Quasi symplectic integrators for stochastic differential equations

Two specialized algorithms for the numerical integration of the equations of motion of a Brownian walker obeying detailed balance are introduced. The algorithms become symplectic in the appropriate limits, and reproduce the equilibrium distributions to some higher order in the integration time step. Comparisons with other existing integration schemes are carried out both for static and dynamical quantities.Comment: 7 pages, revtex, 6 eps figure

On the time dependence of the hh-index

The time dependence of the $h$-index is analyzed by considering the average behaviour of $h$ as a function of the academic age $A_A$ for about 1400 Italian physicists, with career lengths spanning from 3 to 46 years. The individual $h$-index is strongly correlated with the square root of the total citations $N_C$: $h \approx 0.53 \sqrt{N_C}$. For academic ages ranging from 12 to 24 years, the distribution of the time scaled index $h/\sqrt{A_A}$ is approximately time-independent and it is well described by the Gompertz function. The time scaled index $h/\sqrt{A_A}$ has an average approximately equal to 3.8 and a standard deviation approximately equal to 1.6. Finally, the time scaled index $h/\sqrt{A_A}$ appears to be strongly correlated with the contemporary $h$-index $h_c$

Engineering interband transport by time-dependent disorder

We show how the evolution of atoms in a tilted lattice can be changed and controlled by phase noise on the lattice. Dependent on the characteristic parameters of the noise, the interband transport can either be suppressed or enhanced, which is of interest for high precision control in experimental realization with Bose-Einstein condensates. The effect of the noise on the survival probability in the ground band is summarized in a scaling plot stressing the universality of our results

Macroscopic Manifestation of Microscopic Entropy Production: Space-Dependent Intermittence

We study a spatial diffusion process generated by velocity fluctuations of intermittent nature. We note that intermittence reduces the entropy production rate while enhancing the diffusion strength. We study a case of space-dependent intermittence and prove it to result in a deviation from uniform distribution. This macroscopic effect can be used to measure the relative value of the trajectory entropy.Comment: 2 postscript figures, enclose

A system-level neural model of the brain mechanisms underlying instrumental devaluation in rats

Goal-directed behaviours are defined by the presence of two kinds of effect on instrumental learning. First, degrading the contingencies between produced actions and desired outcomes diminishes the number of instrumental responses; second, devaluing a reward results in a lower production of instrumental actions to obtain it. We present a computational model of the neural processes underlying instrumental devaluation in rats. The model reproduces the interaction between the basolateral complex of the amygdala (BLA) and the limbic, associative and somatosensory striato-cortical loops. Firing-rate units are used to abstract the activity features of neural populations. Learning is reproduced through the use of dopamine-dependent simple and differential hebbian rules. Constraints from anatomy of the projections between neural systems are taken into account. The central hypothesis implemented in the model is that pavlovian associations learned within the BLA between manipulanda and rewards modulate goal selection through the activation of the nucleus accumbens core (NaccCo). Selection processes happening in the limbic basal ganglia with the activation of the NaccCo decide which outcome is choosen as a goal within the prelimbic cortex (PL). Connections between the BLA and the NaccCo are learned through hebbian associations mediated by feedbacks from the PL to the NaccCo. Information about selected goals from the limbic striato-cortical loop influences action selection in the sensorimotor loop both through cortico-cortical projections and through a striato-nigro-striatal dopaminergic pathway passing through the associative striato-cortical loop. The model is tested as part of the control system of a simulated rat. Instrumental devaluation tasks are reproduced. Simulated lesions of the BLA, the NaccCo, the PL and the dorsomedial striatum (DMS) both before and after training reproduce the behavioural effect of lesions in real rats. The model provides predictions about the effects of still undocumented lesions

Comment on "Influence of Noise on Force Measurements"

In a recent Letter [arXiv:1004.0874], Volpe et al. describe experiments on a colloidal particle near a wall in the presence of a gravitational field for which they study the influence of noise on the measurement of force. Their central result is a striking discrepancy between the forces derived from experimental drift measurements via their Eq. (1), and from the equilibrium distribution. From this discrepancy they infer the stochastic calculus realised in the system. We comment, however: (a) that Eq. (1) does not hold for space-dependent diffusion, and corrections should be introduced; and (b) that the "force" derived from the drift need not coincide with the "force" obtained from the equilibrium distribution.Comment: Comment submitted to a PRL letter; 1 page, 1 figur

Separatrix chaos: new approach to the theoretical treatment

We develop a new approach to the theoretical treatment of the separatrix chaos, using a special analysis of the separatrix map. The approach allows us to describe boundaries of the separatrix chaotic layer in the Poincar\'{e} section and transport within the layer. We show that the maximum which the width of the layer in energy takes as the perturbation frequency varies is much larger than the perturbation amplitude, in contrast to predictions by earlier theories suggesting that the maximum width is of the order of the amplitude. The approach has also allowed us to develop the self-consistent theory of the earlier discovered (PRL 90, 174101 (2003)) drastic facilitation of the onset of global chaos between adjacent separatrices. Simulations agree with the theory.Comment: 10 pages, 4 figures, proceedings of the conference "Chaos, Complexity and Transport" (Marseille, 5-9 June 2007), in pres

