In identifying to-be-improved product component(s), the customer/user requirements which are mainly considered, and achieved through customer surveys using the quality function deployment (QFD) tool, often fail to guarantee or cover aspects of the product reliability. Even when they do, there are always many misunderstandings. To improve the product reliability and quality during product redesigning phase and to create that novel product(s) for the customers, the failure information of the existing product, and its component(s) should ordinarily be analyzed and converted to appropriate design knowledge for the design engineer. In this paper, a new intuitionistic fuzzy multi-criteria decision-making method has been proposed. The new approach which is based on an intuitionistic fuzzy TOPSIS model uses an exponential-related function for the computation of the separation measures from the intuitionistic fuzzy positive ideal solution (IFPIS) and intuitionistic fuzzy negative ideal solution (IFNIS) of alternatives. The proposed method has been applied to two practical case studies, and the result from the different cases has been compared with some similar computational approaches in the literature. The design of most complex products and systems like crane vessel, diesel engines etc., are mainly done by redesigning or making changes on existing predecessor designs until all new arising requirements are met  for the customers, deliberate effort must be made to identify and analyze the failure information of the existing product  method. The FMEA method which was introduced in the 1960s by the United States aerospace industry as a structured and systematic method with apparent reliability and safety requirements  methods have also been presented as alternative methods for the FMEA, among them, we can mention; the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) presented by Safari et al. , for priEF) as an alternative approach for the FMEA method. In this case, the new approach is used for building appropriate design knowledge about the to-be-improved or redesigned product component by analyzing the failure information about the product with the view to prioritizing the failure modes and to provide the designer with relevant information to be used in improving the product reliability and quality during the product redesigning phase. The exponential related-based function is used for the computation of the separation measures from the intuitionistic fuzzy positive ideal solution (IFPIS) and intuitionistic fuzzy negative ideal solution (IFNIS) and for ranking the alternatives. The new exponential related-based function not only considers the deviation between the memberships with the non-membership degrees but also considers the hesitancy degree of the intuitionistic fuzzy set (IFS), unlike the existing matrices methods and functions that only considers the deviation between the memberships with non-membership degrees in the IFS. The weight of the evaluating criteria in this study is determined by using the intuitionistic fuzzy entropy originally proposed by Ye  ∊  is the membership of x ∊ X in A. Since IFS is characterized by two functions which expresses the degree of membership and non-membership of an element x to the set A, then an IFS A in X = {x} is defined as A respectively. Also, the number x in A is referred to as a measure of the degree of hesitancy of element x ∊  in set A. It should be noted that 0 ≤ πA (x) ≤ 1 for each The numbers Definition 2 If the IFS A in X = {x} is defined fully in the form mentclass2pt{minim in Eqs. .1\documeDefinition 3 Let rator Xu . The IFWIn the following will make comparisons between two IFS, by introducing some metric methods by following the score function and accuracy functions.Definition 4 Let S of an intuitionistic fuzzy value can be represented as follow  the more the degree of accuracy of the intuitionistic fuzzy value A.Definition 6 Let Se of the intuitionistic fuzzy number can be represented as;ng to Wu  the expoER, not only considers the deviation between the membership degrees with the non-membership degrees but also considers the hesitancy degree of the IFS.Considering the matrices methods reviewed above, some few drawbacks have been reported in the literature. According to Wu , the resDefinition 7 Let π is the hesitancy degree of the IFS. The new exponential related function ER of the intuitionistic fuzzy number can be defined as;ER can be rewritten asThe exponential related function Proof We can prove Definition 6 by mathematical induction and the similar proof method by comparing two IFNs. Next, we show that the exponential related function ER can achieve the same ranking as the exponential score function.Letandbe two intuitionistic fuzzy number of the exponential related function ER respectively, if α1 ⊃ α2thenProof Assume that ci such that α1 ⊃ α2 without loss of generality, let assume that ER for an arbitrary IFN Now, a generalized exponential related function ER(α1) − ER(α2) is positiveFrom Eqs.  and 12)12) ER to determine the relative closeness coefficients.In this section, we present the algorithm of the IF-TOPSISAi with respect to a criterion Cj are defined first with linguistic variable and then converted to an IFS value xij =  or xij =  Ai ∈ A with respect to the criterion Cj ∈ C for the intuitionistic fuzzy concept.Let consider a MCDM problem where a set of alternatives EF and the intuitionistic entropy weight are given in following steps;The algorithm of the IF-TOPSISStep 1: Set up a group of decision makers (DMs) and aggregate their evaluations; Once the DMs has given their judgment using linguistic variables, the weight vector ER  or Eq. (DMmxn(xij) to form the exponential related matrix Step 2: Using the exponential related function  use Eq.  for the ) or Eq.  for membStep 3: Using the intuitionistic entropy weight method as described in “Step 4: Define the IFPIS ER function-based separation measures in intuitionistic fuzzy environment Step 5: Compute the exponential related wj is the weight of the criteria as described above.Similarly, CCi), which is defined to rank all possible alternatives with respect to the positive ideal solution A+. The general formula is given as;A+ and Step 6: Compute the relative closeness coefficient,  with adequate information on the reliability of the product component and to guide them on designing for reliability. Also to assist the product development team in pinpointing the exact component to adjust, replace or recommended for a redesign. To ensure the effectiveness of the proposed approach, some few practical examples have been presented in this study.In this section, we demonstrate the computational process of the IF-TOPSISCase 1 Let us consider a multi-criteria decision-making problem originally presented by Ye 17), the sing Eq. . The resentclass1pt{minimaThe ranking of the failure modes for the four components as shown in Table Case 2 Let us consider a practical failure detection problem originally presented by Chang and Wen 17), the sing Eq. . The resTo further demonstrate the effectiveness of our proposed model for failure detection, we compare the results of the example in case 4 by analyzing the case with some similar computational approaches including the fuzzy TOPSIS model by Braglia et al. , the intThe rankings of the different approaches show that they are almost in agreement with our proposed approach. The result shows that except for PMs 6, 7, 10, 13 and 15, the failure modes for other PM obtained by our proposed method are different from those obtained using the conventional RPN method. However, the difference is as a result of the limitation in FMEA method as mentioned in “The ability of the new method to reflected and modeled the fuzziness and hesitation of the experts’ subjective assessments of the failure modes with the application of the exponential-related function.The method considers not only the deviation between the membership and non-membership degrees as obtainable in other intuitionistic methods but considers also the hesitancy degree of the IFS.The results from the proposed method for failure detection are more objective and reliable because the criteria weights were determined using an objective weight approach.The implementation procedures of the proposed model and approach are easy and straightforward as compared to the other Multi-criteria decision-making methods and TOPSIS approaches compared in this study.The advantages of the proposed method in this study over the conventional FMEA methods (RPN) can be summarized to include;The main goal of any product redesigning exercise is to create new products and systems that meet the customer requirements as well as the product reliability. In identifying product component(s) to be redesigned, the customer/user requirements which are mainly considered and achieved through customer surveys using the quality function deployment (QFD) tool, often fail to guarantee or cover aspects of the product reliability. Even when they do, there are always many misunderstandings.To improve the product reliability and quality during the product redesigning phase and to create that novel product(s) for the customers, the failure or potential failure information of the existing product, and its component(s) should ordinarily be identified and analyzed. In this study, we have presented an intuitionistic fuzzy TOPSIS model which is based on an exponential-related function for building appropriate design knowledge about the to-be-improved or redesigned product component by analyzing the historical failure information about the product with the view to prioritizing the failure modes and to provide the designer with relevant information to be used in improving the product reliability and quality during the product designing phase. The exponential related-based function has been used for the computation of the separation measures from the intuitionistic fuzzy positive ideal solution (IFPIS) and intuitionistic fuzzy negative ideal solution (IFNIS) and for ranking the alternatives. The new exponential related-based function not only considers the deviation between the memberships and the non-membership degrees but also considers the hesitancy degree of the intuitionistic fuzzy set (IFS). The weight of the evaluating criteria in this study has been determined using the intuitionistic fuzzy entropy originally proposed by Ye , b.To demonstrate the effectiveness of the proposed approach for failure detection, two practical case studies have been presented and evaluated using the proposed approach. Also, the results from the different case study have been compared with some similar computational approaches such as; the conventional Fuzzy TOPSIS model, the integrated weight-based fuzzy TOPSIS (IWF-TOPSIS) model, the intuitionistic fuzzy hybrid TOPSIS (IFH-TOPSIS) approach and finally with the conventional risk priority number (RPN) method.Finally, we can conclude that the new approach proposed in this study, provides a better alternative method for failure identification and analysis as it allows for the fuzziness and hesitation of the experts’ subjective assessments to be reflected and modeled in the evaluation. Also, in applying the proposed model, the particular fault area, and the failed component can easily be identified. In the future, it is recommended that the proposed approach should be applied in solving other multi-criteria decision-making problems with special reference to the two ranking order for the two exponential related functions.


