Structural properties of cohesive powders are dominated by their microstructural composition. Powders with a fractal microstructure show particularly interesting properties during compaction where a microstructural transition and a fractal breakdown happen before compaction and force transport. The study of this phenomenon has been challenging due to its long-range effect and the subsequent necessity to characterize these microstructural changes on a macroscopic scale. For the detailed investigation of the complex nature of powder compaction for various densification states along with the heterogeneous breakdown of the fractal microstructure we applied neutron dark-field imaging in combination with a variety of supporting techniques with various spatial resolutions, field-of-views and information depths. We used scanning electron microscopy to image the surface microstructure in a small field-of-view and X-ray tomography to image density variations in 3D with lower spatial resolution. Non-local spin-echo small-angle neutron scattering results are used to evaluate fitting models later used as input parameters for the neutron dark-field imaging data analysis. Finally, neutron dark-field imaging results in combination with supporting measurements using scanning electron microscopy, X-ray tomography and spin-echo small angle scattering allowed us to comprehensively study the heterogeneous transition from a fractal to a homogeneous microstructure of a cohesive powder in a quantitative manner. The cohesiveness of powders is determined by the size of the individual particles and their grain morphology. If the particles are small enough forces that drive cohesion become dominant. Electrostatic, capillary and van der Waals forces impact the behaviour of cohesive powders and especially their compaction behaviour. Powder compaction makes it possible to understand the impact and strength of the different forces and is an important technological process when it comes to the production of nanocrystals. Besides the forces acting within the powder its microstructure is another important factor determining compaction behaviour. As pointed out in5 fractal powders are a special type of powder, with a compaction behaviour that differs compared to ballistically deposited powders. Fractal powders typically retain their structure until a critical force is applied that breaks down the fractal structure after which the powder4 behaves as if ballistically deposited. Despite the significance of the powder microstructure its characterisation and investigation has traditionally been a challenge due to the variety of length scales that are subject to change during powder compaction. Ranging from micrometre sized structures to macroscopic variations.Powders form the foundation of many technological and fundamental achievements in fields such as the production of nanocrystals6 or small angle X-ray scattering7 and neutrons, such as spin-echo small-angle neutron scattering (SESANS)8. These methods however fail to deliver sufficient spatial resolution. High resolution X-ray tomography11 and scanning electron microscopy (SEM)12 are another approach for the study of microstructures that does give spatial resolution but fails to provide a relevant large field-of-view that is required to study heterogeneous behaviour on a macroscopic scale.Typically, grain morphology of powders are studied using scattering methods with X-rays such as X-ray diffraction14 of the neutron grating interferometry (nGI) method15 and especially the recently developed sub-pixel correlation length imaging (ξDFI) technique18 in combination with supporting methods such as SEM, X-ray computed tomography (X-CT) and SESANS to study the compaction of a cohesive powder. We investigate how compaction with a pyramidal shape, at various densification states, influences the microstructure over the range of centimetres and how it produces a heterogeneous breakdown of the fractal microstructure. Furthermore, we are able to visualize how the structural change from fractal to ballistic is transported through the macroscopic sample by utilising the unique capabilities of ξDFI to study microstructural variations in a large centimetre sized field-of-view that would not be accessible otherwise.In this article we will use the neutron dark-field image (DFI) contrast19. Sipernat-310 is a silica powder designed to have a large surface area of 700 m2/g. The combination of large surface area with the relatively small particle size of 8.5 μm (d50) makes Sipernat-310 an ideal candidate to study cohesive powders, as these are the factors driving cohesion. In addition to the structural properties of Sipernat-310 the material composition of silica, SiO2, makes it a material with relatively low neutron absorption. The absorption cross-section for 4.1 Å neutrons is as low as 0.004 cm−1 20. The low neutron absorption allows us to record dark-field data without many neutrons being attenuated and thus not contributing to the uncertainty of the dark-field signal21.The powder sample studied in this paper is the commercially available Sipernat-310. Sipernat is a series of products of precipitated silica, aluminium and calcium silicatesin-situ powder compaction can be achieved. Furthermore, SEM is a surface sensitive technique, not giving information about the bulk properties of the sample. Therefore, we extend the direct imaging analysis by using X-CT to study agglomerates and larger structures. While X-CT offers a relatively large field-of-view and information about the bulk it does not enable the study of microstructural changes directly due to limited spatial resolution. Here the use of SESANS enables us to observe microstructural changes in the powder during compaction in the bulk, but without spatial resolution. The scattering nature of the technique makes it possible to verify scattering models that describe microstructural changes. All the knowledge gained from the supporting methods of SEM, X-CT and SESANS allowed us to use DFI and especially ξDFI to study the compaction of the powder sample with a pyramidal piston that introduces spatial variation in the microstructure on cm length scales.We start the analysis of the powder compaction with high-resolution SEM imaging to directly image the microstructure of the powder and verify its fractal as well as cohesive properties. However only small field-of-views can be realised and no A loose, not compacted, sample was prepared by pouring the Sipernat-310 powder on a sticky graphite tape, which was then mounted in the SEM. A compressed sample was prepared by using a mechanical device  of G(z) isAs defined inχ is defined asχ leads to the relation of χ and a for the model used here ofThe combination of Equations for γ(r) and 0SESANS to strongly compacted d4SESANS, of the powder as seen in Fig. 0SESANS. The sample is compacted stepwise with the indicated depths all the way to the green line on the bottom, resembling d4SESANS. Figure G(z) for each compaction. We recorded the extracted parameters in Fig. We used this model to fit the SESANS measurements for five different densification states, from loosely poured sample in dΣt and characteristic structure sizes a from the SESANS curves indicate behaviours that allow the observation of fractal breakdown of the microstructure as an averaged signal over the whole sample, thus representing a mixture of fractal and non-fractal structure. From densification state d0SESANS − d2SESANS in Fig. Σt increases. This indicates an increase in concentration without introducing structural changes, keeping the fractal microstructure intact.During powder compaction the extracted 2SESANS to d3SESANS the characteristic structure size decreases while Σt stays constant, indicating a breakdown of the fractal microstructure, which is accompanied by a change in characteristic structure size. The constant Σt is a consequence of an increased concentration, which is offset by the change in structure size. The combined behaviour of decreased characteristic structure size with constant Σt thus indicates a phase transition from fractal to ballistic microstructure in progress.Moving from d4SESANS to d5SESANS is characterised by a decrease in characteristic structure size while at the same time an increasing Σt. This is explained by a further compaction of the ballistic structure without additional phase transitions to other microstructures. Thus, the random orientation of a