SciPhon is a software for the reduction of nuclear resonant inelastic X-ray scattering data. Tests and examples of applications to Fe, Kr, Sn, Eu and Dy data are presented. 57Fe, 83Kr, 119Sn, 151Eu and 161Dy. After data reduction, it provides the partial phonon density of states of the Mössbauer isotope that is investigated, as well as many other derived quantities such as the mean force constant of the chemical bonds and the Debye velocity. The data reduction is, however, not straightforward and involves removal of the elastic peak, normalization and Fourier–Log transformation. Furthermore, some of the quantities derived are highly sensitive to details in the baseline correction. A software package and several novel procedures to streamline and hopefully improve the reduction of the NRIXS data generated at sector 3ID of the Advanced Photon Source have been developed. The graphical user interface software is named SciPhon and runs as a Mathematica package. It is easily portable to other platforms and can be easily adapted for reducing data generated at other beamlines. Several tests and comparisons are presented that demonstrate the usefulness of this software, whose results have already been used in several publications. Here, the SciPhon software is used to reduce Kr, Sn, Eu and Dy NRIXS data, and potential implications for interpreting natural isotopic variations in those systems are discussed.The synchrotron radiation technique of nuclear resonant inelastic X-ray scattering (NRIXS), also known as nuclear resonance vibrational spectroscopy or nuclear inelastic scattering, provides a wealth of information on the vibrational properties of solids. It has found applications in studies of lattice dynamics and elasticity, superconductivity, heme biochemistry, seismology, isotope geochemistry and many other fields. It involves probing the vibrational modes of solids by using the nuclear resonance of Mössbauer isotopes such as  Other Mössbauer isotopes such as 83Kr, 119Sn, 151Eu and 161Dy are routinely measured by NRIXS at the APS and other beamlines around the world. The software introduced here is applicable to those systems as well. The Mössbauer isotope 57Fe has a low-lying nuclear excited state at 14.4125 keV. The approach used in NRIXS is to scan the energy around this transition and measure X-rays scattered by the de-excitation of the 57Fe nuclei. The incident X-rays are monochromated to 1 meV band-pass FWHM . They consist of pulses of 70 ps duration separated by interpulses of 153 ns duration. All electronic X-ray scattering processes including elastic Thomson scattering, Compton scattering and possible fluorescence emissions are instantaneous and rapidly decay. The excited state of 57Fe has a lifetime of 141 ns so the X-rays scattered by nuclear excitation are emitted with a delay. By applying appropriate time discrimination, and only collecting the signal emitted during the inter-pulse period, it is possible to eliminate X-rays from electronic scattering and only consider those produced by nuclear resonant scattering. The energy of the incident X-ray beam is scanned around the nominal nuclear resonance energy of 57Fe (i.e. 14.4125 keV) and the scattered X-rays are collected . The plot of delayed nuclear resonance signal versus energy (E) after proper normalization is called the phonon excitation probability density and is denoted 57Fe can also occur if lattice vibrations  provide the missing energy in a process known as phonon annihilation. Conversely, if the incident X-rays have higher energy than the nominal resonance energy, excitation of 57Fe can still occur if lattice vibrations can absorb the extra energy in a process known as phonon creation. The phonon excitation probability density function et al., 1995et al., 2011et al., 2014et al., 2005et al., 1997et al., 1998The method of NRIXS uses the excitation of Mössbauer isotopes to probe the vibration properties of solids . The analysis of NRIXS data is quite involved. To make most efficient use of precious synchrotron beam time, it is important to develop data processing software such as PHOENIX  It has a graphical user interface (GUI), which facilitates learning of the program and speeds up data processing for the most repetitive tasks.(ii) It provides flexibility in the definition of the baseline.(iii) It allows the user to define the energy range used in data reduction.(iv) It propagates uncertainties not only from counting statistics but also from baseline subtraction and energy scaling.PHOENIX.(v) It outputs all the parameters already given by SciPhon (Science of Phonons) and is a package that can be run under Mathematica. The reason why Mathematica was used is that it makes it easy to develop a GUI that is portable from one operating system to another and from one software generation to another. The software is available from the corresponding author upon request, from scientists at sector 3ID of the APS, and from the website http://originslab.uchicago.edu/Software-and-Facilities.The program is named 2.SciPhon  and the resolution function of the monochromator (∼1.0 meV FWHM). Because the latter is so much larger than the former, the signal formed by nuclear forward-scattered X-rays is a proxy for the resolution function of the monochromator  by normalizing the counts to the flux measured in an ionizing chamber (IC1) located after the monochromator. The third column in the data file is the 1σ error from counting statistics (n is the number of counts in each channel). The user selects the data file by using a standard file browser interface. The directory where the data file is located is the default output directory for SciPhon, where the results of the calculation are exported.The data file contains a header where each line starts with the symbol # and which is discarded by 2.3.The resolution function file contains a header that is discarded. The first column records the energy in meV, the second column contains the counts, and the third column contains the uncertainty from counting statistics. The uncertainty column is not used in the calculation. By default, the software opens the file browser window starting in the directory where the data file is, but the user can then browse other directories to find the resolution function.2.4.SciPhon, the user is thus given the option to truncate the resolution function and only use the potion that is above background level. This is done using an interactive graphics interface where E on a log–linear scale. The user can use this plot to visually assess the energy values beyond which the signal is all background and to set those limits using vertical sliders. Once those energies have been set, SciPhon truncates In samples that do not block X-rays, the resolution function eV Fig. 2. In SciPThe next step in the algorithm is the optional deconvolution of Mathematica . The criteria for judgment were the degree to which the elastic peak approached a Dirac delta function, the lack of deconvolution artifacts near the elastic peak, the accuracy of derived PDOS, and minimal noise amplification. The Richardson–Lucy . The restoration vector can be modified so that no spurious negative counts can be present in the solution vector and noise amplification is limited. Furthermore, to limit noise amplification, the user can limit the number of iterations so that a partial solution is retained while keeping noise amplification within an acceptable range. The iterative solution is appealing because it stands between no deconvolution (no noise amplification but the presence of resolution artifacts) and full deconvolution (significant noise amplification but reduction in resolution artifacts).S(E) was then calculated from this DOS. In NRIXS, the X-rays from nuclear resonant elastic scattering are suppressed relative to those from nuclear resonant inelastic scattering. The elastic peak in the synthetic spectrum was therefore arbitrarily reduced by a factor of ten compared with the rest of the spectrum while in reality the reduction is higher  and S(E). We compared the results following (1) no deconvolution of the resolution function from the data, (2) deconvolution with 10 iterations, and (3) deconvolution with 100 iterations. Near the elastic peak, significant oscillations are present in the deconvoluted data, especially when 100 iterations are performed . Most importantly, it does not add any bias.To test the steepest descent deconvolution technique, we used a synthetic Debye DOS. The rationale for using such a DOS is that it presents a sharp decrease at the Debye energy so the strengths and virtues of the method should be exacerbated. To run the test, we computed a synthetic Debye DOS with a Debye energy cutoff of 30 meV Fig. 4. A synth Fig. 4b. As is e2.5.The background can be measured away from the resonance by setting the energy to −200 meV relative to the resonance energy, where no counts (even from multiple phonon annihilation) should be present and all the signal should come from the background. This background can be measured for a set duration and the resulting counts can be subtracted from the signal. As discussed below, another option is given to the user, which is to apply a baseline subtraction based on the counts measured in the low- and high-energy tails of the spectrum. In the following, we will refer to background for the counts measured at a single energy far from resonance, and baseline for the counts interpolated from the low- and high-energy tails of the spectrum.The user is also asked to enter the experiment temperature, meaning the temperature of the sample as it is being measured. This is used when calculating the phonon annihilation part of the NRIXS spectrum from the phonon creation part. Indeed, an option is given in the software to either use the temperature from the detailed balance or that entered by the user. This is particularly useful for experiments carried out at high temperature, where the temperature given by the detailed balance is very imprecise. The input temperature is also used for elastic peak removal (see the section below).2.6.PHOENIX for removal of the elastic peak is to rescale the resolution function and to fit it to the undeconvoluted elastic peak. The procedure used in SciPhon is different. At two given energies −E and +E, the NRIXS signal must respect the detailed balanceT is the temperature in K. This is the standard way of writing the detailed balance but it can also be written in the formSciPhon, the series is truncated at the second order and near the elastic peak we use the approximationThe procedure used by ak Fig. 5. To do t2.7.et al., 2012et al., 2015et al., 2016et al. . The signal in the tails thus defined is cut out and a baseline defined by linear interpolation between the cut out sections is removed from the rest of the spectrum. The user has the option to bypass this truncation/baseline subtraction routine or to manually modify the baseline values to test the sensitivity of the results to baseline subtraction. This routine significantly improves the reproducibility of force constants measured on the same minerals analyzed in different sessions separated by several months or years.Removal of a constant background is sometimes not adequate in NRIXS. This issue is most clearly seen in measurements performed over a broad energy range. Beyond a certain energy that depends on the material analyzed, no signal should be detectable above background. In reality, significant counts often remain at low and high energies that cannot be accounted for by multiple phonons. Those counts often do not average to the same values on the low- and high-energy ends of the spectra. As a result, some of the quantities derived from  al. 2014 used a r2.8.et al., 2004E and E. For example, for a scan from −120 to +130 meV measured in steps of 0.25 meV, a total of 480 (120/0.25) temperatures can be estimated. SciPhon calculates those