Towards testing interacting cosmology by distant type Ia supernovae

We investigate the possibility of testing cosmological models with interaction between matter and energy sector. We assume the standard FRW model while the so called energy conservation condition is interpreted locally in terms of energy transfer. We analyze two forms of dark energy sectors: the cosmological constant and phantom field. We find a simple exact solution of the models in which energy transfer is described by a Cardassian like term in the relation of $H^{2}(z)$, where $H$ is Hubble's function and $z$ is redshift. The considered models have two additional parameters $(\Omega_{\text{int}},n)$ (apart the parameters of the $\Lambda$CDM model) which can be tested using SNIa data. In the estimation of the model parameters Riess et al.'s sample is used. We also confront the quality of statistical fits for both the $\Lambda$CDM model and the interacting models with the help of the Akaike and Bayesian informative criteria. Our conclusion from standard best fit method is that the interacting models explains the acceleration of the Universe better but they give rise to a universe with high matter density. However, using the tools of information criteria we find that the two new parameters play an insufficient role in improving the fit to SNIa data and the standard $\Lambda$CDM model is still preferred. We conclude that high precision detection of high redshift supernovae could supply data capable of justifying adoption of new parameters.Comment: RevTeX4, 14 pages, 7 figure

Brief Announcement: New Clocks, Fast Line Formation and Self-Replication Population Protocols

In this paper we consider a known variant of the standard population protocol model in which agents can be connected by edges, referred to as the network constructor model. During an interaction between two agents the relevant connecting edge can be formed, maintained or eliminated by the transition function. The state space of agents is fixed (constant size) and the size n of the population is not known, i.e., not hard-coded in the transition function. Since pairs of agents are chosen uniformly at random the status of each edge is updated every Θ(n2) interactions in expectation which coincides with Θ(n) parallel time. This phenomenon provides a natural lower bound on the time complexity for any non-trivial network construction designed for this variant. This is in contrast with the standard population protocol model in which efficient protocols operate in O(poly log n) parallel time. The main focus in this paper is on efficient manipulation of linear structures including formation, self-replication and distribution (including pipelining) of complex information in the adopted model. We propose and analyse a novel edge based phase clock counting parallel time Θ(n log n) in the network constructor model, showing also that its leader based counterpart provides the same time guaranties in the standard population protocol model. Note that all currently known phase clocks can count parallel time not exceeding O(poly log n). The new clock enables a nearly optimal O(n log n) parallel time spanning line construction (a key component of universal network construction), which improves dramatically on the best currently known O(n2) parallel time protocol, solving the main open problem in the considered model [9]. We propose a new probabilistic bubble-sort algorithm in which random comparisons and transfers are allowed only between the adjacent positions in the sequence. Utilising a novel potential function reasoning we show that rather surprisingly this probabilistic sorting (via conditional pipelining) procedure requires O(n2) comparisons in expectation and whp, and is on par with its deterministic counterpart. We propose the first population protocol allowing self-replication of a strand of an arbitrary length k (carrying a k-bit message of size independent of the state space) in parallel time O(n(k + log n)). The pipelining mechanism and the time complexity analysis of the strand self-replication protocol mimic those used in the probabilistic bubble-sort. The new protocol permits also simultaneous self-replication, where l copies of the strand can be created in time O(n(k + log n) log l). Finally, we discuss application of the strand self-replication protocol to pattern matching. Our protocols are always correct and provide time guaranties with high probability defined as 1 - n-η, for a constant η > 0

Polyethyleneimine-mediated transfection of cultured postmitotic neurons from rat sympathetic ganglia and adult human retina

