一种确定混沌伪随机序列复杂度的模糊关系熵测度

将模糊关系的概念引入混沌伪随机序列复杂度的测度方法之中,提出了一种新的混沌伪随机序列复杂度测度方法——模糊关系熵(fuzzy relationship entropy,简记为F-REn)测度方法,并推导了F-REn的两个基本性质.仿真结果表明,该测度方法能够有效测度混沌伪随机序列的复杂度,与近似熵(ApEn)测度方法和符号熵测度方法相比,F-REn测度具有更加好的对序列符号空间的适用性、更加小的对测量维度的敏感性和更加强的对分辨率参数的鲁棒性. 关键词： 混沌伪随机序列 模糊理论 复杂度     

A superconvergent universality induced by non-associativity

The star products in symbolic dynamics, as effective algebraic operations for describing self-similar bifurcation structure in classical dynamical systems, are found to have either associativity or non-associativity. In this Letter, non-associative star products in trimodal iterative dynamical systems are considered. As the left and right operations have different effects, right-associative star products break the conventional Feigenbaum's metric universality. Through high precision parallel computation, it is found that period-p-tupling bifurcation processes described by right-associative star products exhibit a superconvergent universality of double exponential form.     

Cyclic star products and universalities in symbolic dynamics of trimodal maps

Cyclic star products for the triple superstable kneading (TSSK) sequences are presented for symbolic dynamics of trimodal maps of endomorphisms on the interval. Feigenbaum’s metric universalities in unimodal maps are generalized to trimodal maps. Four equal-value universal convergent rates {δ_a,δ_c,δ_η,δ_a,c,η} and three universal scaling factors {_C,_D,_E} are first obtained.     

Symbolic dynamics of one-dimensional maps: Entropies,finite precision,and noise

In the study of nonlinear physical systems, one encounters apparently random or chaotic behavior, although the systems may be completely deterministic. Applying techniques from symbolic dynamics to maps of the interval, we compute two measures of chaotic behavior commonly employed in dynamical systems theory: the topological and metric entropies. For the quadratic logistic equation, we find that the metric entropy converges very slowly in comparison to maps which are strictly hyperbolic. The effects of finite precision arithmetric and external noise on chaotic behavior are characterized with the symbolic dynamics entropies. Finally, we discuss the relationship of these measures of chaos to algorithmic complexity, and use algorithmic information theory as a framework to discuss the construction of models for chaotic dynamics.     

d-dimensional black hole entropy spectrum from quasinormal modes

Starting from recent observations about quasinormal modes, we use semiclassical arguments to derive the Bekenstein-Hawking entropy spectrum for d-dimensional spherically symmetric black holes. We find that, as first suggested by Bekenstein, the entropy spectrum is equally spaced: S(BH)=kln((m(0))n, where m(0) is a fixed integer that must be derived from the microscopic theory. As shown in O. Dreyer, gr-qc/0211076, 4D loop quantum gravity yields precisely such a spectrum with m(0)=3 providing the Immirzi parameter is chosen appropriately. For d-dimensional black holes of radius R(H)(M), our analysis predicts the existence of a unique quasinormal mode frequency in the large damping limit omega((d))(M)=alpha((d))c/R(H)(M) with coefficient [formula: see text], where m(0) is an integer.     

Universality class of fluctuating pulled fronts

It has recently been proposed that fluctuating "pulled" fronts propagating into an unstable state should not be in the standard Kardar-Parisi-Zhang (KPZ) universality class for rough interface growth. We introduce an effective field equation for this class of problems, and show on the basis of it that noisy pulled fronts in d+1 bulk dimensions should be in the universality class of the ((d+1)+1)D KPZ equation rather than of the (d+1)D KPZ equation. Our scenario ties together a number of heretofore unexplained observations in the literature, and is supported by previous numerical results.     

Strong coupling constant from the photon structure function

We extract the value of the strong coupling constant alpha(s) from a single-parameter pointlike fit to the photon structure function F(gamma)(2) at large x and Q(2) and from a first five-parameter full (pointlike and hadronic) fit to the complete F(gamma)(2)data set taken at PETRA, TRISTAN, and LEP. In next-to-leading order and the MS renormalization and factorization schemes, we obtain alpha(s)(m(Z))=0.1183+/-0.0050(expt)(+0.0029)(-0.0028)(theor) (pointlike) and alpha(s)(m(Z))=0.1198+/-0.0028(expt)(+0.0034)(-0.0046)(theor) (pointlike and hadronic). We demonstrate that the data taken at LEP have reduced the experimental error by about a factor of 2, so that a competitive determination of alpha(s) from F(gamma)(2) is now possible.     

