On the nonequilibrium entropy of large and small systems

Thermodynamics makes definite predictions about the thermal behavior of macroscopic systems in and out of equilibrium. Statistical mechanics aims to derive this behavior from the dynamics and statistics of the atoms and molecules making up these systems. A key element in this derivation is the large number of microscopic degrees of freedom of macroscopic systems. Therefore, the extension of thermodynamic concepts, such as entropy, to small (nano) systems raises many questions. Here we shall reexamine various definitions of entropy for nonequilibrium systems, large and small. These include thermodynamic (hydrodynamic), Boltzmann, and Gibbs-Shannon entropies. We shall argue that, despite its common use, the last is not an appropriate physical entropy for such systems, either isolated or in contact with thermal reservoirs: physical entropies should depend on the microstate of the system, not on a subjective probability distribution. To square this point of view with experimental results of Bechhoefer we shall argue that the Gibbs-Shannon entropy of a nano particle in a thermal fluid should be interpreted as the Boltzmann entropy of a dilute gas of Brownian particles in the fluid

Quantum fluctuations in high field magnetization of 2D square lattice J1-J2 antiferromagnets

The J1-J2 square lattice Heisenberg model with spin S=1/2 has three phases with long-range magnetic order and two unconventionally ordered phases depending on the ratio of exchange constants. It describes a number of recently found layered vanadium oxide compounds. A simple means of investigating the ground state is the study of the magnetization curve and high-field susceptibility. We discuss these quantities by using the spin-wave theory and the exact diagonalization in the whole J1-J2 plane. We compare both results and find good overall agreement in the sectors of the phase diagram with magnetic order. Close to the disordered regions the magnetization curve shows strong deviations from the classical linear behaviour caused by large quantum fluctuations and spin-wave approximation breaks down. On the FM side (J1<0) where one approaches the quantum gapless spin nematic ground state this region is surprisingly large. We find that inclusion of second order spin-wave corrections does not lead to fundamental improvement. Quantum corrections to the tilting angle of the ordered moments are also calculated. They may have both signs, contrary to the always negative first order quantum corrections to the magnetization. Finally we investigate the effect of the interlayer coupling and find that the quasi-2D picture remains valid up to |J_\perp/J1| ~ 0.3.Comment: 13 pages, 6figure

Does training with amplitude modulated tones affect tone-vocoded speech perception?

Temporal-envelope cues are essential for successful speech perception. We asked here whether training on stimuli containing temporal-envelope cues without speech content can improve the perception of spectrally-degraded (vocoded) speech in which the temporal-envelope (but not the temporal fine structure) is mainly preserved. Two groups of listeners were trained on different amplitude-modulation (AM) based tasks, either AM detection or AM-rate discrimination (21 blocks of 60 trials during two days, 1260 trials; frequency range: 4Hz, 8Hz, and 16Hz), while an additional control group did not undertake any training. Consonant identification in vocoded vowel-consonant-vowel stimuli was tested before and after training on the AM tasks (or at an equivalent time interval for the control group). Following training, only the trained groups showed a significant improvement in the perception of vocoded speech, but the improvement did not significantly differ from that observed for controls. Thus, we do not find convincing evidence that this amount of training with temporal-envelope cues without speech content provide significant benefit for vocoded speech intelligibility. Alternative training regimens using vocoded speech along the linguistic hierarchy should be explored

Combinatorial Bounds and Characterizations of Splitting Authentication Codes

We present several generalizations of results for splitting authentication codes by studying the aspect of multi-fold security. As the two primary results, we prove a combinatorial lower bound on the number of encoding rules and a combinatorial characterization of optimal splitting authentication codes that are multi-fold secure against spoofing attacks. The characterization is based on a new type of combinatorial designs, which we introduce and for which basic necessary conditions are given regarding their existence.Comment: 13 pages; to appear in "Cryptography and Communications

