The present study investigates different elastomers with regard to their behavior towards liquids such as moisture, fuels, or fuel components. First, four additively manufactured materials are examined in detail with respect to their swelling in the fuel component toluene as well as in water. The chemical nature of the materials is elucidated by means of infrared spectroscopy. The experimentally derived absorption curves of the materials in the liquids are described mathematically using Fick’s diffusion law. The mechanical behavior is determined by uniaxial tensile tests, which are evaluated on the basis of stress and strain at break. The results of the study allow for deriving valuable recommendations regarding the printing process and postprocessing. Second, this article investigates the swelling behavior of new as well as thermo-oxidatively aged elastomers in synthetic fuels. For this purpose, an analysis routine is presented using sorption experiments combined with gas chromatography and mass spectrometry and is thus capable of analyzing the swelling behavior multifacetted. The transition of elastomer constituents into the surrounding fuel at different aging and sorption times is determined precisely. The change in mechanical properties is quantified using density measurements, micro Shore A hardness measurements, and the parameters stress and strain at break from uniaxial tensile tests. Nowadays, polymers are used in a wide range of applications such as hoses, sealings, and membranes, where they come into contact with various surrounding liquids such as water ,2, oils The present paper investigates the swelling behavior of soft elastomers on the basis of various aspects. Firstly, attention is paid to the swelling behavior of additively manufactured soft polymers. The new additive manufacturing processes not only expand their field of application but also raise fundamental questions about the optimal choice of printing process parameters. The present study on the swelling behavior represents an enormously important step in the analysis of the additive manufacturing process. The printed end product differs greatly depending on whether a wet or dry filament was printed. Only the knowledge of how to set the correct printing parameters enables an optimal printing result.The application of soft polymers in sealings and hoses, especially fuel-conveying hoses, motivates the further part of the presented study. Here, pristine as well as thermo-oxidatively aged elastomers are subjected to a study on their swelling behavior. The concrete question is ultimately the operational stability of fuel hoses in which new types of synthetic fuels are conveyed. The diffusion of fuel components into the polymer as well as the diffusion of polymer components into the surrounding liquid are investigated in detail in this study. The influence of swelling on the mechanical properties before and after aging is quantified in detail.Additive manufacturing (AM) gradually comes into focus for the fabrication of functional parts. With respect to soft polymers, the limitations of the AM technologies regarding both the type and the nature of the employed materials hinder the use of conventional elastomers. Instead, 3D printers may operate with other types of existing materials as well as with newly developed ones. AM parts show significantly different mechanical properties compared to the same parts produced with conventionally produced elastomers, e.g., natural rubber. Therefore, generating knowledge on this subject is a fundamental step toward understanding the mechanical behavior of these materials from 3D printing processes and the feasibility of their applications. This contribution aims to give a brief overview of the additive manufacturing of elastomers and to show the influence of liquid media, such as moisture and fuels, on the printing process as well as on the subsequent application. Regarding their chemical composition, the investigated materials are initially analyzed, while the focus of this work lies on swelling tests with water and toluene followed by uniaxial tensile tests.Popularly known as 3D Printing, the origins of AM are associated with the prototyping industry. Nevertheless, it has become a more and more interesting alternative for the production of parts with technical applications in addition to conventional manufacturing methods, such as machining and injection molding. The layer-wise process of joining materials to form parts from 3D model data allows a less wasteful, on-site manufacturing along with the exemption of individual tooling and reduction of postprocessing ,9,10. AMIn this context, we can find the elastomers. Several current technologies are able to print parts based on rubber-like materials. It is important to point out, though, that every AM technology demands a specific type and nature of material, which generally does not allow the use of traditional, vulcanized rubber. One of the main reasons is that the vulcanization process cannot easily be transferred to AM. Some technologies, however, allow the use of conventional liquid silicone rubber. Alternatively, thermoplastic elastomers (TPEs) and photopolymers are employed in the printing of soft, elastic components.One of the downsides associated with those alternative materials is typically the still inferior mechanical behavior ,12 in te®—is one of the most popular, low-cost AM processes. In this technology, the material in filament form is fed through a heated nozzle up to melting and pushed in it by a motor, characterizing the deposition by means of extrusion, after which the material cools down and solidifies into the desired geometry. Since this process demands the use of thermoplastics, TPEs are the choice for the printing of elastomeric parts. PolyJet is a material jetting process, working similar to a standard 2D inkjet printer and equipped with multiple nozzles. These nozzles deposit droplets of photopolymers that are then cured by exposure to UV light. The LAM technology is based upon the extrusion of a liquid or high-viscosity material onto a build plate, where the two-part component materials are mixed in a screw-like manner right before the deposition. Then, heat is provided to carry out the crosslinking by thermal energy.Some of the today’s AM technologies that are able to process elastic materials are fused filament fabrication (FFF), PolyJet, and liquid additive manufacturing (LAM), which are explored in this section and sketched in Overall, AM is a relatively young manufacturing process in the elastomeric field that has a lot to be explored, although very promising. Both the market and the industry can benefit themselves not only with the fabrication of new parts on demand, reducing warehousing costs, but also with the faster replacement of damaged components, particularly those discontinued by original manufacturers. Despite being more cost-effective for small batch sizes, the evolution of the technologies and materials helps in gradually enabling the use of AM for mass production at a competitive market price in comparison with the traditional fabrication methods. Nevertheless, ensuring the quality of the final printed part is imperative to establish AM in the field of rapid manufacturing.®  is a two-component viscous silicone with a hardness of 50 Shore A and printed with the LAM process in an innovatiQ’s LiQ 320 printer . The second material is Filaflex 70 A, a TPU from company Recreus , with a hardness of 70 Shore A.Using this material, parts can be manufactured by a FFF process, which was performed in an Original Prusa i3 MK3S+ 3D printer  for this work. The third and fourth materials can be processed with the PolyJet technology. They consist of the same type of photopolymer of resinous material with the name TangoBlackPlus combined with VeroClear (referred here simply as Tango+), supplied by Stratasys® , but vary in hardness with 70 and 50 Shore A, respectively. For those, a Stratasys® Object500 Connex3 printer  was used. The following subsections present chemical and mechanical investigations for 3D printed elastomers of three main types of currently available materials: liquid silicone rubber (LSR), thermoplastic polyurethane (TPU), and photopolymers. There are four printable materials of interest for this research. SILASTIC™LC 3335, supplied by DowA chemical characterization was performed using infrared (IR) spectroscopy. The changes in weight caused by moisture absorption and exposure to toluene were investigated by means of water uptake and solvent absorption tests. At last, tensile tests allowed comparisons of the mechanical properties of the different elastomer samples before and after the water uptake tests. For the solvent absorption tests, however, no tensile properties were able to be evaluated since the intense toluene swelling damaged the samples.To characterize the polymers, Fourier Transform infrared spectrometer (FTIR) spectra were recorded with an attenuated total reflectance (ATR) unit. The measuring device was a Bruker Tensor 27 with Platinum ATR and 32 scans were taken per sample in the range between 400 and 4000 The absorption bands for the silicone SILASTIC at 1065 and at 1007 ilicones ,14.The TPU Filaflex 70 A shows pronounced absorption bands at 2939 and at 2851 urethane .As the spectra of the Tango+ 70 and the Tango+ 50 are very similar, they are considered together. Just like the TPU, Tango+ also shows the specific bands at 1530 and at 1240 acrylate ,15.Sartorius Secura® 225D-1S precision balance with a range of 120 g and a resolution of 0.0001 g. Each specimen was then stored in a screw glass containing 50 mL of toluene or water, respectively. After defined periods of time, the sample was taken out, dried with a lint-free paper, and weighed. After this, it was stored again in the solvent. To minimize the evaporation of the fluid out of the specimen, special care was taken by an immediate weight measurement. Three specimens were used for each material, and the results of the measurements were expressed in terms of the mean average values and standard deviationsThe geometries of tensile test specimens according to the