The results can be readily applied to the case of complex stack configurations and to more general experimental conditions.Time-Of-Flight (TOF) methods are very effective to detect particles accelerated in laser-plasma interactions, but they show significant limitations when used in experiments with high energy and intensity lasers, where both high-energy ions and remarkable levels of ElectroMagnetic Pulses (EMPs) in the radiofrequency-microwave range are generated. Here we describe a novel advanced diagnostic method for the characterization of protons accelerated by intense matter interactions with high-energy and high-intensity ultra-short laser pulses up to the femtosecond and even future attosecond range. The method employs a stacked diamond detector structure and the TOF technique, featuring high sensitivity, high resolution, high radiation hardness and high signal-to-noise ratio in environments heavily affected by remarkable EMP fields. A detailed study on the use, the optimization and the properties of a single module of the stack is here described for an experiment where a fast diamond detector is employed in an highly EMP-polluted environment. Accurate calibrated spectra of accelerated protons are presented from an experiment with the femtosecond Flame laser (beyond 100 TW power and ~ 10 The interest in this field arises from the possibility to produce, with a compact system, intense bunches of high energy charged particles that can be used for several notable applications6, including inertial confinement fusion7. According to the laser parameters, different acceleration processes can take place during the laser-matter interaction4. In the Target Normal Sheath Acceleration (TNSA) a high-power laser  and sensitivity, but have an intrinsic low energy resolution (~ 1 MeV) and do not distinguish among different ion species. Imaging Plates (IP)10 and CR3911 are also commonly adopted for ion detection. The first may have high sensitivity and dynamic range of 16 bit, with spatial resolution normally limited to 25–50 mμ by the type of IP and by the scanner used for retrieving the impressed image. CR39 is a track detector, and has extremely high sensitivity, allowing for single particle detection and resolution commonly limited to a few microns, at most. In some configurations, from the track dimension it is possible to retrieve some information on the energy of the incoming particle, even if with low resolution of the MeV order. The three mentioned detectors are commonly adopted when performing time-integrated measurement since they do not allow to have any temporal discrimination. Their spatial resolutions allow them to give accurate representation of the angular particle emission properties, and in some cases information on the number of detected particles can be achieved also with good accuracy, for example with the CR39. They are also immune to the intense Electromagnetic pulses (EMPs) in the radiofrequency-microwave range generated in laser-matter interactions of high energy and intensity18. On the other hand, they cannot intrinsically supply accurate information on particle velocity and energy.The study of the acceleration processes that take place in the frame of the laser–plasma interaction requires the development of dedicated diagnostics able to characterize the properties of the accelerated particle beams and thus to outline the differences among the different possible acceleration mechanisms. These diagnostics have to meet some important requirements depending on the characteristics of the accelerated particle beams. Among these, high sensitivity and high energy resolution are needed for the accurate spectrum reconstruction of the accelerated ions. Moreover, the notable dependence of these beams on the angle of emission requires a precise characterization of the particle angular distribution at different directions. This can be done by methods employing stacks of passive detectors as for example Radiochromic films (RCF)20 are instead able to recognize the different charge-over-mass ratios for the incoming ion species and to reconstruct their spectra, but do not have any angular discrimination. The physical dimension of these devices usually gives notable difficulties to place several of them at different directions, on the purpose to retrieve information on the angular beam emission, especially in the cases where the vacuum chamber is of limited dimension.Electrostatic-magnetostatic spectrometers of the Thomson type20. The MCP response is of the order of a few ns, i.e. the fluorescence time, allowing to work in a continuous or gated biasing. In some conditions these can be used for real-time particle detection. The MCP typical spatial resolution, when used for imaging or coupled to electric–magnetic spectrometers, is limited to 4–25 µm by the diameter of the MCP capillaries, although is usually worst due to the common set-ups including pin-holes and drift space. Thanks to the electron multiplication that can span over several decades, they can have very high sensitivity and dynamic range. On the other hand, this leads to a low signal-to-noise ratio with respect to other solutions. Moreover the high cost of such devices limits the number of possible detectors to be fielded, and their use can be in some cases highly problematic due to the high values of EMP fields typical of high energy and high intensity laser–plasma interactions18, that can highly affect the operation of the related electronics. The employment of scintillators together with differential filtering technique has been also proposed21 to retrieve the proton beam profiling as well as a coarse energy estimation while working at high-repetition rate.An additional requirement that the ideal diagnostic system has to satisfy is the capability to work at high repetition rates (i.e. up to kHz), so without having to open the experimental chamber after each shot. This task cannot be fulfilled when passive detectors such as RCF, CR39 or Imaging Plate are used, both in the stack configuration or within Thomson spectrometers. Indeed, the significant limitation of these detectors is that they cannot be used for online detection, being the process of information retrieving not immediate and in the case of CR39 definitely cumbersome. In the case of Thomson spectrometers, active expensive solutions, such the coupling of a phosphorous to a microchannel plate (MCP), can be used26 is commonly adopted to obtain time-resolved characterization of the accelerated ions, overcoming most of the limitations met by the detection methods previously described. It has indeed the potential to meet all the discussed requirements. The possibility to work with real-time readout systems, without the need of opening the chamber after each shot, makes the TOF an ideal candidate for ion diagnostics in high repetition-rate experiments. Energetic ions are usually detected using semiconductor devices made of SiC or diamond29, or scintillators31. In some cases systems composed by MCP coupled to phosphorous may be also used.Eventually, the Time-of-Flight (TOF) technique33.As Thomson spectrometry, TOF technique is not able to give information on the angular distribution of the accelerated particles. Nevertheless, in general the higher compactness, the reduced dimension and cost of some type of TOF detectors, coupled to optimized real-time data retrieving—no matter how many of them are fielded—allow to install several of them along different lines of observation, even at small relative distances from the target and at rather similar angles, providing a simultaneous high-resolution real-time and high-sensitivity measurement of the particle energy distribution along different directions. Thus, all these features allow to effectively overcome the problems encountered when trying to fulfil the same task by placing several Thomson spectrometers around the chamber, and that normally highly limit the number of detection directions to a few units35 and remarkable levels of EMPs are generated. Protons up to several tens of MeV are here produced36, with typical spectra decreasing with energy. So, both high sensitivity and high resolution are required for a suitable description of the most energetic part of the ion emission. Chemical Vapor Deposition (CVD) diamond detectors have the potential to satisfy both these needs, but with the TOF technique energy resolution and sensitivity have somehow opposite requirements. Indeed, improved energy resolution is here commonly obtained in two ways.241Am decay can have FWHM up to 8 ns for a detector with 500 µm thickness37, up to 1.1 ns for one with just 100 µm thickness37 and up to 0.8 ns or below for one with 50 µm thickness38. So thinner detectors should be preferred for better energy resolution, but on the other hand energetic protons will pass through them more easily, leaving there only a small amount of their energy, and this will lead to reduced sensitivity of the detector to them. It was shown by Monte-Carlo SRIM code simulations39 that protons with energies up to ETHRS-100 ~ 4.6 meV will be stopped within the active region of the 100 µm diamond, releasing all their energy in the detector. Alternatively, those with much higher energy will lose a very limited portion of it. If the signal produced in the detector is small with respect to the background noise, the information on the associated particles can be lost. As observed, the emitted proton spectrum in these experiments decreases with energy, and thus this problem is even more significant for the most-energetic protons. For particles passing through the detector whose produced signal is still reasonably higher than the background, it is possible to reconstruct, by means of suitable numerical simulations24, the initial particle energy from the small portion released in the detector and thus estimate the associated number of detected particles. But this will commonly suffer of low precision due to the related large confidence interval. So, high energy resolution will be achieved but with low resolution for the number of particles in the spectrum.By using fast detectors. In TOF, energy resolution is linked to time resolution, and the detector response velocity is mainly limited by the thickness of the active sensitive region, associated with the time of charge collection to the electrodes. The typical monocrystalline diamond detector response to a single 5.486 MeV α particle emitted by By placing the detectors at larger distances from the target. However, this reduces the overall sensitivity by decreasing the solid angle of detection and thus the number of particles intercepted by the detector.Nevertheless, the TOF method has historically shown significant limitations when applied to experiments with high energy and intensity lasers, where both high-energy ions40, but at expenses of the time resolution37, and thus of the related energy resolution accordingly. One key issue for the sensitivity threshold is the background noise associated with the technique. This is due to the intrinsic noise of all the electronic equipment used, and in particular of the oscilloscope, and to the external electromagnetic noise coupled to the overall TOF detecting chain. It is well known that in energetic high power laser facilities the intense laser-matter interaction generates strong EMPs in the radiofrequency-microwave range12, which remarkably affect the signal-to-noise ratio of the electronic devices placed inside and nearby the vacuum chamber, and that commonly scale with the laser intensities41. Since TOF measurements require time-resolved detectors connected with fast electronic readout systems, the presence of remarkable levels of EMPs has, so far, strongly hindered the employment of this technique in experiments with intense ultra-short pulses at very high-power regimes, where instead their features would have been very useful.For these reasons, whenever improved sensitivity for the most energetic ions is required, thicker detectors are used43.In order to fully exploit the TOF potentiality, we present here the basic idea to use a composite structure made of a set of several time-resolved detectors, which can be positioned as a