Seismic anisotropy is a unique observational tool for remotely studying deformation and stress within the Earth. Effects of anisotropy can be seen in seismic data; they are due to mineral alignment, fractures or layering. Seismic anisotropy is linked to local stress and strain, allowing modern geophysics to derive geomechanical properties from seismic data for supporting well planning and fracking. For unravelling anisotropic properties of the crust, the teleseismic receiver functions methodology has started to be widely applied recently due to its ability in retrieving the three‐dimensional characteristics of the media sampled by the waves. The applicability of this technique is tested here by a field test carried out around the Kontinental Tiefbohrung site in southeastern Germany. We compare our results to previous investigations of the metamorphic rock pile of the Zone Erbendorf‐Vohenstrauss, drilled down to 9 km depth, which sampled an alternating sequence of paragneiss and amphibolite, in which a strong foliation has been produced by ductile deformation. The application of the receiver functions reveals the presence of two distinct anisotropic layers within the metamorphic rock pile at 0–4 km and below 6 km depth, with up to 8% anisotropy; the depth of these two layers corresponds to the location of mica‐rich paragneiss which show intense foliation, and finally proves the relation between the signal in the receiver functions, rock texture and presence of cracks. We have now the capability of providing insights from passive seismic data on geomechanical properties of the rocks, useful for geological exploration and engineering purposes, which will help influencing expensive drilling decisions thanks to future application of this seismic technique. Seismic anisotropy and its determination is of great interest because it is a key for constraining preferred alignment of structures within the Earth such as due to sedimentary layering, stress‐induced cracks and/or dykes and sills  metamorphic body which has been drilled down to 9 km depth, and investigated both ing Fig. b has beeet al. et al. , and is coinciding with the strike direction of the rock foliation Rabbel . The inf. et al. , which d. et al. .et al.  due to the positive interference of oriented microcracks and texture of the rocks. In particular, Kern et al.  find thaet al. in situ.Moreover, encountered horizontal stress direction in the borehole are around N150°  of 30°–100° and magnitude The amount of collected teleseismic traces allows a reasonable backazimuthal coverage Figs  and 3: e4a posteriori probability‐density function of the sv at depth following the reversible‐jump Markov chain Monte Carlo (rjMcMC) approach developed by Piana Agostinetti and Malinverno ; this main layer is divided into three sublayers. The second layer in our parameter space has been set without anisotropy parameters . The latter layer (or lower anisotropic layer) has been set with anisotropy, which would correspond to the lower (deeper) gneiss package (U3).The one‐dimensional shear velocity model beneath the two stations has been investigated by Bianchi and Bokelmann  who genelinverno . In thislinverno . The rjMokelmann . The vs After some initial tentative, we select the parameter space that guarantees the best misfit reduction within a reasonable number of sampled models. To cross‐check that our parameter space does not bias our findings, we include in the Supporting Information Material additional results using different parameter spaces. The defined parameter space is shown in Table S1.et al. Modelling the receiver function (RF) is a classical inverse problem characterized by strong non‐uniqueness. Interfaces depths and S‐wave velocity, anisotropy percentage and plunge of the anisotropic symmetry axis display a clear trade‐off, which makes it difficult to draw simple quantitative inferences from the observations. The stochastic sampling used by the neighbourhood algorithm to explore the multidimensional parameter space for a range of acceptable velocity models uses the properties of Voronoi cells with the aim of finding an ensemble of models with acceptable data fit. We generated 1000 initial random samples inside the parameter space, and the 50 cells with the lowest misfit were resampled to produce 500 new samples. This process was repeated 500 times, for a total of 101,000 models explored for each station. We evaluate the standard deviation of the models parameters on the ensemble of models which generate synthetics that fit the data with 1.10 times lower misfit than the best‐fit model. The best fit model is then interpreted as representative of the ensemble. Synthetics are calculated using the RAYSUM code  of the four layers (three sublayers within the U1 + 1 layer in U3) of the velocity model bearing anisotropy.We therefore focus here on the description of the anisotropy into the two main layers U1 and U3) in the upper 10 km of the crust. For station KW01, three sublayers of the U1 have anisotropy with a slow axis trending to the SW, for each of these the plunge is less than 25° from the horizontal, and the percentage of anisotropy is increasing from the shallower to the deeper (from 5% to 8%). At 6.5 km depth, a deeper anisotropic layer is encountered (U3), which displays a symmetry axis trending to the NE. The counts of single iteration best‐fit values for the anisotropic layers  are here shown for the robustness of the results. For station KW06, we run a first search using a two‐layered parameter space with one inclined interface, for constraining the high amplitudes observed within the first second of the receiver functions (RFs) , thus we exclude the presence of anisotropy there because such a geometry does not generate any relevant signal on the T component of the RF. By enlarging the values of anisotropy magnitude (0 to −15%) and plunge (0° to 90°) for the layers in U1 and U3, we show that the choice of the boundaries of our parameter space does not affect the results of the NA search. In this case, we include models without anisotropy . The results are shown in Fig. S3. Best‐fit and standard deviation values highlight that a strong anisotropy is still present in layers U1 and U3 (between −5% and −9%), and that the plunge of the symmetry axes are not close to vertical.6We have determined the anisotropic parameters for a sequence of layers under two seismic stations near the Kontinental Tiefbohrung (KTB) borehole, and we will later compare these in detail with the subsurface structure which is known from the KTB borehole.et al. The lithological units of the zone of Erbendorf‐Vohenstrauss (ZEV) extend down to the final depth of the borehole and are divided into paragneiss, amphibolites and variegated  Fig.  Emmerma. The whoet al. et al. The metamorphic rocks show a steep dip between 60° to 80° towards SW or NE and are strongly folded with subhorizontal axial planes and NNW–SSE trending fold axes  has been detected that is oriented NW–SE parallel to the foliation planes of the metamorphic body  are striking in NW–SE orientation, but faulting and foliation dip towards opposite directions and affecting the wave propagation; we argue that the causes of the deviation from being parallel to the texture are due to the combined influence of faults and cracks.To compare with rock fabrics, we inspect the retrieved trend and plunge angles of the slow anisotropic axes, and project them on the SW–NE cross section of the ZEV summarizing the main orientation of the foliation and of the faults , a passive seismological technique, in the Kontinental Tiefbohrung (KTB) area in Southern Germany, we have acquired some unique proof of the direct correspondence between in situ anisotropy; in particular, we infer the presence of two distinct anisotropic layers within the upper crust. The depth of these two layers corresponds to the location of mica‐rich paragneiss which show intense foliation, this let us gain larger information with respect to previous in situ studies where anisotropy was identified as due to the entire Zone of Erbendorf‐Vohenstrauss (ZEV) thickness. We infer higher anisotropic percentages at shallower depths probably related to the presence of cracks. Concerning the causes of the seismic anisotropy, we conclude that for the lower anisotropic layer the symmetry axis of the slow shear‐wave is perpendicular to the main foliation of the paragneiss, and is ascribed as due to the alignment of the minerals (micas), whereas for the upper anisotropic layer, the slow anisotropic axis deviates from being perpendicular to the foliation plane, probably due to the presence of intense faulting and of the crack system. Moreover, RF can provide important information on the depth location of seismic anisotropy, and can be used as a complementary or explorative tool for underground exploitation, due to its computational efficiency and low cost.We gain information below two seismic stations located nearby the KTB drilling hole, where we verify the presence of


Vitreoretinal surgeries require precise, dexterous, and steady instruments for operation in delicate parts of the eye. Robotics has presented solutions for many vitreoretinal surgical problems, but, in a few operations, the available tools are still not dexterous enough to carry out procedures with minimum trauma to patients. Vitrectomy is one of those procedures and requires some dexterous instruments to replace straight ones for better navigation to affected sides inside the eyeball.L × W × H), suitable for approaching distant positions inside the eyeball.In this paper, we propose a new vein puncturing solution with a 4-DOF motion to increase the workspace inside the eye. A two-member concentric tube-based 25G needle is proposed whose shape is optimized. To operate the concentric tube needle, a novel and miniaturized actuation system is proposed that uses hollow shaft motors for the first time. The presented prototype of actuation system has a stroke of 100 mm in a small size of 148 × 25 × 65 mm (Experimental results validate that the targeting accuracy of the needle is less than one millimeter and the needle tip can apply a force of 23.51 mN which is enough to perform puncturing. Furthermore, the proposed needle covers maximum workspace of around 128.5° inside the eyeball. For the actuation system, experiments show that it can produce repeatable motions with accuracy in submillimeter.The proposed needle system can navigate to the sites which are difficult to approach by currently available straight tools requiring reinsertions. Along with the miniaturized actuation system, this work is expected to improve the outcome of vitrectomy with safe and accurate navigation. Eye, one of the most delicate parts of the human body, requires steady and accurate tools with enough dexterity to cause the least trauma to patients. Vitreoretinal surgery is a part of ophthalmic surgery that deals with the issues related to the retina. Due to inflammation in the retinal arteries and veins, clouding of vitreous fluid (gel-like substance present behind the lens of the eyes), and swelling of the retina, vision is severely obscured resulting in uveitis . This kiRobotics has provided viable solutions to many clinical issues for almost three decades  and firsMost of the tools available to date for tasks like puncturing and vein cannulation are straight using 30G needles with a catheter . The da CTR is almost a decade old in the field of robotics and clinically applicable actuation units are required for their acceptance in the surgical room . DiffereA 4-DOF needle based on the CTR approach for puncturing and vein cannulation is presented in this paper. It consists of two pre-curved segments; a cannula and