In proton minibeam radiation therapy, proton minibeams are typically produced by modulating a uniform field using a multislit collimator. Multislit collimators produce minibeams of fixed length and width, and a new collimator has to be manufactured each time a new minibeam array is required, limiting its flexibility. In this work, we propose a scanning dynamic collimator for the generation of proton minibeams arrays. The new collimator system proposed is able to produce any minibeam required on an on-line basis by modulating the pencil beam spots of modern proton therapy machines, rather than a uniform field. The new collimator is evaluated through Monte Carlo simulations and the produced proton minibeams are compared with that of a multislit collimator. Furthermore, a proof of concept experiment is conducted to demonstrate the feasibility of producing a minibeam array by repositioning (i.e. scanning) a collimator. It is concluded that besides the technical challenges, the new collimator design is producing equivalent minibeam arrays to the multislit collimator, whilst is flexible to produce any minibeam array desired. Contrary to conventional proton therapy, pMBRT uses multiple coulomb scatting to its advantage: proton minibeams get increasingly wider as a function of depth, which may result in a homogeneous target dose coverage1, while normal tissues at the entrance will benefit from the spatial fractionation of the dose. Indeed, pMBRT has already demonstrated a significant reduction of normal tissue toxicities both in the skin6 and brain7. Additionally, an equivalent or superior life span has been observed in tumour-bearing rats treated with pMBRT as compared to standard (broad beam) proton therapy (PT)10.In this non-homogeneous dose deposition pattern, regions of low and high dose are observed12. All of these aspects have an impact on the biology response4.One of the crucial issues in pMBRT is its technical implementation, and, particularly, the generation of minibeams. The generation method influences the shape and size of minibeams, the peak-to-valley dose ratio (PVDR) but as well potential neutron contamination4. Those were placed either at the end of a passive beamline13 or at the exit of a pencil beam scanning nozzle14. The main advantage of minibeam generation with multislit collimators is that it enables its implementation at any proton therapy centre15. The main drawbacks are their inefficiency, inflexibility (a custom collimator may have to be fabricated for each case) and introduce a source of secondary neutrons close to the patient16.Up to now, all MBRT experiments with protons of clinically relevant energies (i.e. ≥ 70 MeV) have been performed with planar minibeams generated using multislit collimators18. Potentially this technology could be used to generate minibeams. However, there are several limitations that inhibit direct translation in pMBRT: (i) achieving the positioning accuracy needed for minibeams would be extremely difficult as the leafs/blocks should be moved with an accuracy of a few micrometer, (ii) following the beam divergence would be very challenging, and (iii) more likely the device would be too large to allow for small air gaps.Multi-leaf collimators (MLCs) and dynamic collimators (DCs) have been implemented in active scanning proton beam therapy for penumbra reduction19. So far, the only facility having implemented magnetic focusing for pMBRT is the SNAKE microprobe in Munich20. However, the maximum beam energy at this installation is limited to 20 MeV5 which is too low for most clinical applications. Schneider et al. have proposed a new nozzle21. Despite the advantages of this minibeam generation method, the fact of involving a new/different nozzle, make it difficult to be retrofitted in already existing facilities and most likely, it could only be coupled to newly constructed beamlines.A potential solution may be the use of magnetic focusingHere, the concept of a scanning dynamic collimator system for proton minibeam generation is proposed. It aims to overcome the limitations of the multislit collimator system providing the flexibility desired for the investigation of the proton minibeam properties, both at the physical and biological layer. In this system a dynamic collimator that allows the selection of the minibeam size is coupled with a scanning capable system that gives the ability to generate any minibeam array required. Firstly, we present the system and evaluate through Monte Carlo simulations its ability to create minibeam arrays similar to a multislit collimator. Then a proof of concept experiment is conducted in order to evaluate the feasibility of the scanning collimator minibeam generation method when combined with a proton spot scanning system.The concept of a scanning dynamic collimator for proton minibeam generation is proposed. This scanning dynamic collimator is adapted to the pencil beam scanning capabilities of the modern proton therapy machines and allows to select slit width and length, and centre-to-centre distance dynamically in order to produce a fully customized minibeam array.The system consists of two main elements see Fig. : (i) a sTwo dynamic collimator designs are proposed: (i) an aperture-like collimator and (ii) a two-plane collimator. Another option, which however limits the flexibility of the system, would be an interchangeable (fixed) single slit collimator. In this case, a set of predefined slit widths and length would be available.14. This choice is based on a compromise between a good collimation that leads to a high entrance peak-to-valley dose ratio and neutron production12. In this investigation the collimators used have a thickness of 5 cm and the collimators lateral extension is 5 cm, unless otherwise stated.The collimator blocks are made of brass, since brass is the material of choice for proton minibeam collimatorsThis collimator consists of 4 blocks of radiation blocking material Fig. a. Each bThe realization of this dynamic collimator has many technical challenges. The blocks have to move with high accuracy to limit the gap in between. A tongue and groove approach, similar to that used in multi-leaf collimators could be included. This collimator results in a small footprint and would be more likely suited for small apertures.In this dynamic collimator design the length-wise and width-wise collimation is done at different planes Fig. b. The toThe scanning capabilities of the proposed system are exploited in order to create the minibeam array. Two ways of scanning are proposed, the point-by-point and the line-by-line scanning collimator.In the point-by-point scanning collimator system the length of the slit can be fixed in such length that one pencil beam spot in about the centre of the slit passes with minimal collimation at the slit length direction see “”. In ordThis scanning approach could benefit from an aperture like collimator see “”.Another possibility is the maximum length of the single slit dynamic collimator to be large enough to produce the maximum desired minibeam. The two-level collimator, which is more suitable for large field lengths, would be more appropriate. For each desired minibeam, the collimator takes the appropriate length; the spot is scanned over the collimator see Fig. b produci23, as has been reported before14. The beam parameters from the characterisation from De Marzi et al24 were used. In this parameterization the beam spot at the vacuum window is characterized by the (i) energy and energy spread of the beam, (ii) spot size, (iii) beam divergence and (iv) beam correlation. Using this parameterization, the magnetic field strength of the two scanning magnets can be calculated as a function of the spot position at the isocentre, allowing the creation of any field needed.The proposed system was evaluated by means of Monte Carlo simulations. The nozzle of the ICPO beam line was modelled using the TOPAS simulation toolThe advantage of the hexapod system is its capability to follow the beam divergence. When a position other than the central (i.e. without applying a magnetic field at the scanning magnet) is required, the beam is deflected to reach this position. The importance of following this deflection angle is demonstrated. Two cases are investigated: (i) the case of repositioning and rotating the collimator following the beam deflection and (ii) repositioning the collimator so that the beam spot targets the collimator slit, but without rotating the collimator  of a fixed collimator are compared with a parallel plate collimator. A slit width of 400 μm is used.The performance in terms of dose distributions of the two-plane collimator is compared to that of a single slit collimator. The aperture collimator is not investigated as is considered to be equivalent to the single slit collimator. The slit width is 400 μm with a 5 cm slit length.To evaluate the new scanning collimator design, the minibeams generated by a multislit collimator were compared with the scanning single slit and two-plane collimator. To produce the minibeam array with the scanning collimators, the collimators and beam were repositioned accordingly.In the previous section a scanning dynamic collimator for proton minibeam production was proposed. In this section we conduct a proof of concept experiment in order to evaluate the feasibility of the scanning component of the minibeam collimator. In this proof of concept experiment we focus on generating a minibeam array by repositioning the collimator. Therefore, rather than having a dynamic collimator, a single slit collimator is used. The single slit is repositioned to produce the desired minibeam array. This allows to confirm that the new collimator design would work when positional uncertainties are present; i.e. when combined with a real proton therapy beamline.The experimental setup consists of the stand with the single slit collimator placed between the gantry and the water tank Fig. ; left. TThe un-modulated proton field was 3 spots wide horizontally (x-axis) and 8 spots vertically (y-axis). The field was repositioned so that it remained centred to the slit, when the slit had to be moved to a new position in order to form another minibeam. The horizontal displacement and angle of the collimator were calculated for each slit  radiochromic film on the surface of the (empty) water tank.The collimator system was initially aligned at the position of the central minibeam. That included some trial and error procedure where the position (divergence and displacement) of the collimator was changed and the minibeam pattern was inspected with a film. When the single minibeam pattern was satisfactory, the position of the slit was kept.The slit was moved to the next position using the collimator position parameters that had been calculated. The corresponding proton spot pattern was used for the irradiation. Again, a trial and error procedure was used to evaluate the correct alignment. When a satisfactory single minibeam pattern was achieved, the position was kept and moved to the next position.The previous process was repeated for all single slits in a minibeam array. When the necessary number of single minibeam arrays was reached, a full array was compiled by using the positions