The functional results of total elbow arthroplasty (TEA) are controversial and the medium- to long-term revision rates are relatively high. The aim of the present study was to analyze the stresses of TEA in its classic configuration, identify the areas of greatest stress in the prosthesis–bone–cement interface, and evaluate the most wearing working conditions.By means of a reverse engineering process and using a 3D laser scanner, CAD (computer-aided drafting) models of a constrained elbow prosthesis were acquired. These CAD models were developed and their elastic properties, resistance, and stresses were studied through finite element analysis (finite element method—FEM). The obtained 3D elbow-prosthesis model was then evaluated in cyclic flexion–extension movements (> 10 million cycles). We highlighted the configuration of the angle at which the highest stresses and the areas most at risk of implant mobilization develop. Finally, we performed a quantitative study of the stress state after varying the positioning of the stem of the ulnar component in the sagittal plane by ± 3°.The greatest von Mises stress state in the bone component for the 90° working configuration was 3.1635 MPa, which occurred in the most proximal portion of the humeral blade and in the proximal middle third of the shaft. At the ulnar level, peaks of 4.1763 MPa were recorded at the proximal coronoid/metaepiphysis level. The minimum elastic resistance and therefore the greatest stress states were recorded in the bone region at the apex of the ulnar stem (0.001967 MPa). The results of the analysis for the working configurations at 0° and 145° showed significant reductions in the stress states for both prosthetic components; similarly, varying the positioning of the ulnar component at 90°  resulted in better working conditions with a greater resulting developed force and a lower stress peak in the ulnar cement.The areas of greatest stress occur in specific regions of the ulnar and humeral components at the bone–cement–prosthesis interface. The heaviest configuration in terms of stresses was when the elbow was flexed at 90°. Variations in the positioning in the sagittal plane can mechanically affect the movement, possibly resulting in longer survival of the implant.Level of evidence: 5 Total elbow prosthesis  is an orthopedic surgical technique that involves the total replacement of the elbow joint. First performed in 1925 by Robineau . The unlAlthough there has been a certain increase in the number of TEA operations, this number remains far below that of prosthetic replacements of joints such as the hip, knee, and shoulder, which have a shorter survival and a higher rate of reoperation. Basically, in elbow prosthetic replacement, there is a higher rate of revision compared to other more prosthetic and less frequently revised joint districts. The data reported in the literature show that most cases of elbow prosthesis failure are due to aseptic loosening phenomena (18–48%) –5, polyeTo date, there is little literature available on TEA positioning, on the biomechanical functioning of a TEA, and on how possible modifications of the implants, the mounting configuration, and the surgical technique can improve the functionality of a prosthetic elbow and consequently the long-term survival.The aim of our work was to study the tension stresses, the different geometric configurations, and the positioning of the prosthetic components. This was performed to identify the optimal prosthetic configuration and positioning in order to evaluate the reduction in stress conditions during flexion–extension movement in the aforementioned bone–prosthesis–cement interface.®, the third generation of the St. George prosthesis, without a radial capital component . After analyzing each of them, the improvement action was subsequently undertaken in order to find a mounting configuration that would minimize the tension at the bone–prosthesis–cement interface for a static load of 2 kg, with the recommended working conditions simulated for repetitive flexion–extension efforts (> 10 million cycles) in a prosthetic patient. The analysis began with the generation of a number of "satisfactory" planes which cut the models at different heights along their lengths Fig. . Each ofE), Poisson's ratio, or transversal contraction coefficient (ν).In order to reduce the computational load of the FEM analysis, it was decided to clean the surfaces of the prosthesis models—having been obtained using a 3D scanner, they each had a mesh that made the surface rather irregular. It was considered acceptable to bore the holes and flatten the surfaces by removing material: the objective of the study was, in fact, to analyze the stress state in the cement and not the response of the prosthesis Fig. . After tThe prosthesis is made of a chromium-cobalt-molybdenum (Co-Cr-Mo) alloy, while the cement is a thermoplastic polymer of polymethylmethacrylate (PMMA). In particular, the characteristics of PMMA were obtained from the data provided by Completo et al. , the cha k is large enough for them to avoid being stretched. The idea was to test the model when the muscles exert their maximum force, which consequently corresponds to the maximum force that they would be able to withstand. We therefore arrived at the final 90° configuration (Fig. As for the loads, it was decided that a force would be applied to the distal ulna which reflects the optimal conditions for each of the chosen angle configurations between arm and forearm, and the total moment arm that the muscles exert was then determined; from this bending moment, the resulting force on the extremity of the ulna was subsequently determined. The muscles were simulated as springs whose elastic coefficiention Fig.  in whichThe first analysis to be presented is that relating to the 90° configuration between arm and forearm. First of all, the stress states at the bone level were recorded, measuring them in terms of the von Mises criterion or criterion of maximum distortion at both the ulna and the humerus Fig. . In partThe results obtained for the maximum and minimum post-implantation bone strain of the ulnar prosthetic component are those shown in Fig. The von Mises stress states were therefore also recorded at the level of the concrete lining layer. The results obtained are illustrated in Fig. The results show peaks in the von Mises stresses of 10.544 MPa and 27.573 MPa for the ulnar components in the 0° and 145° configurations, respectively. The maximum values recorded were, on the contrary, 1.8739 MPa and 1.436 MPa for the humeral components in the same configurations (Table The main result in the present study is that during flexion–extension movement with a load of 2 kg applied distally to the elbow, as occurs during minimal daily activity, a high stress on the bone and cement is generated. The greatest concentration of these stresses in the von Mises equivalent is localized in the distal part of the humeral component and in the most proximal part of the ulnar component. These are the areas where a high concentration of stress could cause implant failure if the applied force is prolonged . FurtherThere are various types of TEA, which, based on the connection between the humeral and ulnar components, can be categorized into constrained, semi-constrained, and unconstrained. Currently, most systems are semi-constrained. Therefore, they present a certain degree of laxity at the junction of the components. In the present study, the authors decided to use a constrained system in order to reduce the computational load of the FEM analysis and to evaluate the results as a whole rather than to consider the two semi-prostheses as separate entities. A choice was also made to cement the components, since, as stated by Fevang et al. , cementeThe results of TEA have improved over the last few decades, and this can be attributed primarily to better biomechanical knowledge of joints and implants. TEA, moreover, is a technically demanding orthopedic procedure in which the precision of the restoration of the center of rotation of the implant as well as the correct positioning of the components are associated with better functional results, fewer complications, and therefore longer survival. However, high revision rates are reported, probably due to aseptic loosening from incorrect alignment between the axis of the constraint and the anatomical axis of rotation. In fact, due to aseptic loosening, rates of implants are reported to be between 47 and 77% with various types of prostheses , 11. FewIn a retrospective study on 25 patients operated on for TEA for rheumatoid arthritis or elbow fracture, Lenoir  evaluateEven in the absence of implant loosening, positioning errors still seem to negatively affect the functional results, probably exerting inappropriate stress on the soft tissues. In Lenoir's study, it was also argued that neither the valgus index nor the rotation index is associated with clinical outcomes . UltimatThe main limitation of the present study is represented by the use of simplified mathematical models that may not be fully comparable to complex anatomical situations in vivo; also, it is not possible to relate the study to long-term implant survival. Further, our evaluation takes into account the most common stresses in flexion–extension and not in pronation–supination movements, so it is not possible to evaluate torsional stresses. However, it can be considered that recommending modest activity in daily life may reduce the risk of possible mobilization of the prosthetic components –18.The areas of greatest stress occur in specific regions of the ulnar and humeral components at the bone–cement–prosthesis interface. The heaviest configuration in terms of stresses is the one with an elbow flexion angle of 90°, with the stresses mainly concentrated in the ulnar component. Variations in positioning in the sagittal plane can mechanically affect the movement, possibly resulting in longer survival of the implant. For this reason, a slight posterior offset of the humeral component and a slight anterior offset of the ulnar component are recommended.