stylet, and the shape of whole CTR is optimized to cover more workspace inside the eye and disallow repeated insertions. A novel miniaturized actuation system for 4-DOF CTR is also presented here which uses hollow shaft stepper motors for the first time. The developed actuation system is repeatable and provides two degrees of freedom (translation and rotation) for each member. The contribution of this paper is: (1) a new 4-DOF concentric tube needle to carry out puncturing and vein cannulation in vitrectomy, (2) optimized design to cover more workspace inside the eyeball, and (3) a novel and miniaturized actuation system for CTR using hollow shaft motors.The currently available straight tools have an issue of repeated reinsertions if a new target has to be reached inside the eyeball. In some cases, surgeons push out the eye of the patient to reach distant targets causing pain. Such actions will cause trauma to patients and necessitate stitching for scleral closure. Thus, a tool that can turn inside the eyeball without moving its initial trocar position would be more desirable. Figure To achieve that goal, we propose a 4-DOF needle system shown in Fig. ®. A surgical target was chosen that is situated 45 mm away from the insertion point. The shape of the segments was solved using the approach presented in [To reach distal targets situated behind the retina, the curved length of the whole needle structure was fixed to 45 mm . Both cannula and stylet are nitinol tube and wire, respectively, and their shape was optimized in MATLABented in :1\documeθ0, x0, and y0 are initial projection angle and 2D position of the insertion point, respectively. The curvature and the arc length of cannula and stylet are a, b s1, and s2, respectively. Equation Here, As the needle segments are of nitinol, shape setting process was applied to achieve the pre-curved structure. Using the optimized curvature and arc length values, an aluminum jig was developed to constrain the segments. An air furnace was used to heat the nitinol segments at 550 °C at a heating rate of 10 °C/min. The segments were kept at the final temperature for 15 min and cold-water quenching was performed afterward. To make the puncturing tip on stylet, nitinol wire was laser cut in a triangular shape with vertices angle of 45°.Most of the actuation systems present till date are either bulky or complex or compromise the performance of CTR . To desiIn this work, two modules were developed for driving two segments of the puncturing needle with each having 2-DOF. A total of four motors were used: two for translation and two for rotation. A lead screw assembly was attached to two motor’s shafts to convert the rotational motion into translational one. M4 × 0.7 and M6 × 1 screws with corresponding nuts were used for translation in modules of cannula and stylet, respectively. An aluminum linear rail with two sliders was attached to the base of the actuation system. The translating bodies  provided by ROBOTDIGG were used to drive the motors. MyRIO controller from National Instruments Co. was used to control the rotation of the motors through a computer. At this stage, a simple position control PID controller was implemented in LabView program provided by National Instruments Co. The control setup used for experimentations is shown in Fig. Different sets of experiments were performed to validate the efficacy of the proposed needle system.The shape optimization algorithm discussed before was used for solving the geometry of needle and provides parameters for shape setting. To validate the mechanical stability, strain induced in each segment because of the provided curvature value to needle segments is calculated. Equation ϵ is the maximum strain, k is the curvature, and y is the distance from neutral axis for each segment. By substituting values in Eq. Here, The actuation system was designed to provide a stroke of 50 mm at both the cannula and stylet module. To validate it in the developed prototype, the accuracy of stroke was measured. An optical marker was attached on the top of the translating bodies of cannula and stylet module, as shown in Fig. The repeatability for translational motion of both modules was also checked using the same experimental setup. The translating body was initially moved to a random position (pivot position). Then, it was moved in one direction and brought back to the same pivot position. The translating body was moved four times to-and-fro from the pivot position; twice forward and twice backward. Each motion is repeated three times and the experimental technique is schematically shown in Fig. ® to find the tip trajectory for real-time motion. The recorded video had a total of 2126 frames and pixel points of the tip of the needle were recorded after every 20 frames. Using the pixel difference from the checkerboard edges, millimeters per pixel value was computed which lead to the real-time tip position in 2D coordinates. These 2D coordinates are smoothed and real-time motion of the needle is shown in Fig. The developed prototype of the needle was analyzed to reach its optimized target in real time and error was computed. The experimental setup for checking the targeting accuracy of the needle is shown in Fig. In addition to targeting accuracy, the actual workspace covered by the needle in free space was also measured. The same experimental setup was used for workspace analysis, but, in this case, two cameras (one for the top view and one for side view) were mounted for video recording. Half of the pre-curved length of cannula segment was actuated from the insertion port and rotated around its axis. Using image processing, the position of the rotating cannula tip was tracked. Afterward, the whole pre-curved length of cannula body was actuated and rotated. Similarly, the stylet was initially actuated half and rotated like in case of cannula, but, here, the cannula was also rotated to get the combined workspace at the tip. Subsequently, the full length of stylet was actuated, and both segments were rotated and analyzed for subtended workspace. The obtained data points were fit to a circle and smoothen. The subtended workspace by the whole needle is shown in Fig. Using the data of subtended workspace, the maximum angle swept by the needle was also calculated. A triangle was created using two lines (OP1 and OP2) from the farthest moved points (P1 and P2) by the needle tip to the insertion point (O) and by joining these farthest moved points by the line P1P2, as shown in Fig. A puncturing force of around 15 mN is required for tasks of vein puncturing and membrane peeling in retinal surgeries , 19. To To avoid stitching of sclera in vitreoretinal surgeries, the procedure should be carried out by a minimum number of incisions and smaller tool diameters. The currently available straight tools for vitrectomy have two major limitations. (1) If there are multiple surgical targets, the straight tools are required to be reinserted increasing the number of incisions. (2) In the case of distant targets, the surgeons push out the eye of the patient which cause pain and trauma. Therefore, the proposed needle system is bendable and does not need reinsertions if a new surgical target has to be reached. In addition, the relative motion of cannula and stylet can generate 4-DOF motion and can help in reaching distant targets. The needle system was also used in the albumen and different targets were accessed without any difficulty making it viable for vitreoretinal procedures. Along with the clinical advantages, the proposed needle system improves the CTR design used previously in  by increThe presented prototype of needle and actuation system in this work is earlier versions and needs further developments. First, for operation in the eye, force sensing and tremor cancelation are very important. If the force exerted on the sclera and retinal structures is more than the permissible value, serious damage may occur. The stylet tip can generate more than the required 15 mN force which may be helpful to puncture the vessel, but it should be controlled to be in the range of the required value. To curtail this issue, force sensing is vital in any ophthalmic surgery robot, and the immediate future goal is to implement force sensing in both cannula and stylet. By limiting the applied force, the stylet will only puncture the vessel except for going through it and this will also avoid damage to the neighboring structures.Second, the current version of the actuation system is already miniaturized, but surgeons mostly prefer handheld or joystick-operated devices. Therefore, a surgically ergonomic actuation system will be developed and a motor-based telerobotic actuation is the most desirable candidate till date.Third, the designed prototype can only be used for puncturing tasks at this stage. By modifications in the actuation device, the stylet tip can also be used for membrane peeling. Another application can be on-site drug delivery after puncturing. For this purpose, the length of cannula should be increased, so that it can also reach the surgical target and the stylet should be retracted. The design of the proposed version of the needle system has a possibility to retract the stylet, but it is limited due to the current version of the actuation system. The future prototypes of the needle and actuation system will compensate for stylet retraction, so that the drug can be delivered through the cannula to the punctured vein.Fourth, the optimization algorithm at this stage does not consider the torsional stability of segments and a more advanced optimization algorithm is in development. The inverse kinematics of the concentric tube structure will be solved too for more detailed analysis.Fifth and last, if the incision in sclera is around 0.9 mm, the patient may require stitching after the surgical process. If the incision size is reduced to 0.6 mm or less, post-surgery stitching is not required. The current dimensions of the needle system lie in the gray area for stitching and will be miniaturized to be less than 0.6 mm in the future version.In the end, experiments validated the potentials of the developed prototypes of puncturing needle for vitrectomy and the novel actuation system for concentric tube robots. The presented prototype of the needle can cover sufficient workspace inside the eyeball and exert tip force necessary for puncturing. The proposed actuation system is accurate and can produce repeatable motions. Further efficacy of the needle and actuation system will be validated by analysis of the future versions with above-mentioned changes.L × W × H).This work presents a new 4-DOF puncturing needle to maneuver behind the retina and reach distal targets with increased workspace to solve issues encountered by a straight tool. A concentric tube-based approach was used and the proposed 25G needle has 4-DOF with two pre-curved segments; cannula and stylet. To drive this concentric tube robot (CTR), a novel and miniaturized actuation using hollow shaft stepper motors was also developed. It provides a stroke of 100 mm in a small size of 148 × 25 × 65 mm (The experimental results validated that the developed actuation system produces repeatable motions and the needle can reach the surgical targets with accuracy in submillimeter. It can cover an extended workspace of 128.5° which improves the design of CTR for eye surgery. The tip of stylet was specifically designed for puncturing tasks and provides a force of 23.51 ± 0.81 mN.The future versions of presented systems will include a force sensor to limit the amount of force inside the eyeball. In addition, a surgically ergonomic actuation system will be developed to assist surgeons in clinical trials.