temperatures and displays them on the screen, so that the user can get a sense of the reliability of the temperature estimate. Not all temperatures have the same error because the counts vary from one energy bin to another. Assuming Poisson statistics, the uncertainty on The temperature of the sample can be calculated in NRIXS by using the detailed balance SciPhon calculates Mathematica. Once the single-phonon contribution has been calculated, Assuming that the lattice is harmonic, meaning that the potentials vary as the square of the atomic displacements, it is possible to calculate the DOS  al. 1998 and Stur al. 1998 showed,  al. 1998, that thSciPhon recalculates PHOENIX and it allows extrapolation of A potential difficulty with NRIXS is that the signal at high energy can influence the calculated parameters even when the signal is near or below the baseline. To mitigate this issue, 2.10.et al., 2001et al., 2003et al., 2011M is the mass of the nuclear resonant isotope and ρ is the density. In SciPhon, the user is asked to enter the density ρ and bulk modulus K of the material being examined. The function E. For a pure Debye behavior, it should be constant over some interval. In practice, this is not often achieved, partly because the low-energy range of the spectrum is below the elastic peak. To address this difficulty, the function 3. The user can move two vertical sliders that define the energy range over which the data are fitted by this function. A black vertical marker indicates the energy that the user has previously defined to remove the elastic peak from the spectrum by extrapolation (a) calculated by fitting the function K, it is possible to calculate et al., 2001et al., 2016K and ρ, we use approximate solutions to these equations,SciPhon reports this value, which expectedly is always close to 0.3 for metals.An important use of NRIXS in geophysics and high-pressure mineral physics is the determination of seismic velocities at high pressure–temperature Lamb–Mossbauer factorMean-square displacement−1]. Note that the wavenumber k should not be mistaken for the Boltzmann constant Kinetic energy per atom KE. This is the energy associated with atomic motions along the direction of the X-ray beam,UInternal energy per atom . This is the total energy of the iron sublattice and it comprises kinetic energy from atomic motions and potential energy from chemical bonds. For a harmonic oscillator, the internal energy is equally partitioned between kinetic and potential energy, so we haveF〉Mean force constant 〈. The third central moment of et al.  and the moments of S(E) to calculate the β-factors at any temperature as a function of the moments of S(E),M and SciPhon calculates and reports all these coefficients. Truncating the formula above, we obtain the approximate formulaSciPhon reports the value of  al. 2012 and Hu e al. 2013 establis3.2.Mean square displacement and Lamb–Mössbauer factor. The atoms oscillate in their potential around an equilibrium position. The magnitude of these oscillations is quantified by the mean square displacement . This can be calculated from a thermalized moment of the PDOS,M is the mass of the nuclear resonant isotope. The Lamb–Mössbauer factor is calculated from the mean square displacement through  (meV). The data ranges defined by the users varied from  . All other parameters derived from the NRIXS data also agree well, including the Debye velocity. The range of Debye velocities is from 3839 ± 56 m s−1 to 3960 ± 52 m s−1. All the parameters derived from the data also agree well with the mean goethite values published by Blanchard et al.  after refinement] than with SciPhon but still within error. The difference is most likely due to the fact that a constant background is subtracted with PHOENIX while a linearly interpolated baseline is subtracted from the data with SciPhon. The most obvious difference between the SciPhon and PHOENIX outputs are the values of the resilience. SciPhon gives a value of ∼88 N m−1, while PHOENIX gives a value of ∼27 N m−1. The critical temperatures in PHOENIX and SciPhon are very close (∼1200 K). Resilience .et al., 19992 and SnO calculated by PHOENIX and SciPhon. As shown, there is excellent agreement between the two. We also examined the parameters calculated by PHOENIX and SciPhon and there is again excellent agreement between the two. The only major disagreement concerns the resilience, which SciPhon calculates at 159 N m−1 while PHOENIX gives a value of 51 N m−1. As discussed above in the context of 57Fe NRIXS measurements, the critical temperature estimates agree between SciPhon and PHOENIX but there is no internal consistency between the critical temperature and resilience calculated by PHOENIX. Another difference concerns the vibrational entropy and vibrational specific heat, which differ by a factor of three . The values calculated by SciPhon are directional, meaning that they would have to be multiplied by a factor of three to account for the bulk material if it was isotropic. This factor of three is not the cause for the discrepancy between the two softwares for the resilience.An important difference between iron and tin is that the Lamb–Mössbauer factor of tin compounds is usually small and multi-phonon contributions are significant , for SnO,2,4+ (SnO2) and Sn2+ (SnO) is2O3. The polynomial expansion to the β-factors for Eu are (the temperature T is in K), for EuO, 2O3,3+ (2+ (2O3 (haematite) . At room temperature (25°C), the calculated fractionations are 6.2‰ for Sn, 2.5‰ for Fe and 0.34‰ for Eu. At a temperature of 1100°C that is more relevant to magmatic systems, the calculated fractionations are 0.32‰ for Sn, 0.13‰ for Fe and 0.02‰ for Eu. The isotopic composition of Sn can be measured with a precision of less than ±0.04‰  buffer, which taken at face value would indicate that Sn is dominated by Sn4+ in terrestrial magmas while Sn2+ could be present in significant amounts in reduced lavas . If one assumes that the material has a Debye PDOS, the even moment of g(E) can be expressed as even powers of the Debye energy cutoff,56Fe/54Fe ratio, this would givea and b are fit parameters that can be calculated based on NRIXS measurements or ab initio studies that give the third-order polynomial expansion of the β-factor. For the 56Fe/54Fe ratio, Dauphas et al.  It has a GUI, which facilitates learning of the program and speeds up data processing for the most repetitive tasks.(2) It provides flexibility in the definition of the baseline/background.(3) It allows the user to define the energy range used in data reduction.(4) It propagates uncertainties from counting statistics, as well as baseline subtraction and energy scaling.(5) It outputs all the parameters that can be extracted from the NRIXS spectrum and partial PDOS. This includes a built-in function to calculate the Debye velocity from the PDOS as well as all data needed to calculate reduced partition function ratios used in isotope geochemistry.(6) It uses an original approach to remove the elastic peak using an interpolation that respects the detailed balance.SciPhon yields values that are most often consistent with the values derived by PHOENIX. The baseline subtraction procedure used in SciPhon has been proven to yield reproducible data. SciPhon is routinely used by our group and others and data generated by it have already been published in top journals (Dauphas et al., 2014et al., 2015et al., 2015et al., 2016et al., 2017Extensive testing was performed to ensure that the software performs as expected. 10.1107/S1600577518009487/fv5085sup1.txtCSV file containing the PDOS values for all the compounds examined in the paper. DOI:


Car parking is of central importance to congestion on roads and the urban planning process of optimizing road networks, pricing parking lots and planning land use. The efficient placement, sizing and grid connection of charging stations for electric cars makes it even more important to know the spatio-temporal distribution of car parking densities on the scale of entire cities. Here, we generate car parking density maps using travel time measurements only. We formulate a Hidden Markov Model that contains non-linear functional relationships between the changing average travel times among the zones of a city and both the traffic activity and flow direction probabilities of cars. We then sample the traffic flow for 1,000 cars per city zone for each city from these probability distributions and normalize the resulting spatial parking distribution of cars in each time step. Our results cover the years 2015–2018 for 34 cities worldwide. We validate the model for Melbourne and reach about 90% accuracy for parking densities and over 93% for circadian rhythms of traffic activity. If we consider that cars that burn fuels other than electricity are directly responsible for 14% of global greenhouse gas emissions2 and 3.3 million premature annual deaths worldwide3, we find that there exist large potentials for environmental savings. Knowing where cars are parked at what times could support urban planning in the process of optimizing road networks, pricing parking lots and planning land use.Car parking is of central importance to congestion on roads and their social, environmental and economic impacts on society. An imbalance between on- and off-street parking prices for instance leads to cruising for cheaper on-street parking lots which in turn is responsible for 8–74% of traffic in downtown areas4. On the other side, the batteries of parked electric cars can be valuable storage capacities that can be used for balancing grid operation with large shares of intermittent renewable energy sources7. For an efficient placement, sizing and grid connection of charging stations, it is therefore important to know the spatio-temporal distribution of car parking densities on the scale of entire cities10.The electrification of the mobility sector makes it even more important to know where cars are parked at what times. At times and locations where large numbers of cars are parked with high density and must charge simultaneously for their upcoming trips, their additional electricity consumption can cause stresses to the local grid12. The existing theories focus on the stream variables speed, flow and concentration of vehicles16; in these, density always refers to the concentration of vehicles on roads. Car parking density maps instead would require data about the number of cars parked in each region of a city at various times of a day. We find that the main barriers for measuring such data directly are the costs and efforts of placing and operating sensors.The existing literature on urban traffic does not provide data on spatio-temporal parking densities on the scale of entire cities. Classic traffic system research aims at the development of optimal transport networks by minimizing congestion on roads17 and generate the desired parking density maps for 34 cities around the globe. We further provide complete code and instructions on extending the presented model for a wider range of traffic and parking system analyses18.In this analysis, we explore if car parking density maps on the scale of entire cities can be estimated from travel time measurements among different zones of a city only. We formulate a Hidden Markov Model in which states are the locations of cars and emission measurements are the changing travel times among the zones of that city throughout a day. We apply the model to travel time data that is measured from undertaken Uber rides19. We formulate non-linear functional relationships between the changing average travel times among the zones of a city and both the traffic activity and flow direction probabilities of cars. We derive origin-destination matrices for each hour of the day and for all zones of an entire town with these functional relationships. We then sample the traffic flow for 1,000 cars per city zone for each city