New approach to the treatment of separatrix chaos and its application to the global chaos onset between adjacent separatrices

We have developed the {\it general method} for the description of {\it separatrix chaos}, basing on the analysis of the separatrix map dynamics. Matching it with the resonant Hamiltonian analysis, we show that, for a given amplitude of perturbation, the maximum width of the chaotic layer in energy may be much larger than it was assumed before. We apply the above theory to explain the drastic facilitation of global chaos onset in time-periodically perturbed Hamiltonian systems possessing two or more separatrices, previously discovered (PRL 90, 174101 (2003)). The theory well agrees with simulations. We also discuss generalizations and applications. Examples of applications of the facilitation include: the increase of the DC conductivity in spatially periodic structures, the reduction of activation barriers for noise-induced transitions and the related acceleration of spatial diffusion, the facilitation of the stochastic web formation in a wave-driven or kicked oscillator.Comment: 29 pages, 16 figures (figs. are of reduced quality, original files are available on request from authors), paper has been significantly revised and resubmitted to PR

Noise assisted transport in the Wannier-Stark system

We investigated how the presence of an additional lattice potential, driven by a harmonic noise process, changes the transition rate from the ground band to the first excited band in a Wannier-Stark system. Alongside numerical simulations, we present two models that capture the essential features of the dynamics. The first model uses a noise-driven Landau-Zener approximation and describes the short time evolution of the full system very well. The second model assumes that the noise process' correlation time is much larger than the internal timescale of the system, yet it allows for good estimates of the observed transition rates and gives a simple interpretation of the dynamics. One of the central results is that we obtain a way to control the interband transitions with the help of the second lattice. This could readily be realized in state-of-the-art experiments using either Bose-Einstein condensates or optical pulses in engineered potentials

Geochemistry and mineralogy of lacustrine sediment from Fucino Lake (Abruzzo, central Italy): palaeoclimatic and palaeoenvironmental implications.

Fucino basin is the largest intermountain tectonic depression of the central Apennines (Abruzzo, Italy). It hosts a thick and continuous succession of fine-grained lacustrine sediments interbedded with several fall-out deposits from the pery- Tyrrhenian Quaternary volcanic centres. In co-operation with international scientific partners (CNR-IGG of Pisa, Institut für Geologie und Mineralogie of Cologne, School of Earth Sciences of Melbourne) we performed multi-proxy geochemical analyses (XRF scanning for Si, K, Ca, Ti, Mn, Fe, Rb, Sr and Zr; total organic carbon, TOC; total inorganic carbon, TIC; total nitrogen and sulphur; oxygen and carbon stable isotopes) on a long core (87 m) retrieved from the Fucino basin in June 2015. On the basis of a tephrostratigraphic age-model developed at the CNR-IGAG in Rome the core span continuously between ca. 3000 and 160,000 yr. In this thesis we investigated an interval constrained between two Latium tephra layers corresponding to the 84.6 ± 5.1 and 36.2 ± 1.6 ka time-span. This period of time covers basically the ignition of the last glaciation (the transition between MIS5 and MIS4 in the marine isotope scale) and part of the last Pleniglacial period which was characterised by abrupt climatic and environmental changes on both global and regional scale. From time series of our proxy data we recognised complex low frequency trends with superposed higher frequency oscillations. We interpreted observed variations in terms of palaeohydrological and palaeoenvironmental changes in the lake catchment. On the basis of the most significative proxies (Ti, Ca, TOC%, TIC%, δ18O) we divided the record into three different periods: the first spanning between 85 and 68 ka, the second between 68 and 50 ka and the third between 50 and 36 ka. In our interpretation, the first period was characterised by low minerogenic input, high lake primary productivity and an enhanced precipitation. The second period had generalised high minerogenic input and low lake primary production, although it was mainly characterised by high-frequency and high- amplitude oscillations suggesting high frequency environmental instability. The beginning of the third period is marked by an abrupt increase in minerogenic input and by a prominent decrease in lake primary production. Overall, minerogenic input was high and lake productivity low. This period was mainly characterised by rather stable environmental conditions which were supported by less intense and abrupt variations in the hydrological regime. The last 2-3 ky of our record displayed a restoration of high-frequency and high-amplitude oscillations. By comparing our record with other regional (Monticchio Lake pollen record) and external (North Atlantic marine cores, Greenland ice cores) climatic archives and with Northern Hemisphere insolation curves we recognised a strong climatic coherence at a regional scale. We interpreted the 84,6-68 ka period as representative of late MIS5 interglacial conditions, the 68-50 ka period as representative of the onset of MIS4 fully glacial conditions and the 50-36 ka period as representative of MIS3 mild glacial conditions over the Western Mediterranean basin. Rapid oscillations in the hydrological regime over the lake catchment and in soil erosion rates can be regarded as the expression of Heinrich events and DO events, recognised in the North Atlantic, over the Mediterranean