Power-law distributions and Levy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements

A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda w_i(t)$ at the individual level with a global coupling through a constraint which does not allow the $w_i$'s to fall below a lower cutoff given by $c \cdot \bar w$, where $\bar w$ is their momentary average and $0<c<1$ is a constant. The dynamic variables $w_i$ are found to exhibit a power-law distribution of the form $p(w) \sim w^{-1-\alpha}$. The exponent $\alpha (c,N)$ is quite insensitive to the distribution $\Pi(\lambda)$ of the random factor $\lambda$, but it is non-universal, and increases monotonically as a function of $c$. The "thermodynamic" limit, N goes to infty and the limit of decoupled free multiplicative random walks c goes to 0, do not commute: $\alpha(0,N) = 0$ for any finite $N$ while $\alpha(c,\infty) \ge 1$ (which is the common range in empirical systems) for any positive $c$. The time evolution of ${\bar w (t)}$ exhibits intermittent fluctuations parametrized by a (truncated) L\'evy-stable distribution $L_{\alpha}(r)$ with the same index $\alpha$. This non-trivial relation between the distribution of the $w_i$'s at a given time and the temporal fluctuations of their average is examined and its relevance to empirical systems is discussed.Comment: 7 pages, 4 figure

Which phase is measured in the mesoscopic Aharonov-Bohm interferometer?

Mesoscopic solid state Aharonov-Bohm interferometers have been used to measure the "intrinsic" phase, $\alpha_{QD}$, of the resonant quantum transmission amplitude through a quantum dot (QD). For a two-terminal "closed" interferometer, which conserves the electron current, Onsager's relations require that the measured phase shift $\beta$ only "jumps" between 0 and $\pi$. Additional terminals open the interferometer but then $\beta$ depends on the details of the opening. Using a theoretical model, we present quantitative criteria (which can be tested experimentally) for $\beta$ to be equal to the desired $\alpha_{QD}$: the "lossy" channels near the QD should have both a small transmission and a small reflection

Familial influences on sustained attention and inhibition in preschoolers

Background: In this study several aspects of attention were studied in 237 nearly 6-year-old twin pairs. Specifically, the ability to sustain attention and inhibition were investigated using a computerized test battery (Amsterdam Neuropsychological Tasks). Furthermore, the Teacher's Report Form (TRF) was filled out by the teacher of the child and the attention subscale of this questionnaire was analyzed. Methods: The variance in performance on the different tasks of the test battery and the score on the attention scale of the TRF were decomposed into a contribution of the additive effects of many genes (A), environmental effects that are shared by twins (C) and unique environmental influences not shared by twins (E) by using data from MZ and DZ twins. Results: The genetic model fitting results showed an effect of A and E for the attention scale of the TRF, and for some of the inhibition and sustained attention measures. For most of the attention variables, however, it was not possible to decide between a model with A and E or a model with C and E. Time-on-task effects on reaction time or number of errors and the delay after making an error did not show familial resemblances. A remarkable finding was that the heritability of the attention scale of the TRF was found to be higher than the heritability of indices that can be considered to be more direct measures of attention, such as mean tempo in the sustained attention task and response speed in the Go-NoGo task. Conclusion: In preschoolers, familial resemblances on sustained attention and inhibition were observed. © Association for Child Psychology and Psychiatry, 2004

Weakly-Bound Three-Body Systems with No Bound Subsystems

We investigate the domain of coupling constants which achieve binding for a 3-body system, while none of the 2-body subsystems is bound. We derive some general properties of the shape of the domain, and rigorous upper bounds on its size, using a Hall--Post decomposition of the Hamiltonian. Numerical illustrations are provided in the case of a Yukawa potential, using a simple variational method.Comment: gzipped ps with 11 figures included. To appear in Phys. Rev.

