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It has been previously demonstrated [Panov et al. Physics of Atomic Nuclei 84(2021)1037] that the TAIGA-HiSCORE Cherenkov array, originally built for cosmic ray physics and ultrahigh-energy gamma-ray astronomy studies using the extensive air shower method, can be used in conventional optical astronomy for wide-field searches for rare nanosecond optical transients of astrophysical origin. The FOV of the facility is on the scale of 1~ster, and it is capable of detecting very rare transients in the visible light range with fluxes greater than approximately 3000~quanta/m$^2$/10~ns (10~ns is the apparatus integration time) and pulse durations of 10\,ns. Among the potential sources of distant nanosecond optical transients are the evaporation of primary black holes, magnetic reconnection in the accretion disks of black holes, and signals from distant lasers of extraterrestrial civilizations. The paper describes the methods and results of the search for optical transients using the TAIGA-HiSCORE Cherenkov array from 2018 to 2022 (four winter seasons of data collection). No reliable astrophysical candidates for optical transients were found. We set an upper bound on the flux of the searched events as $\sim 1\times10^{-3}$\,events/ster/h., Comment: 20 figures, 46 pages

The physical motivations, present status, main results in study of cosmic rays and in the field of gamma-ray astronomy as well future plans of the TAIGA-1 (Tunka Advanced Instrument for cosmic ray physics and Gamma Astronomy) project are presented. The TAIGA observatory addresses ground-based gamma-ray astronomy and astroparticle physics at energies from a few TeV to several PeV, as well as cosmic ray physics from 100 TeV to several EeV. The pilot TAIGA-1 complex is located in the Tunka valley, ~50 km west from the southern tip of the lake Baikal., Comment: Submission to SciPost Phys. Proc., 10 pages, 2 figures

The corrected dependence of the mean depth of the EAS maximum $X_{max}$ on the energy was obtained from the data of the Tunka-133 array for 7 years and the TAIGA-HiSCORE array for 2 years. The parameter $\langle\ln A\rangle$, characterizing the mean mass compositon was derived from these results. The differential energy spectrum of primary cosmic rays in the energy range of $2\cdot 10^{14}$ - $2\cdot 10^{16}$\,eV was reconstructed using the new parameter $Q_{100}$ the Cherenkov light flux at the core distance 100 m.}, Comment: 6 pages, 3 figures, Submitted to SciPost Phys.Proc

The Tunka-Grande experiment is a scintillation array with about 0.5 sq.km sensitive area at Tunka Valley, Siberia, for measuring charged particles and muons in extensive air showers (EASs). Tunka-Grande is optimized for cosmic ray studies in the energy range 10 PeV to about 1 EeV, where exploring the composition is of fundamental importance for understanding the transition from galactic to extragalactic origin of cosmic rays. This paper attempts to provide a synopsis of the current results of the experiment. In particular, the reconstruction of the all-particle energy spectrum in the range of 10 PeV to 1 EeV based on experimental data from four observation seasons is presented., Comment: 7 pages, 3 figures, submission to SciPost Phys. Proc

A wide-angle Cerenkov array TAIGA-HiSCORE (FOV $\sim$0.6 sr), was originally created as a part of TAIGA installation for high-energy gamma-ray astronomy and cosmic ray physics. Array now consist on nearly 100 optical stations on the area of 1 km$^2$. Due to high accuracy and stability ($\sim$1 ns) of time synchronization of the optical stations the accuracy of EAS arrival direction reconstruction is reached 0.1$^\mathrm{o}$. It was proven that the array can also be used to search for nanosecond events of the optical range. The report discusses the method of searching for optical transients using the HiSCORE array and demonstrates its performance on a real example of detecting signals from an artificial Earth satellite. The search for this short flares in the HiSCORE data of the winter season 2018--2019 is carried out. One candidate for double repeater has been detected, but the estimated probability of random simulation of such a transient by background EAS events is not less than 10%, which does not allow us to say that the detected candidate corresponds to a real astrophysical transient. An upper bound on the frequency of optical spikes with flux density of more than $10^{-4} \mathrm{erg/s/cm}^2$ and a duration of more than 5\,ns is established as $\sim 2 \times 10^{-3}$ events/sr/hour., Comment: 15 pages, 6 figures, reported at the conference ISCRA-2021, Accepted for publication in Physics of Atomic Nuclei