Two ways to create rigid versions of flexible models are explored. The rigid model can assume the Model’s Geometry (MG) as if the molecule is not interacting with any other molecules or the ensemble averaged geometry (EG) under a particular thermodynamic condition. Although the MG model is more straightforward to create, it leads to relatively poor performance. The EG model behaves similarly to the corresponding flexible model (the FL model) and, in some cases, agrees even better with experiments. While the difference between the EG and the FL models is mostly a result of flexibility, the MG and EG models have different dipole moments as a result of an effective induction in the condensed phase. For the three water models studied, the property that shows the most difference is the temperature dependence of density. The MG version of the water model by adaptive force matching for ice and liquid does not possess a temperature of maximum density, which is attributed to a downshift of the putative liquid–liquid phase transition line, leading to the hypothesized second critical point of liquid water to manifest at negative pressure. A new three-phase coexistence method for determining the melting temperature of ice is also presented. I.Many water models ignore the geometrical flexibility of the molecule and still provide a good description of various properties of this challenging material.A systematic study of the effect of eliminating the flexibility of a semi-rigid model is lacking in the literature. It is not entirely clear which physical properties are most affected by explicitly modeling the vibrations of the OH bond and HOH angle in water. In force field development, constraining stiff vibrations as rigid is a routine practice,In this study, we explore two different practices for generating rigid versions of a flexible model. As will be discussed later, similar considerations also apply when a flexible version of a rigid model is created. Although we will restrict ourselves to water models the general principle should apply to other semi-rigid small molecules. We showed that the most straight-forward model geometry based approach for generating rigid models would lead to systematic errors, whereas simply using the mean geometry under the desired thermodynamic condition will lead to a large improvement in measured properties. Some properties, such as temperature dependence of density, are found to be quite sensitive to small differences in the rigid body geometry.To confirm the generality of our conclusion, we created rigid versions of three different flexible water models, BLYPSP-4F,The study will be presented in five sections. After the Introduction, the methods for generating rigid versions of a flexible model are presented in Sec. II.The relative merits and shortcomings of flexible and rigid models have been studied before,The most straightforward way to create a rigid model is to use the Model Geometry (MG) of the force field. In this case, the geometry of an isolated monomer will be maintained with a restraint algorithmqH is the charge on the H atom, rOH is the OH bond length, and a is the parameter that defines the M site based on OH bond vectors,kθ is the vibrational force constant for the HOH bend.As a result of intermolecular interactions in the condensed phase, the average geometry of a flexible water model in both the liquid and solid states will deviate from the model geometry.Due to the effective polarizability, an average water molecule in the condensed phase has a smaller HOH angle than that of the model; similarly, the average bond length is also longer.It is worth noting that the average geometries depend on simulation conditions, such as temperature and pressure. It has been proposed that the average water geometry can be used as a proxy to measure pressure in a nanodroplet.In this work, we choose liquid water at 1 bar and 298 K as the reference thermodynamic condition. A detailed procedure for measuring the ensemble geometry (EG) will be provided in Sec. supplementary material.It should be noted that the rigid version of the models constrains the bond length and angles but otherwise uses identical parameters as the flexible model, including the locations of the M site. For convenience, all model parameters and the definition of the M site are supplied in the III.r6 term with repulsion, the C6 determined with such a procedure is less reliable than that from a separate SAPT fit. Consequently, the WAIL potential is better used without long range correction to dispersion.For measuring the average geometry of the EG model, a box containing 1728 water molecules was simulated for 3 ns at 298 K and 1 bar. The geometry was extracted with MDTrajSince a rigid model simulation would not be able to capture the small geometry difference between water in ice and liquid phases, we are particularly interested in studying the effect of using a rigid model for simulations of ice–water equilibrium. Supercooled water and ice are two systems where the need for long trajectories is most compelling and can benefit the greatest from rigid versions of the models.TM, is the direct coexistence method.TM depends on choices and relaxation parameters of the barostat. A typical barostat will scale the coordinates of all atoms. This is true even for anisotropic barostats. Although such barostats use different scaling factors for different lattice directions, in each direction, both the ice and water coordinates are scaled at the same rate, ignoring the differences in the compressibilities of the solid and liquid phases. The substantial change in the density associated with the phase change of ice poses a particularly large challenge. Rather than localized expansion at the growth interface, a typical barostat will scale uniformly in the direction normal to the growth surface, which is not entirely physical.One of the most straightforward methods for determination of the melting temperature, TM of the model. The two liquid regions are separated by a vapor phase to allow expansion and contraction during phase changes. At least two simulations starting from different temperatures are needed to judge convergence. We will refer to such temperatures as the target temperatures and label the two target temperatures as TH and TL. The target temperature is the initial temperature of the NVE simulation. If the initial temperature is above TM, the slab will be cooled down as ice melts. If the initial temperature is below TM, ice will grow and the exothermic freezing process will warm up the slab. Expansion and contraction during phase transitions are accommodated with the vapor region.In this work, we avoid the use of both barostats and thermostats by simulating an ice–water mixture in the microcanonical ensemble. The method will be referred to as the NVE three-phase coexistence method. The idea is to prepare liquid–ice–liquid (LIL) slabs at two or more temperatures near the melting temperature TM. The lateral pressure of such a slab should not be zero due to the presence of interfaces and associated surface tension. We ensure that ice in the LIL slab has the a, b lattice vectors being that of the bulk ice at 0 bar. The normal pressure on the slab is the equilibrium vapor pressure at the triple point of water, which is for all practical purposes, 0 bar as far as our simulation is concerned. The TM of ice only has a weak dependence on pressure. At 0 bar, the TM is only 0.01 K higher for real water. Thus, we believe measuring the TM at 0 bar is sufficient.The liquid is made sufficiently thick so the liquid–vapor interface would not affect the ice–water interface. The lateral dimensions are determined by the density of ice at target temperatures near HT and LT to determine TM. The six slabs were created following the electrostatic switching method of Lindberg and WangIn our study, six LIL slabs were built from six ice initial conformations and run at Each proton disordered ice box containing 300 water molecules is stacked four times in the z-dimension. The stacked ice box without any liquid or vacuum will be equilibrated at the target temperature and 0 bar for 1 ns with temperature and pressure controlled using the Nosé–Hoover thermostat and Parrinello–Rahman barostat. The relaxation times for the thermostat and barostat are 2 and 5 ps, respectively. The average box dimensions were determined by averaging over the last 0.9 ns of the simulations. The box size determination will be performed at every target temperature for each of the six proton disordered configurations for each water model.melt for 200 ps in an NVT simulation. It should be noted that the Tmelt is the temperature used to melt the ends to create the LIL slab and it is not the TM to be measured. The Tmelt for each model is summarized in TM study. In the first 100 ps of the cooling, the 600 ice molecules remain frozen; in the second 100 ps, all 1200 water molecules will be equilibrated at the target temperature. The melting and cooling steps will be performed with a stochastic rescaling thermostatA vacuum of 1 nm is added to the equilibrated ice box at the average box dimension. The 600 ice molecules at the center of the slab are frozen, and the 300 water molecules on each side are allowed to melt at Tsupplementary material, along with the corresponding LIL slabs, to facilitate subsequent studies using the NVE three-phase coexistence method.Six ice boxes of WAIL water created to sample different proton orientations are provided in the TH and TL used for each model. TH and TL should be sufficiently close to the TM to prevent the LIL slab from completely melting or freezing over. Such incidences can easily be detected by visual inspection of the slab or the temperature trace. The LIL temperature from the two simulations will not agree even after a long period of time if one of the configurations no longer has solid–liquid coexistence. We pick TH to be above the TM and the TL to be below TM, although this is not strictly required. It is convenient for us since our previous work on these models already provided us with a reasonable guess of the TM. For water models with unknown TM, few explorative NVE three-phase coexistence simulations will allow TM to be approximated quickly.TM. To judge equilibrium, a 1 ns rolling average of the temperature will be monitored and equilibrium is considered to be reached once the rolling averages from the two initial conditions are within 0.1 K of each other. Once equilibrium is reached, the temperature is averaged for 10 ns. The average temperature in this 10 ns window is supplementary material. The NVE implementation in Gromacs has no problem conserving total energy with a 0.5 fs time step size. We note that a slow drift in total energy can be tolerated as long as there is still solid–liquid coexistence as the potential energy change associated with the phase transition will absorb the energy loss or gain from an imprecise integrator.We also report the total energy as a function of time for 20 ns