Pattern-diluted associative networks were introduced recently as models for the immune system, with nodes representing T-lymphocytes and stored patterns signalling protocols between T-and B-lymphocytes.It was shown earlier that in regime of extreme pattern dilution, a system N T Tlymphocytes can manage numberHere we study this model extensive load B = αN , also high degree agreement immunological findings.We use graph theory statistical mechanical analysis based on replica methods to show...

We adapt belief-propagation techniques to study the equilibrium behavior of a bipartite spin glass, with interactions between two sets N and P=αN spins each having an arbitrary degree, i.e., number interaction partners in opposite set. An equivalent view is then system neurons storing P diluted patterns via Hebbian learning, high storage regime. Our method allows analysis parallel pattern processing on broad class graphs, including those asymmetry heterogeneous dilution; previous replica...

A variety of enhanced statistical and numerical methods are now routinely used to extract important thermodynamic kinetic information from the vast amount complex, high-dimensional data obtained molecular simulations. For characterization properties, Markov state models, in which long-time dynamics a system is approximated by chain on discrete partition configuration space, have seen widespread use recent years. However, obtaining properties for systems with high energy barriers remains...

We apply a mean-field model of interactions between migrating barchan dunes, the CAFE model, which includes spontaneous calving, aggregation, fragmentation, and mass-exchange, yielding steady-state size distribution that can be resolved for different choices interaction parameters. The is applied to empirically measured distributions dune sizes in two swarms north circumpolar region Mars, three Morocco, one Mauritania, each containing more than 1000 bedforms. When bedforms are rescaled by...

We introduce a clustering coefficient for nondirected and directed hypergraphs, which we call the quad coefficient. determine average its distribution in real-world hypergraphs compare value with those of random drawn from configuration model. find that exhibit nonnegligible fraction nodes maximal coefficient, while do not such hypergraphs. Interestingly, these highly clustered can have large degrees be incident to hyperedges cardinality. Moreover, are observed an analysis based on pairwise...

We study the tailoring of structured random graph ensembles to real networks, with objective generating precise and practical mathematical tools for quantifying comparing network topologies macroscopically, beyond level degree statistics.Our family can produce graphs any prescribed distribution degree-degree correlation function, its control parameters be calculated fully analytically, as a result we calculate (asymptotically) formulae entropies complexities, information-theoretic distances...

Associative network models featuring multi-tasking properties have been introduced recently and studied in the low load regime, where number P of simultaneously retrievable patterns scales with N nodes as ∼ log .In addition to their relevance artificial intelligence, these are increasingly important immunology, stored represent strategies fight pathogens lymphocyte clones.They allow us understand crucial ability immune system respond multiple distinct antigen invasions.Here we develop...

Abstract Protein-protein interaction networks (PPINs) have been employed to identify potential novel interconnections between proteins as well crucial cellular functions. In this study we fundamental principles of PPIN topologies by analysing network motifs short loops, which are small cyclic interactions 3 and 6 proteins. We compared 30 PPINs with corresponding randomised null models examined the occurrence common biological functions in loops extracted from a cross-validated...

Markov state models (MSMs) provide some of the simplest mathematical and physical descriptions dynamical thermodynamical properties complex systems. However, typically, large dimensionality biological systems studied makes them prohibitively expensive to work in fully Markovian regimes. In this case, coarse graining can be introduced capture key processes-slow degrees system-and reduce dimension problem. Here, we introduce several possible options for such graining, including previously...

We apply our recently developed information-theoretic measures for the characterisation and comparison of protein–protein interaction networks. These are used to quantify topological network features via macroscopic statistical properties. Network differences assessed based on these properties as opposed microscopic overlap, homology information or motif occurrences. present results a large–scale analysis Precise null models in analyses, allowing reliable interpretation results. By...

By using a supersymmetric approach we compute the complexity of metastable states in Sherrington-Kirkpatrick spin-glass model. We prove that is exactly equal to Legendre transform thermodynamic free energy, thus providing recipe find once energy known. Our results suggest supersymmetry may be useful tool for calculation entropy generic glassy systems.

