Clustering properties of a generalised critical Euclidean network

Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its $i$th predecessor of degree $k_i$ with a link of length $\ell$ using a probability proportional to $k^\beta_i \ell^{\alpha}$. For $\alpha > -0.5$, the network is scale free at $\beta = 1$ with the degree distribution $P(k) \propto k^{-\gamma}$ and $\gamma = 3.0$ as in the Barab\'asi-Albert model ($\alpha =0, \beta =1$). We find a phase boundary in the $\alpha-\beta$ plane along which the network is scale-free. Interestingly, we find scale-free behaviour even for $\beta > 1$ for $\alpha < -0.5$ where the existence of a new universality class is indicated from the behaviour of the degree distribution and the clustering coefficients. The network has a small diameter in the entire scale-free region. The clustering coefficients emulate the behaviour of most real networks for increasing negative values of $\alpha$ on the phase boundary.Comment: 4 pages REVTEX, 4 figure

Generation of continuous variable squeezing and entanglement of trapped ions in time-varying potentials

We investigate the generation of squeezing and entanglement for the motional degrees of freedom of ions in linear traps, confined by time-varying and oscillating potentials, comprised of an DC and an AC component. We show that high degrees of squeezing and entanglement can be obtained by controlling either the DC or the AC trapping component (or both), and by exploiting transient dynamics in regions where the ions' motion is unstable, without any added optical control. Furthermore, we investigate the time-scales over which the potentials should be switched in order for the manipulations to be most effective.Comment: 10 pages, submitted to Quantum Information Processing (special issue on Quantum Decoherence and Entanglement

Quasistatic Scale-free Networks

A network is formed using the $N$ sites of an one-dimensional lattice in the shape of a ring as nodes and each node with the initial degree $k_{in}=2$. $N$ links are then introduced to this network, each link starts from a distinct node, the other end being connected to any other node with degree $k$ randomly selected with an attachment probability proportional to $k^{\alpha}$. Tuning the control parameter $\alpha$ we observe a transition where the average degree of the largest node $$ changes its variation from $N^0$ to $N$ at a specific transition point of $\alpha_c$. The network is scale-free i.e., the nodal degree distribution has a power law decay for $\alpha \ge \alpha_c$.Comment: 4 pages, 5 figure

Why social networks are different from other types of networks

We argue that social networks differ from most other types of networks, including technological and biological networks, in two important ways. First, they have non-trivial clustering or network transitivity, and second, they show positive correlations, also called assortative mixing, between the degrees of adjacent vertices. Social networks are often divided into groups or communities, and it has recently been suggested that this division could account for the observed clustering. We demonstrate that group structure in networks can also account for degree correlations. We show using a simple model that we should expect assortative mixing in such networks whenever there is variation in the sizes of the groups and that the predicted level of assortative mixing compares well with that observed in real-world networks.Comment: 9 pages, 2 figure

Optimum electrode configurations for fast ion separation in microfabricated surface ion traps

For many quantum information implementations with trapped ions, effective shuttling operations are important. Here we discuss the efficient separation and recombination of ions in surface ion trap geometries. The maximum speed of separation and recombination of trapped ions for adiabatic shuttling operations depends on the secular frequencies the trapped ion experiences in the process. Higher secular frequencies during the transportation processes can be achieved by optimising trap geometries. We show how two different arrangements of segmented static potential electrodes in surface ion traps can be optimised for fast ion separation or recombination processes. We also solve the equations of motion for the ion dynamics during the separation process and illustrate important considerations that need to be taken into account to make the process adiabatic

General Stability Analysis of Synchronized Dynamics in Coupled Systems

We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on the master stability function and Gershgorin disc theory, to yield constraints on the coupling strengths to ensure the stability of synchronized dynamics. Systems with specific coupling schemes are used as examples to illustrate our general method.Comment: 8 pages, 1 figur

Doublecortin-like expressing astrocytes of the suprachiasmatic nucleus are implicated in the biosynthesis of vasopressin and influences circadian rhythms

We have recently identified a novel plasticity protein, doublecortin-like (DCL), that is specifically expressed in the shell of the mouse suprachiasmatic nucleus (SCN). DCL is implicated in neuroplastic events, such as neurogenesis, that require structural rearrangements of the microtubule cytoskeleton, enabling dynamic movements of cell bodies and dendrites. We have inspected DCL expression in the SCN by confocal microscopy and found that DCL is expressed in GABA transporter-3 (GAT3)-positive astrocytes that envelope arginine vasopressin (AVP)-expressing cells. To investigate the role of these DCL-positive astrocytes in circadian rhythmicity, we have used transgenic mice expressing doxycycline-induced short-hairpin (sh) RNA's targeting DCL mRNA (DCL knockdown mice). Compared with littermate wild type (WT) controls, DCL-knockdown mice exhibit significant shorter circadian rest-activity periods in constant darkness and adjusted significantly faster to a jet-lag protocol. As DCL-positive astrocytes are closely associated with AVP-positive cells, we analyzed AVP expression in DCL-knockdown mice and in their WT littermates by 3D reconstructions and transmission electron microscopy (TEM). We found significantly higher numbers of AVP-positive cells with increased volume and more intensity in DCL-knockdown mice. We found alterations in the numbers of dense core vesicle-containing neurons at ZT8 and ZT20 suggesting that the peak and trough of neuropeptide biosynthesis is dampened in DCL-knockdown mice compared to WT littermates. Together, our data suggest an important role for the astrocytic plasticity in the regulation of circadian rhythms and point to the existence of a specific DCL+ astrocyte-AVP(+) neuronal network located in the dorsal SCN implicated in AVP biosynthesis.Microscopic imaging and technolog

