Escaping from a complex maze, by exploring different paths with several decision-making branches in order to reach the exit, has always been a very challenging and fascinating task. Wave field and quantum objects may explore a complex structure in parallel by interference effects, but without necessarily leading to more efficient transport. Here, inspired by recent observations in biological energy transport phenomena, we demonstrate how a quantum walker can efficiently reach the output of a maze by partially suppressing the presence of interference. In particular, we show theoretically an unprecedented improvement in transport efficiency for increasing maze size with respect to purely quantum and classical approaches. In addition, we investigate experimentally these hybrid transport phenomena, by mapping the maze problem in an integrated waveguide array, probed by coherent light, hence successfully testing our theoretical results. These achievements may lead towards future bio-inspired photonics technologies for more efficient transport and computation. Studying quantum transport in biological systems is difficult so developing an artificial platform that can be used to understand quantum transport is desirable. Here, Caruso, et al. demonstrate how a quantum walker can quickly reach the output of a maze by partially suppressing the presence of interference. Transport problems are very popular in several fields of science, as biology, chemistry, sociology, information science, physics and even in everyday life. One of the most challenging transport problems is represented by efficiently traversing a maze, that is, finding the exit in the shortest possible time of a topologically complex network of interconnected sites . The effThe problem of solving mazes has fascinated mankind since the ancient times. One famous maze is the Cretan one, designed by the architect Daedalus, build to hold the mythological creature Minotaur that was eventually killed by the hero Theseus. To find the Minotaur he used the most typical maze-solving strategy: exploring several possible alternatives, while marking the visited paths . Around 60 years ago, Shannon realized the first ever experiment on maze-solving that was based on physical means, in particular an electromagnetic mouse TheseusIn the framework of quantum mechanics, even a single particle, represented by a wavefunction, shows interference effects. Exploiting this property, a quantum walker is able to propagate in the fastest way inside perfectly ordered lattices5789121314192024252627In the last years, several technological platforms have been employed to investigate quantum transport phenomena, such as NMR303235373940414241444548Here, we investigate the role of a partial suppression of interference effects in the transport dynamics through maze-like graphs. In particular, we theoretically demonstrate that an optimal mixing of classical and quantum dynamics leads to a remarkably efficient transmission of energy/information from the input to the exit door of a generic maze. In addition, we show that it is possible to reproduce experimentally these dynamics in a photonic simulator, unfolding the maze onto a femtosecond-laser-written three-dimensional waveguide array, where noise is implemented by modulating the propagation constants of the waveguides during the writing process. The results provide a clear demonstration that a controlled amount of decoherence in the walker can produce an enhanced transport efficiency in escaping the maze and that these phenomena can be investigated in an experimentally accessible platform and not only in abstract models.N nodesThe maze structure is created here by the so-called random Depth-First Search algorithm applied on a square lattice of ρ describing the state of the system evolves according to the Lindblad master equation:Following the framework of quantum stochastic walks28H, which implements the quantum walk dynamics, is mixed with an incoherent evolution describing a classical random walk, given by the operators Li,j. The balance between the two parts of the Lindblad superoperator is given by the value of the parameter p. In particular, for p=0 a fully coherent (pure interference) dynamics is observed, whereas p=1 corresponds to the case of classical random walk, that is, classical random hopping with no interference; for intermediate values, a mixing of the two types of behaviour is obtained. An irreversible transfer process from the exit site to an external sink is added and the walker's probability in getting the exit at time t is quantified by transfer efficiency function to the sink A purely unitary evolution, given by the hermitian Hamiltonian p≃0.1, that is, ∼10% of mixing), with respect to the limiting cases of purely coherent and fully classical dynamics. Such transport enhancement is based on an intricate interplay between coherence and noise and shows peculiar features that makes it a fascinating field to investigate. In fact, an analogous optimal mixing has been very recently demonstrated over a large family of complex networks for p≃0.1 (ref. P(t) being the population remaining on the network, that is the probability that at time t the energy quantum has failed to exit the network—see the right side of t for the plotted As shown in the left side of 0.1 ref.  and expe0.1 ref. . In addiT1-like processes), a similar behaviour would be obtained by considering a pure dephasing process (T2-like)—see . In the theoretical model, this site should behave like a sink that absorbs energy irreversibly. In our photonic implementation, the sink is implemented by a long chain of waveguides (62 waveguides), which approximates well a one-way energy transfer process, with negligible probability for the light to be coupled back to the system.t, considered in the theoretical model, is mapped onto the propagation length, which we still label as t.Structures composed of uniform waveguides correspond to the purely coherent case (QW). Fully coherent transport dynamics in such maze can be studied straightforwardly by fabricating