Dental diseases are common in man and range from a toothache to cancers of the head and neck. Dental conditions can affect our capacity to function effectively in areas such as smiling, chewing and speaking. The objective of this study was to describe the main types of dental conditions presenting at the University Hospital between January 2006 and December 2011 and to determine factors associated with the top five diagnosed conditions as well as the acute and chronic conditions. A retrospective review of all 5012 clinical records of dental patients visiting the dental unit within the period stated was carried out. A total of 4196 records which passed the inclusion/exclusion criteria were analysed. Most of the patients who presented were adults. The top 5 dental conditions were apical periodontitis (50.4 %), reversible pulpitis (23.3 %), Gingivitis (11.4 %), Periodontitis (6.2 %) and Halitosis/bad breadth (8.8 %). The top 5 conditions constituted over 75 % of the cases seen. About 84 % of the presentation was acute whilst 16 % was chronic. For the entire dataset and also the top five conditions, approximately 53.0 % were males and 47.0 %. Males outnumbered females on all occasions except for halitosis and most patients presented within 1 month of experiencing symptoms of dental disease. Some significant association was found between the presence of multiple chronic conditions and reversible/irreversible pulpitis. The main dental conditions presenting at the University Hospital during the stated period (i.e. between January 2006 and December 2011) were: apical periodontitis (50.4 %), reversible pulpitis (23.3 %), gingivitis (11.4 %), periodontitis (6.2 %) and halitosis/bad breadth (8.8 %). The most common diseases in man include dental diseases such as gingivitis and caries. Different parts of the mouth such as the teeth, gums or other tissues may be affected by dental disease. Apart from a toothache, which is a commonly experienced dental disease, others may manifest as inability to speak, smile or even chew with a varying degrees of severity . In 2006, dental caries accounted for 80 % of dental extractions performed in Public Dental Clinics whilst periodontal disease accounted for 13 %.Calculus still remains the commonest presentation of gum disease. In 2003, 73 % at age 12, 56 % of adults aged 35–44 and 74 % of adults aged 55+ have calculus.Studies reviewing the pattern of all oral diseases presented at any specified dental clinics are so few and virtually non-existent. Most of the research done involves the selection of one condition or a particular age group such as children and adolescents. This study provides a composite picture of all the diseases presenting at the Dental Unit of the University Hospital and enables us to describe the top five conditions, categorizing them into acute or chronic and assess any associations with the past medical history.The study was conducted at the Dental Unit, of the University Hospital, Legon. The University of Ghana Hospital was built to cater for the health needs of students, staff and their dependants. Over time the hospital has assumed the functions of a district hospital and has a wide catchment area. This quasi-government institution has medical, surgical, maternity, paediatric, casualty and emergency, dental, operating theatre and public health units and a bed capacity of 121. To meet the growing demand for specialist services, specialist consultancy services such as paediatrics, general surgery, obstetrics and gynaecology, orthopaedic surgery were introduced in 1996/97 and the dental unit started as part of the specialist consultancy services that same year. A full dental wing was constructed after which regular dental services was started in 2005. The University Hospital Dental Unit is a general dental practice providing first primary dental care, and patients presenting a range of conditions.The university classifies staff and students into the following groups; junior members (students), junior staff, senior staff, senior members and private patients. “Staff” means a person other than senior members in the employment of the University. “Junior Staff” are members of staff below the rank of Administrative Assistant or its equivalent. “Senior Staff” means member of staff not below the rank of Administrative Assistant or its equivalent.A “Junior Member” means a person in status pupillary enrolled for the time being in the University, whether in a campus based or distance education programme. “Senior Member” means the academic, administrative, professional employees and members of convocation or persons who would become members if they were not of <2 years standing from their first degrees or equivalent qualifications. Broadly speaking, “private patients” are those who are not staff or members or dependants of the staff and senior members and therefore are not associated with the university.A retrospective review of clinical records of dental patients who visited the dental unit of the University Hospital between January 2006 and December 2011 was conducted.All the records of patients seen from January 2006 till December 2011 were obtained. The population comprised consecutive records of all patients seen over this period.Secondary data made of patients records was retrieved by trained data collectors. The training was done by the principal investigator using a sample patient record. All the parameters listed in the folder were explained to them to facilitate the understanding of the information to be captured. Data collectors were graduates who were awaiting their national service.In order to get an all-inclusive population, all the records of patients seen within the period 2006–2011 were included in the study. Therefore a total of 5012 paper based consecutive records was retrieved and entered into the data collection sheets.Any record without a diagnosis, age and sex was excluded from the analyses. This was done because the dependent variable is the diagnoses and some demographic inputs will be required in its analyses. In total, 4196 records made it to the analyses stage because they met the inclusion and exclusion criteria whilst 816 paper based records were omitted from the study.Apical periodontitis and or irreversible pulpitis;Reversible pulpitis;Gingivitis;Periodontitis;Halitosis/bad breath;Impacted tooth/pericoronitis;Dentoalveolar abcess;Maxillary sinusitis;Mucosal ulceration/lesion;Fractured tooth;No abnormality found;Others e.g. locked jaw, ameloblastomas.The dependent variable was diagnoses such as dentoalveolar abcess, irreversible pulpitis, enamel hypoplasia and reversible pulpitis. The full list of the dependent variables as illustrated in Table Whilst an acute condition will have symptoms appearing and changing rapidly, a chronic condition will develop and worsen over an extended period of time. Therefore duration and presentation of the symptoms aided in categorizing the condition as acute such as (irreversible pulpitis) and chronic (reversible pulpitis). It is important to note that depending on the duration of the symptom, a condition such as a fractured incisor may be categorized as acute or chronic. Where the condition is better classified as acute or chronic, it was added to the acute group since it was the acute exacerbation that precipitated the visit.The independent variables are as follows; age , sex, associated professional category . Other independent variables include chief complaint characteristic , duration of chief complaint , past medical history , past dental history . The rest are the conditions of the oral mucosa , condition of the teeth , investigations  and the first item on the treatment plan .This section describes the output obtained by analysing the data obtained from the university hospital. The total sample size is 4196 out of 5012 records which contain demographic information of patients, the various diagnoses of patients, chief complaints, investigations and other relevant information. The analysis is in two sections; that is, descriptive statistics and some tests of relationships between certain variables (Chi square test of independence).The decline in the numbers seen from 2006 till 2009/2010 for most of the categories may probably reflect the staffing and enrolment status of the university as a whole.A sample of 4196 was selected based on already predefined inclusion and exclusion criteria from all patients’ records available from 2006 to 2011. Table The top 5 conditions constitute over 75 % of the cases seen and have similar male to female distribution as the entire data set. About 84 % showed acute presentations whilst 16 % showed chronic presentations. The predominance of acute presentations shows the fact that patients usually present when they are in pain or significant discomfort.The male to female proportions in both the acute and chronic group are almost evenly distributed.The young adults and older adults together constitute approximately 70 % of the cases seen for the entire data set and the top 5 acute and chronic conditions as well. This is consistent with the population profile of the University of Ghana. The age group which least patronized the clinic was the elderly group which averagely contributes about 3–5 % of the various sub-groups already described. This finding is consistent with Bhadbhade , who notAs illustrated in Table The top five dental conditions seen here are a reflection of patients’ attitude to dentistry as a whole. Most people attend the clinic when they are in pain and are unable to chew. At that stage of apical periodontitis, patients are presented with the unpleasant options of either carrying out a root canal or an extraction.Table It is important to note that in cases where a patient presented with multiple diagnoses, the diagnosis most consistent with the key presenting complaint during the first visit was selected. In the very few cases where this was not possible, a diagnosis was randomly chosen out of the lot.Table As illustrated in Table The factors of age, duration of symptoms as well as the presence of multiple chronic conditions is related to the diagnoses arrived at during the dental visit as shown in Table The following conclusions are drawn from the test of relationship between the top five diagnoses, the severity of condition and some variables. p values <0.05 show significant relationships between the two variables. With respect to age, the p value of the Chi square test above shows that the age group of patients is related to the condition of apical periodontitis and gingivitis but not enamel caries, periodontitis and halitosis. It also shows that their various age group is related to the severity of their condition. The p value of the Chi square test above shows that the duration of symptom of patients is related to the condition of enamel caries, halitosis and the severity of the presenting condition but not apical periodontitis, gingivitis, enamel caries and periodontitis.Although the tests above shows some significant associations between past dental history on one hand and gingivitis, periodontitis and reversible pulpitis, on the other hand no relationship was found with halitosis, apical periodontitis and severity of presentation. Past medical history did not indicate any relationship with any of the parameters described. The p value of the Chi square test above shows that the multiple chronic conditions of patients is related to apical periodontitis, enamel caries and the severity of presenting complaint but it is not related to gingivitis, halitosis and periodontitis.More males reported to the Dental Unit of the University Hospital than females and this is probably due to the University population profile or the fact that men are more predisposed to dental problems due to poor attitudes to oral health and its practice.Although the majority (79.1 %) of patients have no significant past medical history, about 16 % have either hypertension, diabetes or both and these chronic conditions are significantly associated with related to apical periodontitis, enamel caries and the severity of presenting complaint.The factors of age, duration of symptoms and the presence of multiple chronic conditions is related to the diagnoses arrived at during the dental visit.More people presenting at the University Hospital come with acute dental conditions for emergency treatment. Most of the patients present after about 1 month of experiencing symptoms. Also fewer people are attending the clinic for preventive oral health care.This raises an important point for policy formulators to firstly step up oral health education and prevention services as well as prepare the dental clinic adequately to deal with the expected numbers of acute cases that will present.


