Random acyclic networks

Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the model's properties, including connection probabilities and component sizes, as well as a fast algorithm for simulating the model on a computer. We compare the predictions of the model to a real-world network of citations between physics papers and find surprisingly good agreement, suggesting that the structure of the real network may be quite well described by the random graph.Comment: 4 pages, 2 figure

Earthquake forecasting based on data assimilation: sequential Monte Carlo methods for renewal point processes

Data assimilation is routinely employed in meteorology, engineering and computer sciences to optimally combine noisy observations with prior model information for obtaining better estimates of a state, and thus better forecasts, than achieved by ignoring data uncertainties. Earthquake forecasting, too, suffers from measurement errors and partial model information and may thus gain significantly from data assimilation. We present perhaps the first fully implementable data assimilation method for earthquake forecasts generated by a point-process model of seismicity. We test the method on a synthetic and pedagogical example of a renewal process observed in noise, which is relevant for the seismic gap hypothesis, models of characteristic earthquakes and recurrence statistics of large quakes inferred from paleoseismic data records. To address the non-Gaussian statistics of earthquakes, we use sequential Monte Carlo methods, a set of flexible simulation-based methods for recursively estimating arbitrary posterior distributions. We perform extensive numerical simulations to demonstrate the feasibility and benefits of forecasting earthquakes based on data assimilation

Data assimilation insights on selecting the most valuable atmospheric measurements

We discuss how objective guidance on selecting the most valuable atmospheric measurements on future Mars spacecraft missions can be provided through already developed Martian atmospheric data assimilation systems, and in particular through Observing System Simulation Experiments (OSSEs) which are widely used to design instruments for the Earth’s atmosphere

Cognitive function and oral health among ageing adults

Objectives: There is inconclusive evidence that cognitive function is associated with oral health in older adults. This study investigated the association between cognitive function and oral health among older adults in England. Methods: This longitudinal cohort study included 4416 dentate participants aged 50 years or older in the English Longitudinal Study of Ageing during 2002‐2014. Cognitive function was assessed at baseline in 2002/2003 using a battery of cognitive function tests. The self‐reported number of teeth remaining and self‐rated general oral health status was reported in 2014/2015. Ordinal logistic regression was applied to model the association between cognitive function at baseline and tooth loss or self‐rated oral health. Results: Cognitive function at baseline was negatively associated with the risk of tooth loss (per each 1 standard deviation lower in cognitive function score, OR: 1.13, 95% CI: 1.05‐1.21). When cognitive function score was categorized into quintiles, there was a clear gradient association between cognitive function and tooth loss (P‐trend = 0.003); people in the lowest quintile of cognitive function had higher risk of tooth loss than those in the highest quintile (OR: 1.39, 95% CI: 1.12‐1.74). A similar magnitude and direction of association were evident between cognitive function and self‐rated oral health. Conclusion: This longitudinal study in an English ageing population has demonstrated that poor cognitive function at early stage was associated with poorer oral health and higher risk of tooth loss in later life. The gradient relationship suggests that an improvement in cognitive function could potentially improve oral health and reduce the risk of tooth loss in the ageing population

Resonant inelastic x-ray scattering study of charge excitations in La2CuO4

We report a resonant inelastic x-ray scattering study of the dispersion relations of charge transfer excitations in insulating La$_2$CuO$_4$. These data reveal two peaks, both of which show two-dimensional characteristics. The lowest energy excitation has a gap energy of $\sim 2.2$ eV at the zone center, and a dispersion of $\sim 1$ eV. The spectral weight of this mode becomes dramatically smaller around ($\pi$, $\pi$). The second peak shows a smaller dispersion ($\sim 0.5$ eV) with a zone-center energy of $\sim 3.9$ eV. We argue that these are both highly dispersive exciton modes damped by the presence of the electron-hole continuum.Comment: 5 pages, 3 figure

The optical depth of the Universe to ultrahigh energy cosmic ray scattering in the magnetized large scale structure

This paper provides an analytical description of the transport of ultrahigh energy cosmic rays in an inhomogeneously magnetized intergalactic medium. This latter is modeled as a collection of magnetized scattering centers such as radio cocoons, magnetized galactic winds, clusters or magnetized filaments of large scale structure, with negligible magnetic fields in between. Magnetic deflection is no longer a continuous process, it is rather dominated by scattering events. We study the interaction between high energy cosmic rays and the scattering agents. We then compute the optical depth of the Universe to cosmic ray scattering and discuss the phenomological consequences for various source scenarios. For typical parameters of the scattering centers, the optical depth is greater than unity at 5x10^{19}eV, but the total angular deflection is smaller than unity. One important consequence of this scenario is the possibility that the last scattering center encountered by a cosmic ray be mistaken with the source of this cosmic ray. In particular, we suggest that part of the correlation recently reported by the Pierre Auger Observatory may be affected by such delusion: this experiment may be observing in part the last scattering surface of ultrahigh energy cosmic rays rather than their source population. Since the optical depth falls rapidly with increasing energy, one should probe the arrival directions of the highest energy events beyond 10^{20}eV on an event by event basis to circumvent this effect.Comment: version to appear in PRD; substantial improvements: extended introduction, sections added on angular images and on direction dependent effects with sky maps of optical depth, enlarged discussion of Auger results (conclusions unchanged); 27 pages, 9 figure

An investigation of the RWPE prostate derived family of cell lines using FTIR spectroscopy

Interest in developing robust, quicker and easier diagnostic tests for cancer has lead to an increased use of Fourier transform infrared (FTIR) spectroscopy to meet that need. In this study we present the use of different experimental modes of infrared spectroscopy to investigate the RWPE human prostate epithelial cell line family which are derived from the same source but differ in their mode of transformation and their mode of invasive phenotype. Importantly, analysis of the infrared spectra obtained using different experimental modes of infrared spectroscopy produces similar results. The RWPE family of cell lines can be separated into groups based upon the method of cell transformation rather than the resulting invasiveness/aggressiveness of the cell line. The study also demonstrates the possibility of using a genetic algorithm as a possible standardised pre-processing step and raises the important question of the usefulness of cell lines to create a biochemical model of prostate cancer progression

Variational assimilation of Lagrangian data in oceanography

We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional space-time circulation of the ocean. This problem is solved using the four-dimensional variational technique and the adjoint method. In this problem the control vector is chosen as being the initial state of the dynamical system. The observed variables, namely the positions of the floats, are expressed as a function of the control vector via a nonlinear observation operator. This method has been implemented and has the ability to reconstruct the main patterns of the oceanic circulation. Moreover it is very robust with respect to increase of time-sampling period of observations. We have run many twin experiments in order to analyze the sensitivity of our method to the number of floats, the time-sampling period and the vertical drift level. We compare also the performances of the Lagrangian method to that of the classical Eulerian one. Finally we study the impact of errors on observations.Comment: 31 page

Testing the robustness of laws of polysemy and brevity versus frequency

The pioneering research of G.K. Zipf on the relationship between word frequency and other word features led to the formulation of various linguistic laws. Here we focus on a couple of them: the meaning-frequency law, i.e. the tendency of more frequent words to be more polysemous, and the law of abbreviation, i.e. the tendency of more frequent words to be shorter. Here we evaluate the robustness of these laws in contexts where they have not been explored yet to our knowledge. The recovery of the laws again in new conditions provides support for the hypothesis that they originate from abstract mechanisms.Peer ReviewedPostprint (author's final draft