neurons论文范文

混沌学 Chaos theoryIn mathematics, chaos theory describes the behavior of certain dynamical systems – that is, systems whose state evolves with time – that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, which manifests itself as an exponential growth of perturbations in the initial conditions, the behavior of chaotic systems appears to be random. This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions, with no random elements involved. This behavior is known as deterministic chaos, or simply chaos.Chaotic behaviour is also observed in natural systems, such as the weather. This may be explained by a chaos-theoretical analysis of a mathematical model of such a system, embodying the laws of physics that are relevant for the natural system.OverviewChaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices. Observations of chaotic behaviour in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations. Everyday examples of chaotic systems include weather and climate.[1] There is some controversy over the existence of chaotic dynamics in the plate tectonics and in economics.[2][3][4]Systems that exhibit mathematical chaos are deterministic and thus orderly in some sense; this technical use of the word chaos is at odds with common parlance, which suggests complete disorder. A related field of physics called quantum chaos theory studies systems that follow the laws of quantum mechanics. Recently, another field, called relativistic chaos,[5] has emerged to describe systems that follow the laws of general relativity.As well as being orderly in the sense of being deterministic, chaotic systems usually have well defined statistics.[citation needed] For example, the Lorenz system pictured is chaotic, but has a clearly defined structure. Bounded chaos is a useful term for describing models of disorder.HistoryThe first discoverer of chaos was Henri Poincaré. In 1890, while studying the three-body problem, he found that there can be orbits which are nonperiodic, and yet not forever increasing nor approaching a fixed point.[6] In 1898 Jacques Hadamard published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature.[7] In the system studied, "Hadamard's billiards," Hadamard was able to show that all trajectories are unstable in that all particle trajectories diverge exponentially from one another, with a positive Lyapunov exponent.Much of the earlier theory was developed almost entirely by mathematicians, under the name of ergodic theory. Later studies, also on the topic of nonlinear differential equations, were carried out by G.D. Birkhoff,[8] A. N. Kolmogorov,[9][10][11] M.L. Cartwright and J.E. Littlewood,[12] and Stephen Smale.[13] Except for Smale, these studies were all directly inspired by physics: the three-body problem in the case of Birkhoff, turbulence and astronomical problems in the case of Kolmogorov, and radio engineering in the case of Cartwright and Littlewood. Although chaotic planetary motion had not been observed, experimentalists had encountered turbulence in fluid motion and nonperiodic oscillation in radio circuits without the benefit of a theory to explain what they were seeing.Despite initial insights in the first half of the twentieth century, chaos theory became formalized as such only after mid-century, when it first became evident for some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behaviour of certain experiments like that of the logistic map. What had been beforehand excluded as measure imprecision and simple "noise" was considered by chaos theories as a full component of the studied systems.The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calculations practical, while figures and images made it possible to visualize these systems. One of the earliest electronic digital computers, ENIAC, was used to run simple weather forecasting models.An early pioneer of the theory was Edward Lorenz whose interest in chaos came about accidentally through his work on weather prediction in 1961.[14] Lorenz was using a simple digital computer, a Royal McBee LGP-30, to run his weather simulation. He wanted to see a sequence of data again and to save time he started the simulation in the middle of its course. He was able to do this by entering a printout of the data corresponding to conditions in the middle of his simulation which he had calculated last time.To his surprise the weather that the machine began to predict was completely different from the weather calculated before. Lorenz tracked this down to the computer printout. The computer worked with 6-digit precision, but the printout rounded variables off to a 3-digit number, so a value like 0.506127 was printed as 0.506. This difference is tiny and the consensus at the time would have been that it should have had practically no effect. However Lorenz had discovered that small changes in initial conditions produced large changes in the long-term outcome.[15] Lorenz's discovery, which gave its name to Lorenz attractors, proved that meteorology could not reasonably predict weather beyond a weekly period (at most).The year before, Benoit Mandelbrot found recurring patterns at every scale in data on cotton prices.[16] Beforehand, he had studied information theory and concluded noise was patterned like a Cantor set: on any scale the proportion of noise-containing periods to error-free periods was a constant – thus errors were inevitable and must be planned for by incorporating redundancy.[17] Mandelbrot described both the "Noah effect" (in which sudden discontinuous changes can occur, e.g., in a stock's prices after bad news, thus challenging normal distribution theory in statistics, aka Bell Curve) and the "Joseph effect" (in which persistence of a value can occur for a while, yet suddenly change afterwards).[18][19] In 1967, he published "How long is the coast of Britain? Statistical self-similarity and fractional dimension," showing that a coastline's length varies with the scale of the measuring instrument, resembles itself at all scales, and is infinite in length for an infinitesimally small measuring device.