Ground state energy of qq-state Potts model: the minimum modularity

A wide range of interacting systems can be described by complex networks. A common feature of such networks is that they consist of several communities or modules, the degree of which may quantified as the \emph{modularity}. However, even a random uncorrelated network, which has no obvious modular structure, has a finite modularity due to the quenched disorder. For this reason, the modularity of a given network is meaningful only when it is compared with that of a randomized network with the same degree distribution. In this context, it is important to calculate the modularity of a random uncorrelated network with an arbitrary degree distribution. The modularity of a random network has been calculated [Phys. Rev. E \textbf{76}, 015102 (2007)]; however, this was limited to the case whereby the network was assumed to have only two communities, and it is evident that the modularity should be calculated in general with $q(\geq 2)$ communities. Here, we calculate the modularity for $q$ communities by evaluating the ground state energy of the $q$-state Potts Hamiltonian, based on replica symmetric solutions assuming that the mean degree is large. We found that the modularity is proportional to $\langle \sqrt{k} \rangle / \langle k \rangle$ regardless of $q$ and that only the coefficient depends on $q$. In particular, when the degree distribution follows a power law, the modularity is proportional to $\langle k \rangle^{-1/2}$. Our analytical results are confirmed by comparison with numerical simulations. Therefore, our results can be used as reference values for real-world networks.Comment: 14 pages, 4 figure

Efficient out-coupling of high-purity single photons from a coherent quantum dot in a photonic-crystal cavity

We demonstrate a single-photon collection efficiency of $(44.3\pm2.1)\%$ from a quantum dot in a low-Q mode of a photonic-crystal cavity with a single-photon purity of $g^{(2)}(0)=(4\pm5)\%$ recorded above the saturation power. The high efficiency is directly confirmed by detecting up to $962\pm46$ kilocounts per second on a single-photon detector on another quantum dot coupled to the cavity mode. The high collection efficiency is found to be broadband, as is explained by detailed numerical simulations. Cavity-enhanced efficient excitation of quantum dots is obtained through phonon-mediated excitation and under these conditions, single-photon indistinguishability measurements reveal long coherence times reaching $0.77\pm0.19$ ns in a weak-excitation regime. Our work demonstrates that photonic crystals provide a very promising platform for highly integrated generation of coherent single photons including the efficient out-coupling of the photons from the photonic chip.Comment: 13 pages, 8 figures, submitte

Pattern formation of indirect excitons in coupled quantum wells

Using a nonlinear Schr\"odinger equation including short-range two-body attraction and three-body repulsion, we investigate the spatial distribution of indirect excitons in semiconductor coupled quantum wells. The results obtained can interpret the experimental phenomenon that annular exciton cloud first contracts then expands when the number of confined excitons is increased in impurity potential well, as observed by Lai \emph{et al.} [Lai $et al.$, Science \textbf{303}, 503 (2004)]. In particular, the model reconciles the patterns of exciton rings reported by Butov \emph{et al.} [Butov $et al.$, Nature \textbf{418}, 751 (2002)]. At higher densities, the model predicts much richer patterns, which could be tested by future experiments.Comment: 5 Revtex4 pages, 3 figure

Ellipsometric measurements of the refractive indices of linear alkylbenzene and EJ-301 scintillators from 210 to 1000 nm

We report on ellipsometric measurements of the refractive indices of LAB-PPO, Nd-doped LAB-PPO and EJ-301 scintillators to the nearest +/-0.005, in the wavelength range 210-1000 nm.Comment: 7 pages, 4 figure

FTO Biology and Obesity: Why Do a Billion of Us Weigh 3 kg More?

Few would dispute that the current obesity epidemic has been driven by lifestyle and environmental changes. However, it is clear that individuals respond differently to these “obesigenic” changes and this variation in response has a strong genetic element. Genome-wide association studies have revealed that single nucleotide polymorphisms in Fat mass and obesity-associated transcript (FTO) are robustly associated with body mass index and obesity. Although the effect of these risk alleles are modest, with heterozygous and homozygous carriers weighing approximately 1.5 and 3 kg more respectively, there are an estimated one billion homozygous carriers in the world, spanning multiple different ethnicities and populations. Yet despite its broad impact, the biological function of FTO, particularly its role in controlling energy balance, remains unknown. Although the study of severe Mendelian obesity has been invaluable in illuminating critical pathways controlling food intake, the major burden of disease is carried by those of us with “common obesity,” which to date has resisted yielding meaningful biological insights. FTO has at last given us a handle on a huge, worldwide, common problem. In this review, we focus on the available genetic and in vivo evidence to date that implicates FTO in the control of energy balance

Through the looking-glass:Mirror feedback modulates temporal and spatial aspects of bimanual coordination

