A hybrid girder bridge adopts a steel segment at the mid-span of the main span of a continuous concrete girder bridge. The critical point of the hybrid solution is the transition zone, connecting the steel and concrete segments of the beam. Although many girder tests revealing the structural behavior of hybrid girders have been conducted by previous studies, few specimens took the full section of a steel–concrete joint due to the large size of prototype hybrid bridges. In this study, a static load test on a composite segment to bridge the joint between the concrete and steel parts of a hybrid bridge with full section was conducted. A finite element model replicating the tested specimen results was established through Abaqus, while parametric studies were also conducted. The test and numerical results revealed that the concrete filling in the composite solution prevented the steel flange from extensive buckling, which significantly improved the load-carrying capacity of the steel–concrete joint. Meanwhile, strengthening the interaction between the steel and concrete helps to prevent the interlayer slip and simultaneously contributes to a higher flexural stiffness. These results are an important basis for establishing a rational design scheme for the steel–concrete joint of hybrid girder bridges. Under the effect of a multifaceted load, a prestressed concrete (PSC) girder bridge ,2,3,4 wiSince the structural form of hybrid girders was proposed, a large number of studies have been carried out to study a better connection type between steel and concrete parts to facilitate the transition of stresses from one to the other. Kim tested three connection types on small-scale steel–PSC hybrid girders, and a connection consisting of parallel perfobond ribs was recommended ,15. ChenThe analysis of steel-to-concrete connections refers not only to hybrid beams but also to classical and non-standard composite beams. Su revealed the influence of the steel–concrete interaction on the overall mechanical performance of composite girders ,23,24. TAlthough many girder tests revealing the structural behavior of hybrid bridges have been conducted, few specimens took the full section of the steel–concrete joint due to the large dimensions of a prototype hybrid bridge. Tests results from a partial section of a girder may reveal the local stress conditions of the steel–concrete joint in the hybrid girder, but its overall structural behavior cannot be obtained directly. When laboratory tests cannot be performed, the size effect on the structural performance were typically evaluated through numerical models. The present research aims to experimentally and numerically investigate the overall mechanical behavior of the steel–concrete joint in hybrid girders. A simply supported composite girder taking the full section of a prototype bridge was tested for a detailed structural performance investigation. A finite element model of the specimen was established through Abaqus and calibrated with the test results. Then, parametric studies were also conducted to derive rational design criteria of the joint section. The objective of the present study is to take the first step in investigating the overall flexural behavior of a steel–concrete joint in hybrid girders and help establish appropriate design criteria for the transition zone and the joint section. The results obtained here need to be complemented with further tests mainly focused on the local mechanisms of response of the joint.The steel–concrete joint section in the longitudinal direction proposed in this study is based on a composite steel–concrete solution in the transverse direction. Therefore, a simply supported composite girder was manufactured and tested. The specimen was inspired on the transition segment of the Anhai Bay bridge, which is a key link in the construction of China’s first cross-sea high-speed railway. The Anhai bridge, located in Quanzhou City, is a three-span hybrid-beam rigid-frame bridge with a span arrangement of 135 + 300 + 135 m. In the main span, the 103 m long steel box girder is connected monolithically to the concrete box girder by a transition segment (5 m long) at each end with a cross-section depth of approximately 5.9 m  proposed by Sidoroff [The concrete damage plasticity model ,32,33 wa GB50010 . The plaectively . EquatioSidoroff .(1)σ= is shown in OC: Specimen with a concrete section only.OSN: Specimen with a steel section only and a steel plate thickness equal to N mm.COM: Specimen with a composite section and a steel plate thickness equal to 3 mm.Models with different steel flange thickness (the other section parameter kept the same as in the test specimen) were established to study its influence on the flexural behavior. According to the test results, the failure mode of the specimen was fracture of the steel bottom flange along with steel local buckling of the upper flange. The stiffening ribs on the upper flange determined the position of the local buckling but did not have a significant impact on the strain variation during the loading. The concrete girder prevented the steel flange from extensive buckling, which significantly improved the load-carrying capacity of the specimen.According to the test, there was an obvious phenomenon of steel–concrete interlayer slip both at mid-span (at 140 kN) and quarter-span (at 240 kN) in the steel bottom flange. The steel bottom flange was observed to be completely detached from the concrete. Thus, strengthening the interaction between the steel and concrete helps to prevent the interlayer slip and simultaneously contributes to a higher flexural stiffness.Based on the numerical analysis, the FEM model was proved to be reliable with sufficient accuracy. The deviation from the experimental results could be attributed to the lack of accuracy of the material constitutive laws as well as to the not fully correct simulation of the steel–concrete interlayer interaction.Based on the numerical parametric analysis, it is observed how the load-carrying capacity of the specimen with a composite section is much larger than that of specimens with a solo concrete sections and solo steel sections. While the steel girder provided greater load-carrying capacity, the concrete in the composite section prevented local buckling and increased the load-carrying capacity of the joint section. In addition, an increase of steel flange thickness in the specimen with a solo steel section had limited influence on the initial stiffness, while the composite section drastically increases it.Based on the parametric analysis, the load-carrying capacity showed a linear relation with the steel flange thickness, indicating that the flexural strength depended mainly on the steel girder. As the main failure mode of the test specimen was steel flange fracture, this conclusion is consistent with the experimental results. Thus, the primary function of the concrete filling was to prevent the steel local buckling, while it had limited influence on the load-carrying capacity of the joint section. In addition, the increase of the steel flange thickness also contributed to an improvement of the initial stiffness.A simply supported composite girder modelling the full section of a prototype hybrid bridge was fabricated and tested in this study. Finite element models of the specimen were built and calibrated for the posterior simulation and parametric analysis. Based on the experimental and numerical results, the following conclusions were drawn:Although some relevant conclusions have been already obtained from the study shown in this paper, still some limitations of the presented research have to be pointed out. For instance, for financial reasons, only one specimen was tested in this study. More test specimens with different design parameters are considered in the subsequent studies to obtain additional test data. In addition, as the test was designed to model the global performance and strength of the proposed connection, the small-scale model is hard to analyze the phenomenon of local buckling on the top flange that is due to local stress of the composite section of the specimen. Other local failure mechanisms, for instance the detachment of the steel and concrete in the top and bottom flanges, are due to the constraints imposed by the design of a small-scale specimen. Whether these local mechanisms can occur in the hybrid girder should be investigated by a larger scale test in the future study.


Hyperthermia is a thermal cancer treatment that consists of a selective increase in the tumor temperature to a supra-physiological value for 60–90 min. Heating via microwaves using a phased array applicator proved to be a very useful, non-invasive energy carrier. Although hyperthermia is currently employed for many anatomical sites in combination with standard techniques, there are still open challenges that prevent its more widespread use in the clinic. The aim of this article is to review the work carried out in the framework of a national project concerning the introduction of new tools for microwave hyperthermia and to unify these approaches. The proposed methodologies are interconnected and potentially allow an improvement in treatment planning using a single device.The aim of the article is to provide a summary of the work carried out in the framework of a research project funded by the Italian Ministry of Research. The main goal of the activity was to introduce multiple tools for reliable, affordable, and high-performance microwave hyperthermia for cancer therapy. The proposed methodologies and approaches target microwave diagnostics, accurate in vivo electromagnetic parameters estimation, and improvement in treatment planning using a single device. This article provides an overview of the proposed and tested techniques and shows their complementarity and interconnection. To highlight the approach, we also present a novel combination of specific absorption rate optimization via convex programming with a temperature-based refinement method implemented to mitigate the effect of thermal boundary conditions on the final temperature map. To this purpose, numerical tests were carried out for both simple and anatomically detailed 3D scenarios for the head and neck region. These preliminary results show the potential of the combined technique and improvements in the temperature coverage of the tumor target with respect to the case wherein no refinement is adopted.  