arrays with different lengths and characterizing the output distribution when coherent light is injected in the desired initial site (IN). It is worth noting that in this realization, the evolution parameter A controlled amount of noise is introduced in the structure by segmenting the waveguides corresponding to the sites of the maze. This is achieved by modulating the writing speed in the fabrication process, which induce a proportional variation of the propagation constant, while keeping the coupling coefficient unvariedThe waveguide array implementing the sink is in all cases composed by uniform, not-segmented, waveguides. To characterize the transfer efficiency to the sink, the output facet of each fabricated structure is imaged onto a CMOS camera  to the exit (solution). By considering a model that mixes the behaviour of a classical walker and a quantum one, we have found an optimal condition leading to extremely efficient and fast transmission. For large enough maze size, this leads to a remarkably high enhancement of more than five order of magnitudes in the transfer efficiency with respect to both the classical and purely quantum limits. This result is a clear example that decoherence is not always a detrimental phenomenon that should be avoided in quantum processes and it may provide some insight on the reason why nature evolution has made the observation of purely coherent phenomena so difficult.By exploiting the unique capabilities of the femtosecond laser writing technology, we have unfolded the maze and implemented it in a three-dimensional waveguide array, where a suitable modulation of the waveguide properties allowed us to mimic a partial decoherence of the walker. Our measurements have faithfully confirmed the theoretical predictions and, in particular, the remarkable role of a partial suppression of interference in enhancing transport dynamics in mazes. It is also worth noting that our technological platform has enabled an experimental simulation of a noise-assisted problem in well-controlled conditions and over complex topologies, and can thus represent a very powerful tool for further studies in this direction. These results, together with future full circuit reconfigurability, will pave the way to much more complex integrated photonics devices exploiting interference, quantum features and noise effects for improved problem-solving efficiency, and remarkably fast transmission of information in ICT applications and of energy in novel solar technologies.Another experimental demonstration of enhanced quantum transport by controlled decoherence has been reported during the preparation of this manuscriptN nodes, where all neighbour sites are separated by a wallDepth-First Search algorithm is the simplest maze generation algorithm and is based on the following iterative procedure that is applied to a regular square grid of The fabricated structures are probed by coherent light. Laser light at 850 nm wavelength is injected into the input waveguide. The output distribution is imaged onto a CMOS camera by means of a 0.12 numerical aperture objective. Numerical integration on different parts of the acquired image allows to retrieve the fraction of light present in the sink waveguide array. The advantages of this method are, on one hand, insensitivity to coupling losses of the input beam and, on the other hand, the possibility of a fast acquisition of the output of many waveguides.n modes of random uniformly distributed intensity. As a matter of fact, the contribution of such errors on the experimentally measured efficiencies is relevant only for the shortest lengths, where the light intensity in the sink is particularly low.A careful analysis of the measurement error has been performed. A possible source of error is the quantization of the intensity levels of the CMOS sensor, as well as its finite spatial resolution. To analyse this error contribution, we simulated the numerical integration of gaussian modes, with the same size as the measured ones, but random intensity and peak position, discretized both in the (256) intensity levels and in the pixels of the spatial profile. present in the sink after a certain propagation distance, with respect to the overall output power, as is done in our characterization process, may not correspond precisely to the fraction of input power transferred to the sink. In fact, the transfer efficiency is slightly overestimated.Furthermore, cascading waveguide segments with different fabrication speed (to mimic noise) causes small additional losses, at each interface between different waveguide segments. Importantly, these losses are present only in the waveguides representing the maze and not in the sink waveguides. Because of those losses, measuring the fraction of power random noise map implemented.Overall additional losses can be measured quite accurately, by simply measuring and comparing the insertion losses of the fabricated devices . However, the precise contribution of these losses on each measured transfer efficiency can be hardly retrieved. In fact, the transfer process is not uniform during the propagation and depends on the Thus, to statistically quantify such overestimation, we numerically simulated the light propagation in waveguide structures analogous to the fabricated ones, for 100 random different noise distributions , both in the case of waveguides with no losses  and in the case of waveguides yielding uniform additional losses with respect to the waveguides of the sink, in such a way that the overall losses of the structure correspond to the experimentally measured ones . We evaluated in each case the estimation error of the transfer efficiency and calculated the error statistical distribution. The data that support the findings of this study are available from the corresponding authors upon request.How to cite this article: Caruso, F. et al. Fast escape of a quantum walker from an integrated photonic maze. Nat. Commun. 7:11682 doi: 10.1038/ncomms11682 (2016).Supplementary Figures 1-7, Supplementary Notes 1-4 and Supplementary References.


