Quadratic deformation of Minkowski space

We present a deformation of the Minkowski space as embedded into the conformal space (in the formalism of twistors) based in the quantum versions of the corresponding kinematic groups. We compute explicitly the star product, whose Poisson bracket is quadratic. We show that the star product although defined on the polynomials can be extended differentiably. Finally we compute the Eucliden and Minkowskian real forms of the deformation.Comment: Presented at XVII European Workshop on String Theory 2011. Padova (Italy) September 05-09; Fortschr. Phys. 1-7 (2012

A perturbative approach to non-linearities in the information carried by a two layer neural network

We evaluate the mutual information between the input and the output of a two layer network in the case of a noisy and non-linear analogue channel. In the case where the non-linearity is small with respect to the variability in the noise, we derive an exact expression for the contribution to the mutual information given by the non-linear term in first order of perturbation theory. Finally we show how the calculation can be simplified by means of a diagrammatic expansion. Our results suggest that the use of perturbation theories applied to neural systems might give an insight on the contribution of non-linearities to the information transmission and in general to the neuronal dynamics.Comment: Accepted as a preprint of ICTP, Triest

Precision radial velocities of double-lined spectroscopic binaries with an iodine absorption cell

A spectroscopic technique employing an iodine absorption cell (I_2) to superimpose a reference spectrum onto a stellar spectrum is currently the most widely adopted approach to obtain precision radial velocities of solar-type stars. It has been used to detect ~80 extrasolar planets out of ~130 know. Yet in its original version, it only allows us to measure precise radial velocities of single stars. In this paper, we present a novel method employing an I_2 absorption cell that enables us to accurately determine radial velocities of both components of double-lined binaries. Our preliminary results based on the data from the Keck I telescope and HIRES spectrograph demonstrate that 20-30 m/s radial velocity precision can be routinely obtained for "early" type binaries (F3-F8). For later type binaries, the precision reaches ~10 m/s. We discuss applications of the technique to stellar astronomy and searches for extrasolar planets in binary systems. In particular, we combine the interferometric data collected with the Palomar Testbed Interferometer with our preliminary precision velocities of the spectroscopic double-lined binary HD 4676 to demonstrate that with such a combination one can routinely obtain masses of the binary components accurate at least at the level of 1.0%.Comment: Accepted for publication in The Astrophysical Journa

Relay synchronization in multiplex networks

Relay (or remote) synchronization between two not directly connected oscillators in a network is an important feature allowing distant coordination. In this work, we report a systematic study of this phenomenon in multiplex networks, where inter-layer synchronization occurs between distant layers mediated by a relay layer that acts as a transmitter. We show that this transmission can be extended to higher order relay configurations, provided symmetry conditions are preserved. By first order perturbative analysis, we identify the dynamical and topological dependencies of relay synchronization in a multiplex. We find that the relay synchronization threshold is considerably reduced in a multiplex configuration, and that such synchronous state is mostly supported by the lower degree nodes of the outer layers, while hubs can be de-multiplexed without affecting overall coherence. Finally, we experimentally validated the analytical and numerical findings by means of a multiplex of three layers of electronic circuits.the analytical and numerical findings by means of a multiplex of three layers of electronic circuits

On the gluon content of the eta and eta' mesons

A phenomenological analysis of radiative $V\to P\gamma$ and $P\to V\gamma$ decays is performed with the purpose of determining the gluonic content of the $\eta$ and $\eta^\prime$ wave functions. Our results show that within our model there is no evidence for a gluonium contribution in the $\eta$, $Z_\eta^2=0.00\pm 0.12$, or the $\eta^\prime$, $Z_{\eta^\prime}^2=0.04\pm 0.09$. In terms of a mixing angle description this corresponds to $\phi_P=(41.4\pm 1.3)^\circ$ and $|\phi_{\eta^\prime G}|=(12\pm 13)^\circ$. In addition, the $\eta$-$\eta^\prime$ mixing angle is found to be $\phi_P=(41.5\pm 1.2)^\circ$ if we don't allow for a gluonium component.Comment: 16 pages, 3 figures, JHEP style. First part of data fitting changed, conclusions not modifie

Critical Behaviour of the Number of Minima of a Random Landscape at the Glass Transition Point and the Tracy-Widom distribution

We exploit a relation between the mean number $N_{m}$ of minima of random Gaussian surfaces and extreme eigenvalues of random matrices to understand the critical behaviour of $N_{m}$ in the simplest glass-like transition occuring in a toy model of a single particle in $N$-dimensional random environment, with $N\gg 1$. Varying the control parameter $\mu$ through the critical value $\mu_c$ we analyse in detail how $N_{m}(\mu)$ drops from being exponentially large in the glassy phase to $N_{m}(\mu)\sim 1$ on the other side of the transition. We also extract a subleading behaviour of $N_{m}(\mu)$ in both glassy and simple phases. The width $\delta{\mu}/\mu_c$ of the critical region is found to scale as $N^{-1/3}$ and inside that region $N_{m}(\mu)$ converges to a limiting shape expressed in terms of the Tracy-Widom distribution

Stability of the replica symmetric solution for the information conveyed by by a neural network

The information that a pattern of firing in the output layer of a feedforward network of threshold-linear neurons conveys about the network's inputs is considered. A replica-symmetric solution is found to be stable for all but small amounts of noise. The region of instability depends on the contribution of the threshold and the sparseness: for distributed pattern distributions, the unstable region extends to higher noise variances than for very sparse distributions, for which it is almost nonexistant.Comment: 19 pages, LaTeX, 5 figures. Also available at http://www.mrc-bbc.ox.ac.uk/~schultz/papers.html . Submitted to Phys. Rev. E Minor change

Explosive first-order transition to synchrony in networked chaotic oscillators

Critical phenomena in complex networks, and the emergence of dynamical abrupt transitions in the macroscopic state of the system are currently a subject of the outmost interest. We report evidence of an explosive phase synchronization in networks of chaotic units. Namely, by means of both extensive simulations of networks made up of chaotic units, and validation with an experiment of electronic circuits in a star configuration, we demonstrate the existence of a first order transition towards synchronization of the phases of the networked units. Our findings constitute the first prove of this kind of synchronization in practice, thus opening the path to its use in real-world applications.Comment: Phys. Rev. Lett. in pres