We use mathematical methods from the theory of tailored random graphs to study systematically effects sampling on topological features large biological signalling networks. Our aim in doing so is increase our quantitative understanding relation between true networks and imperfect often biased samples these that are reported public data repositories used by biomedical scientists. derive exact explicit formulae for degree distributions correlation kernels sampled networks, terms underlying...

The two-star model is the simplest exponential random graph that displays complex behavior, such as degeneracy and phase transition. Despite its importance, this has been solved only in regime of dense connectivity. In work we solve finite connectivity regime, far more prevalent real world networks. We show undergoes a condensation transition from liquid to condensate along critical line corresponding, ensemble parameters space, Erdös–Rényi (ER) graphs. fluid can produce graphs with narrow...

We study the out-of-equilibrium dynamics of spherical ferromagnet after a quench to its critical temperature. calculate correlation and response functions for spin observables which probe length scales much larger than lattice spacing but smaller system size, find that asymptotic fluctuation–dissipation ratio (FDR) X∞ is same as local observables. This consistent with our earlier results Ising model in dimension d = 1 2. also check bond observables, both long range, give FDR. In second part...

We study the resilience of complex networks against attacks in which nodes are targeted intelligently, but where disabling a node has cost to attacker depends on its degree.Attackers have meet these costs with limited resources, constrains their actions.A network's integrity is quantified terms efficacy process that it supports.We calculate how optimal attack strategy and most attack-resistant network degree statistics depend removal function resources.The intelligent found strongly faced by...

Markov processes are widely used models for investigating kinetic networks. Here we collate and present a variety of results pertaining to network models, in unified framework. The aim is lay out explicit links between several important quantities commonly studied the field, including mean first passage times (MFPTs), correlation functions Kemeny constant, highlight some subtleties which often overlooked literature, while providing new insights. Results include (i) simple physical...

The similarity between neural and (adaptive) immune networks has been known for decades, but so far we did not understand the mechanism that allows system, unlike associative networks, to recall execute a large number of memorized defense strategies in parallel. explanation turns out lie network topology. Neurons interact typically with other neurons, whereas interactions among lymphocytes are very specific, described by graphs finite connectivity. In this paper use replica techniques solve...

We consider a simplified model for gene regulation, where expression is regulated by transcription factors (TFs), which are single proteins or protein complexes. Proteins in turn synthesised from expressed genes, creating feedback loop of regulation. This leads to directed bipartite network link TF exists if the codes contributing TF, and regulates gene. Both genes TFs modelled as binary variables, indicate, respectively, whether not, not. scenario be synthesised, all its must expressed....

In this work we propose a novel method to calculate mean first-passage times (MFPTs) for random walks on graphs, based dimensionality reduction technique Markov State Models, known as local-equilibrium (LE). We show that broad class of which includes trees, LE coarse-graining preserves the MFPTs between certain nodes, upon making suitable choice coarse-grained states (or clusters). prove relation is exact graphs can be into one-dimensional lattice where each cluster connects only through...

Dynamic processes of interacting units on a network are out equilibrium in general. In the case directed tree, dynamic cavity method provides an efficient tool that characterises trajectory process for linear threshold model. However, because computational complexity method, analysis has been limited to systems where largest number neighbours is small. We devise implementation which substantially reduces with discrete couplings. Our approach opens up possibility investigate properties...

We construct a model of cell reprogramming (the conversion fully differentiated cells to state pluripotency, known as induced pluripotent stem cells, or iPSCs) which builds on key elements biology viz. cycles and lineages. Although has been demonstrated experimentally, much the underlying processes governing fate decisions remain unknown. This work aims bridge this gap by modelling types set hierarchically related dynamical attractors representing cycles. Stages cycle are characterised...

Boolean networks are popular models for gene regulation, where genes regarded as binary units, that can be either expressed or not, each updated at regular time intervals according to a random function of its neighbouring genes.Stable expression profiles, corresponding cell types, attractors the network dynamics.However, character updates does not allow link explicitly existence biological mechanism with which interact.We propose bipartite approach integrates and regulatory proteins...