in the TM of the TIP4P/IceTM of TIP4P/Ice was determined to be 274 ± 1 K, which is in good agreement with prior estimates ranging from 268 to 272 K.TM from 270 to 272 K,TM in the range from 268 to 270 K.TM of the two-phase coexistence method. The density of ice in the NVE-three-phase coexistence method is not affected by the surface tension, which is consistent with a TM in closer agreement to free energy based estimates.To provide proper validation of the NVE three-phase coexistence method, the TM, the radial distribution functions (RDFs), density as a function of temperature, surface tension (γ), dielectric constant (ε), heat capacity (Cv), heat of vaporization (ΔHvap), and diffusion constant (D) are measured for each model.In addition to Unless otherwise noted, all simulations were performed using Gromacs 2019.6 with a constant number of particles at 1 bar and 298 K. The temperature and pressure were controlled with Nosé–Hoover thermostat and Parrinello–Rahman barostat, with 2 and 5 ps relaxation times, respectively. Long range corrections to van der Waals were used for the BLYPSP-4F and q-TIP4P/4F models.TM study. NVE simulations with a 2 fs time step are challenging due to energy drifts. Thus, a 0.5 fs time step was used for all NVE simulations regardless of model flexibility. A 1 fs time step might be sufficient for rigid body NVE simulations, but we have not fully tested this.All flexible models were simulated with a 0.5 fs time step, and all rigid models were simulated with a 2 fs time step except for the NVE steps of the The linear constraint solver (LINCS) algorithmThe density as a function of temperature is measured using a 343 water box. Data within a 20 K range around the density maximum are used to fit the temperature of maximum density (TMD) of each model. For each temperature shown in ε was computed from the variance of the box dipole, M, using the formula from the fluctuation and dissipation theorem:V is the volume of the box and the temperature T is 298 K. Since none of the force fields studied in this work has explicit polarizability to model electronic polarization, Eq. ε. Thus, it would not be appropriate to compare such an εo with the experimental ε of water, which also includes the high frequency component of the dielectric due to electronic response. We report also in ε, which is 1.78 × εo, to account for the high frequency component of the water dielectric constant.The Cv was estimated with the finite difference method using two different NVE simulations using configurations sampled from an NVT trajectory. Due to the fluctuations in the NVT simulation, from any instantaneous configuration, the average temperature of an NVE simulation starting from such a configuration will not be 298 K but will remain fairly close. The Cv was computed with the equationΔT is the difference in the mean temperature of the two NVE simulations. The two NVE simulations were performed for 4 ns each using 1728 water boxes.γ was computed from a 1728 water liquid slab using an orthorhombic box with a 6 nm vacuum between the two interfaces. The Coulombic interaction was modeled with standard 3D particle mesh Ewald, and a long 1.75 nm van der Waals cutoff was used for BLYPSP-4F and q-TIP4P/F models.The ΔHvap was computed with the following formula:Vliq is the potential energy of the liquid phase and Vgas is the intramolecular configuration energy in the gas phase. The angle bracket indicates ensemble average. Since the models used a dipole moment larger than the gas phase dipole to implicitly include polarization effects in the condensed phase, the polarization self-energy correction,ΔEself, is used in Eq. ΔEself is computed withμm is the model dipole moment, μg is the experimental dipole moment of water in the gas phase, and the polarizability, α, is 1.44 Å3.ΔEself for each model is provided in the supplementary material.The For rigid models, the intramolecular energy is zero. For flexible models, separate gas phase simulations were performed for 5 ns with a single water molecule in a box of the same size as the corresponding liquid simulation. The gas phase simulation used the stochastic scaling thermostatD was computed using the Einstein formula from a 5 ns NVT simulation using a 1728 water box at 298 K. The temperature was controlled with the Nosé–Hoover thermostat using a 5 ps relaxation time. The mean square displacement was fitted from 5 to 15 ps.The IV.ΔHvap of the flexible models is in closer agreement with the EG models, which is about 3 kJ/mol higher than the corresponding MG model. The better agreement between the FL and EG models is actually an interesting cancellation of the larger polarization self-energy correction of the EG model with the intramolecular distortion energy of the FL model. It should be noted that none of the rigid models have intramolecular energies. The average intramolecular energy of the FL model is not the same in the liquid and the gas phases. While the FL model assumes the shape of the model in the gas phase, its average shape is that of the EG model in the liquid. The geometrical distortion causes the average intramolecular energy to be larger for the liquid when compared to the gas, which will be referred to as the intramolecular distortion energy. In a sense, this distortion energy is a polarization self-energy as the FL model is polarized by closing the HOH angle and stretching the OH bond in the condensed phase. Thus, it is not entirely surprising that the intramolecular distortion energy of the FL model is of a similar magnitude when compared to the increased polarization self-energy of the EG model.Various properties of the water models are summarized in The diffusion constants show a fairly large variation with respect to the FL, MG, and EG models. In each case, the EG model reduces the diffusion constants by 10%–15% and the diffusion constant of the MG model is a substantial 25%–65% higher when compared to the corresponding FL model. The faster diffusion for the MG models is easy to interpret as the models have a slightly smaller dipole moment, leading to a slightly weaker hydrogen bond, and hence faster hydrogen bond rearrangements. The smaller diffusion constant for the EG models when compared to the FL models probably reflects the role of flexibility in the diffusion process. OH vibration should transiently weaken a hydrogen bond and facilitate hydrogen bond rearrangements, which leads to a faster rate of diffusion for the FL models relative to the EG models.γ, the difference between the EG models and the corresponding FL models is small, with the EG model providing a γ about 1 mN/m higher for the BLYPSP-4F and WAIL models and 2 mN/m higher for q-TIP4P/F. The reduction in γ for the MG model is more substantial, being 5% for the two AFM based models and 10% for q-TIP4P/F.For surface tension, ε, the difference is rather small between the FL and EG models for the two AFM based potentials. It is worth noting that the scaled ε of the EG models is slightly smaller than the corresponding FL model, leading the EG models to be in better agreement with experiments. We note that the small reduction in ε leading to a better agreement with experiments may not be completely fortuitous. The ε is proportional to the fluctuation in dipole moments. With the OH bond fluctuating between the classical turning points without proper treatment of quantum effects, it is possible a FL model would overestimate dipole fluctuations, thus slightly overestimate ε. However, a path integral calculation would be needed to verify such a hypothesis.For ε when compared to the FL model. The εo for the FL version of the q-TIP4P/F model is in good agreement with that reported previously.ε between FL and EG in case of q-TIP4P/F is not entirely clear to us. It has been pointed out previously that a repulsion term between the water hydrogen and the site carrying the negative charge is important for water models due to the breakdown of the point charge approximation at short distances.The q-TIP4P/F EG model has a substantially smaller ε around 10% smaller than the corresponding EG models. This trend is consistent with the 4%–5% smaller dipole moments of the MG models when compared to EG.For all three water models, the corresponding MG models give a Cv shows the largest difference between rigid and flexible models, while the difference between different force fields is smaller. This can be explained by the equipartition theorem. If the interactions are fully harmonic, the Cv is only determined by the degrees of freedom (DOF) available to the system. The difference between the various force fields is a result of anharmonicity, and the difference between the flexible and rigid versions of each force field is a result of losing the three intramolecular DOF in the rigid models. The equipartition theorem suggests the difference should be 3R, which is 25 J/K mol. The observed difference between the EG and FL models is very close to 25 J/K·mol, consistent with the expected value. The EG version of the two AFM based models gives Cv that is in very good agreement with experiments, which is not surprising considering the quantum nature of the intramolecular vibrations is better approximated with such rigid models.Cv between the MG and EG models is very small for the two AFM based models, with the MG Cv slightly lower than that of the EG by 3–4 kJ/mol. The difference is 10 J/K·mol for q-TIP4P/F. The larger difference is probably a result of the fact that the q-TIP4P/F model has more anharmonicity in the intermolecular surface with the sharply repulsive 1/r12 term.The difference in r12 repulsion term and the lack of repulsion between hydrogen and the site carrying a negative charge in the q-TIP4P/F potential. The form of intermolecular energy used in q-TIP4P/F is quite popular among water potentials; we thus anticipate other potentials sharing similar intermolecular energy expressions to behave like q-TIP4P/F.It is interesting that for almost all properties shown in The temperature dependence of density for each model is shown in T–P diagram. While the TMD can be observed as water approaches the Widom line,PC, as shown in PC of the MG version of the WAIL model could become negative.The TMD of the MG version of WAIL water cannot be found in the temperature range studied. The leading hypothesis for the existence of the TMD has been attributed to a second liquid–liquid critical point in supercooled water.TM of the MG ice is 15–20 K lower than that of the corresponding FL ice for the three models. It is interesting that the TM of EG ice is 3–5 K higher than that of the corresponding FL ice. While the 3–5 K difference is not much larger than the uncertainty, it is worth pointing out that the EG TM is consistently higher than the FL TM for all three models. This suggests that the trend of the EG model having a slightly higher TM may not be accidental. The 5 K difference in the case of WAIL brings the WAIL TM to even better agreement with experiments.The TM for the EG WAIL model may