We designed a real time, single-laser focus tracking system using low coherence properties of the machining femtosecond laser itself in order to monitor and correct the sample position relative to the focal plane. Using a Michelson Interferometer, the system collects data arising from part of the beam backscattered at the ablation spot. The data is analyzed by a custom software for position correction (employing an XYZ automated translation stage). With the focus tracking enabled we were able to etch channels with a stable cross-section profile on a bovine tooth with relief amplitude tens of times greater than the Rayleigh length of the system, keeping the sample inside the confocal parameter during most of the processing time. Moreover, the system is also capable of monitoring crater depth evolution during the ablation process, allowing for material removal assessment. FLM needs tight and constant focusing of the beam on the surface under treatment to maintain the laser intensity and a precise lateral resolution. In most laser machining systems, this restricts processing to samples with flat profiles, and a wide range of subjects cannot be rectified or polished without losing their primary functions. To extend their applicability, machining systems should compensate for non-flat and irregular samples. We present here results of a focus tracking system for femtosecond pulses based on low coherence interferometry (LCI), using the machining beam itself as a probe. This approach enabled the etching of grooves on a bovine tooth with surface curvature amplitude greater than the confocal parameter (CP) of the system, maintaining the groove characteristics stable. Our setup also allowed monitoring the ablation crater evolution in real time.Femtosecond laser machining (FLM) has received a lot of interest4. Cao et al. summarized many of the leading methods on their work4.In order to cope with variations when machining with lasers, the system should compensate for deviations in the lens-to-sample distance, keeping the sample surface on the system focus and its spot size constant. Several approaches have been proposed to actively perform this task5. In this technique, a beam from a broadband light source is split, by a Beam Splitter (BS), into two different optical paths  has a mirror of reflectivity As at a distance r + z. In this case, z represents the optical path difference, OPD. As the light makes a round trip to each mirror, there’s a factor 2 increasing the OPD. For simplicity, we assume a 50:50 beam splitter; refractive index of 1 for the whole system; mirrors with perfect reflectivity; and a light source with a spectral distribution G(k). The intensity at the detector can then be described as a function of the wavenumber k, and OPD z:Probing the lens-to-sample distance may be performed optically using interferometric methods such as Low Coherence Interferometry7 on the signal is easily seen when analyzing the real part of Equation z > 0, as shown in Equation k) and a periodic pattern defined by z , will result in a narrower FFT[G(k)], which is associated with the system’s axial resolution8.The influence of the OPDentclass1pt{minimay z Fig. . Computay z Fig. . Also no9. Since a fraction of the incident beam gets invariably reflected from the sample surface when machining, it may act as the mirror in the Sample Arm. Then, one can monitor the position of the surface under machining by the variations in the periodic structure of the resulting spectral signal, in the same way shown in Fig. A LCI measurement with the machining beam is feasible due to the broadband spectrum of femtosecond pulses9 of the source. For a typical femtosecond (Ti:Sapphire) amplified system with a 40 nm spectral bandwidth (FWHM), the resulting axial resolution is about 6 μm. This value is smaller than the confocal parameter for a 10 mm Gaussian beam focused by a 25 mm effective focal length (EFL) lens, which is around 12 μm, denoting that such a resolution is enough to keep the sample inside the confocal range of the system.The axial resolution for LCI setups depends on the coherence lengthThe objective of the present work is to demonstrate the viability of a laser machining system assisted by a LCI setup to track the surface relief and correct the sample position in relation to the focal plane in real timer value  and confocal parameter of 49.6 μm. The reflected light is directed towards the spectrometer through the BS and some fraction goes to a CCD camera  through the PBS.To make use of LCI for focus correction as proposed, we assembled an optical setup according to Fig. lue Fig.  could beTo find out the focal plane for the system a series of grooves were etched on a glass slide while varying its distance to the lens. In this step, no interferometry measurements were made. Optical and scanning electron microscopy were applied to evaluate the visual aspect and machining quality of the grooves, allowing to determine the focal plane.r so that the focal position coincided with an OPD of 300 μm . This method is fully described in a previous work10.The glass slide was positioned at the obtained focal plane, the laser intensity was decreased and the LCI was switched on. The slide was kept still and the M2 translation stage was used to adjust Based on real-time analysis of the LCI feedback Fig. , an algo11, the focus tracking system was tested on a bovine tooth. The sample was placed at the focal plane of the system and two separate regions were studied .Aiming to demonstrate the potential use in clinical/medical applicationsied Fig. : with , and the focus tracking system is disabled. The sample LCI data is recorded through time at the spot being etched.2. A single spot on the sample was studied throughout 2500 overlapped laser pulses, with its LCI profile recorded.As a demonstration of the ablation monitoring capability, a layered metal sample (Brazilian coin – steel coated with bronze) was studied. It was placed at the focal plane and processed with (11.72 ± 0.22) µJ femtosecond pulses, corresponding to a fluence of 16.5 J/cmTooth surface profile measurements Fig.  at the hOn the first run, with focus tracking disabled, the system recorded the axial surface position, shown in Fig. With active focus tracking enabled the system intervened, moving the axial translation stage Fig. .Figure 4The focus tracking results presented some data points that are far from the desired region . These instances are related to the raster direction change, in which the lateral motion reverses direction  is the surface position (height) and μ1 is the groove first moment (center of gravity):The performance of our system enabled a steady and uninterrupted ablation process, as seen in Fig. These moments were used since the groove’s shapes vary and cannot be well described by analytical functions. Summations were used instead of integrals due to the discrete sampling. Further details about the grooves characterization is supplied in the supplementary information Fig. As may be verified in Fig. 0, around 700 ms, when machining started). One can see that the system was able to show the surface being etched away by the ablation process due to the changes in its LCI profile, akin to an Optical Coherence Tomography14 measurement. The monitoring was performed in real time.Using the same system, the results obtained for crater evolution monitoring are shown in Fig. 0–t1 in Fig. 1–t3). This is further exacerbated by the second phenomenon: less light reaches the center of the crater as it grows deeper, since part of the beam (with intensity below the ablation threshold) gets scattered by its walls and backscatterd by the edges15, which is why the first surface is still visible on the LCI signal throughout the experiment  and steel, which is corroborated by the fact that the bronze layer thickness is 34 µm . Once the bronze layer is removed from the surface  were evaluated in a complementary study. Samples of both materials were weighted using an analytical scale and a 1 cm2 area was laser machined ; the samples were weighted once more and the mass difference (before and after ablation) was determined. Steel presented 25% less material removed than copper, further suggesting a smaller ablation rate on steel, as observed after t1.To better understand the behavior change between t11, or being dependent on normal angle of incidence17. The proposed setup, by using LCI measurements, enables a wider range of applications. Nevertheless, to achieve better results and faster machining velocity, three improvements should be investigated: (1) engineered optics to enhance collection of light from the sample, retrieving a stronger signal; (2) triggered spectrometer, to synchronize the collection with the laser pulses and (3) faster processing and software refinements.We demonstrated a LCI setup that uses the same light source to machine and monitor the sample’s surface. The system kept the surface inside the focal range of the laser for most of the experiment, which resulted in a stable width of the etched grooves, even for surface height variations in excess of 1000 μm, many times greater than the beam confocal parameter. One of the advantages of the presented method is that the measurement is performed at the very same spot where the ablation takes place and it does not require an additional light source to perform the interferometry measurements. Another outcome from the setup was the demonstration that it is possible to monitor the crater evolution and, as consequence, derive the ablation rate in real time. There are demonstrations on the literature of similar results, based on different phenomena, however they have limitations for real world applications, such as requiring the perforation samples18 or to perform cornea surgery.As perspectives, the system could use sub ablative intensities in order to map surfaces or even make tomographic images of biological tissues before starting the ablation, since the setup is identical to OCT or white light profilometers. For transparent samples, the system could be calibrated to have the focal spot below the surface, allowing, e.g., to create waveguides in curved glassesSupplementary Information


We describe a new data product combining the spin‐averaged electron flux measurements from the Radiation Belt Storm Probes (RBSP) Energetic Particle Composition and Thermal Plasma (ECT) suite on the National Aeronautics and Space Administration's Van Allen Probes. We describe the methodology used to combine each of the data sets and produce a consistent set of spectra for September 2013 to the present. Three‐minute‐averaged flux spectra are provided spanning energies from 15 eV up to 20 MeV. This new data product provides additional utility to the ECT data and offers a consistent cross calibrated data set for researchers interested in examining the dynamics of the inner magnetosphere across a wide range of energies. A new combined electron flux data product for the Van Allen Probes mission is describedResults from cross calibration of the RBSP‐ECT instrument suite are presentedThis data product represents the first ever complete electron spectra throughout the inner magnetosphere from tens of electron volts to tens of megaelectron volts Both spacecraft feature a comprehensive suite of instrumentation to study the particles, waves, and fields in the radiation belts  and pitch angle‐resolved fluxes (included in the Level 3 files) available at the spin time cadence (≈11 s). However, many studies using the ECT data are interested in combining data from multiple ECT instruments, which can introduce additional challenges including cross calibration, time cadence issues and different modes of operation. Over the course of the Van Allen Probes mission, there has been a considerable effort by each of the instrument teams to understand instrument responses and improve the agreements between the instruments of the suite. Building on this work, in this paper we describe our efforts to formalize the cross calibration the ECT instruments and produce a combined, spin‐averaged electron flux data product that spans the entire ECT energy range. This is not meant to replace the currently available data products from each of the instruments, but rather to provide a useful and complementary data set for the entire ECT suite. The combined data product described here will be the first in a series of new ECT data products. Work is underway to continue the methods outlined here to produce both a combined pitch angle‐resolved product and ultimately a phase space density product in adiabatic coordinates.The remainder of the paper is structured as follows: In section 2The Van Allen Probes mission was launched in August 2012 into a near geosynchronous transfer orbit to study the dynamics of the inner magnetosphere including the radiation belts, ring current, and plasma populations. As part of the mission, the ECT instrument suite have operated continuously since October 2012, providing measurements of the energetic particle environment. Over the early part of the mission, the instruments underwent several major changes to energy channel