Smooth free involution of HCP3H{\Bbb C}P^3 and Smith conjecture for imbeddings of S3S^3 in S6S^6

This paper establishes an equivalence between existence of free involutions on $H{\Bbb C}P^3$ and existence of involutions on $S^6$ with fixed point set an imbedded $S^3$, then a family of counterexamples of the Smith conjecture for imbeddings of $S^3$ in $S^6$ are given by known result on $H{\Bbb C}P^3$. In addition, this paper also shows that every smooth homotopy complex projective 3-space admits no orientation preserving smooth free involution, which answers an open problem [Pe]. Moreover, the study of existence problem for smooth orientation preserving involutions on $H{\Bbb C}P^3$ is completed.Comment: 10 pages, final versio

Polychromatic solitons in a quadratic medium

We introduce the simplest model to describe parametric interactions in a quadratically nonlinear optical medium with the fundamental harmonic containing two components with (slightly) different carrier frequencies [which is a direct analog of wavelength-division multiplexed (WDM) models, well known in media with cubic nonlinearity]. The model takes a closed form with three different second-harmonic components, and it is formulated in the spatial domain. We demonstrate that the model supports both polychromatic solitons (PCSs), with all the components present in them, and two types of mutually orthogonal simple solitons, both types being stable in a broad parametric region. An essential peculiarity of PCS is that its power is much smaller than that of a simple (usual) soliton (taken at the same values of control parameters), which may be an advantage for experimental generation of PCSs. Collisions between the orthogonal simple solitons are simulated in detail, leading to the conclusion that the collisions are strongly inelastic, converting the simple solitons into polychromatic ones, and generating one or two additional PCSs. A collision velocity at which the inelastic effects are strongest is identified, and it is demonstrated that the collision may be used as a basis to design a simple all-optical XOR logic gate.Comment: 9 pages, 8 figures, accepted to Phys. Rev.

Muon spin rotation measurements of the superfluid density in fresh and aged superconducting PuCoGa5_5

We have measured the temperature dependence and magnitude of the superfluid density $\rho_{\rm s}(T)$ via the magnetic field penetration depth $\lambda(T)$ in PuCoGa$_5$ (nominal critical temperature $T_{c0} = 18.5$ K) using the muon spin rotation technique in order to investigate the symmetry of the order parameter, and to study the effects of aging on the superconducting properties of a radioactive material. The same single crystals were measured after 25 days ($T_c = 18.25$ K) and 400 days ($T_c = 15.0$ K) of aging at room temperature. The temperature dependence of the superfluid density is well described in both materials by a model using d-wave gap symmetry. The magnitude of the muon spin relaxation rate $\sigma$ in the aged sample, $\sigma\propto 1/\lambda^2\propto\rho_s/m^*$, where $m^*$ is the effective mass, is reduced by about 70% compared to fresh sample. This indicates that the scattering from self-irradiation induced defects is not in the limit of the conventional Abrikosov-Gor'kov pair-breaking theory, but rather in the limit of short coherence length (about 2 nm in PuCoGa$_5$) superconductivity.Comment: 11 page

Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schr\"odinger equation and describe three types of nonlinear impurity modes --- one- and two-hump symmetric localized modes and asymmetric localized modes --- for both focusing and defocusing nonlinearity and two different (attractive or repulsive) types of impurity. We obtain an analytical stability criterion for the nonlinear localized modes and consider the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site.Comment: 18 pages, 22 figure

Discovering study-specific gene regulatory networks

This article has been made available through the Brunel Open Access Publishing Fund.Microarrays are commonly used in biology because of their ability to simultaneously measure thousands of genes under different conditions. Due to their structure, typically containing a high amount of variables but far fewer samples, scalable network analysis techniques are often employed. In particular, consensus approaches have been recently used that combine multiple microarray studies in order to find networks that are more robust. The purpose of this paper, however, is to combine multiple microarray studies to automatically identify subnetworks that are distinctive to specific experimental conditions rather than common to them all. To better understand key regulatory mechanisms and how they change under different conditions, we derive unique networks from multiple independent networks built using glasso which goes beyond standard correlations. This involves calculating cluster prediction accuracies to detect the most predictive genes for a specific set of conditions. We differentiate between accuracies calculated using cross-validation within a selected cluster of studies (the intra prediction accuracy) and those calculated on a set of independent studies belonging to different study clusters (inter prediction accuracy). Finally, we compare our method's results to related state-of-the art techniques. We explore how the proposed pipeline performs on both synthetic data and real data (wheat and Fusarium). Our results show that subnetworks can be identified reliably that are specific to subsets of studies and that these networks reflect key mechanisms that are fundamental to the experimental conditions in each of those subsets

Spin and Charge Structure Factor of the 2-d Hubbard Model

The spin and charge structure factors are calculated for the Hubbard model on the square lattice near half-filling using a spin-rotation invariant six-slave boson representation. The charge structure factor shows a broad maximum at the zone corner and is found to decrease monotonically with increasing interaction strength and electron density and increasing temperature. The spin structure factor develops with increasing interaction two incommensurate peaks at the zone boundary and along the zone diagonal. Comparison with results of Quantum Monte Carlo and variational calculations is carried out and the agreement is found to be good. The limitations of an RPA-type approach are pointed out.Comment: 18 pages, revtex, 13 postscript figures, submitted to Phys. Rev.

The incommensurate charge-density-wave instability in the extended three-band Hubbard model

The infinite-U three-band Hubbard model is considered in order to describe the CuO_2 planes of the high temperature superconducting cuprates. The charge instabilities are investigated when the model is extended with a nearest-neighbor repulsion between holes on copper d and oxygen p orbitals and in the presence of a long-range Coulombic repulsion. It is found that a first-order valence instability line ending with a critical point is present like in the previously investigated model without long-range forces. However, the dominant critical instability is the formation of incommensurate charge-density-waves, which always occur before the valence-instability critical point is reached. An effective singular attraction arises in the proximity of the charge-density wave instability, accounting for both a strong pairing mechanism and for the anomalous normal state properties.Comment: 15 pages in RevteX. Figures available from M. Grill