ballistic system is further compressed and inhomogeneities have disappeared, as seen in the X-ray tomographies and the SEM images of the compacted powder.Densification d16λ represents the incoming wavelength of the neutron, Ls the sample to G2 grating distance and p2 the period of G2  of the sample in each pixel of an image. Thus, we are able to produce spatially resolved function of the sample that characterises the microstructure of the sample pixelwise with scattering functions, that are the same as measured in SESANS16.The combination of SEM, X-CT and SESANS illustrates the behaviour of the powder during compaction for multiple length scales and made it possible to find a scattering model that describes the microstructure of the powder. In the following we apply ξDFI to study this behaviour during compaction with a pyramidal shaped piston. We refer to ξDFI as the method of changing the autocorrelation length ξ of the neutron grating interferometer, which is defined byThe compaction device as shown in Fig. s as shown in Fig. TaPy25. The change in dark-field signal for the variation in distance was analysed with a MATLAB script that fits the change in each pixel with a custom function as shown in Fig. In order to extract the projected density correlation function, we recorded DFI data sets at 11 equidistant values of Lξ. This experimental approach allows us to scan the same functions as in SESANS measurement, but in each pixel of an image, by varying ξ, which is analogous to the spin echo length z. Thus, we a are able to extract the fitting parameters presented in Fig. in-situ. This is possible due to the high penetration power of neutrons.The recording of DFIs at varying sample to G2 distances allows us to scan the autocorrelation length of an imaging setup by tuning the parameterThe DFI contrast in neutron grating interferometers is described by the same equation as SESANS:Σt and the characteristic structure size a as shown in Fig. Thus, we use the same fitting model that has proven to describe the microstructure well in the SESANS measurements to extract 0DFI), two intermediate compaction states (d1DFI and d2DFI) and one fully compacted state (d3DFI). At each of the compaction states we recorded a full scattering function in each pixel of the image and fitted the model and created maps of the fitting parameters Σt and a.We built a powder compaction setup from Aluminium, as illustrated by the sample in Experimental section Fig. 0DFI to d3DFI. The top part of the Figure presents the Σt maps of the powder at varying compaction states. The values correspond to the blue bars in Fig. Σt significantly and only visualises the change from a macroscopically heterogeneous system to a homogeneous system.Figure 1DFI and d2DFI where close to the impinging pyramid, especially in the corners, the fitted values show a significantly decrease in comparison to the not compacted state in d0DFI. The smaller value extends downward with a propagation front that becomes larger for d2DFI compared to d1DFI. The bottom of the sample does not show any change in microstructure in d1DFI and d2DFI and stays the same as in d1DFI. Thus, we observe the breakdown of the fractal microstructure of the powder at the edges of the pyramid and extended towards the bottom of the sample where the fractal nature is still intact.The parameter maps in the bottom part of Fig. 3DFI corresponds to the bottom part of Fig. 3DFI. This state exhibits no heterogeneities anymore for all probed length scales, from SEM images over X-ray tomographies to the DFI measurements.The final compaction state d5 this behaviour is an important factor for compaction properties of a powder. We observed the homogenising behaviour for length scales of μm in SEM to mm in X-ray tomography.The combined information from SEM, X-CT, SESANS and ξDFI illustrates the structural change of a cohesive powder from a fractal microstructure to a homogeneously compacted state. As pointed out in5. We used the SESANS results to verify scattering models by fitting them to the SESANS data. We then used this model for the DFI data to extract spatially resolved information.The phase transition from a fractal structure of the loosely poured powder to a homogenous distribution is characterised by a decrease in size of the inhomogeneities measured using SESANS. This breakdown of the fractal structure does not happen immediately but only after some initial compaction, as proposed inThe parameter maps in Fig. a. This is the result of forces acting upon the powder and causing the fractal structure to collapse. This also shows that while some of the force is transported through the powder, as evident by the partial homogenisation of the density parameter Σt it is not enough to break the fractal in the bottom of the sample. The fractal breakdown rather happens as a propagation front and covers an increased part of the sample with increased compaction.Just under the impinging pyramid we observe a change in parameter At full compaction the samples microstructure is homogeneous, in accordance with the SEM measurements and does not show any inhomogeneities anymore. Thus, we observe the breakdown of the fractal structure in parts of the sample during compaction, while other parts still retain their fractal structure.5, in Figure 12 in the reference. The simulation suggests that a compaction of an initially loose, cohesive powder leads to a fractal breakdown close to the piston coming from the top. The subsequent breakdown of the fractal structure in the whole sample, then happens by pressure transport through a propagation front. This is in accordance with the ξDFI measurements in Fig. a initially drops close to the pyramidal piston. This is an indication for the breakdown of the fractal microstructure, as argued above. The measurements show how ξDFI offers unique insight into the fractal breakdown of a powder structure and shows that the behaviour is in good agreement with simulations that show a behaviour that has not been visualised in transmission experimentation before.This measurement confirms the contact dynamics simulation (CDS) as reported in literatureThe experimental data presented in this work shows the application of a set of characterisation techniques to comprehensively study the heterogeneous transition from a fractal to a homogeneous microstructure. We combined SEM imaging with high resolution with X-CT with a large field-of-view to investigate the compaction of a cohesive powder at the micro and macro scale. In order to comprehensively study the microstructural changes we applied SESANS and confirmed a scattering model that describes two-phase random media. During compaction we were able to present the evolution of the characteristic size of the inhomogeneities in the sample.The combined knowledge gained from SEM, X-CT and SESANS was then used to apply ξDFI to a compaction experiment of the same powder using a pyramidal shaped piston that introduces spatial variations in the sample. The combination of macroscopic imaging resolution with microstructural information by fitting the model confirmed with SESANS enabled us to visualise the propagation front of the breakdown of the fractal microstructure using ξDFI.The scanning electron microscope used for the results presented in this work was a ZEISS NVISION microscope. Eight images have been recorded at four magnifications (M1–M4) of 200x, 500x, 2000x and 5000x with corresponding pixel sizes of 560 nm, 223 nm, 56 nm and 22 nm, respectively.26. The X-ray source is a Hamamatsu L212161-07 micro focus tube which was operated at 60 kV tube voltage and 100 μA tube current. A Varian 2530HE flat panel detector was used. The detector was configured to collect 16-bit images with a gain setting of 2 and 5 seconds exposure time per sample rotation position. A total of 626 projections have been recorded over 360 degrees adding up to 52 minutes exposure time per tomography.The X-ray tomography experiment was conducted at the ICON beamline at the Paul Scherrer Institut using its X-ray tomography optionThe SESANS data was recorded at HOR Reactor at the Reactor Institute at TU Delft, Netherlands. Spin Echo SANS is performed at a dedicated beamline that can probe structure sizes from 20 nm up to 20 μm using a monochromatic beam of 2 Å.The ξDFI experiments were conducted at the beamline ICON at PSI. A dedicated setup at the 5th Talbot distance was used. A sketch of the setup is shown in Fig.