Standard DIN 53504:2017-03-S2  for SILAt and in the equilibrium state, respectively, D is the diffusion coefficient, h is the sample thickness, and n is the summation index.The solid lines in The hygroscopic nature of the four chosen elastomeric materials was analyzed in a Water uptake test. The results are plotted along with the fitted curves based on Fick’s Law from Equation  in FigurA considerable part of the absorption for all materials occurs during the first hours of the experiment; in the first 24 h, more than half of the saturation is already achieved. This evidences the importance of the environment in functional applications. While water does not play a major role in the conventional rubber-like material LSR, the same cannot be affirmed for the photopolymers and the TPU. In fact, it is already known that TPEs in general are hygroscopic, which should be taken into consideration, notably before and during the FFF printing process. Filaments with increased moisture levels lead to extrusion failures and the generation of voids on the streaming, caused by steam formation on the heated nozzle . MoreoveThe effect of moisture on the mechanical behavior of the printed samples was evaluated by tensile tests on a Zwick Roell 1445 universal testing machine with a force sensor of 500 N and an optical extension sensor ProLine lightXtens 2-1000 at ambient temperature, a preload of 0.1 MPa and a strain rate of 200 mm min:2017-03 . The strThe curves show a decrease in stiffness and ultimate stress for the photopolymers Tango+, which is more pronounced for Tango+ 70 than for Tango+ 50. Indeed, there is a decrease of 50% on the tensile strength for Tango+ 70, although the elongation at break has a change of only 12%. For Tango+ 50, the tensile stress is lower by 31%, while the elongation at break decreases by 8%. It could be inferred that the higher the hardness for Tango+, the greater the effect of water saturation on the ultimate strength. Further investigations could corroborate that hypothesis.Filaflex 70 A also shows that moisture influences its tensile properties. While the stress decreases by only 8%, the elongation at break increases by 10%. This is due to the hydrophilic character of the polymer chains. The water surrounds the chains like a lubricant and allows them to slide off each other more easily when pulled. This results in a higher elongation at break.The LSR elastomer does not show any indication of alterations in the behavior before water uptake and after water saturation. The deviations in the stress–strain curves can be attributed to the variability of the individual samples in general. In fact, the small influence on the tensile results could already be expected due to the low saturation content for the LSR.The present work explores the effects of absorption of toluene and water on three types of available 3D printed elastomers: liquid silicone rubber, thermoplastic elastomer, and photopolymer. Moreover, chemical analyses via IR Spectroscopy and mechanical analyses via uniaxial tensile tests complement the investigations. The results reveal the intense swelling response of all materials when exposed to toluene, while more diverse outcomes are displayed for water absorption. Furthermore, not only the chemical composition of the materials but also the nature of the printing technology have a direct impact on both the absorption behavior and the mechanical performance.It should be considered that the AM processes are subject to variations not only on the tensile results but also on mechanical testing in general, according to the printing conditions as well as the postprocessing. The LSR and the photopolymers, for example, can go through a postcuring stage, increasing their stiffness; FFF printers allow the user to change the path and the direction of the material deposition. AM can lead to greater process deviations than the conventional and established manufacturing techniques. For that reason, 3D printing optimization is one of the current challenges in order to deliver functional parts in similar and reliable performance.In addition, new materials emerge as a way to improve the quality of the printed parts. Nevertheless, since AM is a flexible process, the printing of the geometry can always be adapted to exhibit specific properties. As an example, we find the percentage of infill influencing on the compression of the part. For elastomeric materials with higher hardness, it is possible to increase the compressibility by decreasing the infill percentage. The investigations presented here are a significant step toward the study of the feasibility of 3D printed elastomeric parts for technical applications. Knowledge on water uptake and toluene absorption, for instance, is beneficial when deciding the printing material for a defined geometry in a specific application. It can be noted that special attention must be taken when using the studied photopolymers and TPU in water applications, as moisture absorption cannot be neglected. Silicone could be better suited for moist environments, on the other hand. The toluene absorption tests show the relevance on applications involving contact with fuels, in which the silicone and the TPU revealed an intense swelling behavior, while the photopolymers were not able to withstand the solvent. With such a piece of information, the process of selecting the material and manufacturing options in AM becomes accessible in future works.Synthetic fuels are attracting considerable interest as alternative energy sources in the aviation sector ,22. The 2 emissions and saving resources, innovative solutions are required. Although other technologies such as hydrogen or fuel-cell-powered [Up to now, conventional kerosene, such as Jet A-1, made from non-renewable crude oil, is the main energy source in the aviation sector . To tack-powered  and batt-powered  are cons-powered . The adv-powered . The fue-powered ,31; seco-powered  and Defe-powered . To stay-powered  and Anne-powered  were est-powered , becauseHowever, some fuels are already certified and tested thoroughly. Apart from fulfilling the fuel specifications, the ongoing challenge is material compatibility, since liquid fuels are in contact with soft elastomeric materials such as sealings, tank hoses, and linings. The next decade is likely to witness a considerable rise in the demand for synthetic fuels attributable to the ambitious goals of different advocacy groups. The aim of the International Air Transport Association (IATA) is to reduce global aviation-caused COtil 2050 . One inttil 2050 . On accotil 2050 , and swetil 2050  may be itil 2050 . On a bitil 2050  or ultimtil 2050 , leakagetil 2050 . WhereasCarbon black filled and stabilized NBR with a ready-to-use formulation containing 18 wt% acrylonitrile is used here, cf. −3 ,30 and iSartorius precision balance mentioned in Sartorius. The hardness was measured with a digi test II, by bareiss® equipped with a micro Shore A hardness test head. Tensile tests were conducted with the universal testing machine used in Each sample was tested as a threefold measurement. Samples are pristine or aged for 3 d as well as for 7 d at 120 °C. For clear identification purposes, the specimens were marked clearly with cut-off edges. At first the samples were weighed, and their thickness was measured. The samples were then immersed in ReadiJet and taken out after distinct sorption times of 30 min . The GC oven was heated with 50 K minby Exxon ,46. An aIt is important that the concentration of the standards is in the same range as the samples. Furthermore, it is beneficial to analyze independent samples with known aromatics content additionally to verify the calibration. The additives DEHP and 6PPD were quantified with external standards of the pure substances in acetone in appropriate concentrations. The known concentrations were plotted versus the peak areas of the additives in the chromatogram to obtain the calibration graph and function .In the following section, the results are shown in dependency on the aging history and sorption time. Pristine samples are represented by light grey (◯), aged samples for 3 days at 120 °C by dark grey (◁), and 7 days at 120 °C by black color (☐). In Before the samples are immersed  adds valuable chemical information to the mechanical testing results. It allows one to separate the overall mass change into the uptake of fuel and the desorption of additives. Furthermore, it is possible to analyze the composition of the absorbed liquid in the elastomer with respect to its chemical nature. In the near future, a significant rise in the demand of synthetic fuels is expected, which makes this topic interesting to investigate experimentally.The swelling behavior of soft polymers is of great interest in the wide applications of elastomeric materials. The presented studies investigates the water, the fuel, and the fuel component toluene uptake using versatile testing methods. The first study highlights the pronounced swelling capability of several state-of-the-art additively manufactured materials depending on the solvent. As expected, the absorption of toluene is considerably more pronounced and reaches double the original weight (>100% mass gain). The absorption of water, on the other hand, reaches <5% but is of just as much interest, since water is omnipresent due to humidity and directly influences the printing result. For the additive manufacturing process, a concrete comparison between dry-printed material and wet-printed material is presented. Furthermore, the aspect of thermo-oxidative aging is investigated while the swelling behavior of pristine and aged elastomers in synthetic fuel ReadiJet is quantified. The characterization includes new experimental strategies such as a combination of sorption experiments with gas chromatography and mass spectrometry to precisely analyze the diffusion process from the surrounding liquid in and additives out of the elastomer. The quantified change in density and volume, the change in Shore hardness and the change in mechanical properties (elongation and stress at break) via tensile test highlight their need for experimental investigation.