BACKGROUND: Chemical methods of transfection that have proven successful with cell lines often do not work with primary cultures of neurons. Recent data, however, suggest that linear polymers of the cation polyethyleneimine (PEI) can facilitate the uptake of nucleic acids by neurons. Consequently, we examined the ability of a commercial PEI preparation to allow the introduction of foreign genes into postmitotic mammalian neurons. Sympathetic neurons were obtained from perinatal rat pups and maintained for 5 days in vitro in the absence of nonneuronal cells. Cultures were then transfected with varying amounts of a plasmid encoding either E. coli β-galactosidase or enhanced green fluorescence protein (EGFP) using PEI. RESULTS: Optimal transfection efficiency was observed with 1 μg/ml of plasmid DNA and 5 μg/ml PEI. Expression of β-galactosidase was both rapid and stable, beginning within 6 hours and lasting for at least 21 days. A maximum yield was obtained within 72 hours with ∼ 9% of the neurons expressing β-galactosidase, as assessed by both histochemistry and antibody staining. Cotransfection of two plasmids encoding reporter genes was achieved. Postmitotic neurons from adult human retinal cultures also demonstrated an ability to take up and express foreign DNA using PEI as a vector. CONCLUSIONS: These data suggest that PEI is a useful agent for the stable expression of plasmid-encoded genes in neuronal cultures

Fast Space Optimal Leader Election in Population Protocols

The model of population protocols refers to the growing in popularity theoretical framework suitable for studying pairwise interactions within a large collection of simple indistinguishable entities, frequently called agents. In this paper the emphasis is on the space complexity in fast leader election via population protocols governed by the random scheduler, which uniformly at random selects pairwise interactions from the population of n agents. The main result of this paper is a new fast and space optimal leader election protocol. The new protocol operates in parallel time O(log2n) equivalent to O(n log2n) sequential pairwise interactions, in which each agent utilises O(log log n) states. This double logarithmic space utilisation matches asymptotically the lower bound [Equation] log log n on the number of states utilised by agents in any leader election algorithm with the running time [Equation], see [7]. Our solution relies on the concept of phase clocks, a fundamental synchronisation and coordination tool in the field of Distributed Computing. We propose a new fast and robust population protocol for initialisation of phase clocks to be run simultaneously in multiple modes and intertwined with the leader election process. We also provide the reader with the relevant formal argumentation indicating that our solution is always correct and fast with high probability

Rendezvous of Distance-aware Mobile Agents in Unknown Graphs

We study the problem of rendezvous of two mobile agents starting at distinct locations in an unknown graph. The agents have distinct labels and walk in synchronous steps. However the graph is unlabelled and the agents have no means of marking the nodes of the graph and cannot communicate with or see each other until they meet at a node. When the graph is very large we want the time to rendezvous to be independent of the graph size and to depend only on the initial distance between the agents and some local parameters such as the degree of the vertices, and the size of the agent's label. It is well known that even for simple graphs of degree $\Delta$, the rendezvous time can be exponential in $\Delta$ in the worst case. In this paper, we introduce a new version of the rendezvous problem where the agents are equipped with a device that measures its distance to the other agent after every step. We show that these \emph{distance-aware} agents are able to rendezvous in any unknown graph, in time polynomial in all the local parameters such the degree of the nodes, the initial distance $D$ and the size of the smaller of the two agent labels $l = \min(l_1, l_2)$. Our algorithm has a time complexity of $O(\Delta(D+\log{l}))$ and we show an almost matching lower bound of $\Omega(\Delta(D+\log{l}/\log{\Delta}))$ on the time complexity of any rendezvous algorithm in our scenario. Further, this lower bound extends existing lower bounds for the general rendezvous problem without distance awareness

Ultrasonic oil-film thickness measurement: An angular spectrum approach to assess performance limits

The performance of ultrasonic oil-film thickness measurement in a ball bearing is quantified. A range of different viscosity oils (Shell T68, VG15, and VG5) are used to explore the lowest reflection coefficient and hence the thinnest oil-film thickness that the system can measure. The results show a minimum reflection coefficient of 0.07 for both oil VG15 and VG5 and 0.09 for oil T68 at 50 MHz. This corresponds to an oil-film thickness of 0.4 μm for T68 oil. An angular spectrum (or Fourier decomposition) approach is used to analyze the performance of this configuration. This models the interaction of component plane waves with the measurement system and quantifies the effect of the key parameters (transducer aperture, focal length, and center frequency). The simulation shows that for a focused transducer the reflection coefficient tends to a limiting value at small oil-film thickness. For the transducer used in this paper it is shown that the limiting reflection coefficient is 0.05 and the oil-film measurement errors increase as the reflection coefficient approaches this value. The implications for improved measurement systems are then discussed