definitions, operational modes, and flux conversion factors. Therefore, in the subsequent sections, we will focus on data from September 2013 onward, when the major operational changes were mostly complete. A brief discussion of the treatment of the data from the early part of the mission can be found in section 2.1The lowest energy instrument of the ECT suite, HOPE measures ∼15‐eV to 51‐keV electrons by utilizing time‐of‐flight mass spectrometry with channel electron multiplier detectors  includes a correction to account for long‐term changes in the HOPE detection efficiencies. Using onboard measurements of the absolute detection efficiency .The middle energy ECT instrument, MagEIS, utilizes a strong magnet  to steer energetic electrons into a set of solid state detectors, providing measurements of ∼30‐keV to 4‐MeV electrons across 21 energy channels  provides a common time base for all the instruments, (2) improves the counting statistics, and (3) facilitates analysis of longer time periods.The cross calibration focus on three areas: (1) the HOPE‐MagEIS cross calibration, (2) MagEIS‐REPT cross calibration, and (3) background correction at the REPT high energies. As described above, each of the ECT instruments utilizes different detection techniques that are appropriate for different energy regimes. Therefore, in order to produce consistent and valid spectra, the basic methodology in each of these areas is the same: (1) remove data with high backgrounds and/or poor counting statistics. (2) Where the instrument energy ranges overlap, select the most appropriate and reliable measurements at each energy range. We begin with a discussion of the HOPE‐MagEIS cross calibration.3.1MagEIS has two electron energy channels that overlap with the HOPE energy range at 32 and 51 keV. The absolute detection efficiency for electrons on HOPE falls off rapidly for energies greater than 1 keV. As a consequence, the high‐energy channels generally have a low‐detection efficiency and can often suffer from poor counting statistics. Therefore, in the event of disagreement in the overlap region, we will defer to the MagEIS measurements. Figure Figures Simply placing the count threshold on HOPE (above 5 keV) results in excellent agreement in the overlap region 96% of the time. Figure For the remaining ∼4% of points, the HOPE data require additional corrections in order to better match the MagEIS data. When needed, these are applied as two separate time‐dependent corrections. The first of these is a correction applied at all L‐shells during times when there is a significant disagreement with MagEIS. This correction is only applied to days where the daily median ratio between MagEIS and REPT at 32 keV is <0.4 or >2.5, indicating that more than half of the measurements for that day differ by more than a factor of 2.5. This correction is very uncommon: Through December 2018, it was only needed for 2 days on RBSP‐A and 15 days on RBSP‐B. For these days, the HOPE data are multiplied by the 2‐day running mean of the MagEIS/HOPE ratio. An example of this corrected spectrum for RBSP‐B on 17–18 March 2015 is shown in Figure A complete list of these days where the correction factors have been applied is provided in the L < 2.5). Generally, the design of the HOPE instrument was successful in minimizing backgrounds throughout the outer radiation belt. However, in the inner zone, there is a significant background due to the population of high‐energy protons. This background is not influenced by the HOPE Electrostatic Analyzer voltage and will therefore add the same number of counts to each energy channel. Therefore, in order to correct for this, the number of background counts in the 32‐keV channel is determined using the ratio to MagEIS. These counts are then subtracted at each energy and the fluxes are recalculated. This results in a larger correction at the highest energies where there are fewer counts. An example of this correction is shown in Figure The second adjustment is a correction for shield‐penetrating background in the inner zone  MagEIS‐HIGH channel. Similar to HOPE, MagEIS is least sensitive at the highest energies. Therefore, the first step is to identify times where the MagEIS‐HIGH channels have sufficient signal‐to‐noise ratio. Figure −8 power law spectrum, which is typical for this energy range  and (b) show the first energy pair at  1.8 MeV. For both RBSP‐A and RBSP‐B, the fluxes in REPT channel are consistently higher than those measured in the adjacent MagEIS channel by more than a factor of 2. One potential source for this disagreement is the long tail in the energy‐dependent efficiency of REPT for this channel which can lead to higher measured flux values. For the combined data product, in order to produce a consistent spectrum, this difference needs to be addressed in some way. Therefore, we chose to not include data from the first REPT energy channel (1.6–2.0 MeV) in the combined ECT spectrum and use only the measurements from MagEIS to cover this energy range (1–2 MeV).Panels (c)–(f) show next two energies ( 2.1 and  2.6 MeV), where the comparison is generally very good, with 90% of fluxes agreeing to within a factor of 2. This is especially true for the 2.6‐MeV channels, where the nominal bin energies of MagEIS and REPT are very close together and the REPT energy‐dependent efficiency is much more peaked and narrow. For the next two energy channel pairs at 3.6 and 4.2 MeV, the fluxes agree similar to what is seen at lower energies. However, at these energies, only a small fraction (<20%) of the MagEIS measurements have sufficient foreground signal to satisfy the error requirements. Therefore, while the MagEIS measurements at these energies give additional confidence to the REPT measurements, the highest two MagEIS channels are not included int the combined ECT spectrum and REPT is used to cover this energy range (>3 MeV).Overall, the agreement between MagEIS and REPT is very good and produces a reliable spectrum in the overlap region. Two examples of these spectra in the MagEIS‐REPT overlap region are shown in Figure 3.3Throughout the outer zone, there are times when the REPT energy channels have very low counts and the measurements are dominated by backgrounds that are most likely due to galactic cosmic rays. While the galactic cosmic ray background will affect all energy channels equally, it is especially noticeable at the higher energies (>5 MeV), which are often closer to their noise floor. This results in a flattening of the spectrum, an example of which is shown in the E is the background fit, A, B, C, and D are the fitting coefficients, and t is time. In order to minimize the foreground signal, the fit is calculated using only the fluxes near apogee (L>6). The data are fit twice, first using all times, then a second time excluding the data that was greater than 2*E. This second fit is performed to ensure that the background fit is not overestimating and eliminating too much data, which is particularly important for the lower energy channels. After the second fit, all fluxes  less than 2*E are marked as invalid. This technique is only used for REPT channels 4–12 (>4.2 MeV). For the lower energy channels, the foreground signal is always much stronger than the background, so no correction is needed. Therefore, for these channels, similar to what was done for MagEIS, the fluxes are marked invalid if they are near the three‐ to four‐count level.The galactic cosmic ray background is not constant and varies slowly over solar cycle timescales  across 6 orders of magnitude in energy. In addition to these combined flux spectra, we also provide spectra that have been fit with a spline function. These fit spectra offer several key advantages including providing a consistent set of energy channels for the entire Van Allen Probes mission, eliminating the need to interpolate across changes in the MagEIS energy definitions. In this section, we describe the methodology used to fit the data.L > 2.5), the upper energy limit is set at the last valid energy channel, whereas in the inner zone (L < 2.5), the upper limit is set at the last MagEIS‐M75 channel  to identify these times.The second parameter is the smoothing factor The first of these validation steps is a simple test of the residual of the fit. By definition, as shown in equation y is the interpolation, z is the spline fit, and m are the missing values. As noted in equation s=0.25, there is a large, nonphysical peak near 10 keV. A small increase of the smoothing to 0.4 largely removes this feature and produces a more reliable spectrum. Finally, Figure The second validation step examines the fit's behavior across gaps in the input spectrum. These intervals are the most common cause for problems, as the fits are not properly constrained by the data and can therefore contain nonphysical features. To identify these times, we look at the number of consecutive missing values in the input spectrum. For times with significant data gaps in the HOPE/MagEIS energy range (>18 channels below 100 keV) or the MagEIS/REPT energy range (>6 channels above 100 keV), the data gap is carried over to the fit spectra and all output energies within the data gap are set to fill. Then, for times with more than four consecutive energy channels are missing , the fit is compared to a linear interpolation across the data gap(s) using the root‐mean‐square deviation (RMSD):The final validation step is to identify and remove times that have nonphysical artifacts such as spikes or step functions. This consists of two checks on the derivatives of the fit. The first is an examination of the fit's second derivative. Typically, the maximum absolute value of the second derivative is ≤75. Therefore, we apply a correction to times when the maximum of the second derivative is twice the typical maximum. For these points, the smoothing is increased by 0.25. If the second derivative is still too large after the increased smoothing then all energies with one decade of the maximum are set to fill values. The second check is on the first derivative at high energies. Any points above 5 MeV that have a positive slope are set to fill values.An example of a fit spectrum is shown in Figure 5The combined data product described here will greatly benefit scientific studies of the inner magnetosphere and radiation belts. The use of multisatellite observations has been key to many recent studies. The fit spectra in this data set directly facilitate those types of studies, providing a continuous function that can be sampled at different energies for direct comparison to other complementary data sets, including GPS .In this section, we describe some of the major known caveats of this data product at the time of initial release. For the most up‐to‐date list of known caveats as well as changes in future data releases, users should consult the accompanying documentation available on the RBSP‐ECT website (6.1L < 2.5), all the energy channels >1 MeV are not included in the fit and therefore set to fill values. This does not necessarily mean that there are no electrons at those energies at any times. This cutoff was chosen based on the results of Fennell et al. .The results shown in the above sections, and the initial release of this data product are only for the period of September 2013 onward, when the instrument energy channels and operational modes settled to their final values. Prior to this period, there are various intervals where the energy channels or flux conversion factors change. Data files will also be available back to at least January 2013. For these pre‐September 2013 files, it is likely that there will be some issues with data reliability and several modifications to the methodology used during this period. Users should consult the accompanying documentation available on the RBSP‐ECT website (7This paper describes a new data product combining the spin‐averaged electron fluxes from all of the ECT instruments. While the currently available ECT data have been used in numerous studies, there are several challenges for studies that utilize data from multiple instruments. The goal was to produce a consistent, reliable and cross‐calibrated data set, representing the first complete electron spectra throughout the inner magnetosphere from electron volts up to tens of megaelectron volts. The combined data set will bring additional utility to the ECT data and will be especially useful for researchers interested in studying effects, which span two or more of the ECT instrument's energy ranges. As new data releases become available, the combined data product will be updated and refined. Any updates to the techniques described here will be available on the ECT web page.The methodology and techniques described here will also be used to generate higher level combined data ECT products. We are currently working on a combined pitch angle‐resolved flux data product, which will incorporate many of the techniques outlined here. This will eventually lead to an official release of phase space density calculated using the combined ECT data set.Supporting Information S1Click here for additional data file.