from the resulting probability distributions and normalize the resulting spatial distribution of cars in each time step. The resulting parking density maps are hence independent from the number of sampled cars and can be scaled to arbitrary vehicle fleet sizes.We generate car parking density maps from Uber travel time data for 34 cities worldwideThe resolution of the generated maps in time is one hour. The time periods for which we generate the results depend on the availability of the underlying Uber travel time measurements. At the time of writing this, Uber provides travel time data for the years 2015–2018 and distinguishes these by weekdays, weekends and the quarter of a year. In addition to these, Uber also provides travel time statistics that are collected regardless of the day type; these datasets cover a larger variety of trips than the separated datasets and therefore have lower sparsity.The resolution of the generated maps in space varies and depends on how Uber divides cities into different zones. Figure We subsequently validate the presented results in two steps for the city of Melbourne during the years 2015–2017 for both travel time data that is separated by day types and those that are not separated by day types. In a first step, we validate the circadian rhythm of traffic activity that we generate by our model. In a second step, we validate the car parking densities that result from our traffic flow model for 100–105 city zones; the city zones that we validate are given by the location of the operated underground parking sensors in Melbourne. Our choice of Melbourne for validation is arbitrary and motivated by the availability of measured traffic count and parking density data; we make this choice independent from the performance of our model.20.A first substantial hypothesis in our model is, that whether a car drives to another city zone or stays parked in its origin zone is a function of changing travel times from the car’s current location to all possible destination zones throughout a day. This means, that the higher the measured travel times at a certain time of a day in a particular city zone are, the more likely it is that a car will undertake a trip to another destination at that given time of the day. This generates a characteristic circadian rhythm of traffic activity for each sampled day. We validate our sampled circadian rhythms with vehicle count data from street segments in the city of Melbourne that we use as an indicator for traffic activityTable 25: first, a relatively high morning rush hour traffic between 8:00–10:00 am; second, a moderate lunch time traffic between 11:00 am–1:00 pm; third, a peak evening rush hour traffic between 4:00–6:00 pm; fourth, a relatively low midnight traffic between 1:00–3:00 am. We can observe that both the measured and the sampled circadian rhythms contain the four characteristic features of urban traffic activity.Figure 20. The validated city zones are given by the location of the operated underground sensors which is mostly around the city center of Melbourne.The second substantial hypothesis in our model is that the destination zone that a car will choose for a trip is a function of the traffic activity in that zone at that given time of the day. This means, that the higher the measured travel times to a particular city zone are, the more likely it is that cars will choose that zone as a destination. This generates characteristic flow directions of cars and, together with the first hypothesis, the parking density of cars among the zones of a city. We validate the characteristics of our modeled car parking densities with underground parking sensor measurements in about 100 from the total of 2,357 modeled city zones in MelbourneTable Figure We explore, if temporal car parking density maps can be modeled on the scale of an entire city, given travel time measurements between the zones of that city only. Using the Hidden Markov traffic Model that we present and the travel time data that is published by Uber, we find that parking densities can be estimated with about 90% accuracy for both weekdays and weekends. The circadian rhythm of daily commuting traffic can further be sampled with an accuracy of over 93% with our model. Although Uber users may not take an Uber ride for their daily commute but rather for extraordinary trips, which creates a large sparsity and bias in most of the data, we find that the measured travel time data is most of the time representative enough for creating the desired car parking density maps on the scale of entire cities.26 and Wardrop’s second principle of equilibrium27. Our theory, however, differs in the fundamental hypothesis that the density of cars parked in an area is a function of the changes in travel time between the origin and destination pairs that relate to this area throughout a day.The research question we ask is new and the data that we generate is the first of its kind in the literature. In contrast to classic traffic system research, our theory estimates the density of car parking by sampling individual driving behaviour. It contains elements of the Cumulative Vehicle Count Curves (N-curves)25. The parking densities and commuting trends that we model based on our central hypotheses mostly match with those that are measured in the city of Melbourne20. We choose Melbourne for the validation of our results based on the parking and traffic data that is publicly available.Our results are consistent with those of previously performed traffic system analysesThe performance of the presented model depends on the sparsity of the origin-destination travel time matrices that we use to sample the traffic flow of cars. We can observe that the travel time data that is collected without separation by weekdays and weekends has a lower sparsity and leads to more accurate parking density trends Fig.  than theFigure We are given the arithmetic mean of hourly travel time measurements between different zones of a city Fig.  and want28. The data includes both central and suburban regions of a city which are divided into up to 5,260 zones. The raw travel data, as it is published by Uber, consists of four entry types. We let N be the number of zones in which the city is divided and T be the number of discrete time steps in which one day is divided. The four entry types of the travel data can then be defined for all t = 1…T and i, j = 1…N as:μij,t: = the mean travel time from zone i to zone j at daytime tσij,t: = the standard deviation of travel time from zone i to zone j at daytime tgeo_μij,t: = the geometric mean travel time from zone i to zone j at daytime tgeo_σij,t: = the geometric standard deviation of travel time from zone i to zone j at daytime tThe Uber Movement project provides statistical data about travel times between different zones of a city. At the time of writing this, data is available for 34 cities worldwide with one second resolution. The data distinguishes between each quarter of several years. Depending on the city of interest, data is available from the years 2015 until 2018. For each quarter of these years, three types of datasets are available. The first type of dataset contains the aggregated measurements of travel time during weekdays and weekends. The second type of dataset contains measurements for weekdays only, and the third type of dataset contains measurements of weekends only. Detailed information on how the statistics were derived can be retrieved from Uber’s official methodology paper28. This naturally generates a bias in the data that is larger the less Uber rides were undertaken in the time period and city of interest. Tables The sparsity of the datasets plays an important role for the performance of the here presented model. These sparsities depend on the number of Uber users in the provided cities and the provided time periods. Measurements are only given between zones and at times, in which a sufficient amount of Uber rides were undertaken, so as to ensure a sufficiently good representation of overall trafficSi be the number of vertices of the polygon of zone i, and xi,j and yi,j be the longitudinal and latitudinal coordinates of vertex j. We represent each city zone polygon by the centroid, also known as the center of gravity, of this polygon. We compute the area Ai of each city zone i and the coordinates of the i-th centroid (longi|lati) for all i = 1…N and j = 1…Si, where j = 0 represents the same vertex as j = Si, as:Each zone of a city is described by a polygon with up to several hundred vertices. A separate file provides the latitudinal and longitudinal coordinates of these vertices for each polygon of each city. We let lat can then be expressed as 111.3 km ⋅ cos(lat). If we replace the average distance of 71.5 km per longitudinal degree with this expression within the Pythagorean theorem, we can calculate the distance dij between two zones i and j at the points (longi|lati) and (longj|latj) as:The easiest way to calculate the distance between two points on the planet is to assume that latitude and longitude are straight lines. Using a constant distance of 111.3 km between each latitudinal degree and an average distance of 71.5 km per longitudinal degree, we can simply calculate the distances with the Pythagorean theorem. A more accurate way of doing this is to consider that longitudinal lines are not simply straight but rather bend depending on the latitudinal position: the distance between two longitudinal lines is around 111.3 km at the equator and 0 at the north and south poles. The dependence on the latitudinal position Xt: = the distribution of cars among all city zones at time step tWe define the state of the traffic system as the distribution of cars among city zones. The state in each time step belongs to a finite set of possible states if the number of sampled cars is finite and constant. We can extend the state space of our traffic model by assigning more properties to a car than just its location. Such properties can for instance be the states of charge of electric car batteries or the number of transported persons. We describe the location of a car at a given time t = 1…T by its city zone and introduce:X contains NV possible arrangements. Every state Xt is only dependent on its previous state Xt−1 which gives us a discrete-time Markov chain model. For the state transition probabilities at times t = 1…T − 1 it hence holds that:If we let V be the number of cars that we want to simulate, the state space ΩNV)2. For each time step t = 1…T-1, we write:We let the state transition of our model be given by the uncertain flow of cars among all city zones and denote this as The transition probabilities can then be described by:μij,t only. This gives us a Hidden Markov Model as the number of cars flowing among city zones is not directly measured but derived as a function of the changing mean travel time throughout the day. The mean travel times are called emission measurements.The problem that we want to solve can be formulated as finding the car flow probabilities A: = binary random variable that describes whether a car drives or parksa ∈ Ωa = {0, 1}. We determine the probabilities for possible values that A can take by letting the driving activity of cars in a zone be a function of the sum of mean travel times from that zone to all other zones. We assign a probability of driving according to the sum of mean travel time out of a zone in each hour compared to its minimum and maximum values throughout the entire day. For this purpose, we introduce two parameters:We denote the values that a random variable can assume in lower cased letters and let 0 stand for parking and 1 for driving, hence pmin: = the probability that a car will drive, given the minimum sum of mean travel time out of a zonepmax: = the probability that a car will drive, given the maximum sum of mean travel time out of a zoneFor describing whether a car drives to