The recent progress in the radio detection technique for air showers paves the path to future cosmic-ray radio detectors. Digital radio arrays allow for a measurement of the air-shower energy and depth of its maximum with a resolution comparable to those of the leading optical detection methods. One of the remaining challenges regarding cosmic-ray radio instrumentation is an accurate estimation of their efficiency and aperture. We present a probabilistic model to address this challenge. We use the model to estimate the efficiency and aperture of the Tunka-Rex radio array. The basis of the model is a parametrization of the radio footprint and a probabilistic treatment of the detection process on both the antenna and array levels. In this way, we can estimate the detection efficiency for air showers as function of their arrival direction, energy, and impact point on the ground. In addition, the transparent internal relationships between the different stages of the air-shower detection process in our probabilistic approach enable to estimate the uncertainty of the efficiency and, consequently, of the aperture of radio arrays. The details of the model will be presented in the contribution., Comment: Proceedings of the 37th International Cosmic Ray Conference (ICRC2021), 12-23 July 2021, Berlin, Germany - Online

Radio detection of air showers produced by ultra-high energy cosmic rays is a cost-effective technique for the next generation of sparse arrays. The performance of this technique strongly depends on the environmental background, which has different constituents, namely anthropogenic radio frequency interference, synchrotron galactic radiation and others. These components have recognizable features, which can help for background suppression. A powerful method for handling this is the application of convolution neural networks with a specific architecture called autoencoder. By suppressing unwanted signatures, the autoencoder keeps the signal-like ones. We have successfully developed and trained an autoencoder, which is now applied to the data from Tunka-Rex. We show the procedures of the training and optimization of the network including benchmarks of different architectures. Using the autoencoder, we improved the standard analysis of Tunka-Rex in order to lower the threshold of the detection. This enables the reconstructing of sub-threshold events with energies lower than 0.1 EeV with satisfactory angular and energy resolutions., Comment: Proceedings of the 37th International Cosmic Ray Conference (ICRC2021), 12-23 July 2021, Berlin, Germany - Online

Tunka-Rex (Tunka Radio Extension) was a detector for ultra-high energy cosmic rays measuring radio emission for air showers in the frequency band of 30-80 MHz, operating in 2010s. It provided an experimental proof that sparse radio arrays can be a cost-effective technique to measure the depth of shower maximum with resolutions competitive to optical detectors. After the decommissioning of Tunka-Rex, as last phase of its lifecycle and following the FAIR (Findability - Accessibility - Interoperability - Reuse) principles, we publish the data and software under free licenses in the frame of the TRVO (Tunka-Rex Virtual Observatory), which is hosted at KIT under the partnership with the KCDC and GRADLCI projects. We present the main features of TRVO, its interface and give an overview of projects, which benefit from its open software and data., Comment: Proceedings of the 37th International Cosmic Ray Conference (ICRC2021), 12-23 July 2021, Berlin, Germany - Online. arXiv admin note: substantial text overlap with arXiv:1906.10425

The EAS Cherenkov light array Tunka-133, with $\sim$ 3 km$^2$ geometric area, is taking data since 2009.The array permits a detailed study of energy spectrum and mass composition of cosmic rays in the energy range from $6\cdot 10^{15}$ to $10^{18}$ eV. We describe the methods of time and amplitude calibration of the array and the methods of EAS parameters reconstruction. We present the all-particle energy spectrum, based on 7 seasons of operation., Comment: 12 pages,18 figures

Sparse digital antenna arrays constitute a promising detection technique for future large-scale cosmic-ray observatories. It has recently been shown that this kind of instrumentation can provide a resolution of the energy and of the shower maximum on the level of other cosmic-ray detection methods. Due to the dominant geomagnetic nature of the air-shower radio emission in the traditional frequency band of 30 to 80 MHz, the amplitude and polarization of the radio signal strongly depend on the azimuth and zenith angle of the arrival direction. Thus, the estimation of the efficiency and subsequently of the aperture of an antenna array is more complex than for particle or Cherenkov-light detectors. We have built a new efficiency model based on utilizing a lateral distribution function as a shower model, and a probabilistic treatment of the detection process. The model is compared to the data measured by the Tunka Radio Extension (Tunka-Rex), a digital antenna array with an area of about 1 km$^2$ located in Siberia at the Tunka Advanced Instrument for Cosmic rays and Gamma Ray Astronomy (TAIGA). Tunka-Rex detects radio emission of air showers using trigger from air-Cherenkov and particle detectors. The present study is an essential step towards the measurement of the cosmic-ray flux with Tunka-Rex, and is important for radio measurements of air showers in general., Comment: Contribution to the 36th International Cosmic Ray Conference

