Collective synchronization in populations of globally coupled phase oscillators with drifting frequencies

We generalize the Kuramoto model for coupled phase oscillators by allowing the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such drifting frequencies were recently measured in cellular populations of circadian oscillator and inspired our work. Linear stability analysis of the Fokker-Planck equation for an infinite population is amenable to exact solution and we show that the incoherent state is unstable passed a critical coupling strength K_c(\ga, \sigf), where \ga is the inverse characteristic drifting time and \sigf the asymptotic frequency dispersion. Expectedly $K_c$ agrees with the noisy Kuramoto model in the large \ga (Schmolukowski) limit but increases slower as \ga decreases. Asymptotic expansion of the solution for \ga\to 0 shows that the noiseless Kuramoto model with Gaussian frequency distribution is recovered in that limit. Thus varying a single parameter allows to interpolate smoothly between two regimes: one dominated by the frequency dispersion and the other by phase diffusion.Comment: 5 pages, 5 figures, accepted in Phys. Rev.

Network inference by combining biologically motivated regulatory constraints with penalized regression

LANO

Solving the riddle of the bright mismatches: hybridization in oligonucleotide arrays

HDONA technology is predicated on two ideas. First, the differential between high-affinity (perfect match, PM) and lower-affinity (mismatch, MM) probes is used to minimize cross-hybridization. Second, several short probes along the transcript are combined, introducing redundancy. Both ideas have shown problems in practice: MMs are often brighter than PMs, and it is hard to combine the pairs because their brightness often spans decades. Previous analysis suggested these problems were sequence-related; publication of the probe sequences has permitted us an in-depth study of this issue. Our results suggest that fluorescently labeling the nucleotides interferes with mRNA binding, causing a catch-22 since, to be detected, the target mRNA must both glow and stick to its probe: without labels it cannot be seen even if bound, while with too many it won't bind. We show that this conflict causes much of the complexity of HDONA raw data, suggesting that an accurate physical understanding of hybridization by incorporating sequence information is necessary to perfect microarray analysis.Comment: 4 figure

Transport and conservation laws

We study the lowest order conservation laws in one-dimensional (1D) integrable quantum many-body models (IQM) as the Heisenberg spin 1/2 chain, the Hubbard and t-J model. We show that the energy current is closely related to the first conservation law in these models and therefore the thermal transport coefficients are anomalous. Using an inequality on the time decay of current correlations we show how the existence of conserved quantities implies a finite charge stiffness (weight of the zero frequency component of the conductivity) and so ideal conductivity at finite temperatures.Comment: 6 pages, Late

The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature

Motivated by recent investigations of transport properties of strongly correlated 1d models and thermal conductivity measurements of quasi 1d magnetic systems we present results for the integrable spin-1/2 $XXZ$ chain. The thermal conductivity $\kappa(\omega)$ of this model has $\Re\kappa(\omega)=\tilde\kappa \delta(\omega)$, i.e. it is infinite for zero frequency $\omega$. The weight $\tilde\kappa$ of the delta peak is calculated exactly by a lattice path integral formulation. Numerical results for wide ranges of temperature and anisotropy are presented. The low and high temperature limits are studied analytically.Comment: 12 page

Replica Symmetry Breaking in Attractor Neural Network Models

The phenomenon of replica symmetry breaking is investigated for the retrieval phases of Hopfield-type network models. The basic calculation is done for the generalized version of the standard model introduced by Horner [1] and by Perez-Vicente and Amit [2] which can exhibit low mean levels of neural activity. For a mean activity $\bar a =1/2$ the Hopfield model is recovered. In this case, surprisingly enough, we cannot confirm the well known one step replica symmetry breaking (1RSB) result for the storage capacity which was presented by Crisanti, Amit and Gutfreund [3] (\alpha_c^{\hbox{\mf 1RSB}}\simeq 0.144). Rather, we find that 1RSB- and 2RSB-Ans\"atze yield only slightly increased capacities as compared to the replica symmetric value (\alpha_c^{\hbox{\mf 1RSB}}\simeq 0.138\,186 and \alpha_c^{\hbox{\mf 2RSB}}\simeq 0.138\,187 compared to \alpha_c^{\hbox{\mf RS}}\simeq 0.137\,905), significantly smaller also than the value \alpha_c^{\hbox{\mf sim}} = 0.145\pm 0.009 reported from simulation studies. These values still lie within the recently discovered reentrant phase [4]. We conjecture that in the infinite Parisi-scheme the reentrant behaviour disappears as is the case in the SK-spin-glass model (Parisi--Toulouse-hypothesis). The same qualitative results are obtained in the low activity range.Comment: Latex file, 20 pages, 8 Figures available from the authors upon request, HD-TVP-94-

Reactive Hall response

The zero temperature Hall constant R_H, described by reactive (nondissipative) conductivities, is analyzed within linear response theory. It is found that in a certain limit, R_H is directly related to the density dependence of the Drude weight implying a simple picture for the change of sign of charge carriers in the vicinity of a Mott-Hubbard transition. This novel formulation is applied to the calculation of R_H in quasi-one dimensional and ladder prototype interacting electron systems.Comment: 4 pages, 3 Postscript figure

Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}

Using the Bethe ansatz method, the zero frequency contribution (Drude weight) to the spin current correlations is analyzed for the easy plane antiferromagnetic Heisenberg model. The Drude weight is a monotonically decreasing function of temperature for all 0<Delta< 1, it approaches the zero temperature value with a power law and it appears to vanish for all finite temperatures at the isotropic Delta=1 point.Comment: 5 pages, 2 Postscript figure

Low-temperature transport in Heisenberg chains

A technique to determine accurately transport properties of integrable and non-integrable quantum-spin chains at finite temperatures by Quantum Monte-Carlo is presented. The reduction of the Drude weight by interactions in the integrable gapless regime is evaluated. Evidence for the absence of a Drude weight in the gapless regime of a non-integrable system with longer-ranged interactions is presented. We estimate the effect of the non-integrability on the transport properties and compare with recent experiments on one-dimensional quantum-spin chains.Comment: accepted for publication (PRL

Outbursts on normal stars. FH Leo misclassified as a novalike variable

We present high resolution spectroscopy of the common proper motion system FH Leo (components HD 96273 and BD+07 2411B), which has been classified as a novalike variable due to an outburst observed by Hipparcos, and we present and review the available photometry. We show from our spectra that neither star can possibly be a cataclysmic variable, instead they are perfectly normal late-F and early-G stars. We measured their radial velocities and derived the atmospheric fundamental parameters, abundances of several elements including Fe, Ni, Cr, Co, V, Sc, Ti, Ca and Mg, and we derive the age of the system. From our analysis we conclude that the stars do indeed constitute a physical binary. However, the observed outburst cannot be readily explained. We examine several explanations, including pollution with scattered light from Jupiter, binarity, microlensing, background supernovae, interaction with unseen companions and planetary engulfment. While no explanation is fully satisfactory, the scattered light and star-planet interaction scenarios emerge as the least unlikely ones, and we give suggestions for further study.Comment: 8 pages, 7 figures. Accepted for publication in A&