another zone or stays parked in the same zone, we introduce a binary random variable:pmin and pmax and perform a model selection based on validation results to make a good choice of these parameters. We later present an algorithm that utilizes validation results of average driving times for parameter tuning. Two conditions that pmin and pmax must satisfy are:One can assign arbitrary initial values to For each zone of the city, we derive a set of 24 Binomial probability distributions, that is one for each hour of the day. We define the probabilities of an event P(A = a) for zones i = 1…N and times t = 1…T as:Mij,t being the subset of travel time data that is available at time step t, a formulation of Eq.  that a car in zone i = 1…N chooses a destination zone j = 1…N at time t = 1…T and their respective normalization factors as:We also let the popularity of destination zones be a function of changing travel times throughout a day and ask ourselves how likely it is that a car in zone i travels to zone j at a given point t in time. For this purpose, we compare the mean travel time of an origin and destination pair in each hour with its minimum and maximum values throughout the entire day. We hence assign a numeric value between 0 and 1 to each origin and destination pair and for each direction. Note that we do not use the sums of mean travel times here but rather perform a min-max scaling of the data in each time step. The closer this value is to one, the more popular a destination zone is at that given hour. We generate a valid Multinomial probability distribution whose probabilities sum up to 1 for each zone and each hour of the day by normalizing all values with a factor C: = discrete random variable that describes the joint events of driving (A = a) and choosing a destination (B = b)The desired transition probabilities c ∈ ΩC = {0, ..., N}. A value of zero means that a car does not drive (A = 0) and hence stays parked in its origin zone. Any other value indicates that a car is chosen to drive (A = 1) and chooses the respective destination zone (B = 1…N) that is given by the value of C other than zero. For a simplified notation and calculation, we assume the random variables A and B to be independent and write:We describe the state space of C with μij,t and described by the probability distribution of P(C = c) as:Note that the same holds for both the arithmetic and geometric mean of travel time. We summarize that the uncertain flow of cars among the zones of a city X0: = the initial distribution of cars among all city zonesTo sample the traffic flow, we need to define a realistic initial state of the system. The problem of finding such a state is commonly referred to as the Initial Value Problem. We introduce:We uniformly assign a location zone to each car and calculate the state transitions for an entire day. We expect the initial uniform distribution of cars to converge towards a naturally shaped distribution after all transition probabilities are applied to the traffic system. We then assume the last state of an entirely modeled traffic day as the solution to the Initial Value Problem and set:To analyze any values of interest, we can assign state transition properties to each undertaken trip. Here, we let the transition properties of our model be the travel distance and duration of each trip. Similar to the state of the system, also the state transition properties can be extended. Such extensions can for instance be carbon emissions, fuel consumption and transported amount of people for each trip. We introduce for all v = 1…V, i, j = 1…N and t = 1…T:29. We use the mean  and standard deviation  from the original datasets to describe the stochastic distributions of dij) are further used for describing dij for creating a larger variety of individual trip distances. In order to avoid negative duration and distances, we truncate the probability distributions. We choose arbitrary lower and upper ranges of 0.1 times the mean and normalize the probability density functions accordingly. We let tdur and tdis describe random variables and formulate the truncated probability distributions of As for many other natural processes, we assume the stochastic distribution of travel duration and distance to be GaussianWe sample the state transitions and therewith the traffic of cars among all city zones by generating a random variable between 0 and 1 for each car in each time step. We then compare the value of the random variable with one of the Multinomial distributions of edrive and edest determine the functional relationship between travel time data and the joint Origin-Destination probabilities of the modeled traffic system. In order to find a good choice for them, we must evaluate the values of interests in our model with real world observations. The values that we are mainly interested in in this modeling task are the circadian rhythm of traffic activity and the spatio-temporal distribution of car parking densities. We hence use measurements of these two values to make a good choice for edrive and edest. The subsequent subsections describe how the validation works in detail. In this subsection we describe an algorithm for finding a good solution for both parameters. Finding optimal values for edrive and edest turns out to be a non-convex optimization problem. Optimizing via gradient descent is hence strongly dependent on the initial parameter values. The first part of the optimization process is hence about finding a good starting point. In order to do this, we evaluate the results of traffic activity and parking density for several values of edrive and edest between zero and one, as well as between one and e.g. 10. Both edrive and edest are used as exponents in the functional relationship of Eq. (: = current parameterEn)( = η: = constant step size parameterThe parameters p of Eq. . We streEn)( that is given with the current parameter en)( and the new error gradient ∇En)( > 0):En)( < 0), we update the best found values:We test different initial parameters and set the one with the lowest evaluation error as the best found parameter pmin and pmax determine the range of probabilities for deciding whether a car drives or parks given the time of day and zone of presence; they were initially set to arbitrary values that satisfy the conditions in (8) and (9). Once we have first sampling results, we can use pmin and pmax to normalize our traffic system according to one or more set point values. We defined the two state transition properties travel duration and travel distance which we can use both for normalization. Here, we use the share of driving time within the lifetime of a vehicle for normalization and introduce:Aset: = the realistic amount of driving timeAdrive: = the sampled amount of driving timeThe parameters Adrive is Aset = 0.05. Alternatively, one can use other values such as the average number of trips, the average fuel consumption or the average travel distance of cars as values for normalization. The only condition is that these values must be recorded as state transition properties. A computationally effective way is to normalize each dataset separately. In this case, we normalize the traffic system with respect to the time steps t = 1…T and calculate:If we assume that the realistic amount of driving time within the lifetime of a car is around 5%, the set point value to which we must approach ctime considers the time resolution of our simulation. For our analysis, the original datasets entail mean travel times μij,t with one second resolution. This gives a time constant of ctime = 24⋅60⋅60. For one minute resolution, we would respectively calculate ctime = 24⋅60, and ctime = 24 for an hourly resolution. A more accurate but computationally intensive way is to normalize the traffic system throughout all datasets that are available for each city. In this case, we consider weekly, seasonal and inter annual variations of traffic patterns. With G being the number of datasets that we want to normalize and The constant Adrive to Aset. In each iteration, we update either pmin or pmax by solving one of two equations. Which parameter we update, depends on the relation between Adrive and Aset. In each n-th iteration, we calculate:We use a numeric iterative algorithm to iteratively calculate the parameter values that approach pmax and then pmin once the range of possible values is reached for pmax. The upper range of pmax here is 1 and the lower range the actual value of pmin in each iteration.With this conditioning, the algorithm first tunes Pi,t: = the sum of sampled cars parking in zone i during time step tDi,t: = the sum of sampled cars driving in zone i during time step tThe sampled traffic activity and parking density of cars in each zone can be derived from the state transition entries. If 20 Each vehicle count sensor measures the number of vehicles that passes the respective street segment and distinguishes between 22 types of different vehicles. Each parking sensor measures the arrival and departure times of cars being parked in their respective bays. A separate set of files provides information on latitudinal and longitudinal coordinates of the parking bays that are equipped with sensors. We use the mutual information of these files to first allocate the sensors and then to assign each sensor to one distinct city zone. Sensors are assigned to the city zone to which they have the shortest beeline distance. The parking density of each zone in each time step is then calculated as the share of time in which all its sensed parking bays are occupied by a car. With M being the subset of city zones for which parking measurements are available we introduce for all m ∈ M and t = 1…T:The generated results can be validated for cities in which vehicle counts on street segments and parking measurements are available for the same period of time as the travel time data that we use for sampling. The city of Melbourne provides such data. Vehicle count sensors and between 5,073–9,288 underground parking sensors provide measurements of traffic activity between 2014–2017 and on-street parking bay occupancy with one second accuracy for the years 2011–2017m ∈ M and t = 1…T, we calculate the sampled parking densities We validate our model by calculating the Mean Squared Error between sampled and measured traffic activities and parking densities. We scale all sampled and measured values with respect to their minimum and maximum values among all time steps t = 1…T in order to be able to make sensible comparisons. For all validatable zones FTraf between the measured and sampled values are then calculated as:m ∈ M, with |M| being the number of elements of set M, as:The percentual fits 19. We further sample parking densities with the same parameters for all datasets. The state transition properties that result from these samples are provided in the sampling_parameters.csv for each city. Users can increase the accuracy of the individual parking density maps that we provide by performing the additional computational work that is involved with the model selection that we introduce in the Jupyter Notebook instructions18.The performance of the presented model depends on the sparsity of the travel time data. The travel time data that is collected by Uber and that we have processed in this analysis contains different degrees of sparsity for each city and each dataset Tables  & 4. We