The Tunka Radio Extension (Tunka-Rex) is a digital antenna array located in the Tunka Valley in Siberia, which measures the radio emission of cosmic-ray air-showers with energies up to EeV. Tunka-Rex is externally triggered by the Tunka-133 air-Cherenkov timing array (during nights) and by the Tunka-Grande array of particle detectors (remaining time). These three arrays comprise the cosmic-ray extension of the Tunka Advanced Instrument for cosmic rays and Gamma Astronomy (TAIGA). The configuration and analysis pipeline of Tunka-Rex have significantly changed over its runtime. Density of the antennas was tripled and the pipeline has become more developed forming now sophisticated piece of reconstruction software. During its lifecycle Tunka-Rex has demonstrated that a cost-effective and full duty-cycle radio detector can reconstruct the energy and shower maximum with a precision comparable to optical detectors. Moreover, it was shown that cosmic-ray instruments, that use different detection techniques and are placed in different locations, can be cross-calibrated via their radio extensions. These results show the prospects of application of the radio technique for future large-scale experiments for cosmic-ray and neutrino detection. For the time being Tunka-Rex has ceased active measurements and focuses on the data analysis and publication of corresponding software and data in an open-access data center with online analysis features. In this report we present the current status of the array and give an overview of the results achieved during these years as well as discuss upcoming improvements in instrumentation and data analysis, which can be applied for the future radio arrays., Comment: Presented at the 36th International Cosmic Ray Conference (ICRC 2019)

The Tunka Radio Extension (Tunka-Rex) is a digital antenna array operating in the frequency band of 30-80 MHz, measuring the radio emission of air-showers induced by ultra-high energy cosmic rays. Tunka-Rex is co-located with the TAIGA experiment in Siberia and consists of 63 antennas, 57 of them in a densely instrumented area of about 1km2. The signals from the air showers are short pulses, which have a duration of tens of nanoseconds and are recorded in traces of about 5{\mu}s length. The Tunka-Rex analysis of cosmic-ray events is based on the reconstruction of these signals, in particular, their positions in the traces and amplitudes. This reconstruction suffers at low signal-to-noise ratios, i.e. when the recorded traces are dominated by background. To lower the threshold of the detection and increase the efficiency, we apply advanced methods of signal reconstruction, namely matched filtering and deep neural networks with autoencoder architecture. In the present work we show the comparison between the signal reconstructions obtained with these techniques, and give an example of the first reconstruction of the Tunka-Rex signals obtained with a deep neural networks., Comment: Proceedings of the 3rd International Workshop on Data Life Cycle in Physics, Irkutsk, Russia, April 2-7, 2019

The Tunka Radio Extension (Tunka-Rex) is a cosmic-ray detector operating since 2012. The detection principle of Tunka-Rex is based on the radio technique, which impacts data acquisition and storage. In this paper we give a first detailed overview of the concept of the Tunka-Rex Virtual Observatory (TRVO), a framework for open access to the Tunka-Rex data, which currently is under active development and testing. We describe the structure of the data, main features of the interface and possible applications of the TRVO., Comment: Proceedings of the 3rd International Workshop on Data Life Cycle in Physics, Irkutsk, Russia, April 2-7, 2019

The paper is a script of a lecture given at the ISAPP-Baikal summer school in 2018. The lecture gives an overview of the Tunka Advanced Instrument for cosmic rays and Gamma Astronomy (TAIGA) facility including historical introduction, description of existing and future setups, and outreach and open data activities., Comment: Lectures given at the ISAPP-Baikal Summer School 2018: Exploring the Universe through multiple messengers, 12-21 July 2018, Bol'shie Koty, Russia