stack, one after to the other along the direction of the impinging ions emitted from the laser-matter interaction, as shown in Fig. 44 and monolithic diamond-based ΔE–E charged particle telescope for identification of fragments coming from the nuclear reactions45.The main advantage of this novel design is the capability to detect high-energy particles with good sensitivity, without sacrificing energy resolution. The sensitivity features of thick diamonds can thus be replaced with the layered multiple thin diamonds, insuring fast time response and high radiation hardness. It is worth to underline that the technology of diamond detectors is already mature for such complex structures. Devices based on multiple diamond detectors are reported in the literature for other applications: proton recoil telescope based on two diamonds for fast neutrons diagnostic12) to the related electronic devices. This is known to be a major issue especially for devices working at larger frequency bandwidths12 and will thus be more serious for the fast (i.e. thin) detectors. The capability to deal with this fundamental issue is one of the key factors for the successful and effective implementation of these methodologies in the future and will be thus here described in detail.Whenever these schemes will be applied to detect ions emitted by intense matter interactions, with high energy and intensity laser pulses up to the femtosecond and attosecond time-scales, the main limitations to the method sensitivity will be given by the coupling of giant EMPs  device was used to measure the longitudinal profile of the accelerated electron bunches56. Accelerated ions were detected by a CVD diamond detector, schematically shown in Fig. The diagnostic methodology was tested and optimized during an experimental campaign performed on 10 μm aluminium flat targets, irradiated with the FLAME Ti:Sapphire laser at INFN, Laboratori Nazionali di Frascati, having 800 nm fundamental wavelength, 3 J maximum energy, 30 fs pulse duration and 25 µm focal spot, The TOF measurements employing diamond detectors are intrinsically characterized by large dynamic-range signals. To retrieve all the useful information from them, to accurately estimate the energy of the incoming particles and to compute their spectrum, it is necessary to distinguish the finest details without cutting the most intense portion of the signal. The signal collected from the diamond detector was thus divided in two parts by a calibrated splitter, both having the same shape but half of the original amplitude and stored in two different channels of the same oscilloscope. The acquisition set-up is schematically depicted in Fig. photopeak and the particle contribution. The first is generated by the ionizing electromagnetic radiation emitted during the laser-matter interaction and, depending on the specific experimental conditions, can be higher or lower than the second. The photopeak is a clear and very useful signature of the laser-matter interaction instant. Its temporal position gives a reliable absolute reference for determining the arrival times-of-flight of particles from the target to the detector, as discussed in detail later. The photopeak is then followed by a tail produced by the detection of fast electrons37, and of UV and soft X-rays coming from the expanding plasma, whose temperature is decreasing along time. The duration of this tail can be up to several nanoseconds.A typical TOF measurement obtained with this set up is shown in Fig. The second main peak comes instead from the time superimposition of particles arriving to the detector. Both ions and electrons can produce a signal, but the electrons arriving at the same time instants of the ions have much lower energies, and thus their contribution result typically negligible with respect to them. Anyway, whenever required, the application of a very low magnetic field close to the diamond is usually sufficient to deflect them and to avoid their arrival to the detector, practically without modifying the trajectories of the ions.2 intensity. It is evident that channel one  provides information about the main signal generated inside the diamond but, because of the finite dynamic range of the scope, there is poor resolution on the smaller details which, instead, can be obtained from channel three (Ch3 in the figure) which was set to a finer scale. Since the two channels of the same oscilloscope are accurately synchronized, from Ch3 the temporal position of the photopeak was retrieved and used as absolute reference for data shown in Ch1. The consistency of this comparison is confirmed by the coincident temporal position of the protons maximum energy given by the initial point of the main signal , performed employing the aluminium filter in similar conditions to the previous #38, is reported in Fig. The signal obtained for the shot #5  = . In the limiting case of fully-stripped ions , it is iM, EpM) = , where:It is possible to determine the same condition in the energy domain. So, the proton energy range associated with the extremes of the time interval of Eq.  can be wAnd for So, for a given experiment of TNSA mechanism, or in general for any laser-matter process where ions are accelerated because of a potential drop, we can consider as a general criterion that if in a TOF scheme we are able to detect the maximum proton energy entclass1pt{minimaRL–P, under the assumption of emission limited to a unit of solid angle, and uniform within it. Of course, this has limited accuracy4, and a more realistic determination of these amounts would require the simultaneous use of several detectors at different angles, capable to characterize the angular variation of the emitted ion spectra, according to what reported in literature58. Anyway, this is out of the purpose of the present work, and we use these estimations only as useful indicative parameters of the interaction regime. According to these premises, the following parameters were extracted: RL–P = 58. This large overestimation can be easily explained by taking into account that other particles besides protons contributed to the detected signal. In particular, by applying those considerations to the same shot #38, under the conservative assumption of fully stripped light ions reaching the diamond, it results  =  or, in terms of proton energy,  = . By limiting the estimation of RL–P to this interval, the value 58.From the spectrum reported in Fig. L = 2.65 J, IL = 1.8 × 1019 W/cm2), reported in Fig. RL–P = The analysis of the data collected from those shots where an aluminium filter was used provided a further confirmation of the obtained results and of the developed theoretical evaluations. Taking as reference the de-embedded signal obtained for the shot #5 . where higher EMP levels are expected. The technique was tested at FLAME laser and, in order to understand its possible application to facilities affected by even higher EMP pollution levels, some preliminary and successful tests were performed in experiments at the Vulcan Petawatt laser61 with laser energy 2, and also very recently at the Phelix laser with 2 (these latter results will be presented in a separate publication).The capability of performing such on-line accurate measurements in these environments with high EMP levels but without the use of Faraday cages, is of crucial importance to monitor and characterize effectively the particles accelerated via laser-plasma interaction in high-repetition laser-matter experiments. This is a key point for high-intensity and high-energy laser facilities for both laser-plasma acceleration and inertial confinement fusion ), where high levels of EMP are classically produced. Since the EMP fields are known to scale with laser energy and intensityThe potential high energy resolution is one of the key factors of the TOF technique and was here proved by using thin-fast diamonds in an advanced implementation of this scheme.By using these advanced and optimized methodologies, fast diamond detectors can be thus successfully adopted as a main constituent of a layered diamond detector system made of a stack of them. Such configuration will allow to get a composite detector with effective thickness of extended dimension without losing energetic resolution and featured by high radiation hardness, thanks to the independent thin diamonds available throughout the structure. The single module was here studied and characterized in an energy range where protons were completely stopped inside the active diamond layer. This allowed to evaluate its temporal response leading to the high energy resolution and to retrieve the proton spectra exploiting the performed offline calibration. Protons with higher energies will leave only a portion of this energy to the diamond layer. As discussed in this work, for them a layered structure of active detectors is the key for a tailored advanced detection system, capable to reconstruct the proton spectrum with high energy resolution and with all the significant advantages discussed for this single diamond module, which will be extended to a wider range of particle energies.These considerations confirm that the described methodology, together with the overall advanced associated detector system, is a promising candidate for the fast, accurate, high-resolution, high sensitivity, high radiation hardness and online detection of energetic ions in experiments of high energy and high intensity matter interaction with ultra-short laser pulses up to the femtosecond and even future attosecond range.29, where high levels of EMP fields are generated. Thanks to their wideband gap of 5.5 eV, their high carrier mobility, and their radiation hardness63, diamonds are particularly useful to monitor UV, X photon emission and accelerated particles in laser-plasma experiments66. Indeed, they have low leakage current, fast time-response, and insensitivity to visible and infrared light which avoids any effect due to possible coupling of any stray light coming from the main laser beam to the detector. This is important to get an intrinsic low background level. To fully investigate the management of the EMP issue in the most demanding conditions, we used here a fast detector consisting of a 50 μm intrinsic diamond layer grown by chemical vapour deposition technique on a commercial 4 mm × 4 mm × 0.5 mm High Pressure High Temperature (HPHT) substrate. The detector operates in planar configuration with superficial interdigital aluminium contacts with 20 µm width and 20 μm spacing29, which allow for fast time detection of moderate energy particles. The time resolution of this detector was offline obtained from detection of single α particles of 241Am source, and it resulted Δt = 0.8 ns38. By considering a Gaussian fitting of the associated single-particle detected signal, this means a 3-dB frequency bandwidth The detector was developed and optimized to work in the harsh environments of high-power and high-energy laser-matter interactionsThe diamond detector was linked to the splitter through a cable connected with a custom large-capacity, high-frequency Millimetrica Bias-Tee (MIL-BT 010-6000). This isolated the scope from the − 150 V bias voltage for the diamond, without losing significant information over the frequency range (300 kHz–6 GHz), suitable and tailored for signals coming from the diamond detector.The splitting of the main diamond signal in two halves by a calibrated splitter, as shown in Fig. 24. Anyway, they do not consider the specific experimental response of the detector to a specific particle with a specific energy.The determination of accurate energy spectra for incoming particles from the TOF signals generated by the detector is a delicate issue. In some cases, simple mathematical reasoning is used to get the energy-domain spectra from the stored time-domain signals, as very recently reportedWe describe here instead a detailed procedure for getting accurate spectra from a diamond detector, including the experimental calibrations of its response. First, in the next section, a detailed description of the EMP management, allowing to obtain signals almost free from electromagnetic noise, is reported. Then we show the procedure