The number of suicides has increased in the last decades in several developed countries. For instance, Spain has experienced a gradual but steady increase in suicides since the 80’s and it is currently the leading external cause of death in the country. At the same time, the dualisation of the labor market, with a strong and persistent incidence of temporary contracts, has increased the instability of employment conditions. Both developments have a stronger incidence for individuals with lower levels of education. Therefore, in this paper we use rich administrative data in order to estimate the impact of the wide spread use of temporary contracts on suicides. In order to do that we exploit a reform that liberalised the use of fix-term contracts in Spain in 1984. Our results show strong long-term effects of the reform, which increased the suicide mortality rate of affected cohorts  by at least 25.3%. We believe that this result has important policy implications and should be taken into account in the design of the national suicide prevention plans. Suicide is a global phenomenon and the leading external cause of death in high-income countries . While tA limitation of existing literature is that it uses a dichotomous analysis of unemployment not reflecting the dynamics of employment instability. This type of analysis does not deal with the complexity of employment conditions and only identifies part of the labour market instability affecting suicidal behaviour. Job insecurity cannot be limited to the unemployment condition and has to be considered as a many-sided notion that includes the quality of employment, economic conditions, type of contracts, job sector, among others concepts. Caroli and Godard (2016)  propose Throughout the last decades, many European countries have implemented downsizing reforms in their EPL systems, promoting flexibilisation of the labour market through fixed-term contracts. As a consequence of such reforms, labour market segmentation has arisen, whereby some workers enjoy lower employment stability, lack of career development, and low rates of upgrading from temporary contracts to permanent ones , while oIn our paper, we study the long-term impact of the liberalization of fixed-term contracts on suicide mortality rates. We believe that this represents an important contribution to the literature as well as in policy terms given the current limitations to understanding the link between working conditions and suicidal behaviour. More specifically, we evaluate the 1984 Spanish Labour Market Reform which liberalised the use of fixed-term contracts. While, compared to other high income countries, Spain has a relatively lower age-standardized suicide mortality rates, it represents an ideal setting to evaluate the impact of the reform in the long run due to its early liberalisation of fixed-term contracts . After tDeaths statistics from the Spanish Statistical Office (INE) to track cohorts of individuals before and after the reform. We do the analysis by gender and education, particularly focusing on three different levels of education: high school dropouts, high school first-level graduates, and high school second-level graduates. As the minimum legal working age in Spain is 16 years, we assign the labour market entry of high school dropouts to be 16 and, for the other levels of educational attainment we assign the graduation date as the labour market entry age.To shed light on the issue, we use the restricted access version of the Deaths statistics according to cause of deaths dataset, under restricted access conditions. Although existing literature finds a link between macroeconomic economic conditions and mental health outcomes and suicide rates [One of the main methodological challenges when studying suicides is the low base rate of suicide and the complexity and variety of the channels that are compatible with this outcome . Therefode rates –18, our Several identified risk factors for suicides relate to medical, psychosocial, cultural, genetic, and socioeconomic conditions –21. TheiIdeally, we would have data for the whole period and would be able to use a duration model of the suicide mortality hazard rate by our different education and gender subgroups for a complete analysis. The main limitation of our analysis is that while we find evidence on the suicide rates for a subgroup of less educated males in the long run, it is likely that other subgroups such as dropouts males suffered the impact of the reform on their likelihood to commit suicide in other periods, such as during economic recessions or during the COVID-19 pandemic. Another possible hypothesis is that the difference in the impact of the reform between high-school dropouts and first-level graduates is due to social priorities across both groups. Phillips and Hempstead (2017)  find thaMoreover, we also report the long-term impact on drug overdose mortality and find also a significant effect of the reform for male high school first-level graduates. This further suggests that the liberalisation in the regulation of fixed-term contracts and the channels through which the reform affects suicides have also an impact on other health outcomes.The key identification assumption used in our RD design is the continuity around both sides of the reform cutoff point. Previous concerns on this issue for labour market outcomes were addressed using a difference-in-differences specification by García-Pérez et al. (2019) . The reqOur paper makes, at least, two contributions. First, despite previous literature evaluating the role of job insecurity and employment protection on self-assessed health and health disorders, as far as we are aware of, this is the first paper identifying the causal impact of employment stability and the liberalisation of fixed-term contracts on cause-specific mortality. Some of the existing literature exploring the role of temporary employment on mortality  or the aThe second contribution of the study is related to the timing of the analysis as our focus is on the long-term impacts of the reform. While there is previous literature finding a negative impact of fixed-term contracts on labour market outcomes in the long run, our results show the first evidence of the long-term impact of fixed-term contracts on suicide rates. This is an important contribution in terms of policy implications given the recent reforms in European EPL systems and the widespread use of fixed-term contracts in several countries. Understanding the contributing factors to suicides is essential for suicide prevention policies and legislation. Furthermore, examining long-run outcomes allows us to uncover the undocumented effects of fixed-term contracts on health outcomes.However, this paper has some limitations due to data availability. First,we are not able to explore the impact of fixed-term contracts on suicides in the short-run and for different age groups. This is a relevant question to address as suicide is one of the leading causes of death among young people. Second, our estimations could only evaluate a period of economic growth whereas the impact during an economic recession is left to be studied. An extensive literature evaluating the effects of negative macroeconomic conditions and unemployment find these periods are associated with an increase of completed suicides. Therefore, evaluating the impact of fixed-term contracts on other economic conditions is important as the effect of fixed-term contracts will likely be larger during economic stress periods. Third, further research should develop heterogeneity effects of the impact of the fixed-term contracts on suicides. For instance, differences in family structures, job sectors, or locations  are likely to establish distinct suicide rate outcomes.The rest of the paper is organised as follows. Section 2 outlines the characteristics of the labour reform and the suicide situation in Spain. Section 3 describes the data and the empirical methodology. Empirical results are reported and discussed in Section 4. Section 5 presents some robustness checks and extensions, and Section 6 concludes.Real Decreto 1989/1984 published in the BOE . It consisted of the liberalisation of temporary contracts and a reduction of dismissal costs. This meant that temporary contracts were no longer required to be only used for temporary reasons but could be signed for all activities and their duration was limited between a minimum of six months and a maximum of three years. Moreover, fixed-term contracts had low dismissal severance payments compared to permanent contracts. On one hand, firing costs at termination were 8 days per salary per year of job tenure in the case of temporary contracts. On the other hand, permanent contracts severance payments depended on whether the cause of dismissal was considered fair or unfair. Dismissal was only considered as fair if the firm was able to argue that the employee was not capable of performing the job tasks or if it was required due to economic or technological reasons. While unfair cost firing was equal to 45 days of salary per year of job tenure with a maximum of 42 months of wages, for fair dismissals cost firings amount to 20 days with a maximum of one year’s wages. As the 1984 labour reform did not modify permanent contracts, incentives for firms to employ fixed-term contracts increased and there was a strong substitution of permanent by temporary workers [The Workers’ Statute introduced in Spain in 1980 designed temporary contracts to be used only for temporary reasons such as seasonal jobs. These restrictions on temporary contracts meant that they were rarely used in the early-1980s. However, aiming job creation due to high unemployment rates, the Spanish government implemented a labour liberalisation reform in 1984. The reform regulating the temporary contracts was passed in August 1984 but was implemented on October 17th by the  workers .Temporary contracts represented a low percentage of the total number of non-agricultural private sector employees until the labour reform was passed on the last trimester of 1984  After thIn a recent publication, García-Pérez et al.  argue thTherefore, to estimate these long-term effects we use a RDD strategy comparing individuals who reach the labour market entry age of 16, or in their graduation date if required, before and after the reform. This empirical strategy allows us to evaluate the long-term impact of the Spanish 1984 labour reform on completed suicides for different educational attainment level groups. Our paper aims to understand whether entering the labour market under different situations (wide availability or not of temporary contracts) increases long-term vulnerability to suicidal behaviour.Premature death from suicide in Spain is the current leading external cause of death and responsible for more than twice the traffic accidents deaths. According to OECD latest statistics from 2017, Spain has a yearly suicide rate of 7.0 suicides per 100.000 persons. However, considerable gender differences are common in suicides, and suicides rates in Spain reach 10.9 suicides per 100.000 men while falling to 3.6 for women. Suicide rates differ considerably across developed countries and Spain has a relatively low number of suicides compared to other OECD countries. For instance, the United States has a yearly suicide rate of 14.0 suicides per 100.000 persons, France has a suicide rate of 12.3, and Belgium of 15.9 suicides per 100.000 persons.During the last decades, the Spanish deaths due to other external causes such as drug consumption or traffic accidents have been successfully prevented through several campaigns. For instance, the Spanish government implemented national strategic plans to deal with traffic accidents in 1980  and drug consumption in 1985 . However, Spain has experienced a gradual, but steady, increase in suicides over the years, given the lack of an effective suicide strategy plan. Spain has historically integrated suicide prevention into their national mental health plan . In recent years, suicide prevention has been considered by healthcare professionals and policy-makers as a main priority to deal with in following mental health strategic plans. As we can see in Preventing suicide: a global imperative [National suicide prevention strategies: Progress, examples and indicators [On the other hand, global effort to address suicide has surged in recent years. In 2014, the WHO published a suicide prevention report: perative , making dicators . It seemTurning to Spain, although Spanish suicide rates are lower than most other developed countries, it is still an important cause of death in all age groups, and particularly concerning working-age people. Suicide rate increases with age, especially for men, and the number of completed suicides peaks for individuals 40–59 years old, age range comprising 41% of completed suicides in 2018, as it can be seen in Therefore, we consider that understanding and estimating the EPL impact on completed suicides is relevant for suicide prevention policies and of interest to healthcare institutions. In Spain, the National Health System is highly decentralized to the 17 Spanish Autonomous Communities, which are in charge of the management and provision of health care. While, the management and provision of health care of the two Autonomous Cities, Ceuta and Melilla, are in charge of the Spanish government. Among their functions, the regional governments are in charge of the design and implementation of health-related legislation. However, the Spanish Ministry of Health is responsible for the coordination of national plans, and therefore the development of effective prevention strategy plans will require a multi-actor collaboration at different administrative levels.Death Statistics which contains individual death data by the cause of death. This dataset registers all deaths occurred in Spain and, from 2012 onwards, includes individuals educational level attainment. We use data from all available years, 2012 to 2018, and differentiate between two periods depending on macroeconomic conditions. According to the Encuesta Población Activa (EPA), the Spanish Labour Market started registering an increase of employed individuals from the first quarter of 2014 onwards, after six years of decreasing absolute numbers. For each death, the dataset contains personal information on the date of death, the country of birth, gender, year and month of birth, the Spanish Autonomous Community of birth and death, educational level attainment and the cause of death. In our sample, we select the cohorts born between 1964 and 1972 so individuals are aged 41–54 during 2012–2018. We exclude foreign-born from the data and, therefore, restrict the analysis to the Spanish native sample.We use the Death Registers conducted by the Spanish National Institute of Statistics (INE). Under an agreement with the INE, we were granted access to the restricted licence version of the accidental reasons.The information available on the cause of death follows the classification criteria by the 10th revision of the International Statistical Classification of Diseases and Related Health Problems, ICD-10 . MoreoveIn order to obtain the mortality rates by educational level attainment groups, we combine the deaths dataset with the 2011 Census. The reference date of the Population Census is the 1st November 2011, therefore we assume the 1st January 2012 population to be similar to the reported in the 2011 Census. For each subsequent quarters, we extract the number of deaths that occurred during that particular quarter to the previous population by education, gender and quarterly cohort group. Then, we match the obtained populations to the corresponding deaths and calculate the quarterly cohorts mortality rates per 100.000 individuals.ESO in Spain). On the other hand, second-level high school graduates correspond to college-preparatory high school or basic Vocational and Technical Schools . Hence, the first trimester cohorts graduating in 1984 are considered as the entry-age to the labour market for these specific education groups. For instance, the cohort born in the first trimester of 1968 is the first cohort affected by the 1984 reform in the case of first-level high school graduates. In contrast, for second-level high school graduates, the first cohort affected is the cohort born in the first trimester of 1966.The reform was fully implemented by October 1984 and the quarterly cohorts selected for our analysis depend on the individual educational level attainment and the corresponding age of labour market entry. In the case of high-school dropouts, an entry-age of 16 is considered, as the minimum working age in Spain is set at 16-years-old. However, first-level high school graduates and second-level high school graduates entering the labour market the last trimester of 1984, must have graduated in the summer of 1984. On one hand, first-level high school graduates are those who studied until the course corresponding to the 16 years of age   argumentYct is the cause-specific mortality rate per 100,000 individuals for each cohort and year of death. A linear cohort trend is included by subtracting the cutoff from the cohort’s birth trimester (BirthTrimc − C). Then, we interact the trend with a dummy variable (afterc) that captures the cohorts affected by the reform, allowing us to include a different trend only for these cohorts. ϕt is a year of death fixed effect and ϵct is the error term. Standard errors are clustered by cohort.As existing literature suggests that macroeconomic conditions have an impact on suicide risk, we restrict the analysis to an economic upswing period in Spain (2014–2018). Then, we collapse the individual-level data by the trimester of birth control (c) and the year of death (t). We run a cohort regression discontinuity design , includiafterc variable, a binary variable equal to 1 for cohorts born at the cutoff trimester or after, and equal to 0 for cohorts born before. Therefore, the coefficient of interest is β3, which estimates the differential effect of the reform in the cause-specific mortality rates for the treated and untreated groups. Under the assumption of continuity around both sides of the reform cutoff point, β3 measures the long-term causal effect of the liberalisation of fixed-term contracts on cause-specific mortality rates . This key identification assumption was already addressed by García-Pérez et al. (2019) [The impact of the reform is captured by the . (2019)  through The bandwidth used for the regression discontinuity analysis is selected to include 16-trimester cohorts before and 16-trimester cohorts after the cutoff. While a larger bandwidth yields more precise estimates, since more cohorts are used, it can lead to a biased estimation of the treatment effect. Therefore, this concern is addressed by reducing the bandwidth in Before focusing on our analysis of the long-term impact of the liberalization of fixed-term contracts on suicide, we rely on the estimates of García-Pérez et al. (2019)  on the iGarcía-Pérez et al. (2019)  also shoafter for high school first level male graduates is estimated by the jump in suicide mortality rates at the cutoff trimester cohort.To that end, we differentiate between different groups, which allows us to use the cohort regression discontinuity design of women (columns (1), (4) and (7)). Then, we report the results separated by gender. Moreover, high school dropouts, born between the fourth trimester in 1964 and the third trimester in 1972, are reported in Columns (1) to (3). The estimations for high school first level graduates, born between the first trimester in 1964 and the fourth trimester in 1971, are reported in Columns (4) to (6). Finally, estimations for high school second level graduates, born between the first trimester in 1962 and the fourth trimester in 1969, are reported in Columns (7) to (9).As mentioned, We find that the reform increased the quarterly suicide mortality rate for high school first-level graduates males at conventional significance levels (column (5)). This effect corresponds to a 25.3% increase on the suicide rates in the long run for those cohorts that entered the labour market after the liberalization of fixed-term contracts. The fact that the effect is driven by males is supportive of previous literature finding that employment instability particularly affects men’s health outcomes. This large impact on suicides is consistent with the findings that less educated cohorts entering the labour market under lax fixed-term contract legislation had substantially worse long-term labour outcomes in the long run.The main channel through which the suicide rates increases is by changing the nature of the first contract when entering the labour market. Existing literature highlights the strong impact of the first employment experience on the future career. The liberalisation in the regulation of fixed-term contracts affected especially the first contract for less educated young workers while the effect on higher educated workers was not significant. This can be further related to the different incentives employers have to invest on training workers under a permanent contract respect to those under a temporary contract. Thus, we believe that this provides evidence that one of the main channels that explain the large impact on suicide rates in column (5) is the change in the first type of contract when entering the labour market which, in turn, leads to strong negative labour outcomes in the long run.after coefficient is not significant for high school dropouts (columns (1) to (3)) or for high school second level graduates (columns (7) to (9)). The latter is expected due to long-term labour outcomes of this higher education group not being particularly affected by the reform. However, high school dropouts were strongly affected by the liberalisation of fixed-term contracts, hence the lack of an impact on suicide rates may indicate different types of mechanisms among different educational groups. For example, it is possible that high school dropouts with tendency to commit suicide had particularly high suicide hazard rates before the period for which the data is available, specially during economic recessions. In this case, the subsample of dropouts during our sample period would be less affected by the reform (as they would have been impacted before) and we would not find a significant effect. Moreover, a larger impact of the reform could be expected on high school first level graduates as, according to the literature, suicides due to career issues are more common for this education group than for high school dropouts. Nevertheless, it is important to understand and disentangle the channels through which the liberalisation of fixed-term contracts affect less educated workers and different education groups, which is outside the scope of this paper.Furthermore, the We also report in Our identification strategy, based on a cohort regression discontinuity design, identifies the causal effects conditional on some assumptions that we test in this section. More specifically, the issues that we address in this section are: (i) the right size of the bandwidth, (ii) the functional form, and (iii) the continuity assumption at the cutoff point.In our baseline results, we include 16-trimester cohorts before and 16-trimester cohorts after the implementation of the reform. As a robustness test, we check for the potential risk of including observations far from the cutoff point by reducing the bandwidth. In this nonparametric method, we limit the analysis to a closer surrounding of the cutoff, where local linear regressions are more likely, and estimate the treatment effect as local randomization. We reduce the bandwidth to 10-trimester cohorts and 6-trimester cohorts as shown in after coefficient for the 10 trimester-bandwidth estimates a 26.7% increase in the suicides rates (column (1)). Alternatively, the after coefficient for the 6 trimester-bandwidth estimates a 41.8% increase in the suicides rates (column (2)). Although all estimates indicate a large impact of the liberalisation in the regulation of fixed-term contracts on the suicide rates in the long run, the stronger impact shown when the 6 trimester-bandwidth is used reinforces the causal interpretation. While the rectangular kernel used in our RDD has a more straightforward interpretation, in the light of the results of the robustness test carried out, a triangular kernel weighting could be