Liquid chromatography combined with tandem mass spectrometry is an important tool in proteomics for peptide identification. Liquid chromatography temporally separates the peptides in a sample. The peptides that elute one after another are analyzed via tandem mass spectrometry by measuring the mass-to-charge ratio of a peptide and its fragments. De novo peptide sequencing is the problem of reconstructing the amino acid sequences of a peptide from this measurement data. Past de novo sequencing algorithms solely consider the mass spectrum of the fragments for reconstructing a sequence.We propose to additionally exploit the information obtained from liquid chromatography. We study the problem of computing a sequence that is not only in accordance with the experimental mass spectrum, but also with the chromatographic retention time. We consider three models for predicting the retention time and develop algorithms for de novo sequencing for each model.Based on an evaluation for two prediction models on experimental data from synthesized peptides we conclude that the identification rates are improved by exploiting the chromatographic information. In our evaluation, we compare our algorithms using the retention time information with algorithms using the same scoring model, but not the retention time. The amino acid sequences of peptides in a sample can be analyzed by liquid chromatography coupled with tandem mass spectrometry . First,Several algorithms for de novo sequencing –8 considretention time and depends on certain chemical properties of the peptide. This process results in the temporal separation of the peptides in a sample. Predicting the retention time of a peptide from its amino acid sequence is a challenging task  contains the optimal score of a path pair ending at the vertex v, respectively at the edge . As a base case, we add a loop edge  to the graph and initialize DP, the algorithm considers all possible balanced extensions of the corresponding path pair with outgoing edges of v. By Lemma v and the last edge  of the two paths. The score of the resulting new path pair can be computed by addingDP. The table entry of the new path pair is updated if the new score exceeds the value stored in this entry at this step of the algorithm. The optimal score for a string of mass M is equal to the maximum value of an entry a, b) in G. A path pair with this score can be reconstructed starting from this entry. The combination of the corresponding prefix and reversed suffix then leads to the desired string of mass M. The time complexity of DeNovod is the maximal out-degree of a vertex in G and p is the maximal length of an edge label  of any path pair ending in v, respectively , and its retention time to compute a solution for our problem. There can be multiple path pairs ending in the same vertex and the same edge with different retention times. If we consider an optimal solution and its sequence of path pairs computed by the algorithm, a path pair v and . Nevertheless, its score is optimal among all path pairs with the same retention time that end in v and . Therefore, we need to store for each possible retention time t the optimal score of a path pair ending in vertex v and edge .However, it is not sufficient to only store the optimal score DP an array containing a score for every possible retention time t. DP[t] is the optimal score for a path pair ending in v, respectively , with retention time t. For a given vertex v and an edge , the algorithm performs balanced extensions by all outgoing edges  of v. For every balanced extension and every feasible retention time t, the algorithm then computes the new retention time DP is reached in line 7, all optimal scores for path pairs ending in vertex v and edge  have been computed. This holds by induction, as every possible balanced extension leading to a path pair ending in v and  has already been considered . Moreover, the array in DP is not further modified as soon as the algorithm reaches the vertex v and the edge  in line 7. Therefore, the invariant holds that, if the algorithm considers a vertex v and an edge  in line 7, the corresponding entry DP contains the optimal score for each feasible retention time.DeNovoDP, the optimal score of a string with retention time t is DP.After computing all entries d is the maximal out-degree of a vertex in G and p is the maximal length of an edge label. The additional overhead of DeNovot for each entry DP and compute the new retention time The running time of DeNovo·|E|·d·p , where dv, respectively , we have to consider all retention times in DP, but up to M. In practice, most entries DP contain only few scores, as we only store the score for a retention time t if there is a path pair ending in v and  with predicted retention time t. Therefore, it is advisable to use a memory-efficient data structure instead of an array to reduce the memory consumption of the algorithm.The number of scores to be stored varies depending on the entry and the retention time coefficients. For a path pair ending in k best-scoring strings, using similar techniques as described in  in line 7, all optimal scores for path pairs ending in vertex v and edge  have been computed correctly, as all balanced extensions leading to such path pairs have already been considered. Given the optimal score of a path pair, the algorithm performs every possible balanced extension with an outgoing edge of v, computes the new score and retention time, and updates the corresponding entries.If the algorithm reaches an entry a, b). The algorithm additionally verifies that both the prefix and the suffix path label have more than DP, where M. Therefore, the running time is in d is the maximal out-degree of a vertex in G and p is the maximal length of an edge label.We reconstruct a solution starting from a path pair ending in some vertex P, Q) as follows. The retention time of the path label P, Q) by summing the retention times of both path labels  isP, Q).The neighborhood-based model predicts the retention time of a string els Fig. . That isP, Q) as follows. Consider a balanced extension of the prefix path P by an edge  with Q is defined analogously  ending in vertex v and edge  the optimal score for each retention time t, last character v, and a Boolean variable pre indicating if P is the prefix path. As a base case, the algorithm stores the optimal score for a path pair ending in vertex 0 and the loop edge  as G in ascending order. After considering all possible path pairs, the optimal score can be computed by considering all entries DeNovov and an edge , where M and d is the maximal out-degree of a vertex, p is the maximal length of an edge label, and M.The algorithm considers at most In this section, we study the performance of our algorithms for de novo peptide sequencing with retention time prediction. In our evaluation, we want to clearly expose the effect of considering the retention time information rather than studying the identification rates compared to state-of-the-art de novo sequencing software, such as UniNovo  or Novorument}Δ  , as thisument}Δ   for one We first describe the considered dataset and a method for estimating the parameters of the three models. Then, we compare the identification rates of the proposed algorithms to the identification rate of DeNovoument}Δ  .http://www.peptideatlas.org, identifier PASS00289, [We use the SWATH-MS Gold Standard (SGS) dataset  with meSS00289, . The rawSS00289, . The speSS00289,  using thSS00289,  has beenWe used the sequences identified by Comet as gold standard and considered a peptide to be identified by one of the considered algorithm, if the exact sequence has been computed as the best-scoring solution, respectively one of the 5, 10, or 100 best-scoring solutions.In this work, we are mainly interested in the algorithmic problem of using retention time information for de novo sequencing and do not focus on efficient procedures for estimating the coefficients of retention time prediction models. We use linear regression for estimating the coefficients for our three retention time models.T is the measured retention time, and We randomly split the 944 spectra into a training set with 80% of the spectra (755 spectra) and a test set with the remaining 20% of the spectra (189 spectra). We use the training set to estimate the retention time coefficients and the test set to select a tolerance parameter ct. Standard software tools for statistical methods [ct, such that For example, we estimate the coefficients of the linear model by first computing the character frequency vector for each string in the dataset. The character frequency vector of a string is a vector of length  methods  can be uWe chose the tolerance parameter The neighborhood-based prediction model has a very large predictive error for several sequences due to the small training dataset. Several coefficients are estimated based on few observations and others cannot be estimated at all. Therefore, we cannot extensively evaluate the identification rates of our algorithm with the neighborhood-based prediction model, as a much larger training dataset for estimating all parameters would be necessary. For our limited evaluation, we ignore the 5 largest and the 5 smallest retention time errors when picking the tolerance parameter and use We analyzed the 944 considered spectra with DeNovoFigure ument}Δ  , DeNovo\However, a filtering approach that considers the top 100 sequences reported by DeNovoThe length of a peptide affects its retention time. However, the considered prediction models do not take into account the peptide’s length and use the same coefficients for all peptide lengths. There is not necessarily a linear correlation between the length of a peptide and its retention time, as the coefficients can be positive or negative. Our models do not perform equally well on short and long peptides. Figure An accurate retention time prediction model is crucial for exploiting the retention time information successfully. The identification rates of our algorithms depend on the choice of the tolerance parameter In our evaluation, we considered a limited training dataset for estimating the retention time coefficients. While we have to estimate a small set of coefficients for our linear prediction model, the neighborhood-based prediction model has many retention time coefficients. Estimating these coefficients requires a large training dataset, as each coefficients needs to be estimated based on a sufficiently large set of observations. A much larger training set would be necessary to get a robust estimate of the retention time coefficients for this model. Our models fail to predict the retention time of some sequences accurately considering the available training data. To avoid excluding the correct sequence from the search space, we had to chose large tolerance parameters. By improving the predictive power of the models, e.g. using a larger training set or a more sophisticated parameter estimation, the tolerance parameter can be decreased, which increases the identification rates of our algorithms.To get a glimpse on the performance of DeNovoOur prediction models do not consider several other properties of a peptide that affect its retention time. For example, the length of a peptide has an influence on its retention time. More evolved prediction models , 19 inteThe running time of our prototypical implementations is in some cases not yet practical. DeNovoribed in . We obseIn this paper, we propose the first algorithms for exploiting the retention time information in de novo peptide sequencing. We study three retention time prediction models and develop algorithms for computing a sequence that matches the experimental mass spectrum as well as possible and is in accordance with the observed retention time. The experimental evaluation of our algorithms shows that identification rates can definitively be improved by exploiting this additional information. Yet, the proposed algorithms score sequences with a very simplistic scoring function that only counts explained and measured masses and does not consider any other available information. For real-world applications, a more evolved scoring function using all available information needs to be integrated. While  introduc


