tongan ‘akau tau in the collection of the Chatham Historical Society on Cape Cod, Massachusetts, this chapter traces what can be known of its history as a highly regarded prestige gift item among New Englanders from the middle of the nineteenth century until its entry into the museum. As a thing that an early owner could alienate legitimately, its presence in Chatham is not unethical, yet it nonetheless imposes stewardship responsibilities—consultation with the originating community—that such a small institution is poorly placed to meet. This requires understanding and patience rather than disapprobation.Less
This chapter examines the place of Oceanic clubs in New England collections. During the nineteenth century, they occupied an equivocal position in the New England mental repertory as indices of savage sophistication, and as souvenirs of colonial childhood or travel. Focusing on a Tongan ‘akau tau in the collection of the Chatham Historical Society on Cape Cod, Massachusetts, this chapter traces what can be known of its history as a highly regarded prestige gift item among New Englanders from the middle of the nineteenth century until its entry into the museum. As a thing that an early owner could alienate legitimately, its presence in Chatham is not unethical, yet it nonetheless imposes stewardship responsibilities—consultation with the originating community—that such a small institution is poorly placed to meet. This requires understanding and patience rather than disapprobation.
Gary Ka-wai Cheung
- Published in print:
- 2009
- Published Online:
- September 2011
- ISBN:
- 9789622090897
- eISBN:
- 9789882207011
- Item type:
- chapter
- Publisher:
- Hong Kong University Press
- DOI:
- 10.5790/hongkong/9789622090897.003.0006
- Subject:
- History, Asian History
On July 8, a border conflict erupted in Sha Tau Kok, a New Territories village bordering Shenzhen, taking the tension to an unprecedented level. Hundreds of demonstrators gathered in the area. When ...
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On July 8, a border conflict erupted in Sha Tau Kok, a New Territories village bordering Shenzhen, taking the tension to an unprecedented level. Hundreds of demonstrators gathered in the area. When the police attempted to disperse the crowd by firing baton shells and tear gas, automatic fire opened on the post. At this time a riot company on its way up to support the post was fired upon by rifles and machine gun. Several people died in that event. Meetings between the Hong Kong government and the mainland officials were held. Deals were generated, easing the tension in the border area and fostering a working relationship between mainland border authorities and the Hong Kong government. Leftists inspired by the border conflict resorted to violent means in the confrontation with the colonial government. Nine emergency regulations were then promulgated by the government. More demonstrators gathered at the North Point tram, injuring several policemen.Less
On July 8, a border conflict erupted in Sha Tau Kok, a New Territories village bordering Shenzhen, taking the tension to an unprecedented level. Hundreds of demonstrators gathered in the area. When the police attempted to disperse the crowd by firing baton shells and tear gas, automatic fire opened on the post. At this time a riot company on its way up to support the post was fired upon by rifles and machine gun. Several people died in that event. Meetings between the Hong Kong government and the mainland officials were held. Deals were generated, easing the tension in the border area and fostering a working relationship between mainland border authorities and the Hong Kong government. Leftists inspired by the border conflict resorted to violent means in the confrontation with the colonial government. Nine emergency regulations were then promulgated by the government. More demonstrators gathered at the North Point tram, injuring several policemen.
Patrick H. Hase
- Published in print:
- 2008
- Published Online:
- September 2011
- ISBN:
- 9789622098992
- eISBN:
- 9789882207592
- Item type:
- chapter
- Publisher:
- Hong Kong University Press
- DOI:
- 10.5790/hongkong/9789622098992.003.0005
- Subject:
- History, Asian History
This chapter starts by considering the burning of the matsheds during 3 and 14 April. The action on 15 April (Battle of Mui Shue Hang) is described. While this Battle of Mui Shue Hang was ...
