**3. Discussion**

In this study, we have identified a corkscrew region in ABCG transporters whose conservation suggests a role in substrate specificity. Though no experimental work has yet been carried out to deliberately explore the functional effects of mutations to the corkscrew, some of its residues have been mutated as part of other studies, or observed as naturally occurring single nucleotide polymorphisms (Supplementary Table S7). Particularly notable in this regard is Cox et al. 2018 [37], which includes mutagenesis of five residues with the conservation pattern (ABCG1, ABCG4), (ABCG2), (ABCG5), (ABCG8), including the very well-studied residue R482A. Mutations of three of these five (T402A, S440A, and I543A) compromise transport of both mitoxantrone and pheophorbide A. T402 mutations have previously been described [38,39] as having decreased transport activity. Several others have observed diminished transport by ABCG2 with mutation of these residues, including mutations to S384, T434, and S441 [38,40–45]. Recently, diminished ATPase activity has been observed in ABCG5 [20] with mutation of A540 to phenylalanine, a residue also sharing this conservation pattern.

Other mutagenesis studies have included residues identified in this analysis as conserved in all aligned proteins. Many of these result in poor expression of mature protein [34,37,46], such as mutation of E138 in ABCG2 [34]. Though some have discernible effects on transport, surprisingly, mutation of P480 to alanine, despite being a mutation to a residue conserved in all sequences used in this analysis, and with dramatic chemical differences, has no effect on transport in ABCG2 [37,47]. This provides a cautionary example that care must be taken when interpreting these results. Other mutations to these positions are found as variants in vivo, some causing sitosterolemia, such as mutations

to E146 in ABCG5, analogous to E138 in ABCG2 [48–57]. A summary of this, including disease-causing variants, can be found in the Supplementary Materials.

Comparing the ways mammalian ABCGs are conserved shows functionally and evolutionarily important signatures that are well represented in previous mutagenesis studies. Differences in the substrate specificity of subfamily members correspond to patterns of conservation that, when mapped onto 3D structures, are ideally placed to modulate the communication of conformational change between domains, suggesting that this may be responsible for some of the differences in substrate specificity. Particularly, grouping ABCG1 and ABCG4 together identifies a pattern, which we have named the corkscrew network. This is also important to a previously identified structural feature, the polar relay, and suggests a unifying hypothesis for substrate specificity in the subfamily: that allostery in this network underlies functional divergence. Appropriate experiments to test the importance of the corkscrew network of residues to differences in ABCG function promise to reveal interesting factors in their transport mechanism.


*Article* **On the Validation of Claims with Excess Zeros in Liability Insurance: A Comparative Study**

#### **Marjan Qazvini**

Department of Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia, 62200 Putrajaya, Wilayah Persekutuan Putrajaya, Malaysia<EMAIL_ADDRESS>
Received: 27 May 2019; Accepted: 19 June 2019; Published: 30 June 2019

**Abstract:** In this study, we consider the problem of zero claims in a liability insurance portfolio and compare the predictability of three models. We use French motor third party liability (MTPL) insurance data, which has been used for a pricing game, and show that how the type of coverage and policyholders' willingness to subscribe to insurance pricing, based on telematics data, affects their driving behaviour and hence their claims. Using our validation set, we then predict the number of zero claims. Our results show that although a zero-inflated Poisson (ZIP) model performs better than a Poisson regression, it can even be outperformed by logistic regression.

**Keywords:** validation; generalised linear modelling; zero-inflated poisson model; telematics

#### **1. Introduction**

There are two main types of machine learning: (i) predictive or supervised learning in which the machine trains data and learns the relationship between inputs and outputs and (ii) descriptive and unsupervised learning in which machine uses the inputs and discovers the outputs (Murphy 2012). Classification and regression are two supervised learning approaches which are well-known in general insurance. One of the objectives of the insurance companies is to charge premiums which is commensurate with the risk characteristics of their policyholders and for this, they classify the policyholders into homogeneous groups according to, say, age, sex, type of policy, subscription to telematics-based insurance pricing (see, Section 3), etc. Regression analysis and its extensions such as generalised linear modelling (GLM) are strong tools in insurance pricing. Unlike regression models, GLM is not constrained to a normal distribution and can be applied to any distribution from an exponential family. For example, a logistic regression model handles binary responses and thus is suitable for a Bernoulli distribution and a Poisson regression model applies to count data and deals with discrete random variables. GLM has long been used in actuarial practice to model claims amounts and claims frequency in the insurance portfolio (Haberman and Renshaw 1996; McCullagh and Nelder 1998).