Classical big-bounce cosmology: dynamical analysis of a homogeneous and irrotational Weyssenhoff fluid

A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff fluid in general relativity is performed using the 1+3 covariant approach that enables the dynamics of the fluid to be determined without assuming any particular form for the space-time metric. The spin contributions to the field equations produce a bounce that averts an initial singularity, provided that the spin density exceeds the rate of shear. At later times, when the spin contribution can be neglected, a Weyssenhoff fluid reduces to a standard cosmological fluid in general relativity. Numerical solutions for the time evolution of the generalised scale factor in spatially-curved models are presented, some of which exhibit eternal oscillatory behaviour without any singularities. In spatially-flat models, analytical solutions for particular values of the equation-of-state parameter are derived. Although the scale factor of a Weyssenhoff fluid generically has a positive temporal curvature near a bounce, it requires unreasonable fine tuning of the equation-of-state parameter to produce a sufficiently extended period of inflation to fit the current observational data.Comment: 34 pages, 18 figure

New Isotropic and Anisotropic Sudden Singularities

We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterised by divergences in the time-rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-time singularities in a Bianchi type $VII_{0}$ universe with anisotropic pressures and construct specific examples of anisotropic sudden singularities in these universes.Comment: Typos corrected. Published versio

Surface Dynamics of Crude and Weathered Oil in the Presence of Dispersants: Laboratory Experiment and Numerical Simulation

Marine oil spills can have dire consequences for the environment. Research on their dynamics is important for the well-being of coastal communities and their economies. Propagation of oil spills is a very complex physical-chemical process. As seen during the Deepwater Horizon event in the Gulf of Mexico during 2010, one of the critical problems remaining for prediction of oil transport and dispersion in the marine environment is the small-scale structure and dynamics of surface oil spills. The laboratory experiments conducted in this work were focused on understanding the differences between the dynamics of crude and weathered oil spills and the effect of dispersants. After deposition on the still water surface, a drop of crude oil quickly spread into a thin slick; while at the same time, a drop of machine (proxy for weathered) oil did not show significant evolution. Subsequent application of dispersant to the crude oil slick resulted in a quick contraction or fragmentation of the slick into narrow wedges and tiny drops. Notably, the slick of machine oil did not show significant change in size or topology after spraying dispersant. An advanced multi-phase, volume of fluid computational fluid dynamics model, incorporating capillary forces, was able to explain some of the features observed in the laboratory experiment. As a result of the laboratory and modeling experiments, the new interpretation of the effect of dispersant on the oil dispersion process including capillary effects has been proposed, which is expected to lead to improved oil spill models and response strategies

Universe from vacuum in loop-string cosmology

In this paper we study the description of the Universe based on the low energy superstring theory modified by the Loop Quantum Gravity effects.This approach was proposed by De Risi et al. in the Phys. Rev. D {\bf 76} (2007) 103531. We show that in the contrast with the string motivated pre-Big Bang scenario, the cosmological realisation of the $t$-duality transformation is not necessary to avoid an initial singularity. In the model considered the universe starts its evolution in the vacuum phase at time $t\to - \infty$. In this phase the scale factor $a\to 0$, energy density $\rho \to 0$ and coupling of the interactions $g^2_s \to 0$. After this stage the universe evolves to the non-singular hot Big Bang phase $\rho \to \rho_{\text{max}} < \infty$. Then the standard classical universe emerges. During the whole evolution the scale factor increases monotonically. We solve this model analytically. We also propose and solve numerically the model with an additional dilaton potential in which the universe starts the evolution from the asymptotically free vacuum phase $g^2_s \to 0$ and then evolves non-singularly to the emerging dark energy dominated phase with the saturated coupling constant $g^2_s \to \text{const}$.Comment: JHEP3 LaTeX class, 19 pages, 9 figures, v2: added some comments and references, v3: new numerical result added, new figure