The metallic glasses (MGs) are conjectured to be heterogeneous—their microscopic structures are embedded with localized, soft and loosely packed atomic regions, which are termed as flow units (FUs). Detailed knowledges on the structure and dynamical features of FUs are essential for understanding the plasticity of MGs. In our study, by performing dynamical tests on MGs in molecular dynamics simulations, we show that mechanical hysteretic loops are formed in the strain-stress curves due to the undergoing plastic events. By analyzing the activated times of each atom in different dynamical tests, we map the exact locations of FUs and the distribution of their activation probability in the initial structure of MGs. More importantly, we demonstrate that the FUs are indeed liquid-like according to the Lindemann criterion of melting. Recent studies suggest that the structures of MGs are heterogeneous18, consisting of densely and loosely packed regions21. The latter is referred as flow units (FUs), which are believed to be the basic units of deformation, plasticity and viscoelasticity in MGs24. However, it is much more desirable to know where the FUs locate in MGs and what structural and dynamical features they have, which are essential for understanding the plastic events from the initial structures in MGs. A few experiments prove that before the yield of MGs, the nucleation of the shear bands have already formed and taken effect on the mechanical response26. A typical example is shown by the mechanical hysteretic loops in the dynamical tests, indicating the plastic behavior of MGs in elastic regime26. The dynamical test conducted in elastic regime offers an effective way to stimulate the FUs and explore their mechanical response, dynamical behavior and spatial distribution without damaging the whole systems.Because metallic glasses (MGs) do not possess slip systems or lattice dislocations as in crystalline materials24. However, no clear evidence has been revealed. The dynamics of both the FUs and solid-like regions, including the excitations and the percolations of FUs, are the fundamental processes that determine the mechanical property of MGs. However, few works have been devoted to exploring the vibration state and the related physical state of the two regions. To rationalize this hypothesis that MGs are mixture of liquid-like FUs and solid-like matrix, it is highly desirable to identify the fluidity of the heterogeneous structures in MGs.It has been conjectured that the FUs are loosely packed, liquid -like and embedded in the densely-packed regions, that are solid-like and form the skeleton of the MGsIn this study, we carry out multiple dynamical tests with different maximum loading stresses in the apparent elastic regime on a model CuZr MG system via molecular dynamics simulations. The mechanical hysteretic loops are observed in strain-stress curves which indicate the activation of FUs in these processes. Whether an atom is activated or not is represented by the changes in the number of its nearest neighbors. By mapping the activated times of atoms in the multiple dynamical tests onto the initial configuration, the exact locations of FUs and the heterogeneous feature of MG structures are unambiguously revealed. The FUs are loosely packed and activated in dynamical tests with a broad activation probability distribution. Analyses on the vibration spectrum show that the atoms in the FUs prefer to participate more in the low-frequency vibrational modes, implying the soft characteristic of the FUs in MGs. Furthermore, the dynamics and liquid-like feature of FUs in MGs at room temperature are quantitatively characterized in terms of the Lindemann criterion of melting as well as the extensive trajectories of atoms in FUs.64.5Zr35.5 metallic alloy with the interatomic interactions described by realistic embedded-atom method potential27. The system containing 40,000 atoms in a cubic with periodic boundary conditions in three dimensions was fully relaxed and equilibrated at 2000 K, and then quenched down to 300 K with a cooling rate of 1 × 1012 K/s. Subsequently, the quenched sample was relaxed for 2 ns at 300 K. All MD simulations were performed in isothermal-isobaric (NPT) ensemble with pressure adjusted to be zero and the MD step is 2 fs. To identify FUs in the MG sample, dynamical tests with different maximum loading stress σmax were performed in the apparent elastic regime. In specific, the uniaxial tensile stress was applied to the sample in z direction with a constant loading rate of 2 × 109 GPa/s until a maximum loading stress σmax was reached, and then the applied tensile stress was fully unloaded with the same rate. The dynamical tests were repeated for the same initial configuration but with different maximum loading stresses σmax. In our study 22 dynamical tests were performed to examine the response of FUs in the sample.Classical molecular dynamics (MD) simulations were performed for the model system of Cumax. The strain-stress curve in the tensile loading up to plastic regime is also presented for comparison. The yield stress is estimated to be about 2.10 GPa and all the dynamical tests applied to the sample are in the apparent elastic regime. As shown in Fig. 26. The mechanical hysteretic loops in strain-stress curves indicate that the MG samples have experienced plastic deformations in the apparent elastic regime. The plasticity even occurs in the case of σmax = 0.79 GPa as shown in the inset in Fig. Figure 26. The regions experiencing irreversible rearrangements in dynamical tests are referred as FUs. The irreversible rearrangements, namely the activation of FUs, result in the plastic deformation in the elastic regime and mechanical hysteresis in the dynamical tests. As σmax increases, the areas of the hysteretic loops increase as shown in Fig. max and can be well fitted by an exponential form.From structural perspective, the plastic deformation in apparent elastic regime of the MGs results from the irreversible atomic rearrangementsmax to obtain the activation energy information. The inset in Fig. max and the slope of the curve is related to the activation energy. The results indicate that the activation energies of FUs are quite different and have a distribution in MGs: some FUs have small activation energies which can be easily activated under very small stress, while others can only be activated under large loading stress. The distribution of the activation energy due to the dynamic and structural heterogeneities in MGs19 is consistent with that obtained in experiments28. Note that according to the previous studies30, the hysteretic loops in dynamical tests could be related to the anelasticity. However, it is not the case in our study, since the time scale in the unloading process (300~1000 ps) is much longer than that used for the anelastic recovery in previous studies (10~30 ps)29, so that the contribution of anelasticity to hysteretic loops in our dynamical tests is negligible, and the hysteretic loops mainly result from the local plastic events of FUs.To further confirm the activation behavior of FUs in MGs in dynamical tests, we examine the dependence of the loop area on 1/σNN before stress loading and after unloading, which has been used to identify slow particles over a time difference31. The nearest neighbors of atoms are determined by Voronoi tessellation method13. Small values of ΔNN indicate that the atoms deform elastically during certain dynamical test. After fully unloaded, the initial configurations of these atoms are almost recovered. In contrast, larger values of ΔNN indicate that the atomic rearrangements are irreversible and the atoms experience plastic deformation. Thus, the atoms with large ΔNN are the representatives of FUs in MGs, and we may characterize the atoms with large ΔNN to get information on the atomic structural and dynamical features in FUs.To quantify the atomic rearrangements and identify the FUs in MGs, we measured the number of changes in the nearest neighbors of each atom Δi is defined as 13, where i. The indexes 0 and 1 denote the atomic configurations before loading and after unloading in the dynamical test, respectively. Therefore, the atomic mobility defined here can be used to measure the displacement an atom moves in a dynamical test.We also analyze the motion of each atom between the initial and final configurations in the dynamical tests to examine the mobility of atoms. Here the mobility of atom NN and Δr2 of atoms in different dynamical tests. The atoms are sorted in terms of their atomic mobility from low to high and divided into 20 groups, each containing 5% (2000) of the total atoms. In each group, the average ΔNN is