In this study, we consider motor third party liability (MTPL) insurance. One of the problems in modelling claims frequency in this class of insurance is the number of zero claims and building a model that can capture all these zero claims. Zero claims in MTPL does not necessarily mean that there has been no accident during the term of a policy, rather it means that there has been no reported accident to the insurance company. This particularly happens under a no claim discount (NCD) system as some policyholders, known as *bonus hunger*, prefer to benefit from a discount by not reporting a claim. Another problem which is related to the previous one is the problem of *over-dispersion*. In a Poisson regression model, claims are distributed according to a Poisson distribution with equal mean and variance. Therefore, to build an appropriate model we need to test our dataset for the presence of over-dispersion (Peruman-Chaney et al. 2013; Wilson and Einbeck 2018). Binomial regression, negative binomial (NB) regression and zero-inflated Poisson (ZIP) model are techniques that can handle over and under dispersed data with the latter being able to distinguish between structured and unstructured zeros. Lambert (1992) considers a ZIP model where the probability of only possible observation, i.e., 0 and the parameter of a Poisson distribution depend on some covariates. Lambert (1992) applies this technique to model the number of defects in manufacturing. Since then, this model has been applied in different settings including insurance pricing. For example, Lee et al. (2002) use this model to analyse the impact of lifestyle and motivations on car crashes involving young drivers in Australia. Yip and Yau (2005) use ZIP to model claims frequency in car insurance. They compare different types of zero-inflated count models and conclude that a zero-inflated double Poisson regression model is a good fit for their dataset. Boucher et al. (2007) compare zero-inflated, hurdle and compound frequency models and conclude that the bonus rate is an important factor for policyholders to report the claim. In another study, Boucher et al. (2009) consider the problem of bonus hunger and construct a ZIP model to distinguish between the distribution of the number of claims and the number of accidents.

Model fitting and the selection of risk factors can be challenging in some cases. There are some papers that consider these problems. For example, Tang et al. (2014) propose a method to determine the variables in a ZIP model. They combine EM algorithm and adaptive LASSO and find that their technique performs better for the non-inflated part of the ZIP regression. Liu and Pitt (2017) also apply LASSO and ridge regression to address this issue in a bivariate negative binomial regression model. See, also, Cantoni and Auda (2018), Chowdhury et al. (2019) and Chen et al. (2019) among others.

The impact of mileage as a risk factor is considered by Lemaire et al. (2015). They conclude that annual mileage is a powerful predictor of the number of claims at-fault. Tselentis et al. (2017) provide a review of some Usage-based motor insurance (UBI) including Pay-as-you-drive (PAYD), Pay-how-you-drive (PHYD) and Pay-at-the-pump (PATP). PATP is a pricing method that considers fuel consumption as a rating factor but did not get enough attention from researchers. These new pricing methods require telematics data. In recent years, there is much research on telematics data and mileage based (MB) insurance. Boucher et al. (2017) apply generalised additive models and consider both time and mileage in insurance pricing. See the following papers on the relevance of including the mileage as a risk factor (Ayuso et al. 2019; Guillen et al. 2019; Verbelen et al. 2018).

In addition to regression analysis, neural network, decision tree, random forest and boosting algorithms such as XGBoost, etc., are other machine learning techniques that can be applied to model claims frequency and insurance pricing. However, although these models have good predictive power, unlike regression models, it is difficult to interpret their parameters and their computation time is long. Weerasinghe and Wijegunasekara (2016) study neural network, decision tree and multinomial logistic regression models. Their results show that the neural network has the best predictive performance among the three models. However, they state that to understand the relationship between independent and dependent variables, the logistic regression is the best model. Fauzan and Murfi (2018) compare XGBoost, neural network and random forest models and find that in terms of the Gini index, XGBoost is a more accurate algorithm. See, also, Spedicato et al. (2018) and Gao et al. (2019) and the references therein.

In this study, we consider the classical Poisson and logistic regression and compare our findings with a ZIP model. We divide our dataset into training and validation (hold-out) set to predict the number of zero claims. This paper is organised as follows. In the next section, we present models and notation. Section 3 discusses our dataset. In Section 4, we build our models and in Section 5 we test their validation. Finally, Section 6 concludes.

#### **2. Methodology and Notation**

Risk classification is an important concept in general insurance pricing. An insurance company tries to determine the insurance premium according to risk characteristics of policyholders such as age, sex, type of policy and car model, etc. Regression analysis is a well-known technique to incorporate such risk (rating) factors. In this section, we review Poisson regression, Logistic regression and ZIP model.

