Universality classes in directed sandpile models

We perform large scale numerical simulations of a directed version of the two-state stochastic sandpile model. Numerical results show that this stochastic model defines a new universality class with respect to the Abelian directed sandpile. The physical origin of the different critical behavior has to be ascribed to the presence of multiple topplings in the stochastic model. These results provide new insights onto the long debated question of universality in abelian and stochastic sandpiles.Comment: 5 pages, RevTex, includes 9 EPS figures. Minor english corrections. One reference adde

Virtual Reality to Simulate Visual Tasks for Robotic Systems

Virtual reality (VR) can be used as a tool to analyze the interactions between the visual system of a robotic agent and the environment, with the aim of designing the algorithms to solve the visual tasks necessary to properly behave into the 3D world. The novelty of our approach lies in the use of the VR as a tool to simulate the behavior of vision systems. The visual system of a robot (e.g., an autonomous vehicle, an active vision system, or a driving assistance system) and its interplay with the environment can be modeled through the geometrical relationships between the virtual stereo cameras and the virtual 3D world. Differently from conventional applications, where VR is used for the perceptual rendering of the visual information to a human observer, in the proposed approach, a virtual world is rendered to simulate the actual projections on the cameras of a robotic system. In this way, machine vision algorithms can be quantitatively validated by using the ground truth data provided by the knowledge of both the structure of the environment and the vision system

Design strategies for direct multi-scale and multi-orientation feature extraction in the log-polar domain

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Corrections to scaling in the forest-fire model

We present a systematic study of corrections to scaling in the self-organized critical forest-fire model. The analysis of the steady-state condition for the density of trees allows us to pinpoint the presence of these corrections, which take the form of subdominant exponents modifying the standard finite-size scaling form. Applying an extended version of the moment analysis technique, we find the scaling region of the model and compute the first non-trivial corrections to scaling.Comment: RevTeX, 7 pages, 7 eps figure

Near-optimal combination of disparity across a log-polar scaled visual field

The human visual system is foveated: we can see fine spatial details in central vision, whereas resolution is poor in our peripheral visual field, and this loss of resolution follows an approximately logarithmic decrease. Additionally, our brain organizes visual input in polar coordinates. Therefore, the image projection occurring between retina and primary visual cortex can be mathematically described by the log-polar transform. Here, we test and model how this space-variant visual processing affects how we process binocular disparity, a key component of human depth perception. We observe that the fovea preferentially processes disparities at fine spatial scales, whereas the visual periphery is tuned for coarse spatial scales, in line with the naturally occurring distributions of depths and disparities in the real-world. We further show that the visual system integrates disparity information across the visual field, in a near-optimal fashion. We develop a foveated, log-polar model that mimics the processing of depth information in primary visual cortex and that can process disparity directly in the cortical domain representation. This model takes real images as input and recreates the observed topography of human disparity sensitivity. Our findings support the notion that our foveated, binocular visual system has been moulded by the statistics of our visual environment

A cortical model for binocular vergence control without explicit calculation of disparity

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Hyperbolicity Measures "Democracy" in Real-World Networks

We analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. In our interpretation, a network with small hyperbolicity is "aristocratic", because it contains a small set of vertices involved in many shortest paths, so that few elements "connect" the systems, while a network with large hyperbolicity has a more "democratic" structure with a larger number of crucial elements. We prove mathematically the soundness of this interpretation, and we derive its consequences by analyzing a large dataset of real-world networks. We confirm and improve previous results on hyperbolicity, and we analyze them in the light of our interpretation. Moreover, we study (for the first time in our knowledge) the hyperbolicity of the neighborhood of a given vertex. This allows to define an "influence area" for the vertices in the graph. We show that the influence area of the highest degree vertex is small in what we define "local" networks, like most social or peer-to-peer networks. On the other hand, if the network is built in order to reach a "global" goal, as in metabolic networks or autonomous system networks, the influence area is much larger, and it can contain up to half the vertices in the graph. In conclusion, our newly introduced approach allows to distinguish the topology and the structure of various complex networks

On the scaling behavior of the abelian sandpile model

The abelian sandpile model in two dimensions does not show the type of critical behavior familar from equilibrium systems. Rather, the properties of the stationary state follow from the condition that an avalanche started at a distance r from the system boundary has a probability proportional to 1/sqrt(r) to reach the boundary. As a consequence, the scaling behavior of the model can be obtained from evaluating dissipative avalanches alone, allowing not only to determine the values of all exponents, but showing also the breakdown of finite-size scaling.Comment: 4 pages, 5 figures; the new version takes into account that the radius distribution of avalanches cannot become steeper than a certain power la