calculated and plotted as curves in Fig. NN are immobile, while the atoms with large ΔNN are more mobile. As atomic mobility increases, the values of ΔNN increase abruptly. These atoms in FUs are much more mobile and experience irreversible rearrangements under stress. It is also shown that for most atoms the values of ΔNN are less than 2 and immobile, so that the atomic configurations of these atoms are almost unchanged in the loading-unloading dynamical tests, and mainly experience elastic deformation. These atoms form the so-called solid-like elastic matrix in MGs. It is clearly seen that only a small fraction of atoms with large ΔNN experiences irreversible rearrangements and makes contribution to the mechanical hysteretic loops in dynamical tests. According to Fig. NN ≥ 2 are assumed to be activated atoms in FUs during the dynamical tests. We also tested the different choice of ΔNN, for example, ΔNN ≥ 3 was used to identify the FUs in the samples, which does not qualitatively violate the results and conclusions obtained below.Figure Na of each atom activated (ΔNN ≥ 2) among the 22 dynamical tests. If an atom is activated in all 22 dynamical tests, we have Na = 22, while Na = 0 means that an atom is never activated in these tests. The activation probability of each individual atom is determined as P = Na/Ntest (Ntest = 22) and their distribution is shown in Fig. To reveal the intrinsic FU structure in MGs where the irreversible atomic rearrangement is prone to occur, we statistically count the times f(P)~Pα−eP/β− as shown in the upper right inset in Fig. f represents the fraction of atoms; α and β are fitting parameters and fitted to be 0.85 and 0.61, respectively. The fitted parameters imply that if the activation probability is larger than 0.61, the regions with the corresponding atoms can be regarded as FUs in MGs, which is responsible for the stress-induced irreversible atomic rearrangements in MGs in elastic deformation regime and consistent with the experimental measurements27. The spatial distribution of the FUs and elastic matrix can be exhibited by mapping the activated times Na of all the atoms into the initial configuration as shown in the lower left inset in Fig. Na of atoms, respectively. It is clearly seen that the atoms with larger Na are highly localized regions embedded in the elastic matrix, confirming the structural heterogeneity22. The FUs in MGs are almost enclosed by the elastic matrix, roughly forming the so-called core-shell structure as observed in experiments24. These findings also indicate that the structural characteristic of FUs could be used to evaluate where the irreversible atomic rearrangements would occur from the initial structures of MGs and with what probability. This is comparable to the local Deybe-Waller factor which has been used to predict the spatial distribution of the long-time dynamic propensities32. In our work, explicit initial structural information is provided.The distribution of activation probability of atoms can be well-fitted by a power-law form with exponential cutoff, i is activated or not in the dynamic test m: NN > 2 and NN < 2. The cov is the ordinary covariant function. The elements Cmn show the correlations of the activation distributions pi for the two dynamic tests m and n. In the matrix, the tests are sorted by their applied maximum loadings, which also show the temporal evolution of the system.We show below that the 22 dynamical tests are found to be independent of each other, which further demonstrates the FUs are intrinsic in MGs. In Fig. m = n − 1 and m = n + 1) show the correlations between two dynamic tests with close maximum loadings. As can be seen, the values of these elements sharply decrease to about 0.3. The values of other off-diagonal elements (m > n − 1 and m < n − 1), that denote correlations between two dynamic tests with larger difference in the maximum loadings, persist around 0.3~0.4. The sharp decreasing reveals the poor temporal correlations of the dynamic tests, which imply the activations in the MGs are fast processes. In spite of the poor temporal correlations, considering that the random distributions give value of zero for the correlations, the spatial distributions for the activations are still highly correlated  during the whole elastic loading process. These high correlations are not due to the adjacency in time sequence, but owing to the tendency of the activations occurring on the intrinsic FU structure in the MGs. For elements with large m or n, the correlations begin to drop because of the increase in the spatial randomness of the activations due to percolations. This matrix offers a clear scenario occurring in the MGs: the activations are created and annihilated rapidly during the loading, but the activations are prone to happen on the intrinsic FU structures in the MGs.As shown in Fig. NN ≥ 2) in different dynamical tests to characterize the local atomic packing of FUs in MGs. Figure 38. It is interesting to find that the CN distribution of the selected atoms in the dynamical test of the smallest σmax locates the farthest away from the average distribution, and then moves toward the average distribution as σmax increases. This tendency is illustrated more clearly by the change of average CNs in FUs (ΔNN ≥ 2) with σmax increasing in Fig. max (0.79 GPa), the average CN values for Cu and Zr in FUs (ΔNN ≥ 2) are 13.75 and 16.77 respectively, much larger than the average CN values of 12.8 and 15.9 in the whole sample. As σmax increases, the average CN of both Cu and Zr atoms with ΔNN ≥ 2 decreases.We simply analyze the coordination number (CN) of the activated atoms  . Figure 43. Thus, the atoms with higher activation probability in FUs are closely correlated with the “soft spots”. This is also consistent with the results that local structures involved in the low-frequency vibrations may have higher rate of structural transition44. Moreover, the more disordered regions in amorphous argon were found to be related to the excess of the low-frequency vibrations45. This may also imply that the atomic structures in FUs of metallic glasses could be more distorted.To get dynamical characteristics of the FUs in MGs, isothermal relaxation was performed in NVT ensemble for the initial configuration at 300 K for 2 ns via MD simulations, and the vibration power spectrum and long-time dynamics of atoms with different activated times δ, which is a criterion of melting44, was adopted to quantitatively characterize the fluidity of the FUs in MGs. δ is defined as, μ is the atom displacement in the time interval of 2 ns at 300 K, and RNN is the average nearest neighbor distance and chosen as the position of first peak in radial distribution function. The lower panel in Fig. δ of Cu atoms grouped with activated times. It is clearly shown that the averaged δ is monotonically increasing as activated times increase. Based on the Lindemann criterion, the melting of a crystalline solid and converting to liquid state is usually found to occur when δ reaches 0.07 or above47. It is clearly shown that the δ value of the atoms with Na = 0 is below 0.07, while those of the atoms with Na > 0 is above 0.07. We also doubled the simulation time scale to 4 ns to check its effect on the δ value, and the atom displacement was almost the same and the above results do not change. Therefore, the atoms with zero activation probability can be regarded as in solid state, while the atoms activated in dynamical tests are essentially in liquid state, especially for the atoms with much higher activation probability. In summary, FUs in MGs are indeed liquid-like.The Lindemann parameter δ < 0.07 in solid state, the motions of these atoms are mostly confined in the cages formed by their nearest neighbors and rattling. However, for the atoms in FUs with largest activation probability, their trajectories are much more broad and extensive, even far away from their initial positions. Therefore, the atoms with δ < 0.07 are indeed liquid-like. On the other hand, the liquid-like atoms in FUs tend to form clusters and distribute inhomogeneously in MGs as shown in the left lower inset in Fig. The liquid-like feature of FUs in MGs can be clearly illustrated by the typical trajectories of atoms with different activation probabilities [see the inset in Fig. In conclusions, based on statistical studies on the changes of the number of nearest neighbors of dynamical tests, we find the exact spatial location and activation probability of FUs in the initial structure of MG. We find that the FUs in MGs are loosely packed soft sites, liquid-like, participating more in the low-frequency vibrational modes and exhibiting relatively larger atomic mobility.


