45 research outputs found
Properties of sparse random matrices over finite fields
Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit of large matrices, using techniques from the physics of disordered systems. For the case of a finite field GF(q) with prime order q, we present results for the average kernel dimension, average dimension of the eigenvector spaces and the distribution of the eigenvalues. The number of matrices for a given distribution of entries is also calculated for the general case. The significance of these results to error-correcting codes and random graphs is also discussed
Typical behavior of relays in communication channels
The typical behavior of the relay-without-delay channel under low-density parity-check coding and its multiple-unit generalization, termed the relay array, is studied using methods of statistical mechanics. A demodulate-and- forward strategy is analytically solved using the replica symmetric ansatz which is exact in the system studied at Nishimori's temperature. In particular, the typical level of improvement in communication performance by relaying messages is shown in the case of a small and a large number of relay units. © 2007 The American Physical Society
Interacting nonequilibrium systems with two temperatures
We investigate a simplified model of two fully connected magnetic systems maintained at different temperatures by virtue of being connected to two independent thermal baths while simultaneously being interconnected with each other. Using generating functional analysis, commonly used in statistical mechanics, we find exactly soluble expressions for their individual magnetization that define a two-dimensional nonlinear map, the equations of which have the same form as those obtained for densely connected equilibrium systems. Steady states correspond to the fixed points of this map, separating the parameter space into a rich set of nonequilibrium phases that we analyze in asymptotically high and low (nonequilibrium) temperature limits. The theoretical formalism is shown to revert to the classical nonequilibrium steady state problem for two interacting systems with a nonzero heat transfer between them that catalyzes a phase transition between ambient nonequilibrium states
Spin models on random graphs with controlled topologies beyond degree constraints
We study Ising spin models on finitely connected random interaction graphs
which are drawn from an ensemble in which not only the degree distribution
can be chosen arbitrarily, but which allows for further fine-tuning of
the topology via preferential attachment of edges on the basis of an arbitrary
function Q(k,k') of the degrees of the vertices involved. We solve these models
using finite connectivity equilibrium replica theory, within the replica
symmetric ansatz. In our ensemble of graphs, phase diagrams of the spin system
are found to depend no longer only on the chosen degree distribution, but also
on the choice made for Q(k,k'). The increased ability to control interaction
topology in solvable models beyond prescribing only the degree distribution of
the interaction graph enables a more accurate modeling of real-world
interacting particle systems by spin systems on suitably defined random graphs.Comment: 21 pages, 4 figures, submitted to J Phys
Statistical Mechanics Analysis of LDPC Coding in MIMO Gaussian Channels
Using analytical methods of statistical mechanics, we analyse the typical
behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with
binary inputs under LDPC network coding and joint decoding. The saddle point
equations for the replica symmetric solution are found in particular
realizations of this channel, including a small and large number of
transmitters and receivers. In particular, we examine the cases of a single
transmitter, a single receiver and the symmetric and asymmetric interference
channels. Both dynamical and thermodynamical transitions from the ferromagnetic
solution of perfect decoding to a non-ferromagnetic solution are identified for
the cases considered, marking the practical and theoretical limits of the
system under the current coding scheme. Numerical results are provided, showing
the typical level of improvement/deterioration achieved with respect to the
single transmitter/receiver result, for the various cases.Comment: 25 pages, 7 figure
Replication-based inference algorithms for hard computational problems
Inference algorithms based on evolving interactions between replicated solutions are introduced and analyzed on a prototypical NP-hard problem: the capacity of the binary Ising perceptron. The efficiency of the algorithm is examined numerically against that of the parallel tempering algorithm, showing improved performance in terms of the results obtained, computing requirements and simplicity of implementation. © 2013 American Physical Society
A mean field theory of coded CDMA systems
We present a mean field theory of code-division multiple access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems
The interplay of microscopic and mesoscopic structure in complex networks
Not all nodes in a network are created equal. Differences and similarities
exist at both individual node and group levels. Disentangling single node from
group properties is crucial for network modeling and structural inference.
Based on unbiased generative probabilistic exponential random graph models and
employing distributive message passing techniques, we present an efficient
algorithm that allows one to separate the contributions of individual nodes and
groups of nodes to the network structure. This leads to improved detection
accuracy of latent class structure in real world data sets compared to models
that focus on group structure alone. Furthermore, the inclusion of hitherto
neglected group specific effects in models used to assess the statistical
significance of small subgraph (motif) distributions in networks may be
sufficient to explain most of the observed statistics. We show the predictive
power of such generative models in forecasting putative gene-disease
associations in the Online Mendelian Inheritance in Man (OMIM) database. The
approach is suitable for both directed and undirected uni-partite as well as
for bipartite networks
Non-thermal transitions in a model inspired by moral decisions
This work introduces a model in which agents of a network act upon one another according to three different kinds of moral decisions. These decisions are based on an increasing level of sophistication in the empathy capacity of the agent, a hierarchy which we name Piaget's ladder. The decision strategy of the agents is non-rational, in the sense they are arbitrarily fixed, and the model presents quenched disorder given by the distribution of its defining parameters. An analytical solution for this model is obtained in the large system limit as well as a leading order correction for finite-size systems which shows that typical realisations of the model develop a phase structure with both continuous and discontinuous non-thermal transitions
Citrullination facilitates cross-reactivity of rheumatoid factor with non-IgG1 Fc epitopes in rheumatoid arthritis
Rheumatoid factor (RF) and anti-citrullinated protein antibodies (ACPAs) are the two most prevalent autoantibodies in rheumatoid arthritis (RA), and are thought to have distinct autoantigen targets. Whilst RF targets the Fc region of antibodies, ACPAs target a far broader spectrum of citrullinated peptides. Here we demonstrate significant sequence and structural homology between proposed RF target epitopes in IgG1 Fc and the ACPA target fibrinogen. Two of the three homologous sequences were susceptible to citrullination, and this modification, which occurs extensively in RA, permitted significant cross-reactivity of RF+ patient sera with fibrinogen in both western blots and ELISAs. Crucially, this reactivity was specific to RF as it was absent in RF− patient and healthy control sera, and could be inhibited by pre-incubation with IgG1 Fc. These studies establish fibrinogen as a common target for both RF and ACPAs, and suggest a new mechanism in RF-mediated autoimmune diseases wherein RF may act as a precursor from which the ACPA response evolves