Recent technological improvements in the field of genetic data extraction give rise to the possibility of reconstructing the historical pedigrees of entire populations from the genotypes of individuals living today. Current methods are still not practical for real data scenarios as they have limited accuracy and assume unrealistic assumptions of monogamy and synchronized generations. In order to address these issues, we develop a new method for pedigree reconstruction,  Learning the correct relationships between individuals from genetic data is a basic theoretical problem in the field of genetics, and has many practical consequences. A wide variety of statistical methods for genetic analysis assume the relationships between individuals are known, and can manifest relatedness information to improve inference. The current state-of-the-art methods for relationship inference consider pair-wise genetic similarity, and use it to infer the relationship between each pair of individuals. Reconstructing the pedigrees of an entire population directly has the potential to use more elaborate relationship information, and thus obtains a better prediction of the familial relationships in the population. In contrast to the full set of pair-wise relationships in a population, genetic pedigrees provide a lossless and conflict-free structure for depicting the relationships between individuals. In an effort to make pedigree reconstruction practical we developed a new method, which is an order of magnitude more accurate than previous methods, and is the first method that has the ability to reconstruct polygamous pedigrees. PLOS Computational Biology Methods article.This is a Pedigree reconstruction is an important problem in the field of computational genetics, with many potential applications such as genealogy inference, heritability estimation, and victim identification The level of difficulty of the problem is highly dependent on the pedigree in consideration. Particularly, small inbred populations pose a considerable challenge since the probability for multiple mating events within any two families is high, and therefore individual pairs usually have more than two last common ancestors (LCAs). Moreover, in small inbred populations there is a complex relationship pedigree graph due to mating within the family.COP/CIPRecently, three methods tackling pedigree reconstruction from the genotypes of extant individuals were proposedIn this work, we point out an important and naturally arising issue of pedigree reconstruction from extant populations, overlooked by all previous methods. We observe that the mother and father of a sibling-group have exactly the same descendants (as must be the case for monogamous couples). Since the genotypes of the parents are unobserved, a pairwise relationship analysis relying on the extant descendants will result in maternal relatives having the same likelihood of being related to the mother and to the father, and vice versa see . Thus, pSimilarly to previous methods, we reconstruct the pedigree generation by generation, starting with the last generation, and assuming all of the genotypes of the population come from the same generation. In iteration In contrast with previous methods, we present an alternative graph representation that accounts for the above-mentioned ambiguity, and uses the transitive property of the full-sibling relationship to correctly find the full-sibling groups. We begin each iteration by constructing a contracted siblings graph  of  see . Since vThe key idea of our method lies in a procedure for the assignment of the edges in Under the monogamy assumption, we finish reconstructing the current generation by adding two common-parents to each sibling clique in We now describe the construction of the graph node see .IBD features: The number of IBD segments, and the total length of IBD sharing . Smaller population sizes correspond to inbred populations with multiple relationships between families. Larger populations correspond to outbred populations, with simpler pedigree structures. We also study the effect of population bottlenecks on the reconstruction quality. In order to test Similarly to previous methods, we use a Wright-Fisher (WF) simulator that includes recombination and genders. We add several new features, which makes this simulator more flexible. First, we add the ability to control polygamy through a polygamy probability parameter Additionally, we experiment with a more realistic forward simulator that does not assume synchronized generations, and allows polygamy. We simulate inheritance as a function of time, where individuals can have children after the age of 20, and die at an age drawn from a capped exponential distribution with mean 50. The birthrate is changed according to the current population size, and is tuned to reach a predefined target population size. This simulator produces actual recombined haplotypes, from the haplotypes of 160 Many different measures can be accounted in evaluating the quality of reconstructed pedigrees. We first use a previously defined score, to compare We define sensitivity as the fraction of correctly constructed (distance wise) related pairs from the total number of related pairs in the original pedigree. PPV is defined as the fraction of correctly constructed related pairs from the total number of related pairs in the reconstructed pedigree. More formally, define We run Scores such as sensitivity and PPV have the disadvantage of not weighing mistakes according to their magnitude. A second disadvantage is that the minimal meiotic distance does not capture the full complexity of a real pedigree . For these reasons, we suggest to alternatively measure pedigree quality by calculating the root mean square IBD-length error (We tested the competing methods on monogamous Wright-Fisher simulated population, of constant sizes: 100, 200, 500, and 1000. When it was possible, we ran Considering The simplified Wright-Fisher model that was used in pedigree reconstruction methods up to this day assumes a constant population size. Real populations sizes are obviously not constant, and it is known that population bottlenecks and expansion affect the IBD distribution in the population. We have conducted an experiment to test the effect of population size shifts on the distribution of chosen IBD features, and as a consequence on the quality of the resulting pedigree. We have run the Wright-Fisher simulation with changing initial population sizes of 100,200,300,400,500 and fixed the final population size at 500. By looking at the distribution of IBD features between all pairs of individuals, it is clear to see that the number of IBD segments and the mean IBD segment length have an inverse relationship with the initial population size. This corresponds to a higher proportion of relatives in the populations with smaller initial size. We have found that populations that grow from 100 to 500 