We investigate the modification of the magnetic dipole resonance of a silicon nanosphere, which is illuminated by a focused azimuthally polarized beam, induced by a metal substrate. It is found that the magnetic dipole of the silicon nanosphere excited by the focused azimuthally polarized beam and its image dipole induced by the metal substrate are out of phase. The interference of these two anti-parallel dipoles leads to a dramatic line width compression in the magnetic dipole resonance, manifested directly in the scattering spectrum of the silicon nanosphere. The quality factor of the modified magnetic dipole resonance is enhanced by a factor of ∼ 2.5 from ∼ 14.62 to ∼ 37.25 as compared with that of the silicon nanosphere in free space. Our findings are helpful for understanding the mode hybridization in the silicon nanosphere placed on a metal substrate and illuminated by a focused azimuthally polarized beam and useful for designing photonic functional devices such as nanoscale sensors and color displayers. Dielectric nanoparticles with large refractive indices and diameters ranging from 100 to 250 nm, which support distinct Mie resonances in the visible to near-infrared spectral range, have become the focus of many studies in recent years because they are considered as the promising building blocks for metamaterials working at optical frequencies . The coeThe electric and magnetic resonances excited in dielectric nanoparticles with large refractive indices can be manipulated by using various methods –31. Thisπ-illumination with two AP beams  and the interface between air and the PEC substrate in the x−y plane with z=0. The magnetic moment is given by: The narrowing of the MD line width can be understood by using the image theory and the approach based on Green’s function . We consider a MD located at the position z component of the dyadic Green’s functions for the PEC substrate b1 and k0 are the Mie coefficient and vacuum wavenumber, respectively.where −116πz03 , and theH0=.The magnetic field at the center of the MD is given by: The extinction cross section of the MD can be written as : 6\docuPin denotes the power of the incident light.where z direction is excited in the Si NS. Meanwhile, a mirror image oriented in the −z direction is induced by the PEC substrate, as schematically shown in Fig. Due to the rotational symmetry of the AP beam and the Si NS, a MD oriented in the +In the above studies, it has been demonstrated theoretically and numerically that a sharp MD resonance can be created in the scattering spectrum of a Si NS by using the combination of a metal substrate and an AP beam. As some examples, we will show in the following numerical simulation the possible applications of the sharp MD resonance in nanoscale sensing and color display. For practical applications, the metal substrate is chosen to be a 50- nm-thick Au film, which has been used in our previous study . The phyPreviously, it has been demonstrated that intensity shift sensors based on Si NS dimers possess much higher sensitivity than wavelength shift sensors based on plasmonic nanoparticles/nanostructures . In addiRecently, it has been successfully demonstrated that color control can be realized by using dielectric nanoparticles with large refractive indices, which supporting Mie resonances, instead of lossy plasmonic nanoparticles/nanostructures –55. HoweIn summary, we have investigated theoretically and numerically the dramatic narrowing of the MD resonance of a Si NS, which is illuminated by using a focused AP beam, when placing it on a metal substrate. Owing to the rotational symmetry of the AP beam and the Si NS, only the multipoles of magnetic type are excited. It is found that the interference of the MD and its mirror image induced by the metal substrate is responsible for the dramatic narrowing of the line width from ∼ 53 to ∼ 20 nm. It is shown by numerical simulation that the sharp MD resonance in the scattering spectrum of the Si NS may find applications in nanoscale sensing with high sensitivity and color display with improved chromaticity and spatial resolution.


Transfer, in which capability acquired in one situation influences performance in another is considered, along with retention, as demonstrative of effectual learning. In this regard, interlimb transfer of functional capacity has commanded particular attention as a means of gauging the generalisation of acquired capability. Both theoretical treatments and prior empirical studies suggest that the successful accomplishment of a physical training regime is required to bring about generalised changes that extend to the untrained limb. In the present study, we pose the following question: Does interlimb transfer occur if and only if the training movements are executed? We report findings from JG—an individual recruited to a larger scale trial, who presented with  deficits of motor control. We examined whether changes in the performance of the untrained right limb arose following practice undertaken by the impaired left limb, wherein the majority of JG’s attempts to execute the training task were unsuccessful. Comparison was made with a group of “control” participants drawn from the main trial, who did not practice the task. For JG, substantial gains in the performance of the untrained limb  indicated that effective learning had occurred. Learning was, however, expressed principally when the unimpaired (i.e. untrained) limb was utilised to perform the task. When the impaired limb was used, marked deficiencies in movement execution remained prominent throughout. It is a widespread, if generally implicit, assumption that motor learning is contingent upon the engagement of specific motor control processes   provided written informed consent to the procedures, which were approved by the relevant Queen’s University Belfast Ethics Committee and conducted in accordance with the Declaration of Helsinki. We take this opportunity to note that JG did not wish for representations to be made on his behalf, which may have led to specialist medical consultations or brain imaging.The participant was seated with his upper limbs supported on horizontal platforms, with lateral motion prevented by foam-covered posts placed on either side of each arm. The head, neck, torso and feet were also fully supported. The forearms were stablised in mid-pronation and the elbows semi-flexed 100–120°). Each hand was securely fixed within a manipulandum  data were first collected separately for each limb, and for each direction of applied torque . To establish MVT, the participant was instructed to apply as much “force” as possible in the specified direction for approximately 3 s. Three attempts were made for each direction, with successive attempts separated by a rest period of 30 s. The peak torque achieved during each trial was calculated, and these values averaged over the three trials to provide a measure of MVT (i.e. separately for each limb and direction). These MVTs were used subsequently to scale the magnitude of the torques required to acquire visual targets in the behavioural tasks.° intervals around the circumference of a circle) surrounding a central ‘home’ zone  with respect to both the MVT for radial deviation, and the MVT for flexion (or relative to the MVT for extension when the right limb was used). The diameter of the cursor and the target each corresponded to approximately 1.15° of visual angle .The participant was instructed to use torques generated at his wrist to move a circular yellow cursor on the computer monitor Fig. b. The cuone Fig. b. This hThere are certain practical advantages that accrue from the use of isometric tasks. Among the most important of these in the context of the larger study, was the facility to define the torques necessary to displace the cursor in terms of the capability of each participant. In some arms of the study, this was set to 40% of MVT. While it is possible to manipulate the test and training forces applied during dynamic movements in a comparable fashion, the technical demands are considerable  for 50 ms, a tone  signalled successful target acquisition. At this time, both the cursor and the target were extinguished. In the event that a target was not acquired within a period of 4 s following its presentation, the target was extinguished and the screen refreshed. The participant was asked to relax—to return the cursor to the home zone, immediately upon removal of the target. The next target appeared 2–3 s later.The right (transfer) limb was always assessed before the left (training) limb. Prior to the initial pre-training assessment for each limb, the participant undertook eight practice trials (one to each target position). In each of the subsequent assessments, each limb was employed in four blocks of 32 trials . Within a block each target appeared on four occasions. There was a rest period of approximately 1 min between successive blocks. The total duration of each assessment session was about 40 min.The pre-training assessment was conducted on a Thursday, followed by 3 days of rest. The training sessions undertaken by JG (outlined in the next section) were performed on 5 consecutive days during the next week (Monday–Friday). A post-training assessment session was conducted on the first Monday following the training week. The retention assessment took place 10 days later. A second retention assessment was undertaken for JG only after a period of 1 year (364 days) had elapsed.The MVT values obtained during the pre-training assessment were used in both that session and (for the left limb) during the training sessions that followed. The MVT values obtained during the post-training assessment were used in both that session and in the retention assessment that took place 10 days later. The objective was that induced changes in coordination were resolved separately from any variations in torque generating capacity. A further set of MVT values were obtained and used in the second retention assessment that took place 1 year later . Within a block, each target appeared on four occasions. There was a minimum rest period of 1 min between successive blocks that JG was at liberty to extend if he desired. The total duration of each training session was approximately 20 min.With a view to characterising further the abnormalities in motor control exhibited by JG, we undertook an additional set of measurements in which both the left and the right hands were instrumented with triaxial  accelerometers . In the course of recordings of 20 s duration (sampled at 1000 Hz), four conditions were employed . In the first, JG rested his forearms and hands on his legs. In the second, both arms were held outstretched . In the third and fourth conditions, JG flexed and extended either his left or his right elbow at a comfortable pace. In these latter conditions, five cycles of movement were performed .The resultant acceleration time series were high pass filtered at 0.5 Hz to remove the component of the signal corresponding to the cyclic movements (frequency ≈ 0.2 Hz). As there are no known physiological  frequency components of movement kinematics detectable above 40 Hz  is not a distinguishing characteristic of JG’s left arm. Rather, some features of essential tremor  are present. Although the differentiation of tremor types  in many classification schemes remains inexact, it is typically held that essential tremor presents clinically in both postural and kinetic task contexts. There may also be bilateral manifestation when the upper limb is engaged  indicated the degree to which the movement trajectory deviated from a straight line path between the starting position and the target position. The smoothness  of the trajectory for the interval between movement onset and target acquisition was defined as the spectral arc length (SAL)  during the 100 ms interval following movement initiation. Aside from this restriction, the heading deviation was calculated for all trials. The remaining measures were derived only for trials on which the target was acquired.The application of traditional inferential techniques to data derived from a single case study is complicated by the fact that the errors of observations obtained from a single person tend to exhibit serial dependency. The feature (i.e. autocorrelation) violates the assumption of independence of errors that is an element of most parametric and nonparametric methods. It has the potential to generate biased descriptive and inferential statistics, and to increase the likelihood of Type I errors . The degree to which a set of trials (i.e. to a specific target) exhibited directionality was assessed using Rao’s Spacing Test. Contrasts between sets of trials performed prior to and following training were conducted using Rao’s Test of Homogeneity.The striking aspect of JG’s initial performance when using his left limb was consistent failure to produce the joint torques necessary to acquire the targets. Indeed, with respect to the three targets that required wrist extension torques, ulnar deviation torques, and their combination, JG was unable to acquire the target on any of 48 attempts (16 to each target position)  of trials  limb. JG’s overall level of performance during the (post) session undertaken 3 days following the cessation of training was improved  relative to that observed prior to training (23%). It was, however, striking that the degree to which this improvement was expressed varied markedly across the workspace. When seeking during the post session to acquire targets for which wrist extension torques, ulnar deviation torques, and their combination were required, JG was able to acquire the target on only 3 of 48 attempts.  