Observability and Synchronization of Neuron Models

Observability is the property that enables to distinguish two different locations in $n$-dimensional state space from a reduced number of measured variables, usually just one. In high-dimensional systems it is therefore important to make sure that the variable recorded to perform the analysis conveys good observability of the system dynamics. In the case of networks composed of neuron models, the observability of the network depends nontrivially on the observability of the node dynamics and on the topology of the network. The aim of this paper is twofold. First, a study of observability is conducted using four well-known neuron models by computing three different observability coefficients. This not only clarifies observability properties of the models but also shows the limitations of applicability of each type of coefficients in the context of such models. Second, a multivariate singular spectrum analysis (M-SSA) is performed to detect phase synchronization in networks composed by neuron models. This tool, to the best of the authors' knowledge has not been used in the context of networks of neuron models. It is shown that it is possible to detect phase synchronization i)~without having to measure all the state variables, but only one from each node, and ii)~without having to estimate the phase

Weak localization in multiterminal networks of diffusive wires

We study the quantum transport through networks of diffusive wires connected to reservoirs in the Landauer-B\"uttiker formalism. The elements of the conductance matrix are computed by the diagrammatic method. We recover the combination of classical resistances and obtain the weak localization corrections. For arbitrary networks, we show how the cooperon must be properly weighted over the different wires. Its nonlocality is clearly analyzed. We predict a new geometrical effect that may change the sign of the weak localization correction in multiterminal geometries.Comment: 4 pages, LaTeX, 4 figures, 8 eps file

Single File Diffusion of particles with long ranged interactions: damping and finite size effects

We study the Single File Diffusion (SFD) of a cyclic chain of particles that cannot cross each other, in a thermal bath, with long ranged interactions, and arbitrary damping. We present simulations that exhibit new behaviors specifically associated to systems of small number of particles and to small damping. In order to understand those results, we present an original analysis based on the decomposition of the particles motion in the normal modes of the chain. Our model explains all dynamic regimes observed in our simulations, and provides convincing estimates of the crossover times between those regimes.Comment: 30 pages, 9 figure

Current noise through a Kondo quantum dot in a SU(N) Fermi liquid state

The current noise through a mesoscopic quantum dot is calculated and analyzed in the Fermi liquid regime of the SU(N) Kondo model. Results connect the Johnson-Nyquist noise to the shot noise for an arbitrary ratio of voltage and temperature, and show that temperature corrections are sizeable in usual experiments. For the experimentally relevant SU(4) case, quasiparticle interactions are shown to increase the shot noise.Comment: 4 pages, 2 figures, to be published in Phys. Rev. Lett. (revised version

Dephasing due to electron-electron interaction in a diffusive ring

We study the effect of the electron-electron interaction on the weak localization correction of a ring pierced by a magnetic flux. We compute exactly the path integral giving the magnetoconductivity for an isolated ring. The results are interpreted in a time representation. This allows to characterize the nature of the phase coherence relaxation in the ring. The nature of the relaxation depends on the time regime (diffusive or ergodic) but also on the harmonics $n$ of the magnetoconductivity. Whereas phase coherence relaxation is non exponential for the harmonic $n=0$, it is always exponential for harmonics $n\neq0$. Then we consider the case of a ring connected to reservoirs and discuss the effect of connecting wires. We recover the behaviour of the harmonics predicted recently by Ludwig & Mirlin for a large perimeter (compared to the Nyquist length). We also predict a new behaviour when the Nyquist length exceeds the perimeter.Comment: 21 pages, RevTeX4, 8 eps figures; version of 10/2006 : eqs.(100-102) of section V.C correcte

Dark energy from primordial inflationary quantum fluctuations

We show that current cosmic acceleration can be explained by an almost massless scalar field experiencing quantum fluctuations during primordial inflation. Provided its mass does not exceed the Hubble parameter today, this field has been frozen during the cosmological ages to start dominating the universe only recently. By using supernovae data, completed with baryonic acoustic oscillations from galaxy surveys and cosmic microwave background anisotropies, we infer the energy scale of primordial inflation to be around a few TeV, which implies a negligible tensor-to-scalar ratio of the primordial fluctuations. Moreover, our model suggests that inflation lasted for an extremely long period. Dark energy could therefore be a natural consequence of cosmic inflation close to the electroweak energy scale.Comment: 5 pages, 2 figures, uses RevTeX. Physical discussion extended, misprints corrected, references added. Matches published versio