previously stored.The following procedure was followed for the experimental measurements:This process was followed for compiling a 3 and 5 minibeams array.The concept of a scanning dynamic collimator was introduced in the previous section. In this section the design choices presented are evaluated and the minibeam dose distributions produced by the new design are compared with the dose distributions by the multislit collimator. Then the results from the proof of concept experiment are reported.The effect of the beam deflection angle, slit length and collimator design to the dose distributions was studied by means of Monte Carlo simulations.max was observed. These results demonstrate the necessity for following the beam deflection angle. In the proposed system this is achieved by the use of the hexapod.Large reduction in the entrance dose was observed when the collimator was not rotated to follow the beam deflection angle, for a proton beam of 100 MeV Fig. a. In theIn the case of the point-by-point scanning method a small collimator can be used. The minimum size of this collimator was calculated. In our proton system, for a beam of 100 MeV we get a spot of 6.7 mm at the isocentre . This results to a very flexible design that makes it possible to compile any desired minibeam array. The resulting device can be retrofitted to any machine and removed when is not needed. By using a hexapod for the scanning stage a conical shape can be achieved that will allow the collimator to be positioned as close to the patient as possible. Its weight is not expected to be more than 50 kg.Alongside with the innovative aspect of the device come the technical challenges. Firstly, the scanning dynamic collimator needs to be synchronised with the beam delivery system, and remain at a good synchronization state during the irradiation. The synchronisation is significantly more challenging in the case of a point-by-point scanning method. However, the line-by-line scanning method can substantially reduce the necessity for online synchronization. The collimator could be moved to a new line at known intervals with the beam turned on and off accordingly. Secondly, the alignment (i.e. the position and angle of the collimator) of the system with regard to the beam spot positioning is very crucial. This can be further seen in the proof of concept experiment and in particular in the 5-slit minibeam array, where a misalignment is observed resulting to unequal peaks in the dose profile.In the proof of concept experiment the combination of using manual stages for the movement and the film for the measurements had limited the alignment accuracy. The effect of the misalignment can be seen in particular in the 5 slit minibeam array Fig. , where tA new proton minibeam collimator was presented. The new collimator design introduces the concept of a scanning dynamic collimator for the production of a minibeam array. The new minibeam generation method is specifically adapted to modern pencil beam scanning proton therapy systems and allows to produce any minibeam length and width desired online.Our simulations showed that the new collimator design is able to produce equivalent dose distributions with the multislit collimator that is currently in use. In addition, we conducted a proof of concept experiment to demonstrate the feasibility of the concept. In this experiment, a minibeam array was produced by repositioning a single slit collimator to pre-calculated positions.Supplementary Information.


Functional laser texturing by means of Direct Laser Interference Patterning is one of the most efficient approaches to fabricate well-defined micro textures which mimic natural surfaces, such as the lotus effect for self-cleaning properties or shark skin for reduced friction. While numerous technical and theoretical improvements have been demonstrated, strategies for process monitoring are yet to be implemented in DLIP, for instance aiming to treat complex and non-plane surfaces. Over the last 35 years, it has been shown that the sound pressure generated by a laser beam hitting a surface and producing ablation can be detected and analysed using simple and commercially available transducers and microphones. This work describes the detection and analysis of photo-acoustic signals acquired from airborne acoustic emission during DLIP as a direct result of the laser–material interaction. The study includes the characterization of the acoustic emission during the fabrication of line-like micro textures with different spatial periods and depths, the interpretation the spectral signatures deriving from single spot and interference ablation, as well as a detailed investigation of the vertical extent of the interference effect based on the ablated area and its variation with the interference period. The results show the possibility to develop an autofocusing system using only the signals from the acoustic emission for 3D processing, as well as the possibility to predict deviations in the DLIP processing parameters. Moreover, laser micro-processing is replacing conventional methods in many other areas such as welding of materials5, drilling of boreholes6 and cutting of thin material7. As part of this replacement process, approaches for process monitoring and control have been established. For instance, in the field of laser welding and drilling, process monitoring includes the analysis of the mid- and long wave infrared radiation via infrared cameras or pyrometers for investigating the heat development, CCD and CMOS cameras to capture process lighting, as well as microphones for recording the process noise8.Laser based tools for micromachining and surface functionalization provide today enormous potentials for the processing of various materials. In particular, the selective change in the surface topography is playing an increasingly important role to enhance the surface properties of many products or devices, for example reducing the adhesion of ice9. An advanced technology for the texturing surfaces with micro- and nanoscale structures is Direct Laser Interference Patterning (DLIP) and consists in coherently superimposing two or more laser beams to create a periodic interference pattern within the laser spot size. The interference pattern can be defined by the wavelength and polarization of the laser light, the number of beams and their intersection angles, and allows a large degree of freedom in surface design11. Furthermore, this texturing approach has already been demonstrated on a variety of material such as copper12, ceramics13 and glass14 and can be consider suitable for any material which can be treated by laser.These monitoring approaches are nowadays slowly adapted into functional laser texturing, especially for already well-established approaches such as Direct Laser Writing (DLW), where a single laser beam is scanned over the material surface, creating microstructures through the ablation process15. In particular, for the 3D processing of components and parts, an optimal process control of the working distance is fundamental17. Besides the direct approach of splitting the laser beam and measuring the partial beam with a sensor19, optical detectors can also monitor the process from a lateral position. The low light generation in micro laser machining with pulsed lasers and the positioning of the photodetector, at small working distance complicates this approach8. In contrast to optical methods, acoustic methods offer both the advantage of a non-contact measurement and the possibility to set the system relatively far away from the working position. As a result, several studies for evaluating the airborne or surface acoustic emission (AE) during the laser micromachining process have been conducted21. Evgueni et al.22 were able to show that the surface-acoustic emissions in copper foils can be recorded with a contact microphone, retrieving relevant process information such as the change in pulse energy. However, the results showed that process monitoring based only on the AE is still challenging due to the complex non-linear ablation processes and the underlying time-varying statistical and AE spectral signatures. Furthermore, the quality of the structure-borne emission was found to depend on the distance between the origin of the emission source and the contact microphone, and can only be recorded on the surface of the material. In a later work, a correlation between change of the focus position to the work piece and AE was shown23. Similarly, the airborne AE can be utilized as demonstrated by Weber et al.24, for finding the focus position for direct laser processing with picosecond laser pulses, whereby an additional visual evaluation with a CCD camera was used for achieving higher accuracy. Advanced solutions based on real-time multi-sensor systems are already available for quality monitoring, e.g. to measure the surface roughness25.In both mentioned approaches, the working position and the size of the laser spot are critical process parameters, which have a significant influence on the final result and even shifts of a few micrometres in the working position can lead to deviations in the process results26. However, if the heat accumulation on the surface is not substantial, either due to the material properties or the heat input of the process itself, no signals can be detected through this method. On the other hand, an optical system for quality inspection has been developed, which takes advantage of the back reflection of the light diffraction of periodic textures. Through this method, different patterns (e.g. line- and dot-like pattern) can be analyzed and the retrieved signals can be correlated with the quality of the microstructures27. However, due to the nature of its working principle, microstructures which tend not to reflect light (e.g. due to surface oxidation or large structure depth) can be hardly detected through this optical method. Complementary to this technique, scatterometry can also be utilized as quality monitoring for surfaces functionalised through DLIP28. Also in this case, the quality of the measurement depends on the amount of reflected light. It has to be mentioned that all the above-mentioned and explored process monitoring approaches for DLIP, are based mainly on the evaluation of the quality of a periodic pattern and do not gain any information from the ablation process itself.Different approaches for process monitoring in DLIP have been also investigated. It has been demonstrated that the heat accumulation after texturing can be monitored by measuring the heat radiation with a high speed infrared camera in an off-axis position. It was shown that for materials like stainless steel and aluminium the quality of the structure can be correlated with the thermal effectsThe objective for this work, is to demonstrate the utilization of the AE method as a possible candidate for process monitoring in DLIP. In particular, the informational properties carried by the signal are examined and a correlation of the obtained information with the shape of the interference volume is performed.11. In order to acquire acoustic signals during the texturing processes, a microphone has been placed at 50 mm from the ablation position