not be accidental. On the other hand, with a lack of understanding of the mechanism for the higher TM, there is no proof that proper modeling of quantum nuclear effects will cause the WAIL model to produce an improved TM. Performing path integral calculations to determine the TM is very challenging. Presumably, the effective centroid potentialAs mentioned previously, the classical Hooke’s picture of the OH vibration is not correct considering the quantum nature of this high frequency mode. The QM ground state has its probability maximum at the equilibrium bond length rather than the vibrational turning point as in the classical Hooke’s picture. The EG model thus better approximates the most probable QM geometry when compared to the FL model. We argue that the slightly improved agreement of the V.A flexible water model requires the use of small time steps. There are cases where it is desirable to simulate a rigid version of a flexible model to improve computational efficiency. This work shows that simply constraining the geometry of the rigid model using the bond length and bond angle of the flexible model will lead to a model (the MG model) that behaves quite differently from the flexible model (the FL model). Several properties see quite substantial changes. For example, the diffusion constants of the MG models are 50% higher and the TMD of MG models shifts down by 30 K and becomes undetectable in the case of WAIL. In the majority of the cases, the cause for the different performance is not due to rigidity but the difference in the mean dipole moments in water. This is supported by the EG models showing much closer agreement with the FL models for most properties, except for the diffusion constant and heat capacity.Cv, surface tension γ, dielectric constant ε, and melting temperature TM. While for Cv, the improvement of 3R is obviously the result of the EG models’ ability to better capture the QM nature of the highly quantized OH vibrations, some of the improvements in other properties could be fortuitous. However, these could also be perceived as evidence that proper treatment of nuclear quantum effects could be important for the proper modeling of these properties.For the two AFM models, where the model was developed solely by fitting to high quality electronic structure calculations, most properties of the corresponding EG models are better than those of the FL model. Properties that show an improvement include heat capacity In addition, while we attribute the difference between the MG and EG models to a change in the dipole, other factors may also play a role. For example, the small geometry change could affect the hydrogen bond length, and the small angle change could affect tetrahedrality. Careful delineation is not easy and will be worthy of careful study in the future.We note that various efforts have been made to create flexible versions of rigid models. In most cases, the equilibrium bond length and angles for such flexible models were taken from the rigid models. In such a case, the mean dipole of the flexible water model created will be higher than that of the corresponding rigid model in condensed phase simulations, similar to the relationship between the MG and FL models in this study. Thus, care has to be taken when creating flexible versions of rigid models. The parameters of the flexible models should be adjusted to mimic the relationship between EG and FL models to ensure the flexible models behave similarly when compared to the rigid ones.The simulation showed an interesting disappearance of TMD for the MG version of the WAIL potential, which could be attributed to the putative liquid–liquid critical point of this model residing in the negative pressure regime.TM of the water models without the use of any thermostats and barostats. This method eliminates potential artifacts from the thermostats and barostats and demonstrates good stability in determining TM.In addition, a new NVE three phase coexistence method is presented in this work, which is able to compute the supplementary material. Six ice boxes along with the corresponding LIL slabs are also provided in the supplementary material.The intermolecular component of the configuration energy, the self-polarization energy, parameters for the three models simulated, and a graph showing the total energy as a function of time during the NVE three-phase coexistence simulation can be found in the


Federated learning protects the privacy information in the data set by sharing the average gradient. However, “Deep Leakage from Gradient” (DLG) algorithm as a gradient-based feature reconstruction attack can recover privacy training data using gradients shared in federated learning, resulting in private information leakage. However, the algorithm has the disadvantages of slow model convergence and poor inverse generated images accuracy. To address these issues, a Wasserstein distance-based DLG method is proposed, named WDLG. The WDLG method uses Wasserstein distance as the training loss function achieved to improve the inverse image quality and the model convergence. The hard-to-calculate Wasserstein distance is converted to be calculated iteratively using the Lipschit condition and Kantorovich–Rubinstein duality. Theoretical analysis proves the differentiability and continuity of Wasserstein distance. Finally, experiment results show that the WDLG algorithm is superior to DLG in training speed and inversion image quality. At the same time, we prove through the experiments that differential privacy can be used for disturbance protection, which provides some ideas for the development of a deep learning framework to protect privacy. With the enhancement of the performance of computer hardware, artificial intelligence fields such as machine learning and deep learning have ushered in new breakthroughs in massive data sample training. Distributed training reduces training time in large-scale data set training while improving the security of private data. In 2016, Google proposed the concept of ,4,5, perIn order to infer the information of training data from the gradient, there are early attempts at reversing the gradient to pursue the proxy information of the original data. The sample attributes of some training samples or data sets makes the gradient lead to the leakage of some shallow information. For example, the training binary classification model can determine whether the data record with certain attributes is included in the batch of other participants. However, this only causes a small amount of shallow information leakage. In “Deep Leakage from Gradient” , it was This paper proposes a gradient inversion attack algorithm based on DLG, which uses the Wasserstein distance to measure the distance between the virtual gradient and the real gradient.Theoretical analysis is given about continuity and differentiability of Wasserstein distance; the analysis results show that Wasserstein distance substitution for Euclidean as a loss function of gradient is feasible in gradient inversion.Experiments are carried on image data in public data set, and the result verifies that WDLG algorithm can invert images with better performance.In this paper, we propose the Wasserstein Deep Leakage from Gradient (WDLG) method. The proposed method uses Wasserstein distance  as loss The rest of the paper is organized as follows: Training data in distributed platforms such as federated learning can reduce training time and improve the security of private data, so they are widely used in machine learning model training, but their security is still threatened. Initially, some information was leaked through attribute inference, and until the emergence of DLG, the original information was completely leaked by iteratively optimizing the gradient. This makes the security of the training mechanism of federal learning shared gradient greatly threatened. More importantly, later researchers conducted more in-depth research based on DLG, from single image restoration, shallow network, low-resolution images to multi-image restoration, large-scale deep network, high-resolution images. Because the Wasserstein method is continuous and differentiable, it can provide a stable and smooth gradient when used as a training loss function. Therefore, the Wasserstein algorithm is used to optimize the gradient inversion algorithm to make its inversion ability stronger. This section conducts specific related work research from three directions: distributed training, Wasserstein algorithm, and gradient inversion.Large-scale machine learning model training requires a large amount of intensive computing. Many studies focus on distributed training to reduce machine learning model training time and ensure data privacy. The distributed training can be roughly divided into two types: centralized training ,11 and dIn many practical applications, training data privacy needs to be protected. Joint learning has become a common strategy for training neural networks without transmitting data ,20. ModeThe core idea is to share the gradient However, through the inference of membership, references ,22,23 inThe origin of Wasserstein distance is the optimal transportation problem . Also knIn deep learning, least squares, KL divergence, and cross entropy are often used as loss functions. These traditional distances are compared by the probability density function of the corresponding points, but most of them ignore the geometric characteristics between the probability distributions. EM distance can well reflect the geometric characteristics between probability distributions. The EM distance can find the Wasserstein average that is more capable of describing morphological features than the Euclidean average. It not only calculates the distance between the two distributions but also shows the evolution state matrix between the two distributions. Using EM distance as a deep learning loss function to measure the distance between two distributions can make the two distributions converge stably regardless of whether the distribution intersects. Based on the above advantages, more and more deep learning models use EM distance as the loss function. Among them, the most famous WGAN  uses EM Gaiping  showed tThe earliest inversion of data using optimization methods was proposed by Wang et al. . Zhu et Algorithm 1: Deep Leakage from Gradients.Input: Output: private training data x, y1:2:   Initialize dummy inputs and labels.fordo3:   4:      Compute dummy gradients.5:      Second norm loss function.6:      Update data to match gradients.end for7:   return8:   end procedure9:It can be seen that optimized gradient inversion is based on DLG. DLG shows that it is possible to steal images from gradients by stealing images in pixels. In step As shown in Algorithm 1, the DLG leaks training data through gradient matching, randomly initializing virtual input The loss function is assumed to be second-order differentiable, which is optimized by gradient. We use the idea of DLG to iteratively