The purpose of this study was to present a surgical technique for taking out universal screw and nail caps which were difficult to removed. We used a variety of industrial hex wrenches, dental drills, and other equipment to take out internal hex nuts with different specifications (32 pieces) and universal screws (15 pieces) in 28 patients. A total of 32 nuts were taken out, 3 of which were polished by the industrial drill. A total of 17 were spun by hand, 2 were spun by locking pliers, 10 were turned by “I” type screwdriver, and 3 were turned by bone blade. A total of 15 screws were taken out, 9 of which were removed with a wrench and the other 6 by means of locking pliers after re‐fixing with a truncated titanium rod. The novel technique is simple and provides a solution following failure of a supporting device. The pedicle screw internal fixation system is widely used for the treatment of spinal fractures and degenerative instability10–T12 in 3 cases, T11–L1 in 4 cases, T12–L2 in 8 cases, L3–L5 in 5 cases, and L4–L5 in 8 cases. Fractures had healed and bone graft fusions were intact in all patients.The 28 patients in this study were aged between 33 and 62 years, with an average age of 43 years. Among them, there were 22 men and 6 women, 16 with spinal fractures and 12 with degenerative diseases of the spine. The operation time ranged from 10 to 83 months after the last operation. Internal fixation sites: TAll patients were operated on in prone position under general anesthesia, and internal fixation screws were exposed through conventional posterior midline incision. This study focused only on the screw removal procedure.A wide variety of industrial‐sized hex wrenches Fig.  were steA wrench was selected that best matched the hexagon in the groove. It was placed in the groove at the end of the screw to loosen the screw. If the hexagonal groove in the tail of the screw had slid or was covered by bone tissue, we cut the titanium rod which had been removed earlier to approximately 1 cm with a rod breaker device, which is a commonly used instrument for spinal internal fixation surgery, and selected a nut to fix the 1‐cm titanium rod firmly in the groove of the end of the screw Fig. , consoliAll screws were completely removed. All patients in this study were followed up, with a follow‐up time between 11 and 24 months, and an average follow‐up time of 13 months. All the postoperative incisions healed well. All patients were followed up with X‐ray and CT examination after surgery, indicating good bone healing at the nail tract, no foreign body residue, no pain in the spine with good activity, and no complications of infection and nerve injury.The method is easy to implement and is a novel technique that has not been described previously in the published literature. It provides a solution following failure of a supporting device. However, grinding the nail will prolong the operation time. If a new type rod of breaker instrument that is similar to titanium mesh scissors can be designed, the titanium rod could be cut off directly by the tail of the screw without increasing soft tissue damage.Attention should be paid to the application process: (i) the inner hexagon wrench should be placed at the lowest position of the nut groove and it is best matched with the inner hexagon, and rotating the wrench should not be done with force to avoid causing the screw groove to slip; (ii) when grinding the nut with the dental drill from the inside out, use its side to grind the groove wall of the nut or tilt the drill from the top down, and choose between the two arms of the nail tail; (iii) the industrial hexagon wrench and dental drill should be updated timely to avoid screwing pedical screw nut slippery and breaking dental drill when grinding; and (iv) when grinding the two sides of the nut, the upper and lower openings of each side should be as wide as possible, and the screwdriver or bone blade should be changed if necessary during the grinding process to avoid openings that are too wide on both sides of the nut.


