Retrieving information from a noisy "knowledge network"

We address the problem of retrieving information from a noisy version of the ``knowledge networks'' introduced by Maslov and Zhang. We map this problem onto a disordered statistical mechanics model, which opens the door to many analytical and numerical approaches. We give the replica symmetric solution, compare with numerical simulations, and finally discuss an application to real datas from the United States Senate.Comment: 10 pages, 4 figures. Writing of the last section improved; version accepted in JSTA

Techniques for the Visualization of Positional Geospatial Uncertainty

Geospatial data almost always contains some amount of uncertainty due to inaccuracies in its acquisition and transformation. While the data is commonly visualized (e.g. on digital maps), there are unanswered needs for visualizing uncertainty along with it. Most research on effectively doing this addresses uncertainty in data values at geospatial positions, e.g. water depth, human population, or land-cover classification. Uncertainty in the data’s geospatial positions themselves (positional uncertainty) has not been previously focused on in this regard. In this thesis, techniques were created for visualizing positional uncertainty using World Vector Shoreline as an example dataset. The techniques consist of a shoreline buffer zone to which visual effects such as gradients, transparency, and randomized dots were applied. They are viewed interactively via Web Map Service (WMS). In clutter testing with human subjects, a transparency-gradient technique performed the best, followed by a solid-fill technique, with a dots-density-gradient technique performing worst

Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems

Classical spin systems with nonadditive long-range interactions are studied in the microcanonical ensemble. It is expected that the entropy of such a system is identical to that of the corresponding mean-field model, which is called "exactness of the mean-field theory". It is found out that this expectation is not necessarily true if the microcanonical ensemble is not equivalent to the canonical ensemble in the mean-field model. Moreover, necessary and sufficient conditions for exactness of the mean-field theory are obtained. These conditions are investigated for two concrete models, the \alpha-Potts model with annealed vacancies and the \alpha-Potts model with invisible states.Comment: 23 pages, to appear in J. Stat. Phy

Oscillating elastic defects: competition and frustration

We consider a dynamical generalization of the Eshelby problem: the strain profile due to an inclusion or "defect" in an isotropic elastic medium. We show that the higher the oscillation frequency of the defect, the more localized is the strain field around the defect. We then demonstrate that the qualitative nature of the interaction between two defects is strongly dependent on separation, frequency and direction, changing from "ferromagnetic" to "antiferromagnetic" like behavior. We generalize to a finite density of defects and show that the interactions in assemblies of defects can be mapped to XY spin-like models, and describe implications for frustration and frequency-driven pattern transitions.Comment: 4 pages, 5 figure

Ensemble Inequivalence in Mean-field Models of Magnetism

Mean-field models, while they can be cast into an {\it extensive} thermodynamic formalism, are inherently {\it non additive}. This is the basic feature which leads to {\it ensemble inequivalence} in these models. In this paper we study the global phase diagram of the infinite range Blume-Emery-Griffiths model both in the {\it canonical} and in the {\it microcanonical} ensembles. The microcanonical solution is obtained both by direct state counting and by the application of large deviation theory. The canonical phase diagram has first order and continuous transition lines separated by a tricritical point. We find that below the tricritical point, when the canonical transition is first order, the phase diagrams of the two ensembles disagree. In this region the microcanonical ensemble exhibits energy ranges with negative specific heat and temperature jumps at transition energies. These two features are discussed in a general context and the appropriate Maxwell constructions are introduced. Some preliminary extensions of these results to weakly decaying nonintegrable interactions are presented.Comment: Chapter of the forthcoming "Lecture Notes in Physics" volume: ``Dynamics and Thermodynamics of Systems with Long Range Interactions'', T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens Eds., Lecture Notes in Physics Vol. 602, Springer (2002). (see http://link.springer.de/series/lnpp/

Lyapunov exponents as a dynamical indicator of a phase transition

We study analytically the behavior of the largest Lyapunov exponent $\lambda_1$ for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results to a simple model, proposed for the DNA denaturation, which emphasizes a first order-like or second order phase transition depending on the ratio of two length scales: this is an excellent model to characterize $\lambda_1$ as a dynamical indicator close to a phase transition.Comment: 8 Pages, 3 Figure

Elevated troponin i levels but not low grade chronic inflammation is associated with cardiac-specific mortality in stable hemodialysis patients

Background: Elevated cardiac troponin I (TnI) levels are associated with all-cause mortality in stable hemodialysis patients. Their relationship to cardiac-specific death has been inconsistent, and the reason for their elevation is not well understood. We hypothesized that elevated TnI levels in chronic stable hemodialysis patients more specifically track with cardiac mortality, and this mechanism is independent of other contributors of cardiac mortality, such as inflammation. Methods. We conducted a single-centre, cohort study of prevalent hemodialysis patients at a tertiary care hospital. Plasma TnI levels were measured with routine monthly blood tests in clinically stable patients for two consecutive months. Plasma TnI was measured by immunoassay and a value above the laboratory reference range (0.06 μg/L) was considered elevated. The primary outcome of death was adjudicated separately for this study, and classified as cardiac, non-cardiac, or unknown. Cox proportional hazard models were used to examine the association of TnI with the all-cause and cardiac-specific mortality, adjusting for potential confounders, including C-reactive protein (CRP) as a marker of inflammation. Results: Of 133 patients followed for a median of 1.7 years, there were 38 deaths (58% non-cardiac, 39% cardiac, 3% unknown). Elevated TnI was associated with adjusted HR for all-cause mortality of 2.57 (95% CI 1.30-5.09) and an adjusted HR for cardiac death of 3.14 (95% CI 1.07-9.2), after accounting for age, time on dialysis, diabetes status, prior coronary artery disease history, and C-reactive protein. Although CRP was also independently associated with all-cause mortality, it did not add prognostic information to TnI for cardiac-specific death. Conclusion: Elevated TnI levels are independently associated with cardiac and all-cause mortality in asymptomatic hemodialysis patients. The mechanism for this risk is likely independent of inflammation, but may reflect chronic subclinical myocardial injury or unmask those with subclinical atherosclerotic heart disease. Whether those with elevated TnI levels may benefit from additional investigations or more aggressive therapies to treat cardiovascular disease remains to be determined. © 2013 Alam et al.; licensee BioMed Central Ltd

Phase transitions of quasistationary states in the Hamiltonian Mean Field model

The out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell's theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell's theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.Comment: 6 pages, 7 figure

Combinatorial models of rigidity and renormalization

We first introduce the percolation problems associated with the graph theoretical concepts of $(k,l)$-sparsity, and make contact with the physical concepts of ordinary and rigidity percolation. We then devise a renormalization transformation for $(k,l)$-percolation problems, and investigate its domain of validity. In particular, we show that it allows an exact solution of $(k,l)$-percolation problems on hierarchical graphs, for $k\leq l<2k$. We introduce and solve by renormalization such a model, which has the interesting feature of showing both ordinary percolation and rigidity percolation phase transitions, depending on the values of the parameters.Comment: 22 pages, 6 figure