individuals in five generations have similar IBD feature distributions to populations with constant population size of size 200. Interestingly the quality of the resulting pedigree of these populations remains unchanged when the initial population size is gradually decreased from 500 to 200. Only at initial size of 100 does the quality decrease. Sensitivity levels for initial population size of 100 are 0.96,0.75, and 0.54 for 2,3 and 4 generations. The largest decrease is for 3-generation pedigrees where the sensitivity is decreased by 10% on average. The PPV remains above 0.95 for generation 2,3 but is decreased from 0.85 to 0.71 in generation 4.To asses the quality of Similarly to the monogamous case, hips See .We test the performance of ysis see .We next use Running  tasksee . FurtherIn this paper, we take a step towards making pedigree reconstruction from present living populations, a realistic objective. By developing better quality assessment tools, we were able to come to the conclusion that our method reconstructs pedigrees with significantly higher quality then previous methods, and in comparable running times. ique see -B might


Vassallia, Eutatus and Macroeuphractus). The principal goal of this work is to comparatively assess the biomechanical capabilities of the mandible based on FEA and to relate the obtained stress patterns with diet preferences and variability, in extant and extinct species through an ecomorphology approach. The results of FEA showed that omnivorous species have stronger mandibles than insectivorous species. Moreover, this latter group of species showed high variability, including some similar biomechanical features of the insectivorous Tolypeutes matacus and Chlamyphorus truncatus to those of omnivorous species, in agreement with reported diets that include items other than insects. It remains unclear the reasons behind the stronger than expected lower jaw of Dasypus kappleri. On the other hand, the very strong mandible of the fossil taxon Vassallia maxima agrees well with the proposed herbivorous diet. Moreover, Eutatus seguini yielded a stress pattern similar to Vassalia in the posterior part of the lower jaw, but resembling that of the stoutly built Macroeuphractus outesi in the anterior part. The results highlight the need for more detailed studies on the natural history of extant armadillos. FEA proved a powerful tool for biomechanical studies in a comparative framework.Finite element analyses (FEA) were applied to assess the lower jaw biomechanics of cingulate xenarthrans: 14 species of armadillos as well as one Pleistocene pampathere (11 extant taxa and the extinct forms  The mammalian superorder Xenarthra comprises a group of peculiar, mostly South American, placental mammals forming a monophyletic group with highly heterogeneous morphology. It includes the orders Cingulata and Pilosa, which showed a huge disparity of forms ,2, most Herein, we will focus on the armored xenarthrans, the Cingulata, which contain three major groups: armadillos , Euphractinae , Chlamyphorinae  and Tolypeutinae  [Living representatives of cingulates belong to Dasypodidae, and are included in 21 extant species  and ninebassous) .In comparison with other mammals, the Xenarthra present peculiar features that define the clade; the most distinctive trait within Cingulata is the presence of carapace, which differs morphologically in the different groups. Other peculiar features are observed in the dental anatomy: simplified teeth, characterized by absence of enamel, homodonty and hypsodonty are present in almost all known species . The dieAlthough it has been proposed that diet in armadillos might be difficult to predict from the shape of the masticatory apparatus, as some species will be able to fed on items for which their morphology is not optimal , VizcaínIn this article we propose a new insight to deepen on the knowledge of the relationship between morphology and feeding ecology of Cingulata. To carry out this goal, Finite Element Analysis (FEA) was used to analyze the mandibles of 14 species of Cingulata. FEA is a noninvasive modeling technique that is based on a numerical analysis and the principle of dividing a system into a finite number of discrete elements –25 on whIn particular, the aims of this study were: 1) To evaluate the biomechanical behavior of the mandible of some extant and extinct armadillos and one pampatherid under certain loads; 2) to test if there is any relationship between the stress patterns of the lower jaw and the proposed diets in extant and extinct species.For doing so, planar models of mandibles belonging to several cingulate species were analyzed through FEA methods to understand the adaptive significance of this biological structure  and why Vassallia maxima Late Miocene-Early Pliocene, FMNH 14424 [Macroeuphractus outesi Late Pliocene (MLP 69-IX-9-3)/ . On one hand, E. seguini has been also proposed as an herbivore [Macroeuphractus outesi has been considered like the most carnivorous extreme in the range of carnivore-omnivore [The extinct taxa analysed here have been subject of phylogenetic and morphological studies –17. Fromgetation , 17, 28.erbivore , whilst omnivore , 28.Plane models of the mandible of 14 species of armadillos were analyzed, and stress patterns were obtained using FEA. In continuum mechanics, plane elasticity refers to the study of particular solutions of the general elastic problem in bodies that are geometrically mechanical prisms  . In partOur goal was generate a model as simple as possible that better predicts and explains the relationships between the variables under study. There is always a trade-off between the reality and the predictive power, as more close to reality implies more complex model (includes more variables) and cannot be used to generalize or to predict the studied relationship on different taxa. In sum, a complex model is very useful for a descriptive purpose, or to check the exact behavior of a biological structure under different situations, but when the final goal is to extract a general relationship and/or predict the ecological patterns on different taxa in a comparative framework (i.e. including many different species in the study), as the present case, simpler models are preferred. The discrimination between different diets in armadillos with such simple models is actually clearer rather than in complex models.et al. [The steps for model construction were modified from the methodology summarized by Fortuny et al. , 43: 1) et al. , 6-node Two main muscles  were considered in the geometry. The insertion area of each muscle was identified and included in the model as a surface. As the amount of force that a muscle can produce depends on its active section , the sizFor the generation of the FE mesh, , trianguMacaca mulatta were used herein; E (young’s modulus)-21,000 MPa, n (Poissons ratio): 0.45; [For the mandibles studied, isotropic and linear elastic bone