limb. When assessed 3 days  following cessation of the 5 days of training undertaken by the opposite limb, 10 days (93%) and 1-year (95%) later, there were very few instances in which the task was not completed successfully  limb. As three of the eight target locations were not acquired by JG prior to training (i.e. in the extension/ulnar deviation quadrant), there was no basis upon which to contrast the movement times associated with the small number of successful attempts completed in the sessions that followed. With respect to two other target locations , the movement times exhibited 3 days following the cessation of training (post) were shorter than those obtained during the pre session. No other changes were noted  limb. With the exception of targets that required radial deviation torques only for their acquisition (for which the shortest movement times were evident prior to training), the movement times obtained following the 5 days of training undertaken by the opposite limb were shorter than those exhibited prior to the commencement of training  limb. There was only one instance of a difference between the value recorded prior to training  and that obtained following training. A larger value was observed during the retention1 session for the radial deviation/extension target (= 0.19%MVT).Right (transfer) limb. With respect to targets that required a combination of wrist flexion and radial deviation torques for their acquisition, the path deviation values were markedly lower following training  than prior to training . With the exception of the retention2 session (conducted 1 year later), this was also the case for the extension target .Left (training) limb. There were no instances following training in which SAL values fell outside of the 95% credible intervals derived on the basis of the pre-test values.Right (transfer) limb. With respect to targets that required a combination of wrist extension and ulnar deviation torques for their acquisition, SAL values  were of lower magnitude  following training of the opposite limb—indicating that the trajectories were smoother. This was also the case for movements directed to flexion targets , and to a much lesser degree for the combinations of wrist flexion and radial deviation.Left (training) limb. As inspection of Fig. Right (transfer) limb. With respect to all torque impulses generated during the pre-training assessment session, the heading deviations were characterised by a “clockwise” bias  testing regime. A comparison was therefore made with five right-handed older  male “control” participants drawn from the main trial (i.e. those most closely matched), who also performed the pre, post, and retention assessments—by applying torques at 20% MVC . In the course of their five “training” sessions, these participants were required to simply count (“in their head”) the number of occasions upon which an infrequent (~ 15–25% probability) blue target appeared at random among standard green targets over the course of each set of 128 trials, and report this value at the end of the set. Their limbs were placed in the manipulanda in the usual fashion, however no movements were generated—the participants sat passively, and the cursor that would otherwise indicate wrist joint torques was not displayed.For the present purposes, attention is restricted to changes in MT Table  from preWhen the change in MT assessed at post is considered Fig. a, it becA broadly similar pattern of outcomes was apparent when the changes in performance from pre-training to retention were considered Fig. b. For thIn the present case study, we sought to examine the following question: does interlimb transfer occur if and only if the training movements are executed? The opportunity to do so came about serendipitously as a consequence of the profound difficulty exhibited by JG in generating wrist flexion–extension and ulnar deviation torques as the means to acquire visual targets. To put the extent of this deficit in context, over the course of 48 attempts during the pre-test session, and 240 attempts during the training sessions, JG was able to acquire the three targets that required ulnar deviation torques wrist extension torques, and their combination, on approximately one in nine attempts. When assessed again 3 days following the end of the training period, JG was unable to acquire either the ulnar deviation target or the target that required combined ulnar deviation and extension torques—in the course of 32 attempts. His rate of success in acquiring extension targets was marginally greater (3 of 16 attempts).The lack of success was not simply due to a deficit in generating joint torque per se. The magnitude of the torque required to acquire each target was scaled to 20% of JG’s assessed capability. Indeed, in the MVT task, JG was able to separately generate extension and ulnar deviation torques. Although it was of lower magnitude (≈ 65%) than that produced by his right limb, the value recorded for wrist extension was within 2.5 standard deviations of the (left side) mean for European males in the range 60 to 69 years  also exceeded most conspicuously the variations in movement time exhibited by a control group that did not train Fig. a.It is possible to conceive of the possibility that there were gains in right limb performance accrued by JG during the pre-training assessment, that were somehow reactivated/consolidated  in association with characteristics of essential tremor, may suggest some degree of disruption of cerebellar function. Nonetheless, neural deficits of other origin (such as those associated with Parkinson’s disease) or musculoskeletal pathology cannot be excluded. Beyond their unilateral (left) manifestation, the most striking aspect of the difficulties in motor control exhibited by JG, was the degree to which their expression was contingent upon the specific patterns of muscle engagement that were required. The generation of rapid and precise wrist extension and ulnar deviation torques posed an almost insurmountable challenge. In contrast, the production of wrist flexion torques, or combinations of wrist extension and radial deviation torques was accomplished more readily.The circumscribed nature of the deficits in generating coordinated goal directed joint torques raises the possibility that the interlimb transfer effects—which were evident both for targets within the quadrant for which JG experienced difficulties, and for targets in the other quadrants, were contingent upon training-related refinements of motor planning (rather than of execution per se). The adequacy of motor planning is often assessed on the basis of the initial directional error  were exhibited for impulses directed to targets in the wrist extension/ulnar deviation quadrant. They were not, however, accompanied by decreases in the heading deviation registered at 100 ms. Indeed, for targets that required combined wrist extension and ulnar deviation, the heading deviation was greater following training of the left limb. Evidently therefore, training-induced alterations in the adequacy of motor planning  were not the basis of the interlimb transfer of functional capacity exhibited by JG.When he attempted to acquire targets in the extension/ulnar deviation quadrant, feedback conveying the terminal accuracy of his attempts was seldom available to JG. During the period of 4 s that was permitted for each attempt, he did, however, receive continuous visual feedback of the cursor (representing the torque being applied) relative to the target. Within limits imposed by his deficiencies in coordination, visual feedback of target proximity may have facilitated a form of latent learning that was exploited when movements of the opposite limb were performed subsequently.There is an extensive body of work that concerns the distinction between ‘learning’ and ‘performance’  at least as rapidly as he had done when assessed 3 days following the cessation of training Fig. b. In allIt should be emphasised that this study has several limitations. For example, three of the participants included in the control group were older by JG by more 10 years. With the obvious exceptions of age cohort (young or older) and gender, the researchers undertaking the assessments were blinded as to the group allocation of individual participants during the conduct of the study. As it was only upon the conclusion of the study that we were in a position to match control participants to the characteristics of JG , there was no scope to ensure greater similarity in terms of age. Although the size of the control group precludes a quantitative analysis of age-related variation, inspection of Table It is a further limitation that a clinical assessment of JG was not available. The observations that were made, and the measurements that were obtained, do not provide a sufficient basis upon which to resolve the aetiology of his condition. As noted previously, JG did not express a desire for the research team to make representations that may have led to specialist medical consultations or assessment. As a consequence, it remains undetermined whether his movements were mediated by a (relatively) normal nervous system acting on an impaired musculoskeletal system, or by a compromised nervous system acting on a relatively normal musculoskeletal system. Although the balance of evidence would appear to favour the latter interpretation, without further diagnostics tests, it is not possible to distinguish causes.One might also pose the question: are isometric tasks distinct from free motion tasks, in terms of the nature the learning to which they give rise? While there was minimal joint rotation, the muscles involved in the isometric task necessarily shortened and lengthened. Cutaneous and tendon organ receptors are likely to have provided additional correlated proprioceptive feedback. It is acknowledged that the mapping between the joint torques and cursor movements was arbitrary, and it was a requirement that this was learned. Necessarily, however, this is the case whenever one learns to use many new tools (e.g. a computer mouse). It is assumed, therefore, that the task shared the key features of most voluntary movements—a set of neural commands generated with the intent of evoking a particular outcome . There is also empirical evidence to support the contention that isometric tasks—such as the one employed in the present study, give rise to forms of learning that appear equivalent to those which characterise dynamic tasks  limb was assessed. Evidently, it is not necessary for training movements to be executed in order for interlimb transfer to occur. While the changes in brain connectivity and local neuronal adaptations that mediate the long-term retention of functional capabilities acquired initially via interlimb transfer remain to be resolved (cf. Ruddy et al.


