A cluster expansion approach to exponential random graph models

The exponential family of random graphs is among the most widely-studied network models. We show that any exponential random graph model may alternatively be viewed as a lattice gas model with a finite Banach space norm. The system may then be treated by cluster expansion methods from statistical mechanics. In particular, we derive a convergent power series expansion for the limiting free energy in the case of small parameters. Since the free energy is the generating function for the expectations of other random variables, this characterizes the structure and behavior of the limiting network in this parameter region.Comment: 15 pages, 1 figur

Acylsulfonamide safety-catch linker : promise and limitations for solid-phase oligosaccharide synthesis

Safety-catch linkers are useful for solid-phase oligosaccharide synthesis as they are orthogonal to many common protective groups. A new acylsulfonamide safety-catch linker was designed, synthesized and employed during glycosylations using an automated carbohydrate synthesizer. The analysis of the cleavage products revealed shortcomings for oligosaccharide synthesis

Competing Phases, Strong Electron-Phonon Interaction and Superconductivity in Elemental Calcium under High Pressure

The observed "simple cubic" (sc) phase of elemental Ca at room temperature in the 32-109 GPa range is, from linear response calculations, dynamically unstable. By comparing first principle calculations of the enthalpy for five sc-related (non-close-packed) structures, we find that all five structures compete energetically at room temperature in the 40-90 GPa range, and three do so in the 100-130 GPa range. Some competing structures below 90 GPa are dynamically stable, i.e., no imaginary frequency, suggesting that these sc-derived short-range-order local structures exist locally and can account for the observed (average) "sc" diffraction pattern. In the dynamically stable phases below 90 GPa, some low frequency phonon modes are present, contributing to strong electron-phonon (EP) coupling as well as arising from the strong coupling. Linear response calculations for two of the structures over 120 GPa lead to critical temperatures in the 20-25 K range as is observed, and do so without unusually soft modes.Comment: 8 pages, 6 figures, 1 table, accepted for publication in Phys. Rev.

Carbon coating of the SPS dipole chambers

The Electron Multipacting (EM) phenomenon is a limiting factor for the achievement of high luminosity in accelerators for positively charged particles and for the performance of RF devices. At CERN, the Super Proton Synchrotron (SPS) must be upgraded in order to feed the Large Hadron Collider (LHC) with 25 ns bunch spaced beams. At such small bunch spacing, EM may limit the performance of the SPS and consequently that of the LHC. To mitigate this phenomenon CERN is developing a carbon thin film coating with low Secondary Electron Yield (SEY) to coat the internal walls of the SPS dipoles beam pipes. This paper presents the progresses in the coating technology, the performance of the carbon coatings and the strategy for a large scale production.Comment: 7 pages, contribution to the Joint INFN-CERN-EuCARD-AccNet Workshop on Electron-Cloud Effects: ECLOUD'12; 5-9 Jun 2012, La Biodola, Isola d'Elba, Italy; CERN Yellow Report CERN-2013-002, pp.141-14

Majorana fermions in ferromagnetic chains on the surface of bulk spin-orbit coupled ss-wave superconductors

Majorana fermion (MF) excitations in solid state system have non-Abelian statistics which is essential for topological quantum computation. Previous proposals to realize MF, however, generally requires fine-tuning of parameters. Here we explore a platform which avoids the fine-tuning problem, namely a ferromagnetic chain deposited on the surface of a spin-orbit coupled $s$-wave superconductor. We show that it generically supports zero-energy topological MF excitations near the two ends of the chain with minimal fine-tuning. Depending on the strength of the ferromagnetic moment in the chain, the number of MFs at each end, $n$, can be either one or two, and should be revealed by a robust zero-bias peak (ZBP) of height $2ne^2/h$ in scanning tunneling microscopy (STM) measurements which would show strong (weak) signals at the ends (middle) of the chain. The role of an approximate chiral symmetry which gives an integer topological invariant to the system is discussed.Comment: 9 pages, 4 figure

The peculiar velocity field: constraining the tilt of the Universe

A large bulk flow, which is in tension with the Lambda Cold Dark Matter ($\Lambda$CDM) cosmological model, has been observed. In this paper, we provide a physically plausible explanation of this bulk flow, based on the assumption that some fraction of the observed dipole in the cosmic microwave background is due to an intrinsic fluctuation, so that the subtraction of the observed dipole leads to a mismatch between the cosmic microwave background (CMB) defined rest frame and the matter rest frame. We investigate a model that takes into account the relative velocity (hereafter the tilted velocity) between the two frames, and develop a Bayesian statistic to explore the likelihood of this tilted velocity. By studying various independent peculiar velocity catalogs, we find that: (1) the magnitude of the tilted velocity $u$ is around 400 km/s, and its direction is close to what is found from previous bulk flow analyses; for most catalogs analysed, u=0 is excluded at about the $2.5 \sigma$ level;(2) constraints on the magnitude of the tilted velocity can result in constraints on the duration of inflation, due to the fact that inflation can neither be too long (no dipole effect) nor too short (very large dipole effect); (3) Under the assumption of a super-horizon isocurvature fluctuation, the constraints on the tilted velocity require that inflation lasts at least 6 e-folds longer (at the 95% confidence interval) than that required to solve the horizon problem. This opens a new window for testing inflation and models of the early Universe from observations of large scale structure.Comment: 7 pages, 7 figures, match the published version in Phys.Rev.

Augmented L1 and Nuclear-Norm Models with a Globally Linearly Convergent Algorithm

This paper studies the long-existing idea of adding a nice smooth function to "smooth" a non-differentiable objective function in the context of sparse optimization, in particular, the minimization of $||x||_1+1/(2\alpha)||x||_2^2$, where $x$ is a vector, as well as the minimization of $||X||_*+1/(2\alpha)||X||_F^2$, where $X$ is a matrix and $||X||_*$ and $||X||_F$ are the nuclear and Frobenius norms of $X$, respectively. We show that they can efficiently recover sparse vectors and low-rank matrices. In particular, they enjoy exact and stable recovery guarantees similar to those known for minimizing $||x||_1$ and $||X||_*$ under the conditions on the sensing operator such as its null-space property, restricted isometry property, spherical section property, or RIPless property. To recover a (nearly) sparse vector $x^0$, minimizing $||x||_1+1/(2\alpha)||x||_2^2$ returns (nearly) the same solution as minimizing $||x||_1$ almost whenever $\alpha\ge 10||x^0||_\infty$. The same relation also holds between minimizing $||X||_*+1/(2\alpha)||X||_F^2$ and minimizing $||X||_*$ for recovering a (nearly) low-rank matrix $X^0$, if $\alpha\ge 10||X^0||_2$. Furthermore, we show that the linearized Bregman algorithm for minimizing $||x||_1+1/(2\alpha)||x||_2^2$ subject to $Ax=b$ enjoys global linear convergence as long as a nonzero solution exists, and we give an explicit rate of convergence. The convergence property does not require a solution solution or any properties on $A$. To our knowledge, this is the best known global convergence result for first-order sparse optimization algorithms.Comment: arXiv admin note: text overlap with arXiv:1207.5326 by other author