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This chapter starts by considering the burning of the matsheds during 3 and 14 April. The action on 15 April (Battle of Mui Shue Hang) is described. While this Battle of Mui Shue Hang was successfully undertaken by the British troops, it was clearly only a success because of the fire-power of Fame's guns. It had been decided that the Flag-Raising Ceremony would be brought forward a day, from 17 April to 16 April, since the military action being taken, where the British had not yet formally taken the territory over, was extremely doubtful in International Law. The Battle of Lam Tsuen Gap and the Battle of Shek Tau Wai on 17 and 18 April, respectively, are summarized. A particular problem for the British troops was that the artillery failed to take part in the Battle of Lam Tsuen Gap, and, indeed, in any of the engagements of the Six-Day War, other than the shelling with shrapnel of the insurgents at the She Shan ridge at mid-day on 17 April. On 16 April, there was information that the insurgents at Castle Peak were planning an attack on Yaumatei. An unpleasant incident that took place during the fighting was the murder of Tang Cheung-hing. On 19 April, the insurgents surrendered and there were troop movements in the Western New Territories.Less
This chapter starts by considering the burning of the matsheds during 3 and 14 April. The action on 15 April (Battle of Mui Shue Hang) is described. While this Battle of Mui Shue Hang was successfully undertaken by the British troops, it was clearly only a success because of the fire-power of Fame's guns. It had been decided that the Flag-Raising Ceremony would be brought forward a day, from 17 April to 16 April, since the military action being taken, where the British had not yet formally taken the territory over, was extremely doubtful in International Law. The Battle of Lam Tsuen Gap and the Battle of Shek Tau Wai on 17 and 18 April, respectively, are summarized. A particular problem for the British troops was that the artillery failed to take part in the Battle of Lam Tsuen Gap, and, indeed, in any of the engagements of the Six-Day War, other than the shelling with shrapnel of the insurgents at the She Shan ridge at mid-day on 17 April. On 16 April, there was information that the insurgents at Castle Peak were planning an attack on Yaumatei. An unpleasant incident that took place during the fighting was the murder of Tang Cheung-hing. On 19 April, the insurgents surrendered and there were troop movements in the Western New Territories.
Elliot Wolfson
- Published in print:
- 2006
- Published Online:
- May 2012
- ISBN:
- 9780520246195
- eISBN:
- 9780520932319
- Item type:
- book
- Publisher:
- University of California Press
- DOI:
- 10.1525/california/9780520246195.001.0001
- Subject:
- Religion, Judaism
This book explores the nexus of time, truth, and death in the symbolic world of medieval kabbalah. Demonstrating that the historical and theoretical relationship between kabbalah and western ...
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This book explores the nexus of time, truth, and death in the symbolic world of medieval kabbalah. Demonstrating that the historical and theoretical relationship between kabbalah and western philosophy is far more intimate and extensive than any previous scholar has ever suggested, the book draws an extraordinary range of thinkers such as Frederic Jameson, Martin Heidegger, Franz Rosenzweig, William Blake, Julia Kristeva, Friedrich Schelling, and a host of kabbalistic figures into deep conversation with one another. The book discusses Islamic mysticism and Buddhist thought in relation to the Jewish esoteric tradition as it opens the possibility of a temporal triumph of temporality and the conquering of time through time. The framework for this examination is the rabbinic teaching that the word emet, “truth,” comprises the first, middle, and last letters of the Hebrew alphabet, alef, mem, and tau, which serve, in turn, as semiotic signposts for the three tenses of time—past, present, and future. By heeding the letters of emet we discern the truth of time manifestly concealed in the time of truth, the beginning that cannot begin if it is to be the beginning, the middle that re/marks the place of origin and destiny, and the end that is the figuration of the impossible disclosing the impossibility of figuration, the finitude of death that facilitates the possibility of rebirth. The time of death does not mark the death of time, but time immortal, the moment of truth that bestows on the truth of the moment an endless beginning of a beginningless end, the truth of death encountered incessantly in retracing steps of time yet to be taken—between, before, beyond.Less
This book explores the nexus of time, truth, and death in the symbolic world of medieval kabbalah. Demonstrating that the historical and theoretical relationship between kabbalah and western philosophy is far more intimate and extensive than any previous scholar has ever suggested, the book draws an extraordinary range of thinkers such as Frederic Jameson, Martin Heidegger, Franz Rosenzweig, William Blake, Julia Kristeva, Friedrich Schelling, and a host of kabbalistic figures into deep conversation with one another. The book discusses Islamic mysticism and Buddhist thought in relation to the Jewish esoteric tradition as it opens the possibility of a temporal triumph of temporality and the conquering of time through time. The framework for this examination is the rabbinic teaching that the word emet, “truth,” comprises the first, middle, and last letters of the Hebrew alphabet, alef, mem, and tau, which serve, in turn, as semiotic signposts for the three tenses of time—past, present, and future. By heeding the letters of emet we discern the truth of time manifestly concealed in the time of truth, the beginning that cannot begin if it is to be the beginning, the middle that re/marks the place of origin and destiny, and the end that is the figuration of the impossible disclosing the impossibility of figuration, the finitude of death that facilitates the possibility of rebirth. The time of death does not mark the death of time, but time immortal, the moment of truth that bestows on the truth of the moment an endless beginning of a beginningless end, the truth of death encountered incessantly in retracing steps of time yet to be taken—between, before, beyond.
