Statistical physics of irregular low-density parity-check codes

Low-density parity-check codes with irregular constructions have recently been shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulation results. We compare the performance of irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.

Subthalamic nucleus neurones in slices from 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine-lesioned mice show irregular, dopamine-reversible firing pattern changes, but without synchronous activity

The loss of dopamine in idiopathic or animal models of Parkinson's disease induces synchronized low-frequency oscillatory burst-firing in subthalamic nucleus neurones. We sought to establish whether these firing patterns observed in vivo were preserved in slices taken from dopamine-depleted animals, thus establishing a role for the isolated subthalamic-globus pallidus complex in generating the pathological activity. Mice treated with 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) showed significant reductions of over 90% in levels of dopamine as measured in striatum by high pressure liquid chromatography. Likewise, significant reductions in tyrosine hydroxylase immunostaining within the striatum (>90%) and tyrosine hydroxylase positive cell numbers (65%) in substantia nigra were observed. Compared with slices from intact mice, neurones in slices from MPTP-lesioned mice fired significantly more slowly (mean rate of 4.2 Hz, cf. 7.2 Hz in control) and more irregularly (mean coefficient of variation of inter-spike interval of 94.4%, cf. 37.9% in control). Application of ionotropic glutamate receptor antagonists 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) and 2-amino-5-phosphonopentanoic acid (AP5) and the GABAA receptor antagonist picrotoxin caused no change in firing pattern. Bath application of dopamine significantly increased cell firing rate and regularized the pattern of activity in cells from slices from both MPTP-treated and control animals. Although the absolute change was more modest in control slices, the maximum dopamine effect in the two groups was comparable. Indeed, when taking into account the basal firing rate, no differences in the sensitivity to dopamine were observed between these two cohorts. Furthermore, pairs of subthalamic nucleus cells showed no correlated activity in slices from either control (21 pairs) or MPTP-treated animals (20 pairs). These results indicate that the isolated but interconnected subthalamic-globus pallidus network is not itself sufficient to generate the aberrant firing patterns in dopamine-depleted animals. More likely, inputs from other regions, such as the cortex, are needed to generate pathological oscillatory activity. © 2006 IBRO.

Validation of a multi-component digital dissolution model for irregular particles

A new mesoscale simulation model for solids dissolution based on an computationally efficient and versatile digital modelling approach (DigiDiss) is considered and validated against analytical solutions and published experimental data for simple geometries. As the digital model is specifically designed to handle irregular shapes and complex multi-component structures, use of the model is explored for single crystals (sugars) and clusters. Single crystals and the cluster were first scanned using X-ray microtomography to obtain a digital version of their structures. The digitised particles and clusters were used as a structural input to digital simulation. The same particles were then dissolved in water and the dissolution process was recorded by a video camera and analysed yielding: the overall dissolution times and images of particle size and shape during the dissolution. The results demonstrate the coherence of simulation method to reproduce experimental behaviour, based on known chemical and diffusion properties of constituent phase. The paper discusses how further sophistications to the modelling approach will need to include other important effects such as complex disintegration effects (particle ejection, uncertainties in chemical properties). The nature of the digital modelling approach is well suited to for future implementation with high speed computation using hybrid conventional (CPU) and graphical processor (GPU) systems.