All posts under category "Condensed Matter / Cond-Mat.dis-Nn"
The statistical distribution of levels of an integrable system is claimed to be a Poisson distribution. In this paper, we numerically generate an ensemble of N dimensional random diagonal matrices as a model for regular systems. We evaluate the corresponding nearest-neighbor spacing (NNS) distributi
Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in mathematical graph theory, and in computer science. Counting pro
We show that heterogeneous degree distributions in observed scale-free topologies of complex networks can emerge as a consequence of the exponential expansion of hidden hyperbolic space. Fermi-Dirac statistics provides a physical interpretation of hyperbolic distances as energies of links. The hidde
The effects of the finite size of the network on the evolutionary dynamics of a Boolean network are analyzed. In the model considered, Boolean networks evolve via a competition between nodes that punishes those in the majority. It is found that finite size networks evolve in a fundamentally differen
Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of distributed computation. However, in many real networks nodes comm
We consider a version of random motion of hard core particles on the semi-lattice $ 1, 2, 3,...$, where in each time instant one of three possible events occurs, viz., (a) a randomly chosen particle hops to a free neighboring site, (b) a particle is created at the origin (namely, at site 1) provided
The shear strength and stick-slip behavior of a rough rock joint are analyzed using the complex network approach. We develop a network approach on correlation patterns of void spaces of an evolvable rough fracture (crack type II). Correlation among networks properties with the hydro -mechanical attr
Molecule-based devices are envisioned to complement silicon devices by providing new functions or already existing functions at a simpler process level and at a lower cost by virtue of their self-organization capabilities, moreover, they are not bound to von Neuman architecture and this may open the
We point out the connection between mathematical knot theory and spin glass/search problem. In particular, we present a statistical mechanical formulation of the problem of computing a knot invariant; p-colorability problem, which provides an algorithm to find the solution. The method also allows on
The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean Networks (RBNs) are commonly used a simple generic model for certain dynamics of complex systems. Traditionally, RBNs are interconnected ra
Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that restricts network dynamics to gradient-like flows. In contrast, bio
The existence of a phase transition with diverging susceptibility in batch Minority Games (MGs) is the mark of informationally efficient regimes and is linked to the specifics of the agents' learning rules. Here we study how the standard scenario is affected in a mixed population game in which agent
We summarize several decades of work in finding values for the percolation threshold p_c for site percolation on the square lattice, the universal correction-to-scaling exponent Omega, and the susceptibility amplitude ratio C^+/C^-, in two dimensions. Recent studies have yielded the precise values p
Irreversible opinion spreading phenomena are studied on small-world networks generated from 2D regular lattices by means of the magnetic Eden model, a nonequilibrium kinetic model for the growth of binary mixtures in contact with a thermal bath. In this model, the opinion or decision of an individua
In an informal way, a number of thoughts on the financial crisis 2008 are presented from a physicist's viewpoint, considering the problem as a nonergodicity transition of a spin-glass type of system. Some tentative suggestions concerning the way out of the crisis are also discussed, concerning Keyne
We study a system composed from two interdependent networks A and B, where a fraction of the nodes in network A depends on the nodes of network B and a fraction of the nodes in network B depends on the nodes of network A. Due to the coupling between the networks when nodes in one network fail they c
An error correcting code using a tree-like multilayer perceptron is proposed. An original message $mbi{s}^0$ is encoded into a codeword $boldmath{y}_0$ using a tree-like committee machine (committee tree) or a tree-like parity machine (parity tree). Based on these architectures, several schemes feat
Social groups are fundamental building blocks of human societies. While our social interactions have always been constrained by geography, it has been impossible, due to practical difficulties, to evaluate the nature of this restriction on social group structure. We construct a social network of ind
With the proliferation of ultra-high-speed mobile networks and internet-connected devices, along with the rise of artificial intelligence, the world is generating exponentially increasing amounts of data - data that needs to be processed in a fast, efficient and smart way. These developments are pus
We investigate the electrical current and flow (number of parallel paths) between two sets of n sources and n sinks in complex networks. We derive analytical formulas for the average current and flow as a function of n. We show that for small n, increasing n improves the total transport in the netwo
We investigate the Multiple Equilibria phase of generalized Lotka-Volterra dynamics with random, non-reciprocal interactions. We compute the topological complexity of equilibria, which quantifies how rapidly the number of equilibria of the dynamical equations grows with the total number of species.
We introduce a robust, error-tolerant adaptive training algorithm for generalized learning paradigms in high-dimensional superposed quantum networks, or emph{adaptive quantum networks}. The formalized procedure applies standard backpropagation training across a coherent ensemble of discrete topologi
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