The Tunka Radio Extension (Tunka-Rex) is an antenna array spread over an area of about 1~km$^2$. The array is placed at the Tunka Advanced Instrument for cosmic rays and Gamma Astronomy (TAIGA) and detects the radio emission of air showers in the band of 30 to 80~MHz. During the last years it was shown that a sparse array such as Tunka-Rex is capable of reconstructing the parameters of the primary particle as accurate as the modern instruments. Based on these results we continue developing our data analysis. Our next goal is the reconstruction of cosmic-ray energy spectrum observed only by a radio instrument. Taking a step towards it, we develop a model of aperture of our instrument and test it against hybrid TAIGA observations and Monte-Carlo simulations. In the present work we give an overview of the current status and results for the last five years of operation of Tunka-Rex and discuss prospects of the cosmic-ray energy estimation with sparse radio arrays., Comment: Proceedings of E+CRS 2018

The Tunka Radio Extension (Tunka-Rex) is a digital antenna array for the detection of radio emission from cosmic-ray air showers in the frequency band of 30 to 80 MHz and for primary energies above 100 PeV. The standard analysis of Tunka-Rex includes events with zenith angle of up to 50$^\circ$. This cut is determined by the efficiency of the external trigger. However, due to the air-shower footprint increasing with zenith angle and due to the more efficient generation of radio emission (the magnetic field in the Tunka valley is almost vertical), there are a number of ultra-high-energy inclined events detected by Tunka-Rex. In this work we present a first analysis of a subset of inclined events detected by Tunka-Rex. We estimate the energies of the selected events and test the efficiency of Tunka-Rex antennas for detection of inclined air showers., Comment: ARENA2018 proceedings

The Tunka Radio Extension (Tunka-Rex) is a digital antenna array, which measures the radio emission of the cosmic-ray air-showers in the frequency band of 30-80 MHz. Tunka-Rex is co-located with TAIGA experiment in Siberia and consists of 63 antennas, 57 of them are in a densely instrumented area of about 1 km\textsuperscript{2}. In the present work we discuss the improvements of the signal reconstruction applied for the Tunka-Rex. At the first stage we implemented matched filtering using averaged signals as template. The simulation study has shown that matched filtering allows one to decrease the threshold of signal detection and increase its purity. However, the maximum performance of matched filtering is achievable only in case of white noise, while in reality the noise is not fully random due to different reasons. To recognize hidden features of the noise and treat them, we decided to use convolutional neural network with autoencoder architecture. Taking the recorded trace as an input, the autoencoder returns denoised trace, i.e. removes all signal-unrelated amplitudes. We present the comparison between standard method of signal reconstruction, matched filtering and autoencoder, and discuss the prospects of application of neural networks for lowering the threshold of digital antenna arrays for cosmic-ray detection., Comment: ARENA2018 proceedings

The Tunka Radio Extension (Tunka-Rex) is a digital radio array operating in the frequency band of 30-80 MHz and detecting radio emission from air-showers produced by cosmic rays with energies above 100 PeV. The experiment is installed at the site of the TAIGA (Tunka Advanced Instrument for cosmic rays and Gamma Astronomy) observatory and performs joint measurements with the co-located particle and air-Cherenkov detectors in passive mode receiving a trigger from the latter. Tunka-Rex collects data since 2012, and during the last five years went through several upgrades. As a result the density of the antenna field was increased by three times since its commission. In this contribution we present the latest results of Tunka-Rex experiment, particularly an updated analysis and efficiency study, which have been applied to the measurement of the mean shower maximum as a function of energy for cosmic rays of energies up to EeV. The future plans are also discussed: investigations towards an energy spectrum of cosmic rays with Tunka-Rex and their mass composition using a combination of Tunka-Rex data with muon measurements by the particle detector Tunka-Grande., Comment: ARENA2018 proceedings

Modern detectors of cosmic gamma-rays are a special type of imaging telescopes (air Cherenkov telescopes) supplied with cameras with a relatively large number of photomultiplier-based pixels. For example, the camera of the TAIGA-IACT telescope has 560 pixels of hexagonal structure. Images in such cameras can be analysed by deep learning techniques to extract numerous physical and geometrical parameters and/or for incoming particle identification. The most powerful deep learning technique for image analysis, the so-called convolutional neural network (CNN), was implemented in this study. Two open source libraries for machine learning, PyTorch and TensorFlow, were tested as possible software platforms for particle identification in imaging air Cherenkov telescopes. Monte Carlo simulation was performed to analyse images of gamma-rays and background particles (protons) as well as estimate identification accuracy. Further steps of implementation and improvement of this technique are discussed., Comment: 5 pages, 2 figures. Submitted to CEUR Workshop Proceedings, 8th International Conference "Distributed Computing and Grid-technologies in Science and Education" GRID 2018, 10 - 14 September 2018, Dubna, Russia