used to include in the results the effects due to the long cables employed to manage the EMP pollution affecting the diamond signal. Eventually, a novel methodology is described to get the calibrated energy spectrum. To this purpose, we analyze the response of the diamond detector and discuss in detail also the overall spectrum accuracy for the energy and the number of particles.18. This generally depends on the specific type of laser matter interaction and its intensity is known to scale with the laser energy and intensity on focus41. There are several mechanisms of generation for the intense EMP fields in the experimental conditions of this campaign, with a classical TNSA scheme67. The common main source is the neutralization current flowing through the target holder to the chamber floor, caused by the fast electron emission from the target due to the intense laser-matter interaction. A typical EMP signal, measured inside the experimental vacuum chamber during the present experimental campaign, is shown in Fig. 32 (3-dB-bandwidth up to 5.5 GHz). It was positioned at 31 cm from the target and had 15 cm height from the chamber floor and -3 cm shift in the x direction with respect to the target position, as shown in Fig. 12 (a paper is in preparation about this issue). By following the procedure described in detail in reference17, from the acquired measurement it was possible to get an estimation of the associated maximum peak-to-peak electric field ~ 25 kV/m, that is coherent with what expected for these experimental conditions41. Such high level of EMP fields produced, in the first test shots of the campaign, diamond signals strongly affected, and sometimes even hidden, by the EMP oscillations68. One of the diamond signals collected during these first shots is shown in Fig. It is well known that in high power laser-matter interactions the effect of the EMPs on diagnostics with electronical components can be remarkableSeveral precautions were here adopted to obtain signals from the diamond detectors with high signal-to-noise ratio even in these environments with high electromagnetic pulse pollution. In particular, two types of EMP field coupling had to be avoided: that directly with the detector and that with the overall acquisition system. We give here details on how the implemented techniques acted on the EMP fields and their coupling to the whole diamond-detector measurement setup.29 of the diamond detector holder shown in Fig. r provides a cutoff frequency, c is the speed of light, which highly limits the EMP coupling without covering the active surface of the diamond detector69. The same principle was applied to the TOF line. The final connection with the diamond detector is a pipe of 65 cm length and 11 the cutoff frequency was: z with dependence 11 mode as a function of the frequency is shown in Fig. The EMP coupling with the device was minimized thanks to an ad-hoc mounting structurementclass2pt{minim21 scattering parameter is given in Fig. In order to reduce the EMP coupling with the acquisition system, the main transmission link consisted of ~ 15 m RG223 double-shielded coaxial cables, used to transport the signal from the detector to the scope. They have a shielding effectiveness higher than 80 dB for the frequency ranges related to the performed experiments and resulted very suitable to suppress the direct transmission of the EMP fields traveling in air to the inner coaxial conductor of the cable, through their outer shielding conductor. The coaxial cables, together with the calibrated splitter and the custom bias-tee, were offline characterized in the frequency domain by the Agilent N5230A Vector Network analyser. The obtained S16, giving high attenuation to possible contributions at high frequencies. On one side this improved the filtering of the high-frequency components of possible EMPs coupled to the detector. But on the other side it might have introduced limitations to the fast response of the detector setup. As observed, the 3 dB low-pass bandwidth of the interdigital diamond detector resulted 625 MHz. According to Fig. 21 scattering parameter for this frequency was 0.2492 (~ 12 dB), which indeed resulted a very suitable compromise.They behaved as effective low-pass filters16.The propagation of the EMP fields outside the experimental chamber can be classically modelled with the 1/r law. The use of long cables allowed the positioning of the scopes far from the experimental chamber, and thus decreased the possible direct coupling of EMP fields with the scopes themselves16.EMPs have a typical exponentially-decreasing time profile and become usually comparable to the background noise in ~ 100 ns, as shown in Fig. These long cables worked on the EMP rejection in several ways.Those cables were also surrounded by several ferrite toroids, with bandwidths 0.5–5 MHz, 1 MHz–1 GHz, 2–30 MHz, 20–200 MHz, respectively, providing damping of the current flowing on the outer conductor of the cables caused by the applied external EMP fields. This avoided that those currents could reach the oscilloscopes and generate EMP noise coupled directly to it.By means of these methods it was possible to obtain detected diamond signals with high signal-to-noise ratio. The EMP high frequency oscillations shown in Fig. 17 was required to recover the signal at the detector site from the one recorded on the oscilloscope. The de-embedded signal 17:The signal collected by the CVD diamond detector was transmitted to the scope through the long coaxial link, having a frequency-dependent attenuation. Thus, a suitable de-embedding procedureIn Fig. d the distance of the detector from the interaction point. Therefore, the time instant when the laser-matter interaction occurs can be determined as i = d/ti the associated detected flight velocity. In this way, by TOF methods accurate information on particle velocity can be achieved. From these measurements calibrated particle spectra can be obtained, if the type of particle reaching the detector is known or assumed for a given time interval38. Under this condition, for a generic ion species the energy associated with the detection time can be obtained from the relation: To retrieve the accelerated particles spectrum, as a first step it is necessary to define an absolute time-reference related to the laser-matter interaction instant. As discussed, at the moment of laser interaction with matter, a burst of UV-X rays is generated and detected by the diamond detector. The detection time entclass1pt{miniman index, with The finite temporal resolution Δt of the detector, obtained with the mentioned calibration, affects the energy tolerance of the measurement performed with the diamond detectors. For a generic time interval, indicated with the nth interval. The negative sign is because energy is a monotonically decreasing function of time. In case of non-relativistic particles nth interval. Thus, the absolute value of the relative error on the energy is equal to twice the relative error on the measurement of the time of ion arrival to the detector. So, for the same The relative error on energy, given by the finite temporal resolution, can be written as:62.As already mentioned, the interdigital diamond configuration consists of a 50 μm intrinsic diamond layer, capable to fully stop protons with energy up to ~ 3 MeV. The signal generated by incoming protons is proportional to the particle energy. The induced charge signals collected at the sensitive electrode can be considered as due to the motion of electron/hole pairs generated in the bulk of the diamond sample, and charge pulses are formed only in regions where an electric field (E) is present. For this reason, the region where the charges are more efficiently collected is that closer to the electrode surface. As a consequence, the response of the interdigital diamond detector is high for particles with energies low enough to be completely stopped inside this high-efficiency layer, and it starts to decrease for those having higher energies, and thus larger ranges, up to the case where they will generate a signal on the detector comparable to the noise level. Indeed, it is well known that the charge collected in diamond detectors due to 39, the range of protons in diamond varies from 1.5 to 25 μm. An electronic chain consisting of a charge-sensitive preamplifier ORTEC142A and an ORTEC572 shaping amplifier was used. The calibration of the electronic chain was performed using a Si detector and a precision pulse generator ORTEC419 relating the pulse heights provided by the reference Si detector with those from the diamond devices.In order to evaluate the CCE curve, the diamond detector was previously characterized at the AN2000 microbeam facility of the National Laboratories of Legnaro  by using proton beams of energy respectively 0.3 MeV, 1 MeV, 1.4 MeV and 2 MeV. The beam was focused to a spot size of ~ 5 μm on the sensitive electrodes of diamond. As evaluated by the SRIM Monte Carlo Simulation codeThe CCE of the detector as a function of the investigated proton energies is reported in Fig. As expected, for low energy protons, the induced charge is equal to the generation charge (i.e. By considering that equal CCE is obtained for other particles having the same range in the detector, from these measurements it is possible to determine the CCE also for other ion species.nth time interval, the value of the associated charge generated in diamond can be computed:R is the characteristic load impedance and nth time interval, and the related average of the The number of incoming ions of known specie can be retrieved according to the following relation:Hence, the error on the estimation of the number of impinging particles can be expressed in terms of the In general, to retrieve the proton spectrum in case a filter is used between the target and the detector, it is necessary to correct the number of particles estimated from Eq.  as it fomentclasspt{minimated Eqs.  accordinThis relation actually links arrival time and energy in the case a filter is used, and can be inverted numerically to find the associate As a rule of thumb we can consider that the effect of the drift space located after the filter starts to be relevant when the time needed by a particle to travel through it is one tenth of the time needed to travel the main drift space D. To evaluate for which proton energy this happens it is convenient to express the filter attenuation factor as a function of the parameter D = 105 cm; a value of In the present experiment We can conclude that in the present study the effects of the drift n in Eq. . Neverthn in Eq.  is very


