The Little-Hopfield model on a Random Graph

We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and where the spin dynamics is governed by a synchronous execution of the microscopic update rule (Little-Hopfield model).We solve this model within replica symmetry and by using bifurcation analysis we prove that the spin-glass/paramagnetic and the retrieval/paramagnetictransition lines of our phase diagram are identical to those of sequential dynamics.The first-order retrieval/spin-glass transition line follows by direct evaluation of our observables using population dynamics. Within the accuracy of numerical precision and for sufficiently small values of the connectivity parameter we find that this line coincides with the corresponding sequential one. Comparison with simulation experiments shows excellent agreement.Comment: 14 pages, 4 figure

The path-integral analysis of an associative memory model storing an infinite number of finite limit cycles

It is shown that an exact solution of the transient dynamics of an associative memory model storing an infinite number of limit cycles with l finite steps by means of the path-integral analysis. Assuming the Maxwell construction ansatz, we have succeeded in deriving the stationary state equations of the order parameters from the macroscopic recursive equations with respect to the finite-step sequence processing model which has retarded self-interactions. We have also derived the stationary state equations by means of the signal-to-noise analysis (SCSNA). The signal-to-noise analysis must assume that crosstalk noise of an input to spins obeys a Gaussian distribution. On the other hand, the path-integral method does not require such a Gaussian approximation of crosstalk noise. We have found that both the signal-to-noise analysis and the path-integral analysis give the completely same result with respect to the stationary state in the case where the dynamics is deterministic, when we assume the Maxwell construction ansatz. We have shown the dependence of storage capacity (alpha_c) on the number of patterns per one limit cycle (l). Storage capacity monotonously increases with the number of steps, and converges to alpha_c=0.269 at l ~= 10. The original properties of the finite-step sequence processing model appear as long as the number of steps of the limit cycle has order l=O(1).Comment: 24 pages, 3 figure

The signal-to-noise analysis of the Little-Hopfield model revisited

Using the generating functional analysis an exact recursion relation is derived for the time evolution of the effective local field of the fully connected Little-Hopfield model. It is shown that, by leaving out the feedback correlations arising from earlier times in this effective dynamics, one precisely finds the recursion relations usually employed in the signal-to-noise approach. The consequences of this approximation as well as the physics behind it are discussed. In particular, it is pointed out why it is hard to notice the effects, especially for model parameters corresponding to retrieval. Numerical simulations confirm these findings. The signal-to-noise analysis is then extended to include all correlations, making it a full theory for dynamics at the level of the generating functional analysis. The results are applied to the frequently employed extremely diluted (a)symmetric architectures and to sequence processing networks.Comment: 26 pages, 3 figure

An associative network with spatially organized connectivity

We investigate the properties of an autoassociative network of threshold-linear units whose synaptic connectivity is spatially structured and asymmetric. Since the methods of equilibrium statistical mechanics cannot be applied to such a network due to the lack of a Hamiltonian, we approach the problem through a signal-to-noise analysis, that we adapt to spatially organized networks. The conditions are analyzed for the appearance of stable, spatially non-uniform profiles of activity with large overlaps with one of the stored patterns. It is also shown, with simulations and analytic results, that the storage capacity does not decrease much when the connectivity of the network becomes short range. In addition, the method used here enables us to calculate exactly the storage capacity of a randomly connected network with arbitrary degree of dilution.Comment: 27 pages, 6 figures; Accepted for publication in JSTA

Statistical Mechanics of Dilute Batch Minority Games with Random External Information

We study the dynamics and statics of a dilute batch minority game with random external information. We focus on the case in which the number of connections per agent is infinite in the thermodynamic limit. The dynamical scenario of ergodicity breaking in this model is different from the phase transition in the standard minority game and is characterised by the onset of long-term memory at finite integrated response. We demonstrate that finite memory appears at the AT-line obtained from the corresponding replica calculation, and compare the behaviour of the dilute model with the minority game with market impact correction, which is known to exhibit similar features.Comment: 22 pages, 6 figures, text modified, references updated and added, figure added, typos correcte

Improved calibration of groundwater models using baseflow estimates for sub-catchments. Case-study: Upper Alzette, Luxembourg

Using MODFLOW the groundwater system of the Upper Alzette catchment was modelled. In general, calibration of groundwater models involves an inverse modelling strategy, using the measured groundwater heads in observation wells. An additional calibration strategy was employed considering the water balances of a number of subcatchments. Baseflow for each of the subcatchments was estimated and used as a criterion for an additional calibration. This analysis clearly showed that considering sub-water balances in the calibration process greatly improves the model results. The uncertainty of the model results was assessed, defining a spatially distributed ‘range’ for the simulated groundwater levels.status: publishe

Hydrologische modellering als basis voor het bepalen van potenties voor vegetatie en natuur in het kader van Ecosysteemvisies in Vlaanderen. Case-Study: Visbeek

In het kader van het Milieubeleidsplan (MINA-plan 2, Actie 105) van de Vlaamse Overheid werden tussen 1997 en 2002 voor een tiental rivier- en beekvalleien in Vlaanderen Ecosysteemvisies uitgewerkt. In valleigebieden met ondiepe grondwaterstanden en aanzienlijke zones met kwel vormt de grondwaterhydrologie een belangrijke abiotische randvoorwaarde voor vegetatie en natuur. Hydrologische condities zijn er doorslaggevend voor de mogelijkheden om bepaalde vegetatietypes te ontwikkelen en vormen een essentieel onderdeel van de ecosysteemvisies. Bovendien heeft hydrologische modellering de mogelijkheid om gebiedsdekkende informatie te leveren over de randvoorwaarden, alsook veranderingen in de hydrologie door te rekenen met behulp van scenario’s. Ze biedt op deze wijze een belangrijke meerwaarde voor ecohydrologische studies. De Vakgroep Hydrologie en Waterbouwkunde van de Vrije Universiteit Brussel nam in vijf van deze Ecosysteemvisies de hydrologische modellering voor haar rekening. Voor de Ecosysteemvisie van de Visbeek- Kindernouwbeek (Nete bekken) worden de belangrijkste resultaten getoond. Naast een inschatting van grondwaterparameters (kwantiteit), werd eveneens een inschatting gemaakt van de mogelijke aanrijking met nutriënten van een natuurzone via het grondwater (kwaliteit).status: publishe

Automatic Proba-V processor: TREX-tool for raster data exploration

The processing tool TREX, standing for ‘Tool for Raster data EXploration’ is presented and evaluated in the Biebrza wetlands in northeastern Poland. TREX was designed for the automatization of processing satellite data from the Proba-V satellite into maps of NDVI or LAI in any defined by the user projection, spatial resolution, or extent. The open source and access concept of TREX encourages the potential community of users to collaborate, develop, and integrate the tool with other satellite imagery and models. TREX reprojects, shifts, and resamples original data obtained from the Proba-V satellite to deliver reliable maps of NDVI and LAI. Validation of TREX in Biebrza wetlands resulted in correlations between 0.79 and 0.92 for NDVI data (measured with ASD Field Spec 4) and 0.92 for LAI data (measured with LiCOR—LAI-2000 Plant Canopy Analyzer)