The paper is devoted to the issues of raw binary data documenting, parsing and verifying in astroparticle data lifecycle. The long-term preservation of raw data of astroparticle experiments as originally generated is essential for re-running analyses and reproducing research results. The selected high-quality raw data should have detailed documentation and accompanied by open software tools for access to them. We consider applicability of binary file format description languages to specify, parse and verify raw data of the Tunka Advanced Instrument for cosmic rays and Gamma Astronomy (TAIGA) experiment. The formal specifications are implemented for five data formats of the experiment and provide automatic generation of source code for data reading libraries in target programming languages (e.g. C++, Java, and Python). These libraries were tested on TAIGA data. They showed a good performance and help us to locate the parts with corrupted data. The format specifications can be used as metadata for exchanging of astroparticle raw data. They can also simplify software development for data aggregation from various sources for the multi-messenger analysis.

We present an improved method for the precise reconstruction of cosmic ray air showers above $10^{17}$ eV with sparse radio arrays. The method is based on the comparison of predictions for radio pulse shapes by CoREAS simulations to measured pulses. We applied our method to the data of Tunka-Rex, a 1 km$^2$ radio array in Siberia operating in the frequency band of 30-80 MHz. Tunka-Rex is triggered by the air-Cherenkov detector Tunka-133 and by scintillators (Tunka-Grande). The instrument collects air-shower data since 2012. The present paper describes updated data and signal analyses of Tunka-Rex and details of a new method applied. After efficiency cuts, when Tunka-Rex reaches its full efficiency, the energy resolution of about 10% given by the new method has reached the limit of systematic uncertainties due to the calibration uncertainty and shower-to-shower fluctuations. At the same time the shower maximum reconstruction is significantly improved up to an accuracy of 35 g/cm$^2$ compared to the previous method based on the slope of the lateral distribution. We also define and now achieved conditions of the measurements, at which the shower maximum resolution of Tunka-Rex reaches a value of 25 g/cm$^2$ and becomes competitive to optical detectors. To check and validate our reconstruction and efficiency cuts we compare individual events to the reconstruction of Tunka-133. Furthermore, we compare the mean of shower maximum as a function of primary energy to the measurements of other experiments., Comment: published version

Tunka-Rex (Tunka Radio Extension) is an antenna array for cosmic-ray detection located in Siberia. Previous studies of cosmic rays with Tunka-Rex have shown high precision in determining the energy of the primary particle and the possibility to reconstruct the depth of the shower maximum. The next step is the reconstruction of the mass composition and the energy spectrum of cosmic rays. One of the main problems appearing within this task is to estimate the detection efficiency of the instrument, and the exposure of the observations. The detection efficiency depends on properties of the primary cosmic rays, such as energy and arrival direction, as well as on many parameters of the instrument: density of the array, efficiency of the receiving antennas, signal-detection threshold, data-acquisition acceptance, and trigger properties. More than that, the configuration of detector changes with time. During the measurements some parts of the detector can provide corrupted data or sometimes do not operate. All these features should be taken into account for an estimation of the detection efficiency. For each energy and arrival direction we estimate the detection probability and effective area of the instrument. To estimate the detection probability of a shower we use a simple Monte Carlo model, which predicts the size of the footprint of the radio emission as function of the primary energy and arrival direction (taking into account the geometry of Earth's magnetic field). Combining these approaches we calculate the event statistics and exposure for each run. This is the first accurate study of the exposure for irregular large-scale radio arrays taking into account most important features of detection, which will be used for the measurement of primary cosmic-ray spectra with Tunka-Rex., Comment: Proceedings of the 35th ICRC 2017, Busan, Korea

