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We use the cavity method to study parallel dynamics of disordered Ising models on a graph. In particular, we derive a set of recursive equations in single site probabilities of paths propagating along the edges of the graph. These equations are analogous to the cavity equations for equilibrium models and are exact on a tree. On graphs with exclusively… (More)

- Izaak Neri, Norbert Kern, Andrea Parmeggiani
- Physical review letters
- 2011

We study the totally asymmetric simple exclusion process (TASEP) on complex networks, as a paradigmatic model for transport subject to excluded volume interactions. Building on TASEP phenomenology on a single segment and borrowing ideas from random networks we investigate the effect of connectivity on transport. In particular, we argue that the presence of… (More)

- Izaak Neri, Norbert Kern, Andrea Parmeggiani
- Physical review letters
- 2013

We introduce the totally asymmetric simple exclusion process with Langmuir kinetics on a network as a microscopic model for active motor protein transport on the cytoskeleton, immersed in the diffusive cytoplasm. We discuss how the interplay between active transport along a network and infinite diffusion in a bulk reservoir leads to a heterogeneous matter… (More)

- Édgar Roldán, Izaak Neri, Meik Dörpinghaus, Heinrich Meyr, Frank Jülicher
- Physical review letters
- 2015

We show that the steady-state entropy production rate of a stochastic process is inversely proportional to the minimal time needed to decide on the direction of the arrow of time. Here we apply Wald's sequential probability ratio test to optimally decide on the direction of time's arrow in stationary Markov processes. Furthermore, the steady-state entropy… (More)

- I Neri, N S Skantzos, D Bollé
- 2008

We derive critical noise levels for Gallager codes on asymmetric channels as a function of the input bias and the temperature. Using a statistical mechanics approach we study the space of codewords and the entropy in the various decoding regimes. We further discuss the relation of the convergence of the messsage passing algorithm with the endogeny property… (More)

- Meik Dörpinghaus, Édgar Roldán, Izaak Neri, Heinrich Meyr, Frank Jülicher
- ArXiv
- 2015

We present an analytic method of assessing the typical performance of low-density parity-check codes on finite-state Markov channels. We show that this problem is similar to a spin-glass model on a 'small-world' lattice. We apply our methodology to binary-symmetric and binary-asymmetric channels and we provide the critical noise levels for different degrees… (More)

We study the behavior of the inverse participation ratio and the localization transition in infinitely large random matrices through the cavity method. Results are shown for two ensembles of random matrices: Laplacian matrices on sparse random graphs and fully connected Lévy matrices. We derive a critical line separating localized from extended states in… (More)

- Luca Ciandrini, Izaak Neri, Jean Charles Walter, Olivier Dauloudet, Andrea Parmeggiani
- Physical biology
- 2014

In cells and in in vitro assays the number of motor proteins involved in biological transport processes is far from being unlimited. The cytoskeletal binding sites are in contact with the same finite reservoir of motors (either the cytosol or the flow chamber) and hence compete for recruiting the available motors, potentially depleting the reservoir and… (More)

We present the exact analytical expression for the spectrum of a sparse non-hermitian random matrix ensemble, generalizing two standard results in random-matrix theory: this analytical expression constitutes a non-hermitian version of the Kesten-McKay measure as well as a sparse realization of Girko's elliptic law. Our exact result opens new perspectives in… (More)