properties have been assumed. In the absence of data for Cingulata or any close relative, as well as any mammal clade with similar bone structure, the mandible properties of ): 0.45; . The cho): 0.45; , which rMacroeuphractus outesi and Vassallia maxima, due to the lack of published measures of thickness, data from Pampatherium, the closest taxon with similar cranial-mandible features [The thickness of the model has been assumed constant in the whole mandible and obtained from the individual average of three measurements; i) mandibular width at the first jugal, ii) mandibular width at half of the level of antero-posterior length of the jugal series and iii) mandibular width at the posterior end of the jugal series. For the extinct features  has beenTo analyse the stress state results, Von Mises equivalent stresses were obtained for each mandible. The Von Mises criterion is an isotropic criterion used to predict the yielding of ductile materials determining an equivalent state of stress. Considering bone a ductile material  and accoIn order to define the location of the landmarks where Von Mises stresses would be recorded, previous simulations were made in three different armadillo’s mandibles, with distinctive features and diets, with the aim to evaluate the distribution and variability of stress patterns. This test enabled us to evaluate the parts of the mandible where there was more variability in the stress distribution and were would be more interesting to record those data.et al., [A is the area of a reference model, SB the area of a scaled model, TA is the thickness of a reference model and TB the thickness of a scaled model [In order to scale the mandibles of all species to render the forces applied comparable, the quasi-homothetic transformation proposed by Marcé-Nogué et al.,  iwas apped model .The musculature used to determine the vector forces in the FEA models includes temporalis and masseter. Muscle reconstruction allowed obtaining the vector direction of the muscular force that was applied to the models . The valChaetophractus villosus, which was the reference model for this study.Muscles were modeled from the insertion areas, and the direction of the vector joining the centroid of the muscular attachment in the lower jaw and the centroid of the equivalent muscle attachment in the skull was used as an estimator of force direction. As the objective of this study was to develop a comparative analysis , we wereOn the other hand, in other mammals the proportional development of masseter or temporalis might be indicator of different abilities or diets –52. TherEutatus seguini were reconstructed from features of the skeleton elements, following Vizcaíno et al. [Macroeuphractus outesi and Vassallia [The areas of origin and insertion of the masticatory musculature of the extant armadillos and extinct o et al.  and Smito et al. . Publishassallia , 28The boundary conditions were defined and placed, representing the loads, displacements, and constraining anchors that the structure experiences during the some functions . AccordiOn the other hand, the values of stress were recorded at specific locations previously defined (landmarks) and later used for quantitative analysis. These data were used in statistical analysis to test for differences between the different diets. These landmarks were defined as biologically homologous as possible between the models .Two sets were defined simulating different situations; Set 1) simulate the mandible constrained at the most anterior part, Set 2) simulate the mandible constrained at the beginning of the tooth row . The twoStatistical analyses were performed using Past 2.13 .Kruskal-Wallis tests were developed to analyze the relationship between diet and biomechanical properties. This test was applied to each set and landmark, using as groups the classification made at Two Principal Component Analysis (PCA) on the stress values for all landmarks recorded, developed using the variance-covariance matrix, were carried out for each set. The aim of these analyses was to evaluate the stress values in a multivariate manner and to look for diet related patterns. The PCA generate new variables that are a lineal combination of the previous ones, but in that case with the first PC explaining as much variance as possible.I It is a method for reducing information, very useful to look for pattern in the data.The visual representation of stress distribution for each mandible is a useful indicator for qualitative comparisons of their behavior under equivalent loads Figs  and 3. IAn unusually high stress appears where the boundary conditions are set as a simple support. These stresses are artificially inflated by the constraints imposed on the model due to a numerical singularity . The numIn Set 1  all mandPriodontes maximus shows high stress at the ventral part of the tooth row. Both P. maximus and C. unicinctus have different biomechanical display along the mandible although the localization of some stressed areas coincides. The higher stress values are located at the anterior area of the mandible (without considering the inflated region due to the boundary conditions), which extends to the corpus being smaller at the posterior side of the mandible, taking very low values at the coronoid process.Specialist insectivore Dasypus sabanicola, Dasypus kappleri, Dasypus novemcinctus, Tolypeutes matacus and Chlamyphorus truncatus), all the members of the genus Dasypus displays similar patterns. However, it is not clear if this is a consequence of similarity in diet or phylogenetic signal, as all three species belong to the same subfamily. D. novemcinctus and D. sabanicola are the most alike with the highest values of stress at the anterior region of the mandible, which extends through the ventral part of the corpus until the mandible angle and goes up the ramus. Small values of stress are located at the upper area of the corpus mandible, where the upward shift leads to the ascending ramus. The sections with smallest stresses are the coronoid process and the elbow at the most posterior distal side of the mandible. D. kappleri, however, has little stress in the upper section of the corpus of the mandible and shows stress at the mandibular angle that extends towards the ramus shift as in the previously mentioned species, although less markedly. It also presents a slightly stressed region at the base of the proximal anterior side of the mandible, which extends through the corpus center. T. matacus shows a similar pattern.Within the generalist insectivores , these taxa have some coincident stress patterns. Z. pichiy and E. sexcinctus are the most similar considering the anterior part of the mandible; they show high levels of stress along the tooth row and slightly higher along the corpus with the basal region less stressed. Z. pichiy also presents values of stress at the mandibular angle, which is also present in specialist insectivores. In