2D approach for modelling self-potential anomalies. Application to synthetic and real data

The aim of this work is to present a 2-D Matlab code based on the finite element method for providing numerical modelling of both groundwater flow and self-potential signals. The distribution of the self-potential is obtained by starting with the solution of the groundwater flow, then computing the source current density, and finally calculating the electrical potential. The reliability of the algorithm is tested with synthetic case studies in order to simulate both the electric field resulting from the existence of a leak in the dam and SP signals associated with a pumping test in an unconfined aquifer. In addition, the algorithm was applied to field data for the localization of piping sinkholes. The results show that the outputs of the algorithm yielded satisfactory solutions, which are in good agreement with those of previous studies and field investigations. In details, the synthetic data and SP anomalies calculated by using the code are very close in terms of sign and magnitude, while real data tests clearly indicated that the computed SP signals were found to be consistent with the measured values

Structured Prediction Problem Archive

Structured prediction problems are one of the fundamental tools in machinelearning. In order to facilitate algorithm development for their numericalsolution, we collect in one place a large number of datasets in easy to readformats for a diverse set of problem classes. We provide archival links todatasets, description of the considered problems and problem formats, and ashort summary of problem characteristics including size, number of instancesetc. For reference we also give a non-exhaustive selection of algorithmsproposed in the literature for their solution. We hope that this centralrepository will make benchmarking and comparison to established works easier.We welcome submission of interesting new datasets and algorithms for inclusionin our archive.<br

Tests of Gravity from Imaging and Spectroscopic Surveys

Tests of gravity on large-scales in the universe can be made using both imaging and spectroscopic surveys. The former allow for measurements of weak lensing, galaxy clustering and cross-correlations such as the ISW effect. The latter probe galaxy dynamics through redshift space distortions. We use a set of basic observables, namely lensing power spectra, galaxy-lensing and galaxy-velocity cross-spectra in multiple redshift bins (including their covariances), to estimate the ability of upcoming surveys to test gravity theories. We use a two-parameter description of gravity that allows for the Poisson equation and the ratio of metric potentials to depart from general relativity. We find that the combination of imaging and spectroscopic observables is essential in making robust tests of gravity theories. The range of scales and redshifts best probed by upcoming surveys is discussed. We also compare our parametrization to others used in the literature, in particular the gamma parameter modification of the growth factor.Comment: 18 pages, 10 figures, to be submitte

On random tomography with unobservable projection angles

We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on $\mathbb{R}^3$ is to be recovered from observation of finitely many of its two-dimensional projections in random and unobservable directions. Such a problem is distinct from the classic problem of tomography where both the projections and the unit vectors normal to the projection plane are observable. The problem arises in single particle electron microscopy, a powerful method that biophysicists employ to learn the structure of biological macromolecules. Strictly speaking, the problem is unidentifiable and an appropriate reformulation is suggested hinging on ideas from Kendall's theory of shape. Within this setup, we demonstrate that a consistent solution to the problem may be derived, without attempting to estimate the unknown angles, if the density is assumed to admit a mixture representation.Comment: Published in at http://dx.doi.org/10.1214/08-AOS673 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Study of noise effects in electrical impedance tomography with resistor networks

We present a study of the numerical solution of the two dimensional electrical impedance tomography problem, with noisy measurements of the Dirichlet to Neumann map. The inversion uses parametrizations of the conductivity on optimal grids. The grids are optimal in the sense that finite volume discretizations on them give spectrally accurate approximations of the Dirichlet to Neumann map. The approximations are Dirichlet to Neumann maps of special resistor networks, that are uniquely recoverable from the measurements. Inversion on optimal grids has been proposed and analyzed recently, but the study of noise effects on the inversion has not been carried out. In this paper we present a numerical study of both the linearized and the nonlinear inverse problem. We take three different parametrizations of the unknown conductivity, with the same number of degrees of freedom. We obtain that the parametrization induced by the inversion on optimal grids is the most efficient of the three, because it gives the smallest standard deviation of the maximum a posteriori estimates of the conductivity, uniformly in the domain. For the nonlinear problem we compute the mean and variance of the maximum a posteriori estimates of the conductivity, on optimal grids. For small noise, we obtain that the estimates are unbiased and their variance is very close to the optimal one, given by the Cramer-Rao bound. For larger noise we use regularization and quantify the trade-off between reducing the variance and introducing bias in the solution. Both the full and partial measurement setups are considered.Comment: submitted to Inverse Problems and Imagin

EEG-Based Quantification of Cortical Current Density and Dynamic Causal Connectivity Generalized across Subjects Performing BCI-Monitored Cognitive Tasks.