We study how quantum systems that propagate in the spacetime of a rotating planet are affected by the curved background. Spacetime curvature affects wavepackets of photons propagating from Earth to a satellite, and the changes in the wavepacket encode the parameters of the spacetime. This allows us to evaluate quantitatively how quantum communications are affected by the curved spacetime background of the Earth and to achieve precise measurements of Earth’s Schwarzschild radius and equatorial angular velocity. We then provide a comparison with the state of the art in parameter estimation obtained through classical means. Satellite to satellite communications and future directions are also discussed. Quantum communications is a rapidly growing field which promises several technical improvements to current classical communications. One example is the use of quantum cryptography which would make communications more secure, thanks to more robust protocols than the classical ones . More fuKnowing quantitatively how quantum communications are affected by the curved spacetime background would enable to compensate undesirable relativistic effects in future quantum technologies. Precise values of the necessary corrections in such quantum communication setups can only be obtained with an accurate knowledge of the spacetime parameters. We thus need to employ techniques from the field of quantum metrology, which aims at exploiting quantum resources, such as entanglement, to estimate physical parameters . Within ad hoc implementation of proper time in a classical quantum mechanics scheme. Furthermore, it was shown that these effects can have potentially high impact on specific types of quantum key distribution (QKD) protocols [Typical applications of quantum metrology range from phase estimation in quantum optics to estimating the gravitational potential with Bose Einstein Condensates (BECs) , 6. Howerotocols . This diIn this work we extend the analysis carried out in previous works which investigated quantum estimation techniques in scenarios where photons are exchanged between Earth and a satellite . There, We find the error bound on the equatorial angular velocity of the Earth and compare it with that achieved with cutting edge technology. The rate of improvement of quantum optical technologies and the rapid increase of the control over quantum systems suggest that in the near future our scheme might provide a reliable way to outperform current technologies based on classical means.The paper is organised as follows. In Section A and B indices denote evaluations at Alice’s and Bob’s events respectively.Throughout the whole paper we employ geometrical units notation , namely M, radius J and Kerr parameter  In this work we consider a spherical planet that rotates slowly. The Kerr metric can be used, to good approximation, to model the spacetime background around the rotating planet . Our worA photon is sent radially by Alice from a laboratory on Earth’s equator to Bob who is in a satellite circularly orbiting at radius mentclass2pt{minimω and peaked at In this work we employ photons which are geometrically radial, namely with vanishing angular velocities K with proper time It is possible to rewrite the annihilation operator  of the sf is the total shifting function that will be made explicit later (notice that we are not using the same definition for f as in [Alice now prepares and sends a wave packet entclass1pt{minimaentclass1pt{minima f as in ). Then oσ and with a frequency distribution of the form: δ defined by: f in terms of the spacetime parameters.A convenient choice of wave packet is a normalised Gaussian wave packet of width entclass1pt{minimak is the tangent vector to the affinely parametrised null geodesic that the photon follows. For simplicity of the computations, we restrain our study to a satellite that follows a circular orbit, i.e. we have θ-motion. Also our photon is geometrically radial, hence: The general frequency shift formula for a photon emitted from Alice on Earth and received by Bob in the satellite reads , 14: 10\A and B subscripts on the quantities Δ and κ denote evaluation at The velocity of our observers are , 16: 12\rator in  thus reanator of , after ee photon .ϵ. One can also notice that, in this limit, photons received on satellites orbiting at radius Plugging  and 20)20) in 1, we obtaA last relevant check is to verify the absence of frequency shift in flat spacetime. Unsurprisingly, we get from the relevant limit of  that in In this section, we apply quantum estimation techniques to find the ultimate bounds on the precision of measurements of parameters of the Earth.In our result  for the We have used the following values: δ: δ parameter of the following form: δ displayed in the Schwarzschild scenario papers [total frequency shift  precision, one can employ  to expreticed in , there iδ and We are also interested in the precision one can achieve for the measurement of Earth’s equatorial angular velocity. The relation between Δδ encoded in the final state δ through the Cramér-Rao inequality as N is the number of probes in the experiment.The most important quantity in quantum metrology is the quantum Fisher information H, which allows to directly compute the bounds on measurements of interest through the well known Cramér-Rao theorem . In parts denotes the squeezing parameter, σ the spread of the frequency distribution of the photon, and Following , we emplIn this section we will focus on applying the previous techniques to estimate the ultimate error bounds on the Schwarzschild radius chnology , 18. TheFor orbits at altitude around nt}δS in  vanishesrried in , it come−8 [We shift our attention to estimating the bound for the equatorial angular velocity of the Earth. We get: der 10−8 , as wellder 10−8  and of oder 10−8 . HoweverC subscript are the same as Bob’s but substituting ϵ with η. Similarly to Bob’s ϵ, I is Earth’s moment of inertia. For a photon sent from Charlie on a low Earth orbit  are propagated to the other user . The optical modes from memories A1 and B1 are then entangled at the receiver’s lab and similarly for A2 and B2. Alice then beam splits A1 and A2 and each output branch of the beamsplitter is measured by a detector. Bob performs the same operation with B1 and B2. If each user has one detector clicking, the protocol has been working successfully. The probability for Alice and Bob to share the same bit, i.e., the probability for memories A1, B1 and A2, B2 to have the same state is δ parameter and the wave packet distributions. The QBER is the rate of bits that were not shared between Alice and Bob, i.e. In order to complete our analysis of the possible means of detecting these effects, we can compute the QBER for a simple QKD protocol, following closely what has been done in . Alice aδ in (−6 for communications to LEO orbits and 10−4 to GEO orbits. For orbits at radii −10. Hence, these orbits are recommended to reduce the QBER in Earth to satellite quantum communications.In the Earth to satellite setup, the contribution of the rotation to δ in  is negli−4 too. However, taking into account atmospheric effects in the ground to satellite case would make the satellite to satellite scheme more accurate.In the satellite to satellite case, the Schwarzschild part of the shift is always dominant. The value of the shift between a LEO and a GEO satellite is similar to the GEO orbits case in the Earth to satellite scheme, hence the value for the QBER for quantum communications between a LEO and a GEO satellite is of order 10In this paper we have derived an expression for the general relativistic frequency shift of a photon travelling through Earth’s rotating surrounding spacetime. We have specialised to photons travelling with vanishing angular velocities from an equatorial laboratory on Earth towards a satellite revolving in the equatorial plane of the Kerr spacetime. This study provides analytical insight and successfully extends previous results obtained for Schwarzschild spacetime , 8. We h


