24,685 research outputs found
Invariant template matching in systems with spatiotemporal coding: a vote for instability
We consider the design of a pattern recognition that matches templates to
images, both of which are spatially sampled and encoded as temporal sequences.
The image is subject to a combination of various perturbations. These include
ones that can be modeled as parameterized uncertainties such as image blur,
luminance, translation, and rotation as well as unmodeled ones. Biological and
neural systems require that these perturbations be processed through a minimal
number of channels by simple adaptation mechanisms. We found that the most
suitable mathematical framework to meet this requirement is that of weakly
attracting sets. This framework provides us with a normative and unifying
solution to the pattern recognition problem. We analyze the consequences of its
explicit implementation in neural systems. Several properties inherent to the
systems designed in accordance with our normative mathematical argument
coincide with known empirical facts. This is illustrated in mental rotation,
visual search and blur/intensity adaptation. We demonstrate how our results can
be applied to a range of practical problems in template matching and pattern
recognition.Comment: 52 pages, 12 figure
Spatial modelling for mixed-state observations
In several application fields like daily pluviometry data modelling, or
motion analysis from image sequences, observations contain two components of
different nature. A first part is made with discrete values accounting for some
symbolic information and a second part records a continuous (real-valued)
measurement. We call such type of observations "mixed-state observations". This
paper introduces spatial models suited for the analysis of these kinds of data.
We consider multi-parameter auto-models whose local conditional distributions
belong to a mixed state exponential family. Specific examples with exponential
distributions are detailed, and we present some experimental results for
modelling motion measurements from video sequences.Comment: Published in at http://dx.doi.org/10.1214/08-EJS173 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Voltage imaging of waking mouse cortex reveals emergence of critical neuronal dynamics.
Complex cognitive processes require neuronal activity to be coordinated across multiple scales, ranging from local microcircuits to cortex-wide networks. However, multiscale cortical dynamics are not well understood because few experimental approaches have provided sufficient support for hypotheses involving multiscale interactions. To address these limitations, we used, in experiments involving mice, genetically encoded voltage indicator imaging, which measures cortex-wide electrical activity at high spatiotemporal resolution. Here we show that, as mice recovered from anesthesia, scale-invariant spatiotemporal patterns of neuronal activity gradually emerge. We show for the first time that this scale-invariant activity spans four orders of magnitude in awake mice. In contrast, we found that the cortical dynamics of anesthetized mice were not scale invariant. Our results bridge empirical evidence from disparate scales and support theoretical predictions that the awake cortex operates in a dynamical regime known as criticality. The criticality hypothesis predicts that small-scale cortical dynamics are governed by the same principles as those governing larger-scale dynamics. Importantly, these scale-invariant principles also optimize certain aspects of information processing. Our results suggest that during the emergence from anesthesia, criticality arises as information processing demands increase. We expect that, as measurement tools advance toward larger scales and greater resolution, the multiscale framework offered by criticality will continue to provide quantitative predictions and insight on how neurons, microcircuits, and large-scale networks are dynamically coordinated in the brain
Quantum computation via translation-invariant operations on a chain of qubits
A scheme of universal quantum computation on a chain of qubits is described
that does not require local control. All the required operations, an Ising-type
interaction and spatially uniform simultaneous one-qubit gates, are
translation-invariant.Comment: Comment after Eq. (2) inserted, journal versio
Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction
We consider an infinite chain of particles linearly coupled to their nearest
neighbours and subject to an anharmonic local potential. The chain is assumed
weakly inhomogeneous. We look for small amplitude discrete breathers. The
problem is reformulated as a nonautonomous recurrence in a space of
time-periodic functions, where the dynamics is considered along the discrete
spatial coordinate. We show that small amplitude oscillations are determined by
finite-dimensional nonautonomous mappings, whose dimension depends on the
solutions frequency. We consider the case of two-dimensional reduced mappings,
which occurs for frequencies close to the edges of the phonon band. For an
homogeneous chain, the reduced map is autonomous and reversible, and
bifurcations of reversible homoclinics or heteroclinic solutions are found for
appropriate parameter values. These orbits correspond respectively to discrete
breathers, or dark breathers superposed on a spatially extended standing wave.
Breather existence is shown in some cases for any value of the coupling
constant, which generalizes an existence result obtained by MacKay and Aubry at
small coupling. For an inhomogeneous chain the study of the nonautonomous
reduced map is in general far more involved. For the principal part of the
reduced recurrence, using the assumption of weak inhomogeneity, we show that
homoclinics to 0 exist when the image of the unstable manifold under a linear
transformation intersects the stable manifold. This provides a geometrical
understanding of tangent bifurcations of discrete breathers. The case of a mass
impurity is studied in detail, and our geometrical analysis is successfully
compared with direct numerical simulations
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