Let *yi* ∈ {0, 1, 2, ... } be a dependent or response variable such as number of claims, for *i* = 1, ... , *n* that follows a Poisson distribution with parameter *λi*. Assuming a log link function and that *λi* is a linear combination of rating factors *β*0 + *β*1*xi*1 + ··· + *βkxik* we have

$$E[y\_i|\mathbf{x}\_i] = \lambda\_i = \exp\{\beta\_0 + \beta\_1 \mathbf{x}\_{i1} + \dots + \beta\_k \mathbf{x}\_{ik}\}, \quad y\_i \sim \text{Pois}(\lambda\_i) \text{ for } i = 1, 2, \dots, n. \tag{1}$$

When we consider the average number of claims for each policyholder, we need to specify a unit measure or exposure. We cannot expect two policyholders with the same risk characteristics, but different terms, to be equally risky. Normally, the length of coverage is considered as an exposure. However, in recent years, it is argued that even if policyholders join at different times, some may drive fewer distances than others. Therefore, when such information is available as in telematics data, mileage travelled is considered as a more appropriate exposure (Guillen et al. 2019). In our study, all policyholders are under observation for one year and thus the exposure for each policyholder is 1.

We use logistic regression when *yi* ∈ {0, 1} is a binary, also called dichotomous variable. In that case,

$$E[y\_i|\mathbf{x}\_i] = \pi\_i(\mathbf{x}) = \mathbf{g} \left(\beta\_0 + \beta\_1 \mathbf{x}\_{i1} + \dots + \beta\_k \mathbf{x}\_{ik}\right)$$

where *g* is a logistic link function to ensure that *πi* is between 0 and 1. Hence

$$\pi\_i(\mathbf{x}) = \frac{\exp\left\{\beta\_0 + \beta\_1 \mathbf{x}\_{i1} + \dots + \beta\_k \mathbf{x}\_{ik}\right\}}{1 + \exp\left\{\beta\_0 + \beta\_1 \mathbf{x}\_{i1} + \dots + \beta\_k \mathbf{x}\_{ik}\right\}}\tag{2}$$

or, more commonly

$$\log\left(\frac{\pi\_i(\mathbf{x})}{1-\pi\_i(\mathbf{x})}\right) = \beta\_0 + \beta\_1 \mathbf{x}\_{i1} + \dots + \beta\_k \mathbf{x}\_{ik}.$$

In this paper, we use logistic regression to answer the question: "What is the probability of a claim (*yi* = 1) and zero claims (*yi* = 0) for a given policyholder with particular risk characteristics?"

When the mean and variance of the underlying population is not equal, the assumption of a Poisson distribution is not suitable and a better candidate is a distribution that can allow for over/under dispersion such as a binomial or NB distribution. However, sometimes we deal with a large number of zeros in our dataset. For example, we see in the next section that many policyholders have zero claims, which does not necessarily mean that they were involved in no accidents, but they are low risk. In such cases, we can apply a ZIP model which is a mixture of a point mass at zero, also called structural zeros, and another claims frequency distribution, such as a Poisson or NB, which can be written as

$$\Pr(y\_i = j) = \begin{cases} \pi\_i + (1 - \pi\_i) \Pr(y\_i = 0) & j = 0 \\ (1 - \pi\_i) \Pr(y\_i = j) & j = 1, 2, \dots \end{cases} \tag{3}$$

where *πi* is given by Equation (2) and denotes the probability of zeros when zero is the only possible observation. In a ZIP model, *yi* follows a Poisson distribution with parameters being given by Equation (1).

We can easily implement these models in R and the codes are provided in Appendix A (Frees et al. 2014, 2016).

#### **3. Data**

We use datasets provided by the French Institute of Actuaries for the 2017 pricing game, which is based on French MTPL insurance. The dataset is available in Package 'CASdatasets' by Dutang and Dutang and Charpentier (2019) and to the best of the author's knowledge, this is the first time it is used in a study. The dataset contains some information about the new pricing strategy of the company. The policyholders were given a choice whether they would like to join a new mileage-based (MB) pricing system or not. We would like to see how policyholders' perception regarding this new system affects their driving behaviour and hence their number of claims. There are two types of datasets: (i) underwriting and (ii) claims dataset. Underwriting datasets are available for three years, whereas claims dataset is only publicly available for year 0. Therefore, we only use data from year 0. After merging claims and underwriting datasets, we randomly split our data into training and validation sets with 60% being in training and 40% in the validation set. As some policyholders have more than one car, we assume that each policy covers only one car and therefore consider the number of policies and claims per policy rather than claims per policyholder. We have 100,000 policies (rows in underwriting dataset) and 12,654 policies with claims (rows in claims dataset after consolidation). Table 1 shows the variables we use in our study. In addition to these variables, information about *Insee town code*, *make and model*, *marketing duration* and *age of driving license* are also provided. However, we do not take into account these variables as, for example, there is a considerable number of policies with 113 years for driving license age which is not reasonable.