The Bland–Altman plot is the most common method to analyze and visualize agreement between raters or methods of quantitative outcomes in health research. While very useful for studies with two raters, a limitation of the classical Bland–Altman plot is that it is specifically used for studies with two raters. We propose an extension of the Bland–Altman plot suitable for more than two raters and derive the approximate limits of agreement with  In health research, it is often desired to determine to what degree different raters or methods (either persons or devices) agree on the measurement of a continuous outcome on the same subject . The main aim is to ensure that the variability between raters is small enough to use observations from a single rater in future studies or clinical practice and that it does not make any difference which rater conducted the single measurement.Typically this situation will be dealt with by applying a mixed effect regression model or related methods ,2,3. In m raters result in One of the drawbacks of the classical Bland–Altman plot is that it only applies to a situation with two raters or methods, while for both practical reasons (distributing workload to multiple raters) and statistical reasons , it is desirable to use more than two raters for carrying out agreement studies. The standard suggestion is usually to present multiple Bland–Altman plots for each pairwise comparison of raters ,8, but tSome suggestions include presenting all observations in the same plot, with one marker for each observation instead of each subject, either connecting observations for the same subject by lines  or by distandard  or reducstandard .The aim of this paper is to present a novel extension of the classical BA plot together with a generalized LOA, which only requires one plot and one marker per observed subject. While the main aim of this proposal is the comparison of multiple raters, the plot can be applied to comparisons of multiple methods as well. Especially for this case, it is important to be aware of the assumption of homoscedasticity, which our proposal inherits from the classical Bland–Altman plot; deviations from this assumption damage the interpretation of the Bland–Altman limits of agreement ,13.m raters who observe each of n subjects once, resulting in We are interested in investigating a situation with In this setting, we assume a data generating process similar to the assumptions made by Bland and Altman  for the Each subject’s true value In the classical Bland–Altman plot  and constant variance is While it is intuitive where the sample should be placed, the placement of a 95% LOA requires some additional considerations. Here, we use the property that the empirical variance of Applying this to our model, we observe asymptotically:Therefore, we propose to place our LOA at:s, which in the classical Bland–Altman plot is taken into account by using the t-quantile), nor that the coverage achieved by the LOA should correspond to a n. To communicate the uncertainty of the LOA, we suggest plotting 95% confidence intervals around the line. Here, we did this by applying bootstrapping in each sample with 1000 repetitions and reporting a Note that this formula only takes into account the number of raters, but neither the number of subjects observed  to distinguish which rater was responsible for the largest deviation from this subject’s mean; hence, a color/symbol very common in the plot would indicate a rater with larger uncertainty than the remaining raters, violating the assumption of j. Algorithm 1Extended Bland–Altman plot for multiple raters.m and number of subjects n and individual ratingsObserve number of raters Determine each subject’s mean and standard deviation:Determine the position of the LOA: Estimate the 95% confidence interval for the LOA by bootstrappingDetermine bias indicators for each rater:L with the confidence interval, and Plot One limitation of our suggested plot is losing the information on a possible bias of a specific rater, as well as possible heterogeneity between the uncertainty of raters. To include information on this phenomenon in the plot, we suggest adding tick marks on the y-axis corresponding to:n observations used to produce the plot and for one new observation (To determine how reasonably our LOA agrees with the desired nominal s et al. . Data wennet [boot [R Version 3.6.1  with thennet  and bootet [boot ,20 was uTo investigate the usefulness of the extended BA plot, we applied it to two datasets with multiple raters from the literature. For the first application  left, weFor the second application, we applied the extended BA plot to the glucose measurement data from a method comparison study  with fouWe showed that it is possible to present the agreement of more than two methods or raters in one combined plot and to obtain similar information as can be obtained from a classical BA plot including LOA and the corresponding confidence intervals; moreover, we indicated the possibility of detecting inhomogeneity in variance, as well as bias among raters. We showed by simulation that our suggested formula for the LOA of the extended BA obtains approximately The main strength of this study is that we combined a closed formula for the LOA based on mathematical arguments with transparent simulations documenting that the method behaves well even with small sample sizes. Moreover, we showed that our suggested plot can combine information presented in multiple plots in applications from the literature. A weakness of this study is that the LOA is only an approximation, as it does not fully capture the uncertainty of new observations, as well as only being equipped with approximate bootstrapped confidence intervals.Compared to the literature, the main strength of our approach is that only one plot is required for the comparison of multiple methods or raters and that only one dot is included in the plot for each observation unit, resulting in plots that are easier to comprehend. Moreover, these facts imply that the points on our plot are independent observations facilitating the estimation of accurate LOA and confidence intervals. Although it is possible to indicate bias and variance heterogeneity in our plot, it might be less clear than in some of the methods presented in the literature. Additionally, as our plot is only one-sided due to the non-negativity of standard deviations, this might impede its interpretation for readers used to classical BA plots.An additional weakness of the proposed method is that it shares the assumption of homoscedasticity with the classical BA plot. It is well known from the literature that this assumption can be problematic, especially in the case of method comparison studies ,13. TherThe possibility to present agreement information for more than two raters hopefully increases the possibility to report this information in agreement studies and to better inform the readers. Indirectly, this also might increase the inclination to include multiple raters in agreement studies, improving the generalizability of such studies. This implies that researchers can include the same observations in a graphical presentation as in more advanced analyses in studies with multiple raters, e.g., mixed models, improving the transparency of the studies. The fact that our LOA is presented with BA plots . One of There are still some outstanding questions with regard to our suggested extension of the BA plot. Firstly, it would be desirable to obtain a more precise, non-asymptotic formula for the LOA taking into account the full amount of uncertainty in the observations. Secondly, a closed formula for the confidence interval would be preferable to our bootstrap approach. Finally, implementations of our plot in standard software packages will improve its applicability.


We consider a measure of cooperativity based on the minimal interaction required to generate an observed titration behavior. We describe the corresponding algebraic optimization problem and show how it can be solved using the nonlinear algebra tool SCIP. Moreover, we compute the minimal interactions and minimal molecules for several binding polynomials that describe the oxygen binding of various hemoglobins under different conditions. We compare their minimal interaction with the maximal slope of the Hill plot, and discuss similarities and discrepancies with a view towards the shapes of the binding curves. Thus it quantifies the minimal deviation from an independent system that is required to explain the observed overall binding behavior. The following proposition states that the minimum exists.In other words, the minimal interaction P of degree n with positive coefficients there exists a molecule n sites such that Martini , §4 For Since cooperativity is a property of the binding curve which emerges from the interaction between the sites, the minimal interaction of a binding polynomial is a natural candidate for quantifying cooperativity. In addition, Martini , §4 showConsider the following binding polynomials:P:In this section, we consider the problem of computing the minimal absolute interaction for a given binding polynomial standard form of a continuous optimization problem with objective function and constraints. The set of all molecules W which satisfy the constraints is the feasible set.Problem  is commolinear program. If the objective function is quadratic and the constraints are linear, the problem is also called a quadratic program. Both types of optimization problems are well-studied with plenty of literature and software solutions. If both objective function and constraints are polynomial, the problem is a polynomial optimization problem or an algebraic optimization problem. This is the type of problem that needs to be solved for Problem Generally speaking, there are many approaches for solving optimization problems depending on the type of the objective function and the constraints, which may also include inequalities. If both are linear, the problem is also known as a the objective function contains 11 maxima,the constraints contain polynomials of degree up to 15.In the following, we will briefly discuss the two challenges separately.For molecules with 4 binding sites specifically, Problem  is of thentclass1pt{minimaThe maxima in the objective function of Problem  can be rOne standard way is to reformulate the objective function as a maximum of polynomial functions and linearize the objective function through additional constraints: Abbreviating entclass1pt{minimaAlternatively, one can decompose the space of molecules One can reduce the number of regions that require consideration slightly by exploiting the intrinsic symmetry of the problem.xy, x and y, the minimum of Consider for example the following polynomial optimization problem:For Problem  specificThere exists a natural action of the symmetric group Instead of computing in all P, the polynomial equations in Problem   Imai . One of mentclass2pt{minimScapharca inaequivalvis measured at different temperatures  in our problem. While both Problem Tropical geometry  dependency, which is a classical research topic in these fields Rényi . In part


People have a good intuition of how to move a computer mouse to place a cursor at a desired position on a screen. This is surprising because the hand and the mouse are at different locations and they generally move in different directions and over different distances. But using a computer mouse is not always intuitive: try positioning a cursor after turning the mouse by 90° in your hand. To examine when using a computer mouse is intuitive, we asked participants to move a cursor to targets on a screen by moving a mouse along a surface. We varied the orientation of this surface in space and that of the mouse in the hand. Participants performed best when the mapping between hand and cursor motion was close to what we are accustomed to, either in space or relative to the forearm. We asked participants to quickly move a cursor to a target on a vertical computer screen (38 × 30 cm) by moving a wireless computer mouse. They moved the mouse across a surface that was attached to a sturdy adjustable tripod. When the cursor (a 1.2-cm diameter black dot) remained within the target (a 3.5-cm diameter green dot) for 200 ms, the target jumped to a new position (9 cm away in a randomly selected direction). This continued for 90 s. We compared 13 configurations that only differed in where the mouse was held and the direction in which it had to be moved to move the cursor in a desired direction. Eighteen right-handed adult participants signed informed consent forms, practiced in the normal configuration, and were then tested once in each configuration in random order.The medians of the times taken to reach targets were ranked across configurations for each participant individually. Almost all participants reached targets fastest in the normal configuration with the mouse at hip level in front of their right shoulder . It consFour configurations in which extending the arm did not move the cursor upwards took about twice as long per target. In two of these configurations, the hand moved parallel to the cursor, either along a vertical surface as in When the mouse was held upside down below a surface as in


