3,354 research outputs found
Coverage, Continuity and Visual Cortical Architecture
The primary visual cortex of many mammals contains a continuous
representation of visual space, with a roughly repetitive aperiodic map of
orientation preferences superimposed. It was recently found that orientation
preference maps (OPMs) obey statistical laws which are apparently invariant
among species widely separated in eutherian evolution. Here, we examine whether
one of the most prominent models for the optimization of cortical maps, the
elastic net (EN) model, can reproduce this common design. The EN model
generates representations which optimally trade of stimulus space coverage and
map continuity. While this model has been used in numerous studies, no
analytical results about the precise layout of the predicted OPMs have been
obtained so far. We present a mathematical approach to analytically calculate
the cortical representations predicted by the EN model for the joint mapping of
stimulus position and orientation. We find that in all previously studied
regimes, predicted OPM layouts are perfectly periodic. An unbiased search
through the EN parameter space identifies a novel regime of aperiodic OPMs with
pinwheel densities lower than found in experiments. In an extreme limit,
aperiodic OPMs quantitatively resembling experimental observations emerge.
Stabilization of these layouts results from strong nonlocal interactions rather
than from a coverage-continuity-compromise. Our results demonstrate that
optimization models for stimulus representations dominated by nonlocal
suppressive interactions are in principle capable of correctly predicting the
common OPM design. They question that visual cortical feature representations
can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure
Regular quantum graphs
We introduce the concept of regular quantum graphs and construct connected
quantum graphs with discrete symmetries. The method is based on a decomposition
of the quantum propagator in terms of permutation matrices which control the
way incoming and outgoing channels at vertex scattering processes are
connected. Symmetry properties of the quantum graph as well as its spectral
statistics depend on the particular choice of permutation matrices, also called
connectivity matrices, and can now be easily controlled. The method may find
applications in the study of quantum random walks networks and may also prove
to be useful in analysing universality in spectral statistics.Comment: 12 pages, 3 figure
Nonequilibrium many-body dynamics along a dissipative Hubbard chain: Symmetries and Quantum Monte Carlo simulations
The nonequilibrium dynamics of correlated charge transfer along a
one-dimensional chain in presence of a phonon environment is investigated
within a dissipative Hubbard model. For this generalization of the ubiquitous
spin-boson model the crucial role of symmetries is analysed in detail and
corresponding invariant subspaces are identified. It is shown that the time
evolution typically occurs in each of the disjunct subspaces independently
leading e.g. asymptotically to a non-Boltzmann equilibrium state. Based on
these findings explicit results are obtained for two interacting electrons by
means of a substantially improved real-time quantum Monte Carlo approach. In
the incoherent regime an appropriate mapping of the many-body dynamics onto an
isomorphic single particle motion allows for an approximate description of the
numerical data in terms of rate equations. These results may lead to new
control schemes of charge transport in tailored quantum systems as e.g.
molecular chains or quantum dot arrays.Comment: 13 pages, 9 figures submitted to Phys. Rev.
Topological transformations of speckles
Deterministic control of coherent random light is highly important for
information transmission through complex media. However, only a few simple
speckle transformations can be achieved through diffusers without prior
characterization. As recently shown, spiral wavefront modulation of the
impinging beam allows permuting intensity maxima and intrinsic -charged
optical vortices. Here, we study this cyclic-group algebra when combining
spiral phase transforms of charge , with - and -point-group
symmetry star-like amplitude modulations. This combination allows statistical
strengthening of permutations and controlling the period to be 3 and 4,
respectively. Phase saddle-points are shown to complete the cycle. These
results offer new tools to manipulate critical points in speckles.Comment: 14 pages, 10 figures, 4 table
Symmetries, Stability, and Control in Nonlinear Systems and Networks
This paper discusses the interplay of symmetries and stability in the
analysis and control of nonlinear dynamical systems and networks. Specifically,
it combines standard results on symmetries and equivariance with recent
convergence analysis tools based on nonlinear contraction theory and virtual
dynamical systems. This synergy between structural properties (symmetries) and
convergence properties (contraction) is illustrated in the contexts of network
motifs arising e.g. in genetic networks, of invariance to environmental
symmetries, and of imposing different patterns of synchrony in a network.Comment: 16 pages, second versio
Quantum Control Theory for State Transformations: Dark States and their Enlightenment
For many quantum information protocols such as state transfer, entanglement
transfer and entanglement generation, standard notions of controllability for
quantum systems are too strong. We introduce the weaker notion of accessible
pairs, and prove an upper bound on the achievable fidelity of a transformation
between a pair of states based on the symmetries of the system. A large class
of spin networks is presented for which this bound can be saturated. In this
context, we show how the inaccessible dark states for a given
excitation-preserving evolution can be calculated, and illustrate how some of
these can be accessed using extra catalytic excitations. This emphasises that
it is not sufficient for analyses of state transfer in spin networks to
restrict to the single excitation subspace. One class of symmetries in these
spin networks is exactly characterised in terms of the underlying graph
properties.Comment: 14 pages, 3 figures v3: rewritten for increased clarit
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