[20] Arguing that a ball of twine appears to be a point when viewed from far away (0-dimensional), a ball when viewed from fairly near (3-dimensional), or a curved strand (1-dimensional), he argued that the dimensions of an object are relative to the observer and may be fractional. An object whose irregularity is constant over different scales ("self-similarity") is a fractal (for example, the Koch curve or "snowflake", which is infinitely long yet encloses a finite space and has fractal dimension equal to circa 1.2619, the Menger sponge and the Sierpiński gasket). In 1975 Mandelbrot published The Fractal Geometry of Nature, which became a classic of chaos theory. Biological systems such as the branching of the circulatory and bronchial systems proved to fit a fractal model.Chaos was observed by a number of experimenters before it was recognized; e.g., in 1927 by van der Pol[21] and in 1958 by R.L. Ives.[22][23] However, Yoshisuke Ueda seems to have been the first experimenter to have identified a chaotic phenomenon as such by using an analog computer on November 27, 1961. The chaos exhibited by an analog computer is a real phenomenon, in contrast with those that digital computers calculate, which has a different kind of limit on precision. Ueda's supervising professor, Hayashi, did not believe in chaos, and thus he prohibited Ueda from publishing his findings until 1970.[24]In December 1977 the New York Academy of Sciences organized the first symposium on Chaos, attended by David Ruelle, Robert May, James Yorke (coiner of the term "chaos" as used in mathematics), Robert Shaw (a physicist, part of the Eudaemons group with J. Doyne Farmer and Norman Packard who tried to find a mathematical method to beat roulette, and then created with them the Dynamical Systems Collective in Santa Cruz), and the meteorologist Edward Lorenz.The following year, Mitchell Feigenbaum published the noted article "Quantitative Universality for a Class of Nonlinear Transformations", where he described logistic maps.[25] Feigenbaum had applied fractal geometry to the study of natural forms such as coastlines. Feigenbaum notably discovered the universality in chaos, permitting an application of chaos theory to many different phenomena.In 1979, Albert J. Libchaber, during a symposium organized in Aspen by Pierre Hohenberg, presented his experimental observation of the bifurcation cascade that leads to chaos and turbulence in convective Rayleigh–Benard systems. He was awarded the Wolf Prize in Physics in 1986 along with Mitchell J. Feigenbaum "for his brilliant experimental demonstration of the transition to turbulence and chaos in dynamical systems".[26]The New York Academy of Sciences then co-organized, in 1986, with the National Institute of Mental Health and the Office of Naval Research the first important conference on Chaos in biology and medicine. Bernardo Huberman thereby presented a mathematical model of the eye tracking disorder among schizophrenics.[27] Chaos theory thereafter renewed physiology in the 1980s, for example in the study of pathological cardiac cycles.In 1987, Per Bak, Chao Tang and Kurt Wiesenfeld published a paper in Physical Review Letters[28] describing for the first time self-organized criticality (SOC), considered to be one of the mechanisms by which complexity arises in nature. Alongside largely lab-based approaches such as the Bak–Tang–Wiesenfeld sandpile, many other investigations have centred around large-scale natural or social systems that are known (or suspected) to display scale-invariant behaviour. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[29] describing the frequency of aftershocks); solar flares; fluctuations in economic systems such as financial markets (references to SOC are common in econophysics); landscape formation; forest fires; landslides; epidemics; and biological evolution (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "punctuated equilibria" put forward by Niles Eldredge and Stephen Jay Gould). Worryingly, given the implications of a scale-free distribution of event sizes, some researchers have suggested that another phenomenon that should be considered an example of SOC is the occurrence of wars. These "applied" investigations of SOC have included both attempts at modelling (either developing new models or adapting existing ones to the specifics of a given natural system), and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.The same year, James Gleick published Chaos: Making a New Science, which became a best-seller and introduced general principles of chaos theory as well as its history to the broad public. At first the domains of work of a few, isolated individuals, chaos theory progressively emerged as a transdisciplinary and institutional discipline, mainly under the name of nonlinear systems analysis. Alluding to Thomas Kuhn's concept of a paradigm shift exposed in The Structure of Scientific Revolutions (1962), many "chaologists" (as some self-nominated themselves) claimed that this new theory was an example of such as shift, a thesis upheld by J. Gleick.The availability of cheaper, more powerful computers broadens the applicability of chaos theory. Currently, chaos theory continues to be a very active area of research, involving many different disciplines (mathematics, topology, physics, population biology, biology, meteorology, astrophysics, information theory, etc.).