Z refers to a partition function. The latter SLE process is a process that can’t be written as a In this article we show the convergence of a loop ensemble of interfaces in the FK Ising model at criticality, as the lattice mesh tends to zero, to a unique conformally invariant scaling limit. The discrete loop ensemble is described by a canonical tree glued from the interfaces, which then is shown to converge to a tree of branching SLEs. The loop ensemble contains unboundedly many loops and hence our result describes the joint law of infinitely many loops in terms of SLE type processes, and the result gives the full scaling limit of the FK Ising model in the sense of random geometry of the interfaces. Some other results in this article are convergence of the exploration process of the loop ensemble (or the branch of the exploration tree) to  Ising model is one of the most studied lattice models in statistical physics. The Ising model  have percolation-type representations called Fortuin–Kasteleyn random cluster models (FK model). Given a graph the Ising model assigns probabilities to configurations of p to each open edge and q per each connected cluster of open edges. We will consider the FK Ising model, i.e., FK model whose parameter value q corresponds to the Ising model, on a square lattice. The lattice we are considering is the usual square lattice The mentclass2pt{minimloop representation of the FK model is defined on so called medial lattice, shown in Fig. simple loops when we resolve the possible double vertices by the modification illustrated in Fig. We will consider a bounded simply connected subgraph of the square lattice. We will make this definition clearer later. An FK configuration in the graph is illustrated in Fig. p and q get mapped under this involution of FK configurations to values p, that is, critical parameterThe duality of the FK configurations described above gives a mapping between the set of configurations with wired boundary conditions and the set of configurations with free boundary conditions, defined on the graph and on its dual, respectively. One can check that the FK model parameter values entclass1pt{minimaThe correspondence of boundary conditions is slightly more complicated for other boundary conditions than the wired and free ones.The parameter is chosen to be critical for several reasons. First of all it is expected that only for this value of the parameter the scaling limit will be non-trivial. For the other values, we get either zero or one macroscopic loop and all the other loops will be microscopic and vanishing in the scaling limit. The only macroscopic loop will be rather uninteresting as it will follow closely the boundary, so that the loop will fluctuate from the boundary only to a distance which vanishes in the scaling limit. In contrast, for the critical parameter the scaling limit will consist of (countably) infinite number of loops as we will be showing.The second reason for selecting this value of the parameter is more technical. For that value, the observable we are defining in Sect. The third reason for the choice of the critical parameter is that at criticality we expect that the loop collection will have a conformal symmetry. This is already suggested by the existence of the holomorphic observable.In fact, the discrete holomorphicity and related techniques allow us to control the scaling limit well and to identify the scaling limit and to show its conformal invariance. And thus can be seen as the most important reason to consider a system at criticality.exploration tree of a loop configuration. The  exploration tree connects the fixed root vertex to any other boundary point. The construction of the branch form the root to a fixed target vertex is the following:start the process at that location on that loop.To initialize the process cut open the loop next to the root vertex and Explore the current loop in clockwise direction until the target point is reached or any point at which it is clear that it is impossible to reach the target point along the current loop .If the target was reached, then stop and return  the path concatenated from the subpaths of loops in the order that they were explored.If the target was not reached yet, cut open the loop next to the current location and jump to that loop and go to Step (2).The construction depends on the direction of the exploration which was chosen in (2) to be clockwise. Instead of a deterministic choice, independent coin flips could be used to decide whether to follow each loop in clockwise or counterclockwise direction. This would lead to a different process. In this article we will use the above construction which suits well our purposes. After all, the main goal is to show convergence of the loop collection, and the above construction agrees well with our observable.Figure admissible if it is simply connected and bounded and its boundary consists of a chain of black octagons and small squares as in Fig. Carathéodory sense with respect to a point n and the conformal and onto maps K of K belongs to the domain of n).The main theorem of this article is the following result. For its formulation, call a discrete domain Let Moreover the law of radial exploration tree of the FK Ising model. These restrictions are technical and they are not needed, for instance, for the convergence in the so-called 4-point case  if A simply connected, non-empty, bounded domain See Fig. G be a simply connected subgraph of the square lattice G with all wired boundary conditions in the special case of the critical FK Ising model, that is, when G which is a (simply connected) subgraph of loop representation is obtained as loops which form boundaries between open cluster and the dual open clusters and is defined as a collection of loops on the corresponding subgraph Let entclass1pt{minimadense collection of non-intersecting loops (DCNIL) ifeach e. Here we use that for every edge Let the collection of all the loops in the loop representation be C of loopsZ is the partition function that normalizes the probability measure.Let’s call a (unordered) collection of loops external boundary.internal boundary. We say that loop touches the boundary if if it intersects Define the collection of boundary touching loops, We consider two boundaries of the domain, one which is the boundary of the domain and one which shifted by one lattice step from the first one towards the interior of the domain. They are both simple loops on the lattice which satisfy the same parity condition as the loops of the random cluster loop representation (the octagons on both sides have uniform color). More specificallyRecall the Carathéodory convergence from Sect. Let us rephrase here the first half of Theorem . Suppose that tree-to-loops map.” The structure of the tree w the incoming edges are w through Next we will construct the inverse of the loops-to-tree map which we will call a “The mapping from the collection of boundary touching loops Similar constructions work in the continuous setting. See  for the Let us repeat here the second half of Theorem The law of The proof of Theorem In this section, we establish a priori bounds for trees and loop ensembles. The setting is relatively general, although we only apply it here to the FK Ising exploration tree of the boundary touching loops.An approach to establish compactness properties of sequences of probability measures based on probability bounds of multiple crossings of annuli by random curves was set up in  extendinX tight over a collection For any fixed measurable space A crossing of an annulus Recall the general setup of : we are for any m such that each m segments of diameter less or equal to r, then there exists a random variable K is a tight random variable for the family if for each All branches of The following claim holds for the collection of the probability laws of FK Ising exploration treesEach of the claims have their own applications below although they are closely related, see .n.We need to verify the first claim and the two other claims follow from it, by results of ; more spLet n such that n and constants By Lemmas <ε. Thus  holds fothe order of exploration of the curves. More specifically, set explored collection of branches.Let For a given domain We call The following definition generalizes Definition 2.3 from . This dex in the set avoidable for avoidable for all (branches). We say that unavoidable for unavoidable for at least one (branch). Here and in what follows we only consider allowed lattice paths when we talk about connectedness.For a given domain Note that branching point of the tree Recall that Next we will write down an estimate in the form of a hypothesis analogous the ones presented in Section 2 of . The estgeometric joint unforced–forced crossing bound Call the event above Let See Fig. geometric joint unforced–forced crossing power-law bound if there exist The family  side of .We want to use Condition If Similarly as in , we try By a similar arguments as in Section 4.1 of , we can As indicated by considerations in Fig. Then we use the crossing estimates of  to reducThe upper bound for existence of a curve can improved to the form The theorem can be proved in the same way as the result that a single interface in FK Ising model satisfies a similar condition, which was presented in Section 4.1 of . Howevern 2.6 of  by consiAs shown in . For any F from below by finite unions of this type of intervals and use monotone convergence theorem to show thatLet M) and t. Therefore clearly, This shows that The claim follows from the next theorem with M and N are martingales. Then the following claims hold.If the process If for some x — in particular Suppose there exists continuous functions Let M, because M is a continuous martingale, see Chapter 2 of [Similarly as in the previous section, we notice that we can do stochastic analysis with ter 2 of . The samWhen Similarly as above we can write Note that when Next result together with Theorem Let This equation for Since index of a Bessel process is defined asLet  / 2. By  Exercise / 2. By  Theorem Notice next that emigroup , p. 446 43Btfrom .The claim follows from Lemma f is not a constant function and if f is Hölder continuous with exponent Let The proof is standard using the definition of Hausdorff measure andZ, and the The drift of a SLE process can be given in general in terms of a partition function a to d which is reflected on bc towards d. Notice that the process with the partition function \documentalent to .Notice that when 2XtYtand  becomes1In the same way, when Processes This claim follows from comparison to Bessel process  and 110110 and aBy comparing to a Bessel process as we did in Sect. hen that  and 92)\documentRecall from the proof of Proposition Now t is such that For fixed Clearlyt′=0}.By  Exerciset′=0}.By  Theorem As a conclusion to this entire article we outline below the proof of Theorem As above, we consider a sequence of domains The basic crossing estimates were established for the FK Ising exploration tree and its branches in Sect. By these results, every sequence of finite subtrees of the approximating domains converges in distribution to a finite subtree of the The precompactness of the probability laws of the full tree and of the loop collection were established in Theorems Since the orientation of the image of the exploration tree when mapped to