and several lines consisting of separated pulses have been marked on a flat stainless steel plate  can be generated. The last element of the module is a focusing lens, which both focusses and overlaps the sub beams on the material’s surface. The system is designed in order to let the sub-beams to intersect approximately 3.6 mm above the focal plane of the focusing lens. This configuration has the advantage to increase the available size of the interference volume (both in height and section) as well as reducing the variation of the spatial period depending on the later position. Furthermore, the setup avoids to concentrate the total available pulse energy in a confined area, making the process more stable and at the same time allowing a better control of the surface topography. The description of the setup can be found in the Materials and Methods section and the working principle has been explained elsewhere31. Thus, the shock waves propagate through the air and reach the microphone, where the resulting airborne AE is transduced into electric signals that can be acquired and analysed. Figure 33.As commonly known for nanosecond laser surface texturing, depending on the laser fluence, the interaction of each laser pulse with the sample surface can result in melting, vaporization of material, ablation, and formation of a vapour-plasma plume, and thus shock waves in the material’s surface as well as and in the surrounding air are formed34. The spectral analysis for various spatial periods can be found in the supplementary section  taking into account the sensitivity of the microphone. An analysis of the frequency band for single laser ablation can be found here32. The MSP is expressed dB of the effective pressure in relation to the sound pressure in air. Previous research have shown that this range is unaffected by the ambient and machine noise and has the amplitude intensity for analysis which is not given by the lower frequencies36.To obtain the characteristic information of the AE from the ablation of one laser pulse, a spectral analysis in the frequency domain was performed by applying a Fast Fourier Transformation over the signalion Fig. . From thIn a second set of experiments, the ablation process reported in Fig. 37. As a result, the FWHM of the interference volume peak (0.65 mm) can be considered as an estimation of the extent of the interference volume. On the other hand, the AE peak related to the focus position of the sub-beams shows a larger (FWHM of 3 mm) and a less intense emission. This can be explained taking into consideration that this AE peak is a result of the incoherent addition of two sound sources with same intensity. In fact, it is known that he incoherent sum of two distinct sound sources (I1 and I2) depends on the logarithm of the product of both intensities instead of the direct sum of I1 and I238. This difference demonstrates the complexity of emission generation during laser ablation, as one could assume that identical laser pulses penetrating the material at the same time would result in identical AEs and thus direct addition of the sound sources. On the other hand, the difference in FHWM of the single beam ablation can be attributed to the separation of the beams, as the energy density of the individual laser pulse outside of the focal length is lower than the material damage threshold. Thus, the emission peak of the DLIP region is limited within some hundreds of micrometres, while for the separated sub-beams it ranges within almost four millimetres. This means that, looking at the integral of the AE signal, the separated sub-beams have a higher AE energy .In order to obtain the characteristics of these signals, the collected data points have been fitted with two Gaussian functions Fig. a which, θ = 7.10°, leading to a spatial period of 8.0 µm, and the largest interference area (position 2) is reached at 36.40 mm. Furthermore, these beams are focussed 3.6 mm underneath the interference volume.In order to graphically explain the AE results, the beams overlap region of the employed DLIP setup has been simulated and represented in the YZ-plane, as shown in Fig. 2 = 0.97) and that minor deviations can be observed in the outer regions of the interference volume (i.e. below -0.4 mm and beyond 0.4 mm) due to the asymmetry of the interference volume caused by the slight focussing of the interfering beams39. This can also be seen in the shape of the ablated laser spot on the material. As above the working position at (1) no distinction can be made between the individual beams, in contrast to below where the shape of the individual beams can be distinguished see (3). At the working position (2), the ablation spot is identical to the Gaussian distribution of the laser beam used.Once the approximate position of the interference volume has been found by analysing the acoustic emission of the DLIP system Fig. , further20. This relationship can be observed in Fig. Figure In successive experiments, the AE deriving from the ablation using different spatial periods has been evaluated repeating the same analysis described in Fig. The full width half maximum (FWHM) of the AE can be assumed to be an estimation of the size (height) of the interference volume and it systematically decreases for decreasing spatial periods.The amplitude of the AE varies applying different spatial periods.The working position shifts upwards  with decreasing spatial periods, i.e. with increasing angles between the interfering beams.The analysis of the results allows the following remarks:37. In particular, the height of the interference volume w) at the interference volume and the angle The observation (1) can be explained taking into account that the height of the intersection volume between the two Gaussian beams decreases with increasing the interference angle . As it can be noticed, the relationship between size of the interference volume and spatial period can be assumed to be linear Fig. b. This oΛ), as follows:λ is the laser wavelength.Substituting the interference angle mentclass2pt{minimw) of 87 µm can be retrieved, which matches the known beam waist size measured with a beam camera (~ 90 µm).Applying this equation in order to fit the datapoints in Fig. 40. In consequence, the amount of ablated material can decrease. In consequence, we have to competitive effects which could partially explain the observed differences. Additional experiments are necessary in the future to understand this effect. As far as observation (3) is concerned, the vertical shift of the interference volume can be described through simple optics assumptions. A systematic analysis of this shift as a function of the spatial period is shown in Fig. 41. This effect is shown in Fig. The variation of the AE intensity mentioned in the observation (2) can be attributed to two possible effects, which must be considered when the spatial period is changed. Firstly, when two laser beams are overlapped under a certain angle, an elliptical laser spot is produced, which can be approximated to a round spot for small intersection angles (e.g. 1–10°). However, when the angle is increased in order to produce interference patterns with smaller spatial period, the spots clearly show an elliptical shape. Thus, when the spatial period is changed from 8 to 2 µm , the size of the laser beam following the direction perpendicular to the interference lines increases by approximately 10 µm for the configuration used (~ 11.1%). Therefore, larger amounts of material can be ablated due to the increased spot’s area, resulting in higher AE levels. On the other hand, it is known for DLIP using ns pulses, that for smaller spatial period, the observed temperature at the maxima positions decreases do to heat diffusionThis work presents a systematic investigation of Acoustic Emission (AE) generated during single-pulse ablation experiments in Direct Laser Interference Patterning (DLIP). As a first objective, the response of the acoustic transducer to the ablation events has been investigated and a correlation between the retrieved data and the optical characteristic of the interference setup used has been found. In particular, it was found that the working position of the interference volume and the ablation of the single beams can be distinguished from each other. The clear change of the sound level obtained through the variation of the Z-positions can be therefore employed to identify the optical interference working position. Moreover, the analyses performed on the AE curves permitted to retrieve characteristic information about the size and shape of the interference volume, as well as the shift of its position as a function of the spatial period. An indication of the accuracy of this approach can be seen in the change in AE in contrast to the amount of interference volume extracted from the acoustic sweep. For a spatial period of 2 µm, the step size was ten times smaller than the FWHM. The next study will focus on the AE induced by the change of other process parameters, such as pulse overlap and hatching distance, with the aim to correlate the acoustic signals with information about structures depth or structure quality. A detailed understanding is necessary to enable the development of an AE autofocus to automatically maintain the working distance at a defined position when processing non-planar surfaces. Furthermore, the transfer of this approach to different materials, such as copper and ceramics, or to materials which can be treated without inducing ablation, will be investigated in future experiments.44 or aerospace43).Flat samples made of X5CrNi18-10 stainless austenitic chromium nickel steel (EN 1.4301/AISI 304) with a thickness of 0.7 mm and dimension of 55 mm × 85 mm were used for the experiments. The surfaces have a surface roughness Sa of ~ 70 nm  and all surfaces were cleaned from contaminations prior to the laser treatment using ethanol. The material was chosen due its relevance in several industrial sectors  in a two-beam configuration was used, where the change of the spatial period, workpiece movement and laser control is done by the surface structuring software SurfaceMod . The used laser source is a Q-switched Nd:YLF laser  with a wavelength of 1053 nm generating 15 ns pulses with a pulse energy of up to 290 µJ (@1 kHz).Figure For the AE measurements, an omnidirectional electret condenser microphone CMA-454PF-W  connected to a MAX4466  preamplifier was installed next to the DLIP processing head and aligned on the back of the DLIP module so that both beams are symmetrical to the sensor. The AE audio sensor has a frequency bandwidth of 20 Hz to 22 kHz, a sensitivity of − 44 dB, a diameter of 10 mm and a height of 5 mm and was mounted diagonally above the laser interaction zone at a distance of 50 mm see Fig. a. The pr11The AE signal was recorded for every laser pulse impinging on the material, while moving high precision motorized axes  at a speed of 5 mm/s and producing separated ablation areas containing a microscopic interference pattern (DLIP-pixels). The measurement of the DLIP working position and the focus of the single beams was performed by varying the Z-position of the DLIP processing head see Fig. b. The inSupplementary Information.