Stratification of COPD patients by previous admission for targeting of preventative care

SummaryBackgroundHospital admissions for exacerbations of chronic obstructive pulmonary disease (COPD) impact considerably on disease evolution and healthcare provision. Building on previous studies, this study postulated that COPD patients could be stratified by risk of admission to determine which groups provide the greatest burden on resources, and how interventions should be targeted to prevent admissions.MethodsCOPD admissions during 1997–2003 in three Strategic Health Authorities in England were analysed (n=80,291). Patients admitted during winter (1 November–31 March) were stratified into three groups according to the number of admissions during the previous year: 0 (NIL), 1–2 (MOD) or ≥3 (FRQ). Winter weeks were classified as “average”, “above average”, “high”, or “very high” risk, compared with the long-term mean.ResultsThe risk of admission during winter for FRQ and MOD patients was 40% and 12% respectively. NIL patients contributed to 70% of winter admissions, and 90% of the variation between “average” and “very high” weeks, versus 9% and 1% for MOD and FRQ.ConclusionsPatients with no previous admissions have lower individual risk, but contribute to a high overall utilisation of health care resources and should be targeted to prevent admissions. Focusing upon high-risk patients (frequent attenders or more severe) may only reduce a small proportion of admissions, and therefore clinicians should ensure that all COPD patients receive appropriate therapy to reduce risk of exacerbations

Generation of maximum spin entanglement induced by cavity field in quantum-dot systems

Equivalent-neighbor interactions of the conduction-band electron spins of quantum dots in the model of Imamoglu et al. [Phys. Rev. Lett. 83, 4204 (1999)] are analyzed. Analytical solution and its Schmidt decomposition are found and applied to evaluate how much the initially excited dots can be entangled to the remaining dots if all of them are initially disentangled. It is demonstrated that the perfect maximally entangled states (MES) can only be generated in the systems of up to 6 dots with a single dot initially excited. It is also shown that highly entangled states, approximating the MES with a good accuracy, can still be generated in systems of odd number of dots with almost half of them being excited. A sudden decrease of entanglement is observed by increasing the total number of dots in a system with a fixed number of excitations.Comment: 6 pages, 7 figures, to appear in Phys. Rev.

Conformal linear gravity in de Sitter space II

From the group theoretical point of view, it is proved that the theory of linear conformal gravity should be written in terms of a tensor field of rank-3 and mixed symmetry [Binegar, et al, Phys. Rev. D 27, (1983) 2249]. We obtained such a field equation in de Sitter space [Takook, et al, J. Math. Phys. 51, (2010) 032503]. In this paper, a proper solution to this equation is obtained as a product of a generalized polarization tensor and a massless scalar field and then the conformally invariant two-point function is calculated. This two-point function is de Sitter invariant and free of any pathological large-distance behavior.Comment: 16 pages, no figure, published versio

Spin-Charge Separation in the t−Jt-J Model: Magnetic and Transport Anomalies

A real spin-charge separation scheme is found based on a saddle-point state of the $t-J$ model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed-point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at {\em finite doping} so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic {\em residual} couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at ($\pi/a$, $\pi/a$) with a doping-dependent width ($\propto \sqrt{\delta}$, $\delta$ is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exits a characteristic temperature scale below which a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a {\em finite} energy regime. In transport, a strong short-range phase interference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-$T$ resistivity and $T^2$ Hall-angle. We discuss the striking similarities of these theoretical features with those found in the high-$T_c$ cuprates and give aComment: 70 pages, RevTex, hard copies of 7 figures available upon request; minor revisions in the text and references have been made; To be published in July 1 issue of Phys. Rev. B52, (1995

Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events

The $B^0$-$\bar B^0$ oscillation frequency has been measured with a sample of 23 million \B\bar B pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives $\Delta m_d = 0.493 \pm 0.012{(stat)}\pm 0.009{(syst)}$ ps$^{-1}$.Comment: 7 pages, 1 figure, submitted to Physical Review Letter

Statistical Outliers and Dragon-Kings as Bose-Condensed Droplets

A theory of exceptional extreme events, characterized by their abnormal sizes compared with the rest of the distribution, is presented. Such outliers, called "dragon-kings", have been reported in the distribution of financial drawdowns, city-size distributions (e.g., Paris in France and London in the UK), in material failure, epileptic seizure intensities, and other systems. Within our theory, the large outliers are interpreted as droplets of Bose-Einstein condensate: the appearance of outliers is a natural consequence of the occurrence of Bose-Einstein condensation controlled by the relative degree of attraction, or utility, of the largest entities. For large populations, Zipf's law is recovered (except for the dragon-king outliers). The theory thus provides a parsimonious description of the possible coexistence of a power law distribution of event sizes (Zipf's law) and dragon-king outliers.Comment: Latex file, 16 pages, 1 figur