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

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

Hydrological connectivity does change over 70 years of abandonment and afforestation in the spanish Pyrenees

24 Pags.- 7 Figs.- 3 Tabls. The definitive version is available at: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-145XRunoff connectivity depends on topography, rainfall, man-made elements (terraces, trails, roads and drainage systems) and vegetation. In this study, we quantified the effects of 70 years of human activities on runoff connectivity in the mountainous Araguás afforested sub-catchment (17·2 ha; Central Spanish Pyrenees). The IC index of hydrological connectivity was chosen to perform this metric over six land use scenarios at high spatial resolution (1 × 1 m of cell size). The current scenario (year 2012) was simulated with three flow accumulation algorithms (MD, MD8 and D8). MD8 was linked with the most frequent hydrological response of the sub-catchment (rainfall intensity and stream flow during 7 years) and generated the most representative pattern of connectivity, especially in the linear landscape elements (LLE). This algorithm was chosen to simulate five past scenarios (1945, 1956, 1973, 1980 and 2006). In all scenarios, the highest connectivity appeared related to trails and roads, as well as to streams and gullies, whereas the lowest appeared related to stonewalls in 1945 and 1956 to hillslopes in 1973, and the following afforestation. Changes in connectivity mainly depended on the changes in the vegetation factor and in a minor way in the total length, spatial location and type of LLE. Afforestation promoted lower and more stable connectivity at both local and catchment scales.This research was supported by a Marie Curie Intra-European Fellowship in the project ‘MED-AFFOREST’ (PIEF-GA-2013-624974). Dr López-Vicente acknowledges the financial support of his postdoctoral contract to the project ‘EroCostModel’ (CGL2014-54877-JIN; Programme Jóvenes Investigadores), and Dr Nadal-Romero was a recipient of a Ramón y Cajal research contract. Both contracts are of the Spanish Ministry of Economy and Competitiveness.Peer reviewe

Replica symmetric evaluation of the information transfer in a two-layer network in presence of continuous+discrete stimuli

In a previous report we have evaluated analytically the mutual information between the firing rates of N independent units and a set of multi-dimensional continuous+discrete stimuli, for a finite population size and in the limit of large noise. Here, we extend the analysis to the case of two interconnected populations, where input units activate output ones via gaussian weights and a threshold linear transfer function. We evaluate the information carried by a population of M output units, again about continuous+discrete correlates. The mutual information is evaluated solving saddle point equations under the assumption of replica symmetry, a method which, by taking into account only the term linear in N of the input information, is equivalent to assuming the noise to be large. Within this limitation, we analyze the dependence of the information on the ratio M/N, on the selectivity of the input units and on the level of the output noise. We show analytically, and confirm numerically, that in the limit of a linear transfer function and of a small ratio between output and input noise, the output information approaches asymptotically the information carried in input. Finally, we show that the information loss in output does not depend much on the structure of the stimulus, whether purely continuous, purely discrete or mixed, but only on the position of the threshold nonlinearity, and on the ratio between input and output noise.Comment: 19 pages, 4 figure

The effects of revegetation in the natural environment and perception of the people linked to Camero Viejo (Iberian System)

During the 20th century, Euro-Mediterranean mountains underwent a process of marginalization, with high rates of emigration, land abandonment, reduction of livestock census and poor use of pasture and forest products. Marginalization, with the abandonment of most of the fields and pastures, encouraged secondary succession processes that favored the expansion of shrubs and forests. Simultaneously, the administration encouraged the reforestation of large areas for economic purposes (the increase of wood and paper pulp production) and environmental objectives (the regulation of floods and prevention of soil erosion and degra- dation). As a result of these changes, Mediterranean mountain landscapes have been simplified and homogenized, fragmentation has been reduced and many of their cultural values are being degraded, a trend that also involves the loss of local knowledge on sustainable land management. The expansion of vegetation shows other negative effects, including an increase of fire risk, a reduction in water availability, the concentration of sediment sources in ancient agricultural terraces (which maintain the most fertile and deepest soils), loss of biodiversity and problems for the economic sustainability of the mountain, due to pasture degradation, and the loss of an attractive landscape. On the other hand, we must take into account that the impacts of land use changes in mountain areas occur not only at a local scale, but also at regional and global scales, as mountain ecosystems provide a range of goods and services to the society. The aim of this study is to investigate the diversity of opinions that people linked to Camero Viejo (Iberian Range) present about the major environmental changes since the mid-twentieth century: (i) vegetation cover dynamics, (ii) soil erosion, (iii) water yield and quality, (iv) fire risk, and (v) changes in wildlife and landscape. This perception will be related to current changes, quantified from land cover and land uses maps, information taken in the administration, and literature of the study area. The final objective is to find out which social groups have a closer or unrealistic perception; in that way, decision-makers could obtain more information to develop and implement new public policies

Geoecology in Mediterranean mountain areas: a tribute to Prof. José María García-Ruiz

The origin of this special issue arose from a scientific meeting held in Logroño (Spain) in October 2014, under the theme Geoecology in extreme environments: mountains and semiarid areas (Arnáez et al., 2014). The main motivation of the event was to recognise, on the occasion of his retirement, the outstanding contribution of Prof. José María García-Ruiz to the progress of Geoecology in Mediterranean mountain areas. Prof. García-Ruiz (Zaragoza, 1949) was lecturer, between 1974 and 1987, at the University of Cáceres and La Rioja. As staff Scientist and later Professor at the Spanish National Research Council (CSIC), he was Head of the Pyrenean Institute of Ecology (IPE-CSIC) (1987–1990) and Head of the Department of Global Change at the same institute, President of the Spanish Society of Geomorphology (1994–1996), besides a productive and tireless researcher..