considered a good model fit too. The results of this first robustness test allows us to conclude that the large impact of the liberalisation in the regulation of fixed-term contracts on suicide rates is robust to bandwidth selection and that the impact ranges between an increase of 25.3% and a higher bound of 41.8%.In both cases, the impact of the reform on suicide rates is positive and of a similar size for males. The trend variable used in the main results specifications. In our analysis, we use linear trends to estimate the local average treatment effect on suicides around the cutoff point. As a robustness test, we test different functional forms for the trend variable to minimize specification bias from the possibility of an incorrect linear functional form, which are reported in trend variable are interacted with the after dummy variable. Thus, the terms of the polynomial (slopes) estimated below the threshold are allowed to be different from the slopes estimated above the cutoff point.We next focus on the functional form of the trend variable. As can be seen in the table, the large impact of the liberalisation in the regulation of fixed-term contracts on male suicide rates is robust to the inclusion of higher order polynomial trends (columns (3) and (4)). However, we choose the linear regression as our baseline model because it reports the minimum Akaike Information Criteria (AIC) among all the estimated models. Moreover, the second polynomial specification reports similar results than the linear fit.seasonal temporary employment, which was already allowed before the reform. Therefore, concerns of spillover effects to untreated are severely mitigated.It should also be noticed that our empirical strategy addresses possible anticipation effects. The last graduate untreated cohorts were born in the last quarter of the year and had between nine and twelve months to look for a permanent job before the reform was implemented on October 17th 1984. Whereas the first graduate treated cohorts were born in the first quarter of the year but were not able to work as they were attending school until the summer before the reform. In the summer of 1984 the reform had already been passed while traditionally being a season reporting high rates of Finally, we also perform placebo tests in order to address concerns on the identification assumption and, hence, to check the random assignment around the threshold.We simulate the implementation of the reform to take place in a pre-reform period (4 years before) in Furthermore, as a second placebo test, we check whether other outcomes that are unlikely related to the reform are affected at the cutoff point. We consider deaths due to external accidents as an ideal candidate for the placebo test. Specifically, the placebo outcome comprises numbers 92, 93 and 97 of the INE reduced list CIE-10. They consist of falls, accidental drowning and submersion, other accidental threats to breathing and other types of unclassified accidents. These accidents are unlikely to be affected by the reform as INE list also includes specific codes for accidents related to drugs, alcohol, mental health or traffic, which we do not included in the placebo test. These placebo tests reinforce our conclusion that the liberalisation in the regulation of fixed-term contracts had a large causal impact on the suicide rates of high school first-level male graduates in the long run.While the main focus of interest in our paper are suicides , the reform can have long-term effects on other cause-specific mortality rates as well. Therefore, in Plan Nacional sobre Drogas, was adopted by the Spanish government in 1985. However, during the decade of the 1990s Spain register record-high drug overdose deaths because of a heroin epidemic, in which young male adults were a particularly susceptible target.It is important to note that mortality rates due to drug overdose are much lower compared to suicides for the cohorts analysed. Moreover, there are large differences in drug consumption patterns between women and men, and the male mortality rate due to drug overdose is much higher than for women. In Spain, a national strategic plan to deal with drug consumption, We estimate the same baseline specification than in after coefficient in column (5) indicates that there is a 71.4% jump in the mortality rate due to drug overdose of the high school first-level male graduates cohorts after the implementation of the liberalization reform. This is a really strong impact but it has to be noted that the number of deaths due to this cause is relatively small so that, potentially, a larger number of observations would be needed for a more precise estimation. In any case, it represent another indicator that the liberalisation in the regulation of fixed-term contracts had a negative impact on health outcomes in the long run. Thus, even if the specification estimates are less precise, it reinforces our main baseline results pointing towards the role of Employment Protection Legislation (EPL) on long-run health outcomes.The positive and significant Suicide is a serious public health problem and one of the leading causes of death in the working-age population of developed countries. Our paper focuses on the estimation of the long-term effects of a reform that liberalised the use of temporary contracts on suicide rates. As argued by Blanchard and Landier (2002) , this tyDeath Statistics from the Spanish National Institute of Statistics (INE). We find that cohorts of male high school first-level graduates who entered the labour market after the reform have higher suicide rates in the long run compared to the cohorts that entered the labour market just before. Specifically, entering the labour market after the liberalisation of fixed-term contracts leads to at least a 25.3% increase in suicide rates in the long run. The main channel of this negative long-term effect is through a higher probability of having a temporary employment relationship as a first contract when entering the labour market after the reform and, hence, accumulating a worse career path for low skilled workers.We evaluate the impact on suicide mortality rates of the reform using a restricted version of the Thus, our findings indicate that a laxer regulation of fixed-term contracts in Spain increased the long-term suicide rates for low-skilled workers. We also find a large impact of the reform on drug overdose mortality rates, indicating that other health outcomes related to suicides are also affected by the reform. Overall, these results suggest that sudden changes in Employment Protection Legislation (EPL) can have large long-term effects on health outcomes, and particularly on suicide rates. Reasonably, this analysis addresses a question of high policy relevance for suicide prevention strategies.One important limitation of this study is the number of years for which data is available with information on both the cause of death as well as the level of education. Therefore, there could be important effects in the suicide rate (particularly for high school dropouts) during the years between the time of the reform and our sample period that we are unable to observe which, in turn, could lead to survival bias in our estimates. However, we believe that, if this type of bias exists in our context, it would lead our estimates towards zero. Thus, we believe that our estimates reflect a lower bound of the true lasting effects of the reform that liberalized the use of temporary contracts on suicide rates.Many questions remain open for future research. For instance, it is crucial to understand the conditions  that reinforce the negative impact of the liberalisation reform, and for which specific sub-groups of the population. This would allow policymakers and healthcare professionals to identify potential vulnerable individuals to suicidal behaviour and boost the effectiveness of prevention policies and action plans adopted.S1 Table(TIF)Click here for additional data file.S1 Fig(TIF)Click here for additional data file.S2 Fig(TIF)Click here for additional data file.S3 Fig(TIF)Click here for additional data file.S4 Fig(TIF)Click here for additional data file.


K independently moving targets by implementing The single-pixel imaging (SPI) technique enables the tracking of moving targets at a high frame rate. However, when extended to the problem of multi-target tracking, there is no effective solution using SPI yet. Thus, a multi-target tracking method using windowed Fourier single-pixel imaging (WFSI) is proposed in this paper. The WFSI technique uses a series of windowed Fourier basis patterns to illuminate the target. This method can estimate the displacements of  Multi-target detection and tracking have widespread applications in military defense ,2, area With the development of optical digital modulating devices (DMDs) and millimeter-wave metasurface materials, the single-pixel imaging (SPI) technique, which can be used to develop an imaging system, has attracted the attention of many scholars in recent years ,14,15,16Jiao et al. proposed a motion estimation and image quality enhancement scheme for a single reconstructed image . The optThe measurement data used for imaging is often redundant for the estimation of motion parameters. From this perspective, scholars have tried to reduce the number of measurements to increase the frame rate of target tracking. Shi et al. proposed a method to obtain the position of the object in the scene from the 1D projected curves . This meK target, Thus, a multi-target tracking method using windowed Fourier single-pixel imaging (WFSI) is proposed in this paper. Inspired by the successful application of the short-time Fourier transform (STFT) in signal processing, we designed a series of window functions that vary with the target positions. The WFSI technique uses windowed Fourier basis patterns to illuminate the target. Combining these different window functions, the problem of tracking multiple targets can be transformed into the problem of tracking a single target. One window function is designed for each target, and two windowed Fourier coefficients are calculated by six measurements to complete the estimation of the displacement of this target. For the A is the average intensity of the pattern, and B denotes the contrast. The Fourier basis patterns can be converted from grayscale to binary by employing image upsampling and the Floyed–Steinberg error diffusion dithering method [The FSI technique can reconstruct high-quality images by acquiring their Fourier spectrum . The trag method . Using tThe Fourier coefficients of the target image can be acquired using the three-step phase-shifting algorithm : (3)FI  3) impliThe scene image containing a moving target can be represented as the sum of the target image and the background image:The Fourier spectrum of the target image is equal to the difference between the Fourier spectrum of the scene image and the background image, so background subtraction can be applied to obtain the Fourier spectrum of the target:Equation , it can It was demonstrated that only 2 Fourier coefficients measurements (6 Fourier basis patterns) are needed to achieve the detection and tracking of a moving target, in the above-mentioned section. However, when there are multiple moving targets in the scene, it is incapable of distinguishing different targets in the spatial frequency domain due to the global-to-point property of the Fourier transform.K targets, the scene Inspired by the STFT, we tried to design different window functions in the spatial domain to transform the multi-target tracking into single-target tracking. If there are Equation  needs toThe spatial window functions K measurements are implemented to calculate 2K Fourier coefficients. After that, using the multi-target tracking method including the independent approach and joint approach, the displacements of the multi-target can be estimated. Lastly, according to the estimated result, the window functions are redesigned to continue the multi-target tracking. The sketch of multi-target tracking using WFSI is shown in Based on the WFSI technique, firstly we design appropriate window functions to transform the multi-target tracking problem into a single-target tracking