We propose a design approach for color absorbers based on a tri-layer metal-dielectric-metal (MDM) planar geometry, which maintains the same color absorbed, over a range of incident angles from 0° to 80° for light with TM polarization. The dielectrics are chosen to satisfy the ideal conditions of resonance. We calculate the ideal thickness of each dielectric layer by using the planar resonance theory. The numerical results show a total absorption above 85% for all colors of the absorber. We analyzed the influence of the of the metallic top layer thickness and we demonstrated the fabrication error tolerance of the proposed absorber. Finally, we present and discuss the physical mechanisms for the coupling of the electromagnetic field and the absorbed optical power in the structure. Electromagnetic absorbers can convert the incident electromagnetic energy on their surface into heat or other forms of energy. They have attracted the researchers attention due to the possibility of being used in a wide range of applications such as thermal emission3, photovoltaic cells4, light coupling5, sensors6, photodetectors7 and solar thermoelectric generators8. Nowadays, many designs of absorbers have been proposed, fabricated and tested. Generally, these absorbers consist of metal/dielectric multilayers, they have a high loss, and they are bulky structures. They also exhibit low wavelength bandwidth flexibility limiting their applications9. In the last decades, the advancement of the knowledge of metamaterials (MMs) associated to plasmonic nanostructures has provided the possibility of controlling and manipulating the interactions of the electromagnetic field with matter, allowing the development of novel structures where the absorption, transmission and reflection of the incident field can be controlled10. The unique optical properties of photonic MMs are strongly dependent on the ideal choice of size, geometry, periodicity, and materials  of the nanostructure11. It has been demonstrated that absorbers with close to unity absorption, with approximately zero transmission and reflection, can be obtained by using nanophotonic MMs with impedance close to that of the free space by considering dielectric/metal layers in their design over a metallic substrate11. Broadband absorbers based on MMs and planar nanoresonators with absorption higher than 80% for visible and infrared radiation have been analyzed and several designs have been proposed. They are metal-dielectric-metal (MDM) structures17 with only one or more types of metals19, they are composed by multilayer pairs of metal/dielectric20. The possibility of being able to control the properties of reflection, transmission and absorption in photonic MMs is of great interest for the development and design of perfect absorbers and resonant optical filters of transmission for the visible and infrared spectrum21. Perfect absorbers based on nanophotonic MMs that operate on the wavelength of the ultraviolet, visible and infrared electromagnetic spectrum, operate in the sub-wavelength regime and require, in most cases, great precision in the fabrication process due to the nanometric size of the structure dimension. One alternative to overcome the complex fabrication process of nanophotonic MMs would be the deposition of continuous thin films of metal/dielectric layers. This way of design does not require expensive neither complex fabrication techniques. The flat metal/dielectric/metal (MDM) multilayer structure is known as a Fabry-Perot (FP) type resonator and with the appropriate choice of metals, dielectric and layer thickness, it produces resonances that can be applied in several electronic optical devices, such as light transmitters24, photodetectors25, modulators26, phototransistors27 and photovoltaic cells28. FP filters face the challenge of shifting to blue in a similar way than other thin film based filters23 for oblique incident waves. The angular tolerance of FP resonators can be improved when specific conditions are previously satisfied29, especially the condition that relates the physical permittivity constants of the metal and the dielectric used in the design of the resonator. In this work we propose a planar FP absorber for all the colors of the visible spectrum. We use the theory of planar FP resonators to find the proper dielectric and its thickness for each specific color. We also evaluate the behavior of the absorbers for large angles of incidence and for possible fabrication errors of the metal thickness.Ideal absorbers are structures where there is no reflection or transmission of the incident electromagnetic field at any wavelength of interestεdielectric ≈ εmetal). In addition, we also evaluated the effects of fabrication errors in the deposition of the top layer of Ag and the physical mechanisms of absorption through the analysis of the spatial distribution of the electromagnetic fields inside the resonant cavity.In summary, in this work we present the proposal of absorbers exploring the properties of a Fabry Perot resonator where the combined effects of the dispersion properties of the dielectrics and metals used in their design result in a wideangle narrowband resonator for incident angles of about 80°. The absorbers are designed for the whole spectrum of visible light. Six different dielectrics have been considered in our study to achieve the resonance conditions , the dispersion frequency as a function of k, tends to ωsp which is the frequency of the surface plasmon. At this frequency the dielectric permittivity of the metal (εm) and the permittivity of the dielectric εd are equal in magnitude but with opposite sign,When λsp = 2πc/ωsp is the wavelength of the free space surface plasmon, because the frequency in k// = 0 will coincide with ωsp then the dispersion band II can become almost completely flat. Furthermore, this plane dispersion range of mode II  and (φref2), respectively. This displacement cancels approximately with the phase shifting of the light propagating in the perpendicular direction (φperp) to the interfaces in the dielectric region. The sum of the total shifting displacement in each round trip for all angles of incidence θ is approximately −2π32. This behavior can be observed in Fig. This situation occurs when the thickness of the dielectric assumes the value of equation II Fig.  indicateentclass1pt{minima33. Consequently, the relative permittivity can be described as 31. Figure 23. The imaginary part of the relative permittivity of Ag increases almost linearly in this interval with values varying from 1.6 to 18.0. Also, the relative permittivity of the selected dielectrics for the absorber design can be observed in Fig. The chosen metal for the nanoabsorber is Ag, the criterion for this choice is that in the visible region the real part of the permittivity is quite small and can be considered nullentclass1pt{minimaentclass1pt{minima35, the results of the absorption dependence for the TM polarization can be observed in Fig. 0). It is also possible to observe that this high absorption is maintained in a wide interval of incident angles, from 0° to 60°, confirming the angle insensitive theory of FP absorbers. Figure In order to calculate the absorption coefficients of the angle insensitive FP structure we used the Finite Element Method - FEMTable λsp of each color shown in the Fig. λcolor showing that the absorber does not shift to the neighboring color spectrum. Moreover, the Ag thickness has a great impact on the optical properties of the proposed absorbers, influencing the resonant wavelengths and angular insensitivity characteristics33. When the top layer of Ag are sufficiently thick (above 30 nm), the angular insensitivity characteristics for the TM polarization will be obtained, however, it increases the reflection by decreasing the absorption at the resonant peak. On the other hand, if the thickness of the Ag layer decreases, the absorption increases for normal incidence, despite the absorption peaks are shifted to the neighboring spectral range for oblique incidence, losing the wideangle absorption characteristics. Several simulations have been carried out in order to find the ideal Ag thickness of the top layer and the designed absorbers exhibit maximum absorption and angular insensitivity. The optimized values are shown in the second column of Table We use the intersection points 21 when Eqs , normalized magnetic field (H) and the absorbed optical power (Pabs) at the absorption peak of the yellow absorber, λ = 580 nm, Fig. Pabs was calculated by multiplying the electric intensity and the imaginary part of the permissiveness of the metal37:α is the normalized coefficient and the electric field E was calculated by FEM. Figure E-field in the dielectric region between the metal film and the substrate, as a result, a standing wave is formed in that region. This occurs due to the constructive interference caused by the choice of the parameters to satisfy Eq. λsp. The spatial distribution of the normalized magnetic field H is shown in Fig. E in the cavity makes Pabs to be absorbed inside the metallic film, both at the upper and lower interface (substrate), as can be seen in Fig. In order to understand and visualize the coupling mechanism of the FP absorber, we calculated the normalized electric field  and geometric  of the structure. The proposed structure has a simple geometry and it is of easy fabrication. It only requires planar film deposition. The absorbers can be used in other regions of the electromagnetic spectrum as long as the discussed resonance conditions are satisfied. The proposed device can be used in optoelectronic devices including sensors, photodetectors, perfect absorbers, among others.