minimize the difference between the virtual gradient and the original gradient and combine the Wasserstein distance as the loss function to improve the efficiency and accuracy of private data gradient inversion.In the original DLG, the training is unstable when the image is reconstructed by the Euclidean distance, and the image inversion effect is not good. In order to solve this problem, this paper uses a more stable algorithm in the training process, even when two distributions differ by a large margin and have no intersection at all, using the Wasserstein distance to measure the distance between them yields a stable, smooth gradient. This section combines the gradient inversion algorithm to iteratively optimize the gradient as a fitting object to obtain a gradient inversion loss function based on the Wasserstein distance. Theoretical analysis proves that the Wasserstein distance has continuity and differentiability, satisfying the basic conditions as a loss function. At the same time, the tag restoration algorithm proposed in the iDLG  algorithThe core idea of the WDLG algorithm is shown In In this paper, the EM distance between the virtual gradient and the real gradient is calculated by the WDLG algorithm, and a more stable and efficient WDLG is proposed based on the EM distance gradient inversion method. As shown in Algorithm 2, the WDLG algorithm needs to randomly generate virtual data through the inverted machine learning model R. If Since the minimized EM distance 𝔻If the supremum in (5) is attained for some Definition: Since  duality  that theDefinition Therefore, adding batch m to the WDLG algorithm yields the algorithm iterative equation.Algorithm 2: Wasserstein Deep Leakage from Gradients.Input: Output: private training data x, y1:2:   Initialize dummy inputs and labels.fordo3:   4:      Compute dummy gradients.5:      Wasserstein distance loss function.6:      Update data to match gradients.end for7:   return8:   end procedure9:We randomly initialize the virtual data and the label Z; and let the function Let Taking the expectation as well as the condition Above, EM distance is continuous and differentiable, conforms to the requirements of DLG loss, and can train inversion data to achieve the best state. In the following sections, we show the practical benefits of the proposed algorithm and provide the comparison with traditional DLG.In this paper, hardware and software environment are a Windows 10 operating system; the processor is Intel Core i5-9400F CPU@2.90GHz; and the memory is 16.00 GBGMet 64-bit operating system, using Python language and Pytorch framework to write experiments.The learning rate is 0.1; the number of images generated is 300; the high-order gradient needs to be calculated; and 500 iterations are optimized for the image. The goal is to match gradients from all trainable parameters. The network used is LeNet network. The WDLG algorithm does not require model convergence or training completion, and its gradient inversion attack can occur at any time during the training process. All experiments use random initialization weights; virtual data and labels are random noises subject to Gaussian distribution. For more detailed information about specific tasks, see the following sections .WDLG inversion is performed on the images of MNIST, Fashion MINIST, SVHN, and CIFAR-10 datasets. The fidelity of the generated image is measured by calculating the mean value of the inverted image and the original image, and the image comparison is performed in different batches of inversion.As shown in Next, as shown in As shown in In terms of image fidelity, as shown in In particular, there is an unexpected finding in training. Both WDLG and DLG algorithms randomly initialize the noise data subject to Gaussian distribution, but we find that when calculating the first gradient inversion iterative training loss distance, the WDLG algorithm always calculates a training loss that is less than twice that of the DLG algorithm. This means that the initial gradient of the WDLG distance is smaller than the original gradient distance, and the similarity is higher. Therefore, it has an advantage at the beginning of training iteration, as shown in The attack success rates of the two schemes are compared under the FashionMNIST and CIFAR-10 data sets. The successful inversion image is divided by the total attack image, and the image inversion success rate shown in The attack success rate of WDLG and DLG inversion algorithm is inversely proportional to the resolution of the inversion image. The higher the pixel of the image is, the more complex the image is, and the lower the success rate of inversion is. The success rate of gradient inversion attack of WDLG and DLG algorithm is almost the same, but WDLG is more dominant in running time.When compared with the recursive gradient attack (RGAP) inversion method, RGAP provides a closed form recursive program to recover data from the gradient of the deep neural network. The mean square error is still used as the measure of image quality, and the experimental results are shown in the We compared the training inversion attack on the image data in the CIAFR-10 dataset under batch 1 and batch 4 and found that the average total loss and mean square deviation between the real image and the inversion image of WDLG algorithm are smaller than those of DLG algorithm. Specific values are shown in the Comparing In order to better enhance the ability of the algorithm and enrich our work, we use the label recovery algorithm proposed by iDLG on the basis of the original algorithm to recover the tags of the training data in advance and no longer invert the tags in the training process. Therefore, we also modify the whole algorithm design to make the gradient inversion algorithm have more accurate label for data recovery training, which can improve not only the inversion image quality and success rate but also the training convergence speed. Experiments are carried out on the original DLG algorithm under the condition of increasing label recovery and Wasserstein distance. A total of 500 iterative experiments are carried out under the LeNet network model and CIFAR10 dataset. When the training loss is lower than that, the image converges, and the attack is successful. The experiment is shown in Then, the training loss refers to the training error when the training process converges finally. Image quality refers to the mean square difference between the restored image and the original image. The smaller the difference is, the higher the image quality is. The convergence speed refers to the number of iterative training when the image is restored. The success rate of attack refers to the percentage of images that successfully leak image information for every 100 images of reverse attack.It can be seen that when using the tag recovery algorithm to extract tags in advance, the inversion loss is reduced, and the image quality, the convergence speed, and the success rate of attack are improved. When using Wasserstein distance as loss function, compared with DLG inversion loss, image quality, convergence speed, and attack success rate are improved, but compared with label restoration algorithm, image quality and convergence speed do not change significantly.For the Wasserstein gradient inversion algorithm proposed by us and a variety of previous gradient inversion algorithms, it is concluded that this kind of inversion attacks always match the virtual gradient with the real gradient through a set of virtual data input models, which makes the noise data iteratively updated and finally form the original data. Based on this, in the exploration of defense methods, adding noise to the gradient to make the gradient inversion attack worse is one of the most direct and effective defense methods. Therefore, we resist the gradient inversion attack algorithm by adding Gaussian differential privacy noise disturbance to the original gradient in the training model and carrying out simulation analysis .The experiment first adds differential privacy disturbance to the original gradient  and thenGradient inversion attacks are carried out on SVHN and FashionMNIST, respectively, in the case of noise of 10. The attack results are shown in By adjusting the noise to =2, =4, and =10, respectively, and using Wasserstein gradient inversion algorithm to attack the image in the CIFAR-100 data set, the image clearly shows that when the noise is =2, the training image under the iterative attack of 448 batches of gradient inversion does not completely disclose information but shows a certain degree of information leakage, as shown in When =4, the training image under the same iterative attack of 448 batches of gradient inversion can hardly see the information of the original image, but there is still a very small amount of data to show, as shown in When =10:00, the training image under the same iterative attack of 448 batches of gradient inversion cannot see the information of the original image at all, which completely defends the gradient inversion attack based on Wasserstein, as shown in From the experimental results, we can see that when the noise increases gradually, the image quality of the Wasserstein gradient inversion attack decreases until no available information can be obtained, which realizes the defense of the gradient inversion attack algorithm. Therefore, the experimental results show that the defense method based on differential privacy disturbance in the original gradient is effective to resist the gradient inversion attack.In this paper, a gradient inversion attack algorithm is proposed named WDLG, which applies Wasserstein distance-based Deep Leakage from Gradients to process image reconstruction for a given average gradient and can obtain higher quality inversion images in a shorter time. Theoretical derivation shows that EM distance is a continuous and differentiable function, which is fit for a loss function in depth learning gradient inversion attack series algorithms. We combine Kantorovich–Rubinstein duality and Lipschitz condition to calculate the WDLG algorithm by iterative calculation which solves the problem of Wasserstein distance being difficult to calculate. The experimental results show that the reconstructed image by WDLG algorithm in gradient inversion is almost the same as the original image; the image quality of the proposed method is better than DLG; and the reconstruction time is less.We show that the training data will be leaked when the gradient of the deep learning network is shared on the dataset. At the same time, we prove through experiments that differential privacy can be used for disturbance protection, which provides some ideas for the development of a deep learning framework to protect privacy.The image restored by WDLG inversion attack in high-resolution image is not good. The future work can be considered under the Wasserstein algorithm, by adding regular terms to constrain, in order to pursue higher quality image inversion effect.