Sources, seasonality, and trends of southeast US aerosol: an integrated analysis of surface, aircraft, and satellite observations with the GEOS-Chem chemical transport model

We use an ensemble of surface (EPA CSN, IMPROVE, SEARCH, AERONET), aircraft (SEAC4RS), and satellite (MODIS, MISR) observations over the southeast US during the summer–fall of 2013 to better understand aerosol sources in the region and the relationship between surface particulate matter (PM) and aerosol optical depth (AOD). The GEOS-Chem global chemical transport model (CTM) with 25 × 25 km2 resolution over North America is used as a common platform to interpret measurements of different aerosol variables made at different times and locations. Sulfate and organic aerosol (OA) are the main contributors to surface PM2.5 (mass concentration of PM finer than 2.5 μm aerodynamic diameter) and AOD over the southeast US. OA is simulated successfully with a simple parameterization, assuming irreversible uptake of low-volatility products of hydrocarbon oxidation. Biogenic isoprene and monoterpenes account for 60 % of OA, anthropogenic sources for 30 %, and open fires for 10 %. 60 % of total aerosol mass is in the mixed layer below 1.5 km, 25 % in the cloud convective layer at 1.5–3 km, and 15 % in the free troposphere above 3 km. This vertical profile is well captured by GEOS-Chem, arguing against a high-altitude source of OA. The extent of sulfate neutralization (f = [NH4+]/(2[SO42−] + [NO3−]) is only 0.5–0.7 mol mol−1 in the observations, despite an excess of ammonia present, which could reflect suppression of ammonia uptake by OA. This would explain the long-term decline of ammonium aerosol in the southeast US, paralleling that of sulfate. The vertical profile of aerosol extinction over the southeast US follows closely that of aerosol mass. GEOS-Chem reproduces observed total column aerosol mass over the southeast US within 6 %, column aerosol extinction within 16 %, and space-based AOD within 8–28 % (consistently biased low). The large AOD decline observed from summer to winter is driven by sharp declines in both sulfate and OA from August to October. These declines are due to shutdowns in both biogenic emissions and UV-driven photochemistry. Surface PM2.5 shows far less summer-to-winter decrease than AOD and we attribute this in part to the offsetting effect of weaker boundary layer ventilation. The SEAC4RS aircraft data demonstrate that AODs measured from space are consistent with surface PM2.5. This implies that satellites can be used reliably to infer surface PM2.5 over monthly timescales if a good CTM representation of the aerosol vertical profile is available

Solving loop equations by Hitchin systems via holography in large-N QCD_4

For (planar) closed self-avoiding loops we construct a "holographic" map from the loop equations of large-N QCD_4 to an effective action defined over infinite rank Hitchin bundles. The effective action is constructed densely embedding Hitchin systems into the functional integral of a partially quenched or twisted Eguchi-Kawai model, by means of the resolution of identity into the gauge orbits of the microcanonical ensemble and by changing variables from the moduli fields of Hitchin systems to the moduli of the corresponding holomorphic de Rham local systems. The key point is that the contour integral that occurs in the loop equations for the de Rham local systems can be reduced to the computation of a residue in a certain regularization. The outcome is that, for self-avoiding loops, the original loop equations are implied by the critical equation of an effective action computed in terms of the localisation determinant and of the Jacobian of the change of variables to the de Rham local systems. We check, at lowest order in powers of the moduli fields, that the localisation determinant reproduces exactly the first coefficient of the beta function.Comment: 65 pages, late

Limit on Bs0B^0_s oscillation using a jet charge method

A lower limit is set on the B_{s}^{0} meson oscillation parameter \Delta m_{s} using data collected from 1991 to 1994 by the ALEPH detector. Events with a high transverse momentum lepton and a reconstructed secondary vertex are used. The high transverse momentum leptons are produced mainly by b hadron decays, and the sign of the lepton indicates the particle/antiparticle final state in decays of neutral B mesons. The initial state is determined by a jet charge technique using both sides of the event. A maximum likelihood method is used to set a lower limit of \, \Delta m_{s}. The 95\% confidence level lower limit on \Delta m_s ranges between 5.2 and 6.5(\hbar/c^{2})~ps^{-1} when the fraction of b quarks from Z^0 decays that form B_{s}^{0} mesons is varied from 8\% to 16\%. Assuming that the B_{s}^{0} fraction is 12\%, the lower limit would be \Delta m_{s} 6.1(\hbar/c^{2})~ps^{-1} at 95\% confidence level. For x_s = \Delta m_s \, \tau_{B_s}, this limit also gives x_s 8.8 using the B_{s}^{0} lifetime of \tau_{B_s} = 1.55 \pm 0.11~ps and shifting the central value of \tau_{B_s} down by 1\sigma