The proposed experimental technique is universal and allows a) determining the coefficient of molecular diffusion of vapor of a volatile liquid in air; b) calculating the coefficient of effective diffusion of vapor in oscillating air. The proposed technique was tested in the study of the diffusion of 2-propanol vapor in air at rest and oscillating air in a channel of variable radius and a porous medium consisting of randomly packed hard spheres of equal diameter and was found to be relevant. Initial experiments with a porous medium show that the proposed experimental technique can also be used to estimate the diffusive tortuosity of porous media. The results of studies, finished and planned, are useful for understanding the physical processes taking place in various technical operations including wood and food drying, drug delivery, etc.  For instance, many scholars have conducted lots of researches on the design of high-efficiency heat exchangers For decades, mechanical oscillations at a frequency above the threshold of human hearing (ultrasound) have been implemented as an effective tool to enhance mass transport of moister for wood It is worth mentioning that steady streaming is also an inherent part of thermal vibrational convection in rotating and oscillating cavities: Under high-frequency oscillations, the non-zero steady flow originates and impacts the mixing of non-isothermal liquid An alternative way to increase heat or mass transfer is to excite oscillations of a fluid (or gas) in a stationary container. For example, longitudinal air oscillations increase the mass transfer of a contaminant by several times due to Taylor dispersion in a long straight tube , 8. The Recently, Kozlov and Polezhaev experimentally studied the effect of air oscillations on the diffusion rate of vapor in air in a channel of variable radius 1 (a). In the experiments, we use a loudspeaker, which is controlled by a digital generator ZETLab The experimental setup is designed to measure the coefficient of effective diffusion of vapor of a volatile fluid in oscillating air in a straight channel of the constant or variable radius or a porous medium. The longitudinal oscillations of the air column in a channel (or in a porous medium) are generated by a loudspeaker 1 a. In the2 of diameter 3 mm is glued to the center of the loudspeaker dust cap. The upper end of the rod goes through a hole in the center of the rubber membrane  air, μair = 29 g/mol is the molar mass of air, μ0 = 60.1 g/mol is the molar mass of 2-propanol, p0 is the vapor pressure of 2-propanol at ambient temperature T. Note that, in the process of deriving air. Near the top edge of the channel of variable radius or porous medium, the vapor concentration equals 0, so that air density is equal to the density of ambient air. The density of vapor saturated air near the lower boundary of the channel (or porous medium) is larger than the density of atmospheric air, thus gas in the vertical channel is stably stratified and convective mass transfer is absent. In the absence of other mechanisms, the vapor is transported by molecular diffusion only.Above the free surface of a volatile fluid, the air is saturated with its vapor; its density can be calculated by the following equationf = 0 – 150 Hz. The amplitude of the fluid oscillations is measured with the use of DSLR Canon EOS 60D with Canon Lens EF-S 35 mm f/2.8 IS STM Macro Led, placed in front of the transparent glass cell and focused on the interface between the fluid and air. The interface is illuminated by white LEDs. The resolution of the camera sensor is 18 MP (5184 × 3456 pixels). Taking into account that the size of the imaging area is around 45 mm × 30 mm, one can estimate that resolution of the digital image is approximately 115 pixels per mm.The frequency of the imposed fluid oscillations varies in the range 8 in transparent glass cell is unstable to the onset of unwanted oscillations, for instance, Faraday ripples. These ripples make it impossible to measure accurately the amplitude of fluid oscillations. To prevent the rise of unwanted oscillations, the free fluid surface is covered by polystyrene ring 9 with an inner diameter of 16 mm, an external diameter of 22 mm, and a height of 4 mm. The upper surface of the ring is coated with the fluid so that it does not block the evaporation. The amplitude of fluid oscillations fb varies from 0 to 1 mm in the studied range of frequencies.The surface of oscillating fluid The vapor diffusion rate depends not so much on the amplitude of fluid oscillations as on the amplitude of air oscillations in a channel or pores. The amplitude of air oscillations can be calculated using the condition of equality of the air flow rate in the transparent glass cell and the channel or porous medium.b). In the transparent cell, the air volume displaced by the oscillating fluid is equal to 4πr12fb. In the channel of various radius, the volume of air passing through the cross-section of radius r is equal to 4πr2air_rb. Due to the incompressibility of air, the condition 4πr12fb = 4πr2air_rb is satisfied, i.e.Consider the method to calculate the amplitude of air oscillations in narrow and wide sections of the channel of various radius b. In theP of randomly packed hard spheres, which is the ratio of the total volume of air pores to the total volume of the porous medium. The porosity of the randomly packed spheres depends, among others, on the ratio of spheres to cell diameter  and porous medium consisting of randomly packed hard spheres (b). The analysis of experimental data in Fig. 2a makes it possible to determine the free surface velocity fdh /dt and then the coefficient of molecular diffusion D. The experimental value of the molecular diffusion coefficient obtained from formula (4) chD = 13 mm2/s is somewhat larger than the reference value D = 9.8 mm2/s fdh /dt into pD and then the diffusive tortuosity τ. For the experimental data in Fig. 2b, the diffusion coefficient pD = 7.0 mm2/s and the diffusive tortuosity τexp = 1.43. Now, we can compare the experimental value τexp with the theoretically predicted one. For random packing of monosized particles, the following equation is valid [19]exp = 1.43.The experimental setup also makes it possible to measure mass the transfer of vapor in the presence of air longitudinal oscillations in a channel or a porous medium. As before, we can use fdh /dt. During an experiment with oscillating fluid, the DSLR camera and the digital generator of the harmonic signal are not synchronized and therefore images of the free surface are captured at various phases of the fluid oscillations. So, plotting the free surface positions as a function of time results in a scatter of experimental data points with edges corresponding to the lowermost and uppermost positions of the free surface  or effD /τD in a porous medium (b). It can be seen that the coefficient of effective diffusion effD increases with an increase in the Peclet number Pe = 2πairdfb/D, here amplitude of air oscillations is determined by the formula (2) or (3), d is the diameter of the narrow section of the channel or the diameter of spherical particles composing the porous medium.The efficiency of air oscillations can be estimated by calculating the ratio e radius a or Deffs medium b. It canA new technique for measuring the diffusion coefficient of vapor of a volatile liquid in atmospheric air is discussed. We study the evaporation of a volatile liquid in a channel of constant (or variable) radius or a thick layer of a porous medium. The diffusion coefficient is calculated from Fick's law considering that mass of evaporated liquid equals to mass of air diffused through the channel or porous medium.In the absence of air oscillations, the technique allows measuring the coefficient of molecular diffusion of vapor in air. Perhaps an even more significant result is that a new approach can be used to measure the coefficient of enhanced vapor diffusion in oscillating air which was first discovered in very recent research The experimental results obtained using the proposed technique are useful for understanding the processes taking place in various technical operations including wood and food drying, drug delivery, etc. Future work will focus on studies of enhanced diffusion in real porous media under ultrasound irradiation.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


In order to respond to the regional coordinated development of the country, it is necessary to put forward a method that can predict and analyze the development trend according to the current development situation. In view of this, the research will carry on the present situation and forecast analysis to the coordinated development of urban agglomeration in Western China. Firstly, the 3E system is used to establish the regional coordination degree evaluation model, and on this basis, the ellipsoid model is introduced for better coordination degree evaluation. In addition, in order to improve the prediction ability of the model, the convolution neural network is used to realize the big data analysis of the model. The results show that the overall coordination degree of the western urban agglomeration is in a weak coordination state in 2015, but the coordination degree of the region will reach 147.35 in 2020. The results show that the overall coordination degree of western urban agglomeration will gradually show a good trend, but the change speed is slow. The above results show that the prediction model in the study has strong practicability, the calculation results can fit the current situation, and the good prediction ability can provide decision-making suggestions for many governments. However, with the energy and environmental crisis brought about by economic development, the economic crisis in regional development is gradually emerging, so how to achieve regional coordinated development and deal with the problems of energy consumption and environmental pollution brought about by development is extremely important . For quality coordination, [−10°∼20°], [50°∼80°]. For good coordination, [−40°∼−10°], [80°∼110°]. For weak coordination, [−70°∼-40°], [110°∼140°]. Mild discordance [-110°∼−70°], [140°∼180°] is moderate uncoordinated, and [−180°∼−110°] is a serious disharmony.In the previous equation, One of the research focuses is to deeply analyze the coordinated relationship among energy, economy, environment, and other factors in regional coordinated development. Based on the ellipsoid model, this paper introduces the big data analysis method of convolution neural network and establishes the regional coordination degree prediction model of the 3E system. Finally, the prediction model of the 3E system coordination degree based on a convolution neural network is constructed, as shown in In the prediction model, a convolution neural network algorithm is used to analyze big data. A convolution neural network is a kind of deep feedforward artificial neural network, which has the advantages of accurate extraction of data features and strong classification ability. As a deep learning model, a convolutional neural network mainly includes an input layer, hidden layer, and output layer, as shown in Xjl represents the input eigenvector, Kijl represents the j convolution kernel of the eigenvector, bji represents the corresponding bias parameter in the calculation, and the calculation after the convolution layer is the downsampling calculation of the pooling layer. When n eigenvectors are input, the calculation method of the output eigenvector is shown as follows:f denotes the downsampling function and βji and bji denote the bias parameter. The calculation formula of characteristic sampling is as follows:αji and bji are all expressed as bias parameters in calculation. The calculation formula of the whole connection layer is as follows:f is the activation function. In the backpropagation, the weight change is calculated layer by layer from the back to the front:where W is the weight of each layer network and δ is the parameter variation coefficient of neuron node. Finally, the data is standardized and the result is limited between , as follows:where In the previous equation, the original data is preprocessed by linearization. The first equation preprocesses the larger eigenvalues, and the second equation preprocesses the smaller eigenvalues.The experiment is based on Windows operating system. The data set is imported for model training and testing. 