Elliot R. Wolfson
- Published in print:
- 2006
- Published Online:
- May 2012
- ISBN:
- 9780520246195
- eISBN:
- 9780520932319
- Item type:
- chapter
- Publisher:
- University of California Press
- DOI:
- 10.1525/california/9780520246195.003.0005
- Subject:
- Religion, Judaism
A zoharic text correlates death and truth through the insight that tau, the last letter of the alphabet, seals both the words mawet, “death,” and emet, “truth.” Death opens consciousness to the ...
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A zoharic text correlates death and truth through the insight that tau, the last letter of the alphabet, seals both the words mawet, “death,” and emet, “truth.” Death opens consciousness to the moment that escapes objectification and thematization, a moment that may be rendered poetically as confrontation with the face, which is most fully visible when it can be seen no more. The apparent migration at death from being to not-being should not be understood as a transition from one state to its opposite but as a suspension of the very possibility of such a transition. It can be deduced from the zoharic text the epistemic axiom that death reveals the truthfulness of time by concealing the timeliness of truth. The midrashic text's exegetical framework highlights that the trinitarian nature of time is ontologically grounded in the truthfulness of God's seal, YHWH.Less
A zoharic text correlates death and truth through the insight that tau, the last letter of the alphabet, seals both the words mawet, “death,” and emet, “truth.” Death opens consciousness to the moment that escapes objectification and thematization, a moment that may be rendered poetically as confrontation with the face, which is most fully visible when it can be seen no more. The apparent migration at death from being to not-being should not be understood as a transition from one state to its opposite but as a suspension of the very possibility of such a transition. It can be deduced from the zoharic text the epistemic axiom that death reveals the truthfulness of time by concealing the timeliness of truth. The midrashic text's exegetical framework highlights that the trinitarian nature of time is ontologically grounded in the truthfulness of God's seal, YHWH.
John W. Troutman
- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9781469627922
- eISBN:
- 9781469627946
- Item type:
- chapter
- Publisher:
- University of North Carolina Press
- DOI:
- 10.5149/northcarolina/9781469627922.003.0005
- Subject:
- Music, History, American
Relying principally on letters, scrapbooks, interviews, and other personal recollections by musicians such as Joseph Puni and Queenie and David Kaili, this chapter illuminates the experiences of ...
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Relying principally on letters, scrapbooks, interviews, and other personal recollections by musicians such as Joseph Puni and Queenie and David Kaili, this chapter illuminates the experiences of steel guitarists laboring in Europe and Asia during the early to mid-twentieth century. Their stories, while often quite personal and unique, speak to common themes encountered by performers navigating interpersonal relationships as well as broader, geopolitical forces during this period. Letters home from steel guitarist Kiwini Panui in London reveal the joys and curiosities of encountering new lands and new peoples, as well as new communities of Hawaiians already abroad. The recollections of Tau Moe and his daughter Dorian, meanwhile, demonstrate not only the challenges encountered by foreign audience dynamics and expectation but also a stunning tale of intrigue behind enemy lines in Nazi Germany. Their extensive touring also launched a craze for steel guitars that continues to shape popular music in India by guitarists such as Garney Nyss, Sri Brij Bhushan Kabra, and Debashish Bhattacharya.Less
Relying principally on letters, scrapbooks, interviews, and other personal recollections by musicians such as Joseph Puni and Queenie and David Kaili, this chapter illuminates the experiences of steel guitarists laboring in Europe and Asia during the early to mid-twentieth century. Their stories, while often quite personal and unique, speak to common themes encountered by performers navigating interpersonal relationships as well as broader, geopolitical forces during this period. Letters home from steel guitarist Kiwini Panui in London reveal the joys and curiosities of encountering new lands and new peoples, as well as new communities of Hawaiians already abroad. The recollections of Tau Moe and his daughter Dorian, meanwhile, demonstrate not only the challenges encountered by foreign audience dynamics and expectation but also a stunning tale of intrigue behind enemy lines in Nazi Germany. Their extensive touring also launched a craze for steel guitars that continues to shape popular music in India by guitarists such as Garney Nyss, Sri Brij Bhushan Kabra, and Debashish Bhattacharya.
