Tomograms and other transforms. A unified view

A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the symplectic and affine groups is treated in some detail. Special emphasis is given to the properties of the scale-time and scale-frequency tomograms. Tomograms are interpreted as a tool to sample the signal space by a family of curves or as the matrix element of a projector.Comment: 19 pages latex, submitted to J. Phys. A: Math and Ge

Spectral Analysis of Multi-dimensional Self-similar Markov Processes

In this paper we consider a discrete scale invariant (DSI) process $\{X(t), t\in {\bf R^+}\}$ with scale $l>1$. We consider to have some fix number of observations in every scale, say $T$, and to get our samples at discrete points $\alpha^k, k\in {\bf W}$ where $\alpha$ is obtained by the equality $l=\alpha^T$ and ${\bf W}=\{0, 1,...\}$. So we provide a discrete time scale invariant (DT-SI) process $X(\cdot)$ with parameter space $\{\alpha^k, k\in {\bf W}\}$. We find the spectral representation of the covariance function of such DT-SI process. By providing harmonic like representation of multi-dimensional self-similar processes, spectral density function of them are presented. We assume that the process $\{X(t), t\in {\bf R^+}\}$ is also Markov in the wide sense and provide a discrete time scale invariant Markov (DT-SIM) process with the above scheme of sampling. We present an example of DT-SIM process, simple Brownian motion, by the above sampling scheme and verify our results. Finally we find the spectral density matrix of such DT-SIM process and show that its associated $T$-dimensional self-similar Markov process is fully specified by $\{R_{j}^H(1),R_{j}^H(0),j=0, 1,..., T-1\}$ where $R_j^H(\tau)$ is the covariance function of $j$th and $(j+\tau)$th observations of the process.Comment: 16 page

Time Scale Approach for Chirp Detection

International audienceTwo different approaches for joint detection and estimation of signals embedded in stationary random noise are considered and compared, for the subclass of amplitude and frequency modulated signals. Matched filter approaches are compared to time-frequency and time scale based approaches. Particular attention is paid to the case of the so-called " power-law chirps " , characterized by monomial and polynomial amplitude and frequency functions. As target application, the problem of gravitational waves at interferometric detectors is considered

Time-frequency detection of Gravitational Waves

We present a time-frequency method to detect gravitational wave signals in interferometric data. This robust method can detect signals from poorly modeled and unmodeled sources. We evaluate the method on simulated data containing noise and signal components. The noise component approximates initial LIGO interferometer noise. The signal components have the time and frequency characteristics postulated by Flanagan and Hughes for binary black hole coalescence. The signals correspond to binaries with total masses between $45 M_\odot$ to $70 M_\odot$ and with (optimal filter) signal-to-noise ratios of 7 to 12. The method is implementable in real time, and achieves a coincident false alarm rate for two detectors $\approx$ 1 per 475 years. At this false alarm rate, the single detector false dismissal rate for our signal model is as low as 5.3% at an SNR of 10. We expect to obtain similar or better detection rates with this method for any signal of similar power that satisfies certain adiabaticity criteria. Because optimal filtering requires knowledge of the signal waveform to high precision, we argue that this method is likely to detect signals that are undetectable by optimal filtering, which is at present the best developed detection method for transient sources of gravitational waves.Comment: 24 pages, 5 figures, uses REVTE

Frequency decoding of periodically timed action potentials through distinct activity patterns in a random neural network

Frequency discrimination is a fundamental task of the auditory system. The mammalian inner ear, or cochlea, provides a place code in which different frequencies are detected at different spatial locations. However, a temporal code based on spike timing is also available: action potentials evoked in an auditory-nerve fiber by a low-frequency tone occur at a preferred phase of the stimulus-they exhibit phase locking-and thus provide temporal information about the tone's frequency. In an accompanying psychoacoustic study, and in agreement with previous experiments, we show that humans employ this temporal information for discrimination of low frequencies. How might such temporal information be read out in the brain? Here we demonstrate that recurrent random neural networks in which connections between neurons introduce characteristic time delays, and in which neurons require temporally coinciding inputs for spike initiation, can perform sharp frequency discrimination when stimulated with phase-locked inputs. Although the frequency resolution achieved by such networks is limited by the noise in phase locking, the resolution for realistic values reaches the tiny frequency difference of 0.2% that has been measured in humans.Comment: 16 pages, 5 figures, and supplementary informatio

A comparison of methods for gravitational wave burst searches from LIGO and Virgo