In Table 1 policy ID refers to the combination of the vehicle ID and policyholder ID. In this study, we have 100,000 policy ID. Bonus coefficient is the percentage of the full premium that policyholders pay allowing for their claims experience and the allocated discount. There are four types of coverage available: Maxi, Median 2, Median 1 and Mini. The time from the last policy alteration, such as the inclusion of a new driver, is represented by situation duration. Payments can be made annually, semi-annually, quarterly and monthly. As it is usual for the liability insurance, some of the claims amounts are negative1. Therefore, we set all claims amounts of less than 30 equal to zero (Ferreira and Minikel 2012; Frees et al. 2014).

**Table 1.** Variables in our datasets.

Subscription to mileage-based (MB) policy refers to a new scheme in which one of the main risk factors is the travel distance and policyholders are charged based on their mileage, also known as PAYD scheme. Policy Usage includes WorkPrivate, Retired, Professional and AllTrips. If a policy covers two drivers, age and gender are provided for both drivers. Different features of the car including age, engine power (represented by Din), fuel type, max speed (provided by manufacturing company), type—Tourism and Commercial, value and weight are provided and will be used as rating factors. In this study, we only consider the number of claims as a dependent variable.

We now provide some explanatory analysis based on the training set. The minimum policy term in our dataset is one year, which means all these policies have been under observation for at least one year. Since claims have occurred in Year 0, we consider car years or earned exposure of one year for all policies. The maximum claims number is 6, the oldest policyholder is 103 years old and the oldest car is 66 years old. Table 2 presents mean and standard deviation of our numerical explanatory variables for all policies, policies without claims and policies with at least one claim based on the training set. In order to examine which variables are considerably different in the group of policies with claims and the group of policies without claims and hence are effective on the frequency of claims, we can apply

1 This happens due to subrogation rights of the insurer.

Mann-Whitney test. The Mann-Whitney test is a nonparametric test of the null hypothesis that it is equally likely that a randomly selected value from one sample is less than or greater than a randomly selected value from a second sample. The Mann-Whitney test shows that the difference in the mean for all these variables is statistically significant with *p*-value < 0.0001, except for policy duration and driver age 2 with *p*-values 0.001232 and 0.004252, respectively.

**Table 2.** The mean and standard deviation of numerical variables in the training set.

Figure 1 shows the distribution of the number of claims. We can observe that zero claims form a large part of our portfolio.

Figure 2 illustrates how policies are distributed across categorical variables. As we can see, most of our policies cover one driver and most of the drivers are men aged between 51 and 70. Our policyholders prefer Maxi and drive tourism cars for work and private purposes. Most of them pay annually and are distributed almost evenly across monthly and biannual payment categories. They have not registered for MB scheme and they use diesel with very few of them using a hybrid car. Next, we see how claims are distributed across categorical variables.

Table 3 presents the distribution of the number of claims across different categories. For the variable *policy usage*, although *professional* usage forms a small portion of our portfolio, claims under *professional* group is more than *private* and *retired* groups. However, from Figure 3 *professional* and *retired* groups have almost the same median loss and except for *all trips* we can see little difference among policies in this group. Under this insurance, the most comprehensive protection is provided by *maxis* and as can be expected this may lead to moral hazard. We can see there are more claims under *maxis* than under other types of coverage. The order of coverage is *maxis*, *median 2*, *median 1* and *mini* and unsurprisingly, the percentage of claims reduces in the same order. Under *mini*, 97.39% of the policies have made zero claims. Perhaps lower coverage is a motivation for policyholders to take more precautious measures. Figure 3 shows the effect of policy coverage on the amounts of claims and as we can see this will be an effective covariate in our model. From Table 3 those policyholders who were willing to subscribe to *MB plan* are less likely to have an accident. Figure 3 shows that the subscribers are less dispersed than those who have not subscribed. From the regulatory point of view, *gender* cannot be used as a discriminatory factor. In fact, we can see there is no considerable difference between *male*'s and *female*'s number of claims. In Figure 2 the least favourable *payment frequency* is *quarterly* payment, but we do not see considerable differences in claim numbers and amounts for different categories of payments. A large number of policies provide coverage only for one driver, but policies with two drivers have a slightly greater chance of making claims. The *age* of the first driver ranges from 19 to 103. We classify the policyholders in different age groups as 18–30, 31–50, 51–70, 71–85 and 85+. Most of the policyholders are in the range 51–70 and the next largest group is between 31 and 50. Both Table 3 and Figure 3 do not show a significant difference in claims frequency and claim amounts for different age categories and it seems that some categories can be combined together. In fact, in the next section we see that instead of these categories, we use *age* as a numerical covariate in our models as some categories are not statistically significant.