Hyperthermia (HT) is a thermal cancer treatment that consists of a selective increase in the tumor temperature to a supra-physiological value 40–44 °C) for from 60 to 90 min. Clinical trials have demonstrated the therapeutic benefit of this treatment in combination with radiotherapy and chemotherapy ,2,3,4,5.0–44 °C fAlthough hyperthermia is in clinical use for many anatomical sites, there are still open challenges. First, the accuracy of hyperthermia treatment planning (HTP) depends on the accuracy with which electromagnetic (EM) and thermal tissue parameters are known. Second, a tool able to provide accurate real-time monitoring of the temperature distribution administered to the patient is required, and it is still not available. Currently, magnetic resonance-based approaches exist ,9; howevThe above-reported issues concerning HT are crucial, especially for challenging anatomical sites such as the head and neck (H&N) region and when real-time feedback control is absent, and thermo-regulation mechanisms are unknown ,10,11.HTP involves obtaining the optimal complex excitation coefficients (phases and amplitudes) of the signals feeding a microwave-phased array applicator. The objective of this procedure is to induce a homogeneous temperature increase in a given target area while avoiding high temperatures in healthy tissues . Once the 3D patient model has been segmented and tissue properties assigned, the HTP flow includes the evaluation of the EM fields in the domain of interest and, hence, the optimization of the phases and amplitudes feeding the applicator. Whether the specific absorption rate (SAR) or temperature distribution should be optimized is still a topic of debate amongst hyperthermia researchers ,11,12,13Optimizing the temperature distribution would seem the most natural approach since the increasing temperature is obviously the basis for obtaining therapeutic effectiveness in hyperthermia treatment. Moreover, systematic studies to assess the actual relation between the predicted temperature and the clinical outcomes have been proposed ,15,16. HConversely, SAR is directly related to the complex excitation coefficients via Maxwell’s equations. Additionally, studies, such as , demonstBecause of the attractive features recalled above, many SAR-based optimization strategies have been proposed in the literature. Some approaches aim at maximizing the SAR within the target volume while minimizing it in the surrounding healthy tissues. In some cases, also global optimizers have been used ,22. In ,24, HTP The optimization of the phases and amplitudes feeding the applicator depends on the adopted 3D EM patient model. One of the main limitations of HTP is the absence of accurate, reliable, and robust knowledge of the in vivo EM and thermal parameters of the different tissues. Currently, trained clinicians create 3D patient models by segmenting patient scans obtained via magnetic resonance imaging (MRI) or computed tomography (CT). Then, the corresponding parameters are associated with each tissue based on the average and ex vivo data ,31. In sAnother limitation is that a proper SAR shaping in a realistic scenario cannot correspond by default to the desired temperature distribution due to the thermal boundary conditions arising from external cooling systems (waterbolus) and physiology  ,38.This paper aims to review and present, in a unified fashion, the work carried out by the authors along several concurrent directions to advance hyperthermia; the framework for these research lines was a national project. Advancements have been pursued in the algorithms for optimal SAR shaping based on convex optimization  and the approach called “FOcusing via Constrained power Optimization” (FOCO). Complementary procedures have also been proposed to mitigate variations of SAR and temperature distributions due to the ex vivo (rather than in vivo) EM modeling of the electromagnetic scenario and thermal boundary conditions see . The impThe innovative contribution of the research activities reported here was centered around a novel optimization framework for the optimal shaping of a wavefield, a relevant problem in many different applications.In particular, the reviewed activities led to the introduction of a novel shaping paradigm based on convex programming and on the approach called “FOcusing via Constrained power Optimization”. This latter was first proposed in the antenna framework for the optimal synthesis of pencil beams  and thenFrom a mathematical standpoint, if we consider a target point properly set within the target area identifying the tumor  or parameters tuning. Unlike the approach in , which a-Multi-frequency FOCO (mf-FOCO) [mf-FOCO) , based o-Sparsity promoted FOCO (sp-FOCO) [sp-FOCO) , introdug theory , that is-Multi-target FOCO (mt-FOCO) [mt-FOCO) , aiming -Average SAR-constrained FOCO (av-FOCO) [av-FOCO) , which eav-FOCO)  is physiav-FOCO) .Starting from the above, four constrained approaches have been proposed, aimed at focusing a wavefield in a target point and based on FOCO. Specifically, these latter are:All the above FOCO-based procedures can be extended to the case of vectorial fields, as discussed in .Some of the above strategies have been clinically tested and comparatively assessed on actual patient data in collaboration with the Hyperthermia Unit of the Department of Radiation Oncology at the Erasmus MC  ,46,50,513 (ΔT50 = +0.39 °C). In addition, being FOCO formulated as a convex optimization problem, the results of the optimization procedure are repeatable and achieved sensibly faster (−44%) [For instance, in , FOCO isIt should be noted that the final thermal distribution obtained with the optimized feedings may be different from the desired one in a realistic scenario due to both the inaccuracies in the ex vivo EM patient model and the thermal boundary conditions (that are not considered in the SAR optimization). To circumvent such issues, two complementary strategies, which can be used singularly or eventually in combination, have been proposed, as presented in the following sections.As already stated in the Introduction, the final SAR map  obtained with the optimized antenna feedings may be different from the actual (desired) one due to the inaccuracies introduced by the ex vivo EM modeling of the patient. By “quantitative modeling of the scenario,” we mean the process of obtaining the parameters of the EM model of the anatomical region to be treated. This is essential not only for accurate patient-specific delivery of the thermal treatment but also for the prediction of the EM field distribution inside the body in many biomedical applications, from safety assessment of medical devices to dosimetry and radioprotection studies. The present state of the art is based on the segmentation of medical images (MRI/CT) and the use of a conventional database of EM and thermal properties of tissues from ex vivo measurements . In thisThe first approach consists in processing the MRI data corresponding to different arrangements of the coils at the resonance frequency ,53. As uIn this respect, the research activities by the authors of  have resTo counteract the resolution issue, an innovative inversion approach has been developed in , which iThe proposed patient-specific representation basis, in the following denoted as “tissue projection”, has been used in conjunction with the well-known contrast source inversion (CSI) scheme  but can The proposed estimation problem amounts to recovering the effective EM properties of tissues found in . Note thfound in ,59.From a technological point of view, the feasibility of the proposed approach relies on dual use of the existing antennas both to deliver a hyperthermia treatment as well as to retrieve in vivo tissues EM parameters. In particular, a multiview-multistatic measurements configuration is suggested, wherein the antennas are organized in such a way that for each transmitting antenna in ason, in , the proFinally, the tissue projection approach is affected by the capability of co-registering MRI and CT images with the MWT system. This is a challenging issue. However, some devices can already circumvent this difficulty in the hyperthermia treatment of H&N tumors .Although it is well known that in a homogeneous infinite medium, the SAR and the corresponding temperature map have the same peak locations , in a reIn , we haveThe temperature correction approach can be generally described by means of the steps reported below.Following standard HTP procedures, a SAR-based optimization is performed to maximize the power deposition on the tumor target region (centered at The optimized squared magnitude of the electric field is reasonably approximated by a (multi-variate) Gaussian fitting function, with different standard deviations along the different axes and peak position The peak position For each point in the refinement region arameter  is definThe center Point 1 is repeated to optimize the SAR on a target region centered around As emphasized in , the proIn the next section, the optimization implemented by FOCO  and the realistic human phantom Duke V3.0   with multiple SAR optimizations, which is a choice made possible by the low computational cost of a convex optimization approach such as FOCO.In both models, the thermal boundary conditions were assigned according to , with coWe refer to the steps reported in step 1). We have considered the For the simplified numerical scenario, as a first step, FOCO was applied to optimize the field focusing on the tumor target, centered at cated in . ribed in . As can 2/m2 and standard deviations step 2). In the reported example, we limited the refinement region (step 3) to a two-dimensional circle step 4), and the maximum value was found for step 5). Finally, FOCO was again applied to focus the EM radiation on a target region centered around the shifted position step 6).To correct this shift, the squared amplitude of the optimized E-field  of the THQ ,38 is restep 1). The corresponding temperature map is reported in step 4) and the optimal focusing point determined by the position maximizing the step 5) and led to the optimized temperature map reported in Regarding the realistic testbed, FOCO was first applied to optimize the SAR distribution on the tumor target centered at The above preliminary examples aim at showing the interconnection between two of the tools proposed in the research initiative here reviewed  and not at assessing the benefits of the resulting T-corrected FOCO and at comparing it with other state-of-the-art approaches. As can be noted in  testbed  and fromAs discussed in , the com3). Lastly, FOCO-based procedures are formulated as a convex optimization problem, hence, are easier to be implemented (as no tuning of parameters is required) and much faster than PSO-based methods. As opposed to non-convex optimizers, the results are then more repeatable and computationally less cumbersome (see above). Moreover, the point target correction based on temperature analysis could further improve FOCO performance with respect to the standard FOCO and make more effective the corresponding thermal treatment. Regarding the clinical implications of the overall activities herein reviewed, some considerations are in order. First, FOCO has been demonstrated to have comparable performance to the current clinical HTP methodologies . In the Second, as far as measurement-based quantitative EM modeling is concerned, the knowledge of EM properties is limited to ex vivo or animal studies with limitations on the knowledge of the dependencies to temperature and intra- and inter-patient variability. Solving this fundamental issue will contribute to the plan-of-the-day approaches to tackling undesired hotspots. Finally, a common trait of the research line reviewed here has been the effort to move from diagnostic or therapeutic devices into theranostic devices. The capabilities of the developed techniques enable, in principle, the possibility of using the same medical device for both diagnostic and therapeutic purposes with non-negligent economic impact of the adoption of MW devices.In this paper, the review of a set of research lines carried out by the authors in the field of microwave cancer hyperthermia has been presented, emphasizing their complementarity and their interconnections. The research activities have been devoted to the development of new tools to increase the effectiveness and patient-specificity of hyperthermia treatments. The crucial issue of optimal design of the array applicator has been addressed. Moreover, two complementary techniques to further optimize the SAR and temperature distributions and ensure an improved temperature coverage of the target area have been developed. The first one relies on a quantitative assessment of the EM scenario via MWT, while the second one takes into account the thermal boundary conditions. They can be used individually or in combination.Finally, the proposed SAR optimization convex-programming procedure (FOCO) has been combined for the first time with the refinement technique proposed in Future works will be aimed at testing the overall proposed strategies (including the one for quantitative modeling of the EM scenario) against the ESHO patient repository . In partMoreover, the case of the extended tumoral region will be addressed by considering the shaping paradigm underlying multi-control points-based approaches ,69 and bFinally, T-corrected FOCO with the Gaussian approximation (or even multiple SAR optimizations) has shown a computational cost that allows sensitivity studies with respect to critical parameters such as perfusion, which are crucial for the applicability of the method in a clinical setting.


