On the Statistical Errors of RADAR Location Sensor Networks with Built-In Wi-Fi Gaussian Linear Fingerprints

The expected errors of RADAR sensor networks with linear probabilistic location fingerprints inside buildings with varying Wi-Fi Gaussian strength are discussed. As far as we know, the statistical errors of equal and unequal-weighted RADAR networks have been suggested as a better way to evaluate the behavior of different system parameters and the deployment of reference points (RPs). However, up to now, there is still not enough related work on the relations between the statistical errors, system parameters, number and interval of the RPs, let alone calculating the correlated analytical expressions of concern. Therefore, in response to this compelling problem, under a simple linear distribution model, much attention will be paid to the mathematical relations of the linear expected errors, number of neighbors, number and interval of RPs, parameters in logarithmic attenuation model and variations of radio signal strength (RSS) at the test point (TP) with the purpose of constructing more practical and reliable RADAR location sensor networks (RLSNs) and also guaranteeing the accuracy requirements for the location based services in future ubiquitous context-awareness environments. Moreover, the numerical results and some real experimental evaluations of the error theories addressed in this paper will also be presented for our future extended analysis

Laplace deconvolution on the basis of time domain data and its application to Dynamic Contrast Enhanced imaging

In the present paper we consider the problem of Laplace deconvolution with noisy discrete non-equally spaced observations on a finite time interval. We propose a new method for Laplace deconvolution which is based on expansions of the convolution kernel, the unknown function and the observed signal over Laguerre functions basis (which acts as a surrogate eigenfunction basis of the Laplace convolution operator) using regression setting. The expansion results in a small system of linear equations with the matrix of the system being triangular and Toeplitz. Due to this triangular structure, there is a common number $m$ of terms in the function expansions to control, which is realized via complexity penalty. The advantage of this methodology is that it leads to very fast computations, produces no boundary effects due to extension at zero and cut-off at $T$ and provides an estimator with the risk within a logarithmic factor of the oracle risk. We emphasize that, in the present paper, we consider the true observational model with possibly nonequispaced observations which are available on a finite interval of length $T$ which appears in many different contexts, and account for the bias associated with this model (which is not present when $T\rightarrow\infty$). The study is motivated by perfusion imaging using a short injection of contrast agent, a procedure which is applied for medical assessment of micro-circulation within tissues such as cancerous tumors. Presence of a tuning parameter $a$ allows to choose the most advantageous time units, so that both the kernel and the unknown right hand side of the equation are well represented for the deconvolution. The methodology is illustrated by an extensive simulation study and a real data example which confirms that the proposed technique is fast, efficient, accurate, usable from a practical point of view and very competitive.Comment: 36 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1207.223

Predictions for the frequency and orbital radii of massive extrasolar planets

We investigate the migration of massive extrasolar planets due to gravitational interaction with a viscous protoplanetary disc. We show that a model in which planets form at 5 AU at a constant rate, before migrating, leads to a predicted distribution of planets that is a steeply rising function of log (a), where a is the orbital radius. Between 1 AU and 3 AU, the expected number of planets per logarithmic interval in orbital radius roughly doubles. We demonstrate that, once selection effects are accounted for, this is consistent with current data, and then extrapolate the observed planet fraction to masses and radii that are inaccessible to current observations. In total, about 15 percent of stars targeted by existing radial velocity searches are predicted to possess planets with masses 0.3 M_Jupiter < M_p sin (i) < 10 M_Jupiter, and radii 0.1 AU < a < 5 AU. A third of these planets (around 5 percent of the target stars) lie at the radii most amenable to detection via microlensing. A further 5-10 percent of stars could have planets at radii of 5 AU < a < 8 AU that have migrated outwards. We discuss the probability of forming a system (akin to the Solar System) in which significant radial migration of the most massive planet does not occur. About 10-15 percent of systems with a surviving massive planet are estimated to fall into this class. Finally, we note that a smaller fraction of low mass planets than high mass planets is expected to survive without being consumed by the star. The initial mass function for planets is thus predicted to rise more steeply towards small masses than the observed mass function.Comment: MNRAS, in pres

Mesoscopic real space structures in aging spin-glasses: the Edwards-Anderson model

Isothermal simulational data for the 3D Edwards-Anderson spin glass are collected at several temperatures below $T_{\rm c}$ and, in analogy with a recent model of dense colloidal suspensions,interpreted in terms of clusters of contiguous spins overturned by quakes, non-equilibrium events linked to record sized energy fluctuations. We show numerically that, to a good approximation, these quakes are statistically independent and constitute a Poisson process whose average grows logarithmically in time. The overturned clusters are local projections on one of the two ground states of the model, and grow likewise logarithmically in time. Data collected at different temperatures $T$ can be collapsed by scaling them with $T^{1.75}$, a hitherto unnoticed feature of the E-A model, which we relate on the one hand to the geometry of configuration space and on the other to experimental memory and rejuvenation effects. The rate at which a cluster flips is shown to decrease exponentially with the size of the cluster, as recently assumed in a coarse grained model of dense colloidal dynamics. The evolving structure of clusters in real space is finally sssociated to the decay of the thermo-remanent magnetization. Our analysis provides an unconventional coarse-grained description of spin glass aging as statistically subordinated to a Poisson quaking process and highlights record dynamics as a viable common theoretical framework for aging in different systems.Comment: 13 pages, 6 figs. Revised text and notation, several typos correcte