Systems consisting of spheres rolling on elastic membranes have been used to introduce a core conceptual idea of General Relativity: how curvature guides the movement of matter. However, such schemes cannot accurately represent relativistic dynamics in the laboratory because of the dominance of dissipation and external gravitational fields. Here we demonstrate that an “active” object (a wheeled robot), which moves in a straight line on level ground and can alter its speed depending on the curvature of the deformable terrain it moves on, can exactly capture dynamics in curved relativistic spacetimes. Via the systematic study of the robot’s dynamics in the radial and orbital directions, we develop a mapping of the emergent trajectories of a wheeled vehicle on a spandex membrane to the motion in a curved spacetime. Our mapping demonstrates how the driven robot’s dynamics mix space and time in a metric, and shows how active particles do not necessarily follow geodesics in the real space but instead follow geodesics in a fiducial spacetime. The mapping further reveals how parameters such as the membrane elasticity and instantaneous speed allow the programming of a desired spacetime, such as the Schwarzschild metric near a non-rotating blackhole. Our mapping and framework facilitate creation of a robophysical analog to a general relativistic system in the laboratory at low cost that can provide insights into active matter in deformable environments and robot exploration in complex landscapes. In such readily accessible systems, researchers have made intriguing connections to gravity such as Kepler-like laws, precession, and the stability of orbits. However, their studies have also found that these systems do not exactly mimic astrophysical gravity. For instance, the scaling between the period and radius is 3 instead of Systems consisting of spheres rolling on curved surfaces5 could allow the tuning of parameters that lead to inexact mimics of GR in passive systems. Indeed, our recent work6 built a framework to understand how the field-mediated dynamics of active agents on flexible membranes demonstrate in the words of Wheeler’s famous aphorism: “Matter tells spacetime how to curve and spacetime tells matter how to move”7. In particular, we showed that the spacetime followed by an active object (a wheeled circular robot) can be tuned by varying system parameters such as the membrane elasticity and the speed of the object.We hypothesized that making the object “active” – an internally driven robot – would allow mechanical systems to better model GR in part because of the ability to study steady states. We further reasoned that the programmability and sensory capabilities of increasingly low-cost and powerful “robophysical” models6 and demonstrate how the activity can lead to an exact mapping to GR. We first show how an active object with a prescribed speed on an elastic membrane produces longer and more controllable trajectories compared with a passive marble. We then deduce the spacetime it follows, and subsequently program the spacetime with a Schwarzschild orbit as an example. We posit that a robot controlled in the way we describe could mechanically mimic blackhole dynamics in the laboratory at a low cost.Here we amplify on and extend the scheme introduced inr, the object must turn according to the instantaneous local slope, z. We enable this behavior by using a vehicle with a differential drive, a mechanism that permits a difference between the speeds of the vehicle’s two wheels to respond to the terrain slope while maintaining a center-of-mass speed prescribed by the motor. The vehicle drives straight on a leveled flat ground. When driving on a tilted flat surface with a constant gradient everywhere, the vehicle turns to align with this constant slope. In a more general case where the vehicle drives on a solid terrain with spatially varying gradient, it responds instantaneously by aligning with the local gradient. Finally, in our setup, the vehicle responds to the local gradient while the terrain (membrane) updates its shape with the evolving position of the vehicle, mimicking the interaction between matter and spacetime7. The membrane shape is affected by three factors. Earth’s gravity causes the membrane to sag with a parabolic profile due to the weight of the membrane itself. The tautness from boundary conditions such as the depth of the central depression of the membrane competes with the sagging. Finally, the local deformation from the vehicle creates an additional dimple in the membrane. We note that the sagging from the membrane’s weight and the deformation from the vehicle are analogous to the bending of background spacetime and the bending due to the moving object respectively in the context of GR.We first consider an active object prescribed with a constant speed on a circular elastic membrane. Later, we will discuss the general case of time-varying speed. To prevent the object from simply following a near-straight-line spatial geodesic with a spatial curvatureOur terrain consists of a spandex membrane fixed to a circular frame with a diameter of 2.4 m. The central depth of the membrane is controlled by an actuator that adjusts the height of the membrane center. The cylindrical chassis of the vehicle is 3D printed and its instantaneous position is tracked by an overhead camera systems (Optitrack).We first compare the trajectories of the active vehicle with those of a passive marble having the same mass as the vehicle. We released the vehicle by placing it on the membrane after being turned on, and released the marble by placing it at the start of a guiding track. The velocity of the vehicle and marble were kept the same upon release by adjusting the voltage on the motor and the releasing height on the guiding track Fig. a, respec8. While a passive marble dissipates energy as To understand these orbits, we follow the models inmentclass2pt{minim→=0 Fig. a. Therefa) depends on the local slope r, a is also a function of r. Additionally, a should depend on velocity in general. However, given that the velocity has constant magnitude as the speed is constant, this dependence is reduced to one degree of freedom. For our convenience, we chose the direction of the velocity, a (thus k(r) is the radial dependence due to the local slope k increases with the local slope k and Though the speed is constant, the change of the velocity  is measured from the height of the static vehicle placed at different radii r. The proportionality C uses the ratio between acceleration and the gradient Integration of the above models for the active vehicle and passive marble Fig. c shows qA functional understanding of the orbital features  would facilitate the creation of an intelligently programmed vehicle. One tool we can use to obtain such insights is the spacetime metric that describes these orbits. Any similarities between the experimentally inferred metric and known metrics could prove useful in understanding how the orbital features depend on system parameters.The orbital dynamics we wish to map could be described by a diversity of metrics. We propose a simple but general metric that is analogous to GR in the weak-field limit and encodes the axi-symmetry of the system. Our metric has the formmentclasspt{minimar.Using k.Notice that the left-hand side of Eqs. , 14 are entclass1pt{minimarom Eqs. . When weentclass1pt{minimanto Eqs. , we find of Eqs. , 14 and entclass1pt{minima of Eqs.  and notiE and L required to fix the metric have actual physical meanings. E is the constant energy associated with the fact that the metric is time-independent. L is the constant angular momentum associated with the metric’s The metric Eq.  gives usike Eqs. , 12. Usiq˙, Eqs. , 12, andier Eqs. , 20, we  in Eqs. , 20. We 10, the effects of curvature are now not restricted to space11. That is, in general, the metric function t) as well as the spatial coordinates. For a static metric , the spacetime becomes splittable when 10 that the spatial curvature is different from the spacetime curvature as it is devoid of gravity, i.e., a free particle initially at rest will remain at rest.Thus our formulation indeed reveals that the vehicle does not simply follow spatial geodesics of the membrane but instead follows geodesics in an emergent spacetime Eqs. , 26 genev is finite and controllable, the active locomotion provides more flexibility and programmability in constructing the desired spacetime in GR. For instance, programming an active agent with acceleration magnitude k decreasing with radius r makes an orbit precess in the same direction as the orbit, while a k increasing with r makes an orbit precess in the opposite direction as the orbit6. Such flexibility and programmability are more challenging to implement in passive and dissipative agents studied in the previous works8.The essential contribution from the active drive is the persistent response to the local curvature, here enabled by the controlled constant speed unseen in passive systems. In fact, when the response of the turning to the local slope vanishes at the limit tric Eq.  with comtric Eq. , 26 redumentclass2pt{minimk(r) and v(r)).The metric Eqs. , 26 has v to vary with the radius r  and active object speed v(r) as shown in Fig. In metric Eqs. , 26, we γ), Eqs. , 18 withG is the gravitational constant, M is the mass of the star, c is the speed of light, and A and the eccentricity e using the minimum and maximum radii: T and semi-major-axis A that follows Kepler’s third law  is to create an elastic material with a radially varying thickness To achieve this relation in experiments, a vehicle must actively vary its speed with radius and a membrane must have a radially-dependent elastic modulus. We can attach a tilt sensor to infer the radius and change the speed accordingly. To program the membrane with radially varying profile In principle, one can even create orbits from a non-diagonal metric by breaking symmetries. Here we show that breaking the axis symmetry can create a spacetime with nonzero Let us consider a P is not simply r. From this, we obtain the equations of motion with respect to time t instead of affine parameter c’s are all functions of r such that The conserved quantities are now generalized to be 12 . There has been much theoretical progress on the analogy between spacetime and solid mechanics26. We posit mechanical devices, such as the one we introduce in this work, could help explore the theoretical proposal with the reverse methodology. For instance, we can design systems to monitor the elasticity of known spacetimes and probe interesting problems such as the occurrence of topological defects and plastic deformations in spacetime.In this work, we demonstrated how the use of an active particle – a wheeled robot – moving on an elastic membrane can generate a system which can mimic the dynamics of bodies in arbitrary spacetime. Given the flexibility in constructing and programming such robophysical devices, our system makes for an attractive target to push toward a mechanical analog GR system. While superficially our system resembles the educational tool used to motivate Einstein’s view of spacetime curvature influencing matter trajectories27, path dependency and contingency of composite models28, and the nature of modeling approximation when carrying out explorative research29 are nontrivial obstacles that may hinder the validity and applicability of these simulations. Physical analog systems provide simple parameter variation, intellectual accessibility, and potentially offer ease of solution due to their classical nature22. With the flexibility of parameters introduced in this paper, the length and time scales not accessible in celestial systems are possible to access in their laboratory analogs. For instance, it is possible to probe physics around or even within the event horizon of a blackhole to probe theories30 that are challenging to test in the original system. See section “We advocate for the potential research applications of our robotic vehicle as an analog system. In astrophysics, we typically are limited to an observational understanding of phenomena borne out of an inability to perform physical experiments with customized parameters. Though simulation provides an alternative, limitations such as sub-grid physics and runtime practicality for high-resolution or multiscale dynamics31. For instance, the spacetime metric of the agents’ motion can both guide our choice of parameter values to alter orbital features, like the precession direction, and influence our design of control schemes that accomplish tasks like helping multiple agents avoid mergers on the membrane6.Beyond its role as a mechanical analog for GR, this framework could also provide a new perspective to understanding active matter undergoing field-mediated interactionsWe simplify the complicated rolling friction and membrane dissipation by employing an effective friction constant that absorbs all dissipative forces. We probe its magnitude by doing the following experiment. We release the marble at the rim of the circular membrane with zero speed and thus zero kinetic energy Fig. . The marWith the help of  in Eqs. , 12, we k in Eqs.  to both sides of Eq.  and acceleration response to designed membrane elasticity k(r). The integration usesWe use the same model in previous section for Schwarzschild spacetime to integrate vehicle trajectory with controlled speed Supplementary Movie S1.Supplementary Information.