An atom placed in a focused laser beam will experience a dipole force due to the gradient in the interaction energy, which is analogous to the well-known optical tweezers effect. This force will be dependent on the velocity of the atom due to the Doppler effect, which could potentially be used to implement a Maxwell’s demon. Photon scattering and other forms of dissipation can be negligibly small, which would seem to contradict quantum information proofs that a Maxwell’s demon must dissipate a minimum amount of energy. We show that the velocity dependence of the dipole force is cancelled out by another force that is related to the gradient in the phase of the laser beam. As a result, a Maxwell’s demon cannot be implemented in this way. There has been considerable interest in classical models5 for Maxwell’s demons as well as those operating at the quantum-mechanical level9. In all cases, the operation of a Maxwell’s demon must dissipate a minimum amount of energy on the order of kBT, where kB is Boltzmann’s constant and T is the temperature11. In this paper, we investigate the possibility of implementing a Maxwell’s demon using the dipole force20 exerted on an atom in a focused laser beam, where the energy dissipation can be negligibly small.Maxwell’s hypothetical demon has spurred the imagination of physicists for 150 yearsU(R) due to the interaction of the dipole moment of the atom with the electric field of the laser, where R is the location of the atom. In a focused laser beam, the gradient in the intensity of the field produces a corresponding gradient in the effective potential U(R). This results in a dipole force14 on an atom that is analogous to the well-known optical tweezers effect21. If an atom is moving along the direction of the laser beam, the Doppler effect will produce a velocity dependence of the dipole force that could potentially be used to implement a Maxwell’s demon as described in more detail in the next section.The energy of an atom in a laser beam will be shifted by an amount kBT must be dissipated in the operation of a Maxwell’s demon.Photon scattering and other forms of energy loss can be negligible, and the dipole force is generally considered to be a coherent process with no inherent dissipation as a result. This raises the question of whether or not the dipole force could be used to implement a Maxwell’s demon without dissipating a significant amount of energy. We resolve this “paradox” by showing that there is another velocity-dependent force on an atom that is related to the gradient in the phase of the laser beam rather than the gradient in the intensity. The velocity dependence of these two forces cancel out in such a way that a Maxwell’s demon cannot be implemented. This situation provides additional insight into the fact that a minimum energy on the order of We begin with a brief review of Maxwell’s demon and the dipole force exerted on an atom in a focused laser beam. The classical motion of an atom is then calculated using Newton’s laws combined with the usual expression for the dipole force. These classical calculations show that the dipole force on an atom is velocity-dependent and could potentially be used to implement a Maxwell’s demon. Schrodinger’s equation is then solved numerically, and the results show that quantum mechanics does not predict a velocity-dependent force on an atom along the direction of propagation of a focused laser beam. The quantum-mechanical motion of the atom is then calculated analytically in the Heisenberg picture, where it can be seen that the dipole force due to the gradient in the intensity of the laser beam is cancelled by another force associated with the gradient in the phase of the field. The combined effect of these two forces does not allow the implementation of a Maxwell’s demon in this way, which is consistent with the fact that the dipole force need not dissipate a significant amount of energy.2 is illustrated in Fig. A variation on Maxwell’s original demon3. Arguments based on classical11 and quantum8 information theory show that the operation of a Maxwell’s demon requires an energy cost of approximately kBT per operation. This includes the resources required to measure the state of the system and erase the memory used by the demon. In that case, the total entropy would not be reduced and the second law of thermodynamics would be upheld.Useful energy could be extracted by using the partition between the two chambers as a piston, for exampleAn example of a potential implementation of a Maxwell’s demon is shown in Fig. 9. What is intriguing about the example in Fig. A Maxwell’s demon has already been implemented using another optical approach that involves photon scattering14, as illustrated in Fig. 24 can also exert a force on an atom as illustrated in Fig. The dipole force of interest here is proportional to the gradient in the intensity of the lightE(R) of the laser beam with the dipole moment d of the atoms. For simplicity, we will assume that the atoms are confined to linear motion along the central axis of the laser beam, with R the distance from the center of the focal point as illustrated in Fig. q is the charge of an electron25. We have chosen the polarization of the electric field to lie along the y axis of Fig. 25, then the energy of the atoms will be shifted by an amount M is the matrix element of π. The detuning Δ for an atom at rest is defined by Δ = (ωL − ωA), where ωL is the angular frequency of the laser beam and ωA is the angular frequency of the transition between the two relevant atomic energy levels. U(R) serves as an effective potential energy for the atoms and the dipole force f(R) on the atoms is equal to 21.The dipole forces of interest here are due to the interaction of the electric field entclass1pt{minimav is the velocity of the atom in the direction of the laser beam, and λ is the wavelength of the light. (We ignore relativistic terms on the order of (v/c)2 throughout, where c is the speed of light.) Thus the dipole force on a moving atom will be velocity dependent and inversely proportional to The angular frequency entclass1pt{minimaPE that an atom is in its excited state is 25 and τ is the radiative lifetime of the atom. The scattering rate can be made negligibly small by choosing a large detuning as is widely done in practical applications, since the dipole force is proportional to 1/Δ′ while the scattering rate is proportional 1/Δ′2. As a result, the dipole force is generally considered to be a coherent process with no intrinsic dissipation. Alternatively, the scattering rate can be reduced to a negligible level by choosing atomic states with a sufficiently long lifetime; photon scattering will be negligible if τ is much larger than the transit time of an atom through the laser beam.For comparison, the rate of photon scattering is given by τ where photon scattering is negligible. (Other authors19 have considered the opposite limit.) We will also assume that the focal length of the laser beam (Rayleigh length) is sufficiently large that the Hamiltonian is slowly varying and the adiabatic theorem applies, in which case there is no dissipation due to a permanent change in the atomic state. No significant amount of energy is dissipated under these conditions.We will consider the limit of large 2 and it is due entirely to the scattering of photons24. A Maxwell’s demon has previously been demonstrated using the scattering of photons, where it was shown that an energy ~kBT/2 per operation must be dissipated in that case9. The use of a focused laser beam and the dipole force would potentially allow a similar operation but with negligible dissipation.An unfocused laser beam can also exert a force on an atom as illustrated in Fig. The dipole force along the direction of the laser beam depends on the velocities of the atoms in that direction. Magnetic forces are also velocity dependent, but there the force in any given direction depends only on the velocity in orthogonal directions. As a result, magnetic forces satisfy Liouville’s theorem which precludes the operation of a Maxwell’s demon in thermal equilibrium, whereas the dipole forces of interest here do not.Figure R = −200 μm from the focal point of the laser, which had a Rayleigh length of 100 μm. The mass of the atom was arbitrarily taken to be 3.3 × 10−31 kg in order to facilitate the numerical quantum-mechanical calculations described below. The laser detuning was Δ = 2π × 5 GHz and the matrix element M of the interaction Hamiltonian was chosen to be λ = 2 μm, which gives a Doppler shift of 2π GHz at the initial velocity of 2 km/s. The Doppler shift corresponds to 20% of the detuning and we would therefore expect a comparable velocity dependence of the force initially, with a smaller Doppler shift as the atom is slowed down by the laser beam.For simplicity, the atom was assumed to travel along the center of the laser beam with an initial velocity of 2 km/sec at a distance of U(R) is not a conservative potential. This is even more visible in the plot of the kinetic energy normalized to its initial value in Fig. Figure U(R) was negligible. An atom with a sufficiently large initial energy to pass through the focal point will experience no net change in kinetic energy due to the symmetry of U(R). It can be seen that more atoms incident from the left than the right will have their velocity reversed and undergo a net change in kinetic energy, as was illustrated schematically in Fig. The classical change in the kinetic energy of an atom due to the dipole force is plotted as a function of its initial energy in Fig. It should be noted once again that these classical calculations only include the usual dipole force and they are intended to show the effects that would occur if that were the only force on an atom.The classical calculations in the previous section suggest that the dipole force could be used to implement a Maxwell’s demon. We now compare those results to a fully quantum-mechanical calculation where both the position and the excitation of the atom were treated quantum-mechanically. The standard Hamiltonian for a two-level atom was used and the time-evolution of the wave function was calculated numerically using Mathematica and the Schrodinger equationHere the Hamiltonian R is once again the center of mass coordinate along the center of the laser beam and Φ(r) is the Coulomb potential of the nucleus, which is a function of the relative coordinate r. The reduced mass is very nearly equal to the mass me of the electron while the total mass of the atom is denoted by m. It was assumed that only two atomic states were coupled by the transverse electric field Ey(R).Here ψG for the ground-state probability amplitude is shown in Fig. −31 kg) was used in order to keep the de Broglie wavelength of the atom on the order of 1 μm, which limited the number of oscillations to a manageable value. Although that is smaller than the mass of an actual atom, the force is independent of the mass and this does not affect the qualitative nature of the results.A typical plot of the real part of the wave function μm. The position of the wave packet  while m is the total mass of the atom.Here 24 we define the operator The motion of an atom can be found most easily by making a unitary transformation to the Heisenberg picture, where as usualR. This reflects the fact that the induced dipole moment is proportional to the electric field, which varies along the length of the laser beam.The Heisenberg operators The time dependence of the Heisenberg operators can be found by differentiating Eq. . Since tThe form of the commutators is unaffected by a unitary transformation and they can be calculated using the fact that Inserting these commutators into Eq.  gives7\dIt should be noted that the unitary transformation gives 26The electric field of the laser will be assumed to be a Gaussian beam focused at the origin  and the Gouy phase g(R) are given byL is the Rayleigh length. The factor of ½ was included in Eq. 10) into Equation  correspoa and b are unknown coefficients that will be determined by inserting Eq. (Here ting Eq.  into Eq.ting Eq.  and solvmentclasspt{minimaDifferentiating Eq.  with resF(R) will be a slowly-varying function of R, in which case In the limit of a large Rayleigh length, Equation  can thenHere we have defined the complex parameter The solution to Eq.  is givenδωD and the term proportional to V0 are much smaller than the