Faster annealing schedules for quantum annealing

New annealing schedules for quantum annealing are proposed based on the adiabatic theorem. These schedules exhibit faster decrease of the excitation probability than a linear schedule. To derive this conclusion, the asymptotic form of the excitation probability for quantum annealing is explicitly obtained in the limit of long annealing time. Its first-order term, which is inversely proportional to the square of the annealing time, is shown to be determined only by the information at the initial and final times. Our annealing schedules make it possible to drop this term, thus leading to a higher order (smaller) excitation probability. We verify these results by solving numerically the time-dependent Schrodinger equation for small size systemsComment: 10 pages, 5 figures, minor correction

Negative Impurity Magnetic Susceptibility and Heat Capacity in a Kondo Model with Narrow Peaks in the Local Density of Electron States

Temperature dependencies of the impurity magnetic susceptibility, entropy, and heat capacity have been obtained by the method of numerical renormalization group and exact diagonalization for the Kondo model with peaks in the electron density of states near the Fermi energy (in particular, with logarithmic Van Hove singularities). It is shown that these quantities can be {\it negative}. A new effect has been predicted (which, in principle, can be observed experimentally), namely, the decrease in the magnetic susceptibility and heat capacity of a nonmagnetic sample upon the addition of magnetic impurities into it

The c-terminal extension of a hybrid immunoglobulin A/G heavy chain is responsible for its Golgi-mediated sorting to the vacuole

We have assessed the ability of the plant secretory pathway to handle the expression of complex heterologous proteins by investigating the fate of a hybrid immunoglobulin A/G in tobacco cells. Although plant cells can express large amounts of the antibody, a relevant proportion is normally lost to vacuolar sorting and degradation. Here we show that the synthesis of high amounts of IgA/G does not impose stress on the plant secretory pathway. Plant cells can assemble antibody chains with high efficiency and vacuolar transport occurs only after the assembled immunoglobulins have traveled through the Golgi complex. We prove that vacuolar delivery of IgA/G depends on the presence of a cryptic sorting signal in the tailpiece of the IgA/G heavy chain. We also show that unassembled light chains are efficiently secreted as monomers by the plant secretory pathway

Complexity-Entropy Causality Plane as a Complexity Measure for Two-dimensional Patterns

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to i) fractal landscapes generated numerically where we compare our measures with the Hurst exponent; ii) liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; iii) 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; iv) and Ising surfaces where our method identified the critical temperature and also proved to be stable.Comment: Accepted for publication in PLoS On

Pareto optimality in multilayer network growth

We model the formation of multi-layer transportation networks as a multi-objective optimization process, where service providers compete for passengers, and the creation of routes is determined by a multi-objective cost function encoding a trade-off between efficiency and competition. The resulting model reproduces well real-world systems as diverse as airplane, train and bus networks, thus suggesting that such systems are indeed compatible with the proposed local optimization mechanisms. In the specific case of airline transportation systems, we show that the networks of routes operated by each company are placed very close to the theoretical Pareto front in the efficiency-competition plane, and that most of the largest carriers of a continent belong to the corresponding Pareto front. Our results shed light on the fundamental role played by multi-objective optimization principles in shaping the structure of large-scale multilayer transportation systems, and provide novel insights to service providers on the strategies for the smart selection of novel routes

Pattern-recalling processes in quantum Hopfield networks far from saturation

As a mathematical model of associative memories, the Hopfield model was now well-established and a lot of studies to reveal the pattern-recalling process have been done from various different approaches. As well-known, a single neuron is itself an uncertain, noisy unit with a finite unnegligible error in the input-output relation. To model the situation artificially, a kind of 'heat bath' that surrounds neurons is introduced. The heat bath, which is a source of noise, is specified by the 'temperature'. Several studies concerning the pattern-recalling processes of the Hopfield model governed by the Glauber-dynamics at finite temperature were already reported. However, we might extend the 'thermal noise' to the quantum-mechanical variant. In this paper, in terms of the stochastic process of quantum-mechanical Markov chain Monte Carlo method (the quantum MCMC), we analytically derive macroscopically deterministic equations of order parameters such as 'overlap' in a quantum-mechanical variant of the Hopfield neural networks (let us call "quantum Hopfield model" or "quantum Hopfield networks"). For the case in which non-extensive number $p$ of patterns are embedded via asymmetric Hebbian connections, namely, $p/N \to 0$ for the number of neuron $N \to \infty$ ('far from saturation'), we evaluate the recalling processes for one of the built-in patterns under the influence of quantum-mechanical noise.Comment: 10 pages, 3 figures, using jpconf.cls, Proc. of Statphys-Kolkata VI

Fibrations of genus two on complex surfaces

We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown that the "geometric data" of the singular fiber determines the fibration on its neighborhood up to a transversely holomorphic $C^{\infty}$-diffeomorphism. The method employed is quite flexible and it applies to good extent to fibrations of arbitrary genus.Comment: This is the final version, June 201

Working group written presentation: Trapped radiation effects

The results of the Trapped Radiation Effects Panel for the Space Environmental Effects on Materials Workshop are presented. The needs of the space community for new data regarding effects of the space environment on materials, including electronics are listed. A series of questions asked of each of the panels at the workshop are addressed. Areas of research which should be pursued to satisfy the requirements for better knowledge of the environment and better understanding of the effects of the energetic charged particle environment on new materials and advanced electronics technology are suggested

Valence-bond states in dynamical Jahn-Teller molecular systems

We discuss a hopping model of electrons between idealized molecular sites with local orbital degeneracy and dynamical Jahn-Teller effect, for crystal field environments of sufficiently high symmetry. For the Mott-insulating case (one electron per site and large Coulomb repulsions), in the simplest two-fold degenerate situation, we are led to consider a particular exchange hamiltonian, describing two isotropic spin-1/2 Heisenberg problems coupled by a quartic term on equivalent bonds. This twin-exchange hamiltonian applies to a physical regime in which the inter-orbital singlet is the lowest-energy intermediate state available for hopping. This regime is favored by a relatively strong electron-phonon coupling. Using variational arguments, a large-N limit, and exact diagonalization data, we find that the ground state, in the one dimensional case, is a solid valence bond state. The situation in the two dimensional case is less clear. Finally, the behavior of the system upon hole doping is studied in one dimension.Comment: 11 pages, 5 figure

Surface Contribution to Raman Scattering from Layered Superconductors

Generalizing recent work, the Raman scattering intensity from a semi-infinite superconducting superlattice is calculated taking into account the surface contribution to the density response functions. Our work makes use of the formalism of Jain and Allen developed for normal superlattices. The surface contributions are shown to strongly modify the bulk contribution to the Raman-spectrum line shape below $2\Delta$, and also may give rise to additional surface plasmon modes above $2\Delta$. The interplay between the bulk and surface contribution is strongly dependent on the momentum transfer $q_\parallel$ parallel to layers. However, we argue that the scattering cross-section for the out-of-phase phase modes (which arise from interlayer Cooper pair tunneling) will not be affected and thus should be the only structure exhibited in the Raman spectrum below $2\Delta$ for relatively large $q_\parallel\sim 0.1\Delta/v_F$. The intensity is small but perhaps observable.Comment: 14 pages, RevTex, 6 figure