Most devices measuring the kinematics of masticatory function are cumbersome to setup and not portable. Data collection would be facilitated, particularly in the elderly, if the device used for the objective measurement of mastication was easily transportable and simple to setup. Accelerometers and gyroscope sensors are lightweight and portable and may be useful alternatives. The definition of the turning point between the opening and closing phases of chewing is important for studies of associations between muscle activity and effects of perturbations. Measures of the mediolateral angle  allow the detection of the turning point between the opening and closing phases. The aim was to determine whether a three‐axial gyroscope sensor can detect the turning point between opening and closing phases of chewing. Fourteen asymptomatic participants chewed gum while the output was recorded from a three‐axial gyroscope sensor  attached to the chin and a 6 degree‐of‐freedom electromagnetic jaw‐tracking device . Bland–Altman plots were used to assess the matching of the recordings made by the three‐axial gyroscope sensor and the jaw‐tracking device. The turning points between the opening and closing phases of chewing matched closely when recorded by a jaw‐tracking device and when using a three‐axial gyroscope sensor. A three‐axial gyroscope sensor can validly detect the turning point between the opening and closing phases during chewing of gum. For example, in the elderly, a loss of chewing ability has been associated with sarcopenia .2.1The 6 degree‐of‐freedom (6DOF) internal sensor  was chosen for its small size  that was attached to the skin on the chin of each participant, with the same method as described previously  were digitally fed into a personal computer through a USB connection and were stored on a hard disk using custom software . This software employed linear interpolation that resulted in a 120 Hz sampling being converted to 1,200 Hz sampling in order for the Polhemus data to be measured simultaneously with the other sensors under the same sampling rate.2.3SD, 27.2 ± 3.0 years).Informed, signed consent was obtained from 14 volunteers .2.4Each participant was seated in an upright and relaxed position with his or her head unsupported and naturally oriented  were analyzed with mathematical analysis software . All the data from the Polhemus were converted so that the output represented incisal displacement against time together with angular data of the sensor attached to the lower teeth. The voltage data from the three‐axial gyroscope sensor were converted into units of angular velocity .For the turning points between the opening and closing phases as determined from the position Z of the Polhemus and as determined from elevation from the Polhemus, the mean difference was 0.009 s. The 95% confidence interval for the lower limit of agreement was −0.003 to −0.006 s. For the upper limit of agreement, the 95% confidence interval was 0.022 to 0.025 s. Thus, the turning points between the opening and closing phases from the elevation angle of the jaw‐tracking device tend to give a larger reading than that from the position Z by between −0.005 and 0.023 s. The mean difference between these two measures was not significantly different from zero. There was no fixed or proportional Figure  bias betSD).For the turning points between the opening and closing phases as determined from the position Z from of the Polhemus and as determined from the X orientation from three‐axial gyroscope sensor, the mean difference was −0.006 s. The 95% confidence interval for the lower limit of agreement was −0.18 to −0.14 s. For the upper limit of agreement, the 95% confidence interval was 0.13 to 0.17 s. The mean difference between these two measures was not significantly different from zero. There was no fixed or proportional . The data suggest that a three‐axial gyroscope sensor can validly detect the turning point between the opening and closing phases during chewing of gum.The first hypothesis was accepted, namely, that there is a close agreement between the occurrence of the turning points between the opening and closing phases of chewing as determined from the trajectories of jaw movement recorded by a jaw‐tracking device and as determined from jaw angles derived from the same jaw‐tracking device. Bland–Altman analysis revealed the agreement and the mean difference (0.008 s) between these two measurements was almost at the level of the sampling rate, namely, 120 Hz. The second hypothesis was also accepted, that is, there is a close agreement between the occurrence of the turning points between the opening and closing phases of chewing as determined from the trajectories of jaw movement recorded by a jaw‐tracking device and as determined from jaw angles derived from a three‐axial gyroscope sensor. The mean difference between the two measures was not significantly different from zero, and the differences lay within the range of limit of agreement  and the skin on the chin move in the same rhythm but with different magnitudes of displacement and velocity (Jemt & Hedegard, Acceptance of the first hypothesis suggests that the measures of the mediolateral angle allow the detection of the turning point between opening and closing phases. Taking the feature of digital sampling into account, the data suggest that these two parameters are identical. Therefore, the healthy participants demonstrated that the elevation angle (see Figure In conclusion, these two sensors, secured by means of adhesive tape to the skin on the chin, establish a portable system that is able to divide the chewing cycle into the main phases of chewing. The accelerometer is able to detect the intercuspal phase, and the gyroscope sensor can detect the opening and closing phases. Future studies will focus on jaw movement smoothness and muscle activity in each phase of the chewing cycle for participants with pain or in older people and where there has been technical difficulty in collecting data given the lack of portability of jaw recording equipment.


In any network, the dependence of connectivity on physical distance between nodes is a direct consequence of trade-off mechanisms between costs of establishing and sustaining links, processing rates, propagation speed of signals between nodes. Despite its universality, there are still few studies addressing this issue. Here we apply a recently–developed method to infer links between nodes, and possibly subnetwork structures, to determine connectivity strength as a function of physical distance between nodes. The model system we investigate is brain activity reconstructed on the cortex out of magnetoencephalography recordings sampled on a set of healthy subjects in resting state. We found that the dependence of the time scale of observability of a link on its geometric length follows a power–law characterized by an exponent whose extent is inversely proportional to connectivity. Our method provides a new tool to highlight and investigate networks in neuroscience. The issue is linked to the question of how geometric distance is relevant in human brain networks. As pointed out by Bullmore and Sporns in their review of 20121, the dependence of connectivity on the physical distance appears to be a trade-off between the complexity required to carry out cognitive tasks and the metabolic costs of establishing and sustaining a huge number of elements and links. More recently, Gollo et al.4 investigated the balance between costs of anatomical wirings and complexity, suggesting that any perturbation might induce neuropsychiatric disorders. While neural connections within the brain are not straight segments, geometric (Euclidean) distance turns out to be a measure apt to describe distance–related issues concerning the brain function6. Geometric distance between network elements was shown to be a relevant parameter for modelling the information transfer between brain regions, e.g. with regard to information transfer delays8. The interplay between geometric distance, connectivity and network topology was also investigated in relation to neurological diseases9. The dependence of functional links on the geometric distance between brain regions was first investigated by Salvador et al.11 and Fair et al.12 by studying correlation coefficients assessed out of functional magnetic resonance imaging (fMRI) recordings. In these works, as well as in more recent ones9, correlation coefficients are proposed to be proportional to the inverse of the square distance. On the other hand, other studies hint at different dependencies of connectivity on distance15. For example, Expert et al.16 claimed that, for sufficiently small ranges, correlations decrease as the inverse of the square root of distance.The fact that the brain has a small–world topology makes up a widespread assumption regarding the investigation of brain connectivity17 that, rather than relying on standard correlation measures, looks at the time scale at which cross–correlation between reciprocally undelayed time series occurs. The new approach is therefore complementary to traditional tools used to assess connectivity, and is expected to provide alternative insights into this issue.In this paper we investigate the dependence on distance of the basic elements of networks, i.e. links between pairs of nodes. Links are assessed by means of a recently introduced method19. A set of 72 brain regions, henceforth referred to as nodes, was randomly selected. Given a pair of nodes, we then investigated the dependence on their distance, henceforth referred to as link length d, of the time scale W at which cross–correlation between time series generated by each node occurs. This dependence turned out to be consistent with a power–law.We used cortical activity reconstructed out of magnetoencephalography (MEG) resting state time series collected from 20 healthy subjects among those available in the Human Connectome Project databaseet al.20, which provides the position of 360 different nodes. For the sake of computational simplicity, we analyzed 1/5 of the available set, namely 72 randomly selected nodes. For each single node a set of 60 time series is available, corresponding to 20 subjects and 3 recordings per subject. The set of nodes results in 2556 pairs. Due to the slight anatomical differences between the subjects, each pair corresponds to a set of 20 link lengths, so that the total number of d values is approximately 50000 within the range from 5 to 160 mm.The reconstruction of the cortical activity was carried out according to the atlas by Glasser W. While ∼ 70000 assessments failed to produce a finite time scale W, the remaining ∼ 83000 ones provided a valid W value within the range from 0.4 s to 48 s.Given a subject, a recording and a pair of nodes, the time scale of observability of the corresponding link was assessed out of the related pair of time series, resulting in approximately 150000 values of d and time scale of observability W. Figure d and W turn out to be significantly correlated. Besides in the (a) part of the figure, the color map representing d and W.The first goal of the present work is to verify whether there is a correlation between link length W and d is nonlinear. As explained in the Methods section, among different functional forms analyzed, a power–law of the kind W on d. The result of this analysis is shown in Fig. d0 to 75 mm (see Methods section), the parameters W0 and γ resulting from a best–fit procedure are Figure entclass1pt{minimaW on d is indeed present in each subject, although with different values of the parameters W0 and γ. Most parameters pairs are clustered in a region where W ranges from 15 mm to 30 mm and γ ranges from 0.2 to 0.7. This result is in agreement with the claim by Expert et al.16. As far as the exponent γ is concerned, a possible explanation of its variability relies on different levels of connectivity, as discussed in the next section. Interestingly, the average subject behaviour, in