the case of the two Chaetophractus species, they display little stress levels compared to all other analyzed mandibles of extant species. This pattern is similar to those of the rest of the omnivores, which in general present less stress than insectivores.Regarding the omnivorous species  explains almost 50% of the variance in the sample , and it ar angle . The negar angle . FollowiV. maxima, which has the smaller ones following PC1.The results for the first principal component are quite similar to those obtained in the Set 1, although the positive part shows intermediate stress values in the middle of the tooth row. The second PC, in opposition, explains a different pattern focused in the anterior part of the ascending ramus . PositivOur hypothesis was that high levels of stress along the mandible would represent a fragile mandible with a reduced capability for thoroughly chewing or processing hard items. On the other hand, low stress patterns would indicate a much more resistant mandible with a stronger capacity of oral processing. However, we have not found a significant correlation between diet and stress values, considering the sample analysed.E. sexcinctus is the only armadillo that can bite when handled [Despite the lack of significant results, a general trend has appeared. As suggested in our biomechanical hypothesis, omnivores show smaller mean stress values for almost all landmarks (being landmark 10 an exception) and clearly reduced variability in their stress values Figs  and 7, n handled  and it h handled . The FEAAs mentioned in the Results section, the lack of statistical significance could be due in part to the small sample size. However, this is not enough to explain the huge variability in the results of both groups of insectivorous species. Therefore, although some species show the biomechanical behavior expected for their proposed diet, others show stress patterns that do not agree with what was expected for the diet in which they had been classified.As mentioned above, some species display stress patterns that are not congruent with their traditional classification. This could be due to three different reasons; i) inaccurate FEA models, ii) incorrect diet classification, iii) a correct diet but processed in a different manner.Tolypeutes matacus and Chlamyphorus trunctatus show stress at the recorded landmarks values well into the range of omnivorous species  to omnivorous armadillos. This species have been reported to have a diet mainly composed of insects, although consuming worms, snails, and small amount of roots and other plants   . Indeed,cinctus)  and 6. Aspecies . Whether this variance is a consequence of the phylogenetic variability of insectivores, dietary variability, or both, is something that should be addressed in the future including more species in the sample.Vassallia maxima has been described primarily as a grazer consuming mainly coarse vegetation with morphological features shared with herbivorous ungulates [The fossil taxon ngulates –18. In tEutatus seguini has been regarded as herbivorous based on the skull and dental morphology [E. sexcintus. Moreover, in E. seguini the coronoid process is inclined posteriorly as in insectivores and it has a remarkable large snout (characteristic shared with insectivores). The FEA results highlight combined characteristics for E. seguini, with a stress pattern similar to that in M. outesi in the anterior part and almost identical  to that in V. maxima in the posterior part , the stress levels at the anterior part of the jaw indicate that probably it fed too in other kind of items.rphology , 16. Othior part . TherefoMacroeuphractus outesi has been biomechanically analyzed in previous works [The extinct euphractine us works . Those aDespite more research has to be done in relation to quantitative analysis of FEA data and the allometric and phylogenetic effects on the results, the differences between the stress patterns that were not congruent with the diet category could be explained under a detailed analysis of the diet of each species. This finding supports the use of FEA models as suitable predictors of biomechanical behavior in ecomorphological studies in armadillos, at least to differentiate between insectivorous and omnivorous species. For detailed feeding predictions more work is needed accounting for the effect of factors other than diet on the lower jaw .D. kappleri has a lower jaw more resistant than its genera counterparts. However it remains unclear whether this is due to a different diet, an allometric effect, or other factors.The results of finite elements analysis (FEA) of the mandibles of several genera of Cingulata have shown to be related, in general terms, to the diet of these species. The difference between omnivorous and insectivorous species is clear. Those species that do not completely met the expectations of stress level for their diet can be explained with a more detailed study of their diet. Vassallia maxima presented a very strong mandible, congruent with an herbivorous diet with a great amount of oral processing and in agreement with Vizcaíno et al. [Eutatus seguini shows a stress pattern similar to Vassalia in the posterior part, but to Macroeuphractus outesi in the anterior part of its very strong mandible. This last species display a strong mandible.For the extinct species studied, all of them outside the range of insectivorous diet, some conclusions can be derived. The fossil taxon o et al.  morphofuFEA analysis on planar models has shown as a powerful tool for biomechanical studies in a comparative framework within Cingulata.S1 TableThe values measured in each landmark are multiplied for a thousand.(DOC)Click here for additional data file.S2 TableThe values measured in each landmark are multiplied for a thousand.(DOC)Click here for additional data file.S3 Table(DOC)Click here for additional data file.S4 Table(DOC)Click here for additional data file.S5 Table(DOC)Click here for additional data file.