The search procedure for burst gravitational waves has been studied using 24 hours of simulated data in a network of three interferometers (Hanford 4-km, Livingston 4-km and Virgo 3-km are the example interferometers). Several methods to detect burst events developed in the LIGO Scientific Collaboration (LSC) and Virgo collaboration have been studied and compared. We have performed coincidence analysis of the triggers obtained in the different interferometers with and without simulated signals added to the data. The benefits of having multiple interferometers of similar sensitivity are demonstrated by comparing the detection performance of the joint coincidence analysis with LSC and Virgo only burst searches. Adding Virgo to the LIGO detector network can increase by 50% the detection efficiency for this search. Another advantage of a joint LIGO-Virgo network is the ability to reconstruct the source sky position. The reconstruction accuracy depends on the timing measurement accuracy of the events in each interferometer, and is displayed in this paper with a fixed source position example.Comment: LIGO-Virgo working group submitted to PR

Enhancement of the non-invasive electroenterogram to identify intestinal pacemaker activity

Surface recording of electroenterogram (EEnG) is a non-invasive method for monitoring intestinal myoelectrical activity. However, surface EEnG is seriously affected by a variety of interferences: cardiac activity, respiration, very low frequency components and movement artefacts. The aim of this study is to eliminate respiratory interference and very low frequency components from external EEnG recording by means of empirical mode decomposition (EMD), so as to obtain more robust indicators of intestinal pacemaker activity from external EEnG signal. For this purpose, 11 recording sessions were performed in an animal model under fasting conditions and in each individual session the myoelectrical signal was recorded simultaneously in the intestinal serosa and the external abdominal surface in physiological states. Various parameters have been proposed for evaluating the efficacy of the method in reducing interferences: the signal-to-interference ratio (S/I ratio), attenuation of the target and interference signals, the normal slow wave percentage and the stability of the dominant frequency (DF) of the signal. The results show that the S/I ratio of the processed signals is significantly greater than the original values (9.66±4.44 dB vs. 1.23±5.13 dB), while the target signal was barely attenuated (-0.63±1.02 dB). The application of the EMD method also increased the percentage of the normal slow wave to 100% in each individual session and enabled the stability of the DF of the external signal to be increased considerably. Furthermore, the variation coefficient of the DF derived from the external processed signals is comparable to the coefficient obtained using internal recordings. Therefore the EMD method could be a very useful tool to improve the quality of external EEnG recording in the low frequency range, and therefore to obtain more robust indicators of the intestinal pacemaker activity from non invasive EEnG recordingsThe authors would like to thank D Alvarez-Martinez, Dr C Vila and the Veterinary Unit of the Research Centre of 'La Fe' University Hospital (Valencia, Spain), where the surgical interventions and recording sessions were carried out, and the R+D+I Linguistic Assistance Office at the UPV for their help in revising this paper. This research study was sponsored by the Ministerio de Ciencia y Tecnologia de Espana (TEC2007-64278) and by the Universidad Politecnica de Valencia, as part of a UPV research and development Grant Programme.Ye Lin, Y.; Garcia Casado, FJ.; Prats Boluda, G.; Ponce, JL.; Martínez De Juan, JL. (2009). Enhancement of the non-invasive electroenterogram to identify intestinal pacemaker activity. 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A tomographic analysis of reflectometry data I: Component factorization

Many signals in Nature, technology and experiment have a multi-component structure. By spectral decomposition and projection on the eigenvectors of a family of unitary operators, a robust method is developed to decompose a signals in its components. Different signal traits may be emphasized by different choices of the unitary family. The method is illustrated in simulated data and on data obtained from plasma reflectometry experiments in the tore Supra.Comment: 27 pages Latex, 17 figure

Meals in western eating and drinking

Meals are a way of organizing eating into events that have a particular structure and form, and they play an indisputable and even self-evident role within the rhythms and routines of everyday life. In late modern societies, concern about the fate of meals has arisen in both public and academic discourse. It has been suggested that eating is characterized today by individualization, destructuration, and informalization and that communal meals are increasingly being replaced by snacks and solitary eating. This chapter focuses on meals in today’s affluent societies and reflects on why meals are considered important, how meals are defined, and what material elements and social dimensions they contain. It looks at how societal and cultural changes and ecological concerns may influence the organization and future of meals, and it suggests that the content of meals will change in response to the need to diminish the ecological burden of food production and consumption. In particular, plant-based options will at least partly need to replace meat and other animal-based foods. However, there is no reason to expect that the meal as a social institution will break down. Despite the fact that not all meals are characterized by conviviality and companionship, they continue to serve as a significant arena of human sociability and togetherness. Sharing food is, after all, an essential part of being human.Non peer reviewe