The genesis of the “complex type” classification of pancreaticobiliary maljunction (PBM) is unclear, and the pancreaticobiliary anatomy is also varied according to each case. We encountered a patient with PBM and incomplete pancreatic divisum (PD). We herein discussed about the embryological etiology of pancreaticobiliary system predicted from PBM with incomplete PD.A 67-year-old man was found to have a dilatation of the common bile duct (CBD) during a medical examination at 62 years of age. The dilatation of the CBD subsequently progressed, and he was admitted to our hospital for surgical treatment. Magnetic resonance cholangiopancreatography revealed a dilatation from the common hepatic duct to the middle bile duct with PBM. Endoscopic retrograde cholangiopancreatography from the papilla of Vater revealed the pancreatic main duct via the pancreatic branch duct, and PBM with dilatation of the CBD and incomplete PD were revealed. We performed an extrahepatic bile duct resection and hepaticojejunostomy because of high risk of malignant transformation. Taping and transection of the bile duct without dilatation on the pancreatic side were performed, and thereafter, two orifices of the common channel and ventral pancreatic duct were ligated. The level of amylase in the bile was 7217 IU/L, and a histological examination of the CBD showed an inflammatory change of CBD, not a malignant transformation.It is somewhat easy to identify the pancreatobiliary anatomy when the cause of embryology of both PBM and PD is thought to be an abnormal embryology of the ventral pancreas. The “complex type” classification of pancreaticobiliary maljunction (PBM) is rare,  and in pWe encountered a patient with PBM and incomplete PD. We herein discussed about the embryological etiology of pancreaticobiliary system predicted from PBM with incomplete PD in order to understand the pancreaticobiliary anatomy.A 67-year-old man was found to have a dilatation of the common bile duct (CBD) (19 mm) during a medical examination at 62 years of age. The dilatation of the CBD subsequently progressed (26 mm), and he was admitted to our hospital for surgical treatment. Abdominal computed tomography revealed a dilatation of the CBD with no tumor or stone. Magnetic resonance cholangiopancreatography revealed a dilatation from the common hepatic duct (CHD) to the middle bile duct Fig.  with PBMWe planned an extrahepatic bile duct resection and hepaticojejunostomy because of high risk of malignant transformation. Laparotomy was performed by a right hypochondrium incision. Taping and transection of the bile duct without dilatation on the pancreatic side were performed, and thereafter, two orifices of the common channel and ventral pancreatic duct were ligated Fig. . The traThe postoperative course was good and uneventful, and the patient was discharged from the hospital on postoperative day 9. The patient is doing well at 1.5 years after surgery.The “complex type” classification of PBM is rare,  and in pAlthough the recommended treatment for a biliary dilatation with the “complex type” classification of PBM is an extrahepatic bile duct resection and hepaticojejunostomy (biliary diversion procedure),  selectinIt is difficult to identify the “complex type” pancreatobiliary anatomy of PBM; however, it is somewhat easy to identify when the cause of embryology of both PBM and PD is thought to be an abnormal embryology of the ventral pancreas.


Finally, despite the fact of the geometrical LoT not being a universal (i.e. Turing-complete) language, we show an empirical relation between a sequence’s probability and its complexity consistent with the theoretical relationship for universal languages described by Levin’s Coding Theorem.Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share the property that they are built from a set of atomic symbols and rules by which these symbols can be combined. In this work we propose an extra validation step for the set of atomic productions defined by the experimenter. It starts by expanding the defined LoT grammar for the cognitive domain with a broader set of arbitrary productions and then uses Bayesian inference to prune the productions from the experimental data. The result allows the researcher to validate that the resulting grammar still matches the intuitive grammar chosen for the domain. We then test this method in the  It was not only difficult for him to understand that the generic term dog embraced so many unlike specimens of differing sizes and different forms; he was disturbed by the fact that a dog at three-fourteen (seen in profile) should have the same name as the dog at three-fifteen (seen from the front). (…)With no effort he had learned English, French, Portuguese and Latin. I suspect, however, that he was not very capable of thought. To think is to forget differences, generalize, make abstractions. In the teeming world of Funes, there were only details, almost immediate in their presence. In his fantasy story, the writer Jorge Luis Borges described a fictional character, Funes, capable of remembering every detail of his life but not being able to generalize any of that data into mental categories and hence –Borges stressed– not capable of thinking.Researchers have modeled these mental categories or conceptual classes with two classical approaches: in terms of similarity to a generic example or prototype –5 or baslanguage of thought (LoT) hypothesis  be a program, then p(0) is the result of executing p starting from point 0  and p(4) is the result of executing the same program starting from point 4 in the octagon .Each program 8](0) or [REP[+1]7, +1](0), etc. To alternate 8 times between points 6 and 7, one can use a reflection production like [REP[A]8](6), or 4](6).Each sequence can be described with many different programs: from a simple concatenation of atomic productions to more compressed forms using repetitions. For example, to move through all the octagon clockwise one point at a time starting from point 0, one can use (0) or [REP[+1]language of geometry so that each sequence could be easily described with few productions.To infer the productions from the observed data, we used the original data from the experiment in . In the The data used in this work comes, except otherwise stated, from Experiment 1 in which participants were 23 French adults  with college-level education. Data from Experiment 2 is later used when comparing adults and children results. In the later, participants where 24 preschoolers .di ∈ Σ8 from our dataset D is thus the sequence of eight positions clicked in each subject’s trial. The detailed procedure can be found in the cited work.On each trial, the first two points from the sequence were flashed sequentially in the octagon and the user had to click on the next location. If the subject selected the correct location, she was asked to continue with the next point until the eight points of the sequences were completed. If there was an error at any point, the mistake was corrected, the sequence flashed again from the first point to the corrected point and the user asked to predict the next location. Each We will now expand the original set of productions in i to select the ithdigit of a well-known number like π or Chaitin’s number  = 3 mod (8) = 3; and PI(1) = 1.In its long ). All diP by sampling from a multinomial distribution of all the possible programs pi that compute di, where each pi has probability of occurrence equal to P(pi ∣ θ).To let the MCMC converge faster (and to later compare the concept’s probability with their corresponding MDL), we generated all the programs that explain each of the observed sequences from the experiment. In this way, we are able to sample from the exact distribution σ = 693, 618).To get an idea of the expressiveness of the grammar to generate different programs for a sequence and the cost of computing them, it is worth mentioning that there are more than 159 million programs that compute the 292 unique sequences generated by the subjects in the experiment, and that for each sequence there is an average of 546,713 programs . Each bar shows the mean probability and the standard error of each of the atomic productions after 50 steps of the MCMC, leaving the first 10 steps out as burn-in.P exactly in order to speed up convergence and to be able to later compare the probability with the complexity from the original MDL model. In θ+0, which corresponds to the atomic production +0, but is representative of the behavior of all θi. . This indicates that the language of geometry is capable of reusing simpler structures that capture geometrical meaning to explain the observed data, a key aspect of a successful model of LoT.We then ran the same inference method using observed sequences from other experiments but only with the original grammar productions (i.e. setting aside the ad-hoc productions). We compared the result of inferring over our previously analyzed sequences generated by adults with sequences generated by children (experiment 2 from ) and thelanguage of geometry could explain adults’ behavior but had problems to reproduce the children’s patterns for some sequences. However, they also showed that penalizing the rotational symmetry (P) could adequately explain children’s behavior. In minimal program of each sequence. On the other hand, the Bayesian model in this work tries to explain the observed sequences produced by children considering the probability of a sequence summing over all the possible programs that can generate it and not just the ones with minimal size. Thus, a production like (P) that might not be part of the minimal program for a sequence might not necessarily be less probable when considering the entire distribution of programs for that same sequence.It is worth mentioning that in  the compthe language of geometry in particular ) for all generated sequences x. The data is plotted with a logarithmic scale for the x-axis, illustrating the inverse logarithmic relationship between R2 = .99, R2 = .94, R2 = .97, R2 = .99 and R2 = .98 for language of geometry, matches the theoretical prediction for infinite sequences in universal languages described in the Coding Theorem. At the same time, it captures the Occam’s razor intuition that the simpler sequences one can produce or explain with this language are