The so augmented device is sensitive to mechanical stress. In combination with an analogue circuit, this sensor unit is capable of encoding the mechanical quantity into a series of spikes with an ongoing adaptation of the output frequency. This allows for a broad application in the context of robotic and neuromorphic systems, since it enables said systems to receive information from the surrounding environment and provide encoded spike trains for neuromorphic hardware. We present numerical and experimental results on this spiking and adapting tactile sensor.The ongoing research on and development of increasingly intelligent artificial systems propels the need for bio inspired pressure sensitive spiking circuits. Here we present an adapting and spiking tactile sensor, based on a neuronal model and a piezoelectric field-effect transistor (PiezoFET). The piezoelectric sensor device consists of a metal-oxide semiconductor field-effect transistor comprising a piezoelectric aluminium-scandium-nitride (Al Herein, sensation defines the ability to convey information by a chain of transducer stages towards the brain3. It is the somatic sensory system which plays a major role in the transmission of mechanical stimuli from the environment to the brain4. The necessary signal conversion is done by mechanoreceptors underneath the skin which are sensitive to physical distortion and therefore necessary for the perception of size, shape and consistence of objects. Some important classes of mechanoreceptors responsible for a neuronal answer to mechanical stimulation are Meissner’s corpuscles, Merkel cells and Pacinian corpuscles, which can be found in glabrous skin7. Regarding mechanical perception Edgar Douglas Adrian launched a series of seminal papers formulating the firing rate hypothesis based on a number of intriguing experiments as early as 1926. Thereby, he also established the term adaptation in the framework of biological signal processing10. Today, the adaptation to a stimulus is considered as a classical response function, which is not just restricted to the encoding of external signals into internal spiking representations. Besides the adaptation of sensory neurons to a constant stimulus, spike-frequency adaptation is also present in neurons even far from sensory systems and can rise not just through cellular12, but also network induced mechanisms14. These biological findings served as a guideline to develop a tactile sensor based on piezoelectric AlxSc1−xN (AlScN) within the fields of neuromorphic engineering and robotics.Neural systems and their surroundings are in an ongoing interaction. Humans, mammals and even simple forms of living species like invertebrates are well adapted to permanently changing environments which ensures their survivalxTi1−xO3 (PZT)15 or BaTiO316 these concepts range from mechanical fluid based17 sensors to electrical approaches based on graphene21, polymers26 , and field-effect transistors coupled capacitively with nanowires28. Moreover, the possible application of pressure sensors for smart prosthetics29 and their capability of connecting them directly to nerve cells were explored30. For a deep and comprehensive overview about recent developments and further possible applications of tactile sensors and eSkin, we refer to the following review articles by Dahiya et al.31 and Soni and Dahiya32. In this context we would like to highlight the piezoelectric oxide semiconductor field effect transistor (POSFET) as a tactile sensor because this device has a few features in common with the here presented PiezoFET35. The POSFET exploits the organic ferroelectric copolymer PVDF-TrFE in the gate stack. Because ferroelectric materials are piezoelectric, the POSFET is a stress sensitive device, too37. Via the piezoelectric effect, stress induced interfacial charges modulate the channel current of the transistor. This enables the tactile sensor function of the device. Although this fundamental working principle is the same for the POSFET and PiezoFET, we would like to emphasise that the here presented PiezoFET based on AlScN exhibits a few distinguishing features. In contrast to the organic copolymer PVDF-TrFE, AlScN is compatible with Si-CMOS technology40. This allows the development of highly compact and integrated tactile sensor units consisting of PiezoFETs and subsequent neuromorphic circuits. Moreover, the ferroelectric copolymer PVDF-TrFE typically needs an initial wake-up procedure which consists of applying an electric field of about 80–100 V/µm. Such a procedure could be unfavourable for densely packed integrated sensor arrays. The electric field is necessary for the polymer device to function fully41. Besides the development of single sensor devices for the conversion of stress into an electrical quantity, also a tremendous progress regarding analogue circuit design was made over the last decades42. This ranges from the development of biologically inspired circuits like the adaptive exponential I&F neuron44 and their integration in spiking deep neural networks45 to mixed signal circuits which exploit events for processing visual information49. For a review on other neuromorphic systems and circuits, as well as mimicking other senses, the reader can refer to Bartolozzi et al.50.During the last years, a tremendous effort was made to develop different concepts regarding touch and tactile sensing. Besides traditional piezoelectric materials as for example PbZr35. In the following, we present the PiezoFET in more detail. Subsequently, the entire unit including the spike generation circuit is described. This encompasses a short introduction of the used neuron model as well as numerical results on the proposed spiking and adapting circuit. Finally, experimental findings performed with the touch sensor to demonstrate the spike coding of the applied forces as well as the exponential adaptation of the system are presented.In the here presented concept, the piezoelectric thin film inside the gate structure of the PiezoFET responds to a mechanical deformation with a polarisation. For the encoding of the signal into spikes, a Leaky Integrate and Fire (LIF) approach is used. Here, the focus was on the development of a circuitry comprising just few components. Therefore, the LIF neuron model we use does not model the conductance of ion channels explicitly. In order to generate spikes, a negative differential resistance is used which is based on the positive feedback coupling of two transistors. This is a difference to other concepts like the spike based readout of the POSFET51. Mechanical stress applied to the AlScN layer induces surface charges which in turn modulate the transistor channel current. Thus, this transistor combines the stress sensing capabilities of a piezoelectric material with the amplification of a field-effect transistor. Furthermore, because the bottom AlScN interface is only a few tenth’s nm apart from the transistor channel this configuration may result in a large signal-to-noise ratio.The concept of the force sensitive PiezoFET is based on a conventional field-effect transistor platform. The signal conversion from a mechanical quantity to an electrical one is achieved by a piezoelectric material. Therefore, a c-axis oriented AlScN layer containing 27% Sc is deposited in between the control gate and the channel of the MOSFET. AlScN is chosen due to its higher piezoelectric coefficient compared to pure AlN while remaining CMOS compatible paired with lower leakage compared to most perovskite piezoelectrics2 (13 nm). The AlN functions as an adhesion layer on which the Pt as a structural seed layer for the c-oriented growth of the AlScN is deposited. We assume that the influence of the 20 nm AlN layer can be neglected because it was sputter deposited directly on the amorphous gate dielectric without a seed layer in between. Therefore, it is either amorphous or has less pronounced piezoelectric parameters compared to the much thicker AlScN film. The n-MOSFET is built on a (100) oriented p-type Si and operates in the subthreshold regime leading to electrons as the majority charge carriers. The orientation of the channel regarding the crystal is in the [110] direction minimizing possible piezoresistive influences by changes in carrier mobility resulting in a changed drain current55. In Fig. 40. The inset of Fig. In Fig. 2 3 nm. The2 3 nm. TheBesides the thermal voltage F is the force acting on the cantilever generated by a current through the electromagnet and the constant magnetic field of the permanent magnet. The force can be attractive or repulsive and arbitrary stress wave forms can be generated by appropriate bias currents. We refer to a positive force when it follows the direction indicated by the arrow in Fig. To verify the function of the PiezoFET, the device was integrated into a Si-cantilever configuration. The schematic 3-dimensional set-up is shown in Fig. entclass1pt{minimaAs the force is applied to the tip of the cantilever the material bends and stress is generated.56. For a rectangular beam the second moment of inertia can be calculated as:The amount of stress Here, the variables 57 as follows:The term entclass1pt{minimasee Fig. –5) the  the \docThe piezoelectric coefficient entclass1pt{minimaThe change in the polarisation voltage is a function of the time derivative of the force As the piezoelectric gate layer is subjected to mechanical stress, the generated voltage is superimposed on entclass1pt{minimamentclasspt{minimaentclass1pt{minimaDS of the PiezoFET and the applied force, as well as its decay after applying a constant force, offers the opportunity to convert mechanical stress into neuronal-like spike trains including spike-frequency adaption. In this way, basal biological functionality can be mimicked by a compact circuitry. The circuit is based on the LIF neuron model. This model resembles basic neuronal functions, by integration of incoming information and output of spike encoded information through a firing and reset process59. The potential The observed relation between the channel current IAs this system does not have a mechanism for spike generation, a threshold After the generation of a spike, the system is reset to its resting state As the integration process is repeated after reaching the reset point, the period for a constant input current is the time between two spiking events As mentioned earlier, in contrast to biology the reset does not generate a spike in this mathematical model. Nonetheless, from the definition of the spike times, a spike train can be derived as the sum over Dirac pulses shifted by corresponding spike times.If a constant input current is assumed, a general solution of Eq.  can be dFrom this the frequency of the model for a constant input current can be calculated as the difference for two successive spiking points. With The coding of mechanical stress into a spiking answer is an essential step to supply neuromorphic systems with relevant environmental information. Thus, exploiting analogue circuit design might pave the way to highly integrated dense and energy-efficient systems. Furthermore, with the design of analogue oscillator circuits, with small distances to the sensor and capabilities for local information processing, complex multiplexer setups with analogue to digital converters may become obsolete. Thus, the presented system is largely bio-inspired and takes advantages of a highly efficient information processing .As the transistor An increase in the loading current d in Eq. .F”). This circuit is responsible for the reset to the resting potential, after reaching a threshold defined by 262. As the applied voltage exceeds the threshold voltage of these transistors, the current increases. This discharges the capacitor The last stage is the firing circuit (“are Eqs. ).In contrast to most thyristor approaches, the gate port is at the n-layer. At this port, the threshold voltage for the spike generation is defined. With an increase in the charging current, the frequency of the oscillator circuit changes described by Eq. . The disIn the following, the aforementioned equations and considerations are used to simulate the overall system. The equations are solved numerically using forward integration. The results are summarized in Fig. To verify the theoretical considerations, the system was built with discrete components on a printed circuit board. The PiezoFET was wire bonded to the circuit. Figure A small threshold was used to shape the measured signal. The onset of a spiking event is marked as “1”, the absence as “0”. The results from various experiments are depicted in Fig. To illustrate the adaption of the firing rate in the artificial receptor, the interspike intervals were analysed. The decay in the firing frequency was fitted by an exponential function. During the experiment an excitation force of approximately 50 mN was applied. It is visible that the exponential decay fits the experimental data. Figure The dependence of the frequency in relation to different intensities is shown. The dependence of the frequency response of the nerves regarding the strength of the stimulus is clearly visible. An increase in the stimulus will also increase the response. Nonetheless, the highest firing frequency is reached right after the onset of the stimulus and decays exponentially in time. This general behaviour is not just present during one excitation of the nerves but also during successive presentations of external stimuli. Although the intensity of the stimulus does