Individual willingness to enter competitive environments predicts career choices and labor market outcomes. Meanwhile, many people experience competitive contexts as stressful. We use two laboratory experiments to investigate whether factors related to stress can help explain individual differences in tournament entry. Experiment 1 studies whether stress responses  to taking part in a mandatory tournament predict individual willingness to participate in a voluntary tournament. We find that competing increases stress levels. This cortisol response does not predict tournament entry for men but is positively and significantly correlated with choosing to enter the tournament for women. In Experiment 2, we exogenously induce physiological stress using the cold-pressor task. We find a positive causal effect of stress on tournament entry for women but no effect for men. Finally, we show that although the effect of stress on tournament entry differs between the genders, stress reactions cannot explain the well-documented gender difference in willingness to compete.The online version of this article (doi:10.1007/s10683-016-9496-x) contains supplementary material, which is available to authorized users. We ask whether stress reactions can explain individual differences in willingness to enter competitive environments. Experimental choices of competitive over non-competitive reward schemes have been shown to predict individual differences in career choices and labor market outcomes including labor market earnings , as well as investigate whether there is a causal effect of stress on the willingness to enter a tournament (Experiment 2).We closely follow the design of Niederle and Vesterlund  and haveWe measure cortisol levels from saliva at three different points during in the experiments. Saliva was sampled using oral swabs and samples were frozen immediately after collection and subsequently sent to the company Salimetrics where each sample was analyzed in duplicate. Cortisol levels are known to rise significantly within a few minutes of the onset of a stressor. After 10–20 min most of the effect has established itself and the effect peaks after 20–30 min  before the start of the study, and immediately after Rounds 1 and 2. Immediately after Round 3 we also ask participants to guess their rank in Rounds 1 and 2 compared to the other three participants in their randomly assigned group. Participants receive $2 for each correct guess.Skin conductance is regarded as a measure of electrodermal activity which is a proxy of psychological and physiological arousal Mendes . We measAt the end of the study, participants answered a short questionnaire that among other things collected information on gender, age and the intake of hormonal medication, such as oral contraceptives. The questionnaire also elicited risk attitudes through a simple, non-incentivized question: “How do you see yourself: Are you generally a person who is fully prepared to take risks or do you try to avoid taking risks?”. The answer is on a scale from 0 (“unwilling to take risks”) to 10 (“fully prepared to take risks”). This question has been found to predict both incentivized choices in a lottery task and risky behaviors in different contexts in representative samples  water for 90 s. The treatment is widely used as a physiological stressor as the painfulness of having the hand in the cold water typically produces a sharp increase in participants’ cortisol levels  water for 90 s, which has been found to not affect cortisol levels. This randomized treatment allows us to study the causal effect of an exogenous increase in cortisol on tournament entry.As in Experiment 1, we collect saliva three times. We adjusted the waiting time for the third saliva measure so that it was taken 15 min after the end of the cold-pressor task, i.e. again close to 20 min after the onset of that particular stressor. Everything else regarding saliva measurements was done as in Experiment 1. The questionnaire for Experiment 2 was different from the one in Experiment 1 only in that it asked participants to report how hard they found it to keep the hand in the water, and to estimate how long they had the hand in the water (if they did not manage to do it for 90 s).The experiments were conducted at the Harvard Decision Sciences Laboratory in Cambridge, MA. Experiment 1 was conducted in March and April 2014 and Experiment 2 in September and October 2014. Participants were recruited through the laboratory’s subject pool and mainly consisted of students at Harvard University. The experiments were programmed in z-Tree . Participants were reminded about this on the day before the experiment, and upon arrival to the laboratory it was made sure by the experimenter that they had followed these instructions.104 people participated in Experiment 1 (50 men and 54 women). Salimetrics was able to obtain reliable cortisol estimates for all three measurements for 101 participants which is the sample we use in our main analysis. Due to problems with the equipment, skin conductance measurements for all the relevant periods were obtained for 87 participants. 105 people participated in Experiment 2 .Participants were seated in the lab one after the other, i.e. not simultaneously, and were seated in isolated cubicles in such a way that they could not see, or interact, with any other participant. It was also not possible for an individual participant to determine how many other participants were present in the laboratory at the same time. Sessions started at 1 pm and 3 pm for Experiment 1 and at 11am, 1:30 pm and 3:45 pm for Experiment 2. Cortisol has a natural diurnal pattern. We control for this by using standardized measures of cortisol as described below and by controlling for session dummies in all regressions.Harvard undergraduates and undergraduates at other top universities are a very selective group which is not representative of the population in general or even the overall student population. However, we think that they are an especially interesting group to study because they make up the professional, academic and political elites of the future. Understanding what drives their willingness to compete, and the astonishing gender difference therein, is therefore especially relevant.Focusing on levels of salivary cortisol and skin conductance is not suitable for our analysis given that levels vary strongly between individuals in ways that are unrelated to the experiment .We therefore use individual baseline levels to standardize the measurements taken during the experiment. That is, we divide the second and third measures of cortisol and mean skin conductance levels during the task performances by the measurements taken at the start of the experiment. Baseline skin conductance levels are defined as the average level of skin conductance during the period between reading the welcome screen and reading the instructions for the first round . Thus for skin conductance we focus on skin conductance response rather than skin conductance levels (see Mendes Table t test) but levels after the competition are significantly higher compared to baseline  and compared to after the piece-rate round . In a similar vein, we find that self-rated stress levels after the piece-rate round are not higher than baseline levels (p = 1.00) while competition levels are 10.6 percent higher than baseline (p = 0.02) and piece-rate levels (p < 0.01).Figure We also analyze skin conductance response and self-reported excitement as two proxies of arousal. The piece-rate and tournament response of skin conductance are defined as average skin conductance during the five-minute piece-rate and tournament performances (rounds one and two respectively), standardized by baseline levels. Figure We next explore whether stress reactions to competing in Round 2 predict willingness to enter the tournament in Round 3. Figure These results are confirmed by the probit results in Table In Fig. This is further explored in Table Given that some studies have found gender differences in the behavioral consequences of stress responses, we will now investigate whether our null result for cortisol hides a differential response of men and women to the stress reaction caused by the tournament. In Column 1 of Table While the effect of the standardized cortisol measures is close to zero for the male subsample, the gender interactions in both Column 1 and Column 2 are large and statistically significant. Women’s reaction to the cortisol responses is positive and significant in both cases. When we add both measures in Column 3, the coefficients on both gender interactions are of similar magnitude but estimates are noisier and not statistically significant. The effect of the two cortisol measurements is jointly significant for the female subsample. In Columns 4 and 5, we split the sample into those whose standardized cortisol levels after the tournament in Round 2 are below and above the median. While there is a strong and significant gender gap in the likelihood of choosing the tournament for those with a below-median cortisol response, the gender difference is much smaller for those with an above-median response.In summary, we find that for men the willingness to enter a tournament does not depend on stress reactions: those who show a strong cortisol increase when competing are just as likely to choose the tournament as those who show a weak response. For women on the other hand, those who experience a strong cortisol response are more likely to choose the tournament and this effect is strong enough that there is no significant gender gap in entry for participants with an above-median standardized cortisol response to competition. We will discuss the gender gap in tournament entry, and how it relates to stress reactions, in more detail in Sect. We now move on to investigate whether there is a causal effect of stress on tournament entry. This will also help us disentangle possible explanations for the gender difference in the predictive power of cortisol responses: is it simply the case that women who show a stronger cortisol response have a preference for competition, or does a stronger stress response actually make women compete more?Given that our third cortisol measurement was taken after the cold-pressor task in Experiment 2 (to check that the manipulation worked) we cannot replicate the cortisol analysis from Experiment 1. However, we measured self-rated stress and excitement and these measurements were taken before the stress treatment. As Fig. Figure Following our finding of a gender difference in the impact of cortisol in Experiment 1, we will now analyze whether there is a gender difference in the impact of the stress treatment. In Column 2 of Table In Columns 5 to 7, we replicate the analysis in Table Together, the results of the two experiments indicate that tournament entry for women, but not men, is partially explained by cortisol reactions. The results of the second experiment suggest that this is at least partially due to a causal effect (higher cortisol levels leading to a higher willingness to enter the tournament for women).A large literature demonstrates that women are less willing to compete than men . In this section we will first demonstrate that our data replicates this pattern. Given that we find a gender difference in the effect of stress reactions on tournament entry, we will then investigate whether stress reactions can help explain the gender gap in willingness to compete.In Table In Table In Columns 3 and 4 we add standardized cortisol at the second and third measurements. The coefficient on the female dummy hardly changes, showing that although competing is stressful and women react differently to stress than men, this has no impact on the aggregate gender gap in willingness to compete. In Columns 5 and 6, we add interactions between the standardized cortisol measures and gender. When we add both measures in Column 6, the interaction of gender with the post-competition measure is large and significant while the effect is close to zero for men, confirming that the effect of stress on willingness to compete is positive and significant for women only.The results of these regressions demonstrate why controlling for stress reactions does not change the gender gap. The coefficient on the female dummy is equal to 19 percentage points. This means that women with an average stress reaction are 19 percentage points less likely to enter the competition than men. The coefficient on the interaction is equal to 20 percentage points. This means that a woman with a stress reaction that is one standard deviation above the average is only 5 percentage points less willing to compete than the average man while a woman with a stress reaction that is one standard deviation below the average is 33 percentage points less willing to compete. In Columns 7 and 8, we show that, due to the effect of cortisol on tournament entry for women, there is a large and significant gender gap in willingness to compete only in the subsample of participants with below-median post-competition  cortisol levels.Some studies find that (acute) stress is good for productivity and performance  or to a causal effect of stress on tournament entry. We find evidence that the randomized exogenous stress treatment has a large and positive effect on women’s willingness to enter tournaments, implying a causal relationship.individual willingness to enter tournaments, it cannot explain the aggregate gender gap in tournament entry: controlling for cortisol reactions has no impact on the overall gender gap. However, our results provide the new insight that women who have a strong cortisol reaction to competing are almost as likely as men to enter the tournament, while women with a weak cortisol reaction are even less likely to choose the tournament than the average woman.In order to design and implement adequate policies that address gender differences in labor market outcomes, it is important to know the mechanisms underlying the gender gap in willingness to compete. To what extent do our results indicate that stress reactions can “explain” the gender gap in competitiveness? We find that for women, willingness to compete is more sensitive to cortisol changes than for men. While this furthers our understanding of Cortisol prepares the individual for an oncoming confrontation or fight and it therefore makes sense that those who experience a stronger cortisol reaction are more willing to face a competition. The question is why we see evidence of this only for women. Potentially, we do not find this effect for men because of their already very high willingness to compete (many men enter the tournament in Round 3 with very low chances to win). It is therefore possible that whereas men compete no matter what in this type of setting, for women stress reactions help to overcome an inclination to avoid competitive situations.While acute stress reactions can be beneficial, chronic stress is associated with a long list of adverse health outcomes. If our result that competitive payment schemes lead to increased stress for the average individual extrapolates to the workplace, it could mean that competitive remuneration schemes and promotion mechanisms have potential implications for long-term health outcomes of employees. This, in turn, opens up an interesting avenue for research into not only the performance effects but also the health consequences of different payment schemes and other workplace practices.Supplementary material 1 (DOC 30 kb)Below is the link to the electronic supplementary material.