Wolfgang Banzhaf and Lidia Yamamoto
- Published in print:
- 2015
- Published Online:
- September 2016
- ISBN:
- 9780262029438
- eISBN:
- 9780262329460
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262029438.003.0004
- Subject:
- Public Health and Epidemiology, Public Health
This chapter examines various reactor algorithms that are frequently used in artificial chemistries. We contrast macroscopic, deterministic reaction algorithms and microscopic, stochastic reaction ...
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This chapter examines various reactor algorithms that are frequently used in artificial chemistries. We contrast macroscopic, deterministic reaction algorithms and microscopic, stochastic reaction algorithms. The Chemical Master Equation is introduced, followed by well-known simulation algorithms such as Gillespie’s direct method and tau-leaping. An overview of algorithms that simulate spatial and multicompartmental chemistries then follows, from numerical integration to stochastic reaction-diffusion algorithms based on subvolumes.Less
This chapter examines various reactor algorithms that are frequently used in artificial chemistries. We contrast macroscopic, deterministic reaction algorithms and microscopic, stochastic reaction algorithms. The Chemical Master Equation is introduced, followed by well-known simulation algorithms such as Gillespie’s direct method and tau-leaping. An overview of algorithms that simulate spatial and multicompartmental chemistries then follows, from numerical integration to stochastic reaction-diffusion algorithms based on subvolumes.
Daniel T. Gillespie and Linda R. Petzold
- Published in print:
- 2006
- Published Online:
- August 2013
- ISBN:
- 9780262195485
- eISBN:
- 9780262257060
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262195485.003.0016
- Subject:
- Mathematics, Mathematical Biology
This chapter discusses concepts and techniques for mathematically describing and numerically simulating chemical systems that into account discreteness and stochasticity. The chapter is organized as ...
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This chapter discusses concepts and techniques for mathematically describing and numerically simulating chemical systems that into account discreteness and stochasticity. The chapter is organized as follows. Section 16.2 outlines the foundations of “stochastic chemical kinetics” and derives the chemical master equation (CME)—the time-evolution equation for the probability function of the system’s state. The CME, however, cannot be solved, for any but the simplest of systems. But numerical realizations (sample trajectories in state space) of the stochastic process defined by the CME can be generated using a Monte Carlo strategy called the stochastic simulation algorithm (SSA), which is derived and discussed in Section 16.3. Section 16.4 describes an approximate accelerated algorithm known as tau-leaping. Section 16.5 shows how, under certain conditions, tau-leaping further approximates to a stochastic differential equation called the chemical Langevin equation (CLE), and then how the CLE can in turn sometimes be approximated by an ordinary differential equation called the reaction rate equation (RRE). Section 16.6 describes the problem of stiffness in a deterministic (RRE) context, along with its standard numerical resolution: implicit method. Section 16.7 presents an implicit tau-leaping algorithm for stochastically simulating stiff chemical systems. Section 16.8 concludes by describing and illustrating yet another promising algorithm for dealing with stiff stochastic chemical systems, which is called the slow-scale SSA.Less
This chapter discusses concepts and techniques for mathematically describing and numerically simulating chemical systems that into account discreteness and stochasticity. The chapter is organized as follows. Section 16.2 outlines the foundations of “stochastic chemical kinetics” and derives the chemical master equation (CME)—the time-evolution equation for the probability function of the system’s state. The CME, however, cannot be solved, for any but the simplest of systems. But numerical realizations (sample trajectories in state space) of the stochastic process defined by the CME can be generated using a Monte Carlo strategy called the stochastic simulation algorithm (SSA), which is derived and discussed in Section 16.3. Section 16.4 describes an approximate accelerated algorithm known as tau-leaping. Section 16.5 shows how, under certain conditions, tau-leaping further approximates to a stochastic differential equation called the chemical Langevin equation (CLE), and then how the CLE can in turn sometimes be approximated by an ordinary differential equation called the reaction rate equation (RRE). Section 16.6 describes the problem of stiffness in a deterministic (RRE) context, along with its standard numerical resolution: implicit method. Section 16.7 presents an implicit tau-leaping algorithm for stochastically simulating stiff chemical systems. Section 16.8 concludes by describing and illustrating yet another promising algorithm for dealing with stiff stochastic chemical systems, which is called the slow-scale SSA.