In the variant of the well studied nurse rostering problem proposed in the Second International Nurse Rostering Competition, multiple stages have to be solved sequentially which are dependent on each other. We propose an integer programming model for this problem and show that a set of newly developed extensions in the form of additional constraints to deal with the incomplete information can significantly improve the quality of the generated solutions. We compare our solution approaches with the results obtained in the competition and show that the extended model achieves results competitive with the competition finalists. The automated generation of high quality staff schedules, in particular for hospitals, has been an important problem for over 40 years. Multiple variants and solution approaches exist [to be found e.g. in surveys by Ernst et al.  and den stepping horizon approach.Ceschia et al.  proposedThis multi-stage setting poses two unique challenges for solvers: The dependencies between weeks make it necessary to take the solutions of previous weeks into account during the evaluation of the quality of a schedule. Publications treating this issue are by Glass and Knight , SalassaFurther, and not explored in the previously mentioned papers, is the fact that due to the incomplete information during all weeks but the last, the generated solution can no longer be guaranteed to be optimal even if each week is solved to optimality. More so, a naive model that is not adapted to this setting will produce imbalanced schedules that incur large penalties in later weeks as options are restricted excessively by the solutions of the previous weeks. It is therefore necessary to allow for the existence of future scheduling periods already during the solution of the current stage. While e.g. Salassa and Vanden Berghe  successfThere have been 15 submissions to the INRC-II, with seven of these advancing to the final round. The results for all participants are available on the competition website,Several IP formulations have been previously used for nurse rostering problems, including the problem proposed in the First International Nurse Rostering Competition INRC2010)  by Integer Programming. As in this problem a multi-stage formulation is used, the application of previous IP approaches is not sufficient to obtain good solutions that take into consideration future scheduling periods. Therefore, novel formulations are needed to cope with this new problem. We first propose a basic IP formulation Sect.  for the We evaluate our formulations in Sect. Practice and Theory of Automated Timetabling Mischek and Musliu .S1. Insufficient staffing for optimal coverage (30): The number of nurses assigned to each shift and skill should not be smaller than the optimum staffing. The penalty is multiplied by the number of missing nurses.S2. Consecutive assignments (15/30): The length of each shift stretch (weight 15) and work stretch (weight 30) should be within the bounds defined for the shift type resp. the contract of the involved nurse. The penalty is multiplied by the number of missing or surplus assignments.S3. Consecutive days off (30): As before, the length of each rest stretch should be within the bounds defined in each nurse’s contract. The penalty is multiplied by the number of missing or surplus days off.S4. Preferences (10): The requests of nurses for shifts (or days) off should be respected.S5. Complete week-end (30): Nurses with the complete-weekend constraint in their contract should either work both days of the weekend or none.S6. Total assignments (20): Over the whole planning horizon, each nurse’s assignments should be within the bounds defined in their contract.S7. Total working week-ends (30): Over the whole planning horizon, each nurse should not work more than the maximum number of weekends defined in their contract.The complete information necessary to evaluate constraints S6 and S7 is available only after the solution for the last week has been fixed, although they should of course be respected by solvers during all weeks. All sequence constraints  also use the border data from the solution for the previous week (this is provided in the history file).There are four hard constraints that have to be fulfilled by any solution to be regarded as feasible:scenario file: N   set of nursesS   set of shiftsK   set of skillsW||   number of weeksn across planning horizon   maximum/minimum assignments for nurse n   maximum/minimum consecutive working days for nurse n   maximum/minimum consecutive days off for nurse n across planning horizon   maximum number of working weekends for nurse n, or none   boolean, 1 iff either both days of a weekend should be worked by nurse n has skill k   boolean, 1 iff nurse s   maximum/minimum consecutive assignments of shift t may be assigned the day after an assignment of shift s   boolean, 1 iff shift The first set of parameters contains values that stay the same over the whole planning horizon. These values are stored in the week. w   number of the current weekd, shift s and skill k   minimum cover requirements for day d, shift s and skill k   optimum cover requirements for day n requested not to work in shift s on day d    id of last shift worked by nurse s worked by nurse n at the end of the previous week equalities model the hard constraints, as described above.For the minimum consecutive shifts constraints, all patterns that compose a sequence shorter than the required length are prevented. For example, if the minimum number of consecutive night shifts (N) is 4, the patterns {xNx, xNNx, xNNNx}, where x is any other shift or a day off, should not appear.Since each pattern incurs a penalty proportional to the number of missing assignments,  the surplus variables are weighted correspondingly, to ensure that a value of at least the number of missing assignments is necessary to deactivate the constraint.s with a maximum of s is not assigned. Note that contrary to the situation for S2a, violations of this constraint by more than one shift assignment result in multiple matches of the pattern and therefore it suffices to use boolean surplus variables.Equations As before, equations n works either of the days on the weekend. Equations The equations modelling these constraints are again analoguous to those from constraints S2c and S2d, except that days of work and days off were swapped.a et al. . OriginaWhile the basic model described in Sect. In order to take this into account and improve the overall solution quality, we propose the following extensions to the model, in the form of additional (soft) constraints.Looking at the total number of shifts for each nurse, one can see that nearly all nurses exceed their maximum number of assignments .However, since there is no penalty on overstaffing, there is no pressure to avoid unnecessary assignments. Indeed, in some cases it can seem advantageous to assign shifts above the optimal staffing levels in order to fulfil sequence constraints or the complete weekend constraints (S7).However, as soon as the available assignments are used up, high penalties are unavoidable as other constraints (in particular cover constraints and sequence constraints) still have to be fulfilled.This can also be seen from Fig. S8*. Overstaffing: The number of nurses assigned to each shift and skill per day should not exceed the optimal coverage levels.This constraint can be added to the basic IP model with the following inequalities:To avoid this situation, we introduced a new constraint penalizing overstaffing:While the overstaffing constraints already reduce the number of excess assignments over the maximum, they do not differentiate between nurses with different contracts. As a result, nurses with part-time or half-time contracts have the same schedules as those with full-time contracts in the earlier weeks. Consequently, they are not available in later weeks without penalties, as their contracts are already maxed out.Ideally, nurses should be employed according to their contracts during all weeks, with full-time nurses having more assignments per week than other nurses. In part this is already done implicitly, because nurses with shorter contracts usually also have shorter work stretch lengths and longer rest stretch lengths.S6*. Average assignments: The total number of assignments up to the current week must be within the bounds defined in the contract, multiplied by the fraction of weeks that have already passed.This extension generalizes constraints S6 to earlier weeks.To ensure that each nurse will be available until the last stage, their assignments should be distributed evenly across all stages.To give an example, if a nurse has a minimum of 10 assignments and a maximum of 22, then after stage 4 (of 8), they should have between 5 and 11 