Using 3D scanning a stereolithography (stl) image was produced of a canine pelvis and this was subsequently refined in computer aided design (CAD). Using the CAD files, the images were imported in MSC Marc software to produce a working finite element (FE) model with 3 dimensional tetrahedral elements with linear shaped functions. The dimensions of a precontoured pelvic osteotomy plate with eight screws and a twisted seven screw straight plate were used to build the 2 fixations implants for the FE models. An equivalent load of 300 N was applied progressively on all FE models in order to facilitate its convergence. The load was applied in a distributed manner on the femur-hip joint contact area in order to simulate the actual behavior of the joint. The aim of the present study was to analyze the difference in stiffness and behavior under loading between a lateral vs ventral plate fixation, with unlocked screws and different gap scenarios, for stabilization of a pelvic osteotomy using finite element analysisFrom both configurations the maximum displacement of the ventral plate with 7 screws without gap had a value of 1.988 mm, while in the DPO plate had a maximum displacement of 2.191 mm. The load applied for each of the different configurations studied when a gap of 1° was considered and also when a condition of no gap was considered. The ventral plate was stiffer than the lateral plate when a gap was not present. When the gap was closed in the ventral plate, the stiffness increased until a point that remained constant.Ventral plate fixation can be as or more stiff as lateral plate fixation and provides flexible fixation. This behavior should reduce screw loosening. Using ventral plate fixation is recommended to reduce screw loosening or failure. Thus,Cadaver pelvis was used to scan and build pelvis model. Artificial bone was used in lab testing. Sourcing of materials was from a dog that died of natural causes and the artificial bones from Sawbones Company (Sweden). Using 3D scanning a stl image was produced of a canine pelvis  and this was subsequently refined in CAD. Using the CAD files, the images were imported in MSC Marc software to produce a working finite element (FE) model with 3 dimensional tetrahedral elements with linear shaped functions. The dimensions of a precontoured pelvic osteotomy plate with eight 3 mm screws and a twisted seven 3 mm screw straight plate were used to build the 2 fixations implants for the FE models. The screws were fixed to behave as unlocked screws. Before the FE simulations were run validation bench tests were carried out using artificial cancellous bone blocks . Osteotomy and plate fixation were set up in the 2 methods: 1. Ventral plate fixation 2. Lateral plate fixation. The load required to cause a deformation of set amount was recorded for 3 experiments for each plate position. This data was used to validate the FE simulation for all configurations.Finite Element (FE) models for each of the plate configurations studied were built to determine and verify the joint stiffness according to the applied load. Each of the FE models proposed that formed each configuration considered the osteotomised pelvis, the different plates and the screws. The geometric models used in the FEM discretization process of each of the parts  were generated by measurements from actual samples of plates and artificial osteotomised pelvis. Due to the fact that the surface of the artificial osteotomised pelvis is very irregular; a 3d scanner was used to obtain its geometrical model. The remaining parts (plates and screws) were modeled directly in the FE MSC Marc software used. For all plate configurations studied, three dimensional FE models with 4-node isoparametric tetrahedral elements were used to mode the pelvis, plates and screws. An average element size of 0.6 mm was used for the cortical and cancellous bone, while for the plates and screws element sizes were for 0.8 mm and 0.9 mm respectively. An outer thin cortical bone and an inner cancellous bone were used to model the pelvis according to the literature. The material properties used for the cortical bone were E = 17,000 MPa and ν = 0.25, while for the cancellous values of E = 150 MPa and ν =0.3 were used. A titanium alloy with E = 107,000 MPa and ν = 0.34 was used for modeling of the plates and screws. The cortical and cancellous bone topography in the osteotomised area of the FE pelvis model was the same for all plate configurations  between the different parts in which the osteotomised pelvis is divided. Figure Figure Figure The maximum displacement obtained from the osteotomised pelvis by applying a maximum load of 300 N when a ventral plate of 7 screws without gap Fig.  and a DPThe ventral ilium is the tension surface of the ilium and therefore is the natural choice for plating. During pelvic osteotomy the ventral ilium is exposed to allow retraction of the soft tissues medially, so there is no extensive extra tissue retraction to enable use of the ventral ilium for fixation. One of the authors (WMcC) routinely adds a ventral plate fixation to triple pelvic osteotomy fixation in giant breeds dogs, and this is a topic of further investigation.Loss of fixation is the core issue in pelvic osteotomy complications. In non-locking plate fixation, the screws loosen in the cranial segment , whereasFrom this study it is observed that when a gap exists the fixation exhibits lower stiffness than the configuration that has no gap. Likewise, an increase in stiffness as the applied load increases is observed for ventral plate configurations. This variation in the stiffness is mainly due to the fact that the gap is closed at the ventral configuration as the load is applied, while in the DPO configurations type, this gap stays open as the load is applied. This means that DPO plates have a high stiffness in the area close to the fracture and prevent the gap from closing as the load increases. From these figures it can be deduced that the configuration of ventral plate of 7 screws without gap presents a higher stiffness than the configuration of DPO plate without gap. When the gap is closed in the ventral plate, the stiffness increases until a point that remains constant. The gap is important because depending on the dog size, the stiffness could take a low value or a high values and it is like a variable joint. The ventral plate has a dynamic aspect to its fixation. This effect does not occur on the pelvic osteotomy plate in which the stiffness keeps constant for all loads studied. Therefore, there is increased risk of screw loosening in the lateral plate.The limitations of this study are that finite element verification using artificial bones may not reflect actual behavior bone loading in vivo.In conclusion, this study shows that ventral plate fixation can be as or more stiff as lateral plate fixation and provides flexible fixation. Using a ventral plate fixation is therefore recommended to reduce screw loosening or failure in double pelvic osteotomy to correct hip dysplasia in young dogs.


Ammotragus lervia) n = 12, little penguins (Eudyptula minor) n = 10, ringtail lemurs (Lemur catta) n = 8, red tailed black cockatoos  n = 7, Indian star tortoises (Geochelone elegans) n = 5 and red kangaroos (Macropus rufus) n = 5 were presented with a stationary object, a moving object and a mirror. Having objects with different characteristics increased the likelihood individuals would find at least one motivating. Conspecifics were all assessed simultaneously for time to first orientate towards object (s), latency to make contact (s), frequency of interactions, and total duration of interaction (s). Differences in curiosity were recorded in four of the six species; the Barbary sheep and red tailed black cockatoos did not interact with the novel objects suggesting either a low level of curiosity or that the objects were not motivating for these animals. Variation in curiosity was seen between and within species in terms of which objects they interacted with and how long they spent with the objects. This was determined by the speed in which they interacted, and the duration of interest. By using the measure of curiosity towards novel objects with varying characteristics across a range of zoo species, we can see evidence of evolutionary, husbandry and individual influences on their response. Further work to obtain data on multiple captive populations of a single species using a standardised method could uncover factors that nurture the development of curiosity. In doing so, it would be possible to isolate and modify sub-optimal husbandry practices to improve welfare in the zoo environment.The personality trait of curiosity has been shown to increase welfare in humans. If this positive welfare effect is also true for non-humans, animals with high levels of curiosity may be able to cope better with stressful situations than their conspecifics. Before discoveries can be made regarding the effect of curiosity on an animal’s ability to cope in their environment, a way of measuring curiosity across species in different environments must be created to standardise testing. To determine the suitability of novel objects in testing curiosity, species from different evolutionary backgrounds with sufficient sample sizes were chosen. Barbary sheep ( Individuals in a single population will often have different behavioural responses when faced with the same conditions . IndividDanio rerio) (Curiosity has been described as a driving force behind increased interaction with one’s environment . In humao rerio) , furtherAmmotragus lervia), little penguins (Eudyptula minor), ringtail lemurs (Lemur catta), red tailed black cockatoos , Indian star tortoises (Geochelone elegans) and red kangaroos (Macropus rufus) were selected as there is currently a lack of research in curiosity involving these species, and there were sufficient sample sizes available for testing within the zoo. Having such a diverse range of species also ensures representation of animals with an assortment of sensory and behavioural differences.The aim of this study was to assess which types of novelty tests would be suitable to assess curiosity in a variety of zoo species. Here we use the following variables to determine the level of curiosity: latency to first orient towards the object, latency to make contact, frequency of interaction, and total duration of interaction with novel objects. Barbary sheep  the ability to identify individual differences within the group; (2) have objects that appeal to the physical capabilities in a range of species; (3) generate a novel response, without eliciting high levels of visible stress  or disrupting routines. Three different novel objects were used to fit these criteria: a stationary object, a moving object and a mirror. Three objects with different physical characteristics were chosen to increase the chances that animals with different sensitivities and interests would be motivated to investigate at least one of them. All objects were visual in nature as other sensors would be difficult to measure. The sizes of the stationary and moving objects were scaled to approximately one third of the average height of the species to control for the size differences between the species. The mirror was scaled down for the tortoises only as the larger mirror could not fit in the enclosure.The stationary objects, made by the primary researcher, were solid fluorescent orange rectangular prisms made from non-toxic recycled cork, which was soft enough to not damage either the animals or the enclosure. The softness of the object was a consideration for future work where particularly strong animals, like great apes, may throw it. The colour was chosen as it was not routinely found in the natural environment and for dichromats, the fluorescence would be different from the surrounding environment. It has been shown in horses (known dichromats), that they are able to discern differences in colour based on brightness . ObjectsThe moving objects, made by the primary researcher, were black and white striped stepped toroidal shapes made by layering expanded polypropylene foam (non-toxic and soft). As with fluorescence, sharp recurring lines are not often found in the natural environment, and the appearance of black and white should not be altered too much in the event of differing visual capabilities. A rope through a hole in the centre of the object was used to move it. The moving object was intended to attract animals that are more stimulated by movement or that are bold enough to overcome the uncertainty of the movement to investigate. Objects in four different sizes were created with the objects measuring 33 × 33 × 33 cm  14.5 × 14.5 × 14.5 cm  8.5 × 8.5 × 8.5 cm (little penguins) 4.5 × 4.5 × 4.5 cm (star tortoises) ., red tailed black cockatoos and red kangaroos. Two small circular mirrors of 11.5 cm diameter were used for the star tortoises. The reflective surface of the mirror allows for a feedback element that the other two objects lacked, adding a different characteristic to the test; possibly attractive to social animals.A 1 × 1.5 m silver acrylic mirror was used for the Barbary sheep, little penguins, ringtail lemursNovel object testing was performed over three consecutive days with a different object being tested each day. The order in which the objects were presented was the same for each species . On each day, the object was placed in the enclosure within sight of the normal feeding area by a keeper or experimenter depending on availability. Testing was performed before the zoo opened to ensure that responses were not influenced by the presence of visitors. As this is a feeding time, the animals were all present except for one case. Due to large enclosure size, only three of the five kangaroos were present for the first stationary object test. To rectify this problem, footage from the first test was used for the three individuals present and then the stationary object was represented on a separate day when the two missing individuals were present and the others were not. Reactions were recorded for the two missing individuals during the second test. Testing began once the keeper had left the enclosure, and ran for 15 min before the objects were removed. The moving object was manually moved, by the experimenter from outside the enclosure. The object was moved approximately 5 cm every 60 s by pulling the rope attached to it. Each object was presented only once to control for the possibility of habituation.Conspecifics were assessed at the same time (with the exception of the stationary object in the red kangaroos) and behaviours of all individuals were digitally recorded for 15 min and analysed for the following: time to orient towards object (s), latency to make contact (s), frequency of interaction and total duration of interaction (s). In cases where an individual did not make physical contact with the object, a minimum distance in body lengths was estimated. The maximum estimate for this was four body lengths. Interaction with both the stationary and moving object was defined as when the animal made physical contact with the object, whereas interaction with the mirror included contact as well as the animal following its own movements in the mirror without contact.Means and standard deviations were calculated for latency to contact (s), time to orient (s) and duration of interaction (s) for each species during each of the three novel object tests. Graphical representations of the ‘time to orient’, ‘latency to contact’ and ‘duration of interaction’ were used to compare differences between species and the tests. Qualitative descriptions of the observations and comparisons between species were the primary reporting method used in this study and the graphical representation with summary statistics helps support these.The results of the novel object tests for all six species are listed in The stationary object elicited a range of responses between species. Neither the Barbary sheep nor the red tailed black cockatoos approached or interacted with the stationary object and variation in individual responses was negligible . The timBarbary sheep were slower to orient towards both the stationary object and mirror compared to the moving object , though As with the stationary object, the Barbary sheep and the red tailed black cockatoos showed no approach or interaction with the mirror . The timUsing the three novel objects, the individual behavioural responses of six different species were evaluated to ascertain if it was possible to: (1) identify individual differences within the group; (2) motivate animals to notice and possibly interact with objects; (3) suit the physical capabilities of a range of species without eliciting high levels of visible stress  or disrupting routines. By addressing these three criteria for the novel objects we decrease the likelihood that animals which do not interact with any of the objects do so due to a low level of curiosity and not due to the object being irrelevant to the species or due to fear. Using the three objects, individual variation in response to the objects within the normal enclosure was seen for four of the six species tested . For the red tailed black cockatoos and Barbary sheep, none of the novel objects elicited any interaction so individual variation could not be assessed. The variation in response between and within species shows how important it is to have multiple objects with varied characteristics to be able to correctly identify curiosity in animals across different species.In studies involving animal motivation and response such as this one, evolutionary and ecological variation is important. The Barbary sheep and the red-tailed black cockatoos are the two species which displayed avoidance behaviours with all three objects. While these species are very different they do share a few similar ecological traits, which may have contributed to the similarity in responses. In wild conditions Barbary sheep have large home ranges  as do reChelonoidis carbonaria, , additional objects that cause variation in individuals may show the effect of personal experience or personality on behaviour. Before implementing a test for curiosity, it would be advisable to identify multiple motivating stimuli within the species being studied to increase the chances of accurately capturing curiosity. This can be done by combining knowledge of both the sensory limitations of the species and the ecological niche they occupy in the wild, as well as studies like this one to identify motivating characteristics of objects. By identifying common factors, such as husbandry practices or ecological similarities, shared by individuals and species which display curious and well adjusted behaviours towards novelty we may be able to modify management practices to improve the lives of captive animals.10.7717/peerj.4454/supp-1Supplemental Information 1Click here for additional data file.10.7717/peerj.4454/supp-2Supplemental Information 2Layouts of enclosures and novel object placement. Objects identified as moving (M), stationary (S) and mirror (X). a) little penguins b) Barbary sheep c) star tortoises d) ring tailed lemurs e)red-tailed black cockatoos f) red kangaroos.Click here for additional data file.