Understanding the microscopic origins of collective reorientational motions in aqueous systems requires techniques that allow us to reach beyond our chemical imagination. Herein, we elucidate a mechanism using a protocol that automatically detects abrupt motions in reorientational dynamics, showing that large angular jumps in liquid water involve highly cooperative orchestrated motions. Our automatized detection of angular fluctuations, unravels a heterogeneity in the type of angular jumps occurring concertedly in the system. We show that large orientational motions require a highly collective dynamical process involving correlated motion of many water molecules in the hydrogen-bond network that form spatially connected clusters going beyond the local angular jump mechanism. This phenomenon is rooted in the collective fluctuations of the network topology which results in the creation of defects in waves on the THz timescale. The mechanism we propose involves a cascade of hydrogen-bond fluctuations underlying angular jumps and provides new insights into the current localized picture of angular jumps, and its wide use in the interpretations of numerous spectroscopies as well in reorientational dynamics of water near biological and inorganic systems. The role of finite size effects, as well as of the chosen water model, on the collective reorientation is also elucidated. The collective nature of reorientational dynamics in water remains poorly understood. Here, the authors show that large angular fluctuations require a highly cooperative dynamics involving correlated motion of many water molecules in the hydrogen-bond network that form spatially connected clusters. Since water molecules are characterized by a rather large dipole moment, which in turn leads to directed interactions between them, the molecular reorientation mechanism has attracted significant interest8.Hydrogen-bond (H-bond) network fluctuations in water are at the heart of a wide range of physical, chemical, and biological processes, ranging from proton transfer in the ionization of water12. The mechanism by which large and quick rotations of a water molecule happen is due to fluctuations in the local coordination patterns of neighboring waters suggesting a process that involves at least three water molecules which alters the local H-bond network topology. When these jumps occur, do other water molecules in this network remain as spectators or are they active participants in a more collective process?Over a decade ago, Laage and Hynes demonstrated that water rotations do not occur solely via small diffusive steps, but instead typically involve sudden large-amplitude angular jumps13 to time-dependent vibrational spectroscopy15 indicate the presence of collective and concerted processes18 underlying reorientational dynamics in water.One of the enormous hurdles in determining a clear answer to this question originates from the difficulty in disentangling fluctuations occurring over a wide spread of both length and timescales, that create and form labile hydrogen bonds with a plethora of hydrogen-bond network patterns. On the other hand, numerous experiments ranging from dielectric spectroscopyHere, using an automatized detection of angular motions determined from molecular dynamics simulations of water, we illustrate a mechanism that unambiguously reveals the collective and correlated nature of water reorientation dynamics. By using an automatic protocol that identifies all abrupt angular motions, with no a priori assumptions on hydrogen-bonding, we demonstrate that there is a heterogeneity in the types of angular jumps that occur and that large reorientations are facilitated by a highly orchestrated motion of dozens of water molecules. We assert that these features are a generic property of the fluctuations in the local topology of the water H-bond network on the THz timescale. We also show that regions with lower local density serve as hot-spot sites in the network where large reorientations can occur simultaneously.By conducting a finite-size analysis, as well as comparing with several water models, we also elucidate the generality of the collective reorientational mechanism. Specifically, while small-box simulations consisting of approximately 1000 waters, and commonly used in previous studies, tend to enhance the relative fluctuations of the H-bond network underlying the angular jumps, the extent of the spatially correlated clusters of the molecules involved, is not affected. Furthermore, the collective reorientational dynamics is found in several water models we examine, with subtle differences in the fraction of defects and asymmetries in the hydrogen-bonding structure both of which can affect the microscopic mechanisms.In order to build our intuition on the collective nature of angular jumps, in Fig. We see that the angular change of the dipole vectors of the eight molecules involved in this event, ranges between 60 and 120 degrees within the selected time interval. This type of angular change clearly modifies the direction in which the dipoles of these eight water molecules point to. Moreover, eye-balling the time series shown, indicates that these reorientation events are simultaneous and possibly correlated in space, which, as we will see shortly, requires a collective reorganization of the hydrogen-bond network. All this suggests that there is a highly coordinated dynamics underlying angular jumps, involving large number of molecules and diverse motions, which will be elucidated in the ensuing analysis.t), and angular magnitude (ΔΘ). As we will see later, the angular changes we identified, have a broad range of angular amplitudes and duration consistent with previous observations of the local angular jump picture. Therefore, we dubbbed all detected molecular reorientations as angular swings, rather than angular jumps. The latter is the predominant term in the literature, but it only refers to large-amplitude angular swings accompanied by H-bond breaking10. Here, we also analyze small angular fluctuations which would essentially correspond to small angular diffusive steps, that don’t necessarily involve H-bond breaking.Quantifying the angular jumps illustrated in Fig. 19. This, in turn, affects local topology of the H-bond network, leading to rearrangements of nearby water molecules and possibly further large reorientation events. Here, we examine the connection between changes in local topology and angular swings in more detail by quantifying the occurrence of these events in time for the entire ensemble of water molecules.Underpinning the large angular jumps in the H-bond network, are fluctuations in the local topology of water molecules. Large angular motions usually create coordination defects which affect the hydrogen bonding patternsFirst, at every time step of the simulation, we calculate the number of waters in the system that are non-defective, i.e., those that accept two and donate two hydrogen bonds, and the number of all the other water molecules, which we refer to as defects. The time series of the fraction of defects with respect to the total number of water molecules in the system is shown in Fig. 20. To quantify better the collective nature of angular swings in the water network, we now look at how many angular swings occur simultaneously in the system. In similar spirit to the idea of propagation of defects13, we assume that the rearrangements of the local H-bond network due to a molecular reorientation can trigger further swings close by in time. Therefore, at every time step, we calculate how many molecules perform angular swings within a specific time interval around it.Large changes in the number of defects in the network suggest that there is a collective process underlying the water reorientations in the H-bond network. This phenomenon is akin to similar effects proposing the role of defects in the mobility of water under supercooling10. Thus, we look at a time window of 1ps, within which we calculate all the angular swings happening in the system. By automatizing the detection of angular motions, we are able to identify all possible sudden angular changes in the waters’ motion, spanning a wide range of duration and amplitude. However, large-amplitude swings are most likely the ones leading to water reorientation and change in local topology, as considered in the literature10. Moreover, the small-amplitude swings do not change much the orientation of the water molecule, and are less likely to affect local topology of the H-bond network.Previous studies report that water reorientation occurs on a time scale of about 1ps that includes not only the angular jump itself, but also the breakage and forming of the H-bond before and after the jump22, their role in reorientational dynamics has remained elusive. In fact, in panels b and c of Fig. θ > 40∘.In Fig. 23. Our findings bare some similarities with recent work by Liu and co-workers25 where they show that an angular jump of a given water molecule could enhance the subsequent jump motions of the same water molecule and surrounding water molecules up to the 2nd coordination shell.Our findings suggest a deep connection between the fluctuations in the underlying local topology of the H-bond network and the nature of angular swings occurring simultaneously in the system. These results reinforce a picture of water reorientations being an outcome of highly coordinated dynamics of water molecules, rooted in the collective fluctuations of the network’s topology consistent with previous proposals by Ohmine and co-workersconcurrently are, we find high correlation on the timescale of 10s of femtoseconds encompassing these angular jumps. However, as we look at the correlations between trajectories of the same molecules over longer times, they become less and less correlated akin to what is expected for any two random molecules in the system  for these distances by repeating the analysis for the time interval of 200 fs, shifting the time window along the whole duration of the simulation. The obtained PDFs for the position of the nearest jumping molecules with respect to another jumping molecule are shown in Fig. ∘, the difference in the PDFs is most evident for the 1st and 2nd nearest neighbor  defined as the inverse of the Voronoi volume taken as a sum of the oxygen and two hydrogens of the jumping waters. Indeed, Fig. 34.Besides the changes in local coordination topology dictated by direction of the hydrogen bonds, density fluctuations are central to understanding both the thermodynamic and dynamical properties of water36 or alternatively, be part of several large angular swings that occur simultaneously.As seen from the previous analysis on the changes in the local environment involving the local topology of the hydrogen bond network, large swings must naturally result in the disruption of the hydrogen bond network of at least one of the nearest neighbors. Furthermore, large angular swings also tend to occur in low-density and more disordered environments. Since density fluctuations involve collective reorganizational processes within the hydrogen bond network, large swings could presumably either lead to consequent angular jumps of the nearby molecules, as suggested in the literatureOne might wonder how much the results we find are affected by the size of the system we consider. In order to discard spurious finite size effects on the collective reorientation mechanism proposed here, we conducted a series of additional simulations for larger system sizes and analyzed their large swings and defect statistics  and another of 8152 water molecules (box size 62.5572 Å) in cubic periodic boxes. In addition, to investigate the generality of the collective reorientational mechanism, we conducted small-box simulations for several point-charge water models, namely TIP5PWater reorientation dynamics include various