32 research outputs found
Random trimer tilings
We study tilings of the square lattice by linear trimers. For a cylinder of
circumference m, we construct a conserved functional of the base of the
tilings, and use this to block-diagonalize the transfer matrix. The number of
blocks increases exponentially with m. The dimension of the ground-state block
is shown to grow as (3 / 2^{1/3})^m. We numerically diagonalize this block for
m <= 27, obtaining the estimate S = 0.158520 +- 0.000015 for the entropy per
site in the thermodynamic limit. We present numerical evidence that the
continuum limit of the model has conformal invariance. We measure several
scaling dimensions, including those corresponding to defects of dimers and
L-shaped trimers. The trimer tilings of a plane admits a two-dimensional height
representation. Monte Carlo simulations of the height variables show that the
height-height correlations grows logarithmically at large separation, and the
orientation-orientation correlations decay as a power law.Comment: 12 pages, 11 figure
Transport in deformed centrosymmetric networks
Centrosymmetry often mediates Perfect State Transfer (PST) in various complex
systems ranging from quantum wires to photosynthetic networks. We introduce the
Deformed Centrosymmetric Ensemble (DCE) of random matrices, , where is centrosymmetric while is
skew-centrosymmetric. The relative strength of the prompts the system
size scaling of the control parameter as . We
propose two quantities, and , quantifying centro-
and skewcentro-symmetry, respectively, exhibiting second order phase
transitions at and . In
addition, DCE posses an ergodic transition at . Thus
equipped with a precise control of the extent of centrosymmetry in DCE, we
study the manifestation of on the transport properties of complex
networks. We propose that such random networks can be constructed using the
eigenvectors of and establish that the maximum transfer fidelity,
, is equivalent to the degree of centrosymmetry, .Comment: 13 pages, 5 figure
Adaptation to changes in higher-order stimulus statistics in the salamander retina
Adaptation in the retina is thought to optimize the encoding of natural light signals into sequences of spikes sent to the brain. While adaptive changes in retinal processing to the variations of the mean luminance level and second-order stimulus statistics have been documented before, no such measurements have been performed when higher-order moments of the light distribution change. We therefore measured the ganglion cell responses in the tiger salamander retina to controlled changes in the second (contrast), third (skew) and fourth (kurtosis) moments of the light intensity distribution of spatially uniform temporally independent stimuli. The skew and kurtosis of the stimuli were chosen to cover the range observed in natural scenes. We quantified adaptation in ganglion cells by studying linear-nonlinear models that capture well the retinal encoding properties across all stimuli. We found that the encoding properties of retinal ganglion cells change only marginally when higher-order statistics change, compared to the changes observed in response to the variation in contrast. By analyzing optimal coding in LN-type models, we showed that neurons can maintain a high information rate without large dynamic adaptation to changes in skew or kurtosis. This is because, for uncorrelated stimuli, spatio-temporal summation within the receptive field averages away non-gaussian aspects of the light intensity distribution
Relaxation dynamics of the Kuramoto model with uniformly distributed natural frequencies
The Kuramoto model describes a system of globally coupled phase-only
oscillators with distributed natural frequencies. The model in the steady state
exhibits a phase transition as a function of the coupling strength, between a
low-coupling incoherent phase in which the oscillators oscillate independently
and a high-coupling synchronized phase. Here, we consider a uniform
distribution for the natural frequencies, for which the phase transition is
known to be of first order. We study how the system close to the phase
transition in the supercritical regime relaxes in time to the steady state
while starting from an initial incoherent state. In this case, numerical
simulations of finite systems have demonstrated that the relaxation occurs as a
step-like jump in the order parameter from the initial to the final steady
state value, hinting at the existence of metastable states. We provide
numerical evidence to suggest that the observed metastability is a finite-size
effect, becoming an increasingly rare event with increasing system size.Comment: 4 pages, 5 figures; v2: 12 pages, 9 figures, published versio
Parameter estimation in spatially extended systems: The Karhunen-Loeve and Galerkin multiple shooting approach
Parameter estimation for spatiotemporal dynamics for coupled map lattices and
continuous time domain systems is shown using a combination of multiple
shooting, Karhunen-Loeve decomposition and Galerkin's projection methodologies.
The resulting advantages in estimating parameters have been studied and
discussed for chaotic and turbulent dynamics using small amounts of data from
subsystems, availability of only scalar and noisy time series data, effects of
space-time parameter variations, and in the presence of multiple time-scales.Comment: 11 pages, 5 figures, 4 Tables Corresponding Author - V. Ravi Kumar,
e-mail address: [email protected]