A Stochastic Model for Electron Multiplication Charge-Coupled Devices - From Theory to Practice

Electron multiplication charge-coupled devices (EMCCD) are widely used for photon counting experiments and measurements of low intensity light sources, and are extensively employed in biological fluorescence imaging applications. These devices have a complex statistical behaviour that is often not fully considered in the analysis of EMCCD data. Robust and optimal analysis of EMCCD images requires an understanding of their noise properties, in particular to exploit fully the advantages of Bayesian and maximum-likelihood analysis techniques, whose value is increasingly recognised in biological imaging for obtaining robust quantitative measurements from challenging data. To improve our own EMCCD analysis and as an effort to aid that of the wider bioimaging community, we present, explain and discuss a detailed physical model for EMCCD noise properties, giving a likelihood function for image counts in each pixel for a given incident intensity, and we explain how to measure the parameters for this model from various calibration images. © 2013 Hirsch et al.

Molecular dynamics study on the phase diagrams of linear and branched chain molecules

The particle transfer molecular dynamics is used to study the phase equilibria of linear and branched chain molecules. The scaling of the critical temperature versus chain length is obtained and the critical densities are found to decrease with increasing chain length, which are in agreement with the results of experiment and theory. The phase diagrams of the linear and the branched chain molecules nearly overlap with each other. Moreover, the radial distribution functions of linear and branched chain molecules in gas phase are very similar, but in the liquid phase, they are different for different kinds of chains.

Calculating the equation of state parameters and predicting the spinodal curve of isotactic polypropylene/poly(ethylene-co-octene) blend by molecular dynamics simulations combined with Sanchez-Lacombe lattice fluid theory

Molecular dynamics simulations are adopted to calculate the equation of state characteristic parameters P*, rho*, and T* of isotactic polypropylene (iPP) and poly(ethylene-co-octene) (PEOC), which can be further used in the Sanchez-Lacombe lattice fluid theory (SLLFT) to describe the respective physical properties. The calculated T* is a function of the temperature, which was also found in the literature. To solve this problem, we propose a Boltzmann fitting of the data and obtain T* at the high-temperature limit. With these characteristic parameters, the pressure-volume-temperature (PVT) data of iPP and PEOC are predicted by the SLLFT equation of state. To justify the correctness of our results, we also obtain the PVT data for iPP and PEOC by experiments. Good agreement is found between the two sets of data. By integrating the Euler-Lagrange equation and the Cahn-Hilliard relation, we predict the density profiles and the surface tensions for iPP and PEOC, respectively. Furthermore, a recursive method is proposed to obtain the characteristic interaction energy parameter between iPP and PEOC. This method, which does not require fitting to the experimental phase equilibrium data, suggests an alternative way to predict the phase diagrams that are not easily obtained in experiments.

Foundational Theory for Understanding Policy Routing Dynamics

In this paper we introduce a theory of policy routing dynamics based on fundamental axioms of routing update mechanisms. We develop a dynamic policy routing model (DPR) that extends the static formalism of the stable paths problem (introduced by Griffin et al.) with discrete synchronous time. DPR captures the propagation of path changes in any dynamic network irrespective of its time-varying topology. We introduce several novel structures such as causation chains, dispute fences and policy digraphs that model different aspects of routing dynamics and provide insight into how these dynamics manifest in a network. We exercise the practicality of the theoretical foundation provided by DPR with two fundamental problems: routing dynamics minimization and policy conflict detection. The dynamics minimization problem utilizes policy digraphs, that capture the dependencies in routing policies irrespective of underlying topology dynamics, to solve a graph optimization problem. This optimization problem explicitly minimizes the number of routing update messages in a dynamic network by optimally changing the path preferences of a minimal subset of nodes. The conflict detection problem, on the other hand, utilizes a theoretical result of DPR where the root cause of a causation cycle (i.e., cycle of routing update messages) can be precisely inferred as either a transient route flap or a dispute wheel (i.e., policy conflict). Using this result we develop SafetyPulse, a token-based distributed algorithm to detect policy conflicts in a dynamic network. SafetyPulse is privacy preserving, computationally efficient, and provably correct.

Laminar Cortical Dynamics of Cognitive and Motor Working Memory, Sequence Learning and Performance: Toward a Unified Theory of How the Cerebral Cortex Works

How do the layered circuits of prefrontal and motor cortex carry out working memory storage, sequence learning, and voluntary sequential item selection and performance? A neural model called LIST PARSE is presented to explain and quantitatively simulate cognitive data about both immediate serial recall and free recall, including bowing of the serial position performance curves, error-type distributions, temporal limitations upon recall, and list length effects. The model also qualitatively explains cognitive effects related to attentional modulation, temporal grouping, variable presentation rates, phonemic similarity, presentation of non-words, word frequency/item familiarity and list strength, distracters and modality effects. In addition, the model quantitatively simulates neurophysiological data from the macaque prefrontal cortex obtained during sequential sensory-motor imitation and planned performance. The article further develops a theory concerning how the cerebral cortex works by showing how variations of the laminar circuits that have previously clarified how the visual cortex sees can also support cognitive processing of sequentially organized behaviors.