problem. Afterwards, 6X axis and Y axis, respectively. For an image with K moving targets, using the projected curve method, less than K window functions. In fact, only one Fourier coefficient is needed to determine the presence of a target in the region. Here, we chose 2 Fourier coefficients because the later tracking methods require 2 Fourier coefficients. It should be noted that the proposed method cannot distinguish between two targets if their spatial locations overlap with each other.Two moving targets are illustrated as an example, as shown in After designing the spatial window functions, the Fourier coefficients of each target image oted as1FIiDi(The windowed Fourier coefficients of each target Equation . Thus, tEquation .The window function ith window function ith target each time, which is denoted ask represents the kth measurement.The multi-target tracking method described above is limited to an assumption that the target moves within the region of the spatial window function, but this assumption is not easily satisfied over a long duration. Updating the center positions of the window functions corresponding to different targets in real time during the measuring process is one useful approach. Therefore, a strategy to dynamically alter the window position is used in this paper. The center of the In this way, if the displacement of a target is estimated accurately and the window length is bigger than the displacement between 2 frames, the target will always be within the window. Therefore, the upper limit of the target velocity that can be estimated by the proposed method is determined by the selected window length. The window length should not be too large. An excessively long window length can lead to overlapping window functions, and the estimated result will produce errors.M targets within a spatial region M single target When the distance between two targets in the scene is less than the length of the designed rectangular window, the multi-target tracking cannot be transformed into single-target tracking. At this point, the choice of window shape becomes very important if we want to distinguish two targets by the window function. However, the designing of special-shaped windows is a more difficult problem. Thus, a joint estimation approach is proposed to solve the problem of target discrimination when different targets are within one window. Due to the linear feature of the Fourier transform, the Fourier spectrum of M targets can be calculated by solving a system of equations corresponding to M. There are two types of methods for solving nonlinear equations: the analytical method and the iterative search method. The analytical method is faster than the search method and it is generally accepted that nonlinear equations have an analytic solution when In the case where the Fourier spectrum of every target has been determined, there are Equation . TherefoEquation  is a nonNumerical simulations are employed to study the proposed method. The scene for the simulation is shown in The first experiment located the targets in the scene at moment X axis shown in X axis. The coordinates of the center points of these three regions on the X axis are Y-axis are denoted as X or Y axis. The size of window function is defined as From the projected curve on the The 18 Fourier coefficients are calculated corresponding to these nine rectangular window functions are calculated according to Equation . Thus, wThe four window functions designed based on the multi-target position are shown in The estimated results of the four targets according to Equation  are showAssuming that the speed of the four targets remains unchanged, the scene image at the moment Significant errors will occur when estimating the displacement of target The results of As the number of targets becomes larger, the computational effort of the joint estimation approach increases significantly. In conclusion, the joint estimation approach is mainly used when multiple targets are close. The independent estimation approach is preferred when the distance between different targets is long.In order to verify the capability of the proposed method, a video experiment was performed. Two balls representing two targets are moving irregularly in the scene at the same time, as shown in We assume that the 240th frame is the moment when the targets are first detected. Multi-target tracking was performed for a total of 391 frames from the 240th frame to the 630th frame. Estimated results in five different frames are shown As shown in The estimated trajectories of the two balls are shown in The positions of the yellow ball are shown in The shape of the window function affects the tracking performance of the proposed method. In this paper, a common rectangular window function was chosen, and the window length was also preset to be a constant. However, in a practical application, the shape and window length of the window function should be related to the target shape, the target motion speed, and other factors. A large window length is required for high-speed targets, and a small window length is required for multi-target estimation. Therefore, a window function with an adjustable shape will be better suited for this method.In the joint estimation approach, only the estimation of two targets is shown in this paper. However, theoretically, this method can be used to estimate more than two targets simultaneously. Fewer than five targets can be estimated directly according to the analytical method. When used for more than five targets, the time consumption of the search method is more demanding. Subsequent work will further extend the proposed joint estimation approach for more targets.K targets by implementing In conclusion, this paper presents a multi-target tracking method using windowed Fourier single-pixel imaging. The proposed method can track


With the rapid development of artificial intelligence in recent years, the research on image processing, text mining, and genome informatics has gradually deepened, and the mining of large-scale databases has begun to receive more and more attention. The objects of data mining have also become more complex, and the data dimensions of mining objects have become higher and higher. Compared with the ultra-high data dimensions, the number of samples available for analysis is too small, resulting in the production of high-dimensional small sample data. High-dimensional small sample data will bring serious dimensional disasters to the mining process. Through feature selection, redundancy and noise features in high-dimensional small sample data can be effectively eliminated, avoiding dimensional disasters and improving the actual efficiency of mining algorithms. However, the existing feature selection methods emphasize the classification or clustering performance of the feature selection results and ignore the stability of the feature selection results, which will lead to unstable feature selection results, and it is difficult to obtain real and understandable features. Based on the traditional feature selection method, this paper proposes an ensemble feature selection method, Random Bits Forest Recursive Clustering Eliminate (RBF-RCE) feature selection method, combined with multiple sets of basic classifiers to carry out parallel learning and screen out the best feature classification results, optimizes the classification performance of traditional feature selection methods, and can also improve the stability of feature selection. Then, this paper analyzes the reasons for the instability of feature selection and introduces a feature selection stability measurement method, the Intersection Measurement (IM), to evaluate whether the feature selection process is stable. The effectiveness of the proposed method is verified by experiments on several groups of high-dimensional small sample data sets. At present, the research on data mining has always been a hot issue in the fields of artificial intelligence, machine learning, and database. The reason why data mining is so valued is that it can extract hidden and unknowable potential value information from a large number of complex data in the database to assist in decision-making. With the continuous emergence of large-scale data mining tasks, such as microarray gene expression data , which cFeature selection is to filter the feature subset from the original feature space, which can effectively reduce the dimension of the feature space . FeatureFilter measures the feature classification ability by analyzing the internal features of the feature subset and is generally used to filter out the feature subset with the highest score. According to the selection of selected subsets, Filter can be divided into two types: based on feature sorting  and featAs for Wrapper, it can be divided into two types: sequential search method  and heurThe emergence of Embedded is to solve the high cost of reconstructing the classification model when Wrapper processes different data sets. Taking the SVM-RFE method proposed by Guyon et al.  based onAlthough there are many mature feature selection methods, these methods emphasize the high classification performance or clustering performance of the feature selection results and ignore the stability of the feature selection results. The stability of feature selection refers to the insensitivity of feature selection results to small fluctuations in training content. In some situations, when the sample content changes slightly, the feature subsets or the feature importance ranking results obtained by feature selections are quite different, and even some incomprehensible feature sequences are output, which seriously reduces the accuracy of the feature selection method. This is the performance of poor feature selection stability. If the feature selection is performed by combining multiple learners in an ensemble way and the best feature selection result is selected from many learners, the stability of the feature selection result can be effectively improved. Li et al.  generateBased on the above research, this paper proposes a random bits forest  recursivRandom forest has many advantages when dealing with high-dimensional small sample data , while rN times to obtain M sample sets, about 36% of the original samples have not been sampled, this part of the data is classified as out-of-bag (OOB) data, and the importance of features is evaluated through out-of-bag data; the process is shown in Random bits forest has been applied to high-dimensional small sample data processing due to its good performance in data classification processing. It inherits the characteristics of random forest screening by the importance of each feature when performing feature selection and combines neural network  to impro(1)Z={,…, }, a random bits forest model is established, the OOB data set of the ithtree as IiOOB is set, and the OOB accuracy rate is Ci.Based on the high-dimensional small sample data set (2)f from the data set Z is taken, the features in OOB are selected randomly to replace, a new data set Z1 is obtained, the OOB accuracy rate Cif of the ith tree is recalculated, and the difference in OOB accuracy before and after feature replacement is obtained:Any feature i=1,2,…, m.where (3)f on OOB accuracy rate can be obtained:According to the difference of accuracy rate, the influence degree of feature (4)Ef is as follows:The variance of (5)f can be inferred as follows:The importance of feature Specific steps are as follows:So far, the importance of each feature in the high-dimensional small sample data set is calculated by random bits forest. However, how to further implement feature selection based on the known importance of each feature is still a problem. Above this, the recursive clustering elimination idea is introduced to realize the screening of feature subsets.The idea of recursive clustering is to cluster the original features into several feature classes and then combine the algorithm to score each feature class, eliminate low-scoring feature classes, and iterate until the initial set termination conditions are met, to obtain the final feature subset. The introduction of recursive clustering ideas can effectively improve the efficiency of random bits forests in feature selection, improve