The effective modelling of high-dimensional data with hundreds to thousands of features remains a challenging task in the field of machine learning. This process is a manually intensive task and requires skilled data scientists to apply exploratory data analysis techniques and statistical methods in pre-processing datasets for meaningful analysis with machine learning methods. However, the massive growth of data has brought about the need for fully automated data analysis methods. One of the key challenges is the accurate selection of a set of relevant features, which can be buried in high-dimensional data along with irrelevant noisy features, by choosing a subset of the complete set of input features that predicts the output with higher accuracy comparable to the performance of the complete input set. Kohonen’s self-organising neural network map has been utilised in various ways for this task, such as with the weighted self-organising map (WSOM) approach and this method is reviewed for its efficacy. The study demonstrates that the WSOM approach can result in different results on different runs on a given dataset due to the inappropriate use of the steepest descent optimisation method to minimise the weighted SOM’s cost function. An alternative feature weighting approach based on analysis of the SOM after training is presented; the proposed approach allows the SOM to converge before analysing the input relevance, unlike the WSOM that aims to apply weighting to the inputs during the training which distorts the SOM’s cost function, resulting in multiple local minimums meaning the SOM does not consistently converge to the same state. We demonstrate the superiority of the proposed method over the WSOM and a standard SOM in feature selection with improved clustering analysis. Clustering is one of the most widely used data analysis methods for numerous practical applications in emerging areas . ClusterThe self-organising neural network map (SOM) by Kohonen  has beenOne of the biggest drawbacks of the SOM algorithm is its inability to automatically identify the features that are relevant for analysis and discard the irrelevant inputs that negatively distort the analysis result . In an aThis paper investigates the application of an existing weighted method approach (WSOM) and proposes an alternative approach for identifying the key features in a number of artificially produced datasets and the real world dataset used in the original WSOM study –8. The sThe self-organising neural network map (SOM) is an unsupervised artificial neural network learning method trained to produce a low-dimensional representation of high-dimensional input samples .A typical SOM consists of the computational layer (map) and the input layers as shown in Fig. x =  for an input sample where d denotes sample dimensions and i the sample number and n denoting the total number of samples.The input layer comprises of the source nodes representing the sample’s features/attributes. There are as many weights for each node as there are number of features (dimensions) in the input layer, represented in the form of an input vector, i.e. j, on the map and associated with a weight vector, i.e. Wj = {wji : j = 1,  … , n; i = 1,  … , d} , the size of which is equal to the dimension of the input vector. The set of weights W parameters are determined by iteratively minimising the cost function below;The computational layer (map) consists of neurons placed in nodes of a 2-dimensional grid (lattice); each neuron is identified by its index position, i.e. nth training step, the Gaussian neighbourhood function is calculated for the map; this is expressed as:At every j) on the map and the winning unit c (xi) at the nth training stepj) to the winning unit c (xi) on the map.σ(n) is the effective width of the topological neighbourhood at the nth training step; this serves as the moderator of the learning step during training iterations. The size of the effective width shrinks with time to facilitate the convergence of the map.α(n) is the learning rate that depends on the number of iterations (n); this is initialised to a value of around 0.1 which decreases from αmax to αmin.WhereIt is possible to use the results of a trained SOM in order to estimate the relevance of feature variables (weights). This is achieved by the use of the quantization error method  which isIrrelevant input features are one of the major factors that distort the ability of learning algorithms for pattern recognition in data, as investigated by –13. NumeFilter methods aim to use statistical approaches to identify what inputs are important and are independent of the classifier, usually applied in the data pre-processing stage prior to training. Some of the commonly used filter methods include the RELIEF algorithm , correlaWrapper methods unlike filter methods aim to identify important inputs by searching for the best subset of features that produce the highest model classification accuracy. Commonly used wrapper methods include the recursive feature elimination method (RFE)  and exhaThe embedded methods learn about the importance of inputs from the model’s training process and one of the examples of this method is the weighted self-organising map (WSOM)  that is Most of the above methods require manual experimentation that consumes the bulk of the effort invested in the entire clustering analysis, with the exception of the embedded methods that identify important inputs from what the model has learnt. These latter methods are the area of focus in this study which aims to achieve the goal of a fully automated clustering process. We are particularly interested in the use of the self-organising map for automated feature selection due to its powerful topology preservation property, with the neighbourhood function Eq.  that enaOn completion of SOM training which is achieved using the batch training method , the nodMj be set of the training samples xi  mapped to node j, and the quantization error for node j is calculated after SOM training as follows:Let The weight features with the lowest quantization error are expected to be the features whose corresponding input sample features are most relevant when comparing the samples against their winning nodes. A further analysis was carried out on the quantization error values for all the node weights in order to automatically separate the group of the relevant inputs from the irrelevant inputs, a parametric statistical test with median split was carried out on the quantization error values to differentiate the group of high values (as irrelevant features) from the group of low values (as relevant features). Since there is no reliance on a hard-coded threshold value to determine irrelevant and relevant features, this means that this step could be used for any amount of data features and results in a fully automated step for this aspect of the process.The weighted SOM (WSOM) function proposed by  is anothΕ = { xi; i = 1,  … , Ν} a set of observations, where each observation xi =  is a vector in Let j has prototype weights  wj = , and a single random weight is assigned to for each input attribute such that; πd = .Each node j in a trained SOM.This method attempts to find the relevance of all the weights of a single vector which are applied against the whole set of input weights but is not able to determine the relevance of an individual weight of each node W and π parameters are determined by iteratively minimising the cost function as follows:The set of weights Rgvw  is as described in Eq . 4. The algorithm is optimised by finding the W , π then these values are modified in order to reduce Rgvw , until the minimum of the cost function is reached.The cost function The method uses the steepest descent algorithm in order to optimise its cost function;{}The gradient descent minimization of the function can be implemented as;P0, and moving from Pi to Pi + 1 in the direction of the local downhill gradient −∇f(Pi) for each iteration of line minimization.The steepest descent algorithm which is utilised by the WSOM method searches for the minimum of a function by computing the gradient of the function, starting at a random point The steepest descent method is guaranteed to find a solution for quadratic functions, which are convex-shaped functions with a single minimum that is equal to the global minimum  as illu. For proFor a full description of the WSOM process, the reader is directed to , 8. In tIn order to assess the efficacy of the WSOM method against a standard SOM implementation, a number of synthetic datasets were developed which had different features, starting with a simple dataset with a small number of attributes and moving to datasets with a larger number of inputs and additional noise. All data sets had equal class distribution (i.e. same number of samples for each class), and normalised, with the exception of Synthetic_Data04 and Synthetic_Data05. These datasets are discussed more fully in the tables. The use of synthetic data rather than real data sets of this type is very important as it allows a full assessment of how well the techniques work and what type of problems they can solve, and where they may encounter difficulties if any.In addition, the dataset used in the original WSOM paper was obtained which is a real world dataset of waveform data and is also described in Table As both methods rely on a random process, the performance of the algorithms was measured based on results of 10 runs for each of the methods on the synthetic datasets, and the results of these runs are shown in Tables To) = 10.0 , cooling rate (α) = 0.99 and maximum iteration (Maxtime) = 1000.However, in order to check whether the weighted SOM cost function Eq.  for SyntIf a cost function has a single global minimum, the best combination of weight values for different runs of the algorithm will be expected to be within the same region and to have a positive linear correlation when compared against each other. Otherwise, if the cost function has multiple local minimums, then the best combination of weight values would be in different regions for different runs of the algorithm and will not be correlated.The normalised correlation matrix of the final weights from the simulated annealing algorithm was computed to show the similarity of the weights produced from six runs of the algorithm against each other; the same experiment was carried out on the standard SOM cost function for comparison.π. This step is required since the global weights and WSOM node weights are linked as described in the cost function, and it is possible due to the random nature of the process that different values could be arrived at for these variables whilst still mapping against similar input samples and the node weights could therefore be different from one run to the next.When undertaking the correlation analysis for the WSOM method, the raw SOM weights cannot be used directly but must be divided by the corresponding global weights In addition, the problem with direct comparison of weights at the same index for the six different simulated annealing runs is that nodes are not necessarily localised to a specific index. In a single run, a node might appear in the first index, whilst in a separate run, the same node might appear in a different index. As such, direct comparison of the weights infers the comparison of random unrelated nodes, which are most likely to be not correlated at all times.To overcome this problem, the indexes of all the nodes weights was re-arranged to correspond to the best matching positions for all the nodes from the six different simulated annealing runs before carrying out the correlation test on the weights.E be set of weight values for a given SOM run . Nodes are correlated if their correlation coefficient is different from zero, and therefore means there is linear relationship between the nodes. There is no correlation for nodes with correlation coefficients close to zero.A null hypothesis test ρ for a given run of the self-organising process compared against another on Synthetic_Data01. The red line on the plots at 0.5 and −0.5 indicate the respective boundaries for positive and negative correlations, with no correlation shown at or around 0.The analysis of the correlation results can be seen in Figs. The bars above the red line indicate the pairs of node weights with correlations significantly different from 0, which implies that there is a significant linear relationship between the weights of the various runs . On the other hand, the bars below the line indicate the pairs of node weights with a correlation coefficient that is not significantly different from 0, which implies that there is no significant linear relationship between the weights .The correlation matrix for the standard SOM Fig.  weights In summary, it can be concluded that the simulated annealing algorithm with the standard SOM cost function finds similar solutions in the majority of the different runs. On the other hand, the algorithm with the weighted SOM cost function finds different solutions for most of the runs, which is most likely to be as a result of multiple local minimums in the cost function.The results given in Tables As seen in Table For the more complicated dataset with overlapping class definition (Synthetic_Data03 and Synthetic_Data04), the analysis of the standard SOM’s training result with the quantization error also failed to identify what was important for the training, as presented in Tables As discussed in Section As seen from the performance of methods on Synthetic_Data03 and Synthetic_Data04, identifying feature relevance based on classification results of the SOM does not provide good results when the SOM has not classified the samples correctly. The results also show that complete removal of the identified irrelevant input features produces worse class identification as shown in runs 1 and 4 in Table A further experiment on the WSOM method with the WaveForm data that was used in the original WSOM paper has revealed that the method is able to group the dataset occasionally (i.e. at some random iteration) during multiple runs, but that other runs show a different set of weightings with a different solution. This provides further evidence to support the conclusion reached of multiple local minimums in the method’s cost function. The same SOM size of 26 × 14 as used by  was usedThe quantization error between the weight values and their matched classified input samples shows more potential for identifying important features; however, these results show that this approach will only work for certain types of data. One of the limitations of the proposed method is its inability to correctly identify irrelevant inputs for a SOM with inappropriate topology size and having highly misdiagnosed classes (i.e. multiple classes mapped to a single node). This implies the requirement for an incremental system with the ability to automatically adjust the SOM’s topology size during training, to allow the spread of class samples across nodes for more accurate input relevance analysis. It is also interesting to note for some of the synthetic datasets that the quantization method correctly identifies the important features despite not being able to correctly classify the groupings in the data. This suggests the need for an additional layer that uses the relevance information from the feature selection method to prune or suppress the irrelevant features and guide the remapping of a self-organising system with the relevant features for a higher clustering performance to achieve a fully automated clustering process, and this will be the subject of future work.