[edit] Chaotic dynamicsFor a dynamical system to be classified as chaotic, it must have the following properties:[30]it must be sensitive to initial conditions, it must be topologically mixing, and its periodic orbits must be dense. Sensitivity to initial conditions means that each point in such a system is arbitrarily closely approximated by other points with significantly different future trajectories. Thus, an arbitrarily small perturbation of the current trajectory may lead to significantly different future behaviour.Sensitivity to initial conditions is popularly known as the "butterfly effect", so called because of the title of a paper given by Edward Lorenz in 1972 to the American Association for the Advancement of Science in Washington, D.C. entitled Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas? The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different.Sensitivity to initial conditions is often confused with chaos in popular accounts. It can also be a subtle property, since it depends on a choice of metric, or the notion of distance in the phase space of the system. For example, consider the simple dynamical system produced by repeatedly doubling an initial value (defined by iterating the mapping on the real line that maps x to 2x). This system has sensitive dependence on initial conditions everywhere, since any pair of nearby points will eventually become widely separated. However, it has extremely simple behaviour, as all points except 0 tend to infinity. If instead we use the bounded metric on the line obtained by adding the point at infinity and viewing the result as a circle, the system no longer is sensitive to initial conditions. For this reason, in defining chaos, attention is normally restricted to systems with bounded metrics, or closed, bounded invariant subsets of unbounded systems.Even for bounded systems, sensitivity to initial conditions is not identical with chaos. For example, consider the two-dimensional torus described by a pair of angles (x,y), each ranging between zero and 2π. Define a mapping that takes any point (x,y) to (2x, y + a), where a is any number such that a/2π is irrational. Because of the doubling in the first coordinate, the mapping exhibits sensitive dependence on initial conditions. However, because of the irrational rotation in the second coordinate, there are no periodic orbits, and hence the mapping is not chaotic according to the definition above.Topologically mixing means that the system will evolve over time so that any given region or open set of its phase space will eventually overlap with any other given region. Here, "mixing" is really meant to correspond to the standard intuition: the mixing of colored dyes or fluids is an example of a chaotic system.Linear systems are never chaotic; for a dynamical system to display chaotic behaviour it has to be nonlinear. Also, by the Poincaré–Bendixson theorem, a continuous dynamical system on the plane cannot be chaotic; among continuous systems only those whose phase space is non-planar (having dimension at least three, or with a non-Euclidean geometry) can exhibit chaotic behaviour. However, a discrete dynamical system (such as the logistic map) can exhibit chaotic behaviour in a one-dimensional or two-dimensional phase space.[edit] AttractorsSome dynamical systems are chaotic everywhere (see e.g. Anosov diffeomorphisms) but in many cases chaotic behaviour is found only in a subset of phase space. The cases of most interest arise when the chaotic behaviour takes place on an attractor, since then a large set of initial conditions will lead to orbits that converge to this chaotic region.An easy way to visualize a chaotic attractor is to start with a point in the basin of attraction of the attractor, and then simply plot its subsequent orbit. Because of the topological transitivity condition, this is likely to produce a picture of the entire final attractor.For instance, in a system describing a pendulum, the phase space might be two-dimensional, consisting of information about position and velocity. One might plot the position of a pendulum against its velocity. A pendulum at rest will be plotted as a point, and one in periodic motion will be plotted as a simple closed curve. When such a plot forms a closed curve, the curve is called an orbit. Our pendulum has an infinite number of such orbits, forming a pencil of nested ellipses about the origin.[edit] Strange attractorsWhile most of the motion types mentioned above give rise to very simple attractors, such as points and circle-like curves called limit cycles, chaotic motion gives rise to what are known as strange attractors, attractors that can have great detail and complexity. For instance, a simple three-dimensional model of the Lorenz weather system gives rise to the famous Lorenz attractor. The Lorenz attractor is perhaps one of the best-known chaotic system diagrams, probably because not only was it one of the first, but it is one of the most complex and as such gives rise to a very interesting pattern which looks like the wings of a butterfly. Another such attractor is the Rössler map, which experiences period-two doubling route to chaos, like the logistic map.Strange attractors occur in both continuous dynamical systems (such as the Lorenz system) and in some discrete systems (such as the Hénon map). Other discrete dynamical systems have a repelling structure called a Julia set which forms at the boundary between basins of attraction of fixed points - Julia sets can be thought of as strange repellers. Both strange attractors and Julia sets typically have a fractal structure.The Poincaré-Bendixson theorem shows that a strange attractor can only arise in a continuous dynamical system if it has three or more dimensions. However, no such restriction applies to discrete systems, which can exhibit strange attractors in two or even one dimensional systems.The initial conditions of three or more bodies interacting through gravitational attraction (see the n-body problem) can be arranged to produce chaotic motion.Minimum complexity of a chaotic systemSimple systems can also produce chaos without relying on differential equations. An example is the logistic map, which is a difference equation (recurrence relation) that describes population growth over time. Another example is the Ricker model of population dynamics.Even the evolution of simple discrete systems, such as cellular automata, can heavily depend on initial conditions. Stephen Wolfram has investigated a cellular automaton with this property, termed by him rule 30.A minimal model for conservative (reversible) chaotic behavior is provided by Arnold's cat map.