We have used the LOw-Frequency ARray (LOFAR) to search for the growing tip of an intra-cloud (IC) positive leader. Even with our most sensitive beamforming method, where we coherently add the signals of about 170 antenna pairs, we were not able to detect any emission from the tip. Instead, we put constraints on the emissivity of very-high frequency (VHF) radiation from the tip at 0.5 pJ/MHz at 60 MHz, integrated over 100 ns. The limit is independent on whether this emission is in the form of short pulses or continuously radiating. The non-observation of VHF radiation from intra-cloud positive leaders implies that they proceed in an extremely gradual process, which is in sharp contrast with the observations of other parts of a lightning discharge. If at all, inter and intra cloud positive leaders show in VHF-images only indirectly through small scale discharges, such as needles, along their tracks9 or through dart  leaders10.The detection of emitted VHF radio waves is an efficient method to image the development of a lightning discharge since VHF is virtually not attenuated in the atmosphere and thus not obscured by clouds. This thus allows for studying the complete development of the discharge. While VHF is very efficient in detecting negative discharges, the detection of positive discharges has proven to be much more difficult. Except for a few cases such as when positive leaders that propagate to ground9, often followed by a dart leader that may propagate all along the track towards the negative leader at the other end. These intermittent VHF emissions along the track, by their intermittent and random nature, cannot be the growing tip of the positive leader.From a large number of observations we know that positive leaders show in VHF very differently from negative leaders. The growing tips of negative leaders are clearly visible by the copious amounts of VHF emitted due to their step-wise propagation. Newly formed positive leaders can sometimes be traced by intermittent VHF emission along their track, known as needles11 which, by coherently adding the signals of about 170 antenna pairs, offers the most sensitive VHF based lightning-imaging method to date.In this work we search for the growing tip of the positive leader. Since, at any time, the positive leader tip must be farther along the channel than the currently observed VHF emission, we search along the positive leader track before the time the track becomes observable by the needle activity (intermittent VHF emission) or by a dart leader. How much earlier is, however, not known and is an issue of much interest. To do so we have performed a specific search for this tip using the LOw-Frequency ARray (LOFAR)We concentrate on one particular section of a rather long positive leader track where we search for evidence of the growing tip all along the track in a few different time windows. These time periods are selected to have a minimum activity elsewhere in the discharge thus to be able to achieve the highest possible sensitivity. The flash in this study is one of very few LOFAR observed flashes that shows VHF-quiet time periods during its development. Assuming the positive leaders propagate continuously, the VHF-quiet periods provide an opportunity for LOFAR to map any radiation sources at the tips of the positive leaders. In spite of the high sensitivity we have not been able to locate the tip and have, instead, set limits on its VHF brightness.12.Our lack of observation of the positive leader tip is rather surprising. Leader tips carry a considerable electric charge in the form of a very dynamic streamer corona. Any accelerating charge will emit electromagnetic radiation where the emission is most intense when the time scale of the acceleration is commeasuring with the oscillation frequency of the radiation. Thus it can be understood why negative leaders are very VHF bright. The non-observation of VHF from the positive leaders thus leads to the conclusion that they propagate in a very gradual, continuous mode, completely contrary to the stepping process seen for negative leaders. In a lightning discharge thus two, totally different, propagation modes appear simultaneously where the negative end is proceeding in an extremely VHF-bright stepping mode while the other, electrically connected, positive end is proceeding in an extremely VHF-quiet continuous mode. It is not clear how this can be reconciled in one consistent model. The observation of the VHF-quiet mode for positive leaders in lightning appear to be consistent with the observations for large-gap sparksIn "For this work we use a 1.5 second LOFAR recording from lightning flashes that occurred on April 24, 2019 at 19:44:32 UTC, which we label as 19A-1. An complete overview of the flashes in this recording is shown in the Supporting Information.11 is a radio telescope consisting of several thousands antennas spread over much of Europe. For these observations we record the signals of antennas in selected Dutch stations only. For the present work we use about 170 dual-polarized antennas spread over 34 clusters , operating in the 30 – 80 MHz VHF-band with base lines up to 100 km. To build images from the observations we use two different procedures. One is using the impulsive imager, described in13, where a time-of-arrival-difference method is used to locate the sources of the VHF pulses over the full extent of the discharge. Time of arrival differences are calculated using interferometric cross correlations. In the second imaging method, called TRI-D15, the volume to be imaged is voxelated where for each voxel the beam-formed intensity is calculated for 100 ns sections of the time trace. For beamforming, a coherent sum over all antenna traces is made while keeping track of their polarization.LOFAR16, due to the galactic background radiation, even for cases where the sources do not produce distinct pulses. The impulsive imager, in contrast, obtains the location of sources for which the emitted pulses can be identified in  all antennas. Both imaging methods use the signals of all recorded antennas.With the TRI-D imager a very complete picture is obtained for all, including weak, sources in a limited volume. With the TRI-D imager it is possible to image weak sources with a sensitivity that reaches below the natural backgroundFigure mentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimTo search for the growing tip of the positive leaders we use the TRI-D imager since it, by employing beamforming techniques, is able to locate much weaker sources than the impulsive imager and also sources that emit more continuously. The best sensitivity is reached when the VHF background, due to strong VHF sources elsewhere in the flash, is minimal. For flash 19A-1 we selected a few VHF-quiet time periods, where most periods fall between times 70 and 83 ms . A typical intensity distribution for an image tesseract (3-D cube and time) is shown in Fig. entclass1pt{minimaentclass1pt{minima16 . A source with strength I gb emits at a spectral energy density, integrated over the full solid angle and over a time slice D km vertically above an antenna. The deposited and energy in the antenna can be expressed in terms of the background power over the slice duration, where the power in the background is determined from the temperature of the galactic background while adding instrumental noise19.The intensity of the sources as determined by the TRI-D imager is usually expressed in units of [gb]In performing imaging in the 0.3 ms time interval around t=83.6 ms we noted an increased intensity for the time span 83.665–83.675, simultaneously in many different tesseracts, thus excluding it being a genuine source in one of the image cubes. Close investigation revealed that this was due to side beams from a genuine source in the vicinity of the image cubes that was not picked-up by the impulsive imager. This time span was thus excluded from the further search. With the TRI-D imager we succeeded to determine the precise location of this source at = km as shown in Fig. N to be small in order to be sensitive to less frequent peaks in VHF emission from the tip and, at the other, not too small to limit the influence of statistical fluctuations. If the tip of the positive leader would glow (in VHF) constantly with an intensity of As a signature of the presence of the growing tip of the positive leader we look for excess intensity in the different image tesseracts along the positive leader as compared to what was found as background, i.e. the intensity at 5 ms before the start of the flash. To quantify the intensity we have opted for using entclass1pt{minimaentclass1pt{minimaThe central times for the tesseracts of 0.3 ms duration were chosen such that there is a minimum of sources elsewhere in the discharge that, by virtue of ‘side beams’, would introduce false sources and thus inadvertently increase the mentclass2pt{minimmentclass2pt{minimmentclass2pt{minimFig. 3 it is shown that stepped positive leaders show stepping times ranging from 30 μs down to a fraction of 5 μs. A time interval of 0.3 ms will therefore contain many steps and the derived intensity limit thus should also apply to the case that the IC positive leader is propagating in a stepping mode.To set an upper limit on the intensity of the positive leader tip we have argued that mentclass2pt{minimAnother evidence for the VHF quietness of the positive leader can be taken from Fig. 3 of a VHF-bright positive leader in a cloud-to-ground (CG) discharge showing clear stepping very similar to what is seen in optical observations20 of rocket triggered positive leaders and positive leaders emanating from high buildings. Another stark contrast is that the VHF-bright positive leaders propagate at velocities of order 12 that when triggered lightning is propagating to higher altitudes there is a growing continuous current on which oscillations are superimposed that are gradually damped.Our observation that the tip of intra- and inter-cloud positive leaders is extremely quiet in VHF is in stark contrast with the observationThese observations suggest that when the positive leader is approaching a well conducting surface, or is well connected to a large conducting body (=Earth) the charge at its tip must be large with an electric field in the streamer zone that surpasses some critical value apparently causing the leader to be impulsive and propagate with a large speed.17, the positive leader is weakly luminous and shows continuous propagation with a constant glow of streamers at the tip. Its velocity is of order Under laboratory conditions, as discussed inWe have performed a search for the tip of a positive cloud-to-cloud leader using the TRI-D imager on data from LOFAR. In the process we have been able to set an upper limit of the VHF-emissivity of the tip at 60 MHz of 17. In the laboratory a smooth propagation of the corona at the tip is seen, creating the positive leader behind it in a continuous motion. In such a smooth and continuous process no (hardly any) VHF will be emitted which is consistent with our upper limit. In addition the propagation velocities reported in17, Our results are consistent with the laboratory observations of a positive leader as discussed inIt is quite interesting to find that the negative end of a lightning leader emits copious amounts of VHF radiation while the positive end is VHF quiet to such an extent that even in the most favorable circumstances its position cannot be determined by the most sensitive LOFAR imaging methods.Supplementary Information.