Stephen Citron
- Published in print:
- 2004
- Published Online:
- October 2013
- ISBN:
- 9780300100822
- eISBN:
- 9780300133240
- Item type:
- chapter
- Publisher:
- Yale University Press
- DOI:
- 10.12987/yale/9780300100822.003.0003
- Subject:
- Music, Popular
This chapter focuses on Jerry Herman's experience in college and after his graduation. It explains that Herman's education at the University of Miami taught him various aspects of the theater ...
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This chapter focuses on Jerry Herman's experience in college and after his graduation. It explains that Herman's education at the University of Miami taught him various aspects of the theater including built scenery and lighting effects, and that he also joined the school's dramatic society and the Zeta Beta Tau. After graduation Herman was drafted in the army, worked in cocktail lounges, and finished the revue titled Parade in 1960.Less
This chapter focuses on Jerry Herman's experience in college and after his graduation. It explains that Herman's education at the University of Miami taught him various aspects of the theater including built scenery and lighting effects, and that he also joined the school's dramatic society and the Zeta Beta Tau. After graduation Herman was drafted in the army, worked in cocktail lounges, and finished the revue titled Parade in 1960.
Bas Edixhoven
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691142012
- eISBN:
- 9781400839001
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691142012.003.0001
- Subject:
- Mathematics, Number Theory
This chapter provides an introduction to the subject, precise statements of the main results, and places these in a somewhat wider context. Topics discussed include statement of the main results, ...
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This chapter provides an introduction to the subject, precise statements of the main results, and places these in a somewhat wider context. Topics discussed include statement of the main results, Schoof's algorithm, Schoof's algorithm described in terms of ètale cohomology, other cases where ètale cohomology can be used to construct polynomial time algorithms for counting rational points of varieties over finite fields, congruences for Ramanujan's tau-function, and comparison with p-adic methods.Less
This chapter provides an introduction to the subject, precise statements of the main results, and places these in a somewhat wider context. Topics discussed include statement of the main results, Schoof's algorithm, Schoof's algorithm described in terms of ètale cohomology, other cases where ètale cohomology can be used to construct polynomial time algorithms for counting rational points of varieties over finite fields, congruences for Ramanujan's tau-function, and comparison with p-adic methods.
Johan Bosman
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691142012
- eISBN:
- 9781400839001
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691142012.003.0007
- Subject:
- Mathematics, Number Theory
This chapter explicitly computes mod-ℓ Galois representations attached to modular forms. To be precise, it looks at cases with l ≤ 23, and the modular forms considered will be cusp forms of level 1 ...
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This chapter explicitly computes mod-ℓ Galois representations attached to modular forms. To be precise, it looks at cases with l ≤ 23, and the modular forms considered will be cusp forms of level 1 and weight up to 22. The chapter presents the result in terms of polynomials associated with the projectivized representations. As an application, it will improve a known result on Lehmer's nonvanishing conjecture for Ramanujan's tau function.Less
This chapter explicitly computes mod-ℓ Galois representations attached to modular forms. To be precise, it looks at cases with l ≤ 23, and the modular forms considered will be cusp forms of level 1 and weight up to 22. The chapter presents the result in terms of polynomials associated with the projectivized representations. As an application, it will improve a known result on Lehmer's nonvanishing conjecture for Ramanujan's tau function.
Bas Edixhoven
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691142012
- eISBN:
- 9781400839001
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691142012.003.0015
- Subject:
- Mathematics, Number Theory
This chapter applies the main result on the computation of Galois representations attached to modular forms of level one to the computation of coefficients of modular forms. It treats the case of the ...