detuning Δ, then the coefficient a can be expanded to first order in a Taylor series to giveHere we have used the fact that the resonant frequency of the harmonic oscillator is a in Eq. .Since the classical electric field is real, it must include the complex conjugate of Eq.  as well.The force R givesDifferentiating the electric field in Eq.  with resy + y*) and The product of , which would require that the electric field and the current be 90° out of phase. But the motion of the atom causes a change in the population of its excited state with a corresponding absorption of a virtual photon. This requires that the electric field and the current not be entirely 90° out of phase, as reflected by the imaginary term in Eq. (ikγ term in the expression for the force in Eq. (The analytic calculations in the previous section show that the velocity-dependent contributions from the gradient in the intensity and the gradient in the phase of the laser beam cancel out, giving a total force along the direction of the laser beam that is independent of velocity. This cancellation is dependent on the imaginary term in Eq.  for the m in Eq. . Withoute in Eq.  would giikγ contribution to the force can be interpreted as the recoil momentum from the absorption of a single virtual photon; that momentum is returned to the field when the atom leaves the focal region provided that the process is adiabatic. Classically, this can be understood as the magnetic force produced by the current in an atom interacting with the magnetic field of the laser beam. Once again, the current and the magnetic field would be 90° out of phase without the imaginary term in Eq. (ikγ term. Magnetic forces were not included in the classical calculations of Fig. From a quantum-mechanical point of view, the m in Eq. , giving ikγ term has been discussed previously20 and it is sometimes referred to as the dissipative force because of its velocity dependence16. Here we have shown that the velocity dependence of the dipole force is cancelled out to lowest order by the contribution from the ikγ term under conditions where photon scattering is negligible. This is necessary to avoid the possibility of constructing a Maxwell’s demon that dissipates negligible energy.The contribution to the force due to the ikγ force no longer cancels the velocity dependence of the dipole force. In fact, velocity-dependent dipole forces have been experimentally observed, but only in the direction transverse to the axis of the laser beam14. The force in the transverse direction cannot be used to implement a Maxwell’s demon as illustrated in Fig. So far we have only considered the force along the direction of the laser beam. There will be a dipole force perpendicular to the direction of propagation if the atom is located off the central axis of the beam, where there is a gradient of the intensity in the transverse direction. There need not be any gradient of the phase in that direction, in which case the 3 along the axis of the laser beam. Although this would allow the operation of a relatively inefficient Maxwell’s demon, incoherent scattering and non-adiabatic effects would no longer be negligible in comparison.The calculations in the previous section only included the lowest-order term in the Taylor series expansion of Eq. . A more kBT.In summary, the existence of a velocity-dependent optical force with negligible dissipation would allow the implementation of a Maxwell’s demon capable of reducing the overall entropy. We have shown that the velocity dependence of the dipole force along the direction of propagation of a focused laser beam is cancelled out by another force related to the gradient in the phase of the field rather than the gradient in its intensity. These results provide a further illustration of the fact that the operation of a Maxwell’s demon requires the dissipation of a minimum amount of energy on the order of


Kawasaki disease is a common childhood vasculitis which may result in cardiovascular morbidity if not adequately treated. Its epidemiology in the African region is not well described. Its features may mimic other childhood infections and hemoglobinopathies and it is rarely diagnosed in the East African region. These are the first reports of this disease from Tanzania.We present two cases of complete Kawasaki disease seen over a 2 year period and diagnosed as per the criteria defined by the American Heart Association. One child was and infant and the other a 3 year old. Both of them presented with a prolonged fever and mucocutaneous findings. None of the children developed coronary artery aneurysms. One was treated with aspirin alone and the other with both aspirin and intravenous immunoglobulin. Both children had complete recovery and did not have any cardiovascular sequelae.Kawasaki disease may be more common in the East African region than previously thought. It should be considered as a differential diagnosis in children who present with a prolonged fever of greater than 5 days and mucocutaneous findings. More awareness about this condition, its epidemiology, diagnosis and management are required in order to prevent the cardiovascular morbidity associated with it. Kawasaki disease is one of the most common vasculitides in childhood. It occurs predominantly in infants and young children and has long term cardiovascular morbidity due to coronary artery lesions if not adequately treated . It is tThe etiology of the disease remains unknown and several hypothesis exist in trying to explain the cause. Epidemiologic data suggest that an infectious agent may be causing the disease in genetically susceptible individuals . The claThe initial symptoms are of a febrile illness lasting longer than 5 days with other mucocutaneous features including a rash, conjuctivitis and adenopathy. Diagnostic criteria exist to make a diagnosis of both complete and incomplete forms of disease . If leftIn sub-saharan Africa, children suffer from many tropical and infectious diseases that present with symptoms similar to those of kawasaki disease such as fever, irritability and a rash. Common conditions include malaria, typhoid fever, meningitis and viral exanthems such as measles and roseola infantum. Other conditions that may mimic this disease include sickle cell dactylitis and infection with group A beta hemolytic streptococcus. A high index of suspicion is hence required to identify cases of kawasaki disease and institute early treatment.We report here 2 cases of kawasaki disease seen at our institution that met diagnostic criteria defined by the American Heart Association. These are the first reports in published literature from the East African region.A.M was a 3 year old female child of African ethnicity who presented in July 2012 with a 8 day history of high grade fever and a 1 day history of swelling of the hands and feet.  but elevated platelets of 644000/μl. The blood and urine culture were both reported as negative after 48 h.The child was then flown out to Nairobi, Kenya for IVIG treatment which she received uneventfully. She was discharged on low dose aspirin and subsequent echocardiograms remained normal.W.I was an 8 month old infant of African ethnicity who presented in August 2013 with a 6 day history of a high grade fever with temperatures upto 39 degrees celsius. . Malaria antigen and blood slide were both negative. He was started on high dose aspirin at 90 mg/kg/day as IV IG was not available in our institution at that time. An echocardiogram was done which showed normal coronary arteries and normal cardiac function.A presumptive diagnosis of incomplete kawasaki disease was made meeting 3 of the five criteria required in addition to the fever. A complete blood count showed mild anaemia with normal platelet count. (WBC: 9.07 *10His fever resolved after 72 h and he developed swelling of the hands and feet which now confirmed the diagnosis of complete kawasaki disease. The aspirin dose was reduced to 5 mg/kg/day after the fever subsided. The platelet count was repeated and it showed elevated platelets of 742,000/μl. The CRP was also high: 153 mg/l.On follow up after a week, the limb swelling had reduced and he had skin exfoliation. His CRP had reduced to 60 mg/l and the platelets were 605,000/μl.A follow up echo done after 1 month was normal and the aspirin was stopped after the hematological parameters had normalised. He has subsequently remained well with no cardiovascular sequelae.Both cases described above presented to us after a prolonged duration of fever and failure to respond to antimalarials and antibiotics. This is a common presentation also described in case reports from Ghana .The first case was 3 year old child while the second was an infant. This is in keeping with epidemiologic studies from Algeria and Japan which have shown that more than 90% of children are less than 5 years of age , 5.The children had the classical mucocutaneous features that are key to making the diagnosis. The first child had limb swelling, a skin rash and oral mucosal changes. The limb swelling was initialy thought to be sickling dactylitis which is a common condition seen in our environment and is one of the presenting signs of sickle cell disease .The second child had non purulent conjuctivitis, swelling of limbs and the skin rash with involvement of the BCG scar which has been described previously . HematolThe first case was treated with both aspirin and IVIG while the second received only aspirin. The role of aspirin remains uncertain in the current era of use of IVIG, however it still remains as part of the standard treatment protocols. The current treatment: IVIG is an expensive drug that is not readily available or affordable to most families in our population. A single vial of 5 g costs as much as 1 million tanzanian shillings which is about 450 US dollars. This hampers effective treatment which is essential to reduce the cardiovascular sequelae.Other treatment options that could be considered are use of corticosteroids. A cochrane review of 7 trials showed benefits of reducing cardiac complications by using steroids as adjunct therapy to IVIG early in the course of illness . Use of The echocardiograms for both children were normal at baseline and on subsequent follow ups. This was reassuring since the incidence of coronary abnormalities is as high as 25–30% in patients who are not treated with IVIG . Echo isKawasaki disease has not commonly been described in sub-saharan Africa. However, these 2 cases were seen over a 2 year period at a single tertiary institution. This raises concern about how many missed cases there may be which are not diagnosed or managed effectively since the fever and mucocutaneous changes eventually resolve within 3 weeks even without specific treatment. The subsequent devastating cardiovascular morbidity of this condition in children with missed diagnosis remains unknown.The pattern of disease in the setting of tropical infections like malaria also remains unknown. Kawasaki like syndromes have been described in adults with HIV infection especially with severe immunosupression . SimilarWe recommend that a diagnosis of kawasaki disease be entertained for any febrile illness lasting longer than 5 days and presenting with mucocutaneous findings. Any child presenting with a prolonged fever should promptly be referred to and evaluated at a tertiary centre. Doctors and other care providers should be made familiar with this condition in order to diagnose, treat and prevent the cardiovascular morbidity and mortality.Cases that are seen at other institutions should be published in literature so that the spectrum of the disease, its epidemiologic characteristics and its outcomes in sub-saharan Africa can be described. Equally important is that IVIG be made available at a subsidised and more affordable cost in order to benefit patients with kawasaki disease and other autoimmune conditions where it is indicated.