also the more probable.This relationship between the complexity Figs We have presented a Bayesian inference method to select the set of productions for a LoT and test its effectiveness in the domain of a geometrical cognition task. We have shown that this method is useful to distinguish between arbitrary ad-hoc productions and productions that were intuitively selected to mimic human abilities in such domain.The proposal to use Bayesian models tied to PCFG grammars in a LoT is not new. However, previous work has not used the inferred probabilities to gain more insight about the grammar definition in order to modify it. Instead, it had usually integrated out the production probabilities to better predict the data, and even found that hierarchical priors for grammar productions show no significant differences in prediction results over uniform priors , 17.We believe that inferring production probabilities can help prove the adequacy of the grammar, and can further lead to a formal mechanism for selecting the correct set of productions when it is not clear what a proper set should be. Researchers could use a much broader set of productions than what might seem intuitive or relevant for the domain and let the hierarchical Bayesian inference framework select the best subset.Selecting a broader set of productions still leaves some arbitrary decisions to be made. However, it can help to build a more robust methodology that –combined with other ideas like testing grammars with different productions for the same task – could pHaving a principled method for defining grammars in LoTs is a crucial aspect for their success because slightly different grammars can lead to different results, as has been shown in .The experimental data used in this work was designed at  to underFinally, we showed an empirical equivalence between the complexity of a sequence in a minimal description length (MDL) model and the probability of the same sequence in a Bayesian inference model which is consistent with the theoretical relationship described in the Coding Theorem. This opens an opportunity to bridge the gap between these two approaches that had been described ad complementary by some authors .S1 FigMCMC steps for the rest of (EPS)Click here for additional data file.S2 FigHistograms of complexity for sequences with length between 4 and 8.(EPS)Click here for additional data file.S3 FigHistograms of probability for sequences with length between 4 and 8.(EPS)Click here for additional data file.


This work presents an experimental and numerical analysis of the mechanical behavior of a fixed-end SAE 1045 steel cylindrical specimen during the torsion test. To this end, an iterative numerical–experimental methodology is firstly proposed to assess the material response in the tensile test using a large strain elastoplasticity-based model solved in the context of the finite element method. Then, a 3D numerical simulation of the deformation process of the torsion test is tackled with this previously characterized model that proves to be able to predict the development of a high and localized triaxial stress and strain fields caused by the presence of high levels of angular deformation. Finally, the obtained numerical results are analytically studied with the cylindrical components of the Green–Lagrange strain tensor and experimentally validated with the measurements of shear strains via Digital Image Correlation (DIC) and the corresponding torque – twist angle curve. The mechanical characterization of the elastoplastic behavior of a material during the torsion test is relevant for the analysis and optimization of manufacturing processes that are nowadays carried out. One of the most elementary cases is the high resistance cables used in cranes, elevators, pulleys, etc. In the manufacturing of these elements, the material is subjected to extreme large torsion deformations, which in turn induce high elastoplastic stresses that complicate predicting the mechanical behavior of the material under service conditions.In the case of pure torsion of cylindrical bars, it is well-known that the distribution of stresses is not uniform in the radial direction, leading to a zero value at the center of the specimen and to a maximum in its periphery, for both the elastic and elastoplastic regimes. Furthermore, some authors have reported the presence of axial deformations or axial forces, depending on the boundary condition used, when the cylindrical specimen is under a large torsional state. The most important case that occurs in the torsion test is the Swift effect , in whicIn recent years, the study of torsion has been mainly focused on experiments to analyze the effect of large deformations on the material response. The large deformations induced in the torsion test were used to observe the changes in the microhardness on the crystalline structure . AnotherSome authors ,5 have pDespite the torsion does not induce a necking zone in the specimen, as typically occurs in the tensile test, a complex stress state in the material is developed due to the zero shear stress condition present in the central fiber of the sample. This condition generates at high levels of deformation a steep gradient in the stress field. The literature available to analyse this problem is based on axisymmetric 2D models ,9, makinIn the present work we analyze the mechanical response of the SAE 1045 steel in the torsion test using cylindrical samples. To this end, a twofold objective is pursued: to characterize the material hardening behavior through the tensile test and to carry out numerical 3D simulations of the torsion test by analyzing and validating the numerical results with the experimental curves. Therefore, this study encompasses experiments as well as numerical simulations. Uniaxial tensile tests have been firstly performed to calibrate, via an iterative experimental–numerical methodology that not only accounts for the engineering and true stress-strain curves but also for the ratio of current to initial diameter evolution at the necking zone, the material parameters of a large strain elastoplastic constitutive model based on the von Mises yield function including a Hollomon hardening law. Then, torsion tests with a fixed-end condition have been carried out where the previously characterized model is used for describing the material response under large angular deformations. In particular, the validity of some analytical expressions of the cylindrical components of the Green–Lagrange strain tensor is assessed by measuring the strain field using a 2D Digital Image Correlation (DIC). Moreover, the numerical prediction of the torque-torsion angle curve is experimentally validated while radial profiles of axial and shear stresses together with axial force evolution during the test are also computed and discussed. This manuscript is organized as follows. The material used for the mechanical tests (tensile and torsion) corresponds to a commercial as-received SAE 1045 steel, whose average chemical composition is shown in The tensile test is used here to establish the constitutive law of the material. P is the recorded axial force, l is the instantaneous extensometer length measured during the test. As it is well known, the true stress and strain (logarithmic) are respectively defined as D. The following properties are obtained from this test: Young’s modulus, Poisson’s ratio and yield limit with the following ASTM standards 132-97 P/A0 and The torsion test provides the relationship between the torque and the angular deformation of the sample. It should be noted that larger homogeneous deformations are achieved in this case compared to those of the tensile test since no necking is developed in the sample. r is the radius of the specimen, Additionally, a 2D Digital Image Correlation (DIC) has been carried out, in which the Lagrangian strain tensor of the central region of the specimen is obtained. The image correlation technique used considers a 2-D analysis that is comparable to the case of 3-D twisting under certain assumptions that have been corroborated. First of all the diameter of the specimen does not change during the test, which has been experimentally verified; see h can be measured directly with the DIC software. It should be noted that the displacement Y is the projection of the arch S. This displacement can be obtained using a 2D DIC analysis for any axial position. It can be shown that the displacement Y and the torsion angle  and a set of phenomenological internal variables  accounting for the non-reversible effects. The stress–strain relationship and the evolution laws for the internal variables adopted here to simulate the material behaviour are briefly described below , An initial guess of the hardening parameters opted in  that con defined .For this purpose, the methodology consists in extending the previous approach to simultaneously account for three curves: (1) axial engineering stress–strain, (2) axial true stress–strain, and (3) ratio of current to initial diameter at the necking zone versus axial elongation. These curves are computed via a numerical simulation of the tensile test since, as already commented, this kind of analysis is needed to properly describe the complex stress and strain patterns that develop during the elongation process. The full iterative fitting algorithm is outlined in With the initial guess of the hardening parameters E, EThe analytical expression for the deformation gradient tensor at the periphery (edge) of the specimen can be written as :(6)F=100on angle . Using tAlthough the simulated ϕ = 20°, a linearly elastic behavior occurs up to almost ϕ = 120° and ϕ = 350°, the steep gradient in the center reflects the narrowing of the elastic region whereas the elastoplastic zone evolves similarly to the case with a small torsion angle. Although the numerical singularity close to the coordinate The computed radial profiles for the shear stress at the middle cross section of the sample are plotted in orted in , a challϕ = 20° and ϕ = 120°, this stress exhibits a noticeable profile for ϕ = 350°.The development of longitudinal stress has been previously analyzed ,7,10, reϕ = 350°, making the stress state clearly triaxial. Once again, this trend is also repeated at any plane parallel to plane 1 along the working zone of