Price of information in games of chance: A statistical physics approach.

Information in the form of , which can be stored and transferred between users, can be viewed as an intangible commodity, which can be traded in exchange for money. Determining the fair price at which a string of data should be traded is an important and open problem in many settings. In this work we develop a statistical physics framework that allows one to determine analytically the fair price of information exchanged between players in a game of chance.

Clustering coefficients for networks with higher order interactions.

We introduce a clustering coefficient for nondirected and directed hypergraphs, which we call the quad clustering coefficient. We determine the average quad clustering coefficient and its distribution in real-world hypergraphs and compare its value with those of random hypergraphs drawn from the configuration model. We find that real-world hypergraphs exhibit a nonnegligible fraction of nodes with a maximal value of the quad clustering coefficient, while we do not find such nodes in random hypergraphs.

Graphie: A network-based visual interface for the UK's primary legislation.

legislation.gov.uk is a platform that enables users to explore and navigate the many sections of the UK's legal corpus through its well-designed searching and browsing features.

Variational kinetic clustering of complex networks.

Efficiently identifying the most important communities and key transition nodes in weighted and unweighted networks is a prevalent problem in a wide range of disciplines. Here, we focus on the optimal clustering using variational kinetic parameters, linked to Markov processes defined on the underlying networks, namely, the slowest relaxation time and the Kemeny constant. We derive novel relations in terms of mean first passage times for optimizing clustering via the Kemeny constant and show that the optimal clustering boundaries have equal round-trip times to the clusters they separate.

Overcoming the complexity barrier of the dynamic message-passing method in networks with fat-tailed degree distributions.

The dynamic cavity method provides the most efficient way to evaluate probabilities of dynamic trajectories in systems of stochastic units with unidirectional sparse interactions. It is closely related to sum-product algorithms widely used to compute marginal functions from complicated global functions of many variables, with applications in disordered systems, combinatorial optimization, and computer science. However, the complexity of the cavity approach grows exponentially with the in-degrees of the interacting units, which creates a defacto barrier for the successful analysis of systems with fat-tailed in-degree distributions.

Maximal modularity and the optimal size of parliaments.

An important question in representative democracies is how to determine the optimal parliament size of a given country. According to an old conjecture, known as the cubic root law, there is a fairly universal power-law relation, with an exponent equal to 1/3, between the size of an elected parliament and the country's population. Empirical data in modern European countries support such universality but are consistent with a larger exponent.

Modelling the interplay between the CD4[Formula: see text]/CD8[Formula: see text] T-cell ratio and the expression of MHC-I in tumours.

Describing the anti-tumour immune response as a series of cellular kinetic reactions from known immunological mechanisms, we create a mathematical model that shows the CD4[Formula: see text]/CD8[Formula: see text] T-cell ratio, T-cell infiltration and the expression of MHC-I to be interacting factors in tumour elimination. Methods from dynamical systems theory and non-equilibrium statistical mechanics are used to model the T-cell dependent anti-tumour immune response. Our model predicts a critical level of MHC-I expression which determines whether or not the tumour escapes the immune response.

Position-Dependent Diffusion from Biased Simulations and Markov State Model Analysis.

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

Correlation functions, mean first passage times, and the Kemeny constant.

Markov processes are widely used models for investigating kinetic networks. Here, we collate and present a variety of results pertaining to kinetic network models in a unified framework. The aim is to lay out explicit links between several important quantities commonly studied in the field, including mean first passage times (MFPTs), correlation functions, and the Kemeny constant.

Mean first passage times in variational coarse graining using Markov state models.

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

Limiting relaxation times from Markov state models.

Markov state models (MSMs) are more and more widely used in the analysis of molecular simulations to incorporate multiple trajectories together and obtain more accurate time scale information of the slowest processes in the system. Typically, however, multiple lagtimes are used and analyzed as input parameters, yet convergence with respect to the choice of lagtime is not always possible. Here, we present a simple method for calculating the slowest relaxation time (RT) of the system in the limit of very long lagtimes.

Bridging topological and functional information in protein interaction networks by short loops profiling.

Protein-protein interaction networks (PPINs) have been employed to identify potential novel interconnections between proteins as well as crucial cellular functions. In this study we identify fundamental principles of PPIN topologies by analysing network motifs of short loops, which are small cyclic interactions of between 3 and 6 proteins. We compared 30 PPINs with corresponding randomised null models and examined the occurrence of common biological functions in loops extracted from a cross-validated high-confidence dataset of 622 human protein complexes.

Extensive parallel processing on scale-free networks.

We adapt belief-propagation techniques to study the equilibrium behavior of a bipartite spin glass, with interactions between two sets of N and P=αN spins each having an arbitrary degree, i.e., number of interaction partners in the opposite set.

Protein networks reveal detection bias and species consistency when analysed by information-theoretic methods.

We apply our recently developed information-theoretic measures for the characterisation and comparison of protein-protein interaction networks. These measures are used to quantify topological network features via macroscopic statistical properties. Network differences are assessed based on these macroscopic properties as opposed to microscopic overlap, homology information or motif occurrences.

Supersymmetric complexity in the Sherrington-Kirkpatrick model.

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