90% of the data is set as the training set, and the remaining 10% is set as the test set. The prediction efficiency of the CNN model is discussed based on the test accuracy of the CNN model, as shown in As can be seen from It can be seen from This paper selects the index data of coordinated development of urban agglomeration in Western China as the relevant index data; calculates the development level of energy, economy, and environment of urban agglomeration in Western China by running the principal component analysis method; and finally calculates the coordination degree of 3E system of urban agglomeration in Western China, as shown in It can be seen from The real line in Regional coordinated development is one of the important preconditions to promote economic development. This paper analyzes and forecasts the prospect of multiregional coordinated development in China, so as to provide corresponding decision support for the reform and optimization of China's multireal estate industrial structure. Taking the coordinated development of multiregions as the research object, this paper constructs the 3E system of regional coordination. Convolution neural network is introduced into the system, and its big data analysis method is used to predict and analyze the regional coordinated development trend. Through the comparative analysis of different network models, it is verified that the convolution neural network has good prediction performance, and the index data of western urban agglomeration is taken as the research object for empirical analysis. The results show that the coordination degree of the 3E system in western urban agglomeration is improved from 92.77. In 2015, it reached 147.35. In 2020, in the latter prediction model, the prediction results show that the coordination degree of the 3E system of western urban agglomeration gradually begins to slow down, which shows that the big data analysis results show that the government's environmental protection measures will gradually make the regional coordinated development better. The research results of this paper can not only analyze the current development status but also predict the development trend in the next few years. This is of great significance for the state and government to carry out regional coordinated development regulation, which will effectively promote the slow development of China's regional rapid development and also promote the economic development of developed regions.


An interesting phenomenon that a layer of crystallized shell formed at the container wall during an orifice flow in a cylinder is observed experimentally and is investigated in DEM simulation. Different from shear or vibration driven granular crystallization, our simulation shows during the flow the shell layer is formed spontaneously from stagnant zone at the base and grows at a constant rate to the top with no external drive. Roughness of the shell surface is defined as a standard deviation of the surface height and its development is found to disobey existed growth models. The growth rate of the shell is found linearly proportional to the flow rate. This shell is static and served as a rough wall in an orifice flow with frictionless sidewall, which changes the flow profiles and its stress properties, and in turn guarantees a constant flow rate.  Ordering phenomena are also widely studied in driven disordered system8. As a non-equilibrium model system, agitated granular matter has often been used in the lab to study mechanisms behind these ordering phenomena. Particle alignment, related to ordering, rheology and entropy in disordered systems, has frequently been induced and investigated in shearing, twisting, shaking or inclined-flow granular media11. Different from these external agitations induced granular ordering, we report in this work observation of a layer of shell crystallized spontaneously at the container wall during an orifice flow without external agitation.Self-assembly widely appears in nature, from ripples in sand, waves of the sea, to spirals on the shell of snails and bacterial snowflakes14. The constancy of the flow rate may be related to either dynamical Janssen effect or existence of a ‘free fall arch’ region15 over the outlet. Continuum modeling of hopper flow by Staron et al. successfully reproduced the constant flow rate and pressure cavity by implementing a plastic rheology in Navier–Stokes’s solver16. These findings imply that when discharging from a hopper, granular material resembles other visco-plastic fluids with a shear stress changing from shear rate γ-independent in elastic limit to 17 as described by Bagnold already in 195418.Flow of granular material from a hopper through an orifice, namely hopper flow here, is featured by its constant flow rate. The flow rate can be described by Beverloo’s scaling law quantitatively:19 or electrical capacitance tomography20 showed, that increasing wall roughness leads to increasing thickness of the shear zone near the wall for sand. Similarly, DEM simulations by Gonzalez show that increasing wall roughness leads to a mass flow-funnel flow transition21. The flow rate from a silo was reported to systematically decrease with increasing the surface roughness of the particles22 or with increasing internal angle of friction of the granular material23. In DEM simulations by Vidyapati the flow rate decreased with increasing interparticle friction, but was insensitive to the wall friction24.Several recent studies focused on frictional properties of the particles and the silo wall which are crucial in setting the flow profile and the flow rate. Experimental observations by X-ray tomography28, where the volume fraction and particle–particle friction played an important role. The initial crystallized ‘nucleus’ appeared not only at the boundary but also in the central region29. Other examples, such as for inclined flow under gravity, ordering arises upon ordered base or driven by the side wall friction30. Our observation of the remaining crystallized granular shell also reminds for comparison with the slow motion of retention of viscous fluid on a vertical plate as investigated by Jeffreys in 193031 and by Gutfinger and Tallmadge32 in non-Newtonian fluids. Compared to fluids, there are two major differences in the granular case: (1) the formation of a crystallized shell is a dynamical process grown upwards from bottom; (2) the crystallized shell in our case grows during the drainage and is still mechanically stable after drainage.In this work we report a peculiar phenomenon observed in experiment and investigated in simulation, that during the drainage a crystallized granular shell develops next to the wall. Development of the shell gradually changes the flow profile inside the silo as it leads to a change in the friction at the boundary without changing the interparticle friction in the bulk. We explore the process leading to the formation of the shell and analyze whether it influences the flow rate. The development of crystalline ordering was reported in other (sheared or shaken) granular systems beforeD as the hopper diameter and d as the particle diameter while d0 as the averaged particle diameter in a particular simulation case. In order to describe the growth of crystallized shells, three types of particles are defined here as one gets closer to the wall: boundary particle, if its radial coordinate is greater than D/2-d0, to ensure no particle locate between this particle and the wall; wall particle, if the particle touches the sidewall , and shell particle, which is a wall particle touching six neighboring wall particles to form a nearly static crystallized shell. To define top surface of the shell, the boundary layer  is divided into several vertical columns. In each column the shell particles are recognized from bottom to top. The last shell particle in this column is defined as the shell particle k when there is no other shell particle located in the range , where zk is the z coordinate of particle k.Crystallized shells of particles next to the wall during the drainage are both observed in our experiments and simulations 33, which is 0.99 for timepoint 12 s of Fig. After starting the flow, local configuration of packing close to sidewall will self-organize into ordered state. The participating particles come from the boundary particles of the initial packing  and the weaken the whole structure. For contrast, small μpp helps to generate more wall particles to enforce the growth of the crystallized shell. Besides friction, as mentioned above, dispersity is known as another important factor for shear-induced ordering35. Our simulations also show that the distribution of particle size does influence the formation of the crystallized shell. The shell does not form when the global dispersity λ is large (0.1 for instance). A small λ guarantees the mechanical stabilization of the shell after the drainage. Figure Large 36 in contact with the wall. This process depends on the local configurations of the flowing region just above the top of the shell. Height of this region is about 2-3d0 as the motions of wall particles will be affected by inner particles. Main ingredient of this selection process is that the shell ‘prefers’ to choose particle that has about the same size 38 and the KPZ theory (δ = 1/3)40.We calculate roughness of this crystallized shellentclass1pt{minimavs. The growth rate vs with varying μpp and μpw are shown in Table vs = 76.0 d0/s when μpp = 0 to 12.6 as μpp grows to 0.1. The crystallized shell is no longer observed if μpp exceeds 0.1. It is also found that friction between particles and sidewall μpw has a minor effect to the formation of the shell. The influences of particle density, initial packing height and gravity to shell growth rate are shown in Table For every snapshot, averaged surface height of shell see Fig. a. We seementclass2pt{minim38, it is natural to associate the growth rate to the particle velocity. Since the flowing particles above the surface of the shell have nearly the same velocity, velocity of potential shell particles can be calculated as: vs and vp  , a plug-like flow occurs and vz is much larger than in cases A and B. Both the shear rate and the granular temperature are then close to zero.In case A, the wall particles are rearranged into hexagonal ordered state after flow begins. Value of local orientational order vz of all particles is still nearly uniform and no obvious shear layer is observed. Thus, the occurrence of shear layers is due to this crystallization. The shear flow region expands upwards until the growing crystallized shell encounters the top surface of the descending level. In our simulation, funnel flow is not observed even if μpp reaches 0.5, perhaps because wall friction is not enough here44. The crystallized shell remains static after the drainage, which is found in our experiment with spherical glass particles and steel particles  and decreases in the situation without the shell (Case C*), which questions the relationship between the flow rate and the roughness (or friction) of sidewalls. The flow rate in Case B* is smaller than that in both of Cases A* and C*, which verifies the influence of particle–particle friction reported in previous studies23.Variations of instantaneous flow rates with time are shown in Fig. We have investigated numerically of the experimental observation that a layer of crystallized shell formed at the container wall during hopper flow. Our simulation shows degree of the particle polydispersity and particle–particle friction are two main factors to prevent the shell formation. Those particles being pushed to the wall by the flowing particles, tend to pile up from the base and grow to the top during the flow. The faster the flow rate is, the faster the growth rate of the shell layer piles. The ratio of the rates depends on the container diameter. The smaller the container the larger the ratio is. Once it is formed, the shell remains there, even when the flow ends. This formed shell serves as a new wall, which guarantees the flow rate constant no matter what wall material is. This phenomenon is interesting not only for its formation of crystallized shell with no need of external drive, but also for its altering the flow properties and stabilizing the flow rate. More simulations and experiments should be done to check this phenomenon in non-spherical particle system in the future.49. DEM is a widely used simulation tool in granular mechanics, in which particle positions, velocities and interactions are tracked by equations of motion, simple contact models being then provided. In our simulation, the soft-particle contact model is used where the interactions consisting of elastic and viscous components in normal and tangential directions are calculated from the overlap and its time rate of change. By the Hertz-Mindlin contact model51, the normal and tangential contact forces between two contacting particles are:G is the shear modulus, Y is the Young’s Modulus, r is the radius of the particles, m is the mass of particles and e is the coefficient of restitution between particles. δijn and δijt are normal and tangential displacement vectors, and δijn and δijt are their modules, respectively. vijn and vijt are normal and tangential relative velocities between the particles i and j. δijn ≡ (Ri + Rj – rij)rij/rij and δijt is determined by integrating vijt. Considering sliding friction, the Coulomb yield criterion Fijt ≤ μsFijn is satisfied by truncating tangential overlap u’ij = μsFijnuij/Fijt51. μs is the sliding friction coefficient between particles. u’ij and uij are truncated and original tangential overlap respectively. Further more, rolling and torsion friction should be introduced for irregular shaped particles. These influences are given by rolling and torsion torques:μr and μt are rolling and torsion frictions respectively, To model the dynamical behavior of particles, our simulations are carried out on multiple GPUs using the DEM code (Discrete Element Method) developed by usUnder gravity field, the equations of motion of the particles are:52. The model parameters used in our simulations are listed in Table These equations are solved by integration using the Velocity-Verlet scheme–10 J). During the packing process, a viscous damping was added to accelerate the packing process and make a reasonable stress distribution in conformity with the Janssen’s effect53. The volume fraction of the packing is roughly 0.60. After the packing process, the orifices of hoppers were opened to let the particles flow.In our simulations, dispersed glass spheres were randomly generated with a small volume fraction within flat bottomed hoppers and then they were packed under gravity till the total kinetic energy of the packing was small enough (< 10λ)d0, (1 + 1/2λ)d0), where λ is named to be the global dispersity of particles. The local orientational factor q655 and the granular temperature56 are calculated in our system. The q6 of the i-th particle is given by:i and j, Q6m is spherical harmonics Ylm when l = 6. In our simulation, granular temperature in z direction is given by:The size distribution of particles in the simulation is uniform in the rage ((1–1/2Ω.57:ith particle in a volume The bracket denotes an average value of particle velocities within a volume The shear rate is given by:In the experiment (shown in Figure Before the experiments, the hopper is set upright vertically with blocked opening, and particles are filled up to the height of 1500 mm. A high-speed camera is fixed on a tripod to shoot videos of the particles close to the wall at a frame rate of 100 fps.Supplementary Video 1.Supplementary Video 2.Supplementary Video 3.Supplementary Information.


Inferring the demographic history of species is one of the greatest challenges in populations genetics. This history is often represented as a history of size changes, ignoring population structure. Alternatively, when structure is assumed, it is defined a priori as a population tree and not inferred. Here we propose a framework based on the IICR . The IICR can be estimated for a single diploid individual using the PSMC method of Li and Durbin (2011). For an isolated panmictic population, the IICR matches the population size history, and this is how the PSMC outputs are generally interpreted. However, it is increasingly acknowledged that the IICR is a function of the demographic model and sampling scheme with limited connection to population size changes. Our method fits observed IICR curves of diploid individuals with IICR curves obtained under piecewise stationary symmetrical island models. In our models we assume a fixed number of time periods during which gene flow is constant, but gene flow is allowed to change between time periods. We infer the number of islands, their sizes, the periods at which connectivity changes and the corresponding rates of connectivity. Validation with simulated data showed that the method can accurately recover most of the scenario parameters. Our application to a set of five human PSMCs yielded demographic histories that are in agreement with previous studies using similar methods and with recent research suggesting ancient human structure. They are in contrast with the view of human evolution consisting of one ancestral population branching into three large continental and panmictic populations with varying degrees of connectivity and no population structure within each continent. Reconstructing the demographic history of populations from the analysis of genomic data is one of the greatest challenges of population geneticists  and anthropogenic factors that have influenced genomic diversity in various species. Also, understanding how past climatic events or human activities have influenced genomic diversity today may become particularly illuminating for conservation biologists regarding the likely long-term consequences of ongoing climate change and human actions .However, to understand how the past influenced the present patterns of genomic diversity one major question is whether our conclusions or inferences may fundamentally change depending on the family of models assumed and the questions asked  . Simulations by Chikhi et al.  introduced by Mazet et al. . We prop Wright, , using t Wright,  for a sai et al.  and Rodri et al.  under vainferring the number of populations rather than setting it a priori. Second, we ask whether it is possible to date and quantify changes in connectivity  rather than changes in population size. For that, we use the piecewise stationary n-island model in which continuous gene flow happens between populations at a constant rate during specific periods  but is allowed to change between periods . This mz et al.  dependinn-island models and inferred connectivity graphs which are a visual representation of the times at which gene flow changed and of the magnitude of these changes. We then applied SNIF to human genomic data using five published PSMC curves . We validated the method with data simulated under piecewise stationary Beyond human data we find that a crucial issue is the estimation of the IICR from genomic data. Indeed, the stochasticity generated during the estimation of the IICR in very ancient times, and possibly recent times, with humps that are difficult to interpret, may lead to the inference of events that may never have taken place.target for demographic inference. With simulated data  this target curve can be obtained under any predefined coalescent model that could be expressed with a simulation tool ). With real genome-wide sequence data, the curve can be estimated with the PSMC method of Li and Durbin . The similarity between the two IICR curves is quantified with a distance metric defined below. We use a genetic algorithm to explore the parameter space  and minimize that distance. We compute the IICR under the non-stationary structured coalescent (NSSC) of Rodríguez et al. Mij to denote the migration rate received by any given island. In addition to this base model, we use an extension, the NSSC, presented in Rodríguez et al. . We note however that throughout the manuscript we will only focus on symmetrical models with constant size .The theoretical framework we use for modeling structure is based on the finite Herbots’s model of the structured coalescent Herbots, , which i Wright, , all thez et al.  which alN(t) = N(0)λ(t) (see Tavaré (λ(t) relative size changing function, and