The Tunka Radio Extension (Tunka-Rex) is an array of 63 antennas located in the Tunka Valley, Siberia. It detects radio pulses in the 30-80 MHz band produced during the air-shower development. As shown by Tunka-Rex, a sparse radio array with about 200 m spacing is able to reconstruct the energy and the depth of the shower maximum with satisfactory precision using simple methods based on parameters of the lateral distribution of amplitudes. The LOFAR experiment has shown that a sophisticated treatment of all individually measured amplitudes of a dense antenna array can make the precision comparable with the resolution of existing optical techniques. We develop these ideas further and present a method based on the treatment of time series of measured signals, i.e. each antenna station provides several points (trace) instead of a single one (amplitude or power). We use the measured shower axis and energy as input for CoREAS simulations: for each measured event we simulate a set of air-showers with proton, helium, nitrogen and iron as primary particle (each primary is simulated about ten times to cover fluctuations in the shower maximum due to the first interaction). Simulated radio pulses are processed with the Tunka-Rex detector response and convoluted with the measured signals. A likelihood fit determines how well the simulated event fits to the measured one. The positions of the shower maxima are defined from the distribution of chi-square values of these fits. When using this improved method instead of the standard one, firstly, the shower maximum of more events can be reconstructed, secondly, the resolution is increased. The performance of the method is demonstrated on the data acquired by the Tunka-Rex detector in 2012-2014., Comment: Proceedings of the 35th ICRC 2017, Busan, Korea

In this paper we propose a 'knee-like' approximation of the lateral distribution of the Cherenkov light from extensive air showers in the energy range 30-3000 TeV and study a possibility of its practical application in high energy ground-based gamma-ray astronomy experiments (in particular, in TAIGA-HiSCORE). The approximation has a very good accuracy for individual showers and can be easily simplified for practical application in the HiSCORE wide angle timing array in the condition of a limited number of triggered stations., Comment: 4 pages, 5 figures, proceedings of ISVHECRI 2016 (19th International Symposium on Very High Energy Cosmic Ray Interactions)

A simple 'knee-like' approximation of the Lateral Distribution Function (LDF) of Cherenkov light emitted by EAS (extensive air showers) in the atmosphere is proposed for solving various tasks of data analysis in HiSCORE and other wide angle ground-based experiments designed to detect gamma rays and cosmic rays with the energy above tens of TeV. Simulation-based parametric analysis of individual LDF curves revealed that on the radial distance 20-500 m the 5-parameter 'knee-like' approximation fits individual LDFs as well as the mean LDF with a very good accuracy. In this paper we demonstrate the efficiency and flexibility of the 'knee-like' LDF approximation for various primary particles and shower parameters and the advantages of its application to suppressing proton background and selecting primary gamma rays., Comment: 7 pages, 1 table, 2 figures; Bulletin of the Russian Academy of Sciences: Physics, 81, 4 (2017), in press

The Tunka Radio Extension (Tunka-Rex) is an antenna array consisting of 63 antennas at the location of the TAIGA facility (Tunka Advanced Instrument for cosmic ray physics and Gamma Astronomy) in Eastern Siberia, nearby Lake Baikal. Tunka-Rex is triggered by the air-Cherenkov array Tunka-133 during clear and moonless winter nights and by the scintillator array Tunka-Grande during the remaining time. Tunka-Rex measures the radio emission from the same air-showers as Tunka-133 and Tunka-Grande, but with a higher threshold of about 100 PeV. During the first stages of its operation, Tunka-Rex has proven, that sparse radio arrays can measure air-showers with an energy resolution of better than 15\% and the depth of the shower maximum with a resolution of better than 40 g/cm\textsuperscript{2}. To improve and interpret our measurements as well as to study systematic uncertainties due to interaction models, we perform radio simulations with CORSIKA and CoREAS. In this overview we present the setup of Tunka-Rex, discuss the achieved results and the prospects of mass-composition studies with radio arrays., Comment: proceedings of ISVHECRI2016 conference

Tunka-Rex is detector for radio emission produced by cosmic-ray air-showers located in Siberia, triggered by Tunka-133, a co-located air-Cherenkov detector during night, and by a scintillator array Tunka-Grande during day. Tunka-Rex demonstrates that the radio technique can provide a cost-effective extension of existing air-shower arrays. Operating in the frequency range of 30-80 MHz, Tunka-Rex is limited by the galactic background, and suffers from the local radio interferences. We investigate the possibilities of the improving of measured data using different approaches, particularly, the multivariate background suppression is considered, as well as improved likelihood fit of the lateral distribution of amplitudes., Comment: XXV ECRS 2016 Proceedings - eConf C16-09-04.3