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

No evidence of a significant role for CTLA-4 in multiple sclerosis

Variation in the cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) gene plays a significant role in determining susceptibility to autoimmune thyroid disease and type 1 diabetes. Its role in multiple sclerosis is more controversial. In order to explore this logical candidate more thoroughly, we genotyped 771 multiple sclerosis trio families from the United Kingdom for the 3? untranslated region variable number tandem repeat, the CT60 single nucleotide polymorphism (SNP) and five haplotype-tagging SNPs. No individual marker or common haplotype showed evidence of association with disease. These data suggest that any effect of CTLA-4 on multiple sclerosis susceptibility is likely to be very small

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

Francis F. Maury, M.D. (1840 to 1879): an often forgotten pioneer in early American surgery.

Francis F. Maury (Fig. 1) was born on August 9, 1840, in Danville, Kentucky, where he was raised on a farm by his mother and father. His father was an Episcopal clergyman of Huguenot descent, whose forefathers had fled from France to escape religious persecution. After receiving a Bachelor of Arts degree from Center College in the summer of 1860, he entered medical school at the University of Virginia. After one full term, he matriculated to Philadelphia’s Jefferson Medical College and completed his medical education as a private student under the direction of Dr. Samuel D. Gross.1, 2 He obtained his Doctorate of Medicine in March of 1862 at the age of only 21 years. Such were his talents as a medical student that he was appointed resident physician at the Philadelphia Hospital one month before his graduation. Although he spent only one year there, he developed a reputation as a tireless, devoted, and charming surgeon. In April 1863, Maury was assigned to duty at the South Street General Hospital to serve as acting assistant surgeon in the U.S. Army for two years. In October 1863, he was appointed assistant professor to Dr. Gross and six months later became chief of Dr. Gross’ surgical clinic at Jefferson Medical College. In November 1865, at the age of only 25 years, he returned to the Philadelphia Hospital, where he was appointed one of the chief surgeons on the retirement of Dr. Gross from that institution. In April of 1866, Maury founded the Summer Course on Venereal and Cutaneous Diseases in the Jefferson Medical College, where he taught until his death.1 Although Maury did not consider himself a dermatologist, his expertise in this emerging field was widely recognized

Reconstruction of spectral solar irradiance since 1700 from simulated magnetograms

We present a reconstruction of the spectral solar irradiance since 1700 using the SATIRE-T2 (Spectral And Total Irradiance REconstructions for the Telescope era version 2) model. This model uses as input magnetograms simulated with a surface flux transport model fed with semi-synthetic records of emerging sunspot groups. We used statistical relationships between the properties of sunspot group emergence, such as the latitude, area, and tilt angle, and the sunspot cycle strength and phase to produce semi-synthetic sunspot group records starting in the year 1700. The semisynthetic records are fed into a surface flux transport model to obtain daily simulated magnetograms that map the distribution of the magnetic flux in active regions (sunspots and faculae) and their decay products on the solar surface. The magnetic flux emerging in ephemeral regions is accounted for separately based on the concept of extended cycles whose length and amplitude are linked to those of the sunspot cycles through the sunspot number. The magnetic flux in each surface component (sunspots, faculae and network, and ephemeral regions) was used to compute the spectral and total solar irradiance between the years 1700 and 2009. This reconstruction is aimed at timescales of months or longer although the model returns daily values. We found that SATIRE-T2, besides reproducing other relevant observations such as the total magnetic flux, reconstructs the total solar irradiance (TSI) on timescales of months or longer in good agreement with the PMOD composite of observations, as well as with the reconstruction starting in 1878 based on the RGO-SOON data. The model predicts an increase in the TSI of 1.2[+0.2, -0.3] Wm-2 between 1700 and the present. The spectral irradiance reconstruction is in good agreement with the UARS/SUSIM measurements as well as the Lyman-alpha composite.Comment: 13 pages, 10 figure

Concurrent Magnetic and Metal-Insulator Transitions in (Eu,Sm)B_6 Single Crystals

The effects of magnetic doping on a EuB_6 single crystal were investigated based on magnetic and transport measurements. A modest 5% Sm substitution for Eu changes the magnetic and transport properties dramatically and gives rise to concurrent antiferromagnetic and metal-insulator transitions (MIT) from ferromagnetic MIT for EuB6. Magnetic doping simultaneously changes the itinerant carrier density and the magnetic interactions. We discuss the origin of the concurrent magnetic MIT in (Eu,Sm)B_6.Comment: 13 pages, 3 figures, final version to appear in Appl. Phys. Lett

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

Surface acoustic wave solid-state rotational micromotor

Surface acoustic waves (SAWs) are used to drive a 1mm diameter rotor at speeds exceeding 9000 rpm and torque of nearly 5 nNm. Unlike recent high-speed SAW rotary motors, however, the present design does not require a fluid coupling layer but interestingly exploits adhesive stiction as an internal preload, a force usually undesirable at these scales; with additional preloads, smaller rotors can be propelled to 15 000 rpm. This solid-state motor has no moving parts except for the rotor and is sufficiently simple to allow integration into miniaturized drive systems for potential use in microfluidic diagnostics, optical switching and microrobotics