not change, the maximum frequency response does decrease with each ongoing presentation see Fig. d.63. Thus, we think that this work is a promising step towards the integration of spiking sensor units into dense interconnected systems as AlScN is a Si-CMOS compatible material51. Instead of using cantilevers, also planar chips with numerous PiezoFETs are feasible for spatial resolved tactile sensor units. The integration of higher numbers of adapting sensors can for example be used as an input for pattern recognition systems as the local activity changes with a variation in the applied force. The straightforward and technically simple implementation of this biologically essential adaptation process into the sensory unit, offers interesting perspectives as an interface stage for linking neuromorphic computing systems with tactile stimuli from the environment.In the first experiments carried out by Adrian et al., the exact differentiation between individual specialized cells and mechanisms was hardly possible. However, the basal biological mechanism of stimulus adaptation in a sensory system was well observable. Inspired by this seminal work, we developed a system for the encoding of mechanical stress induced through an applied force into a spiking response of a leaky integrate and fire neuron model. The depolarization of the build-up charge of the piezoelectric AlScN layer due to leakage currents, offered the opportunity to incorporate the biological important process of adaption in the sensory unit. Furthermore, the numerical and experimental findings are in good agreement. Interestingly, the presented concept and materials allow integration in Si-technology. Thus, densely packed sensor arrays for artificial spiking neural networks or oscillator-based information processing may be realized. Although, the results presented here are based on the bending of a cantilever which results in a horizontal stress on a piezoelectric material by applying a vertical force, the system could be used in biologically inspired force sensor systems as the theoretical considerations are based on the stress to which the device is subjected. Furthermore, a combination with other effects like piezoresistive modulated transistor responses might be useful and feasible as well2 gate oxide and a piezoelectric gate stack of AlScN. The drain and source terminals, as well as the 13 nm SiO2 gate dielectric were fabricated in a fabline at ISIT . The further gate stack was deposited and pattern at Kiel University. In order to archive the columnar growth of the AlScN layer, a Pt seedlayer is used. The AlN layer acts as an adhesion layer for the Pt on the SiO2. As a gate electrode Pt is used as well. All layers of the gate stack are deposited over the whole sample by using pulsed reactive sputtering for AlScN and DC sputtering for Pt, before the gate structure is later defined by ion beam etching. More details on the deposition of the AlScN can be found in Fichtner et al.38.The n-channel FET comprises a 13 nm thick SiOFollowing the processing of the transistor, the wafer is mechanically ground to a thickness of about 475 µm and a 2 mm × 10 mm cantilever is cut from the sample. The position of the transistor is crucial for the performance of the whole system, since a maximization of stress across the transistor directly impacts its performance as a sensor. Therefore, the transistor is located near the point at which the cantilever is fixed.The circuit was built with freely commercially available discrete components on a printed circuit board (PCB). The circuit was designed with Autodesk Eagle. The PCB is based on an epoxy base. The base is coated with 35 µm of copper and positive photo-resist. The copper was etched using an iron(III) chloride solution. The components used to build are out of the shelf transistors and resistors. The used transistors are from the type 2N3906 and 2N3904. The voltage follower used to measure the voltages was built with a general purpose JFET amplifier of the type TL074.The core of the magnetic coil is based on steel from the type 10025-2:2004–10. The core is 100 mm in length and 15 mm in width, forming a long bar with a square base. The coil around the steel is made of 280 turns of varnished copper with a diameter of 0.28 mm. The resulting magnetic field was measured with the teslameter 51662 from Leybold. This data is used to calculate the resulting force, during driving the coil with certain currents.The IV-characteristic of the PiezoFET was measured with a HP 4145A Semiconductor Parameter Analyzer, without the application of an external magnetic field. The permanent magnet at the tip of the cantilever is of the typ NdFeB (N50) with a diameter of 6 mm and a thickness of 1 mm resulting in a weight of approximately 0.21 g. The surface is covered in nickel. The magnet was glued to the tip of the cantilever. During the application of force to the cantilever, all voltages were recorded with a Picoscope 3404D.The simulation was done using Python 3.7 under the use of the libraries Numpy and Scipy for numerical calculations and Matplotlib for visualization. The piezoelectric coefficient


In Information Geometry, the unit sphere of  Gentlemen: there’s lots of room left in α-geometries (first studied by Chentsov himself).Chentsov theorem is the fundamental theorem in Information Geometry. After Rao’s remark on the geometric nature of the Fisher Information (in what follows shortly FI), it is Chentsov who showed that on the simplex of the probability vectors, up to scalars, FI is the unique Riemannian geometry, which “contract under noise” (to have an idea of recent developments about this see ). So FI When building similar objects in infinite dimension or in the noncommutative case several interesting questions arise, mostly involving The purpose of the present paper is to highlight some of the open problems in this area. The epigraph before the Introduction is a half quote of a sentence by Saunders Mac Lane, which is at the beginning of Chapter II in . It is sn-dimensional manifold M is a smooth functionM be First of all we may look differently at An example of divergence on Let The The following result is well known.Theorem 1.The geometries generated by the pull-back of the α-embeddings and the geometries generated by the α-divergencies coincide.Two complete references for the classical contents of M be a set of strictly positive probability densities on How to transfer this to infinite dimensions? Let us restrict M to a sphere in the M, say the The functionFollowing X is a Banach space and X and if x is orthogonal to y.In what follows duality mappingThe X has the duality map property if J is single valued; in such a case we set The space X has the projection property if for any closed convex We also say that Definition 1.A Banach space X is doubly uniformly convex (DUC) if X and its dual Typical examples of DUC are the Proposition 1.Let X be a DUC Banach space.(i) X has the projection property.(ii) X has the duality map property.(iii) (iv) If Proposition 2.Let X be a DUC Banach space.(i) (ii) (iii) The projection operator Using this projection, the trivial connection on X induces a connection on X is a Hilbert space then the above construction gives nothing else that the Levi–Civita connection on the unit sphere of X considered as a Riemann–Hilbert submanifold of X. From this it follows that the unit sphere of a DUC Banach space inherits a kind of manageable “Levi-Civita” connection from the trivial geometry of the ambient space.When the Banach space The above results were proved in ,7 where Beyond the results of  done in ).Young functionLuxemburg normOrlicz space generated by the Young function A embedding. Trivially we have:Let us consider now the cases where the Young function ove (see ) that||curvature in the point R is the radius of the osculating circle, namely the circle that gives the best approximation of the curve in a given point.Let scalar curvature according to the following lines. In general if ∇ is an affine linear connection on a manifold M the curvature is defined as RZ. 201 in )R.On the  manifold Theorem 3.There exists a bijective correspondence between Quantum Fisher Information(s) and Kubo–Ando noncommutative means given by the formulawhere f is the operator monotone function associated to the corresponding mean.Obviously So we have a big family of Riemannian metrics on The quantum Fisher information associated to The WYD(p) metrics are rather special among the quantum Fisher information(s): they are the only one that comes from the pull-back of a dualized pairing, which was proved in . As specormation .Since WYD information appears in infinite dimensions   in  a BanachBecause of the existence of the In Problem 1981–29 in the Arnold’s Problems the author asks to find equations of mathematical physics that can be realized as geodesic flows on infinite-dimensional ellipsoids (see page 354 in ). This qons, see ,23,24 foiolek in . A very Let Lenells and Misiolek prove in  the follTheorem 4.The geodesic equation of In particular, and Problem 5. Can the Arnold problem be solved for the Lenells and Misiolek look at the Problem 6. Complete integrability for the If the answer to the previous question is positive, does this help in understanding when one has complete integrability for the Problem 7. An Orlicz generalization of If the answer to Problem 5 is positive and we can look at the


The reaction of methanol to light olefins and water (MTO) was studied in a fixed bed tubular membrane reactor using commercial SAPO‐34 catalyst. In the fixed bed reactor without membrane support, the MTO reaction collapsed after 3 h time on stream. However, if the reaction by‐product steam is in situ extracted from the reactor through a hydrophilic tubular LTA membrane, the reactor produces long‐term stable about 60 % ethene and 10 % propene. It is shown that the reason for the superior performance of the membrane‐assisted reactor is not the prevention of catalyst damage caused by steam but the influence of the water removal on the formation of different carbonaceous residues inside the SAPO‐34 cages. Catalytically beneficial methylated 1 or 2 ring aromatics have been found in a higher percentage in the MTO reaction with a water removal membrane compared to the MTO reaction without membrane support. The Methanol‐to‐Olefins (MTO) reaction was performed in a membrane reactor with in situ steam removal through on tubular LTA zeolite membrane, where it showed exceptional long‐term stability over 4 hours, while maintaining a stable product distribution. Further examination showed a different coking behavior as the reason for the improvement compared to a fixed bed reactor without membrane support. The majority of light olefins as the basic of our today's chemical industry is produced via steam cracking. Increasingly, alternative ways of light olefin formation are studied.2The application of ceramic membranes for in‐situ water removal was already considered for different reactions like the hydrogenation of COAs mentioned above, coking of the catalyst is a severe problem of the MTO process since it leads to pore blocking of the catalyst and severe diffusion problems.The industrial application of the MTO reaction, a fluidized bed reactor, suffers heavily from attrition and requires the permanent exchange of the catalyst. In the used membrane reactor with fixed catalyst bed, the attrition problems are not existent, but the catalyst regeneration is more complex compared to the fluidized bed reactor.2O3 support, to remove water in situ from the reaction environment.To further influence yield, selectivity and longevity of the catalyst and compare it with state of the art processes, we performed the MTO reaction in a membrane reactor with a SAPO‐34 packed bed catalyst, as shown in Figure Figure The MTO reaction on SAPO‐34 without membrane support exhibits changing product selectivity during the reaction and a significant deactivation of the catalyst after 180 minutes. The desired main products ethene (after 120 min) and propene (100 min) reach maxima in their selectivity at different points during the active period. Simultaneously, the conversion of methanol decreases