Biased random walks on complex networks: the role of local navigation rules

We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to study efficiency of different routing protocols in communication networks. We derive exact expressions for the stationary occupation probability, and for the mean transit time between two nodes. The effect of the cyclic search on transit times is also explored. Results presented in this paper give the basis for theoretical treatment of the transport-related problems on complex networks, including quantitative estimation of the critical value of the packet generation rate.Comment: 5 pages (Phys. Rev style), 3 Figure

Dissipation enhanced vibrational sensing in an olfactory molecular switch

Motivated by a proposed olfactory mechanism based on a vibrationally-activated molecular switch, we study electron transport within a donor-acceptor pair that is coupled to a vibrational mode and embedded in a surrounding environment. We derive a polaron master equation with which we study the dynamics of both the electronic and vibrational degrees of freedom beyond previously employed semiclassical (Marcus-Jortner) rate analyses. We show: (i) that in the absence of explicit dissipation of the vibrational mode, the semiclassical approach is generally unable to capture the dynamics predicted by our master equation due to both its assumption of one-way (exponential) electron transfer from donor to acceptor and its neglect of the spectral details of the environment; (ii) that by additionally allowing strong dissipation to act on the odorant vibrational mode we can recover exponential electron transfer, though typically at a rate that differs from that given by the Marcus-Jortner expression; (iii) that the ability of the molecular switch to discriminate between the presence and absence of the odorant, and its sensitivity to the odorant vibrational frequency, are enhanced significantly in this strong dissipation regime, when compared to the case without mode dissipation; and (iv) that details of the environment absent from previous Marcus-Jortner analyses can also dramatically alter the sensitivity of the molecular switch, in particular allowing its frequency resolution to be improved. Our results thus demonstrate the constructive role dissipation can play in facilitating sensitive and selective operation in molecular switch devices, as well as the inadequacy of semiclassical rate equations in analysing such behaviour over a wide range of parameters.Comment: 12 pages, 6 figures, close to published version, comments welcom

Thermodynamic forces, flows, and Onsager coefficients in complex networks

We present Onsager formalism applied to random networks with arbitrary degree distribution. Using the well-known methods of non-equilibrium thermodynamics we identify thermodynamic forces and their conjugated flows induced in networks as a result of single node degree perturbation. The forces and the flows can be understood as a response of the system to events, such as random removal of nodes or intentional attacks on them. Finally, we show that cross effects (such as thermodiffusion, or thermoelectric phenomena), in which one force may not only give rise to its own corresponding flow, but to many other flows, can be observed also in complex networks.Comment: 4 pages, 2 figure

Can lichen secondary compounds impact upon the pathogenic soil fungi Fusarium oxysporum and F. avenaceum?

The antifungal activity of secondary lichen metabolites extracted by means of acetone and ethanol from Cetraria islandica, Cladonia mitis, C. rangiferina, Pseudevernia furfuracea and Usnea dasopoga on the pathogenic fungi Fusarium oxysporum and F. avenacuem was examined. The activity of extracted compounds was tested after their mixture with PDA medium before solidification. The most active extracts inhibiting the growth of fungal mycelia contained fumarprotocetraric, salazinic and usnic acids, and atranorin. Unparalleled activity was demonstrated by an ethanol extract from mixed C. islandica and P. furfuracea thalli, which accelerated the growth of F. avenaceum compared with the control test with ethanol. The growth rate of the two Fusarium representatives was strongly inhibited by both alcoholic extracts from C. mitis and from C. rangiferina, more strongly than by the extracts from the mixed thalli of the two terricolous taxa. A dose of 1 ml of acetone added to the medium had no significant effect on the growth of the tested fungi; it indicates usefulness of acetone as a solvent for some lichen compounds in this type of experiment

Statistical Convergence in Function Spaces

We study statistical versions of several classical kinds of convergence of sequences of functions between metric spaces (Dini, Arzelà, and Alexandroff) in different function spaces. Also, we discuss a statistical approach to recently introduced notions of strong uniform convergence and exhaustiveness

Is female psychopathy linked with child abuse? An empirical investigation using a person-centered approach