shifts assigned. Assuming that they already had 7 shifts assigned in stages 1–3, this constraint would require them to have between 0 and 4 assignments in stage 4.If these constraints are satisfied during all weeks, it can be guaranteed that also constraints S6 are satisfied for the whole schedule.The following inequalities model these constraints:Here, fractional limits are rounded such that the limits are always integer numbers and the solutions satisfying S6* always also satisfy S6. We also experimented with different rounding schemes, but this did not influence the quality of the generated solutions.S6*b. Average assignments: In each week, the remaining assignments (not yet used in previous weeks) should be divided equally among all remaining weeks.Continuing the example above, the nurse in question would have between 3 and 15 assignments left to distribute over 5 weeks (stages 4–8). This means that according to constraint S6*b, they should have between An alternative version of constraints S6* can be formulated asThe same argument as above also applies to constraints S7, the maximum number of total weekends. Just like assignments in general, also weekends should not be used up in the early stages, but distributed across all weeks to preserve options.S7*. Average working weekends: In each week, the still available working weekends (not yet used in previous weeks) should be divided equally among all remaining weeks.with the corresponding inequalitiesTherefore, an analoguous constraint S7* can be defined:In addition to the global constraints, solutions for different stages influence each other also at the boundary between weeks.Since the staffing requirements for the next week are unknown in each stage, leaving more options to schedule nurses without conflicts is beneficial. If there are only few good assignments for the nurses with a certain skill, satisfying the cover constraints might become difficult if they do not match one of those options.A common way for schedules to restrict the options for the next stage is via the sequence constraints. For example, let the minimum number of consecutive night shifts , work (b) and rest (c) stretches, each regarding the minimum and maximum stretch length and with their own set of surplus variables.The same reasoning applies to work and rest stretches.s at the end of the week with a length b below the minimum shift sequence length (constraint S2a). If such a block is found, this means that for the first Equations s blocks an assignment of s to the first day of the following week, is covered by Eq. s at the end of the week with a length of at least The case, where a long shift stretch of shift The restrictions on work (b) and rest (c) stretches work analogously, except that the weights of the surplus variables differ according to the number of blocked assignments.In the solutions generated for various instances, we found that violations of sequence constraints most commonly appeared at the boundaries between weeks. In many cases, this is the result of patterns similar to those shown in Fig. In general, not checking the feasibility of completing a multi-shift work stretch in the next week can lead to situations where the last shift stretch can not be extended to the minimum length without violating the maximum work stretch length.S10*. Unresolvable Patterns: For work stretches at the end of the week, there should be a way to complete them in the next week without violating either the maximum work stretch length or the minimum shift stretch length.Assume a stretch of shift s is assigned to nurse n at the end of the week. Then an unresolvable pattern has the following structure: First, a block of at least s (B). Then, the remaining b days up to the end of the week are filled with assignments to shift s (C), where This leads to the following additional constraint:s would be required at the start of the next week. However, together with parts (A) and (B), this would bring the total work stretch length to at least To avoid a violation of the minimum shift stretch length, at least Equations To have an impact on the generated solutions, the surplus variables for the added constraints have to be included in the objective function. The objective function f, to ensure that the penalties from the additional constraints of the extended model are not included in the final result.After a solution has been fixed, the actual penalty has to be recalculated using the objective function of the basic model Obviously, all constraints introduced in this section should be ignored in the last week, as there is no further week to influence.All algorithms were implemented in Java 7, and we used the IBM ILOG CPLEX solver,We trained the parameters of our models using the parameter-tuning framework irace  and S7* (Average Weekends) are grouped together. For this comparison, the weight of each additional constraint was set to a value of 1 to ensure that the focus of the optimization still remains on the original constraints. The only exception is constraint S10* (Unresolvable patterns), since a violation of this constraint directly results in a violation of at least one shift stretch length constraint in the next week and thus warrants a weight of 15 .Figure Considering the two variants of S6*, there is next to no difference between the performance of S6* and S6*b.extended model.The solution quality can further be improved by combining multiple extensions. A combination of S6* (and S7*), S8* and S10* produced the best results, each of the extensions further reducing the penalties of the generated solutions. This will be denoted as the Adding also constraints S9* increased the penalties again, even when S9* was assigned a much lower weight than the other extensions. This is probably connected to the fact that solving models including constraints S9* took nearly twice as long on average and thus optimal solutions could not be found for many stages. However, this cannot be the only reason, as results for models without S9* are also better even for instances where each stage could be solved to optimality.To find optimal weights for the extensions S6*/S7* and S8* (the weight for S10* corresponds directly to the weight of the shifts stretch length constraints), we used IRACE. Both The best values reported by IRACE are Considering solution times, CPLEX was able to solve most weeks to optimality, even for the larger instances. Over the whole set of hidden instances, using the extended model, an optimal solution could be found for 274 out of 360 weeks. The average gap between the best solution found and the final lower bound for the remaining 86 weeks was only 1.90%, indicating that substantial improvements are not to be expected even with much longer running times.For the final evaluation, the extended model was used, with weights for the extensions as shown on Table Due to the extensions, the penalty incurred by the generated solutions is reduced by about 40% on average, in some cases even to less than half the penalty of the basic model. Further, there is no instance, where the extended model produced results that were not at least 20% better than those of the basic model.Compared to those of the finalists in the INRC-II, the results of the extended model are competitive (slightly better than the median), although no new best known solutions could be found. The average rank over all instances is 3.45, placing our results firmly into the top half of the finalists.In this paper, we have proposed and evaluated several original extensions of standard IP formulations for nurse rostering problems in order to deal with multi-stage settings, as described for the INRC-II.We have shown that our extensions significantly improve upon the results of the basic model and achieve competitive results compared to the finalists in the competition.The fact that our model could be solved to (near) optimality in most cases, even under the strict time limits imposed by the challenge, indicates that major improvements cannot be expected from varying solution techniques alone. Instead, future research should be focused on further modifications of the model to distribute the penalties more equally between weeks and avoid blocking options for later weeks. Techniques that try to predict the requirements of yet unknown weeks or distinguish between nurses of different skill sets and contracts could result in even better models.


