Selection of tuning parameters in bridge regression models via Bayesian information criterion

We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning parameter in bridge regression models. The choice of the adjusted parameters can be viewed as a model selection and evaluation problem. We propose a model selection criterion for evaluating bridge regression models in terms of Bayesian approach. This selection criterion enables us to select the adjusted parameters objectively. We investigate the effectiveness of our proposed modeling strategy through some numerical examples.Comment: 20 pages, 5 figure

Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime

In cavity quantum electrodynamics (QED), light-matter interaction is probed at its most fundamental level, where individual atoms are coupled to single photons stored in three-dimensional cavities. This unique possibility to experimentally explore the foundations of quantum physics has greatly evolved with the advent of circuit QED, where on-chip superconducting qubits and oscillators play the roles of two-level atoms and cavities, respectively. In the strong coupling limit, atom and cavity can exchange a photon frequently before coherence is lost. This important regime has been reached both in cavity and circuit QED, but the design flexibility and engineering potential of the latter allowed for increasing the ratio between the atom-cavity coupling rate and the cavity transition frequency above the percent level. While these experiments are well described by the renowned Jaynes-Cummings model, novel physics is expected in the ultrastrong coupling limit. Here, we report on the first experimental realization of a superconducting circuit QED system in the ultrastrong coupling limit and present direct evidence for the breakdown of the Jaynes-Cummings model.Comment: 5 pages, 3 figure

Structural insights into Clostridium perfringens delta toxin pore formation

Clostridium perfringens Delta toxin is one of the three hemolysin-like proteins produced by C. perfringens type C and possibly type B strains. One of the others, NetB, has been shown to be the major cause of Avian Nectrotic Enteritis, which following the reduction in use of antibiotics as growth promoters, has become an emerging disease of industrial poultry. Delta toxin itself is cytotoxic to the wide range of human and animal macrophages and platelets that present GM2 ganglioside on their membranes. It has sequence similarity with Staphylococcus aureus β-pore forming toxins and is expected to heptamerize and form pores in the lipid bilayer of host cell membranes. Nevertheless, its exact mode of action remains undetermined. Here we report the 2.4 Å crystal structure of monomeric Delta toxin. The superposition of this structure with the structure of the phospholipid-bound F component of S. aureus leucocidin (LukF) revealed that the glycerol molecules bound to Delta toxin and the phospholipids in LukF are accommodated in the same hydrophobic clefts, corresponding to where the toxin is expected to latch onto the membrane, though the binding sites show significant differences. From structure-based sequence alignment with the known structure of staphylococcal α-hemolysin, a model of the Delta toxin pore form has been built. Using electron microscopy, we have validated our model and characterized the Delta toxin pore on liposomes. These results highlight both similarities and differences in the mechanism of Delta toxin (and by extension NetB) cytotoxicity from that of the staphylococcal pore-forming toxins

Nonlinear vortex light beams supported and stabilized by dissipation

We describe nonlinear Bessel vortex beams as localized and stationary solutions with embedded vorticity to the nonlinear Schr\"odinger equation with a dissipative term that accounts for the multi-photon absorption processes taking place at high enough powers in common optical media. In these beams, power and orbital angular momentum are permanently transferred to matter in the inner, nonlinear rings, at the same time that they are refueled by spiral inward currents of energy and angular momentum coming from the outer linear rings, acting as an intrinsic reservoir. Unlike vortex solitons and dissipative vortex solitons, the existence of these vortex beams does not critically depend on the precise form of the dispersive nonlinearities, as Kerr self-focusing or self-defocusing, and do not require a balancing gain. They have been shown to play a prominent role in "tubular" filamentation experiments with powerful, vortex-carrying Bessel beams, where they act as attractors in the beam propagation dynamics. Nonlinear Bessel vortex beams provide indeed a new solution to the problem of the stable propagation of ring-shaped vortex light beams in homogeneous self-focusing Kerr media. A stability analysis demonstrates that there exist nonlinear Bessel vortex beams with single or multiple vorticity that are stable against azimuthal breakup and collapse, and that the mechanism that renders these vortexes stable is dissipation. The stability properties of nonlinear Bessel vortex beams explain the experimental observations in the tubular filamentation experiments.Comment: Chapter of boo

Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe

In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2+1)-dimensional vacuum gravity in the setting of a spatially closed universe.Comment: 61 pages, draft of review for Living Reviews; comments, criticisms, additions, missing references welcome; v2: minor changes, added reference

Planetary Dynamics and Habitable Planet Formation In Binary Star Systems

Whether binaries can harbor potentially habitable planets depends on several factors including the physical properties and the orbital characteristics of the binary system. While the former determines the location of the habitable zone (HZ), the latter affects the dynamics of the material from which terrestrial planets are formed (i.e., planetesimals and planetary embryos), and drives the final architecture of the planets assembly. In order for a habitable planet to form in a binary star system, these two factors have to work in harmony. That is, the orbital dynamics of the two stars and their interactions with the planet-forming material have to allow terrestrial planet formation in the habitable zone, and ensure that the orbit of a potentially habitable planet will be stable for long times. We have organized this chapter with the same order in mind. We begin by presenting a general discussion on the motion of planets in binary stars and their stability. We then discuss the stability of terrestrial planets, and the formation of potentially habitable planets in a binary-planetary system.Comment: 56 pages, 29 figures, chapter to appear in the book: Planets in Binary Star Systems (Ed. N. Haghighipour, Springer publishing company

Comprehensive characterization of molecular interactions based on nanomechanics

Molecular interaction is a key concept in our understanding of the biological mechanisms of life. Two physical properties change when one molecular partner binds to another. Firstly, the masses combine and secondly, the structure of at least one binding partner is altered, mechanically transducing the binding into subsequent biological reactions. Here we present a nanomechanical micro-array technique for bio-medical research, which not only monitors the binding of effector molecules to their target but also the subsequent effect on a biological system in vitro. This label-free and real-time method directly and simultaneously tracks mass and nanomechanical changes at the sensor interface using micro-cantilever technology. To prove the concept we measured lipid vesicle (approximately 748*10(6) Da) adsorption on the sensor interface followed by subsequent binding of the bee venom peptide melittin (2840 Da) to the vesicles. The results show the high dynamic range of the instrument and that measuring the mass and structural changes simultaneously allow a comprehensive discussion of molecular interactions

How do field of view and resolution affect the information content of panoramic scenes for visual navigation? A computational investigation

The visual systems of animals have to provide information to guide behaviour and the informational requirements of an animal’s behavioural repertoire are often reflected in its sensory system. For insects, this is often evident in the optical array of the compound eye. One behaviour that insects share with many animals is the use of learnt visual information for navigation. As ants are expert visual navigators it may be that their vision is optimised for navigation. Here we take a computational approach in asking how the details of the optical array influence the informational content of scenes used in simple view matching strategies for orientation. We find that robust orientation is best achieved with low-resolution visual information and a large field of view, similar to the optical properties seen for many ant species. A lower resolution allows for a trade-off between specificity and generalisation for stored views. Additionally, our simulations show that orientation performance increases if different portions of the visual field are considered as discrete visual sensors, each giving an independent directional estimate. This suggests that ants might benefit by processing information from their two eyes independently

Spacelike Singularities and Hidden Symmetries of Gravity

We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a self-contained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the infinite-dimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case of the hyperbolic algebra E10, which is conjectured to be an underlying symmetry of M-theory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to eleven-dimensional supergravity.Comment: 228 pages. Typos corrected. References added. Subject index added. Published versio