the sample.At ϕ = 130° retaining a linear evolution after ϕ = 75°, while The axial component of the stress has a nonlinear behavior with respect to the torsion angle as seen in the ϕ = 10°), rapid increase due to the radial progress of plastic effects with relatively high hardening evolution (from ϕ = 10° to ϕ = 75°) and continuous increase once almost the entire transversal section linearly hardens more smoothly (from ϕ = 75° to ϕ = 350°); see The elastoplastic response in the torsion test of the SAE 1045 steel has been characterized considering an associated isotropic constitutive model. Based on the tensile test measurements, an iterative numerical-experimental methodology was firstly used to fit the material hardening parameters. Then, this calibration procedure was satisfactorily validated in the simulation of the mechanical behaviour of the material in the torsion test where realistic predictions were obtained for the whole studied deformation levels. In particular, the shear and axial stresses were evaluated in the plastic regime. For high torsion angles , an important stress localization was observed in the central area of the specimen, an effect that makes numerical modeling necessary for its interpretation. Finally, relevant effects not included in the present study, such as kinematic hardening and damage evolution, could be addressed in future research using this test under cyclic conditions. It is known that due to warping torsion for high levels of deformation, some effects can appear, such as an asymmetric elastoplastic behavior, restraints due to boundary conditions, and noncircular section along the specimen length. These effects have not been taken into account in this study.


Periodontal pathologies are highly widespread throughout the world. Epidemiological studies have shown that as much as 1% of the population is suffering from periodontal disease. In recent years, there has been a growing number of studies linking these diseases with autoimmune diseases, especially with rheumatoid arthritis. This literature review evaluates changes in the relationship between periodontal pathologies caused by the bacterium Porphyromonas gingivalis and rheumatoid arthritis. The systematic review of the literature was performed according to the PRISMA analysis protocol. The review was performed with articles from the PubMed database. Searched articles were not older than 5 years. Only full texts and research performed with people were selected. A total of 56 results were received. A review and analysis of their full texts have been carried out and 10 articles were selected according to the established criteria. They were analyzed and results were presented. The results obtained from the literature were based on the influence of Porphyromonas gingivalis on the pathogenesis of rheumatoid arthritis. In the literature, the activity of this bacterium is explained by the analysis of its enzyme peptidylarginine deiminase and its principle of action. Studies have also been found to prove the presence of Porphyromonas gingivalis not only in the oral cavity but its DNA is also found in synovial fluid and plasma. In the researched articles, direct links between Porphyromonas gingivalis and rheumatoid arthritis have led doctors to draw attention to patients' oral hygiene and the condition of parodentium, as this may be the cause of autoimmune lesions. Treatment of periodontal disease will not only help maintain a healthy oral cavity but prevent the spread of bacteria to the surrounding tissues. Rheumatoid arthritis (RA) is an autoimmune disease, which is very common and it affects about 1% of the total population . The preTasks1. To review and analyze literature on the relationship between rheumatoid arthritis and periodontal disease.2. To review and analyze the literature on the influence of the enzyme PPAD produced by the bacteria Porphyromonas gingivalis causing inflammation in the joints.3. To review and analyze the literature on the human-induced changes that link the Porphyromonas gingivalis bacteria to the pathogenesis of rheumatoid arthritis.Criteria for selecting articles and search methods and strategyAnalysis of literature was performed using the PRISMA analysis protocol. Articles were selected using the keyword "Porphyromonas gingivalis rheumatoid arthritis." Articles that were not older than 5 years, written in the English language, and published in journals were selected. Only the articles which were published on the PubMed were selected.During research in the PubMed database, the keyword "Porphyromonas gingivalis rheumatoid arthritis" yielded a total of 128 results. We only used the latest articles in our research, therefore, a filter for 5-year-old articles was applied. A total of 95 articles were left. We used full texts for the analysis, therefore, we also added another filter of full texts. Now 92 articles were left. We were interested in articles describing the research with the human population; therefore, we applied another filter that identifies the literature that describes the work performed with people. Finally, 56 articles were left.From these articles, we reviewed and selected the literature that researched or discussed the links between Porphyromonas gingivalis and RA (Schedule 1). There were 10 such articles.Literature was selected and analyzed according to the following criteria: 1. The research was performed using the human population as subjects.2. The patients were adults.3. Any relationship investigated between the RA and PD via the enzymes released by the Porphyromonas gingivalis bacterium PPAD (peptidylarginine deiminase).4. The data from the articles were selected based on whether or not they demonstrated or denied the dependence of the more frequent occurrence of the RA as an autoimmune disease depending on the PPAD activity of the enzymes released by Porphyromonas gingivalis.Exclusion criteria: we did not include 46 out of the 56 articles because:1. The subjects were children, and our analysis was performed with studies in adult patients.2. The studies were focused on the weakening of the immune response strength in patients with RA. However, the challenges we were analyzing were not discussed.3. The article described osteoclastogenesis with respect to interleukins .4. The articles did not discuss PPAD operation.5. Only the genetic relationships between PD and RA were investigated.6. Microbiological preventive reviews were performed.7. Articles were not in English.AnalysisRelationship between rheumatoid arthritis and periodontal diseases: In the literature review, we found 10 articles to support the persistence of Porphyromonas gingivalis and rheumatoid arthritis as pathologies directly related to each other. This is substantiated by the study of scientists. Laugisch et al. found that the PPAD enzyme is more active in RA patients, and in the RA patients who have a diagnosis of the PD . HashimoInfluence of the enzyme PPAD produced by the bacteria Porphyromonas gingivalis, causing inflammation in the joints: The influence of Porphyromonas gingivalis on causing the rheumatoid arthritis is based on the activity of the enzyme PPAD. It is an enzyme secreted by the bacteria responsible for citrullination. This enzyme carries out the transformation of the amino acid arginine to the amino acid citruline. The transformation occurs on the enzyme PPAD protein by replacing the amino acid ketamine group with the ketone group. The body responds to this change as an autoimmune response. According to the Fisher Benjamin et al. and Li et al., antibodies to citrullinated proteins in the human body occur much earlier than the diagnosis of RA is determined , 15. TheHuman-induced changes that link the Porphyromonas gingivalis bacteria to the pathogenesis of rheumatoid arthritis: We observed many changes in patients with RA and with Porphyromonas gingivalis with expressed pathology of PD. In the study of Laugisch et al., we observed that the PAD and PPAD activities are higher subsequently in patients with RA . Also, tThe action of the mouth-persistent bacterium throughout the body: Porphyromonas gingivalis is a gram-negative, rod-shaped bacterium that is found in the human oral cavity during periodontal disease. This is a particularly common inflammation of the periodontal tissue, which often does not cause any concern or symptoms to the patient to contact the doctor. During their study, Demmer et al. got results during the independent survey of the First National Health and Nutrition Examination of 2011, which showed that patients who had lost more than 5 teeth or had PD, had a higher incidence of RA . Also, aIn 2015, Laugisch et al. conducted a study to evaluate the activity of the PAD enzyme of the bacteria Porphyromonas gingivalis in the gingival crevicular fluid of humans - an inflammatory exudate that can be collected at the gingival margin or within the gingival crevice, which can then be examined for pathogens present there . This stAlso, Hashimoto et al. in their study examined 72 patients who had never been treated with glucocorticoids or anti-rheumatic drugs . These pThere are cases that show that the patient's RA symptoms are reduced after periodontal treatment. Salemi et al. in 2014 described a case in which a 61-year-old man with RA had arrived at the clinic . A signiThe results obtained from 10 different authors have shown that PPADs produced by Porphyromonas gingivalis bacterium have a significant influence on the pathogenesis of rheumatoid arthritis. Literature reviewing the relationship between rheumatoid arthritis and periodontal disease has been reviewed and analyzed. The results show that the persistence of the bacteria Porphyromonas gingivalis in the oral cavity can affect the etiology of rheumatoid arthritis. This is based on a higher frequency of patients complaining of rheumatoid and periodontal disease simultaneously. Similarly, research has shown that patients with rheumatoid arthritis got better, or were completely healed, when periodontal foci were removed. The literature reviewing the effect of the enzyme PPAD produced by the Porphyromonas gingivalis bacterium on inflammation in the joints has been reviewed and analyzed. The results showed that the bacterium working through this enzyme disturbs not only the balance of amino acids, but also the whole body's immune system. It unbalances the Ag/Ab complexes and the body produces antibodies against citrullination by auto-antigens. The elements described in the literature affecting Porphyromonas gingivalis in the oral cavity and accompanying patients towards the diagnosis of rheumatoid arthritis were reviewed and analysed. The results showed that the DNA of bacteria Porphyromonas gingivalis is found not only in the serum, but also in the synovial fluid, which supports its influence on the pathogenesis of rheumatoid arthritis.