This article addresses the Brazilian government’s response to the covid-19 pandemic, particularly the public health surveillance and epidemic intelligence system. It traces the evolution of disease surveillance as a response to the International Health Regulations in the context of global health. Executive orders published in the official gazette, Diário Oficial da União, are analyzed, as well as the actors and groups formed to tackle the pandemic between January 2020 and March 2022. The founding assumption is that epidemic intelligence must be placed at the service of public health. Bureaucratic tension and changes in protagonism among different groups can be observed as these intelligence mechanisms were dismantled.


IntroductionAcute pancreatitis (AP), characterized by the inflammation of the pancreas, is a common acute surgical condition accounting for approximately 3% of all surgical admissions with abdominal pain and has an incidence of approximately 56 cases per 100,000 population every year. The General Medical Council (GMC), National Institute for Health and Care Excellence (NICE), and Royal College of Nursing best practice guidelines recommend that such patients and their family members should be provided with both verbal and written information about acute pancreatitis and its management in a way that they can understand. The aim of this audit cycle was to find out the compliance with information provided to patients with acute pancreatitis as per the GMC good medical practice and NICE guidelines and assess their satisfaction.MethodA closed-loop audit consisting of two cycles was carried out. Thirty patients who were admitted to the department of general surgery with acute pancreatitis were provided with a questionnaire containing 11 questions asking about the information provided to them about their condition by healthcare professionals; then, interventions were carried out in the form of developing patient information leaflets (PILs) and encouraging healthcare professionals to distribute them and provide information to the patients and their family members.ResultsOverall, improvements were seen in all aspects of the information being provided to patients, and particularly, more than 100% improvement was seen in patient satisfaction related to the information provided to them in the second cycle after the implementation of interventions.ConclusionsThis study concludes that patients should be given all the information they require in accordance with their right to information, in line with GMC best practice, NICE, and Royal College of Nursing best practice guidelines. A very effective way to improve the health outcomes and satisfaction of patients is to give them access to a patient information leaflet, which can allow patients to consider their options and understand what can happen during treatment, especially when doctors have limited time to carry out detailed discussions with the patient. Acute pancreatitis (AP) is a common acute surgical condition and is characterized by the inflammation of the pancreas involving acinar cell injury along with both a local and systemic inflammatory response . In the Patients with acute pancreatitis usually present with severe upper abdominal pain radiating to the back, nausea, and vomiting, and the diagnosis is established usually based on the following features: (a) sudden-onset persistent epigastric pain radiating to the back, (b) elevated lipase/amylase levels , and (c) characteristic radiological findings of contrast-enhanced CT scan and abdominal US scan  . GallstoThe General Medical Council (GMC) best practice guidelines recommend that communication should be established with the patients in a way that helps them understand the information they need or want to know and advise to ensure that plans are made to address the patients' language and communication needs . The NatWe conducted an audit cycle in our hospital to find out compliance with information provided to patients with acute pancreatitis as per the GMC good medical practice and NICE guidelines and assess their satisfaction in terms of the information provided.This article was previously presented as a meeting abstract at the Association of Surgeons in Training (ASiT) Surgical Conference 2023, in Liverpool, UK, and was published as a conference abstract in the British Journal of Surgery.This audit cycle was conducted at the surgical department of Royal Albert Edward Infirmary, a district general hospital (DGH) based in the UK. The audit proposal was sent for approval and was registered with the research and audit department of Wrightington, Wigan and Leigh NHS Foundation Trust before commencing.Thirty patients admitted with biochemical or radiological evidence of acute pancreatitis under the surgical team were included in the first cycle of the audit. All patients who presented with biliary colic, acute cholecystitis, choledocholithiasis, and malignant disease of the pancreas were excluded from the study. A self-structured questionnaire based on the NICE guidelines on the information and support section of acute pancreatitis in accordance with the GMC good medical practice guidelines was designed and provided to the patients included in the audit Table . The purThe results were then discussed at the routine audit meeting, and interventions were implemented in the form of designing and distributing the patient information leaflet (PIL) on acute pancreatitis Figure . The resThe first half of the audit cycle consisted of assessing the 30 questionnaires from patients admitted with acute pancreatitis, and the results showed only 40% patient satisfaction regarding the information provided. All patients admitted were aware of the reason for their admission in the hospital and the causes of acute pancreatitis, and 93% were aware of what acute pancreatitis is. The compliance with the rest of the information was as follows: investigations done to confirm the diagnosis, 60%; treatment of acute pancreatitis, 40%; potential complications, 33%; impact of smoking and alcohol, 73%; verbal information, 73%; and explanation with a diagram, 6%. None of the 30 patients were provided with a written information leaflet. It was further revealed that no patient information leaflet (PIL) was available on acute pancreatitis, despite being a common surgical presentation in our hospital. We designed a PIL and distributed it to the surgical wards after getting it approved by the surgical lead.The results were presented in the audit meeting, and the junior doctors (foundation doctors and registrars) were emailed with the audit results and encouraged to provide the information along with the leaflet to the patients. The ward clerks in the surgical wards were also provided with the leaflet to be kept in the wards and encouraged to provide it to the patients with acute pancreatitis. The second half of the audit was then conducted two months after implementing the interventions to assess compliance with the GMC and NICE good medical practice. The results from both audits have been summarized in the following diagram Figure .This audit cycle examined one of the most important pillars of GMC good medical practice and NICE guidelines regarding the right to information of patients admitted to our hospital with acute pancreatitis, which is one of the common surgical presentations in the hospital. The vast majority of European research conducted over the past five decades have revealed that the incidence of acute pancreatitis is increasing by about 3.4% every year .With this much rise in the incidence, it is now becoming increasingly imperative due to medicolegal reasons to ensure that patients are aware of the medical conditions they are admitted with and are being treated for. Moreover, patient satisfaction is a crucial and frequently used metric for assessing the quality of healthcare service. A simple intervention with the help of a leaflet in our case not only raised awareness among the patients but also increased satisfaction by more than 100%. This has also been evidenced in one of the studies by Gibbs et al. , which eThe study by Dennis et al.  determinStudies conducted by Weiss et al.  and GrahThis study shows a significant improvement in all factors assessed in patients admitted with acute pancreatitis, especially doubling the overall satisfaction of the patients with the information provided to them after interventions in the form of patient information leaflets. This study concludes that patients should be provided with all the necessary information according to their right to information as per GMC best practice and NICE and Royal College of Nursing guidelines. Patient satisfaction is a crucial and frequently used metric for assessing the quality of healthcare service. Effective education improves adherence to therapy, which leads to better outcomes and promotes patient satisfaction. Patient health outcomes and satisfaction can best be achieved by providing them with a patient information leaflet. Patient information leaflets have been crucial in enabling patients to weigh their options and comprehend what they might experience throughout the treatment, especially when doctors have limited time to discuss them with the patient.