A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Utilising computational fluid dynamics (CFD) for the modelling of granular material in large-scale engineering processes

In this paper, the framework is described for the modelling of granular material by employing Computational Fluid Dynamics (CFD). This is achieved through the use and implementation in the continuum theory of constitutive relations, which are derived in a granular dynamics framework and parametrise particle interactions that occur at the micro-scale level. The simulation of a process often met in bulk solids handling industrial plants involving granular matter, (i.e. filling of a flat-bottomed bin with a binary material mixture through pneumatic conveying-emptying of the bin in core flow mode-pneumatic conveying of the material coming out of a the bin) is presented. The results of the presented simulation demonstrate the capability of the numerical model to represent successfully key granular processes (i.e. segregation/degradation), the prediction of which is of great importance in the process engineering industry.

Effect of elevated CO2 on the dynamics of particle-attached and free-living bacterioplankton communities in an Arctic fjord

In the frame of the European Project on Ocean Acidification (EPOCA), the response of an Arctic pelagic community (<3 mm) to a gradient of seawater pCO(2) was investigated. For this purpose 9 large-scale in situ mesocosms were deployed in Kongsfjorden, Svalbard (78 degrees 56.2' N, 11 degrees 53.6' E), in 2010. The present study investigates effects on the communities of particle-attached (PA; >3 mu m) and free-living (FL; <3 mu m > 0.2 mu m) bacteria by Automated Ribosomal Intergenic Spacer Analysis (ARISA) in 6 of the mesocosms, ranging from 185 to 1050 mu atm initial pCO(2), and the surrounding fjord. ARISA was able to resolve, on average, 27 bacterial band classes per sample and allowed for a detailed investigation of the explicit richness and diversity. Both, the PA and the FL bacterioplankton community exhibited a strong temporal development, which was driven mainly by temperature and phytoplankton development. In response to the breakdown of a picophytoplankton bloom, numbers of ARISA band classes in the PA community were reduced at low and medium CO2 (similar to 185-685 mu atm) by about 25 %, while they were more or less stable at high CO2 (similar to 820-1050 mu atm). We hypothesise that enhanced viral lysis and enhanced availability of organic substrates at high CO2 resulted in a more diverse PA bacterial community in the post-bloom phase. Despite lower cell numbers and extracellular enzyme activities in the post-bloom phase, bacterial protein production was enhanced in high CO2 mesocosms, suggesting a positive effect of community richness on this function and on carbon cycling by bacteria.

Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form phi(r) and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v(0). Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.

Ultra-fast spin dynamics in the 2s2p^2 configuration of C^+ studied by time-dependent R-matrix theory

We employ time-dependent R-matrix theory to study ultra-fast dynamics in the doublet 2s2p(2) configuration of C+ for a total magnetic quantum number M = 1. In contrast to the dynamics observed for M = 0, ultra-fast dynamics for M = 1 is governed by spin dynamics in which the 2s electron acts as a flag rather than a spectator electron. Under the assumption that m(S) = 1/2, m(2s) = 1/2 allows spin dynamics involving the two 2p electrons, whereas m(2s) = -1/2 prevents spin dynamics of the two 2p electrons. For a pump-probe pulse scheme with (h) over bar omega(pump) = 10.9 eV and (h) over bar omega(probe) = 16.3 eV and both pulses six cycles long, little sign of spin dynamics is observed in the total ionization probability. Signs of spin dynamics can be observed, however, in the ejected-electron momentum distributions. We demonstrate that the ejected-electron momentum distributions can be used for unaligned targets to separate the contributions of initial M = 0 and M = 1 levels. This would, in principle, allow unaligned target ions to be used to obtain information on the different dynamics in the 2s2p(2) configuration for the M = 0 and M = 1 levels from a single experime

A complete analytic theory for structure and dynamics of populations and communities spanning wide ranges in body size

The prediction and management of ecosystem responses to global environmental change would profit from a clearer understanding of the mechanisms determining the structure and dynamics of ecological communities. The analytic theory presented here develops a causally closed picture for the mechanisms controlling community and population size structure, in particular community size spectra, and their dynamic responses to perturbations, with emphasis on marine ecosystems. Important implications are summarised in non-technical form. These include the identification of three different responses of community size spectra to size-specific pressures (of which one is the classical trophic cascade), an explanation for the observed slow recovery of fish communities from exploitation, and clarification of the mechanism controlling predation mortality rates. The theory builds on a community model that describes trophic interactions among size-structured populations and explicitly represents the full life cycles of species. An approximate time-dependent analytic solution of the model is obtained by coarse graining over maturation body sizes to obtain a simple description of the model steady state, linearising near the steady state, and then eliminating intraspecific size structure by means of the quasi-neutral approximation. The result is a convolution equation for trophic interactions among species of different maturation body sizes, which is solved analytically using a novel technique based on a multiscale expansion.