The goal of this paper is to understand the processes by which solar wind electrons are energized in the Martian magnetosphere and how this compares to processes at Venus and Earth. Each is unique in the source of its magnetic field topology and how this influences electron energization. To achieve this goal, 24 million spectra spanning 13 years have been examined using the electron spectrometer from the Mars Express spacecraft between about 12,000 km and about 250 km altitude, and from all latitudes and local times. The top 10 largest differential energy flux at energies above the differential energy flux peak have been found: seven spectra from the magnetosheath near noon, three from the dark tail (the largest two from the middle and ionospheric edge of the magnetosheath). Spectral comparisons show a decade range in the peak of the electron distributions; however, all distributions show a similar energy maximum dictated by solar wind/planet interaction. Similarly derived, the largest Venus spectrum occurred near the magnetosheath bow shock and had the same shape as the most intense Mars inner magnetosheath spectrum. The Mars and Venus dayside spectra compared to the Mars nightside spectrum that included an enhanced optical signal attributed to discrete “auroral” precipitation show a similar shape. These spectra are also compared to a selected auroral zone electron spectra from the Earth. The Mars and Venus results suggest that there is no more energy needed to generate electrons forming the nightside precipitation than is gained during the solar wind/planet interaction. Top 10 orbit‐selected electron energy spectra from Mars are identified from MEx ASPERA‐3 ELS between 2004 and 2016The Mars and Venus dayside electron spectra are similar, and a discrete “auroral” spectrum from the nightside tail of Mars is also similarNo more energy than that supplied by the solar wind‐planet interaction is required to produce discrete auroral spectrum from the nightside tail of Mars Each planet is unique in the source of its magnetic field topology and how this influences electron energization. To achieve this goal, 24 million spectra spanning 13 years with the Mars Express (MEx) spacecraft , the amount of energy carried by these electrons is revealed: Generally, at low energies, there are many electrons that do not carry very much energy, so their DEF is low, and when the energy is very high, each electron carries more energy, but there are fewer electrons resulting again in a low DEF. The electron spectrum in the magnetosphere of Mars can be qualified by two factors: the DEF of the electrons and the energy of the electrons. Those electron energy spectra maximized along these two factors will describe the maximum extent of the shape of the electron spectrum. The DEF is typically its highest somewhere between very low energy (1 eV) and very high energy (20 keV), and the exact location is dependent on where the electron spectrum is measured. If the electrons enter into an area that is collisionally dominated, the higher‐energy electrons will penetrate deeper into the medium than lower‐energy electrons. Unlike at the Earth, at Mars and Venus the magnetic field (which directs charged particles) can be significantly horizontal, as draped field lines penetrate the atmosphere. This magnetic field configuration leads to energy deposited horizontally instead of vertically as at the Earth. Currently, there is no Tsyganenko , 2002b sWe approach this study without preconceived notions of the expected shape of the electron spectrum or from where the population of the spectrum originates. Our goal is to find the largest electron spectrum at energies above the DEF peak observed in the Mars environment over the time period of a solar cycle in order to determine the energized electron spectrum. To our knowledge, this type of study has never before been performed. Beyond the scope of this study is to evaluate through models the effect depositing these electrons on the atmosphere on Mars; this is left as an exercise for the future.Energetic electron spectra at Mars have been presented  experiment , so the scanner rotation axis is about the spacecraft Z direction. ELS sector pairs 0 and 15 view along either side of the −Z spacecraft direction, and pairs 7 and 8 view along either side of the +Z spacecraft direction. Thus, in 180° of scanner rotation, ELS has the capability of measuring the full 4π sr volume.The ELS instrument is mounted to the main unit of the ASPERA‐3 experiment so that the ELS symmetry axis is perpendicular to the ASPERA‐3 main unit. The main unit is mounted on a rotatable scan platform attached to the upper deck of the spacecraft  was at about 10° to the X‐Z spacecraft plane, which placed ELS measurements close to the X‐Z spacecraft plane. This position was preferred because the ASPERA‐3 main unit was thermally stabilized. In this orientation, ELS sectors 0, 12, 13, 14, and 15 look at the spacecraft, observing electrons emanating from the spacecraft surface, and are not directly measuring the space environment.From launch until January of 2006, the ASPERA‐3 scanner was configured in its launch position  describes the number of electrons that crosses a plane of a certain size within an angular volume, and with respect to energy of the electron for a given amount of time. The DNF at Mars shows a large number of electrons at the smallest energies and a small number of electrons at high energy. Even though electrons are more abundant at low energy, they do not carry a significant amount of energy, whereas at high energy, each electron carries a substantial amount of energy, but there are relatively few electrons. The electron distribution function (DF) describes how the phase space density is distributed in energy or velocity. The DNF has a shallower slope than the DF, which indicates that the phase space density is concentrated at the lower energies. The DEF weights the electron distribution by the amount of energy contained in the electron spectrum. It is similar to the DNF but describes the amount of energy crossing a surface area within an angular volume and with respect to energy of the electron for a given amount of time. Thus, the DEF describes the amount of kinetic energy (energy flux) carried by the electrons at each given energy.In order to examine the electron spectra from the 11‐year solar cycle, all ELS modes were examined between MEx arrival at Mars at the beginning of 2004 and the end of 2016. Four different energy range categories were examined in order to cover the energy range where the maximum DEF could be obtained: (1) ~150 to 500 eV, (2) 500 eV to 1 keV, (3) 1 to 5 keV, and (4) 5 to 10 keV. Data at the instrument time resolution was examined in two classes: (A) the largest single value of DEF and (B) the largest average DEF within each category. The classes were chosen to identify spectra that were very peaked and to distinguish these from those that had gradually changing shapes.k is the ELS sector number and comparisons are made over all sector energies within the category energy range. Class B averages are determined by comparing the straight average within each category :N is the number of samples in each category and ELS sector, andi is an energy step index for energies within the category energy range. The averages described by equation One orbit of data is examined at a time, and each ELS sector is handled independently. Comparisons are made directly for class A, saving the largest single DEF in each category :For each of the 16 ELS sectors, the times with the top 10 largest values were selected with the requirement that there be only one identification per sensor per category per class per orbit. Without imposing this requirement, it was discovered that often the top 10 spectra identified were all from the same spacecraft pass. This defeated the purpose of identifying the top 10 most intense time periods and not the top 10 spectra from the same time period. The search criteria resulted in 1,280 identified spectra (16 sectors × 4 categories × 2 classes × 10 time periods). These were examined to find only the top 10 that showed the largest flux at energies above the DEF peak (keV electrons from spectra with the largest DEF that are continuous up to keV energies).During operation of ELS over such a long time period, several artifacts were observed. These artifacts included lone maximum high‐flux single points, times of instrument interference, power supply thermal disruptions, and other times of data noise from unknown spacecraft sources that occurred. Some of these artifacts occurred in one sector, while others occurred in many sectors. Lone maximum high values typically were noticed above the contiguous electron spectrum and represented a single point in a single sector. These were not reproducible and were random, high statistical variations in the Poisson count, which occurred during low count rates in any sector. Instrument interference is observed mostly restricted to sectors 0 and 15, shows high intensity fluxes that increase or decay in energy with time and repeat on minute time scales. This type of noise occurred mainly in 2005 and has not been observed since the science instrument function of MEx was separated from relay communications. Power supply thermal disruptions are observed mainly in 2005 when there started to be breakdown in the ELS power system. This first appeared as infrequent millisecond dropouts in 2004 and increased to minute time scales in 2006, it was discovered that the heat from the Sun was causing thermal breakdown. The ASPERA scanner was positioned to cool the ASPERA main unit, which reduced the temperature. Data occurring in 2006 after the ASPERA scanner was repositioned is unaffected by this artifact, but some data from 2005 show this effect , which indicated that the selected times were dominated by emission from the spacecraft surface and did not supply an accurate measurement of the environment around Mars. These sectors were also excluded. The resulting spectra were required to be continuous in energy. Spectral data from category 4 (from 5 to 10 keV) were found to be from random points, not forming a continuous spectrum. Thus, category 4 data were excluded from further study. From the remaining data, the criteria of the largest DEF value for energies above the DEF peak showed that spectra that were large in DEF for categories 1 (from ~150 to 500 eV) and 2 (from 500 eV to 1 keV) showed large DEF spectra that did not extend into the 1‐ to 5 keV range. This means that their energy would be deposited at higher vertical altitude or over a shorter horizontal distance than spectra identified as belonging to category 3 (from 1 to 5 keV). Category 3 spectra represent electrons that penetrate deeper into a vertical atmosphere and deposit their energy at lower altitudes or along a longer horizontal path length. Note that category 3 spectra may show a DEF peak at energies lower than those of category 3, but in this case, the spectra is more kappa shaped and the nonthermal high energy tail of the distribution extends the energy deposition range to lower vertical altitudes  were found to contain energy spikes that were often only one energy channel wide and were not representative of the spectrum in general. For these cases, the desire to have large DEF values did not selectively produce continuous spectra. This was probably due to allowing most noise values through the sorting system and not trapping noise values adequately enough to block their presence. Additionally, a few class A data were dominated by large error values that occurred at low count rates. These showed that the largest value of the spectrum was not representative of the spectral shape and the DEF they represented should not have been included within the sorted maximum spectra. The maximum selected DEF spectra determined by class A selection were highly dominated by statistical fluctuations and were found not to produce representative maximum spectra. For this reason, class A data were eliminated from further study.From the remaining 110 possibilities, the values were resorted from the highest DEF to the lowest DEF. Only the sector with the largest DEF was chosen to be in the top 10, while the remaining sectors from that same time period were excluded. These times are given in Table 5The spectrograms containing the top five maximum DEF times are presented in Figure For the data presented in 2005, the ELS protection screen was set at −5 V, repelling all electrons less than 5 eV. At the time of design, the low‐energy environment on Mars was unknown. Based on experience at the Earth  occur on the nightside of the planet. In all three of these nightside cases, the spacecraft is in the umbra of the planet; however, spectrum g is closer to the edge of darkness, and spectra c and j are encountered deeper in the darkness. The spectra from pass a, b, d, e, f, h, and i occur within a few hours of noon. The maximum spectra on the dayside occur as follows: a—mid‐magnetosheath, b—ionospheric side of the magnetosheath, d—mid‐magnetosheath, e—bow shock side of the magnetosheath, f—ionospheric side of the magnetosheath, h—bow shock side of the magnetosheath, i—mid‐magnetosheath. With the exception of g, spectra in the tail contain lower isotropic energy flux between 1 eV and 5 keV than in the magnetosheath.X direction points from Mars toward the Sun, Z is perpendicular to the planet's velocity vector and is directed toward the northern ecliptic hemisphere, and Y completes the right‐handed, orthogonal system) in a cylindrical system with the X direction along the axis of the cylinder (toward the Sun) and the Y and Z axis forming the radius ρ (ρ = sqrt(Y2 + Z2)) perpendicular to the Mars‐Sun line. Here the radius on Mars is 3,397 km. For each orbital segment, a circle marks the spacecraft location at the beginning time on the spectrogram, a cross marks its location at the end time shown on the spectrogram, and a diamond marks the location where the large DEF spectrum occurred.The location of the orbits shown in Figure The spectra at the times given in Table For the top five spectra shown in Figure For the second five spectra shown in Figure 6As discussed in section Without preconceived notion of the electron spectrum, we have examined all of the MEx ELS DEF electron energy spectra from the beginning of 2004 to the end of 2016. Of the approximately 24 million spectra sampled over 13 years in the environment of Mars, MEx has sampled electrons from every region and almost every plasma condition. All of these spectra were examined to find the continuous spectrum having the largest DEF at energies above the DEF peak. From this search the largest top 10 spectra were retained. Of the top 10 spectra, seven were found to be from the magnetosheath and only three were found to be from the tail. These three tail spectra exhibit high fluxes at high energy that are not larger than spectra in the magnetosheath, and the high‐energy shape of the spectrum (between 1 and 5 keV in energy) was similar to those from the magnetosheath. Since MEx reaches altitudes where auroral acceleration processes could energize electrons, one would expect that ELS has surveyed spectra that would show an accelerated population if one existed, which could be larger in energy than the magnetosheath spectrum. The fact that the tail spectra are no larger in energy than spectra in the magnetosheath suggests that the planet has no means to accelerate electrons to energies above that which is generated by the interaction of the planet with the solar wind. The fact that the high‐energy population between the magnetosheath spectra and tail spectra are similar suggests that the electrons from the magnetosheath could be redirected (or channeled) by the magnetic field from the magnetosheath to the Martian tail, such that the high‐energy portion of the energy spectra would not be affected. This would result in similar high‐energy tail spectra compared to those measured in the Martian tail.The top 10 spectrograms indicate that largest spectra are observed in the magnetosheath near the bow shock, in the mid‐magnetosheath, and toward the ionospheric side of the magnetosheath. This suggests that the shape of the electron spectrum is determined at the bow shock and the signature of these high‐energy electrons may be transmitted through the magnetosheath from the bow shock to the ionosphere. It is possible that the high‐energy electrons could skirt along the magnetosheath/ionosphere boundary and precipitate in the tail. The fact that the high‐energy population is observed in the noon‐1400 hr local time sector most likely has to do with the energy imparted to the compressed plasma, and it may exhibit reduced energy from rarefraction as the population travels into the nightside, and then compression again increases the energy to similar levels as the original spectra.Speculating on more possibilities, it may be that the dayside compression mechanism is somehow duplicated in the tail region of the planet. If the solar wind interplanetary magnetic field (IMF) interconnects with the remnant Martian magnetic field as suggested by Brain et al. , a similNote that no spectrum came from the magnetosheath in the flanks of Mars where the plasma is accelerating around the planet, nor were there any from around the polar region where the stretched magnetic field would be slipping around the planet. No spectrum came from the dayside ionosphere where compression might be the largest or in the ionosphere from the terminator region where the ionization sources from the dayside dominate and the ionization sinks from the nightside dominate. The lowest‐altitude spectrum occurs on the nightside at about 750 km altitude despite ELS making measurements to altitudes of 250–350 km. No spectrum was identified in the lower‐altitude regions in the southern hemisphere where the crustal magnetic fields are expected to accelerate plasma. The dominant DEF spectra at large energy come from the dayside magnetosheath of the planet or the nightside umbral tail.2+ UV doublet  at 288.3 and 289.6 nm while SPICAM was pointing in the nadir direction. This feature was reported to exhibit both the highest value of the electron energy flux (reaching up to 10.2 mW/m2) and the highest electron energy peak (530 eV) among their time periods when UV was detected. The SPICAM peak values of the UV emission and the ASPERA‐3 electron energy flux were separated by about 10° in latitude. Note that for the electron flux estimated for the largest DEF, the estimated isotropic electron flux is slightly higher at 12.6 mW/m2  from both planets. Both spectra were found to be similar, with the spectrum from Venus being of slightly larger magnitude below 1 keV and the Mars spectrum being slightly larger above 1 keV. Without knowing the planet from which the spectrum came, it would not be possible to tell the difference. In fact, an additional comparison with the nightside auroral spectrum (g) shows a similar distribution to both the Mars and Venus spectra from the magnetosheath in front of the planets (Figure In order to find out if the large electron spectra are uniquely related to the magnetic field of Mars, a similar search was conducted for the largest DEF spectra observed at Venus between 2006 and 2014 using the similar ELS from the ASPERA‐4 experiment (Barabash et al., s Figure . Again, Auroral spectra have been observed at Earth by many spacecraft as they pass through the auroral zone. Shown in Figure The spectrogram in Figure 7In order to find electron spectra that limit the possible amount of energy deposited by electrons into the atmosphere of Mars, the ELS instrument was used without any preconceived notion of the shape or location of the electron spectrum. Time periods for the 10 largest DEF at energies above the DEF peak that produced continuous spectra were found from a solar cycle of data. By selection of energy spectra in the 1 to 5 keV energy range, these 10 cases should have the greatest influence on the atmosphere around the atmospheric energy deposition peak if the electrons vertically precipitated. The 10 largest time periods were required to be from different orbits. The observations covered a solar cycle from January of 2004 to December of 2016. For each time period, only the sensor with the largest observed DEF was selected. This produced seven spectra from the dayside, within 2 hr just after noon, and three spectra from the nightside where the spacecraft was in the shadow of Mars. The dayside spectra came from the magnetosheath: near the bow shock, in the mid‐magnetosheath, and near the ionosphere.The top 10 spectra all showed a very similar shape in their DEF‐electron energy profile at energies from slightly greater than the peak DEF until the instrument threshold, which most likely reflects a limit to the amount of energy that could be imparted to the electrons. Electron spectra from the dayside reflect the impact of the solar wind on the induced magnetosphere of Mars. Electron spectra observed from the tail achieved this similar limiting energy, suggesting that the planet imparts no more energy to the electrons than is provided by the solar wind‐planet interaction. Rarely is a peak DEF larger than 1 keV found at Mars. This is unlike Earth, where spectra in the auroral zone vary substantially with peak DEF energies that can exceed above 10 keV.A similar study at Venus using the ELS instrument of the VEx ASPERA‐4 experiment found that the maximum continuous DEF spectrum with the maximum energy occurred near the Venus bow shock, just inside the magnetosheath. When the Venus spectrum from near the bow shock was compared to a Mars spectrum near the ionosphere in the magnetosheath, they exhibited the same shape to the point that without prior knowledge, they could not be distinguished from each other. When compared to a nightside auroral electron spectrum at Mars, the shapes of all three spectra were found to be very similar.A comparison of spectra was made to one from the auroral zone of Earth. The Earth spectrum was chosen to have a similar maximum energy as that from the induced magnetospheres of Mars and Venus. This spectrum was similar in shape but did exhibit more of a deviation than the spectra from the planets with the induced magnetospheres. However, additional spectra from the Earth auroral zone showed that the higher energy extent reached much greater maximum energies than at Mars or Venus, indicating that the intrinsic field of the Earth is capable of imparting much more energy into the electron spectrum than what is available in the interaction of the solar wind with induced magnetic field planets.