the classification accuracy of feature selection, and achieve rapid convergence of the algorithm.In the feature clustering stage, the K-means clustering algorithm  is used fir represents the rth feature of cluster ith and jth.Among them, n feature clusters. After the feature clustering is completed, based on the random bits forest feature importance calculation, a feature class score function Score(Si) is defined. The specific formula for calculation is as follows:Through the K-means clustering algorithm, the initial features can be clustered into fipj refers the importance of ith feature in feature class S(i). The specific calculation method refers to formulas ..fipj refAfter the feature scores of each feature class are obtained through the above formula, recursive deletion can be performed according to the feature scores. Because each recursion deletes a certain proportion of feature classes, irrelevant features can be quickly filtered out during the initial stage of feature selection. However, once faced with a situation where the number of features is small, further feature deletion will delete important features in the feature class. Therefore, by setting a series of deletion condition thresholds, once the number of feature classes is less than the set threshold, the operation of deleting feature classes will be transformed into deleting features in the feature classes. In this way, redundant features can be quickly eliminated in the early stage of feature selection, and important features can be effectively identified and screened in the later stage of feature selection. The overall deletion idea is shown in Through the combination of RBF and recursive clustering elimination ideas, the overall RBF-RCE feature selection processing flow is shown in The stability of feature selection refers to the insensitivity of feature selection results to changes in the training set. Highly stable feature selection results can ensure that even when the research object undergoes small fluctuations, the resulting feature selection results will not change significantly or even output results that deviate from the real situation. In recent years, with the in-depth study of feature selection methods, how to maintain the performance of feature selection classification while improving the stability of feature selection has begun to receive more and more attention. This paper analyzes the causes of unstable feature selection and introduces a new measurement method of feature selection stability to evaluate whether the feature selection method is stable.Through the query of the relevant literature and the in-depth analysis of various feature selection algorithms, it can be concluded that there are three main reasons for the instability of feature selection: the feature selection algorithm itself, the number of selected objects, and the data attributes.For the feature selection algorithm itself, since most of the current feature selection algorithms mainly consider improving classification performance or clustering performance when designing evaluation criteria, they do not fully consider the stability of feature selection, resulting in poor stability of feature selection results.K will increase the probability of all relevant features being selectedAn increase in K will increase the number of elements in the intersection between the selected feature subsetsThe increase in The number of selected objects directly affects the stability of the feature selection results. Since the number of features K in the optimal feature subset cannot be known in advance, the specific number of selections is generally set manually. Through research, it is found that the larger the number of selected features, the higher the stability of feature selection. The main reasons are as follows: fi and fj are feature subsets obtained after feature selection by the same feature selection algorithm on the training set Di and Dj, the prior probability of randomly selecting a feature f is as follows . When the value approaches 1, it indicates that the similarity between fi and fj is greater.The value range of the intersection metric simThe intersection measurement method proposed in this paper can measure the stability of feature selection by measuring the similarity between the rankings in the feature ranking vector and realizing the stability evaluation of the feature selection results.In order to verify the effectiveness of the feature selection method proposed in this paper, experiments are carried out with the following groups of high-dimensional small sample data sets. The specific description of the data set is shown in In order to ensure the stability of the experimental results, this paper uses 2/3 of the data set as the training set and the remaining 1/3 as the test set. Repeat 10 times to average the results, and the data sets are all preprocessed. After 10 feature selections, the average of the time consumed by the three algorithms is counted. The results are shown in In terms of time efficiency, for the data sets Colon, DLBCL, and Prostate, RBF-RCE consumes much less time than the other two methods; for the ultra-high-dimensional data set GLI, SVM-RCE exceeds the memory during calculation, and the results cannot be obtained. RBF-RCE takes about 1/3 of the time consumed by RF, indicating that RBF-RCE is more time efficient than SVM-RCE and RF when processing high-dimensional small sample data or even ultra-high-dimensional data and can solve the feature selection problem of ultra-high-dimensional data sets.In terms of classification accuracy, the classification of the three algorithms on different data sets is plotted as shown in Figures 4Based on the classification accuracy of the above three algorithms in different data sets, perhaps because the objective data sets will produce differences in classification performance, the overall RBF-RCE can achieve good results in the classification of high-dimensional and small-sample data sets.After the classification accuracy is considered, the feature selection stability evaluation method based on the intersection metric mentioned in this article is used to determine the feature selection stability of the three methods. Because the feature selection process of RF and SVM-RCE is stable, RF adopts an ensemble method to combine multiple decision trees to improve stability, while the high stability of SVM-RCE is due to the introduction of recursive clustering elimination ideas. Therefore, these two methods are used as references to evaluate the stability of RBF-RCE feature selection.The specific stability evaluation results are shown in Figures 8Based on the above analysis, some conclusions can be drawn. When dealing with high-dimensional and small-sample data sets, such as Colon and DBLCL, when the data dimension is higher than the sample size or in the context of dealing with ultra-high-dimensional data sets, such as GLI, the RBF-RCE feature selection method can eliminate irrelevant feature classes and achieve rapid reduction of feature dimensions, so it can achieve excellent performance in time efficiency. It also optimizes the classification performance of traditional feature selection methods, overcomes the shortcomings of SVM-RCE that cannot process ultra-high-dimensional data, and improves the classification accuracy of traditional RF feature selection methods. Through the feature selection stability measurement method based on intersection metric proposed in this paper, the stability evaluation of several feature selection methods is carried out. The results show that RBF-RCE can finally achieve almost the same stability as traditional feature selection methods on different data sets. It shows that the RBF-RCE feature selection method not only has excellent time efficiency and classification accuracy but also can achieve better feature selection stability and can be used to process high-dimensional small sample data sets. In addition, more research can be carried out in the future based on the uncertainty of actual data. And a fuzzy clustering-based approach  is a gooIn summary, this article combines the feature importance analysis of random bits forests, introduces the idea of recursive clustering elimination, and proposes a new high-dimensional small sample data feature selection method RBF-RCE, which performs better than traditional feature selection methods in terms of time efficiency and classification accuracy. This is also confirmed by tests on actual data sets. On this basis, this article further proposes a feature selection stability measurement method to evaluate the stability of feature selection for many feature selection methods, combined with the intersection measurement, which will help to measure the reliability of the feature selection method whether it can obtain a true and interpretable feature subset that meets actual needs. The research content of this article can provide a new and effective method for the processing of high-dimensional small sample data and can provide a reliable solution for the majority of researchers when facing high-dimensional or even ultra-high-dimensional data sets.


The use of imaging devices to assess directional mechanics of tissues is highly desirable. This is because the directional mechanics depend on fiber orientation, and altered directional mechanics are closely related to the pathological status of tissues. However, measuring directional mechanics in tissues with high-stiffness is challenging due to the difficulty of generating localized displacement in these tissues using acoustic radiation force, a general method for generating displacement in ultrasound-based elastography. In addition, common ultrasound probes do not provide rotational function, which makes the measurement of directional mechanics inaccurate and unreliable. Therefore, we developed a high-frequency ultrasound mechanical wave elastography system that can accommodate a wide range of tissue stiffness and is also equipped with a motorized rotation stage for precise imaging of directional mechanics. A mechanical shaker was applied to the elastography system to measure tissues with high-stiffness. Phantom and ex vivo experiments were performed. In the phantom experiments, the lateral and axial resolution of the system were determined to be 144  The mechanical properties of biological tissues, including muscle, skin, tendons, cartilage, fat, etc., are closely related to pathological states as diseases alter the mechanical properties of tissue. Based on this relation, a clinical examination method called palpation, which qualitatively assesses mechanical properties of tissue with the fingers or hands, has been used for thousands of years to diagnose diseases. Until several decades ago, palpation was only possible on the surface or shallow depths of the body. Since the introduction of elastography in the 1990s, remote palpation inside the human body has also become possible [Several remote palpation methods based on magnetic resonance imaging and ultrasound imaging have been developed. Among these elastography methods, ultrasound-based elastography has important advantages such as higher temporal resolution, low patient exclusion rate, low cost, portability, frequent use by elastography technicians, and widespread availability in hospitals and clinics worldwide . Thus, uSome tissues require high spatial resolution of hundreds of micrometers for proving high quality image for disease diagnostics. Specifically, a heart consists of several layers such as endocardium, myocardium, epicardium, etc. In particular, each layer has the thickness of 0.5∼5 mm. The quantification of directional mechanics of each layer would be beneficial for the better diagnostics of the heart diseases. In addition, high-frequency ultrasound imaging showed the usefulness for eleastography of tissues with thickness less than few millimeters in the previous study . Thus, hThe most commonly used ultrasound-based elastography measures mechanical properties by generating localized displacement in tissue and detecting the movement caused by the displacement ,5,6. It The stiffness of human tissues varies. For example, the brain tissue is soft whereas the tendon, ligament, and cartilage are hard ,11. DiseMost previous