terms of average values of the two parameters among the subjects (blue dot), is in a very good agreement with the behaviour extrapolated by a pooled analysis of all subjects (red dot).The same analysis explained above was applied to each single subject in order to test whether the previous behaviour is characteristic of a single human brain or, rather, is the spurious effect of a cohort analysis. The results are shown in Fig. 21. This property appears to be universal, i.e. independent of the system under investigation. As an example, parallel to the work by Bullmore and Sporns1 concerning trade-off issues in brain connectivity, the work by Gastner and Newman22 addresses distributions of geometric properties in terms of costs and benefits within the framework of geographical networks. However, despite its universality, studies addressing the dependence of connectivity on physical distance are still few. Among these ones, a recent work by Hens et al.23 discusses a general model for signal propagation in networks to classify them in families depending on “the interplay between network paths, degree distribution and interaction dynamics”.As asserted in the Introduction, due to the presence of physical constraints, connectivity has to depend on distanceet al.24 described distance–dependent correlation between fMRI time series by relying on variograms, a tool from spatial statistics to quantify correlation as a function of distance25. Variograms allowed to empirically extract information on the spatial extent of correlations in fMRI connectivity28 and to account for the complicated characteristics of fMRI data29. In addition, variograms were applied to remove spurious correlations due to voxel proximity in fMRI studies within the auditory cortex30 and to monitor the spatial distribution of cellular activity in the brain31. In general, correlation is shown to quickly decrease down to a critical distance and then to saturate. A crucial issue in the investigation of human brain connectivity is to establish whether, and to what extent, structural connectivity, assessed by diffusion tensor imaging and tractography32, determines functional connectivity36. This issue is ultimately linked to how the neuron wiring is related to brain cognitive functions37 and how it is possible to reconstruct physical links out of temporal correlations detected through electrophysiological measurements.In neuroscience, to separate local–scale and large–scale regimes, Bellec Our investigation tackles the problem of determining the dependence of the connectivity strength on the geometric distance in a link between two nodes. Connectivity strength is expressed in terms of time scale of observability assessed by exploiting an analytical tool recently developed that relies on the analysis of time series each stemming from a single node. In the present case, time series are cortical activities reconstructed out of MEG recordings.et al.38, is that the dependence appears to be a power–law of the kind W ∼ dγ, where W is the time scale of observability and d is the geometric distance. The exponent γ takes on values ranging from 0.2 to 0.7. Lower values of γ corresponds to higher levels of connectivity, as explained in the following.What we observe, by using an approach based on the analysis of distributions similar to that discussed by Bialek W measures the time scale at which the cross–correlation between time series generated by two nodes becomes significantly visible. The source of cross–correlation are typically peak–like17 events that occur in both nodes at the same time. This process is countered by noise, which tends to wash out cross–correlation. If nodes are directly connected by physical links, and if the propagation speed of signals between nodes is much faster than the time scale of observability of cross–correlation – as it is the case of neural signals, which propagate in ms, whereas W is at least of order 1 s – the time scale of observability of links is not expected to depend on their length. In this case, γ is expected to be ∼ 0. On the other hand, if no direct link between two nodes exists, a working link has to rely on intemediate nodes that act as relay hubs. The relay process possibly introduces a noise component, which leads to a progressive signal degradation as distance increases. Consequently, the larger the distance d, the less frequent a peak–like co–activating process occurs, and thus the longer is the time window W required to observe peak–like events that occur at the same time.The quantity 40), are considered, as well as if correlation between the activity of nodes is not due to a direct information link but it is rather the manifestation of simultaneous responses to a common stimulation. The approach presented in this paper can be used to identify sets of nodes that form a subnetwork, for example by characterizing them on the basis of a specific behaviour in the On the basis of the large variety of neural connections occurring in the human brain, it is possible that different mechanisms like the two ones mentioned above simultaneously contribute to the observed power–law behaviour. In addition, different behaviours can be expected if particular sets of nodes, for example making up a subnetwork : given the p–value diagram for the pair of nodes, and given a value w of the window width, the efficiency η(w) is defined as the fraction of the running windows of width w that exhibit a p–value smaller than a given significance threshold. In this work, this significance threshold is set to 5%. Efficiency is typically a growing function of w17. A link between two nodes is deemed to exist at a time scale W if the efficiency at the window width W overcomes a second threshold that is here set to 0.5. If the efficiency fails to overcome the threshold, no link is attributed to the pair of nodes.A W defines the minimum time scale at which a link starts to be observable: hereafter, the link is supposed to exist for any time scale larger than W, at least up to the maximum window width of 48 s. It should be noted that observability eventually fades out – so that the corresponding link disappears – once the observation window becomes so wide that the noisy contributions to the time series become dominant again17.The window width W thus provides an estimate of the time scale of the process underlying the activation of links. These time scales are not necessarily related to the information transfer speed across the subnetwork: in the case of brain networks, information transfer occurs at the millisecond scale while the activation of links spans time intervals of second or tens of seconds50.The time scale of observability of a link is a measure of the minimum observation window such that two nodes are deemed to be correlated. For example, in the case of two nodes showing an identical activity over time, the minimum time scale of observability is zero. More realistically, the activity of two nodes turns out to be co–activated only for short periods of time, for example if a subnetwork structure is established for a given purpose and then reallocated after the purpose is accomplished. In this case, correlation is observed only if a sufficiently large window is used, and the time scale of observability turns out to correspond to the repetition time of this co–activation. The value N of candidate nodes of a possible subnetwork structure, there are 17.Given a number 19. The HCP provides the required ethical approval and consent needed for study and dissemination. Procedures for subject recruitment, including informed consent forms and consent to share de–identified data, were approved by the Institutional Review Board of the Washington University in St. Louis. All experimental procedures were performed under the guidelines of the HCP, which adhered to the relevant IRB processes related to that project.The dataset used in this work consists of MEG resting state recordings of 20 healthy subjects  blindly extracted from the public database of the Human Connectome Project (HCP)51 computed out of a brain–enclosing surface mesh with 5000 points, as well as surface reconstructions of the mid–thickness cortical mantle, both segmented from individual anatomical T1–weighted MRI scan . All meshes coordinates are standardized to the MNI space and co–registered to the sensor array. Further details can be found on the HPC website (MEG connectome pipeline version 3.0)19. Cortical activity was reconstructed by means of a minimum norm algorithm52 with unconstrained dipole orientations. We used an 8004 points cortical mesh as a source model, resulting in a grid resolution of approximately 5 mm. Noise covariance was estimated from the available empty–room recordings and no regularization was applied. Preprocessing and source reconstruction were carried out by means of FieldTrip routines53. After the reconstruction process, the time series were resampled from 2035 Hz down to 250 Hz. In order to get equally–long time series of 300 s duration (75000 samples), the first 4 seconds of each time series as well as a final segment of variable length were discarded.In brief, for each subject, three MEG resting state sessions of about 5 minutes each are available. Data were recorded with participants lying in supine position in a whole–head 248 magnetometers MAGNES 3600 scanner . Participants were instructed to rest with open eyes and maintain fixation on a projected red crosshair on a dark background. MEG sensor data, sampled at 2035 Hz, were cleaned by excluding bad channels and other artifacts and removing ocular/cardiac/myogenic activity by means of independent component analysis. The public HCP database provides single–shell volume conduction modelset al.20, which was built by combining structural, diffusion, functional and resting state MRI data from 210 healthy young individuals. The random selection was carried out by the following procedure:number the areas between 1 and 360;toss a number between 1 and 360 by means of a uniform random number generator and thus select the first area;k between 1 and 360;toss another number k is equal to anyone of the previously tossed numbers; if yes, repeat operation 3, otherwise jump to the next step;check whether check whether the new area lies within 1 cm of anyone of the previously selected areas; if yes, repeat operation 3, otherwise accept the new area and jump to the next step;check whether the total number of areas is less than 72; if yes, repeat operation 3, otherwise stop.Table The MNI coordinates of the centroid of each area provide the locations for the 72 sources that identify the respective nodes.Figure W provided a valid result.Figure d corresponding to valid values of W with the histogram of the link length d, also corresponding to valid values of W, assessed on the set of all other subjects. The analysis was carried out by using the Kolmogorov–Smirnov test. In all 20 cases, the p–value turned out to be close to unity. Link length thus follows the same distribution independently of the subject.We also analyzed, for each single subject, the matching of the histogram of link lengths W. While the shape of the histogram shows a maximum in the center of the range as in Fig. W and d. On the other hand, a linear mapping of the abscissa axes appears to be possible in order to (approximately) overlap the histograms of the logarithm of the two variables d and W, as it results from the plots of Figs W being truncated at 48 s, or equivalently d and W, thus ruling out the possibility of exponential or logarithmic functional relationships between d and W.Figure W on the link length d can be described by means of a power–law curve defined by W0 and d0 have the dimension of time and distance, respectively, and the exponent γ is dimensionless. To describe the power–law curve, either W0 or d0 can be arbitrarily set. The choice was to set d0 to 75 mm, which approximately corresponds to the average link length (see Fig. Consequently, the dependence of the time scale of observability