it relates to the distribution of the time to coalescence T2 as:For the demographic histories under these models, we study the IICR of a sample of size 2 (see section e Tavaré ). It wase Tavaré  that theThe IICR is not tied to any particular model, structured or otherwise. It is defined using the distribution of the coalescent times of a sample of size two. It can be approximated to arbitrary numerical precision under the assumptions of the NSSC , and there is a fixed number z et al. . In the γ of demographic events to consider (γ ⩾ 0) and a collection of bounds B in the form of:γ,B as:B, as making i ⩽ γ effectively fixes all deme sizes to 1, and reduces the number of parameters to 2γ + 2.Given a fixed integer γ,B, the associated coalescent process is an instance of the NSSC of Rodríguez et al.  refers to the scaled IICR, and IICR(t) to the unscaled (dimensionless) one. Note that we use g for generations as the variable name for sIICR to further stress the difference. The parameter space for the sIICR can be thought of as a simple one-dimensional addition to Φγ,B:In order to compare the IICR with PSMC inferences, we need to re-scale both the time and the IICR values by a reference deme of size In section F0 and density f0.The search algorithm explores the parameter space and uses an optimality criterion to select the structured scenario that best explains a given target IICR curve, either scaled or unscaled. We also assume that the underlying coalescence times for these target IICRs have cumulative distribution 0 and a parameter space Φγ,B, we want to find a parameter tuple φ in Φγ,B such that the exact IICR curve corresponding to the model defined by φ (denoted by IICRφ) approximates IICR0. We thus want to find the minimal distance:Given a target IICRd, a straightforward definition would be:w(t) is a weight function that should take into account the natural distribution of the information in an IICR. One reasonable solution for w is to take a quantity proportional to the density f0 of the coalescence times because it ensures that the integral in  or exaggerating (if ω > 1) the effect of the weight f0. Unless otherwise noted, we take ω = 1, which corresponds in practice to giving more weight to recent periods of the IICR in direct proportion to the density f0 in an n-island model.We thus consider the family of weight functions:0 is a stepwise discretization over a bounded interval of time, so a numerical approximation of the distance (f0 of the underlying T2 distribution. Given a division of time into τ0 = 0 and 0 in the form of a collection of yj} such that:w(τj), notice that from  can be expressed as:In practice, we need to consider that all we know about IICRdistance  is requiegral in . For insmentclass2pt{minimd in d in  and with known parameter values  and then compared the inferred parameter values to those actually used , we sample demographic scenarios from which we compute the corresponding IICRs. We used two sampling strategies which we call continuous and discrete sampling.Given a parameter space ΦL independent tests, this sampling strategy consists in using uniform or log-uniform distributions for each of the 3γ + 3 random variables:U denotes a uniform distribution (discrete in the case of n and continuous for the rest) and LU10 denotes a log-uniform distribution of base 10. This distribution is used for sampling the times of changes in a logarithmic space in order to take into account the natural distribution of information in an IICR.Assuming that we want to realize ti, we can define the L sampled scenarios by constructing, for 1 ⩽ j ⩽ L, the tuple Mi values in two consecutive components. However, it sometimes produces demographic scenarios in which consecutive ti and/or Mi values may be close to each other, and thus difficult to distinguish. This makes it thus harder on our inferential framework compared to cases where we would choose contrasted scenarios with clearly separated events with major changes in migration rates. In other words, our inferential method was sometimes inferring parameters in the case of extremely difficult scenarios as we show below.After sorting the times L = 400 scenarios. The bounds for sampling and inferring are shown in Table S1. In particular, we note that in practice we disallow deme size changes by fixing the bounds of the si to 1, which consequently reduces the parameter space to just 2γ + 2 parameters.In section “Validation” we show the results obtained using this sampling method with L = 100 independent scenarios from the same parameter space, but using the following set of predefined values:n to take any value between 2 and 50. The choice of the L independent simulated data sets was done using the following procedure. We first considered the following cartesian product of dimension 2γ + 2:L tuples from K without replacement. We then sorted the sampled event times obtaining thus a set of L demographic scenarios. We drew randomly (without replacement) from the set K, rejecting scenarios with identical Mi values in two consecutive components, until we reached L accepted scenarios.Here we sampled φ ∈ Φγ,B. All IICRs were discretized so as to be comparable to PSMC plots .φ ∈ Φγ,B  on these genomes before applying our approach. We thus only ran the PSMC method in the case of the scenarios inferred for the human data so as to integrate the uncertainty due to the PSMC inferential process. The issue of uncertainty is crucial but our aim is not to test the PSMC or other inferential methods. To clarify this we explain below the different types of IICR that could be computed given a scenario n-island model at any time value t, but to generate input data we need a discretization as in . It should be noted that this value of ε is quite small even for double-precision floating-point arithmetic, and thus is only a reasonable choice for validation using exact IICRs .For the validations using the exact IICR in section “Validation using exact target IICRs” we chose for the distance tolerance between a target and an inferred IICR a value of T2 realizations using ms and then building an empirical IICR as in Mazet et al. . The reL = 108 base pairs, using the effective size N inferred by SNIF, a per-base per-generation mutation rate of μ = 1.25 × 10−8 . A summary of how many tests fall within this margin of error (and others) is displayed in Figs. S12 and S19. Altogether, these figures always show the data points near the y = x, hence suggesting that the inferred parameter was identical or very close to the simulated parameters. This is particularly obvious for all the parameters corresponding to scenarios with up to four components, where the nRMSD values stayed below 0.5 . For instance, Fig. t parameters) between the simulated and inferred values for the model parameters. For five- and six-component scenarios the results are still nearly perfect for most of the simulated scenarios but we observe an increasing number of cases  where the parameters are poorly estimated, with the exception of n, M0  which are almost always well estimated also in such cases . In particular, we can appreciate a gradual degradation of the correspondence between simulated and inferred migration values when the number of components c increases, as the nRMSD monotonically increases to over 0.5 for c = 6. These cases can be identified by the dots scattered in the different panels. They start to appear in scenarios with three components, but their number grows with the number of components.A first set of figures Fig. –S18 reprconverged when the maximum number of rounds was reached.These poorly estimated parameters are surprising given the near perfect estimation obtained for most parameter combinations. This is particularly striking because these dots do not seem to be distributed in any clear area of the parameter space. We see at least two possible and nonexclusive interpretations for this result. One is that the search algorithm had not yet ε plays a role in these results, and selecting larger tolerances will tend to produce earlier convergence in general, but not necessarily better results.The maximum number of rounds was set to 500 in all simulations because we had found that less than 50 rounds were more than enough in the first tests carried out with one or two components. The search algorithm might however need more than 500 rounds to reach the optimal solution for scenarios of increasing complexity. We thus asked whether the maximum the number of rounds had been reached in the scenarios analysed and whether the proportion of scenarios with 500 rounds increased with the number of components. We found indeed that the proportion of simulations for which that maximum was reached increased with the number of components. For instance, all five- and six-component scenarios stopped their parameter search at 500 rounds, hence suggesting that at least some had not yet reached an optimum solution. For the cases with one- and two-component scenarios, all 800 independent simulations reached convergence in less than 150 rounds see Fig. . Again, Mi values are very close, thus making the corresponding time of the event challenging to infer.As a test we randomly identified a couple of scenarios with six components that had bad estimates and re-ran the algorithm with 5000 rounds. We found that the distance value consistently decreases with more rounds see Fig. , but thet1 and identify the second change in migration at t2. In such a case the method will assign the inferred t2 value to the set of inferred t1 values and plot it in the t1 panel. This wrongly assigned t2 value will thus appear away from the diagonal in the t1 panel even if it was well-estimated. Such misassignment cases for one parameter will also have consequences for the Mi plots, and thus will generate several misassignments across panels. They are also expected to increase in frequency as the number of components increases and as the ti values become closer to each other. This phenomenon can be observed clearly in the right panels of Fig. c = 5 in Fig. The second possible reason for the poorly estimated parameters in Fig. T2 values show that again the scenarios are generally very well reconstructed  and Mi = 1 for panel (b). This allows us to better appreciate the variance of the inferred migration values in the context of the simulated ones, as well as the component misassignment effect mentioned earlier. Indeed, we note here that the incorrectly inferred migration values are clustered around other simulated values, indicating a mismatch in a particular component assignment which does not affect the rest of the inferred demographic history , and thus the inferred migration value for component i ultimately reflected either Mi−1 or Mi+1. In panel (b) we can observe the same effect with higher intensity because with more components it is more likely for them to be misassigned or misidentified during inference. See Fig. c = 5 components.For example, consider the right