processes happening at different time scales, from very fast vibrational motions causing limited reorientation, to slower reorientation through sudden large-amplitude angular jumps. It remains still an open question how and to which extent each of these processes is involved in the underlying collective hydrogen bond rearrangements. To elucidate the mechanism behind the collective reorganization of water observed in Fig. v(t), with t being time. A new times series, vF(t), was constructed by filtering v(t) using a second-order low-pass digital butterworth filter59 implemented in MATLAB60 with the cutoff frequency of 10 THz. To further smoothen the time series, a mean filter of 10 THz was then subsequently applied. Details of the filtering procedures are specified in the following Methods section. An example of the original unfiltered and the filtered time series of one of the DP vector components are shown in Fig. In order to track down angular changes in water orientation, we rely on two body-fixed vectors, the dipole moment (DP) and the HH vector see Fig. a. From tvF(t) using a finite difference method, and calculate the cross product of this vector with vF(t) in order to obtain a new vectorvF(t). Our protocol defines an angular swing to be a process that does not change the plane of rotation of the body-fixed vector vF(t). This implies that, over the time of one angular swing, the direction of n(t) does not change, as shown in Fig. n(t). More precisely, we look at the following quantityvF(t). Consequently, the start and end times of angular swings can be identified as maxima in q(t), which are fully consistent with extrema in the filtered time series, vF(t), correctly recognizing sudden angular changes as shown in Fig. Using the filtered time series we subsequently compute the derivative of entclass1pt{minimaentclass1pt{minimaq(t), and the magnitude is found by computing the angle between the unfiltered DP or HH vector at the start and at the end point of the swing. The final output of the protocol is the start time (t), duration (Δt), and magnitude (ΔΘ), for each angular swing detected. We perform the procedure both for DP and HH vectors, as some angular fluctuations of water molecules can be better captured through one or the other vector.Finally, having identified the start and end points of the swings, the duration of the swings are taken to be the times between two peaks of smooth with the span of 25 data points (corresponding to the time window of 100 fs). Furthermore, during post-processing of the time series of defect fractions and number of swings, we have additionally applied a low-pass butterworth filter with the cutoff frequency of 0.1 THz (1/10000 in inverse fs), which allows us to clearly capture the fluctuations on the 10 ps scale. The same smoothing procedures were applied for all the water models and system sizes.On the time traces of the molecular dipole moments and HH-vectors, we first applied a 2nd order low-pass digital butterworth filter . The trajectories are sampled every 4 fs, while the cutoff frequency (the frequency at which the magnitude response of the filter is 61. A pair of water molecules are considered to be hydrogen bonded when the distance between the donating and accepting oxygen atoms (OD and OA) is less than or equal to 3.5 Å and the angle formed by the bond vector between the donating hydrogen and oxygen (HD and OD) and that between OD and OA is less than 30∘.To determine the hydrogen bonds, a geometrical criterion is used developed originally by Luzar and ChandlerSupplementary InformationPeer review file


The goal of estimating a soundscape index, aimed at evaluating the contribution of the environmental sound components, is to provide an accurate “acoustic quality” assessment of a complex habitat. Such an index can prove to be a powerful ecological tool associated with both rapid on-site and remote surveys. The soundscape ranking index (SRI), introduced by us recently, can empirically account for the contribution of different sound sources by assigning a positive weight to natural sounds (biophony) and a negative weight to anthropogenic ones. The optimization of such weights was performed by training four machine learning algorithms  over a relatively small fraction of a labeled sound recording dataset. The sound recordings were taken at 16 sites distributed over an area of approximately 22 hectares at Parco Nord (Northern Park) of the city Milan . From the audio recordings, we extracted four different spectral features: two based on ecoacoustic indices and the other two based on mel-frequency cepstral coefficients (MFCCs). The labeling was focused on the identification of sounds belonging to biophonies and anthropophonies. This preliminary approach revealed that two classification models, DT and AdaBoost, trained by using 84 extracted features from each recording, are able to provide a set of weights characterized by a rather good classification performance . The present results are in quantitative agreement with a self-consistent estimation of the mean SRI values at each site that was recently obtained by us using a different statistical approach. Among the elements used to evaluate the environmental status as a whole, one is strictly connected to the acoustic quality of a habitat, recognized as a vital dimension of wildlife conservation ,2. The iThe diffusion of passive acoustic monitoring with a large memory capability, and the possibility of analyzing acoustic recordings by extracting specific spectral and level characteristics through ecoacoustic indices . When uUrban parks represent a unique area of study as retrieving source-specific information from geophony, biophony, and anthropophony remains a challenging task due to interference and confounding factors arising from the simultaneous presence of different sound sources. It should be emphasized that, in the existing literature, the question of defining an indicator that ‘summarizes’ the information about the acoustic environment unbound from human perceptual nature has not generally been considered. In order to fill this gap, we devised an index enabling us to quantify the quality of the local environment sound in a simple fashion. The index is referred to as the soundscape ranking index (SRI), and is assembled by weighting the different soundscape components  present in a habitat/environment. The identification of the different soundscape components requires a time-intensive “manual” labeling or sound truthing of the recorded audio files, and is usually performed by a single expert.In this work, we studied the possibility of predicting the SRI at an urban park in the city of Milan  from the extracted spectral features of audio recordings. This task was pursued by applying a set of ML classification models to our dataset collected over an extended area, where the resulting indexes were grouped, for simplicity and in accord with our previous works, into three main categories denoted as “poor”, “intermediate”, and “good” environment sound qualities. This classification was obtained according to the different contributions of the environment sound sources. These groups are influenced by the choice of the set of weights attributed to each soundscape component . Here, we used the classification capabilities of the chosen ML algorithms to fine-tune the soundscape weights, thus obtaining the optimal separation of the area of study in terms of local environmental sound qualities. The use of ML techniques to study the SRI will allow us to consider much larger datasets than those studied by means of supervised methods requiring human intervention. Work along this line is in progress.The paper is organized as follows. In this section, we briefly describe the area of study, instrumentation, and recording pattern. We include the description of the SRI index, the scheme used for its prediction and optimization based on the features extracted from the spectral analysis of audio recordings in the form of ecoacoustic indices and mel-frequency cepstral coefficients (MFCCs), and the manual labeling. We also illustrate the classification models used to predict the manual labeling from the extracted features of the audio recordings.The Parco Nord (Northern Park) in the city of Milan extends over an area of approximately 790 hectares and is located within a highly urbanized area. Approximately 45% of its surface is dedicated to natural green spaces and vegetation, whereas the remaining surface is devoted to agricultural activities and infrastructures. The area of study is a tree-covered parcel of approximately 22 hectares encircled by agricultural fields, lawns, paths, and roads see . It has We used low-cost digital audio recorders produced by the SMT Security a. They wThe 22 recorders were initially positioned on a regular grid, as shown in In this section, we describe the scheme adopted for the aural analysis of audio files in order to quantify distinctive sound features. An aural survey was carried out to quantify the biophonies, anthropophonies, and geophonies. In particular, a single expert listened carefully to the recordings according to the following scheme: one minute listened to for every three minutes of continuous recording, for a total of seventy minutes of listening per site. The expert focused on quantifying the biophonic activity  and the tecnophonic sources, evaluating the parameters reported in the scheme of Each soundscape component was analyzed to extract information about the sound source and its occurrence and intensity see . FollowiThe anthropogenic noise is mainly attributable to road traffic. For this source, two parameters were evaluated see : (1) noiith sound category is present at the recording r; otherwise, We wish to quantify the quality of the local environment sound by means of a single index, SRI, as proposed recently . In the ℓ refers to the ℓth recording and the coefficients take on the following values: In the present study, a single audio recording, i.e., ous work . It can ous work )(2)SRIℓ that in  we used ℓ, given byThus, Equation  providesIt should be emphasized that the choice of these intervals for classifying the SRI is rather arbitrary. Nonetheless, they are based on rather generic features attributed to human perception, in the sense that the poor (good) quality interval reflects a prevalence of anthropogenic (biophonic) sound sources, whereas the intermediate quality interval reflects a balance/co-existence of both types of sound sources.i was assigned a weight, We first searched for the sound categories, reported in Then, we calculated the spectral features of the sound recording and implemented the optimization scheme illustrated in In order to proceed, both the spectral features and SRIs need to be split into “training” and “test” sets. The training set is used as the input for each classification model, whereas the performance of the test set is quantified according to the metrics described in In this section, we provide a brief description of the classification models used to predict the manual labeling sound categories, and thus the SRI index, from the ecoacoustic indices. In general, machine learning methods are better able to address multicollinearity issues and capture the potential non-linear relationships among variables. While binary classification is a more common application of them, they are also widely used for regressions when the target is continuous. In our case, we used classification algorithms for trinary (poor/medium/good) categories for determining the SRI.Decision tree (DT);Random forest (RF);Support vector machine (SVM);Adaptive boosting (AdaBoost).The models taken into consideration in this study, which were implemented in Python programming language , are thejth class of the target variable was chosen as follows: T is the total number of data items, N is the number of classes of the