Measuring the transmission phase of a quantum dot in a closed interferometer

The electron transmission through a closed Aharonov-Bohm mesoscopic solid-state interferometer, with a quantum dot (QD) on one of the paths, is calculated exactly for a simple model. Although the conductance is an even function of the magnetic flux (due to Onsager's relations), in many cases one can use the measured conductance to extract both the amplitude and the phase of the "intrinsic" transmission amplitude t(D)=-i|t(D)|e(ialpha(D)) through the "bare" QD. We also propose to compare this indirect measurement with the (hitherto untested) direct relation sin((2)(alpha(D)) identical with |t(D)|(2)/max((|t(D)|(2)).     

Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation

Diffusion weighted MRI is used clinically to detect and characterize neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion relies on diffusion-weighted pulse sequences to probe biophysical models of molecular diffusion-typically exp[-(bD)]-where D is the apparent diffusion coefficient (mm(2)/s) and b depends on the specific gradient pulse sequence parameters. Several recent studies have investigated the so-called anomalous diffusion stretched exponential model-exp[-(bD)(alpha)], where alpha is a measure of tissue complexity that can be derived from fractal models of tissue structure. In this paper we propose an alternative derivation for the stretched exponential model using fractional order space and time derivatives. First, we consider the case where the spatial Laplacian in the Bloch-Torrey equation is generalized to incorporate a fractional order Brownian model of diffusivity. Second, we consider the case where the time derivative in the Bloch-Torrey equation is replaced by a Riemann-Liouville fractional order time derivative expressed in the Caputo form. Both cases revert to the classical results for integer order operations. Fractional order dynamics derived for the first case were observed to fit the signal attenuation in diffusion-weighted images obtained from Sephadex gels, human articular cartilage and human brain. Future developments of this approach may be useful for classifying anomalous diffusion in tissues with developing pathology.     

Gravitational dressing of D-instantons

The non-perturbative corrections to the universal hypermultiplet moduli space metric in the type-IIA superstring compactification on a Calabi–Yau threefold are investigated in the presence of 4d, N=2 supergravity. These corrections come from multiple wrapping of the BPS (Euclidean) D2-branes around certain (BPS) Calabi–Yau 3-cycles, and they are known as the D-instantons. The exact universal hypermultiplet metric is governed by a quaternionic potential that satisfies the SU(∞) Toda equation. When the supergravity decouples, the metric is hyper-Kähler. We propose the mechanism that gravitationally dress any (D-instanton) hyper-Kähler metric to the (universal hypermultiplet) quaternionic metric of the same dimension.     

Studies of phase return map and symbolic dynamics in a periodically driven Hodgkin–Huxley neuron

How neuronal spike trains encode external information is a hot topic in neurodynamics studies.In this paper,we investigate the dynamical states of the Hodgkin–Huxley neuron under periodic forcing.Depending on the parameters of the stimulus,the neuron exhibits periodic,quasiperiodic and chaotic spike trains.In order to analyze these spike trains quantitatively,we use the phase return map to describe the dynamical behavior on a one-dimensional(1D)map.According to the monotonicity or discontinuous point of the 1D map,the spike trains are transformed into symbolic sequences by implementing a coarse-grained algorithm—symbolic dynamics.Based on the ordering rules of symbolic dynamics,the parameters of the external stimulus can be measured in high resolution with finite length symbolic sequences.A reasonable explanation for why the nervous system can discriminate or cognize the small change of the external signals in a short time is also presented.     

Next-to-next-to-leading-order logarithmic corrections at small transverse momentum in hadronic collisions

We study the region of small transverse momenta in q&qmacr;- and gg-initiated processes with no colored particle detected in the final state. We present the universal expression of the O(alpha(2)(s)) logarithmically enhanced contributions up to next-to-next-to-leading-order logarithmic accuracy. From there we extract the coefficients that allow the resummation of the large logarithmic contributions. We find that the coefficient known in the literature as B((2)) is process dependent, since it receives a hard contamination from the one-loop correction to the leading-order subprocess. We present the general result of B((2)) for both quark and gluon channels.     