ACTN3 gene. The aim of this study was to compare the response of individuals with different ACTN3 genotypes at simulated 4500 m altitude on the presence of Acute Mountain Sickness (AMS) symptoms. Twenty-three volunteers  spent 4 hours exposed to a simulated altitude of 4500 m inside a normobaric hypoxia chamber. Lactate and glucose concentrations, SpO2, heart rate and the symptoms of AMS were analyzed immediately before entering the chamber and at each hour of exposure. Statistical analysis was performed using IBM SPSS Statistics 21 software.During the process of acclimatization, when our organism needs to adjust several metabolic processes in the attempt of establishing a better oxygenation, it is normal that individuals present some symptoms that can lead to the disease of the mountain. However, not everyone presents such symptoms and individuals native of high altitudes regions present genetic differences compared to natives of low altitudes which can generate a better acute adaptation. One of these differences is the higher proportion of type I muscle fibers, which may originate from the R577X polymorphism of the Our results point to an association between AMS symptoms and the presence of R allele from R577X polymorphism.We conclude that individuals with at least one R allele of the R577X polymorphism seems to be more susceptible to the effects of hypoxia during the acclimatization process and may develop AMS symptoms. ACTN3 gene undergoes a mutation that results in the exchange of an arginine by a stop codon at position 577 of the protein causing some individuals not to express ACTN3, which is a hereditary deficiency  with the symptoms reported through the Lake Louise questionnaire. This result indicates that there is an inverse relationship between the variables, meaning that the lower the value of SpO2, the higher the probability of the volunteer to report a symptom in the questionnaire . Figure In order to verify which physiological variables could explain the presence of AMS symptoms, we performed a GEE in which we used the HR, glucose, lactate and SpOACTN3 gene, we included in the statistical model the ACTN3 and the glucose data after 3 and 4 h of exposure, since it was in these moments that volunteers presented the symptoms of AMS (N = 114). The results are shown in Table To test our hypothesis of the acclimatization difference of the R577X polymorphism of the 2  and ACTN3 . Considering ACTN3 genotypes, RX  and RR  are associated with Lake Louise, when controlled by the glucose levels after 3 and 4 h. The data expressing these associations are shown in Table The statistical model showed association of AMS symptoms with SpO2 over time, we correlated HR, lactate and glucose to verify their behavior against SpO2 but did not find any variable that showed significant values.In order to investigate which physiological variables could explain the decrease in SpO2 since it is the main inducing factor. Interestingly we could demonstrate in our study an association between SpO2 with AMS symptoms which corroborates a three-month study in 506 mountaineers of different nationalities in the Alps between 2200 m and 3817 m, that applied the Lake Louise questionnaire and measured SaO2 and HR and demonstrated that the main symptom of AMS, headache, is directly related to low SaO2, in addition to high perception of effort and low water consumption [2 was associated with the symptoms reported by the volunteers.Several studies have demonstrated the influence of low oxygen pressure at high altitude with AMS, however, in our study we expected that no volunteer would develop AMS. The reason for this assumption is that we have controlled most of the risk factors such as obesity , physicasumption . Our resACTN3 being a risk factor to AMS, since both of our volunteers that developed the symptoms had the same genotype (RR). Therefore, the association between the ACTN3 R577X polymorphism with the presence of AMS symptoms is the main result of our study. Although several genes have been studied in an attempt to find a relationship with the symptoms [ACTN3 R577X genotypes, showing that individuals with at least one R allele are more susceptible to negative effects of hypoxia during acclimatization. This result, to a certain extent, corroborates previous findings that showed a higher prevalence of X allele in professional mountaineers when compared to normal individuals [We also analyzed the probability of symptoms , 38, 39,ividuals ; higher ividuals  and the ividuals  and in iividuals , which cividuals . In addiividuals , exposurACTN3 genotypes is related to the decrease of SpO2, which is mainly responsible for the presence of AMS symptoms, with headache as the main symptom [ACTN3 may have a faster acclimatization in situations of extreme altitude.The association demonstrated in our study between the symptoms of AMS and  symptom , 19. ThiACTN3 R577X gene polymorphism and the susceptibility to develop the symptoms of AMS caused by a decreased SpO2.We conclude that there may be an association between the R allele of the Due to the fact that our study involves genetic variants, the number of analyzed volunteers may not be significant to show a definitive association. Furthermore, in a normobaric chamber, where adverse situations such as cold, wind and physical activity involved in the process of climbing at high altitudes are not present, the effects presented here may have been suppressed. Therefore, based on these restrictions, we suggest that new studies should be performed by other groups in hypobaric hypoxia in order to confirm the findings of this study.


An alternative surgical approach for downsizing an existed modified Blalock‐Taussig shunt is described as a reoperation in a hemodynamically unstable patient. This method was selected in order to minimize the surgical manipulations in the setting of a critically ill infant. The graft was longitudinally incised creating an oblong shape; the width corresponded to the perimeter of the graft (15.7 mm; Figure Perimeter had to be the same as of the 4 mm graft, so we have marked the width of this oblong to the desirable perimeter (12.56 mm; Figure Dissection of the existed shunt from edge to edge was performed Figure A and theThe patient had an uneventful recovery, and the shunt was functional 6 months later Figure B.None declared.DB: had the main idea for this alternative surgical approach and helped to draft the manuscript. MK: participated in the main idea for this surgical approach and in the design of the manuscript and drafted the manuscript. EG: participated in the design of the manuscript. NG: conceived of the manuscript idea and participated in its design. All authors read and approved the final manuscript.