The cervical branches of the vagus nerve that are pertinent to endocrine surgery are the superior and the inferior laryngeal nerves: their anatomical course in the neck places them at risk during thyroid surgery. The external branch of the superior laryngeal nerve (EB) is at risk during thyroid surgery because of its close anatomical relationship with the superior thyroid vessels and the superior thyroid pole region. The rate of EB injury  varies from 0 to 58%. The identification of the EB during surgery helps avoiding both an accidental transection and an excessive stretching. When the nerve is not identified, the ligation of superior thyroid artery branches close to the thyroid gland is suggested, as well as the abstention from an indiscriminate use of energy-based devices that might damage it. The inferior laryngeal nerve (RLN) runs in the tracheoesophageal groove toward the larynx, close to the posterior aspect of the thyroid. It is the main motor nerve of the intrinsic laryngeal muscles, and also provides sensory innervation to the larynx. Its injury finally causes the paralysis of the omolateral vocal cord and various sensory alterations: the symptoms range from mild to severe hoarseness, to acute airway obstruction, and swallowing impairment. Permanent lesions of the RNL occur from 0.3 to 7% of cases, according to different factors. The surgeon must be aware of the possible anatomical variations of the nerve, which should be actively searched for and identified. Visual control and gentle dissection of RLN are imperative. The use of intraoperative nerve monitoring has been safely applied but, at the moment, its impact in the incidence of RLN injuries has not been clarified. In conclusion, despite a thorough surgical technique and the use of intraoperative neuromonitoring, the incidence of neurological complications after thyroid surgery cannot be suppressed, but should be maintained in a low range. The neurological issues that might appear after thyroid surgery are those related to lesions of motor or sensory nerves whose anatomical course is in the neck. The main structures that are jeopardized during thyroid surgery are those arising from the vagus nerve at various heights: the external branch of the superior laryngeal nerve (EB-SLN) and the inferior laryngeal nerve.These nerves and their branches have mainly motor activity on the laryngeal muscles, being responsible for both the motility of the vocal cords and of all the distinctive features of one’s voice.The lesion for the main trunk of these nerves, or of their smaller motor branches, is responsible for the paralysis of different laryngeal muscles that might be clinically evident as a significant impairment of the voice either in its quality and intensity.In a tertiary care referral center, this morbidity should be maintained in a due range, according to different factors that can generally be preoperatively identified: the incidence of a permanent lesion of the inferior laryngeal nerve in a surgery performed for a benign disease should be maintained below 1%. On the opposite side, a higher incidence of permanent lesions can be expected when the indication for surgery is a malignant disease or a recurrent benign or malignant disease (up to 6%). Another factor affecting the complication rate is the surgeon’s experience with the low volume surgeons (those who perform <30 cases per year) being those more prone to have higher rates of permanent nerve damages  until recently, when it was clarified that Galli-Curci suffered from a physiological decline of her performances due to the normal aging process. The nerve has nevertheless maintained its name in several textbooks and papers, although the true story should be remarked, to preserve the integrity of the surgeon who performed the thyroidectomy , 3.The superior laryngeal nerve originates just below the inferior ganglion (nodose ganglion) of the vagus lining below the jugular foramen. About 1.5 cm inferiorly, the nerve divides into two branches: the internal one, which pierces the thyrohyoid membrane in association with the superior thyroid artery and supplies the sensory innervation to the mucosa of the larynx, and the external one , 5.The EB-SLN is about 0.8 mm wide and 8–9 cm long, it courses anteriorly and inferiorly along the inferior pharyngeal constrictor muscles and the branches of the superior thyroid artery. It then curves anteriorly and medially close to the lower edge of the thyroid cartilage and then approaches the larynx within the sterno-thyro-laryngeal triangle, in the region known to surgeons as the “space of Reeve,” whose limits are: the sternothyroid muscle superiorly, the inferior constrictor and cricothyroid muscles medially and the superior pole of the thyroid inferiorly , 6–8.The surgical importance of the EB-SLN is due to the close relationship between the nerve and the superior thyroid vessels. At the level of the cricoid, it divides into two branches, entering separately at the pars recta and pars obliqua of the cricothyroid heads, respectively. In most circumstances, the EB-SLN passes well above the superior thyroid pole, but variations in its caudal extent in relation to the superior pole region have been well-described. For this reason, many anatomic classifications have been proposed –9. The mType 1 (about 60%): the EB-SLN crosses the superior thyroid vessels at least 1 cm above the superior thyroid pole.Type 2a (17%): the EB-SLN crosses at a distance shorter than 1 cm.Type 2b (20%): the EB-SLN crosses below the upper limit of the thyroid.Type Ni (3%): EB-SLN not identified .The surgical implication of this classification system is that both 2a and 2b types are considered at risk during thyroidectomy.Variations in the incidence of Cernea’s type were described in relation to: physical height (increased number of type 1), ethnicity  and thyroid volume (increased number in type 2 in higher volumes) , 7, 8.More recently, Friedman et al. proposed a classification based on the course of the EB-SLN with respect to the inferior constrictor muscle , 12. In The EB-SLN carries motor fibers to the cricothyroid, the muscle that tilts the thyroid cartilage and tenses the vocal cord by modifying the distance between the cricoid and the thyroid cartilages. Vocal fold tension and thickness influence the frequency of the vibration, thus affecting the characteristic timbre of one’s voice.Injury of the EB-SLN causes paralysis and/or weakness of the cricothyroid, resulting in changes in voice quality, voice projection, and production of high-pitched sounds –8, 13–16The EB-SLN is jeopardized when the surgeon is dissecting around the superior pole of the thyroid gland to ligate the superior thyroid artery. The laryngeal head of the sternothyroid muscle should be considered as a landmark for the course of the nerve on the inferior constrictor . In caseThe anatomical variations of this nerve demand careful blunt dissection of the superior thyroid pole, which should start from the avascular space located between the medial aspect of the superior pole and the cricothyroid, allowing a good exposure of the region where the EB-SLN might be found.A gentle traction of the thyroid in a lateral and caudal direction may be helpful to obtain a good exposure of the superior vascular pedicle; moreover, the selective ligation of the vessels of the upper pole as close to the thyroid pole as possible is recommended. Separation of the polar vessels should occur in the inferior to superior direction, to avoid the entrapment of the EB-SLN between the medial aspect of the superior pole and the cricothyroid.Care must be taken to avoid both the stretching of the nerve and an indiscriminate use of monopolar diathermy or energy-based devices for sealing vessels, in order to prevent iatrogenic heat injuries , 8, 13.Intraoperatively, due to its wide anatomic variability, the EB-SLN can be visually