Symbolic dynamics of ventricular tachycardia and ventricular fibrillation

In this paper, the symbolic dynamics analysis was used to analyze the complexity of normal heartbeat signal (NSR), Ventricular tachycardia (VT) and ventricular fibrillation (VF) signals. By calculating the information entropy value of symbolic sequences, the complexities were quantified. Based on different information entropy values, NSR, VT and VF signals were distinguished with satisfactory results. The study showed that a sudden drop of symbolic sequence’s entropy value indicated that the patients most likely entered the episode of ventricular tachycardia and this was a crucial episode for the clinical treatment of patients. It had important clinical significance for the automatic diagnosis.     

Deconfinement and the Hagedorn transition in string theory

We introduce a new definition of the thermal partition function in string theory. With this new definition, the thermal partition functions of all of the string theories obey thermal duality relations with self-dual Hagedorn temperature beta(2)(H) = 4pi(2)alpha('). A beta-->beta(2)(H)/beta transformation maps the type I theory into a new string theory (type I) with thermal D p-branes, spatial hypersurfaces supporting a p-dimensional finite temperature non-Abelian Higgs-gauge theory for p< or =9. We demonstrate a continuous phase transition in the behavior of the static heavy quark-antiquark potential for small separations r(2)(*)相似文献   

格子复杂性和符号序列的细粒化

提出一种新的有限长一维符号序列的复杂性度量——格子复杂性，建立在Lempel Ziv复杂性和一维迭代映射系统的符号动力学基础上.同时提出了符号序列的细粒化方法，可与格子复杂性以及Lempel Ziv复杂性结合.新度量在细粒化指数较小时与Lempel Ziv复杂性基本一致，在细粒化指数增大时显示出截然不同的特性.以Logistic映射为对象的计算实验表明，格子复杂性对混沌区的边缘最敏感.最后还讨论了上述复杂性度量的其他一些重要性质. 关键词： 混沌 复杂性度量 格子复杂性 细粒化     

Parameter scaling in the decoherent quantum-classical transition for chaotic systems

The quantum to classical transition for a system depends on many parameters, including a scale length for its action, variant Planck's over 2 pi, a measure of its coupling to the environment, D, and, for chaotic systems, the classical Lyapunov exponent, lambda. We propose measuring the proximity of quantum and classical evolutions as a multivariate function of (Planck's over 2 pi,lambda,D) and searching for transformations that collapse this hypersurface into a function of a composite parameter zeta= Planck's over 2 pi alpha)lambda beta D gamma. We report results for the quantum Cat Map and Duffing oscillator, showing accurate scaling behavior over a wide parameter range, indicating that this may be used to construct universality classes for this transition.     

Numerical analysis for a discontinuous rotation of the torus

In this paper, we study a class of piecewise rotations on the square. While few theoretical results are known about them, we numerically compute box-counting dimensions, correlation dimensions and complexity of the symbolic language produced by the system. Our results seem to confirm a conjecture that the fractal dimension of the exceptional set is two, as well as indicate that the dynamics on it is not ergodic. We also explore a relationship between the piecewise rotations and discretized rotations on lattices Z(2n).     

Forward-backward asymmetries of lepton pairs in events with a large-transverse-momentum jet at hadron colliders

We discuss forward-backward charge asymmetries for lepton-pair production in association with a large-transverse-momentum jet at hadron colliders. The lepton charge asymmetry relative to the jet direction A(j)(FB) gives a new determination of the effective weak mixing angle sin((2)theta(lept)(eff)(M(2)(Z)) with a statistical precision after cuts of approximately 10(-3) (8x10(-3)) at LHC (Tevatron). This is to be compared with the current uncertainty at LEP and SLD from the asymmetries alone, 2x10(-4). The identification of b jets also allows for the measurement of the bottom-quark-Z asymmetry A(b)(FB) at hadron colliders, the resulting statistical precision for sin((2)theta(lept)(eff)(M(2)(Z)) being approximately 9x10(-4) (2x10(-2) at Tevatron), also lower than the reported precision at e(+)e(-) colliders, 3x10(-4).     

Universal spin-induced time reversal symmetry breaking in two-dimensional electron gases with Rashba spin-orbit interaction

We have experimentally studied the spin-induced time reversal symmetry (TRS) breaking as a function of the relative strength of the Zeeman energy (E(Z)) and the Rashba spin-orbit interaction energy (E(SOI)), in InGaAs-based 2D electron gases. We find that the TRS breaking, and hence the associated dephasing time tau(phi)(B), saturates when E(Z) becomes comparable to E(SOI). Moreover, we show that the spin-induced TRS breaking mechanism is a universal function of the ratio E(Z)/E(SOI), within the experimental accuracy.