An extremal model for amorphous media plasticity

An extremal model for the plasticity of amorphous materials is studied in a simple two-dimensional anti-plane geometry. The steady-state is analyzed through numerical simulations. Long-range spatial and temporal correlations in local slip events are shown to develop, leading to non-trivial and highly anisotropic scaling laws. In particular, the plastic strain is shown to statistically concentrate over a region which tends to align perpendicular to the displacement gradient. By construction, the model can be seen as giving rise to a depinning transition, the threshold of which (i.e. the macroscopic yield stress) also reveal scaling properties reflecting the localization of the activity.Comment: 4 pages, 5 figure

Four-body Efimov effect

We study three same spin state fermions of mass M interacting with a distinguishable particle of mass m in the unitary limit where the interaction has a zero range and an infinite s-wave scattering length. We predict an interval of mass ratio 13.384 < M/m < 13.607 where there exists a purely four-body Efimov effect, leading to the occurrence of weakly bound tetramers without Efimov trimers.Comment: 4 pages, 2 figure

Coexisting ordinary elasticity and superfluidity in a model of defect-free supersolid

We present the mechanics of a model of supersolid in the frame of the Gross-Pitaevskii equation at $T=0K$ that do not require defects nor vacancies. A set of coupled nonlinear partial differential equations plus boundary conditions is derived. The mechanical equilibrium is studied under external constrains as steady rotation or external stress. Our model displays a paradoxical behavior: the existence of a non classical rotational inertia fraction in the limit of small rotation speed and no superflow under small (but finite) stress nor external force. The only matter flow for finite stress is due to plasticity.Comment: 6 pages, 2 figure

Quantitative pretreatment VOI analysis of liver metastases 99mTc-MAA SPECT/CT and FDG PET/CT in relation with treatment response to SIRT

Using quantitive VOI analysis, the percentage Tc-99m-MAA uptake and SUVmax and mean values of liver metastases obtained prior to SIRT were related to treatment response using both a lesion-based and clinical dichotomous approach. Based on the VOI % of Tc-99m-MAA activity, the estimated Y-90-microspheres activity/cc (MBq/cc) was calculated from the effective dose injected. Baseline VOI FDG PET SUVmean and max values and estimated MBq/cc values were related to treatment response using a lesion-based approach (% change in SUVmean >= 50%) and a clinical dichotomous approach. Fifteen treatment sessions were analyzed (13 patients). Using the lesion-based approach (12 treatment sessions) 40 lesions responded and 37 did not. SUVmax and mean values proved significantly different between non-responding and responding lesions; 18:6 (SD 10.8) versus 13.5 (SD 8.4) for SUVmax (p = 0.02) and 11.4 (SD 3.8) versus 6.3 (SD 4.5) for SUVmean (p = 0.002). Using the clinical dichotomous approach (15 treatment sessions / 11 responding), 91 lesions were analyzed; 57 responded. VOI volumes and estimated Y-90-loaded glass microspheres activity (MBq/cc) did not differ between responders and non responders; 24 cc (SD 27) versus 21 cc (SD 21 cc) (p = 0.4) and 1.95 MBq/cc (SD 1.1 MBq/cc) versus 1.90 MB/cc (SD 2.7 MBq/cc) (p = 0.92). On the contrary, SUVmax and mean values proved significantly different between responders and non-responders; 23.7 (SD 9.8) versus 9.4 (SD 3.8) for SUVmax (p = 0.0001) and 13.1 (SD 8.1) versus 4.9 (SD 1.4) for SUVmean. Conclusion: These findings suggest that in patients presenting with high baseline SUVmax and mean values, the administration of higher activities or alternatively, other potentially more useful treatment options might be considered