recognized in some cases only , 17–20, Post-operatively, patients with a lesion of the EB-SLN typically complain of voice fatigue, problems reaching high-pitch sounds that they were used to reach, and the need of an extra effort to speak; they can also complain of various rates of dysphagia.The awareness to these symptoms, that may be subliminal to common people, might be more evident to the so-called “professional speakers,” such as singers, teachers, and lawyers.Several studies have investigated post-operative rates of EB-SLN injury varying from 0 to as much as 58%  and/or electromyography of the cricothyroid  are the only instrumental tools that might allow to achieve good diagnostic standards , 7, 8, aThe inferior laryngeal nerve  arises as the vagus courses anteriorly to the aortic arch. As the heart and the great vessels descend during the embryonic development, the RLNs are dragged down by the aortic arches. On the right side, the nerve recurs around the fourth arch (the right subclavian artery), whereas on the left, the nerve recurs around the sixth arch (the ligamentum arteriosum). The right RLN curves around the right subclavian artery and enters the base of the neck from a more lateral position, with respect to the nerve on the opposite side, a consideration that is extremely important from a strictly surgical point of view, since the anatomy is significantly different on the two different sides. The approximate length of the right RLN from the subclavian artery to the cricothyroid joint, is about 5–6 cm, whereas on the left side is about 12 cm long (from the aorta to the cricothyroid joint) . After lThe RLN in the neck is supplied by both its own vessels (“vasa nervorum”) and by branches of the inferior thyroid artery: this vascularization is particularly important since an excessive dissection of the nerve might theoretically represent a cause of undesired post-operative issues .The course of the RLN with respect to inferior thyroid artery is quite variable: it more commonly courses deep to the inferior thyroid artery, but can also travel anterior to or between its branches , 27  branch can penetrate this ligament , 28. ThiVariations in the pattern of distal bifurcation of the RLN have been widely reported, since, within the larynx, the nerve divides into an external branch providing motor function to the four intrinsic laryngeal muscles, and an internal branch with only sensory activity for the glottis. This division may occur before the RLN enters the larynx near the Berry ligament or the inferior thyroid artery giving origin to up to several extralaryngeal branches extremely varying in sizes. Functional studies of the extralaryngeal nerve branches have well-demonstrated that motor branches to both the abductor and adductor muscles of the larynx are generally located in the anterior division , 27, 29,The non-recurrent laryngeal nerve is associated to a major vascular variant characterized by the absence of the brachiocephalic artery and the formation of a right aberrant subclavian artery that originates from the last branch of the aortic arch and extends rightwards, running behind the esophagus (the “lusorian artery”). The nerve then originates directly from the cervical part of the vagus, at various heights, since it cannot be pulled down by the right subclavian artery during its embryological descent Figure . For thiFrom a surgical point of view, TYPE 1 anomaly implies that the nerve could be injured during superior thyroid pedicle ligation, while TYPE 2 variant implies that, over its transverse course, the non-recurrent laryngeal nerve can mimic the course of the inferior thyroid artery, and thus be misinterpreted by the surgeon, and finally interrupted. Preoperative computed tomography showing the presence of an arteria lusoria or the presence of a “horizontal Y” at US scan  could predict the presence of a non-recurrent laryngeal nerve and therefore reduce the risk of injuring it –34.Transient partial RLN dysfunctions are related to segmental demyelination or focal conduction block, and transient or permanent total nerve dysfunctions result from severe myelin sheath or axonal damage and neural degeneration. Transient palsy can be regarded either as a consequence of neuroapraxia or axonotmesis, depending on whether local myelin damage, usually secondary to compression  or a loss of continuity of axons. An excessive manipulation during surgery might lead to a significant edema or to diffuse microhemorrhage by injury of fragile capillaries, possibly resulting in neuroapraxia or axonotmesis .The final outcome of the damage to a RLN is represented by the paralysis of the sole abducting muscle (posterior cricoarytenoid) of the vocal cords, which might result in a clinical situation ranging from an impaired motility of the cord, up to its atrophy.Consequent symptoms range from hoarseness in unilateral lesions, to stridor and acute airway obstruction in bilateral damage. Temporary or permanent post-operative vocal changes can have a serious impact on the patient’s quality of life, especially in professional voice users.The posterior branches of the RLN often provide innervation to both the cricopharyngeus muscle and the esophagus, thus justifying the impairment in swallowing that is frequently complained by patients after thyroidectomy , 35–37. Post-operative RLN lesion is a relatively rare complication of thyroid surgery in expert hands, the rate of permanent damages occurring approximately between 0.3 and 3% of the cases, and transient palsies in up to 8% of the cases. This wide range of results is described in Table A cornerstone of the recommended surgical technique of thyroidectomy is the active search for and identification of the RLN. It is classically identified in the Simon triangle , formed The use of intraoperative nerve monitoring (IONM) in association to visual identification of the nerve has been safely applied, even if there is lack of high-level evidence that might elucidate the true RLN sparing effect of IONM: this tool should therefore not be used as the sole mechanism for identifying and preserving the nerve, although it can be used to aid in the identification and dissection of the nerve.In conclusion, a “safe” technique for thyroidectomy cannot be described, since every expert thyroid surgeon is burdened by a morbidity rate that cannot ever reach the 0%. Nevertheless, this rate can be “kept to a minimum” when a thorough surgical technique is followed, and the surgeon should always keep in mind that different preoperative indications correspond to a different incidence of morbidity, accordingly informing the patients about it.All Authors  made substantial contributions to conception and design, acquisition of data, and analysis and interpretation of data, and all participated in drafting the article and gave final approval of the version to be submitted and published.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.