Multi-membership gene regulation in pathway based microarray analysis

This article is available through the Brunel Open Access Publishing Fund. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background: Gene expression analysis has been intensively researched for more than a decade. Recently, there has been elevated interest in the integration of microarray data analysis with other types of biological knowledge in a holistic analytical approach. We propose a methodology that can be facilitated for pathway based microarray data analysis, based on the observation that a substantial proportion of genes present in biochemical pathway databases are members of a number of distinct pathways. Our methodology aims towards establishing the state of individual pathways, by identifying those truly affected by the experimental conditions based on the behaviour of such genes. For that purpose it considers all the pathways in which a gene participates and the general census of gene expression per pathway. Results: We utilise hill climbing, simulated annealing and a genetic algorithm to analyse the consistency of the produced results, through the application of fuzzy adjusted rand indexes and hamming distance. All algorithms produce highly consistent genes to pathways allocations, revealing the contribution of genes to pathway functionality, in agreement with current pathway state visualisation techniques, with the simulated annealing search proving slightly superior in terms of efficiency. Conclusions: We show that the expression values of genes, which are members of a number of biochemical pathways or modules, are the net effect of the contribution of each gene to these biochemical processes. We show that by manipulating the pathway and module contribution of such genes to follow underlying trends we can interpret microarray results centred on the behaviour of these genes.The work was sponsored by the studentship scheme of the School of Information Systems, Computing and Mathematics, Brunel Universit

The increase of the functional entropy of the human brain with age

We use entropy to characterize intrinsic ageing properties of the human brain. Analysis of fMRI data from a large dataset of individuals, using resting state BOLD signals, demonstrated that a functional entropy associated with brain activity increases with age. During an average lifespan, the entropy, which was calculated from a population of individuals, increased by approximately 0.1 bits, due to correlations in BOLD activity becoming more widely distributed. We attribute this to the number of excitatory neurons and the excitatory conductance decreasing with age. Incorporating these properties into a computational model leads to quantitatively similar results to the fMRI data. Our dataset involved males and females and we found significant differences between them. The entropy of males at birth was lower than that of females. However, the entropies of the two sexes increase at different rates, and intersect at approximately 50 years; after this age, males have a larger entropy

High-resolution age modelling of peat bogs from northern Alberta, Canada, using pre- and post-bomb 14 C, 210 Pb and historical cryptotephra

High-resolution studies of peat profiles are frequently undertaken to investigate natural and anthropogenic disturbances over time. However, overlapping profiles of the most commonly applied age-dating techniques, including 14C and 210Pb, often show significant offsets (>decadal) and biases that can be difficult to resolve. Here we investigate variations in the chronometers and individual site histories from six ombrotrophic peat bogs in central and northern Alberta. Dates produced using pre- and post-bomb 14C, 210Pb (corroborated with 137Cs and 241Am), and cryptotephra peaks, are compared and then integrated using OxCal's P_Sequence function to produce a single Bayesian age model. Environmental histories for each site obtained using physical and chemical characteristics of the peat cores, e.g. plant macrofossils, humification, ash content and dry density, provide important constraints for the models by highlighting periods with significant changes in accumulation rate, e.g. fire events, permafrost development, and prolonged surficial drying. Despite variable environmental histories, it is possible to produce high-resolution age-depth models for each core sequence. Consistent offsets between 14C and 210Pb dates pre-1960s are seen at five of the six sites, but tephra-corrected 210Pb data can be used to produce more coherent models at three of these sites. Processes such as permafrost development and thaw, surficial drying and local fires can disrupt the normal processes by which chronological markers and environmental records are incorporated in the peat record. In consequence, applying standard dating methodologies to these records will result in even greater uncertainties and discrepancies between the different dating tools. These results show that using any single method to accurately date peat profiles where accumulation has not been uniform over time may be unreliable, but a comprehensive multi-method investigation paired with the application of Bayesian statistics can produce more robust chronologies. New cryptotephra data for the Alberta region are also reported here, including the historical Novarupta-Katmai 1912 eruption, White River Ash (East), and glass from Mt. St. Helens, Mt. Churchill, and probable Aleutian sources

Mutual information rate and bounds for it

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two data sets (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators