In-situ measurements of oxygen, carbon monoxide and greenhouse gases from Ochsenkopf tall tower in Germany

We present 2.5 years (from June 2006 to December 2008) of in-situ measurements of CO2, O2, CH4, CO, N2O and SF6 mixing ratios sampled from 23, 90 and 163m above ground on the Ochsenkopf tower in the Fichtelgebirge range, Germany (50?0104900 N, 11?4803000 E, 1022ma.s.l.). In addition to the in-situ measurements, flask samples are taken at Ochsenkopf at approximately weekly intervals and are subsequently analysed for the mixing ratios of the same species, as well as H2, and the stable isotopes, ?13C, ?18O in CO2. The in-situ measurements of CO2 and O2 from 23m show substantial diurnal variations that are modulated by biospheric fluxes, combustion of fossil fuels, and by diurnal changes in the planetary boundary layer height. Measurements from 163m exhibit only very weak diurnal variability, as this height (1185ma.s.l.) is generally above the nocturnal boundary layer. CH4, CO, N2O and SF6 show little diurnal variation even at 23m owing to the absence of any significant diurnal change in the fluxes and the absence of any strong local sources or sinks. From the in-situ record, the seasonal cycles of the gas species have been characterized and the multi-annual trends determined. Because the record is short, the calculation of the trend is sensitive to inter-annual variations in the amplitudes of the seasonal cycles. However, for CH4 a significant change in the growth-rate was detected for 2006.5–2008.5 as compared with the global mean from 1999 to 2006 and is consistent with other recent observations of a renewed increasing global growth rate in CH4 since the beginning of 2007

Test of Guttmann and Enting's conjecture in the eight-vertex model

We investigate the analyticity property of the partially resummed series expansion(PRSE) of the partition function for the eight-vertex model. Developing a graphical technique, we have obtained a first few terms of the PRSE and found that these terms have a pole only at one point in the complex plane of the coupling constant. This result supports the conjecture proposed by Guttmann and Enting concerning the ``solvability'' in statistical mechanical lattice models.Comment: 15 pages, 3 figures, RevTe

A Moving Bump in a Continuous Manifold: A Comprehensive Study of the Tracking Dynamics of Continuous Attractor Neural Networks

Understanding how the dynamics of a neural network is shaped by the network structure, and consequently how the network structure facilitates the functions implemented by the neural system, is at the core of using mathematical models to elucidate brain functions. This study investigates the tracking dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of neuronal recurrent interactions, CANNs can hold a continuous family of stationary states. They form a continuous manifold in which the neural system is neutrally stable. We systematically explore how this property facilitates the tracking performance of a CANN, which is believed to have clear correspondence with brain functions. By using the wave functions of the quantum harmonic oscillator as the basis, we demonstrate how the dynamics of a CANN is decomposed into different motion modes, corresponding to distortions in the amplitude, position, width or skewness of the network state. We then develop a perturbative approach that utilizes the dominating movement of the network's stationary states in the state space. This method allows us to approximate the network dynamics up to an arbitrary accuracy depending on the order of perturbation used. We quantify the distortions of a Gaussian bump during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable and the reaction time for the network to catch up with an abrupt change in the stimulus.Comment: 43 pages, 10 figure

Gene profiling suggests a common evolution of bladder cancer subtypes

Abstract Background Bladder cancer exists as several distinct subtypes, including urothelial carcinoma (UCa), squamous cell carcinoma (SCCa), adenocarcinoma and small cell carcinoma. These entities, despite showing distinct morphology and clinical behavior, arise from the urothelial lining and are often accompanied by similar precursor/in situ findings. The relationship between these subtypes has not been explored in detail. Methods We compared gene expression analysis of the two most common subtypes of bladder cancer, UCa (n = 10) and SCCa (n = 9), with an additional comparison to normal urothelium from non-cancer patients (n = 8) using Affymetrix GeneChip Human genome arrays (Affymetrix, Santa Clara, CA). The results were stratified by supervised and unsupervised clustering analysis, as well as by overall fold change in gene expression. Results When compared to normal urothelium, UCa showed differential expression of 155 genes using a 5-fold cut-off. Examples of differentially regulated genes included topoisomerases, cancer-related transcription factors and cell cycle mediators. A second comparison of normal urothelium to SCCa showed differential expression of 503 genes, many of which were related to squamous-specific morphology (desmosomal complex, intermediate filaments present within squamous epithelium, squamous cornifying proteins, and molecules upregulated in squamous carcinomas from other anatomic sites). When compared, 137 genes were commonly dysregulated in both UCa and SCCa as compared to normal urothelium. All dysregulated genes in UCa were shared in common with SCCa, with the exception of only 18 genes. Supervised clustering analysis yielded correct classification of lesions in 26/27 (96%) of cases and unsupervised clustering analysis yielded correct classification in 25/27 (92.6%) of cases. Conclusions The results from this analysis suggest that bladder SCCa shares a significant number of gene expression changes with conventional UCa, but also demonstrates an additional set of alterations that is unique to this entity that defines the squamous phenotype. The similarity in deregulated gene products suggests that SCCa may be a much more closely related entity at the molecular level to conventional UCa than previously hypothesized

Breaking Synchrony by Heterogeneity in Complex Networks

For networks of pulse-coupled oscillators with complex connectivity, we demonstrate that in the presence of coupling heterogeneity precisely timed periodic firing patterns replace the state of global synchrony that exists in homogenous networks only. With increasing disorder, these patterns persist until they reach a critical temporal extent that is of the order of the interaction delay. For stronger disorder these patterns cease to exist and only asynchronous, aperiodic states are observed. We derive self-consistency equations to predict the precise temporal structure of a pattern from the network heterogeneity. Moreover, we show how to design heterogenous coupling architectures to create an arbitrary prescribed pattern.Comment: 4 pages, 3 figure

Coarse-grained dynamics of an activity bump in a neural field model

We study a stochastic nonlocal PDE, arising in the context of modelling spatially distributed neural activity, which is capable of sustaining stationary and moving spatially-localized ``activity bumps''. This system is known to undergo a pitchfork bifurcation in bump speed as a parameter (the strength of adaptation) is changed; yet increasing the noise intensity effectively slowed the motion of the bump. Here we revisit the system from the point of view of describing the high-dimensional stochastic dynamics in terms of the effective dynamics of a single scalar "coarse" variable. We show that such a reduced description in the form of an effective Langevin equation characterized by a double-well potential is quantitatively successful. The effective potential can be extracted using short, appropriately-initialized bursts of direct simulation. We demonstrate this approach in terms of (a) an experience-based "intelligent" choice of the coarse observable and (b) an observable obtained through data-mining direct simulation results, using a diffusion map approach.Comment: Corrected aknowledgement

Control of atomic currents using a quantum stirring device

We propose a BEC stirring device which can be regarded as the incorporation of a quantum pump into a closed circuit: it produces a DC circulating current in response to a cyclic adiabatic change of two control parameters of an optical trap. We demonstrate the feasibility of this concept and point out that such device can be utilized in order to probe the interatomic interactions.Comment: 5 pages, 4 figures, uses epl2.cls, revised versio

On the Navier-Stokes equations with rotating effect and prescribed outflow velocity

We consider the equations of Navier-Stokes modeling viscous fluid flow past a moving or rotating obstacle in $\mathbb{R}^d$ subject to a prescribed velocity condition at infinity. In contrast to previously known results, where the prescribed velocity vector is assumed to be parallel to the axis of rotation, in this paper we are interested in a general outflow velocity. In order to use $L^p$-techniques we introduce a new coordinate system, in which we obtain a non-autonomous partial differential equation with an unbounded drift term. We prove that the linearized problem in $\mathbb{R}^d$ is solved by an evolution system on $L^p_{\sigma}(\mathbb{R}^d)$ for $1<p<\infty$. For this we use results about time-dependent Ornstein-Uhlenbeck operators. Finally, we prove, for $p\geq d$ and initial data $u_0\in L^p_{\sigma}(\mathbb{R}^d)$, the existence of a unique mild solution to the full Navier-Stokes system.Comment: 18 pages, to appear in J. Math. Fluid Mech. (published online first

Synchronization of Excitatory Neurons with Strongly Heterogeneous Phase Responses

In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system by dealing explicitly with the heterogeneous phase response curves. We develop a novel method to solve the self-consistent equations for order parameters by using formal complex-valued phase variables, and apply our theory to networks of in vitro cortical neurons. We find a novel state transition that is not observed in previous oscillator network models.Comment: 4 pages, 3 figure