studies assume that the mechanical properties of tissue are homogeneous and isotropic, especially for applications in the liver, breast, and prostate ,15,16,17In this paper, we developed a high-frequency mechanical wave elastography system to measure directional mechanics in a wide range of tissues regardless of stiffness. A motorized rotational stage is applied to the elastography system to detect directional mechanics. This motorized rotational stage allows the system to have high angular resolution, thus increasing the accuracy and reliability of diagnostics. In addition, the system stimulates tissues with a mechanical shaker to generate enough displacement in high-stiffness tissues. This approach eliminates the need for the ultrasound transducer to generate ARF. Thus, the transducer frequency can be sufficiently high to satisfy the image resolution requirements. In other words, this system can acquire high-resolution images and high-precision mechanical properties depending on the measurement direction.Phantom experiments were performed to assess the performance of the system in terms of lateral and axial resolution and showed how small a deformation the system can measure.To demonstrate the imaging capability for stiff anisotropic tissues, we selected swine heart and cartilage. The heart is considered a stiff material, with a shear modulus in the range of 5∼25 kPa depending on diastole/systole, and cartilage is much stiffer, with a shear modulus on the order of MPa. The swine heart experiments indeed show that wave speeds differ for different measurement directions indicating that the mechanical anisotropy is important factor to be examined. The cartilage experiments are performed to show that the system is also useful for measuring directional mechanics of tissues with stiffness in the order of MPa.The mechanical wave imaging system works by generating mechanical waves in tissue and subsequent motion tracking of the induced tissue motion caused by the mechanical waves. The user controls the motorized stage  through a personal computer, and the motorized stage sends trigger signals to the function generator . Then, the function generator synchronously triggers the mechanical shaker , the ultrasound transducer, and the personal computer to acquire the tissue motion data. The shaker is operated with an excitation signal generated by a function generator and amplified by a power amplifier . The shaker generates a tone burst of 750 Hz on the tissue surface, and a mechanical wave is propagated from the excitation point to the observation area. A 38 MHz single-element high-frequency ultrasound transducer is operated with a tracking signal generated by the function generator and a pulser/receiver . Then, the ultrasound transducer generates acoustic waves to track and record the induced tissue motion. The target tissue is attached to a motorized rotation stage, which rotates the target tissue to analyze the directional mechanics of the tissue. The ultrasound transducer is attached on a 3-axis motorized stage, which transports the transducer to the imaging area. In the system, all motorized stages are controlled by a computer via a step motor controller . The transducer moves while the imaging system operates, and all of the above processes are repeated at each imaging location.A 38 MHz lithium niobate ultrasound transducer was fabricated and attached to the 3-axis motorized stage to allow tracking of the displacement caused by mechanical waves. A photographic image of a single-element lithium niobate ultrasound transducer is shown in us level c,d. In tA wave speed is calculated from data acquisition and multiple signal processing. The details are as follows:Data acquisition is initiated by moving the motorized stage. The motorized stage moves at a speed of 250 eference  shows thEvery 50 The backscattered radio frequency signals are interpolated in the time domain by cubic spline interpolation. The interpolated signals are filtered with a bandpass filter with cutoff frequencies of 36 MHz and 40 MHz to reduce low- and high-frequency noise. After filtering, the filtered signals are used to estimate tissue displacement.The displacement of tissue is estimated by applying the conventional cross-correlation method to the bandpass filtered signals . The croThe extracted displacement maps include not only forward waves but also backward waves that occur from reflection. The reflected backward waves make wave speed estimation difficult; thus, the backward waves must be removed with a directional filter as described in reference . The dirThe wave speed in the tissue is estimated from the slope of the time delay in the displacement maps (moving distance vs. estimation time). The time delay is calculated from the cross-correlation between the wave at the start point and the wave at each point. The slope of the time delay is linearized with linear regression, and the linearized slope represents the wave speed. Wave speed map consists of estimated wave speed at each point. Each wave speed map is filtered with 5 × 5 median filter to acquire a smooth image.Phantom experiments were designed to validate the developed imaging system and to identify the spatial resolution of the imaging system. Heterogeneous phantom experiments were designed for the above purposes. The heterogeneous phantoms were divided into layered phantoms for the axial performance and side-by-side phantoms for the lateral performance. Each heterogeneous phantom is made with two concentrations to divide the mechanical property laterally and axially. All phantom experiments were repeated three times for each phantom for more accurate measurements.Two types of tissue-mimicking phantoms, namely, a layered phantom and side-by-side phantom, were fabricated with agar powder. These phantoms were primarily constructed to identify the spatial resolutions. The step-by-step procedure for phantom fabrication was as follows . First, Swine hearts and cartilage were purchased from an online butcher shop that provides meat within one day after butchering. After purchase, the samples were stored in a refrigerator at x is the axial or lateral distance in the phantom and N is the total number of wave speed profiles across two layers in each phantom (the side-by-side and layered phantoms). The parameter ith transition of the wave speed profile. The mean resolution of our imaging system was obtained by averaging the transition widths estimated in different lateral or axial positions.The spatial resolutions of the imaging systems were determined through R methods . The resThe spatial resolutions of the imaging system were determined in two types of heterogeneous phantom experiments. The lateral and axial resolutions were calculated to be 144 Heart experiments were designed to identify mechanical anisotropy. At each acquisition, the rotational stage rotated the heart tissue 360 studies ,28,29. FThe system was used to measure swine hearts in the longitudinal, circumferential, and radial directions. All measurements were performed at a depth of 0 mm. The circumferential and longitudinal directions represent the wave propagation directions at 0p-value of the independent two-sample t-test between the wave speed for the different directions in each layer and each location. In the table, the p-values for the myocardium were corrected by Bonferroni correction, because the comparisons were performed three times among three groups. Each wave speed is significantly different (p < 0.05) from others except for the case of the myocardium and base free wall.This experiment was designed to identify the directional mechanics of the cartilage tissues with our mechanical wave imaging system. We incorporated a mechanical shaker and motorized rotation stage into a wave elastography system for the diagnostics of mechanically anisotropic tissues with a wide range of stiffnesses. Two types of experiments (heart and cartilage) were designed to validate the feasibility of our imaging system on actual tissues.Swine heart experiments were performed on 15 pigs, the results of which are given in in p-values in We clearly observed that the wave speeds differ depending on the measurement direction, location, and layer. The differences are statistically significant as shown by the Previous studies developed the mechanical wave imaging system to measure directional mechanics ,28. In tWe note that it is possible to identify the direction of the fiber orientation using the proposed system: it is the direction in which the mechanical wave propagates at the fastest. This is due to the fact that wave speed is fastest along the direction of the fiber orientation in anisotropic materials . IdentifStrain-based elastography can also measure direction-dependent mechanical properties by measuring the mechanical properties in multiple directions. In order for this, the tissue sample must be rotated in three-dimensional manner in the measurement device. Incorporating the automated rotation in three-dimensional manner for repeatable and accurate measurement may require a complex mechanism. Most importantly, strain-based elastography cannot quantitatively measure the mechanical properties due to the absence of a stress measuring sensor. Thus, the direction-dependent mechanical properties are not quantitatively distinguished in the strain-based elastography. Based on the two points discussed, we view that the proposed imaging system is superior to strain-based elastography and its potential extensions.Next we discuss the measurement of directional mechanics in swine cartilage using mechanical wave imaging, which was performed for the first time to the best of our knowledge. Nevertheless, the results demonstrate that the proposed imaging system can measure the wave propagation speed of relatively hard tissues such as cartilage and that a mechanical wave elastography method can measure the directional mechanics of cartilage qualitatively. In addition, the observed mechanical properties in cartilage are consistent with the measured direction-dependence and the stiffness greater than thousands of kPa in the previous studies ,35. AlthWhile this system is useful for ex vivo evaluation, this system cannot be used for in vivo evaluation due to its size (bulkiness) and low penetration depth. Consequently, the use of this system is limited to ex-vivo research, and modifications enabling a future clinical set-up are required. Ultrasound imaging has been used to image structure of heart and cartilage. Therefore, in order to apply this system in clinical tests, the development of a method for generating mechanical waves inside the human body is necessary. There are several methods to achieve such; first, a compact vibrator can be used for mechanical wave source. The compact vibrator should be inserted in intracardiac probe. The vibrator mounted on probe contacts the cardiac tissue and directly displaces the cardiac tissue to generate a mechanical wave. Alternatively, the displacement may take place in tissue by generating large mechanical wave at the skin near the cartilage or heart. In such systems, the mechanical shaker and ultrasound probe can be physically separated. Clinical examination might be performed after these developments of mechanical wave source. The rotation stage is another problem to be solved in order to apply the imaging system inside the human body. At least three ultrasound transducers should be mounted on the catheter, each of which detects the displacement in a different measurement direction. The wave speed according to fiber orientation and the wave speed perpendicular to fiber orientation can be estimated by applying the measured wave speed to an anisotropic material model. By solving these problems, this imaging system could be applying into clinical test.In this study, we designed a high-frequency (38 MHz) mechanical wave imaging system with a mechanical vibrator capable of measuring the directional mechanics of tissues. The developed system was proposed for ex vivo evaluation of the directional mechanics of tissue at various angles. The imaging system was validated in experiments with phantoms and actual swine heart and cartilage. Based on the phantom experiments, the axial and lateral resolutions were calculated as 168