sub-panel of (a). We see that most repetitions correctly inferred a value close to ti < 10−3 generations) when the simulated Mi value was 0.1 or 0.2 the inferred values seem to vary between 0.05 and 0.3, suggesting that the method identifies periods with low migration rates but that the exact value is difficult to estimate properly, at least in the recent times. These graphs however summarize extremely different scenarios, including scenarios in which consecutive Mi values may be similar. We thus stress that the quality of the inference is dependent on the timing of the changes in migration rates and on the size of the change in Mi values.These connectivity graphs  and n (the number of islands) for the corresponding model. Panels (a) and (b) correspond to three- and four-component scenarios, whereas panels (c) and (d) show the results for two five-component scenarios, one for which we obtained very good estimates and one for which the estimates were poorer. In panels (b) and (c) the inferred and simulated Mi and ti values are on top of each other as can be seen in the connectivity graphs. Similarly, N and n are also well estimated. Here, the IICR plots also overlap, although this does not always guarantee perfect parameter estimation, as is the case in panels (a) and (d). Interestingly, in panel (a) the first change in migration rate (at t1 = 200 generations) is estimated at around 900 generations due to the stochasticity of the IICR plot. This appears to generate some variance in the estimates of N and n but the connectivity graph shows the same trend (increasing connectivity) as in the simulations. In the case of panel (d) we can see that the method had some difficulty in estimating several of the changes in Mi values. This is not surprising as some of the randomly simulated changes do not seem to lead to major changes in the IICR curves. This generates again some variance in the N and n estimates. We also observe a significant variance in the connectivity graph even if several runs overlap nearly perfectly with the simulated connectivity graph.Figure n-island model, and that some scenarios can be extremely well inferred whereas others may be more difficult depending on their effect on the IICR plots. We also observe that for real data it may be helpful to run the analyses for a varying number of rounds, since too few rounds may negatively affect the quality of the fit. Also, once a scenario has been inferred, it is advisable, as an additional validation step, to simulate data under the inferred scenario and use SNIF to re-infer the parameters. This is what we do with the real human data in the next section.Altogether the validation tests and figures above suggest that our framework is able to infer changes in connectivity under the Figures μ = 1.25 × 10−8 and a generation time of 25 years) together with the best fitting IICR for the model with c = 5 and ω = 0.2. Panel (b) shows the connectivity graphs of the same inferred demographic scenario. We note that the connectivity pattern consisting of a period of relatively high connectivity between roughly 500 kya and 2 Mya agrees with previous results published in Rodríguez et al.  can be used to make explicit the knowledge (or beliefs) of the researcher regarding the accuracy of the PSMC curve. We notice that the Yoruba individual cannot be well fitted in the recent past for any value of ω, even outside of the designated period of recent population expansion.The full set of results related to the inference of human demographies can be found in Figs. n and in panel (b) the reference size N that were inferred from each of the five fitted human PSMCs. Of note here is that all individuals except the Yoruba show a consistent value for these inferred parameters across both number of components and value of ω. The larger variance of the estimated values for the Yoruba individual suggests that a symmetrical island model may not be enough to explain the patterns of diversity in all five sampled human IICRs.Figure Figures n-island model, but the piecewise stationarity of our family of models should still be able to pick up the main demographic events. For example, from an n-island perspective, a merger or joining of two populations (going backwards in time) may be represented by an increase in gene flow, although this effect may be confounded by the actual changes in both the sizes of the populations and migration rates taking place during these events. Also of note is the fact that the first merger event is not visible to our method because it marks the start of the recent population expansion and is thus excluded from the distance computation.It is clear that the nature of this model does not lend itself to be exactly modeled by a symmetrical ω did not make a great effect in this set of inferences  of Fig. n and N across the different values of c and ω. This may indicate a weaker link to an underlying n-island model.The inferred number of demes and their relatives sizes for each population can be observed in Fig. c = 5 components and the more recent-weighted value of ω = 1. These results also serve as additional validation that our method will not return the same parameter values regardless of the source of the data. They also suggest that the C3PO model is unlikely to be a good model to understand questions about ancient human structure and evolution.In general, there is little agreement between the demographic histories inferred by our method from the PSMC data and the simulated IICRs from the C3PO model. This is expected because of how the two models have fundamentally incompatible structures, not only regarding the island versus tree aspect, but also due to the size changes in the C3PO model that affect the IICR potentially as much as gene flow does. However, we do identify the approximate timings of the two visible demographic events when using c = 1), and increases linearly with the number of components. For the M parameters it reaches a value of about 0.5 at six components, and we see that the first and last components are better estimated than the middle ones. It is likely that the component misidentification phenomenon is contributing to this effect. The number of islands n and the reference effective size N are consistently well estimated, reaching an nRMSD of about 0.1 in the worst cases. The ti parameters exhibit the worst nRMSD values, varying between 1 and 2 in the worst cases. Although in these cases, the fact that time is log-spaced and spans several orders of magnitude causes outliers to have a disproportionate contribution to this statistic.Our validations show that the inference framework presented here is able to accurately infer structure parameters (number of islands and their sizes) within a symmetrical island model given an IICR estimate like the PSMC. It is also able to date up to five events of changes in migration rate  with good precision and consistency, as long as the underlying model is compatible with a symmetrical island model. The nRMSD  of the simulated vs. inferred scenario parameters is zero for stationary scenarios  displayed less consistent evidence of this finding, which may indicate that more complex models  could be needed to explain the full complexity of the data.N and a comparable period featuring a significant increased of gene flow between 600 Kya and 2 Mya. Note that the timing in years and the deme sizes in Rodríguez et al. . They may also be in the form of multiple IICRk curves where k is the number of sampled haploid genomes. Indeed, the IICR of Mazet et al. (k = 2, and this is the IICR that we have been studying in our previous works. However, the concept can be extended to more haploid genomes in the same way that the MSMC method (Schiffels and Durbin, Tk. The precise concept of the IICRk is currently being developed in a separate study. These approaches may prove beneficial in choosing between structured and non-structured models. Indeed, Grusea et al. (n-island model. Finally, the incorporation of larger samples not only enables exploring more complex scenarios, but it also allows using other summary statistics to complement the IICR, most notably among them the AFS, which is widely used for the purposes of demographic inference.Another potential direction is to use multiple IICR curves simultaneously during the inference process. These multiple IICRs may come in the form of more than one IICR sampled from an asymmetrical demographic model (for which the initial sampling deme t et al.  was defia et al.  shows thIn summary, we have presented here an inference method for automatically estimating demographic parameters under a piecewise stationary symmetrical island model that uses the IICR as its summary statistic. The underlying methodology consists in quantifying the discrepancy between a target IICR and many simulated IICR curves for a large number of candidate scenarios, and using this metric to drive a global optimization process. With a large number of validations we have shown that the method works accurately and consistently for a diverse range of parameter values, and we additionally showed an application to human data that agrees with and improves upon previously published results using similar approaches.N(Rodríguez et al., We believe that despite its current scope, our method can be of great value during the initial exploration of the parameter space for simple models, and thus can also provide a starting point for manually fitting the IICR with models that could express spatial structure and varying Article supplementary materials


An increasing number of people with chronic medical disabilities are living longer and into old age due to the growing medical and technological advancements over the past half century. We used grounded theory to examine the lived experience of aging “with” a disability in a non-elderly population. On average, participants were 37 years of age at the time of interview. The average time since diagnosis was 17 years and ranged from 3 to 34 years. Many worked full-time outside of the home and some held advanced or graduate degrees. Of the 35 participants interviewed, three-quarters expressed worries about the future and aging, specifically related to physical limitations of having CD. The other 25% talked about learning to accept the diagnosis and ‘moving forward’ with their life as they age. All participants described the difficulties of fatigue and energy limitations. Planning of life was limited to 24 hours — a direct consequence of functional limitations of a relapsing-remitting disease. The most prominent theme that emerged from participants’ narratives to explain aging invisibly with a chronic illness was quantifying energy into ‘spoons’, a way of measuring the stock of their energy on any given day. These findings translate into important insights into the process of aging for those who live and age “with” Crohn’s as their everyday lives are immersed in managing the varying whims of this illness.