血糖升高对出血性脑卒中（hemorrhagic apoplexy）的发生发展有极其重要的影响，不但作为重要危险因素参与HA的起始，导致疾病发病率增高，而且对HA发生后病理过程有促进作用，使血肿体积扩大，加重水肿，加重功能损害，影响预后。Hyperglycemia has a very important impact on the occurrence and development of hemorrhagic stroke (hemorrhagic apoplexy). It not only acts as an important risk factor in the initiation of HA, but also increases the incidence of disease, and promotes the pathological process of HA, enlarges the volume of hematoma, aggravates edema, aggravates functional damage, and affects prognosis.高血糖参与HA的发生机制是多方面的，包括:脂代谢异常、颈动脉重塑、内皮功能障碍、血小板功能异常、高凝状态、胰岛素抵抗。而高血糖扩大梗死面积，促进HA发展主要与致酸中毒、缺血损伤区域细胞凋亡等机制有关。Hyperglycemia is involved in the pathogenesis of HA in many aspects, including: abnormal lipid metabolism, Carotid Remodeling, endothelial dysfunction, platelet dysfunction, hypercoagulability, insulin resistance. However, hyperglycemia can enlarge the infarct area and promote the development of HA, which is mainly related to the mechanism of acidosis and apoptosis in ischemic injury area.血管内皮生长因子（VEGF）和环氧合酶（COX-2）与脑血管病的关系，已引起人们的重视。血管内皮生长因子的突出作用是诱导体内血管形成，提高血管通透性；近年来发现它也有刺激神经元、胶质细胞、轴突的生长和成活的作用。环氧合酶(cyclooxygenase，COX)，是催化花生四烯酸(arachidonic acid，AA)合成前列腺素(prostgalandin，PG)以及血栓素(thromboxan，TX)的限速酶。其中COX-1为结构型，存在于大多数组织中，催化生成维持正常结构的PG；COX-2为诱导型，在生理状态下，COX-2在大多数组织中以极低拷贝数表达。但IL-1、TNF等许多炎症刺激因子均可诱导COX-2表达。但目前有关血管内皮生长因子和环氧合酶的研究多集中在与脑缺血的关系上，而关于脑出血后脑水肿的动态变化与VEGF、COX-2表达的相关性研究却不多。The relationship between vascular endothelial growth factor (VEGF) and cyclooxygenase (COX-2) and cerebrovascular diseases has attracted people's attention. In recent years, it has been found that vascular endothelial growth factor can stimulate the growth and survival of neurons, glial cells and axons. Cyclooxygenase (COX) is a rate limiting enzyme that catalyzes the synthesis of prostaglandin (PG) and thromboxane (TX) from arachidonic acid (AA). COX-1 is a structural type, which exists in most tissues and catalyzes the generation of PG maintaining normal structure; COX-2 is an inducible type, which is expressed in a very low copy number in most tissues under physiological conditions. But many inflammatory factors such as IL-1 and TNF can induce COX-2 expression. However, at present, the researches on VEGF and COX-2 are mostly focused on the relationship with cerebral ischemia, but few on the relationship between the dynamic changes of brain edema and the expression of VEGF and COX-2 after cerebral hemorrhage.在认识到高血糖对脑出血损伤危害性同时，控制血糖水平治疗即成为脑血管病治疗手段之一，特别是采用胰岛素降低血糖水平纳入急性脑卒中治疗指南。已有研究发现胰岛素对急性期脑出血周围脑组织的缺血性损伤有保护作用。可能机制为：现已发现脑中存在胰岛素受体，胰岛素可与胰岛素受体结合，降低脑细胞对糖的摄取，从而降低脑细胞内糖的储存，减少乳酸产生的底物，从根本上纠正细胞酸中毒；同时胰岛素还可以降低外周血糖浓度，增加出血周围水肿带的有效血供，造成相对低血糖高灌流状态，从而对脑损害产生改善作用。In recognition of the harm of hyperglycemia to cerebral hemorrhage, the control of blood glucose level has become one of the treatment methods of cerebrovascular disease, especially the use of insulin to reduce blood glucose level has been included in the treatment guidelines of acute stroke. It has been found that insulin has a protective effect on the ischemic injury of brain tissue around acute cerebral hemorrhage. The possible mechanisms are as follows: it has been found that there is insulin receptor in the brain, insulin can combine with insulin receptor, reduce the uptake of sugar by brain cells, thus reduce the storage of sugar in brain cells, reduce the substrate produced by lactic acid, fundamentally correct cell acidosis; at the same time, insulin can also reduce the concentration of peripheral blood sugar, increase the effective blood supply of edema zone around hemorrhage, resulting in relatively low blood supply Hyperperfusion of blood glucose can improve brain damage.为了解这两种细胞因子与糖尿病合并脑出血损伤的关系，本研究在糖尿病模型的基础上，拟通过自体血注入法建立稳定的大鼠脑出血的动物模型，在此基础上动态观察脑出血后行为学和脑含水量的变化趋势，分析VEGF和COX-2在出血后脑组织中的分布特点和表达变化，进而探讨VEGF和COX-2在脑出血后脑组织损伤中的作用和意义，对比糖尿病大鼠和正常血糖大鼠脑水肿体积的差别，初步观察此二因子在糖尿病大鼠和正常血糖大鼠脑出血表达的差异，以期为脑出血的治疗提供新的方法和思路。In order to understand the relationship between these two cytokines and the injury of cerebral hemorrhage in diabetes mellitus, this study is to establish a stable animal model of cerebral hemorrhage by autogenous blood injection on the basis of diabetes model. On this basis, dynamic observation of the change trend of behavior and brain water content after cerebral hemorrhage is made, and the distribution characteristics and expression changes of VEGF and COX-2 in brain tissue after hemorrhage are analyzed, Furthermore, to explore the role and significance of VEGF and COX-2 in brain tissue injury after cerebral hemorrhage, to compare the difference of brain edema volume between diabetic rats and normal glucose rats, and to preliminarily observe the difference of expression of VEGF and COX-2 in cerebral hemorrhage between diabetic rats and normal glucose rats, in order to provide new methods and ideas for the treatment of cerebral hemorrhage.材料与方法Materials and methods1. 实验动物和分组1. Experimental animals and groups健康成年雄性Wistar大鼠，共96只，体重250~280克，由郑州大学实验动物中心提供。按照随机化的原则将实验动物分为4组，即假手术组、正常血糖组、高血糖组和胰岛素干预组。每组均设4个时间点：6h、24h、72h、7d。每个时间点设6只大鼠。96 healthy adult male Wistar rats weighing 250-280 g were provided by the experimental animal center of Zhengzhou University. According to the principle of randomization, the experimental animals were divided into four groups: sham operation group, normal blood glucose group, hyperglycemia group and insulin intervention group. Each group had four time points: 6h, 24h, 72h, 7d. Six rats were set at each time point.2. 高血糖大鼠模型制作及胰岛素干预方法2. Establishment of hyperglycemia rat model and insulin intervention参照STZ诱导法制备高血糖大鼠模型。以STZ 60mg/kg，对高血糖及胰岛素干预组大鼠单次腹腔注射。大鼠正常血糖值为4一6mmol/L，注射后一周检测血糖≥11.1mmol/L为成功模型备选用。高血糖模型成功后，予干预组大鼠普通胰岛素，腹壁皮下注射，3次/d，4U/次，连用3天，测血糖值达正常范围。The hyperglycemia rat model was established by STZ induction. STZ (60 mg / kg) was used for single intraperitoneal injection in the hyperglycemia and insulin intervention group. The normal blood glucose value of rats was 4-6mmol / L, and the blood glucose ≥ 11.1mmol/l was detected one week after injection as the successful model. After the success of hyperglycemia model, rats in the intervention group were given insulin, subcutaneous injection of abdominal wall, 3 times a day, 4U a time, for 3 days, and the blood glucose value reached the normal range.（论文翻译由学术堂提供）