Collective effects in cellular structure formation mediated by compliant environments: a Monte Carlo study

Compliant environments can mediate interactions between mechanically active cells like fibroblasts. Starting with a phenomenological model for the behaviour of single cells, we use extensive Monte Carlo simulations to predict non-trivial structure formation for cell communities on soft elastic substrates as a function of elastic moduli, cell density, noise and cell position geometry. In general, we find a disordered structure as well as ordered string-like and ring-like structures. The transition between ordered and disordered structures is controlled both by cell density and noise level, while the transition between string- and ring-like ordered structures is controlled by the Poisson ratio. Similar effects are observed in three dimensions. Our results suggest that in regard to elastic effects, healthy connective tissue usually is in a macroscopically disordered state, but can be switched to a macroscopically ordered state by appropriate parameter variations, in a way that is reminiscent of wound contraction or diseased states like contracture.Comment: 45 pages, 7 postscript figures included, revised version accepted for publication in Acta Biomateriali

Maximum Likelihood Decoder for Index Coded PSK Modulation for Priority Ordered Receivers

Index coded PSK modulation over an AWGN broadcast channel, for a given index coding problem (ICP) is studied. For a chosen index code and an arbitrary mapping (of broadcast vectors to PSK signal points), we have derived a decision rule for the maximum likelihood (ML) decoder. The message error performance of a receiver at high SNR is characterized by a parameter called PSK Index Coding Gain (PSK-ICG). The PSK-ICG of a receiver is determined by a metric called minimum inter-set distance. For a given ICP with an order of priority among the receivers, and a chosen $2^N$-PSK constellation we propose an algorithm to find (index code, mapping) pairs, each of which gives the best performance in terms of PSK-ICG of the receivers. No other pair of index code (of length $N$ with $2^N$ broadcast vectors) and mapping can give a better PSK-ICG for the highest priority receiver. Also, given that the highest priority receiver achieves its best performance, the next highest priority receiver achieves its maximum gain possible and so on in the specified order or priority.Comment: 9 pages, 6 figures and 2 table

Damped bounces of an isolated perfect quantum gas

The issue of the thermalization of an isolated quantum system is addressed by considering a perfect gas confined by gravity and initially trapped above a certain height. As we are interested in the behavior of truly isolated systems, we assume the gas is in a pure state of macroscopically well-defined energy. We show that, in general, for single-particle distributions, such a state is strictly equivalent to the microcanonical mixed state at the same energy. We derive an expression for the time-dependent gas density which depends on the initial gas state only via a few thermodynamic parameters. Though we consider non-interacting particles, the density relaxes into an asymptotic profile, but which is not the thermal equilibrium one determined by the gas energy and particle number