target variable, and The supervised classification models implemented for the SRI optimization procedure were trained on the 80% of the data and tested on the remaining 20%. Data were split using a stratified procedure to keep the proportions between the classes of the corresponding target variable. Furthermore, class weights were used to take into account the class imbalance of the data set. In fact, training an algorithm with a skewed distribution of the classes can be achieved by giving different weights to both the majority and minority classes. The difference in weights will influence the classification of the classes during the training phase. The whole purpose is to penalize the misclassification made by the minority class by setting a higher class weight and, at the same time, reducing the weight for the majority class. The weight for the A decision tree (DT) is a non-parametric supervised learning method used to predict the value of a target variable by learning simple decision rules inferred from the data features ,55. DTs Several measures were designed to evaluate the impurity of a partition, of which the Gini impurity (GI) is among the most popular ones . Then, fA random forest is a meta estimator that fits a number of decision tree classifiers on various sub-samples of the dataset, and uses averaging to improve the predictive accuracy and control overfitting. Random forests (RFs), or random decision forests, are an ensemble of learning methods used for classification, regression, and other tasks that operates by constructing a multitude of decision trees during the training procedure. For classification tasks, the output of the random forest is the class that is selected by most trees. In other words, it fits a number of decision tree classifiers on various sub-samples of the dataset and uses averaging to improve the predictive accuracy and control overfitting . For thiSupport vector machines (SVMs) are supervised machine learning models that can be used for both classification and regression purposes ,59. TheyOne-vs.-One approach, which breaks down the multiclass problem into multiple binary classification problems using a binary classifier per each pair of classes. Another approach that can be used is the so-called One-vs.-All approach. In this case, a binary classifier per each class is used. The latter approach is used for the SRI optimization procedure.For multiclass classification, the same idea is employed by decomposing the multiclassification problem into multiple binary classification problems. This can be achieved by mapping data points to a high dimensional space to gain mutual linear separation between every two classes. This is called a p-dimensional vector (a list of p numbers) and we want to know whether we can separate such points with a In general, a data point is viewed as a e spaces .For the sake of clarity, let us consider a simple separable classification method in multidimensional space. Given two classes of examples clustered in feature space, any reasonable classifier hyperplane should pass between the means of the classes. One possible hyperplane is the decision surface that assigns a new point to the class whose mean is closer to it. This decision surface is geometrically equivalent to computing the class of a new point by checking the angle between two vectors: the vector connecting the two cluster means and the vector connecting the mid-point on that line with the new point. This angle can be formulated in terms of a dot product operation between vectors. The decision surface is implicitly defined in terms of the similarity between any new point and the cluster mean—a kernel function. This simple classifier is linear in the feature space whereas, in the input domain, it is represented by a kernel expansion in terms of the training examples.x and y computes the similarity or how close they are to each other. This kernel can be mathematically represented as follows:x and y. The RBF kernel support vector machines are implemented using the scikit-learn library [Radial basis function (RBF) kernels are the most generalized form of kernelization and are one of the most widely used kernels due to its similarity to Gaussian distribution . The RBF library .Adaptive boosting has been a very successful technique for solving two-class classification problems. It was first introduced in  with theThe core principle of AdaBoost is to fit a sequence of weak learners  on repeatedly modified versions of the data. The predictions from all of them are then combined through a weighted majority vote (or sum) to produce the final prediction. The data modifications at each so-called boosting iteration consist of applying weights,  containing salient or summative information about the measured data. This process is intended to help the learning procedure by providing significant information about the content of the recordings. Here, we essentially used two types of features: those based on ecoacoustic indices and those based on mel-frequency cepstral coefficients (MFCCs) (see below).The acoustic entropy index (H) highlights the evenness of a signal’s amplitude over time and across the available range of frequencies .The acoustic complexity index (ACI) accounts for the modulation in intensity of a signal over changing frequencies .The normalized difference soundscape index (NDSI) accounts for the anthropogenic disturbance by computing the ratio between technophonies and biological acoustic signals .The bio-acoustic index (BI) is calculated as the area under the mean frequency spectrum above a threshold characteristic of the biophonic activity .The dynamic spectral centroid (DSC) indicates the center of mass of the spectrum .The acoustic diversity index (ADI) provides a measure of the local biodiversity at the community level without any species identification .The acoustic evenness index (AEI) provides reverse information of ADI with high values identifying recordings with the dominance of a narrow frequency band .Ecoacoustic indices (ECOs) are generally used to quantify the soundscape in both marine and terrestrial habitats, and are grouped into categories aiming at quantifying the sound amplitude and its level of complexity and weighting the importance of geophonies, biophonies, and technophonies (soundscape). In this work, we focused on the following set of ecoacoustic indices:spectro available in the R package “seewave” [For each one-minute recording, we computed seven cumulative indices. Each recording is thus represented by seven features (seven indices).For each one-minute recording, we computed each index with a one-second time-step. Then, we calculated seven statistical descriptors : minimum, maximum, mean, median, skewness, kurtosis, and standard deviation. Each recording is thus represented by 49 features .The ecoacoustic indices were calculated in the R environment (version 3.5.1 ). Specifseewave”  in the fseewave” . A dedicThe mel-frequency cepstrum (MFC) has become a convenient alternative for obtaining a reduced amount of data from each audio recording while keeping the core spectral information. The MFC is a representation of sound based on a linear discrete cosine transform (DCT) of a log-power spectrum on a non-linear MEL scale of frequency . The latThe calculation of the MFCCs was performed in the R environment using the default number of MEL filter banks; that is, 40 logarithmically distributed bands over the whole spectrum. Another important issue is the selection of the most convenient time window size for extracting the features of the data set. In this regard, we have to keep in mind that the dataset is obtained by computing a fixed number of features from an audio recording, usually referred to as a “window”.For each one-minute recording, we computed 12 MFCCs in a one-second time window. Then, we calculated seven statistical descriptors resulting from each audio recording: minimum, maximum, mean, median, skewness, kurtosis, and standard deviation. This corresponds to 84 features .For each one-minute recording, we computed 12 MFCCs in a one-second time window. This corresponds to 1428 features (12 MFCCs times 119 time windows: 60 s window with 50% overlap).A large time window size may capture relevant events but would result in a dataset with few instances. On the other hand, a small time window would result in a larger data set but may split the relevant events into several windows. For this reason, as we are trying to classify a summative description of the audio files  data for which the true values are known. A strong discrepancy between the results obtained between training and test data may be indicative of an overfitting issue. It generally contains the following information: true positives, TPs, and true negatives, TN, which are the observations that are correctly predicted, and false positives, FP, and false negatives, FN, which occur when the actual class contradicts the predicted class. The derived metrics are the following :Precision: This represents the ratio of correctly predicted positive observations to the total predicted positive observations. A high precision is related to a low false positive rate:Recall (Sensitivity): This is the ratio of correctly predicted positive observations to all observations in the actual class. Thus, the recall tells us the proportion of correctly identified positives:F1-score: This is defined as the harmonic mean of precision and recall . TherefoThis metric is useful in case both precision and recall are equally important. In our case, we decided to refer to the F1-score as the classification measure.As a validation of the results, we used the k-fold cross-validation technique. It consists of an iterative procedure used to evaluate machine learning models. The procedure has a single parameter called k that refers to the number of folds that a given data sample has to be split into. This technique returns stratified folds; that is, folds obtained by preserving the percentage of samples for each class. At each kth iteration, the kth fold is used as the test set, whereas the other folds are used to train the model.The results presented in this section refer to the audio files recorded on 25 May 2015, from 06:30 a.m. to 10:00 a.m. (CET). As described in The machine learning algorithms selected usually work better on small data sets than deep neural networks. In fact, the latter require extremely large datasets to achieve high performances. Furthermore, a large dataset was not readily available and would be expensive and time-consuming to acquire. Another consideration when selecting classical machine learning algorithms concerns hyper-parameter tuning and the interpretability of these kinds of models. The underlying mechanisms of random forest, Adaboost, and SVMs are more straightforward than those of deep neural networks. Enhancing the interpretability also results in an easier tuning of hyper-parameters. However, for our preliminary study, we leaned on the default values as reported in , with thFor each model, we split the entire dataset, consisting of 1220 audio files, into a training and test set with the following proportion: 80% of the dataset used for training and 20% of the dataset used for testing. As the reference measure to search for the optimal classification, we used the F1-score, which is more suited to our case, i.e., an uneven class distribution due to the limited sample size numerousness. In particular, the table contains the values of the weights and the corresponding classification measures. The weights can vary in an interval, meaning that the optimal classification measure (F1-score) can be obtained for a different combination of weights. The table also contains precision and recall as classification measures. All three measures are given in terms of the mean value ± standard deviation calculated over all classification classes