Related papers: Echo State Condition at the Critical Point
We construct a class of quantum channels in arbitrary dimensions for which entanglement improves the performance of the channel. The channels have correlated noise and when the level of correlation passes a critical value we see a sharp…
In this paper we extend our previous results on the connectivity functions and pressure of the Random Cluster Model in the highly subcritical phase and in the highly supercritical phase, originally proved only on the cubic lattice $\Z^d$,…
In this paper we show that in a multiclass Markovian network with unit rate servers, the condition that the average load $\rho$ at every server is less than unity is indeed sufficient for the stability or positive recurrence for \emph{any}…
Given a complex network, its \emph{L-}paths correspond to sequences of $L+1$ distinct nodes connected through $L$ distinct edges. The \emph{L-}conditional expansion of a complex network can be obtained by connecting all its pairs of nodes…
To better understand the correlation between network topological features and the robustness of network controllability in a general setting, this paper suggests a practical approach to searching for optimal network topologies with given…
A recent analysis of a model of iterative neural network in Hilbert spaces established fundamental properties of such networks, such as existence of the fixed points sets, convergence analysis, and Lipschitz continuity. Building on these…
We consider discrete-space continuous-time Markov models of reaction networks and provide sufficient conditions for the following stability condition to hold: each state in a closed, irreducible component of the state space is positive…
Dynamical criticality has been shown to enhance information processing in dynamical systems, and there is evidence for self-organized criticality in neural networks. A plausible mechanism for such self-organization is activity dependent…
The reliability function gives the rate of exponential convergence to zero of the error probability in a communication channel. In this paper bounds for the reliability function of a quantum pure state channel are given, reminiscent of the…
We introduce a new model, the Recurrent Entity Network (EntNet). It is equipped with a dynamic long-term memory which allows it to maintain and update a representation of the state of the world as it receives new data. For language…
In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…
The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years,…
A probabilistic framework to study the dependence structure induced by deterministic discrete-time state-space systems between input and output processes is introduced. General sufficient conditions are formulated under which output…
In this paper, throughput achieved in cognitive radio channels with finite blocklength codes under buffer limitations is studied. Cognitive users first determine the activity of the primary users' through channel sensing and then initiate…
Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value \epsilon chosen at or just above the percolation threshold…
Many real-world networks are coupled together to maintain their normal functions. Here we study the robustness of multiplex networks with interdependent and interconnected links under k-core percolation, where a node fails when it connects…
Echo-State Networks and Reservoir Computing have been studied for more than a decade. They provide a simpler yet powerful alternative to Recurrent Neural Networks, every internal weight is fixed and only the last linear layer is trained.…
A recurrent idea in the study of complex systems is that optimal information processing is to be found near bifurcation points or phase transitions. However, this heuristic hypothesis has few (if any) concrete realizations where a standard…
ResNets constrained to be bi-Lipschitz, that is, approximately distance preserving, have been a crucial component of recently proposed techniques for deterministic uncertainty quantification in neural models. We show that theoretical…
We identify the role of equal strength interference links as bottlenecks on the ergodic sum capacity of a $K$ user phase-fading interference network, i.e., an interference network where the fading process is restricted primarily to…