Network structure has often proven to be important in understanding the decision behavior of individuals or agents in different interdependent situations. Computational studies predict that network structure has a crucial influence on behavior in iterated 2 by 2 asymmetric ‘battle of the sexes’ games. We test such behavioral predictions in an experiment with 240 human subjects. We found that as expected the less ‘random’ the network structure, the better the experimental results are predictable by the computational models. In particular, there is an effect of network clustering on the heterogeneity of convergence behavior in the network. We also found that degree centrality and having an even degree are important predictors of the decision behavior of the subjects in the experiment. We thus find empirical validation of predictions made by computational models in a computerized experiment with human subjects. While avoiding collusion in traffic, meeting one another or making an exchange, coordination is a vital part of the success of the interaction. Coordination processes are therefore arguably fundamental to understanding the functioning of social, economic and biological systems. Game theoretical models are often used to model coordination problems with a strategic interdependence among actors. The success of this method has led to a wide literature ranging from ‘two by two’ games to complex spatial multi-agent (network) models, and from theoretical studies to experimental tests8. The coordination problem can be especially difficult when agents do not share the same preferences for different options. These situations are often formalized by asymmetric coordination games, such as the ‘battle of the sexes’. Computational models10 and other theoretical studies12 show that network structure is an important predictor of behavior in iterated asymmetric games. Although these models convincingly show that there are network effects on equilibrium behavior, no empirical studies have been conducted to corroborate these findings. Previous research on network effects on other types of games, such as the Prisoners Dilemma, show that the predictions made by computational models are not always evident when tested empirically13. It is therefore crucial to test the predictions and assumptions made by these models. In this paper we empirically test predictions made by computational and theoretical studies in an experimental study with human subjects12.Coordination problems are numerous in everyday lifeα or both players choose β. However, the players differ in their preference for the equilibria. Therefore, the game consists of an element of coordination and an element of competition between the players. There is also a mixed Nash equilibrium, but this equilibrium is inefficient, because the expected payoff is lower for both players compared to any of the pure-strategy Nash equilibria. Miscoordination is the most frequent outcome when human subjects play these one-shot games in an experimental setting6. Both players often choose the behavior according to their own preferred equilibrium, resulting in the lowest payoff for both players. The players often converge to one of the two equilibria when the game is played repeatedly16. In rarer cases players manage to switch simultaneously between the two equilibria, thereby obtaining the best outcome for both players14.The problem with asymmetric coordination games is that it is difficult to make behavioral predictions about the outcome of the game. Table α and β, but again they differ in their payoff for choosing α or β. Although the complexity of the situation is increased in terms of the number of players, it is easier to predict the outcome. The payoffs are balanced pairwise between the players, but the global situation is not, because there will always be a majority for one of the options. Intuitively one can already anticipate that when three people have to decide between two options, and two prefer option β and only one prefers α, the most likely outcome will be β. The three player situation is illustrated in Table α or all players play β. However, in this case the equilibria are not equivalent and therefore not equally likely. The equilibrium ‘all players play β’ yields a higher payoff for the two column players. Also, when the column players both play β, their payoff will at least be two, independent of what player 1 does. When the column players both play α, their payoff will be two maximally. No such coordination possibility exists for player 1 and 2 or 1 and 3. Assuming full information for all players, choosing β is the best option for both column players. Because the row player is aware of this, the best reply would be to play β as well, making ‘all players play β’ the behavioral prediction in an empirical setting.The situation can be made more complex by adding another player. This means there are three players who have to make a decision between α and two nodes which prefer β. In the network on the left of Fig. α or all players playing β. The situation is completely balanced, therefore it is again hard to predict the outcome of the game. The situation illustrated on the left of Fig. β always have to interact with players with a different preference. However, both players with a preference for α also interact with each other, making their pairwise interaction no longer an asymmetric battle of the sexes game, but a symmetric coordination game. Therefore, choosing α yields the highest payoff for the pairwise interaction between these two nodes. The node on the top right has no other choice than to coordinate on the same behavior as the node on the bottom right. The node on the bottom left can therefore infer that the other players will choose α, making it the best response to also choose α. So, ‘all players play α’ is the prediction in this situation.The situation changes again when players only interact with a subset of players in the game, instead of all other players. In Fig. In the 4-player situation one can still reason about what the predictions will be. In situations with more than 4 players it rapidly becomes harder to reason about the behavioral outcome of a game and the situation becomes yet more complicated when there are complex interaction structures added. In these types of situations, computational models are used to develop predictions.19. An interesting finding is the ability of self organization in agreement clusters in cellular automata. Clusters of adjacent nodes can coordinate on one behavior while other parts of the cellular automata can coordinate on the other behavior. Hernández, Muñoz-Herrera and Sánchez introduce a theoretical model for exploring Nash equilibria of battle of the sexes games on Erdös-Rényi networks under the conditions of both complete and incomplete information12. They find a rich set of equilibria where both homogeneous and heterogeneous equilibrium behavior is possible when players have complete information. This set is reduced when players have incomplete information. In a subsequent study, the influence of group size and the strength of preferences on equilibrium behavior is studied11. The stronger the preferences, the harder it is to obtain homogeneous equilibrium behavior. Other related work studies computationally the behavior of dynamic networks in which actors can make or break their links20. This study identifies a set of networks that are stable, in the sense that actors no longer wish to break links or make new ones, often resulting in segregated networks. In addition, some studies consider the influence of heterogeneity in other games such as (weak) Prisoner’s Dilemma games23. An interesting result is that payoff heterogeneity is predicted to have a favorable effect on cooperation. Furthermore, there are some experimental studies with human subjects testing the effects of network structure on the number of rounds the participants need to reach coordination in both symmetric and asymmetric coordination games. Findings indicate that network structure influences the pace at which participants coordinate and network density can help the coordination process in asymmetry coordination games24. Other experimental studies show that with complete information on choices made by all actors in the entire network, participants are quicker in reaching coordination compared to more limited information sets25. However, these experimental studies do not study the effect of network structure on what the equilibrium behavior will be.There are several computational studies exploring the behavior of multiple agents with asymmetric ‘battle of the sexes’ type of dynamics. Several studies explore homogeneous spatial structures such as cellular automataAll this research, based mostly on computational models, yields specific predictions about global behavior on complex situations. However, obtaining those predictions often requires a lot of simplifying assumptions. The question then arises as to how well do these models predict actual behavior given the assumptions they make and the complexity of the situation? This is the main motivation for the experimental work we report in this paper.10 and theoretical studies12; specifically, we consider the influence of network structure on equilibrium behavior in iterated asymmetric ‘battle of the sexes’ games. We focus on the computational model described in Broere et al.9. In this study nodes play iterated 2 × 2 games with their neighbors. Each node gets a preference assigned before the first round of the game (say α or β), that determines whether the node is a row or a column player as shown in Table α or β and the decision of the node is played against all its neighboring nodes. In the first round, the nodes play their preferred behavior with