defined by Equation .In general, we can observe an increase in the classification performance as we provide more detailed information about the spectral content of each recording from 7 to 84 extracted features. For the 1428 features for each recording (1428 MFCCs), we observe a general drop (with the exception of the RF model) in the performance, more likely due to information redundancy contained in the time series. This redundancy is smoothed out by considering the statistical descriptors of the same time series (84 MFCCs).A similar consideration can be carried out for the ecoacoustic indices. In this case, the 7 ECO features, derived by integrating the ecoacoustic indices over the whole length of the recording (1 minute), contain more condensed information; thus, it appears to not be enough to represent the complexity of the soundscape in a single summative index. On the other hand, the 49 ECO features provide a better representation of the spectral dynamics within each single audio recording. AdaBoost and RF models perform better. The AdaBoost model yields an F1-score of 0.70  with 84 MFCCs, and an F1-score of 0.69  with 49 ECO features. The RF model yields an F1-score of 0.71  with 84 MFCCs, and an F1-score of 0.70  with 1429 MFCCs. Hence, the RF model results in a slightly higher classification performance.The highest metric ranking leads to the definition of nearly different sets of coefficients Equation . The DT The possibility of deriving an overall soundscape index summarizing the contribution of all the sound components and being able to rank them in terms of sound “quality” can be one of the empowering ecological tools used to help rapid on-site field and remote surveys. Here, we tested four extracted features see  from recThe idea of predicting an overall ranking index from a limited number of recordings, as initally defined in  and compWe find that the RF model provides a more robust classification as its F1-score distribution presents maxima at higher values than for the AdaBoost model see  for all In order to further validate the obtained results, we computed an SRI map over the study area based on the weights obtained for the RF model, which is reported in As expected, lower SRI values  are found close to the traffic noise sources (Sites 1–4), where the presence of higher traffic noise and less bird singing activity contribute significantly to this outcome. On the other hand, sites belonging to the park interior are less influenced by traffic noise and host higher biodiversity (many birds of different species singing). This result is reflected by the higher SRI values . Sites (5–8) are at intermediate positions and show a sort of transient behavior of SRI values .In The study of the soundscape within urban parks represents an increasingly important issue as they represent the link between natural habitats and highly populated urban areas. The evaluation of the soundscape is usually carried out through the help of ecoacoustics analysis and thus the use of well-known ecoacoustic indices. In this work, we gathered spectral information in the form of ecoacoustic indices and MFCCs to train four machine learning models to predict a single index  carrying information of different sound sources and, in addition, providing a soundscape ranking among different locations within the urban park.The SRI has the advantage of yielding a quick overview of an environment given a set of extracted spectral features. We found that the seven statistical descriptors calculated for the 12 MFCCs  are able to determine the optimal combination of weights that leads to a quite high classification score. Values for the F1-score of approximately 0.70 and 0.71 were obtained for AdaBoost and RF models, respectively. However, the RF model proved to be more robust when tested using the k-fold cross-validation procedure. Indeed, the information carried by the SRI represents a summative representation of the soundscape quality, which is essentially driven by the prevalence of the sound sources acting locally. As such, the SRI can be used to rapidly provide maps of environment sound quality on the basis of few audio recordings. The splitting of the SRI into three main intervals may somehow be adjusted by considering its quantization into smaller bins. This will allow us to obtain finer shades of the environment sound quality.Mapping the SRI yielded similar results to those recently obtained in  through As already stated in the introduction, the availability of a small labeled dataset can undermine the performance of ML models, which represents a limitation of the present study. However, the obtained performance can be considered satisfactory and can represent a benchmark for future developments. As a future development of the present work, we envisage the use of larger labeled datasets. This can be achieved by using additional recordings with the corresponding aural survey, and/or via data augmentation using Monte Carlo techniques. We also envisage the application of NN models to develop more efficient classification schemes. In many situations, there is also the need to use different sound recorders to map extended areas simultaneously. Indeed, this procedure can introduce a bias in the analysis owing to different frequency responses of each sound recorder. This issue also needs to be addressed in our future works.


With the increase in urban rail transit construction, instances of tunnel disease are on the rise, and cracks have become the focus of tunnel maintenance and management. Therefore, it is essential to carry out crack detection in a timely and efficient manner to not only prolong the service life of the tunnel but also reduce the incidence of accidents. In this paper, the design and structure of a tunnel crack detection system are analyzed. On this basis, this paper proposes a new method for crack identification and feature detection using image processing technology. This method fully considers the characteristics of tunnel images and the combination of these characteristics with deep learning, while a deep convolutional network (Single-Shot MultiBox Detector (SSD)) is proposed based on deep learning for object detection in complex images. The experimental results show that the test set accuracy and training set accuracy of the support vector machine (SVM) in the classification comparison test are up to 88% and 87.8%, respectively; while the test accuracy of Alexnet’s deep convolutional neural network-based classification and identification is up to 96.7%, and the training set accuracy is up to 97.5%. It can be seen that this deep convolutional network recognition algorithm based on deep learning and image processing is better and more suitable for the detection of cracks in subway tunnels. With the continuous development of urban subway construction and the continued existence of tunnels constructed even earlier, various types of diseases have appeared in subway tunnels ,2. Due tThe widespread use of image processing technology in various detection fields is the result of the continuous advancement of computer technology, which can solve some of the past shortcomings of traditional detection ,7. The aCracks in subway tunnels are ubiquitous and one of the causes of tunnel diseases. Cracks in subway tunnels not only affect their appearance but also lead to dangers in terms of their carrying capacity and durability, and can even bring about large economic losses and societal safety hazards in severe cases. Yuan W indicated that the detection and investigation of tunnel cracks in subway tunnels are special inspection items . Xue F’sDue to the gradual maturing of image processing technology, scholars have increasingly been studying the technology and applying it in different industries. At present, the detection of cracks in subway tunnels using this technology has also attracted much attention. Wang R showed that in the image processing of crack detection systems, false information and breakpoint problems required more efficient threshold segmentation and breakpoint connection algorithms . Dai Z s(1)Analysis of traditional manual detection and automated detection methodsThe technology for the early detection of subway tunnel cracks is not yet fully mature, and manual detection is the main method used. In recent years, many experts and scholars have been exploring and researching new technologies, and they have gradually created many new methods. According to the degree of complexity and mechanization, tunnel crack detection is divided into traditional manual detection and automatic detection . TraditiAs can be seen from The automatic detection method comprehensively collects various images of the tunnel and then analyzes the collected images to obtain the relevant parameters of the crack. In the example shown in (2)Overall design scheme of the detection systemThe subway tunnel crack detection system needs to not only detect cracks but also perform real-time detection of temperature, humidity, wind speed, wind direction, etc., as well as detect the three-dimensional direction of the tunnel through lidar and inertial navigation sensors . The comAfter processing the collected cracks, the detected cracks are marked and the features are extracted, and finally, they are input into the database, which is also convenient for data management . Data maAs shown in (1)Image preprocessing algorithmR, G, and B, respectively, at the midpoint of the three-channel image.The acquired image is a three-channel image, and the three primary color (RGB) graphics are composed of three color channels. The RGB color mode is the color standard in the industry. It obtains various colors by changing the red (R), green (G), and blue (B) color channels and superimposing them onto each other. RGB represents the red, green, and blue channels. This standard includes almost all colors that human vision can perceive, and it is one of the most widely used color systems. The three-channel information is used when the pixels are processed and turned into grayscale images ,27. The An open operation and a close operation are constructed via an erosion expansion combination to eliminate isolated noise points and overlap small images, respectively. Macroscopically, the erosion operation can melt the edge of the object and make the crack target texture in the image thinner. Therefore, the algorithm first performs grayscale transformation and the erosion operation on the fracture image to filter the scattered noise and the burr on the fracture edge. Let the structuring element of a grayscale image There are two types of grayscale transformations: linear stretching and nonlinear stretching. Linear stretching changes the pixel value of the image by adjusting the slope and intercept of the linear transformation function, thereby transforming the grayscale value range of the original image to another limited range. The linear stretching process is shown in Formula (3):As shown in (2)Image multilevel feature analysis algorithmRectangularity is a characteristic measure that can be used as a cohesion test  because Most of the noise elements in the image have been removed after filtering. Filtering based on the rectangularity of the connected area can filter out most of the speckle noise in the subway tunnel image and retain the elongated crack area. At this time, most of the noise areas in the image have been filtered out, but some large block noise areas connected to the fracture skeleton or with low cohesion have not been filtered out, and thus further operations are needed. The algorithm carries out shape extremum filtering based on the connected region by combining the maximum width Connected regions that all exceed the threshold are called extended large-area block noise regions. These include a connection area width threshold (3)Circumscribed rectangle image extraction of feature texture connected areaIn order to retain all crack regions, non-crack-based types of noise such as wall scratches and water stains in tunnel images are filtered out as much as possible through image preprocessing and layered feature analysis. To this end, before the extraction of the original image corresponding to the connected area, the length–width ratio can be set artificially according to the original image proportions, experimental experience, and crack texture characteristics, and the minimum circumscribed rectangle can be appropriately expanded to ensure that the size proportions of the extracted image are the same or close to the original image and reduce the subsequent image recognition error. The smallest bounding rectangle of the connected area package The principle of expanding the size of the rectangle circumscribed by the longitudinal crack is shown in Formulas (9) and (10):Therefore, when the circumscribed rectangle corresponds to the original image extraction, the minimum circumscribed rectangle is appropriately expanded. While filling the crack area with images, this process ensures that the aspect ratio of the image is as close as possible to the original image and avoids the error caused by the large size difference in the subsequent image classification.