and the concentration of methane strongly increases. On the other hand, the MTO reaction under continuous water removal through a LTA membrane shows a constant productivity of ethene, propene and methane over 250 minutes, without major fluctuations of the product concentrations. This is surprising, since we expected a decrease in the catalyst longevity due to the water removal. The reaction rate remains high, shown by the consistent low amount of unreacted methanol. The yield of light olefins does not exhibit any significant differences between the two measurement setups with and without membrane support. Compared to literature,A possible reason for the breakdown of the MTO reaction in the packed bed reactor without membrane support could be the hydrothermal damage of the SAPO‐34 catalyst due to steam. However, in our case the chabazite (CHA) crystal structure of SAPO‐34 stayed intact during the MTO reaction, as well as after regeneration by coke combustion in synthetic air at 500 °C, as the X‐ray diffraction patterns show . The coked catalysts show a slight shift to lower diffraction angles compared to the fresh SAPO‐34 catalyst, indicating an expansion of the lattice due to the formation of larger hydrocarbon species inside the pores of the SAPO‐34. Therefore, the reason for the collapse of the MTO reaction after 3 h in the packed bed without membrane support seems to be solely the coking. The used SAPO‐34 is a silicoaluminophosphate of the CHA structure with 6.5×11 Å cages, connected through narrow 3.8×3.8 Å windows, consisting of 8‐membered oxygen rings, resulting in a 3D pore system.13C‐labeled methanol showed the direct participation of the polymethylbenzenes in the formation of light olefins.The induction period, starting with empty SAPO cages, is characterized by the sluggish kinetics of the formation of the first C−C bonds from methanol.Surpringsly, the different thermogravimetric (TG) profiles Figure  show simThe coking of the catalysts can additionally be seen by the decrease of the surface area, which was measured via BET nitrogen adsorption at 77.4 K. The results are summarized in Table For the most important points of the characteristic reaction course of the MTO reaction without membrane, we provide a similar study in the SI Figure S4). The addition of an LTA membrane to the MTO reaction has no significant influence on the product composition after our defined reaction time of 250 minutes, as in both cases around 70 % of the carbon from the methanol reacts to ethene. However, the MTO reaction with the LTA membrane still works with the same efficiency, while the MTO reaction without membrane support collapsed. While the ethene yield of the membrane supported reaction should stay on the same level for even longer reaction times, the share of ethene without membrane support decreases due to the increasing amount of unreacted methanol. Moreover, the amount of carbon which reacts to the aforementioned carbon residues is slightly higher for the MTO reaction without membrane, but is located at around 1 % in both cases, see Figure . The addFigure n‐hexane from the acidic solution. Subsequently, the analysis of the organic phase was carried out by GC‐MS, detailed information can be found in the supporting information. The analysis of the three types of spent catalysts (without membrane and with LTA membrane support Sections 1 and 2) are shown in Figure For the detailed characterization of the carbonaceous deposits (coke), gas chromatography‐mass spectrometry coupling (GC‐MS) has been applied. Therefore, a slightly modified extraction method, first introduced by Guisnet et al. was used to recover the confined hydrocarbon species from the SAPO‐34 cages.The GC‐MS results of section 1 of the SAPO‐34 catalyst with the membrane show a similar carbon composition like the catalyst without membrane support. However, the share of phenanthrene, anthracene and pyrene is only 43 %, the share of the medium sized aromatics, like methylated benzenes and naphthalene is therefore higher, compared to the catalyst without membrane. These medium sized aromatics do not hinder the diffusion of educts/products as much and can participate in the conversion of methanol to light olefins. While the SAPO‐34 catalyst without membrane is deactivated after 250 minutes, the catalyst in the membrane reactor is still active. Due to the presence of a high concentration of methylated benzenes and naphthalenes in Section 1 of the SAPO‐34 bed, we assume that this part of the bed membrane is still partially active. Section 2 of the bed has an even lower content of about 25 % of the bulky polyaromatic coke, while most of the hydrocarbon species are present as methylated smaller aromatics. Section 2 is, due to the high share of catalytically active hydrocarbon species, mainly working in the MTO reaction. The color changes of the catalyst are not necessarily connected to the contained aromatics, since the residues are all either colorless or light yellow. The different colors are the reason, why we decided to split the catalyst with membrane support into two sections in the first place and most likely stem from external coke, which does not play a significant role in the deactivation of the MTO reaction compared to the internal coke (hydrocarbon residues inside the SAPO‐34 pores).To further understand these findings, including the formation of the different Sections 1 and 2 of the catalyst bed inside the tubular LTA membrane, comparisons to existing models are required. Haw and Marcus proposed in 2005 a “cigar burn” mechanism to describe the development of the product selectivity of the MTO reaction in a SAPO‐34 catalyst bed, which is comparable to our approach of a membrane reactor with a packed catalyst bed.The formation of the first C−C‐bonds and, more importantly, the formation of the hydrocarbons from the HCP is more focused on the top of the moving working phase, whereas the aromatics inside the cages in the experiment without a membrane are more spread across the whole catalyst bed. As the catalyst bed inside the tubular LTA membrane developed two distinctive different sections, with different species of the carbonaceous deposits, the working phase is possibly a much narrower layer. Moreover, the methanol conversion rate stays high as well, due to the high amount of still active catalyst. On the contrary, the olefin production of the SAPO‐34 catalyst without membrane support changes during the reaction Figure  a. FirstImproving selectivity and longevity of the MTO catalyst is a challenge to date. Control of the chemical composition of hydrocarbon deposits seems to be the key to fulfil this task, either by controlled preformation (“precoking”)Literature reports the beneficial impact of adding water to the feed on the longevity of the catalyst.We found that all types of post‐reaction catalyst (with and without membrane support) contain a similar amount of carbonaceous deposits, but their composition differs severely, even after they converted very similar amounts methanol to light olefins. Therefore, we conclude that the water removal seems to stabilize the catalytic active species (like methylated benzenes) longer, compared to the catalyst without membrane support. We believe the main reason is the assistance of the alkylation of the aromatics rings, where water is split off and can be immediately removed by the LTA membrane. Due to this equilibrium shift re‐alkylation and de‐alkylation may be favored compared to the condensation of the deposits to larger aromatic multi‐ring systems. This would maintain the catalytic active phase longer and explain why this phase moved slower trough the catalyst bed. Furthermore, water removal could benefit the re‐alkylation of the larger aromatic rings  as well, leading to a possibly increased participation of these larger aromatics in the formation of light olefins.The product composition and development of the MTO reaction is influenced by a variety of reaction and material parameters, in particular the reactor type, the reaction temperature, the feed and sweep gas flow. Obviously, the catalyst type, the bulk density and its form and particle and crystal size distribution play the biggest role. We maintained these parameters for all of our experiments except for the addition of the LTA tube membrane, which conclusively led to the change of the carbonaceous deposits composition and the enhanced catalyst lifetime.We demonstrated the positive influence of removing water through an LTA zeolite membrane from a SAPO‐34 catalyst bed during MTO reaction in a tube membrane reactor. While the SAPO 34 catalyst without membrane deactivates after 3 hours, the SAPO 34 catalyst in combination with a water removing membrane maintains a steady conversion rate and selectivity over more than 4 hours. Thermogravimetry and GC‐MS confirmed that the reason for the collapse of the SAPO‐34 catalyst without membrane support is the pore blocking due to high molecular weight polyaromatics such as phenanthrene/ anthracene and pyrene, referred to as coke. In the membrane reactor, however, equal amounts of carbonaceous residues are found, but of less condensed rings such as methylated benzenes and naphthalenes. This type of residues is less likely to block acid sites and pore channels and even beneficial for the MTO reaction. Furthermore, the catalyst bed inside the tubular LTA membrane developed two distinctive different sections with different ratios of the various carbon residues species, called sections 1 and 2, which can additionally be distinguished by their colors. The catalyst bed near to the reactor inlet (section 1) contains a higher amount this high molecular weight polyaromatics and seems to be mostly deactivated. However, the lower section in the direction of the reactor outlet (section 2) contains mainly the catalytically active methylated benzenes and naphthalenes, which take part in the olefin production and give enough space for methanol conversion. We conclude that this zone, containing catalytically active hydrocarbons, moves through the catalyst bed, similar to the cigar burn mechanism. This motion of the coking zone is slower if water is removed since the re‐methylation of the aromatic rings inside the CHA cages is facilitated by the removal of water. Therefore, the water removal through the membrane supports the re‐methylation thus preventing the condensation of the aromatic rings to coke. In this study, we show that the fixed bed reactor setup in combination with a hydrophilic membrane could be an alternative to the existing fluidized bed reactor concept which suffers from an enormous attrition problem and requires, therefore, the permanent addition of new catalyst. Further research on this topic can be done by variation of several reaction parameters, such as temperature or particle size, as well as LTA pore size engineering by ion exchange.2O3 tube had a length of 300 mm and an outer diameter of 10 mm and was coated with a LTA zeolite membrane. The ceramic tube, respectively the reactor itself, were centrally filled with glass wool and 2 g of the SAPO‐34 catalyst was loosely piled on top, the catalyst was not chemically bounded to the LTA membrane. 50 ml/min of N2 were sent through a methanol reservoir, which was heated up to 50 °C and then directed into the tube reactor (WHSV=4.6 g gcat−1 h−1). To extract to retained hydrocarbon species from the spent catalyst, 15 mg of the respective spent SAPO‐34 was completely dissolved into 1.5 mL of 15 % HF for about 20 minutes. Afterwards, the HF solution was mixed with 1.5 mL of n‐hexane and left until the two phases had separated completely. The organic phase was removed and washed with saturated CaCl2 (in H2O) solution to remove possible HF remains. A detailed experimental section can be found in the supporting information.The MTO reaction was performed at 450 °C for 250 minutes in a vertically orientated tube membrane reactor Figure . The Al2The authors declare no conflict of interest.As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re‐organized for online delivery, but are not copy‐edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.SupplementaryClick here for additional data file.