probability one. After every round, the nodes update their probability of playing α or β by means of reinforcement learning27. The probability of choosing either α or β is updated towards what would have been the best choice the previous round. Earlier research investigated the response behavior of human subjects in iterated ‘battle of the sexes’ games in two types of ring networks29. This study found that 96 percent of the decisions of the subjects followed a myopic best response pattern. We therefore choose a similar update rule. The update rule is more explicitly described in In this study we empirically test behavioral predictions from previous computational9. The baseline model is the Erdös-Rényi (ER) random network. This type of network is usually defined as G, where N is the number of nodes in the network and per the probability of drawing an edge between two arbitrary nodes. Thus, for every two nodes in the network the probability that an edge is present is the same. Depending on the choice of the parameters, this usually leads to a network with low clustering and relatively low variation in the degree distribution. The computational study predicts that equilibrium behavior is often homogeneous in these networks, in the sense that all nodes end up choosing the same behavior, all α or all β. However, it is hard to predict which equilibrium the nodes will end up playing, mostly because this is dependent on a complex combination of network characteristics. Both equilibria  are generally equally likely. This situation closely resembles the situations described in Table The computational study compares the equilibrium behavior in three different types of networks30. The algorithm starts with a lattice consisting of N nodes. Each node is connected with n neighboring nodes. The edges are rewired randomly with a constant probability for all edges. Using relatively low values of the rewiring probability, the characteristic of these networks are short average path lengths and high clustering, known as the ‘small world’ network characteristics. The computational study predicts that equilibrium behavior is homogeneous within the clusters, but heterogeneous between clusters, resulting in heterogeneous behavior in the overall network. Similar effects are shown in an experiment with different (learning) dynamics31. This result is pretty intuitive when taking a closer look at the definition of clustering. Clustering is often defined by the ratio of edges within a cluster and the edges outside the cluster33. The higher this average ratio, the higher the clustering of the network. In clustered networks coordinating on the same behavior within the cluster is simply more rewarding because there are on average more edges within the community than outside. This causes different communities to coordinate on different choices. A good predictor of the behavior within the cluster is the preference of high degree nodes. The higher the degree of a node, the higher the probability that the node converges to its preferred behavior.The second type of network studied in the computational study are clustered networks. The clustered networks are obtained by means of the Watts-Strogatz algorithm34. This algorithm starts with one or more nodes and new nodes are added iteratively. In each iteration, the probability for a new node to connect to an existing node depends on the number of links the existing nodes already have; the more links a node already has, the higher the probability that the new node gets connected to it. This creates a ‘rich get richer’ effect. In the computational study, the centralized networks had low-clustering, a few central nodes with high degree centrality and a majority of peripheral nodes with low degree centrality. The equilibrium behavior in these networks is, just like random networks, often homogeneous in the sense that all nodes end up choosing the same option: all α or all β. However, which equilibrium the nodes converge to is easily predicted by the preference of the nodes with high degree centrality. In these networks the nodes with the highest degree centrality could dictate the equilibrium behavior of the overall network. This situation closely resembles the situation of the right network in Fig. The third type of network studied in the computational study are centralized networks. This type of network is constructed using the preferential attachment algorithm proposed by Barabasi and Albert35.Another effect which is present in all types of networks is related to an even degree centrality. Nodes with an even degree centrality can relatively easily coordinate on their preferred behavior compared to nodes with a similar but uneven degree centrality. This situation can be understood by reviewing the 3-player situation described in Table α or all β. So, the information which can be derived from the network is limited. The predicted equilibrium behavior in centralized networks is also homogeneous, but the equilibrium behavior can be predicted by a few nodes with high degree centrality. In clustered networks degree centrality is also a good predictor of behavior, but behavior is restricted to the community the node belongs to. Finally, nodes with an even degree centrality more easily coordinate on their preferred behavior than nodes with an uneven degree centrality. Based on these computational predictions, we will empirically test the following hypotheses:Summarizing, computational studies predict homogeneous equilibrium behavior in random networks, while the predicted probability is often close to 50 percent for either all Hypothesis 1:The correlation of (equilibrium) behavior between the computational model and the empirical results will be higher for centralized networks and clustered networks compared to random networks.Hypothesis 2:The equilibrium behavior is more heterogeneous in clustered networks compared to random and centralized networks.Hypothesis 3:Participants with high degree centrality will more often play their preferred behavior.Hypothesis 4:Nodes with an even degree centrality more often play their preferred behavior than nodes with uneven degree centrality in all networks.36. The experiments where conducted both at Universidad Carlos III de Madrid, Spain and Utrecht University, the Netherlands. In total 140 subjects participated in Madrid between April 9th and April 20th 2018. These participants were invited from the IBSEN volunteer pool37. In addition, 100 subjects participated between May 22nd and May 30th in the Experimental Laboratory for Sociology and Economics (ELSE), Utrecht. These participants were invited using the ORSEE recruitment system38. In total we conducted 12 sessions with 20 participants. Therefore N = 240 in total.In order to test the four hypotheses we carried out a computerized laboratory experiment on networks of size 20. We used the Python based software platform oTreeDuring the experiment, participants played an iterated asymmetric ‘battle of the sexes’ game against multiple other participants at the same time. Every participant interacted with a subset of other players. Interactions are mapped on a network in which the players are nodes and they play the game with the participants to whom they are connected. The payoff table is shown in Table 9.In this study we used three different networks, each to represent the characteristics of random networks, clustered networks and centralized networks. The networks used in the experiments are represented in Fig. Upon arrival participants were seated randomly in the laboratory. All subjects participated in games on all three networks. Before the first round of each network, participants were assigned their ‘type’ at random. The type determined whether they were the row or the column player in Table In each round participants had to decide between ‘blue’ and ‘yellow’. After all participants had made their decisions, they where all informed about their payoff in that round and how many of the participants he/she is connected with played ‘blue’ or ‘yellow’. The participant did not receive information about players in the network he or she was not connected with. Next, the participants were asked to make a new decision for the next round, continuing for 20 rounds. We informed the participants beforehand that they would play 20 rounds. We communicated the exact number of rounds because we did not expect any end game effects. Before the actual rounds were played the participants were asked to read the instructions of the game. After that, they were asked to answer questions about the instructions in order to test whether they understood the game. Before the participants played on the actual networks, three practice rounds on a random network were played.https://github.com/JJBroere/An-experimental-study-of-network-effects-on-coordination-in-asymmetric-games.The experiments lasted an average of 45 minutes. The payoff of each round was accumulated and then divided by the number of opponents (interaction partners in the network). For every 50 points earned, the participants received 1 euro. In addition, they received 5 euros show up fee. The maximum that could be obtained was 17 euros. The average payoff was around 14 euros, the lowest was 10.50 euros, the highest 16.50 euros. After the experiment, participants were asked to leave the room, after which they were invited one by one to collect their earnings in privacy. The experiments in Spain were in Spanish and the experiments in the Netherlands were in English. The instructions in both languages can be found in the Supplementary Materials gc and the behavior of the empirical graph ge for each graph is defined as:xit is the behavior (‘blue’ or ‘yellow’) of node i at round t, N is the number of nodes and R the number of rounds. The function In order to test hypothesis 1, we have to calculate the correlation between the computational model and the empirical results. The correlations are computed with the same starting conditions; the same network and preferences of the actors in the same positions on the network. Given the same starting conditions, how often do the nodes in the computational model make the same choice (blue or yellow) as the people in the experiment? Thus, the correlation of the behavior between the computational graph et al.9.The computational