From Network Structure to Dynamics and Back Again: Relating dynamical stability and connection topology in biological complex systems

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from statistical physics and non-linear dynamics. In this paper, we look at a few examples of biological networks to see how similar questions can come up in very different contexts. We review some of our recent work that looks at how network structure (e.g., its connection topology) can dictate the nature of its dynamics, and conversely, how dynamical considerations constrain the network structure. We also see how networks occurring in nature can evolve to modular configurations as a result of simultaneously trying to satisfy multiple structural and dynamical constraints. The resulting optimal networks possess hubs and have heterogeneous degree distribution similar to those seen in biological systems.Comment: 15 pages, 6 figures, to appear in Proceedings of "Dynamics On and Of Complex Networks", ECSS'07 Satellite Workshop, Dresden, Oct 1-5, 200

Effect of Interband Transitions on the c axis Penetration Depth of Layered Superconductors

The electromagnetic response of a system with two planes per unit cell involves, in addition to the usual intraband contribution, an added interband term. These transitions affect the temperature dependence and the magnitude of the zero temperature c-axis penetration depth. When the interplane hopping is sufficiently small, the interband transitions dominate the low temperature behaviour of the penetration depth which then does not reflect the linear temperature dependence of the intraband term and in comparison becomes quite flat even for a d-wave gap. It is in this regime that the pseudogap was found in our previous normal state calculations of the c-axis conductivity, and the effects are connected.Comment: 8 pages, 5 figure

Boundedness, compactness and Schatten-class membership of weighted composition operators

The boundedness and compactness of weighted composition operators on the Hardy space ${\mathcal H}^2$ of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class membership is also considered; as a result, stronger forms of the two main results of a recent paper of Gunatillake are derived. Finally, weighted composition operators on weighted Bergman spaces $\mathcal{A}^2 \alpha(\mathbb{D})$ are considered, and the results of Harper and Smith, linking their properties to those of Carleson embeddings, are extended to this situation.Comment: 12 page

Scarred Patterns in Surface Waves

Surface wave patterns are investigated experimentally in a system geometry that has become a paradigm of quantum chaos: the stadium billiard. Linear waves in bounded geometries for which classical ray trajectories are chaotic are known to give rise to scarred patterns. Here, we utilize parametrically forced surface waves (Faraday waves), which become progressively nonlinear beyond the wave instability threshold, to investigate the subtle interplay between boundaries and nonlinearity. Only a subset (three main types) of the computed linear modes of the stadium are observed in a systematic scan. These correspond to modes in which the wave amplitudes are strongly enhanced along paths corresponding to certain periodic ray orbits. Many other modes are found to be suppressed, in general agreement with a prediction by Agam and Altshuler based on boundary dissipation and the Lyapunov exponent of the associated orbit. Spatially asymmetric or disordered (but time-independent) patterns are also found even near onset. As the driving acceleration is increased, the time-independent scarred patterns persist, but in some cases transitions between modes are noted. The onset of spatiotemporal chaos at higher forcing amplitude often involves a nonperiodic oscillation between spatially ordered and disordered states. We characterize this phenomenon using the concept of pattern entropy. The rate of change of the patterns is found to be reduced as the state passes temporarily near the ordered configurations of lower entropy. We also report complex but highly symmetric (time-independent) patterns far above onset in the regime that is normally chaotic.Comment: 9 pages, 10 figures (low resolution gif files). Updated and added references and text. For high resolution images: http://physics.clarku.edu/~akudrolli/stadium.htm

Learning Behavioural Context

The original publication is available at www.springerlink.co

Geometric phases for generalized squeezed coherent states

A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally-spaced spectrum and appropriate ladder operators connecting the eigenstates. The formalism is first applied to a general deformation of the oscillator involving both squeezing and displacement. Earlier results are shown to emerge as special cases. The analysis is then extended to multiphoton squeezed coherent states and the corresponding anholonomies deduced.Comment: 15 page

Impurity and interface bound states in dx2−y2+idxyd_{x^2-y^2}+id_{xy} and px+ipyp_x+ip_y superconductors

Motivated by recent discoveries of novel superconductors such as Na$_x$CoO$_2\cdot y$H$_2$O and Sr$_2$RuO$_4$, we analysize features of quasi-particle scattering due to impurities and interfaces for possible gapful $d_{x^2-y^2}+id_{xy}$ and $p_x+ip_y$ Cooper pairing. A bound state appears near a local impurity, and a band of bound states form near an interface. We obtained analytically the bound state energy, and calculated the space and energy dependent local density of states resolvable by high-resolution scanning tunnelling microscopy. For comparison we also sketch results of impurity and surface states if the pairing is nodal p- or d-wave.Comment: 4 pages, 4 figure

Geometric effects on T-breaking in p+ip and d+id superconductors

Superconducting order parameters that change phase around the Fermi surface modify Josephson tunneling behavior, as in the phase-sensitive measurements that confirmed $d$ order in the cuprates. This paper studies Josephson coupling when the individual grains break time-reversal symmetry; the specific cases considered are $p \pm ip$ and $d \pm id$, which may appear in Sr$_2$RuO$_4$ and Na$_x$CoO$_2 \cdot$(H$_2$O)$_y$ respectively. $T$-breaking order parameters lead to frustrating phases when not all grains have the same sign of time-reversal symmetry breaking, and the effects of these frustrating phases depend sensitively on geometry for 2D arrays of coupled grains. These systems can show perfect superconducting order with or without macroscopic $T$-breaking. The honeycomb lattice of superconducting grains has a superconducting phase with no spontaneous breaking of $T$ but instead power-law correlations. The superconducting transition in this case is driven by binding of fractional vortices, and the zero-temperature criticality realizes a generalization of Baxter's three-color model.Comment: 8 page

Towards Person Identification and Re-identification with Attributes

Abstract. Visual identification of an individual in a crowded environ-ment observed by a distributed camera network is critical to a variety of tasks including commercial space management, border control, and crime prevention. Automatic re-identification of a human from public space CCTV video is challenging due to spatiotemporal visual feature varia-tions and strong visual similarity in people’s appearance, compounded by low-resolution and poor quality video data. Relying on re-identification using a probe image is limiting, as a linguistic description of an individ-ual’s profile may often be the only available cues. In this work, we show how mid-level semantic attributes can be used synergistically with low-level features for both identification and re-identification. Specifically, we learn an attribute-centric representation to describe people, and a met-ric for comparing attribute profiles to disambiguate individuals. This differs from existing approaches to re-identification which rely purely on bottom-up statistics of low-level features: it allows improved robustness to view and lighting; and can be used for identification as well as re-identification. Experiments demonstrate the flexibility and effectiveness of our approach compared to existing feature representations when ap-plied to benchmark datasets.

Search for B -> h(*) nu nubar Decays at Belle

We present a search for the rare decays B -> h(*) nu nubar, where h(*) stands for a light meson. A data sample of 535 million BBbar pairs collected with the Belle detector at the KEKB e+e- collider is used. Signal candidates are required to have an accompanying B meson fully reconstructed in a hadronic mode and signal-side particles consistent with a single h(*) meson. No significant signal is observed and we set upper limits on the branching fractions at 90% confidence level. The limits on B0 -> K*0 nu nubar and B+ -> K+ nu nubar decays are more stringent than the previous constraints, while the first searches for B0 -> K0 nu nubar, pi0 nu nubar, rho0 nu nubar, phi nu nubar and B+ -> K*+ nu nubar, rho+ nu nubar are reported.Comment: 6 pages, 2 figures, submit to PR