Dosimetry of ionizing radiation in the presence of strong magnetic fields is gaining increased relevance in light of advances for MRI‐guided radiation therapy. While the impact of strong magnetic fields on the overall response of ionization chambers has been simulated and measured before, this work investigates the local impact of the magnetic field on dose response in an ion chamber. High‐resolution 1D and 2D response maps have been created for two small clinical thimble ionization chambers, the PinPoint chambers 31006 and 31014 .Working on the Imaging and Medical Beam Line of the Australian Synchrotron an intense kilovoltage radiation beam with very low divergence, collimated to 0.1 mm was used to scan the chambers by moving them on a 2D motion platform. Measured current and beam position were correlated to create the response maps. Small neodymium magnets were used to create a field of about 0.25 T. Chamber axis, magnetic field, and beam direction were perpendicular to each other. Measurements were performed with both orientations of the magnetic field as well as without it. Chamber biases of 5 and 250 V in both polarities were used.The local distribution of the response of small thimble‐type ionization chambers was found to be impacted by a magnetic field. Depending on the orientation of the magnetic field, the chamber response near the stem was either enhanced or reduced with the response near the tip behaving the opposite way. Local changes were in the order of up to 40% compared to measurements without the magnetic field present. Bending of the central electrode was observed for the chamber with the steel electrode. The size of the volume of reduced collection near the guard electrode was impacted by the magnetic field.As the here investigated beam and field parameters differ from those of clinical systems, quantitatively different results would be expected for the latter. However, the gyroradii encountered here were similar to those of a 6–7 MV MRI linac with a 1.5 T magnet.Magnetic fields impact the performance of ionization chambers also on a local level. For practical measurements this might mean a change in the effective point of measurement, in addition to any global corrections. Further knowledge about the local response will help in selecting or constructing optimized chambers for use in magnetic fields. On a practical level, this will hopefully lead to a better approach of measuring radiation dose in MR‐guided radiotherapy treatment systems. Specifically this includes the decision of which ionization chamber (or possibly other detector) to use, as well as guidance on how to design an improved detector in order to optimally assess the dose deposited in the patient. The presented results can also be used to verify Monte Carlo simulations of the same setup, which can then be applied in more complex situations and with different beam energies, where measurements are more difficult or impossible.22.1Work was conducted at the Imaging and Medical Beam Line of the Australian Synchrotron,The main beam parameters are listed in Table The chamber was scanned through the beam in a continuous scan using remote‐controlled stepper motors. The ionization currents were recorded at 60 Hz, to produce a point separation of 0.05 mm. Given the approximate beam diameter of 0.1 mm diameter this was considered sufficient. Collection time ranged from few minutes for 1D scans to 2.5 h for the high‐resolution 2D maps.2.2Two ionization chambers, PTW Pinpoint 31006 and 31014  were investigated in this study. They were chosen for their known quality and reliability as well as for their fairly small size. The latter was important as the effort to create a magnetic field increases with the volume for which said field is needed. Additionally, one of the chambers features a steel central electrode while the other one has one made of aluminum, a difference that was thought to be of interest when measuring in a strong magnetic field.A magnetic field was provided by 18 small neodymium button magnets  . The magnets were positioned perpendicular to the chamber axis on either side of the buildup cap Fig. . The capTo assess the magnetic field strength experienced by the ion chambers, measurements with a Hall probe  were performed. Since the probe, which is rectangular in cross‐section, did not fit all the way into the chamber buildup cap used in the experiments, these measurements were performed in a plastic slab setup with space for the probe and the same magnet separation.In the synchrotron beam chambers were scanned free in air with the modified buildup cap in place and with and without the magnets attached. For some scans the direction of the magnetic field was reversed by switching the magnets.As shown in a cut view from above in Fig. The chamber bias voltage was set to the default 250 V as well as to 5 V. The latter was chosen to explore an enhanced effect. Measurements were performed with both polarities.Measurements with nonmagnetic metal in place of the magnets have been performed for a similar measurement setup to confirm that the presence of metal did not impact the pattern of charge deposition in the ionization chamber.3Measurements of the magnetic field strength indicated a field of about 0.25 T in the air volume of the ionization chamber. While the magnets with a 10‐mm diameter measured twice the length of the air cavity of the chambers, there was still some gradual falloff of the magnetic field toward the ends of the chamber with the field strength at the very end of the chamber decreasing down to 88% of that at its center.Line scans of current vs position along the midline of a thimble ion chamber perpendicular to its main axis feature small increases in current on the inside of the chamber walls and a larger double peak at the electrode. This has been observed and described previouslyUsing a standard bias voltage of 250 V 1D scans along the midline of the chamber with the steel electrode showed a small difference between scans taken with and without the magnetic field applied. This effect was found to be enhanced in the measurements with the lower bias voltage of 5 V Fig. . InteresInvestigating the impact of the polarity of the bias showed a stronger effect for +5 V compared to −5 V  in Fig. 4The local distribution of the response of small thimble‐type ionization chambers was found to be impacted by a magnetic field for the commonly investigated geometry where chamber axis, magnetic field, and beam direction are perpendicular to each other. Depending on the orientation of the magnetic field the chamber response near the stem, here represented as measured current, was either enhanced or reduced with the response near the tip behaving the opposite way.These distributions can be explained by the change in pattern of the movement of the electrons in the presence of the magnetic field compared with the generally forward and equally lateral movement in the absence of such field: The paths of the secondary electrons are bent by the magnetic field as described by Meijsing et al, shown in Fig. The distributions in Fig. The found effects correspond with findings from the Monte Carlo simulation by Malkov and Rogers,et al.,The results are also in broad agreement with the effects predicted by Spindeldreier The magnetic field from the permanent magnets used in this study shows a small gradual falloff towards the edges of the chamber, which would not be the case with the field of a commercial MRI device. Given the location of the observed effects this does not take away from the validity of the results. Additionally, different susceptibility of the materials of the components of the chamber would likely have added some small local disturbances of the magnetic field. While the majority of the material is PMMA, which is very MR compatible and would not disturb the field,Lower bias voltages were found to increase the local difference between measurement without and with the magnetic field present. This was seen for the 1D investigations Fig.  as well The steel electrode of the PTW31006 PinPoint chamber appeared to bend slightly under the influence of the magnetic field, as judged by the recorded response. While conceptually not unexpected, this finding is interesting in that it could mean a change in the effective point of measurement of the chamber, especially with stronger fields. A bending electrode would also need special attention in a Monte Carlo simulation.There is some more structure in stem region of the difference plot for the 31014 chamber  than the 31006 chamber . Because the B field affects signal arising in the stem, it is possible that the global response of the chamber at opposite bias voltages may also be B field dependent.5Magnetic fields impact the response of ionization chambers on a local level. The knowledge of where the response changes should be helpful in understanding the response of the whole chamber, and might have other implications, for example, this might mean a change in the effective point of measurement, in addition to any global corrections. Further knowledge about the local response will help selecting or constructing optimized chambers for use in magnetic fields.The authors have no relevant conflicts of interest to disclose.