Childhood abuse is associated with increased psychopathic features among girls, but most prior research is based on data from correctional samples of female delinquents and less is known about how specific forms of childhood abuse affect specific features of psychopathy. Using a school-based community sample of 696 girls aged 9–17 years from Barbados and Grenada, the current study examined latent profiles of psychopathic personality traits and their associations with physical, emotional, and sexual abuse. Latent profile analysis (LPA) revealed four distinct psychopathy groups among girls, including a ‘low psychopathy’ group (41.9% of girls), ‘high psychopathy’ group (4.8%), ‘high interpersonal manipulation and egocentricity’ group (37.4%), and a ‘moderate psychopathy’ group (16%). There was considerable evidence of physical abuse, emotional abuse, and sexual abuse among participants. Sexual abuse was associated with a 116% increased likelihood of membership in the high psychopathy group and a 57% increased likelihood of membership in the high interpersonal manipulation and egocentricity group. These results indicate that sexual abuse is a powerful distal factor in the development of psychopathic personality functioning, especially more severe variants

Identification and rejection of scattered neutrons in AGATA

Gamma rays and neutrons, emitted following spontaneous fission of 252Cf, were measured in an AGATA experiment performed at INFN Laboratori Nazionali di Legnaro in Italy. The setup consisted of four AGATA triple cluster detectors (12 36-fold segmented high-purity germanium crystals), placed at a distance of 50 cm from the source, and 16 HELENA BaF2 detectors. The aim of the experiment was to study the interaction of neutrons in the segmented high-purity germanium detectors of AGATA and to investigate the possibility to discriminate neutrons and gamma rays with the gamma-ray tracking technique. The BaF2 detectors were used for a time-of-flight measurement, which gave an independent discrimination of neutrons and gamma rays and which was used to optimise the gamma-ray tracking-based neutron rejection methods. It was found that standard gamma-ray tracking, without any additional neutron rejection features, eliminates effectively most of the interaction points due to recoiling Ge nuclei after elastic scattering of neutrons. Standard tracking rejects also a significant amount of the events due to inelastic scattering of neutrons in the germanium crystals. Further enhancements of the neutron rejection was obtained by setting conditions on the following quantities, which were evaluated for each event by the tracking algorithm: energy of the first and second interaction point, difference in the calculated incoming direction of the gamma ray, figure-of-merit value. The experimental results of tracking with neutron rejection agree rather well with Geant4 simulations

Average path length in random networks

Analytic solution for the average path length in a large class of random graphs is found. We apply the approach to classical random graphs of Erd\"{o}s and R\'{e}nyi (ER) and to scale-free networks of Barab\'{a}si and Albert (BA). In both cases our results confirm previous observations: small world behavior in classical random graphs $l_{ER} \sim \ln N$ and ultra small world effect characterizing scale-free BA networks $l_{BA} \sim \ln N/\ln\ln N$. In the case of scale-free random graphs with power law degree distributions we observed the saturation of the average path length in the limit of $N\to\infty$ for systems with the scaling exponent $2< \alpha <3$ and the small-world behaviour for systems with $\alpha>3$.Comment: 4 pages, 2 figures, changed conten

Optimised generation of heralded Fock states using parametric down conversion

The generation of heralded pure Fock states via spontaneous parametric down conversion (PDC) relies on perfect photon-number correlations in the output modes. Correlations in any other degree of freedom, however, degrade the purity of the heralded state. In this paper, we investigate spectral entanglement between the two output modes of a periodically poled waveguide. With the intent of generating heralded 1- and 2-photon Fock states, we expand the output state of the PDC to second order in photon number. We explore the effects of spectral filtering and inefficient detection, of the heralding mode, on the count rate, g(2) and purity of the heralded state, as well as the fidelity between the resulting state and an ideal Fock state. We find that filtering can decrease spectral correlations, however, at the expense of the count rate and increased photon-number mixedness in the heralded output state. As a physical example, we model a type II PP-KTP waveguide pumped by lasers at wavelengths of 400 nm, 788 nm and 1930 nm. The latter two allow the fulfillment of extended phase matching conditions in an attempt to eliminate spectral correlations in the PDC output state without the use of filtering, however, we find that even in these cases, some filtering is needed to achieve states of very high purity.Comment: 28 pages, 25 figures, revised expressions for two-photon fidelit