model is run with the same initial conditions (distribution of types) as the empirical result. Because the computational model has a stochastic update rule, we run the model 100 times and report the median correlation between the model and the empirical result. We chose to report the median, because in some cases the distribution can be very skewed. For the full specification of the computational model see pblue is the proportion of nodes playing ‘blue’ in the last 5 rounds of the game.In order to test hypothesis 2 we resort to an analysis of variance (ANOVA) with post hoc tests on the heterogeneity of behavior in the networks in the last 5 rounds. We chose to look at the last 5 rounds instead of just the last round because random switching of behavior in the last rounds can influence the results. By taking the average of the last five rounds, the effects of switching or possible end game effects will be minimized in the analyses. We define heterogeneity of behavior as the variance of participants choosing ‘blue’ in the network:We test hypotheses 3 and 4 by means of a multilevel logistic regression for all subject decisions over all 20 rounds. Three levels are specified, taking into account the repeated measures of the participants and the correlation within networks. The dependent variable is 1 when the participant plays its preferred behavior and 0 otherwise. The predictor variables are the degree centrality of the participant in the network and the evenness of the degree.In Table r = 0.13, sd = 0.09 for random networks over all 20 rounds and r = 0.18, sd = 0.16 for the last five rounds. The random network closely resembles the original two player game in Table r = 0.44, sd = 0.28 and r = 0.51, sd = 0.13 for the last five rounds. This means that the model predicts 76 percent of the empirical observations correctly in the last five rounds. Predictions for these types of networks are significantly better compared to the random network. Finally, for the centralized network, the median correlation is r = 0.74, sd = 0.17 in all rounds and r = 0.92, sd = 0.25 for the last five rounds, meaning that towards the end behavior is predicted correct in almost all cases: in fact, out of 12 sessions the behavior was predicted wrongly only twice. In these cases the empirical behavior converged to the complete opposite direction from the predicted behavior, leading to a correlation of −0.98 and −1. This is reflected in the standard error. However, 10 out of 12 times the empirical results are correctly predicted by the computational model. Based on these results we found evidence in favor of hypothesis 1.The correlation between the empirical results and the computational model is μ = 0.116, sd = 0.099, although six out of twelve networks have not converged. The mean variance in the clustered networks is, μ = 0.183, sd = 0.085, corresponding to a situation in which clustered networks converged most of the time to a state where around half of the participants choose ‘blue’ and the other participants choose ‘yellow’. The mean variance in the networks with a central node is, μ = 0.024, sd = 0.030. This indicates that these networks converge to homogeneous behavior where all participants choose ‘blue’ or all participants choose ‘yellow’ every time. An ANOVA was conducted to compare the effect of the networks on the heterogeneity in the last five rounds. The ANOVA test yielded significant variation among conditions, F = 12.6, p < 0.001. A post hoc Tukey test further shows that the random networks and the clustered networks do not differ significantly at p = 0.101, although it should again be noted that the random network often did not converge. The clustered networks and the networks with a central node differ significantly at p < 0.001; the random network and the centralized network differ significantly at p = 0.019. Although the difference between the clustered network and the random network is not evident, we do believe that the random networks that did not converge yet would converge to the homogeneous state if more rounds where played. The random networks that did converge, all converged to a (mostly) homogeneous state. Furthermore, we found a very clear difference between the random network and the centralized network in terms of heterogeneity of behavior. We therefore conclude that we have empirical evidence in favor of hypothesis 2.In order to test hypothesis 2, we examine heterogeneity of behavior in the last five rounds of the games for the different networks. The mean variance in the random networks is, β = 0.118, sd = 0.013, p < 0.001. The higher the degree centrality, the higher the probability that the participants will play their preferred behavior. There is also a positive statistically significant effect of an even degree centrality, β = 0.164, sd = 0.060, p = 0.006. If a participant has an even degree centrality, the probability that the participant will play his or her preferred behavior is higher as well. Looking at the random networks, there is no statistically significant effect of any of the predictors. In the clustered network there is a statistically significant effect of an even degree centrality, β = 1,033, sd = 0.476, p = 0.029. There is no statistical effect of degree centrality. In the centralized network we do find a statistical significant effect of degree centrality, β = 0.210, sd = 0.085, p = 0.013. However no statistically significant effect of having an even degree centrality. We found evidence in favor of hypothesis 3 and hypothesis 4 when combining all the data. However, the hypotheses could not be confirmed in the networks separately. This could be caused by a lack of statistical power and variation in the degree distribution within some types of networks.In Table In this paper we empirically studied the effects of network structure on behavior in iterated ‘battle of the sexes’ games with human subjects. The hypotheses were derived from computational models from previous studies. The empirical results convincingly show that the computational models have empirical validity. The correlations between the computational model and the empirical behavior indicates that network structure governs the behavior to some extent. As expected, as the network structure becomes less ‘random’, the more accurate the computational model prediction of the behavior of the players. Furthermore, we found evidence that the major network effects found in the computational study have a clear counterpart on the behavior of the game when played with human subjects. Thus, in the clustered networks the equilibrium behavior was clearly more heterogeneous compared to the centralized networks. In random networks we did not find a significant difference with the clustered network. However, this could partially be explained because half of the sessions with the random networks did not converge after 20 rounds and more homogeneity could still be expected. We also found evidence that degree centrality and having an even degree plays a role in determining the behavior of the game.Although the experiments were conducted in relatively small and simple networks, we do believe that the results are generalizable to bigger and more complex network settings. As both the computational and the empirical results show, most of the behavior is limited to the clusters of the network, and within each cluster our reasoning in terms of how majority influences decision presented above seems to apply quite well. When a larger network consists of multiple clusters, the same behavior can be expected within the clusters of the larger network. In larger networks with low clustering the same dynamics can be expected as in smaller networks, however the relative influence of a single node on the equilibrium behavior naturally becomes smaller as the number of nodes in the network becomes larger.The small and limited number of networks studied is however a limitation of the current study. In this study we chose three fixed networks to represent networks used in the computational study; namely an Erdös-Rényi random network, a small world network and a preferential attachment network. There are several caveats to make about these choices. First of all, the networks belong to a class of network defined by their mathematical properties. We did not study any variation between networks within this class. The lack of variation within one network also makes it harder to detect the influence of different nodes. Secondly, the mathematical properties of the networks are often limiting properties as the number of nodes goes to infinity: although the effects are independent of size in the computational study, the networks in this study might in fact be too small to represent the limiting properties of the class of networks. However, studying larger and/or more different networks is complicated and expensive in an experimental context with human subjects, because this would require very large sample sizes and also a large amount of participant fee. The limiting factor is in the between network comparisons. In the current study it required 240 participants to be able to compare 12 networks per type.39. In the case of networks, knowing that there are very many players choosing the option one prefers may help to insist on making the decision that goes in one’s interest, in the hope that eventually one’s neighbors might conform to the global majority. This, along with trying to extend our experiments to larger networks and to more representatives of each class, would be an interesting contribution to establish the knowledge on coordination on networks on firm grounds.All in all, our experiments show that the behavior of people trying to coordinate in a network can be understood reasonably well in terms of local considerations. In other words, subjects react to what they observe around them, the rest of the network does not seem to be relevant. This opens an interesting avenue of research as in other situations, different from the one considered here, global information may be available that changes how people behave. Indeed, it was observed that when the total number of people making one or the other choice is made available to the subjects, global coordination is reached much more easily in a population of moving subjectsSupplementary Materials