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This chapter applies the main result on the computation of Galois representations attached to modular forms of level one to the computation of coefficients of modular forms. It treats the case of the discriminant modular form, that is, the computation of Ramanujan's tau-function at primes, and then deals with the more general case of forms of level one and arbitrary weight k, reformulated as the computation of Hecke operators Tⁿ as ℤ-linear combinations of the Tᵢ with i < k = 12. The chapter gives an application to theta functions of even, unimodular positive definite quadratic forms over ℤ.Less
This chapter applies the main result on the computation of Galois representations attached to modular forms of level one to the computation of coefficients of modular forms. It treats the case of the discriminant modular form, that is, the computation of Ramanujan's tau-function at primes, and then deals with the more general case of forms of level one and arbitrary weight k, reformulated as the computation of Hecke operators Tⁿ as ℤ-linear combinations of the Tᵢ with i < k = 12. The chapter gives an application to theta functions of even, unimodular positive definite quadratic forms over ℤ.
Patrick Vinton Kirch
- Published in print:
- 2015
- Published Online:
- November 2016
- ISBN:
- 9780824853457
- eISBN:
- 9780824868345
- Item type:
- chapter
- Publisher:
- University of Hawai'i Press
- DOI:
- 10.21313/hawaii/9780824853457.003.0017
- Subject:
- Society and Culture, Pacific Studies
This chapter talks about the research conducted in Mangaia, southernmost of the Cook Islands, and the results thereof—particularly at the Tangata-tau rockshelter. Here, the chapter marks a turning ...
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This chapter talks about the research conducted in Mangaia, southernmost of the Cook Islands, and the results thereof—particularly at the Tangata-tau rockshelter. Here, the chapter marks a turning point where Kirch's academic interests shift toward Eastern Polynesian islands. What made Mangaian history different from that of Tikopia or some other small Polynesian islands was that the island of Mangaia was inherently vulnerable to human disturbance. The deep history of Mangaia speaks to the darker side of human nature, when circumstances beyond their control forced people to behave in ways that they would otherwise find abhorrent. Yet what happened on Mangaia in the late period is not unique within Polynesia.Less
This chapter talks about the research conducted in Mangaia, southernmost of the Cook Islands, and the results thereof—particularly at the Tangata-tau rockshelter. Here, the chapter marks a turning point where Kirch's academic interests shift toward Eastern Polynesian islands. What made Mangaian history different from that of Tikopia or some other small Polynesian islands was that the island of Mangaia was inherently vulnerable to human disturbance. The deep history of Mangaia speaks to the darker side of human nature, when circumstances beyond their control forced people to behave in ways that they would otherwise find abhorrent. Yet what happened on Mangaia in the late period is not unique within Polynesia.
Anton Zabrodin
- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780198797319
- eISBN:
- 9780191838774
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198797319.003.0013
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter is a review of the recently established quantum-classical correspondence for integrable systems based on the construction of the master T-operator. For integrable inhomogeneous quantum ...
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This chapter is a review of the recently established quantum-classical correspondence for integrable systems based on the construction of the master T-operator. For integrable inhomogeneous quantum spin chains with gl(N)-invariant R-matrices in finite-dimensional representations, the master T-operator is a sort of generating function for the family of commuting quantum transfer matrices depending on an infinite number of parameters. Any eigenvalue of the master T-operator is the tau-function of the classical modified KP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0th time of the hierarchy. This implies a remarkable relation between the quantum spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, a system of algebraic equations can be obtained for the spectrum of the spin chain Hamiltonians.Less
This chapter is a review of the recently established quantum-classical correspondence for integrable systems based on the construction of the master T-operator. For integrable inhomogeneous quantum spin chains with gl(N)-invariant R-matrices in finite-dimensional representations, the master T-operator is a sort of generating function for the family of commuting quantum transfer matrices depending on an infinite number of parameters. Any eigenvalue of the master T-operator is the tau-function of the classical modified KP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0th time of the hierarchy. This implies a remarkable relation between the quantum spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, a system of algebraic equations can be obtained for the spectrum of the spin chain Hamiltonians.
