A long-standing hypothesis at the interface of physics and neuroscience is that neural networks self-organize to the critical point of a phase transition, thereby optimizing aspects of sensory information processing1–3. This idea is partially supported by strong evidence for critical dynamics observed in the cerebral cortex4–10, but the impact of sensory input on these dynamics is largely unkno...

This paper presents a novel analytical technique of examining the avalanche characteristics of cryptographic substitution boxes (s-boxes) using the Walsh Hadamard spectral analysis of their Boolean maps. Avalanche is a desirable cryptographic property that is necessary to ensure that a cipher is not susceptible to statistical attacks and small difference between two plaintexts results in a sign...

In many studies of self-organized criticality (SOC), branching processes were used to model the dynamics of the activity of the system during avalanches. This mathematical simplification was also adopted when investigating systems with a complicated connection topology including recurrent and subthreshold interactions. However, none of these studies really analyzed whether this convenient appro...

We present a detailed analytical and numerical study of the avalanche statistics of the continuous damage fiber bundle model. In the model, linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. Varying the two parameters of the model, i.e. the maximum number of local failures and the degree of stiffness reduction in singl...

Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with scale-free features typical of critical behaviour. The stochastic version the celebrated Wilson-Cowan model has been widely studied as a system spiking neurons reproducing non-trivial neural activity, from avalanche dynamics to oscillatory behaviours. However, what extent such phenomena are related presence ...

The study of critical phenomena and universal power laws has been one of the central advances in statistical mechanics during the second half of the past century, explaining traditional thermodynamic critical points1, avalanche behaviour near depinning transitions2,3 and a wide variety of other phenomena4. Scaling, universality and the renormalization group claim to predict all behaviour at lon...

Numerical modeling of correlated single-electron tunneling in uniform two-dimensional arrays of small conducting islands separated by tunnel junctions shows the possibility of soliton-antisoliton avalanches. Though the time duration of any avalanche and the total charge, DQ5ne , transferred across the array during the avalanche are always finite in arrays with length N larger than certain criti...

In this paper, we examine the avalanche characteristics of private-key block ciphers constructed using a DES-like architecture. Avalanche is a desirable cryptographic property that is necessary to ensure that a small diierence between two plaintexts results in a seemingly random diierence between the two corresponding ciphertexts. In order to examine the behaviour of DES-like ciphers in relatio...

Spontaneous activity of cortex in vitro and in vivo has been shown to organize as neuronal avalanches. Avalanches are cascades of neuronal activity that exhibit a power law in their size and duration distribution, typical features of balanced systems in a critical state. Recently it has been shown that the distribution of quiet times between consecutive avalanches in rat cortex slice cultures d...