Quantification of dynamic causal interactions among brain regions constitutes an important component of conducting research and developing applications in experimental and translational neuroscience. Furthermore, cortical networks with dynamic causal connectivity in brain-computer interface (BCI) applications offer a more comprehensive view of brain states implicated in behavior than do individual brain regions. However, models of cortical network dynamics are difficult to generalize across subjects because current electroencephalography (EEG) signal analysis techniques are limited in their ability to reliably localize sources across subjects. We propose an algorithmic and computational framework for identifying cortical networks across subjects in which dynamic causal connectivity is modeled among user-selected cortical regions of interest (ROIs). We demonstrate the strength of the proposed framework using a "reach/saccade to spatial target" cognitive task performed by 10 right-handed individuals. Modeling of causal cortical interactions was accomplished through measurement of cortical activity using (EEG), application of independent component clustering to identify cortical ROIs as network nodes, estimation of cortical current density using cortically constrained low resolution electromagnetic brain tomography (cLORETA), multivariate autoregressive (MVAR) modeling of representative cortical activity signals from each ROI, and quantification of the dynamic causal interaction among the identified ROIs using the Short-time direct Directed Transfer function (SdDTF). The resulting cortical network and the computed causal dynamics among its nodes exhibited physiologically plausible behavior, consistent with past results reported in the literature. This physiological plausibility of the results strengthens the framework's applicability in reliably capturing complex brain functionality, which is required by applications, such as diagnostics and BCI

Guidelines for the recording and evaluation of pharmaco-EEG data in man: the International Pharmaco-EEG Society (IPEG)

The International Pharmaco-EEG Society (IPEG) presents updated guidelines summarising the requirements for the recording and computerised evaluation of pharmaco-EEG data in man. Since the publication of the first pharmaco-EEG guidelines in 1982, technical and data processing methods have advanced steadily, thus enhancing data quality and expanding the palette of tools available to investigate the action of drugs on the central nervous system (CNS), determine the pharmacokinetic and pharmacodynamic properties of novel therapeutics and evaluate the CNS penetration or toxicity of compounds. However, a review of the literature reveals inconsistent operating procedures from one study to another. While this fact does not invalidate results per se, the lack of standardisation constitutes a regrettable shortcoming, especially in the context of drug development programmes. Moreover, this shortcoming hampers reliable comparisons between outcomes of studies from different laboratories and hence also prevents pooling of data which is a requirement for sufficiently powering the validation of novel analytical algorithms and EEG-based biomarkers. The present updated guidelines reflect the consensus of a global panel of EEG experts and are intended to assist investigators using pharmaco-EEG in clinical research, by providing clear and concise recommendations and thereby enabling standardisation of methodology and facilitating comparability of data across laboratories

Design and Implementation of Bio-inspired Underwater Electrosense

Underwater electrosense, manipulating underwater electric field for sensing purpose, is a growing technology bio-inspired by weakly electric fish that can navigate in dark or cluttered water. We studied its theoretical foundations and developed sophisticated sensing algorithms including some first-introduced techniques such as discrete dipole approximation (DDA) and convolutional neural networks (CNN), which were tested and validated by simulation and a planar sensor prototype. This work pave a solid way to applications on practical underwater robots

A perturbation analysis of spontaneous action potential initiation by stochastic ion channels

A stochastic interpretation of spontaneous action potential initiation is developed for the Morris- Lecar equations. Initiation of a spontaneous action potential can be interpreted as the escape from one of the wells of a double well potential, and we develop an asymptotic approximation of the mean exit time using a recently-developed quasi-stationary perturbation method. Using the fact that the activating ionic channel’s random openings and closings are fast relative to other processes, we derive an accurate estimate for the mean time to fire an action potential (MFT), which is valid for a below-threshold applied current. Previous studies have found that for above-threshold applied current, where there is only a single stable fixed point, a diffusion approximation can be used. We also explore why different diffusion approximation techniques fail to estimate the MFT