Mirror therapy has become an effective and recommended intervention for a range of conditions affecting the upper limb (e.g. hemiparesis following stroke). However, little is known about how mirror feedback affects the control of bimanual movements (as performed during mirror therapy). In this study, in preparation for future clinical investigations, we examined the kinematics of bimanual circle drawing in unimpaired participants both with (Experiment 1) and without (Experiment 2) a visual template to guide movement. In both experiments, 15 unimpaired right-handed participants performed self-paced continuous bimanual circle-drawing movements with a mirror/symmetrical coordination pattern. For the mirror condition, vision was directed towards the mirror in order to monitor the reflected limb. In the no mirror condition, the direction of vision was unchanged, but the mirror was replaced with an opaque screen. Movements of both hands were recorded using motion capture apparatus. In both experiments, the most striking feature of movements was that the hand behind the mirror drifted spatially during the course of individual trials. Participants appeared to be largely unaware of this marked positional change of their unseen hand, which was most pronounced when a template to guide movement was visible (Experiment 1). Temporal asynchrony between the limbs was also affected by mirror feedback in both experiments; in the mirror condition, illusory vision of the unseen hand led to a relative phase lead for that limb. Our data highlight the remarkable impact that the introduction of a simple mirror can have on bimanual coordination. Modulation of spatial and temporal features is consistent with the mirror inducing a rapid and powerful visual illusion, the latter appearing to override proprioceptive signals.</p

The nature of solar brightness variations

The solar brightness varies on timescales from minutes to decades. Determining the sources of such variations, often referred to as solar noise, is of importance for multiple reasons: a) it is the background that limits the detection of solar oscillations, b) variability in solar brightness is one of the drivers of the Earth's climate system, c) it is a prototype of stellar variability which is an important limiting factor for the detection of extra-solar planets. Here we show that recent progress in simulations and observations of the Sun makes it finally possible to pinpoint the source of the solar noise. We utilise high-cadence observations from the Solar Dynamic Observatory and the SATIRE model to calculate the magnetically-driven variations of solar brightness. The brightness variations caused by the constantly evolving cellular granulation pattern on the solar surface are computed with the MURAM code. We find that surface magnetic field and granulation can together precisely explain solar noise on timescales from minutes to decades, i.e. ranging over more than six orders of magnitude in the period. This accounts for all timescales that have so far been resolved or covered by irradiance measurements. We demonstrate that no other sources of variability are required to explain the data. Recent measurements of Sun-like stars by CoRoT and Kepler uncovered brightness variations similar to that of the Sun but with much wider variety of patterns. Our finding that solar brightness variations can be replicated in detail with just two well-known sources will greatly simplify future modelling of existing CoRoT and Kepler as well as anticipated TESS and PLATO data.Comment: This is the submitted version of the paper published in Nature Astronom

4-(4-Chlorophenyl)-4,5-dihydro-1H-1,2,4-triazole-5-thione

The title compound, 4-(4-chlorophenyl)-4,5-dihydro-1H-1,2,4-triazole-5-thione (1), was synthesized by a hetero-cyclization reaction of 4-chlorophenyl isothiocyanate and formic hydrazide. Compound 1 was characterized by a single-crystal X-ray structure determination as well as 1H and 13C{1H} NMR, IR, and UV spectroscopy, and microelemental analysis. X-ray crystallography on 1 confirms the molecule exists as the thione tautomer and shows the five-membered ring to be planar and to form a dihedral angle of 82.70(5)° with the appended chlorophenyl ring, indicating an almost orthogonal relationship. In the molecular packing, supramolecular dimers are formed via thioamide-N–H⋯S(thione) hydrogen bonds and these are connected by C=S⋯π(triazolyl) and C-Cl⋯π(triazolyl) interactions, leading to a three-dimensional architectur

Nonparametric nonlinear model predictive control

Model Predictive Control (MPC) has recently found wide acceptance in industrial applications, but its potential has been much impeded by linear models due to the lack of a similarly accepted nonlinear modeling or databased technique. Aimed at solving this problem, the paper addresses three issues: (i) extending second-order Volterra nonlinear MPC (NMPC) to higher-order for improved prediction and control; (ii) formulating NMPC directly with plant data without needing for parametric modeling, which has hindered the progress of NMPC; and (iii) incorporating an error estimator directly in the formulation and hence eliminating the need for a nonlinear state observer. Following analysis of NMPC objectives and existing solutions, nonparametric NMPC is derived in discrete-time using multidimensional convolution between plant data and Volterra kernel measurements. This approach is validated against the benchmark van de Vusse nonlinear process control problem and is applied to an industrial polymerization process by using Volterra kernels of up to the third order. Results show that the nonparametric approach is very efficient and effective and considerably outperforms existing methods, while retaining the original data-based spirit and characteristics of linear MPC