(1)Tunnel complex image target detection algorithmConsidering the advantages and disadvantages of image recognition and feature detection algorithms for subway tunnels, an SSD algorithm is developed to detect objects in complex images. The main network structure used by the SSD method is VGG16. The estimated bounding box size ratio The expected bounding box output of each feature map is convolved with two convolution kernels, and the program compares it to the actual label value box. When the intersection-over-union ratio (IOU) exceeds a predetermined threshold, matching target detection occurs. Unlike classification and recognition, target detection needs to judge the position and category of the target in the image at the same time. Therefore, there are great differences in the evaluation methods. The evaluation target is not the whole image, but the prediction boundary box generated in the process of network training and that participates in the loss function calculation and forward and backward propagation. The target detection IOU calculation is shown in IOU is greater than the set threshold, it is a positive sample. Conversely, if the target category of the sample in the prediction boundary box is wrong or the IOU of the target sample for this category is less than the set threshold, it is a negative sample. IOU threshold to evaluate the location of the algorithm’s expected bounding box, calculated as:For each type of target, if there is a target sample for this category in the prediction boundary box and the (2)Image classification and recognition algorithm for tunnel cracksLocal response normalization (LRN) completes the data normalization operation in standard deep convolutional networks, as it is used to improve the generalization ability and training speed of convolutional neural networks. Batch normalization (BN) is used instead of LRN in the upgraded Alexnet deep convolutional network to perform standard data normalization operations. In this Alexnet deep convolution network, a self-learning process is completed through forward propagation and backward propagation. Through forward propagation from the bottom to the top, the output value from the calculation results of the network model is obtained through a layer-by-layer calculation. This speeds up the learning rate of the network and prevents the intermediate layers from changing during training on the image data. This makes it suitable for extracting image features from subway tunnels. For the feature extraction, classification, and identification of cracks in subway tunnel photos, this method uses a lightweight open-source deep learning framework (Caffe) to build an upgraded Alexnet deep convolutional network.The SVM achieves the goal of data classification by maximizing the distance between positive and negative data values based on the concept of structured risk minimization. The SVM uses the hinge loss function to calculate the empirical risk and adds the regularization term to the solution system to optimize the structural risk. It is a sparse and robust classifier. The SVM can be used for nonlinear classification via the kernel method, which is one of the common kernel learning methods. A three-level cascaded SVM classifier can be constructed, where the first two cascaded SVM classifiers are used to gradually predict and score, and then the third-level SVM classifier is used for target confirmation to improve data accuracy ,30. When(1)Selection of model building environmentThe crack detection system is designed for subway tunnel detection, with the aim of identifying cracks arising due to different types of tunnel defects. In order to ensure the efficient performance of the crack detection system in terms of safety, the entire system needs to be installed on a rail vehicle that can provide structural stability for the equipment. Due to the negative impact of the low light intensity in the tunnel on obtaining high-quality images, it is necessary and important to equip the camera with sufficient lighting equipment. The system can only enter the subway tunnel within the maintenance window, and the operating time is only about 2 h. Therefore, the system needs to obtain a large number of tunnel images in a limited time and accommodate a large amount of image data obtained through a single inspection. Considering the actual situation of the tunnel and the cost-effectiveness of hardware equipment, the selection of the system’s main components is discussed in this section.(2)Selection of hardware equipmentFor the choice of hardware, CMOS cameras have attracted great interest in high-speed image processing due to their low power consumption and fast image reading speed. Line-scanning cameras capture images through linear scanning, but due to insufficient lighting, the captured images are prone to being of low quality. Common lighting devices such as flashlights are not suitable for line-scanning cameras. Laser light sources have a high illumination intensity, which can ensure the uniformity of image brightness. Therefore, the high-speed industrial line-scanning CMOS camera Basler racer ral6144 was chosen for image acquisition, and a customized laser light source was selected for illumination. The captured images were transmitted to the computer via an image capture card.To ensure that the captured image contains information about half of the tunnel surface, three cameras and two laser light sources were evenly spaced on the frame, with a spacing of 30° between each device. The image processing system can control the image acquisition system to obtain images of the tunnel surface, store a large number of captured images, and perform image data analysis. An industrial computer equipped with image acquisition control software and image analysis software was used for real-time image acquisition and offline image processing. A small and powerful portable i7 processing industrial computer was used for this.Because nonlinear stretching can only expand or compress the regions with low or high grayscale values, it is not generally suitable for the grayscale transformation of crack images. Therefore, this paper mainly compares linear stretching and histogram equalization. The comparison between the original image and the linear stretching effect is shown in It can be seen from It can be seen from It can be seen from Using deep learning, this paper constructs an SSD deep convolutional neural network and verifies and analyzes it, as shown in As shown in Under the confidence level of 0.1, a total of 1240 cracks were detected, with a detection rate of 92.96%. At the confidence level of 0.5, 878 cracks were detected, and the detection rate was 64.38%. Therefore, in the detection results, especially for small cracks, the repeated box selection of multiple prediction boxes is prone to occur, but this does not affect the overall detection effect. This method needs to be perfected in future research, and the recognition accuracy for complex images in subway tunnels can be improved by further fusion.Due to the difficulty in identifying crack images in subway tunnels, the function was continuously adjusted according to the experimental results during the experiment to improve efficiency and accuracy. In this experiment, a total of 3000 data images were selected, the data images were extracted with features, the output data were normalized, and then the output data were read and trained. Because the initial weights were random, the error in the result was also random, and the training result taken was the best training result selected from multiple experiments. The experimental result can be obtained as long as some output(s) approaches 1 and other outputs approach 0, as then the fracture type can be determined. The experimental classification results are shown in The experimental results show that the detection accuracy with transverse cracks reached 92.3%; the detection accuracy with longitudinal cracks reached 94.0%; and the detection accuracy with oblique cracks reached 90.8%. The output results of the analysis can be obtained for transverse cracks and longitudinal cracks with regular shapes, because, even if they have a certain angle in the horizontal or vertical direction, this would not affect the results of the system judgment, and at the same time, a high classification accuracy can be achieved. This verifies the rationality of feature selection. However, considering that not all cracks are regularly shaped, some misclassified crack images were found during the experiment. Because of the distortion and ductility of the cracks in these images, it is difficult to define their type manually, and the analysis of the misclassified images shows that it is this type of crack image that interferes with the judgment results. At the same time, it can be seen that the set of eigenvectors selected in the experiment can classify and identify cracks well, and the average accuracy rate of the system for the identification of the three types of cracks reached 92.4%.Using the original image sample library for classification and recognition, the training accuracy was 74.7% and 69.2%, respectively. By combining the feature texture after pixel processing with the improved bounding rectangle correspondence, a better sample library was obtained. The training accuracy reached 87.8%, and the test accuracy reached 88%. At the same time, a comparison experiment between subway tunnel image classification and recognition was carried out with the improved Alexnet deep convolutional network, and the experimental results are shown in As can be seen from (1)With the aim of identifying complex crack images in subway tunnels, a deep-learning-based SSD deep convolutional neural network method was proposed.(2)In the experiment, original images and linear-stretched effect maps, as well as the horizontal and vertical projection results, of transverse cracks, longitudinal cracks, and oblique cracks, were compared. In order to verify the application of this method in subway tunnels, an SVM-based classification and identification method was adopted.(3)Experiments show that the method combining image processing and deep learning has better performance than the SVM-based classification and recognition method.(4)There are still several issues that need to be resolved because of the complicated internal environment of subway tunnels, the numerous interference elements, and the constrained number of image samples. Therefore, the algorithm still needs to be optimized and improved, and the scientific basis and rigor of the experiment should be strengthened in future work.


