Related papers: Fitness Fluctuations and Correlation Time Scaling …
We consider biological evolution as described within the Bak and Sneppen 1993 model. We exhibit, at the self-organized critical state, a power-law sensitivity to the initial conditions, calculate the associated exponent, and relate it to…
[Abridged] A sharp cut-off in the primordial scalar power spectrum on large scales has been known to improve the fit to the cosmic microwave background (CMB) data when compared to the more standard, nearly scale invariant power spectrum…
We consider a class of models describing the dynamics of $N$ Boolean variables, where the time evolution of each depends on the values of $K$ of the other variables. Previous work has considered models with dissipative dynamics. Here we…
The $1/f$-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitute evidences of criticality in neuronal systems. Recent in vitro studies…
We describe numerical simulations of the stochastic diffusion equation with a conserved charge. We focus on the dynamics in the vicinity of a critical point in the Ising universality class. The model we consider is expected to describe the…
The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and…
We study erratically moving spatial structures that are found in a driven interface in a random medium at the depinning threshold. We introduce a bond-disordered variant of the Sneppen model and study the effect of extremal dynamics on the…
A approach of finite size scaling theory for discontinous percolation with multiple giant clusters is developed in this paper. The percolation in generalized Bohman-Frieze-Wormald (BFW) model has already been proved to be discontinuous…
We revisit the number theoretic division model of self-organized criticality [Phys. Rev. Lett. 101, 158702 (2008)]. The model consists of a pool of $M-1$ ordered integers $\{2, 3, \cdots, M\}$, and the aim is to dynamically form a primitive…
As is well known, structure formation in the Universe at times after decoupling can be described by hydrodynamic equations. These are shown here to be equivalent to a generalization of the stochastic Kardar--Parisi--Zhang equation with…
We study probability distributions of waves of topplings in the Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>=2. Waves represent relaxation processes which do not contain multiple toppling events. We investigate bulk…
We propose a new method to analyze fluctuations in the strength function phenomena in highly excited nuclei. Extending the method of multifractal analysis to the cases where the strength fluctuations do not obey power scaling laws, we…
Surface growth in random media is usually governed by both the surface tension and the random local forces. Simulations on lattices mimic the former by imposing a maximum gradient $m$ on the surface heights, and the latter by site-dependent…
We study the dynamics of the Bak-Sneppen model on small-world networks. For each site in the network, we define a ``connectance,'' which measures the distance to all other sites. We find radically different patterns of activity for…
See the updated version arXiv:nlin/0111028.
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…
The dynamics of many-body systems spanning condensed matter, cosmology, and beyond is hypothesized to be universal when the systems cross continuous phase transitions. The universal dynamics is expected to satisfy a scaling symmetry of…
Stochastic fluctuations are central to the understanding of extinction dynamics. In the context of population models they allow for the description of the transition from the vicinity of a non-trivial fixed point of the deterministic…
We present force-clamp data on the collapse of ubiquitin polyproteins in response to a quench in the force. These nonequilibrium trajectories are analyzed using a general method based on a diffusive assumption of the end-to-end length to…