In the absence of vaccines, the most widespread reaction to curb the COVID-19 pandemic worldwide was the implementation of lockdowns or stay-at-home policies. Despite the reported usefulness of such policies, their efficiency was highly constrained by socioeconomic factors determining their feasibility and their associated outcome in terms of mobility reduction and the subsequent limitation of social activity. Here we investigate the impact of lockdown policies on the mobility patterns of different socioeconomic classes in the three major cities of Colombia during the first wave of the COVID-19 pandemic. In global terms, we find a consistent positive correlation between the reduction in mobility levels and the socioeconomic stratum of the population in the three cities, implying that those with lower incomes were less capable of adopting the aforementioned policies. Our analysis also suggests a strong restructuring of the mobility network of lowest socioeconomic strata during COVID-19 lockdown, increasing their endogenous mixing while hampering their connections with wealthiest areas due to a sharp reduction in long-distance trips. NPIs encompass a wide variety of policies implemented to reshape the interaction patterns of the population to hamper the potential contagion pathways of infectious individuals. This goal can be accomplished by targeting different factors involved in virus transmission. At the individual level, the transmissibility of a virus in contacts between the infected and susceptible population is reduced by promoting prophylactic measures such as the use of masks6. At the community level, the exposure of susceptible individuals to a virus can be reduced by testing-trace-isolate-quarantine (TTIQ) policies9, shortening the effective infectious window of infectious individuals and isolating their contacts, or by population wide lockdowns and stay-at-home policies, decreasing the number of acquaintances of the entire population by controlling their mobility12.During the first half of 2020, the lack of approved vaccines turned non-pharmaceutical interventions13. In this sense, several studies have found remarkably different mobility patterns across socioeconomic classes classified according to several criteria such as race, ethnicity or income level19. In the context of epidemics, it is worth remarking that, even in uncontrolled scenarios, the coexistence of multiple mobility networks might be highly relevant for the evolution of epidemic outbreaks, leading to heterogeneous epidemic trajectories across the different socioeconomic classes21. In addition to the socioeconomic flavor of daily recurrent mobility patterns, the feasibility of the aforementioned policies also varies across different socioeconomic groups. For example, the adoption of stay-at-home policies is clearly related to the possibility of working at home, an option that is much more accessible to those individuals with higher income levels24. Consequently, a positive correlation between the income level of the population and the levels of mobility reduction achieved through lockdown interventions has been measured in different cities26.The success of community NPIs, such as lockdown or stay-at-home policies, in reducing social contacts is not universal but strongly depends on the complex relationship existing between the socioeconomic characteristics of the population and their mobility27 revealed that 29, a poorly connected area with an inadequate service infrastructure and deficiencies in access to health systems. This pattern is consistent across the other cities here studied, where lower socioeconomic strata are located far from the city centers, with conditions similar to those described in the case of Bogotá31.Here we aim at further investigating the interplay between socioeconomic features and the mobility reduction observed as a consequence of lockdown policies in the three major cities of Colombia: Bogotá, Medellín and Santiago de Cali. As usual in Colombian cities, the population is divided into six different socioeconomic strata according to the quality of their households and neighborhoods. This classification is used to determine the cost of public services and access to government aid. Although there is not a one-to-one correspondence between strata and socioeconomic classes, stratum 1 typically gathers those individuals with less economic resources whereas stratum 6 usually correspond to the wealthiest population. The distribution of the population across strata is not homogeneous. For instance, local surveys carried out in Bogotá in 201732 analyze time variations in the use of public transport, finding higher mobility reductions for the wealthiest socioeconomic strata and a generalized shrinkage of trips distance. Here we use another source for mobility data, which are estimated from the travel patterns of mobile phone users, and extend the analysis to more Colombian cities. The spatio-temporal resolution of this dataset allows us to construct a time-varying multiplex network containing weekly mobility patterns for each stratum. We analyze the properties of such network, providing further evidence of how socioeconomic constraints shaped the outcome of lockdown policies in Colombia. Finally, we go one step further and analyze how lockdown policies altered the structure of the mobility patterns of different strata and their social mixing. By integrating both socioeconomic and mobility data, we reveal that lockdown policies also shaped the social structure of cities, exacerbating the segregation of lowest socioeconomic strata while barely affecting the mobility patterns of the highest ones.Previous studies have already studied the heterogenous impact of lockdown policies on the mobility of different socioeconomic strata in Bogotá. In particular, Dueñas et al.The mobility patterns of the population are sourced from The Google COVID-19 Aggregated Mobility Research Dataset. The dataset contains anonymized mobility flows aggregated over mobile phone users who have turned on the Location History setting, which is off by default. This is similar to the data used to show how busy certain types of places are in Google Maps—helping identify when a local business tends to be the most crowded. The data set aggregates weekly flows of people from region to region, with a spatial resolution of level 12 s2cells areas. These correspond to an area between 3.04 and 6.38 squared kilometres. By default, all metrics defined in this section correspond to weekly values, but can be generalized to quantify averages over any arbitrary number of weeks.33. To provide strong privacy guarantees, all trips were anonymized and aggregated using a differentially private mechanism34 to aggregate flows over time (see https://policies.google.com/technologies/anonymization). This research is done on the resulting heavily aggregated and differentially private data. No individual user data was ever manually inspected, only heavily aggregated flows of large populations were handled.To produce this data set, machine learning is applied to logs data to automatically segment it into semantic tripserr is Laplacian noise. The automated Laplace mechanism adds random noise drawn from a zero mean Laplace distribution and yields  in the tensor would be k, we obtain the number of residents s, We extract demographic and socioeconomic data from the 2018 Colombian census. Specifically, we use the spatial distribution of the population and the economic stratum of households aggregated to the level of census block. This way, for each census block 15, which allows us not to lose detail or aggregate disparate population when merging mobility and socioeconomic data. After this process, the number of residents inside cell i from stratum s is computed as:s in a cell i, s moving from cell i to cell j at a given week t, t. In what follows, we omit the time index in the explanation to ease notation. The sum of these trips across origins and destinations gives us the overall mobility of the population of stratum s during a week, which reads as follows:f with N patches, corresponding to the different s2cells in which each city is partitioned in the mobility data set. For the baseline scenario used to compute the effects of lockdown policies, we consider the mobility patterns recorded for the week starting on 02-02-2020.To construct the mobility networks associated to each stratum, we should aggregate both socioeconomic and demographic information to match the spatial resolution of mobility data, corresponding to level 12 s2cells areas as discussed above. To do this, we associate each census sector with the cell containing its centroid. Let us here remark that Colombian cities typically display high levels of segregation among socioeconomic classess travels, denoted in what follows by i and j. Analogously, the distance a person from stratum Once we have embedded the mobility patterns of the different strata in a multiplex network, we can estimate how mixing between different strata changed over time as a consequence of the implemented lockdown policies. To this aim, we define the entries of the  before the arrival of COVID-19 pandemic in the three cities here analyzed. For this purpose, we compute the matrix To compute the impact of lockdown policies, we represent in Fig. To shed light into how the heterogeneous trends observed in Fig. In Fig. To round off our study, we compute the time evolution of the Shannon entropy of the entries of the mixing matrices corresponding to each stratum and represent them in Fig. 36 through the airport mobility network and the local exponential growth in the number of cases driven by community transmission of the virus. Since vaccines were not available at the time, many countries deployed NPIs to reduce the impact of the pandemic. These containment measures included mobility restrictions to curb the importation of cases from high-incidence areas and local control policies that reshaped the contact patterns of the population responsible for community transmission of the virus.The extremely rapid unfolding of COVID-19 pandemic at the beginning of 2020 arose from the subsequent combination of the international exportation of infectious casesIn this work, we have studied how NPIs altered the mobility patterns of different socioeconomic classes in the three main cities of Colombia. Our analysis reveals a strongly unequal impact of control policies on the different strata into which Colombian society is divided. First, we have reported a consistent positive correlation between the reduction in the number of trips registered for a given area and the average stratum of its residents, implying that those individuals with more economic resources, typically belonging to the highest strata, were more able to reduce their mobility and, therefore, their social activity. Secondly, we have revealed that lockdown policies, in addition to affecting the volume of movements recorded in each city, modified their architecture, reducing the distance involved in the movements and increasing the social similarity in the composition of the origin and destination of the flows recorded. However, this phenomenon was not homogeneous in all strata. The blocking policies hindered long-distance urban trips connecting lowest socioeconomic classes with wealthier areas, leading to a significant increase in the endogenous interactions with geographically proximate individuals and a reduction in the distance of their trips. In contrast, our analysis reveals that the implemented policies hardly affected the mobility patterns of the highest strata.38, mental health issues45, or the increase of social inequalities in different countries as a result of lockdown policies48. Beyond social implications, the exacerbation of social inequalities might also have important implications for the evolution of epidemic outbreaks, as proven by the influence of income gradients on COVID-19 associated mortality51. Apart from NPIs, socioeconomic determinants are also crucial to understand other important factors during COVID-19 pandemic such as the access to health services54, the unequal vaccination willingness observed in the population57 or the heterogeneous occurrence of mental health issues across social and age groups58. We hope that our study will shed light into the interplay between socioeconomic information and epidemic spreading and will pave the way to the design of control policies optimizing the trade-off between their health outcome and the damage of the socioeconomic fabric derived from their implementation.Our results suggest the need for accounting for socioeconomic variables when assessing the feasibility or the expected impact of community NPIs to mitigate an epidemic outbreak. In this sense, despite the clear improvement of the health situation while gaining time for vaccine development, the socioeconomic dimension of NPIs entailed undesired collateral effects such as economic crisisOur results should be interpreted in light of several limitations. First, the Google mobility data is limited to smartphone users who have opted in to Google’s Location History feature, which is off by default. Therefore, we assume the mobility patterns of this set of individuals to be representative of the movements of the entire population. Importantly, these limited data are only viewed through the lens of differential privacy algorithms, specifically designed to protect user anonymity and obscure fine detail. Furthermore, comparisons across rather than within locations are only descriptive since these regions can differ in substantial ways.33.Another limitation of this data set is that the origin of one movement recorded for one individual does not necessarily coincide with its residence, which might introduce some noise when computing the reduction of the mobility associated to each stratum. Nonetheless, previous studies leveraging this kind of data sets have found comparable results to those obtained when analyzing mobility patterns coming from census surveys32.Moreover, to construct the multiplex mobility networks, we have assumed that all socioeconomic strata are proportionally represented in the data set, thus neglecting socioeconomic biases in the use of mobile phone devices, which may vary by location. While this assumption could remain controversial, our results are consistent with those obtained by analyzing variations in public transport usage as a result of lockdown policiesFinally, we have restricted our analysis to cities in Colombia, where socioeconomic classes are highly segregated. This segregation is partly explained by the spatial distribution of these populations across cities, where poor populations tend to be located on informal settlements along the cities’ boundaries. Frequently, these outskirts tend to be more disconnected from city centers and economical hubs due to scarce access to transport services. The generality of our findings when extending our analysis to other societies deserves further investigation and remains as future work.