**Figure 2.** Distribution of policies according to categorical variables.

**Figure 3.** Distribution of log of claims amounts according to categorical variables.

Most of our policyholders drive *gasoline* cars and very few of them have *hybrid* cars.2 According to Table 3, hybrid cars make more claims than gasoline and *diesel* cars. Most policies cover *tourism* cars and claims percentage made by this type of cars is more than *commercial* cars. Our initial analysis suggests that *payment frequency* and *gender* are not significant variables and therefore can be removed from our study. In the next section, we will see that they are indeed insignificant and are not included in our final models.

**Table 3.** Frequency of claims per categorical variables in the training set.

2 According to the game document, hybrid cars were not popular at the time of collecting this dataset.

**Table 3.** *Cont.*

#### **4. Results**

In this section, we use statistical software R and package "pscl" to build Poisson, logistic and ZIP models (Zeileis et al. 2008). Our purpose is to estimate the frequency and the probability of claims and compare our results with a ZIP model using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC).

Table 4 presents three Poisson regression models with their estimated coefficients and their corresponding *p*-values. Model 1 is the full model where we consider all the variables from Section 3. However, according to pricing game document, there is a correlation between vehicle cylinder, weight, value, speed and power and in our dataset, some of the entries for weight, value and cylinder are missing. Therefore, we only incorporate speed and power into our models. We build Model 2 using the stepwise selection of variables that can be implemented in R. In Model 3 we only consider variables which are statistically significant at 0.05.

**Table 4.** Regression coefficient of Poisson models.

As we can see, some of the coefficients are statistically significant at 0.0001. For example, the coefficient associated with the Bonus is significant and positive as expected. The bonus represents the percentage of the full premium and a large percentage shows an adverse claims history of a policyholder. The positive sign indicates that as the percentage of the full premium increases, the mean of claims frequency will increase. The coefficients associated with Coverage are negative for all categories and significant. The coefficient of Median 2 shows that the policyholders with this type of coverage have fewer claims than policyholders with Maxi coverage (the reference level). For example, in Model 1, a policyholder with a Median 2 has fewer claims than a policyholder with a Maxi coverage by exp(−0.1854) = 0.83 and a policyholder with a Mini coverage has fewer claims by exp(−1.2611) = 0.28. The coefficient of the car's power, represented by Din, is positive and significant, which indicates that powerful cars are more likely to be involved in an accident and therefore the mean of claims frequency for the owners of the powerful cars is higher. Unlike Ayuso et al. (2019) and Guillen et al. (2019), we found that Vehicle age has a negative impact on the number of claims. In our study, most of the policyholders are middle-aged and more likely to have old cars. In Section 3 we saw that the mean of the vehicle age is 9.56 for all policies and 7.30 for policies with at least one claim. Our portfolio of middle-aged policyholders also affects the sign of the coefficient associated with Age 1. Our dataset includes drivers as old as 103. Therefore, it seems reasonable to find a positive impact of age on the mean of the number of claims. In Model 1 the coefficients which are not significantly different from zero include Female 1, car usage for Retired and All trips, Hybrid fuel, Type and Speed. The coefficient of Professional usage indicates that Professional usage increases the mean of claims frequency compared to Work and private usage (the reference level) by exp(0.1536) = 1.17. This is in line with Table 3 that policies for professional purposes make more claims. We obtain similar results for gasoline cars as in Table 3. Owners of Gasoline cars have fewer claims than owners of Diesel cars by exp(−0.2621) = 0.77. We can see that the coefficient associated with Driver2 is positive. This seems

reasonable as a policy that covers two drivers is more likely to make claims. The coefficient of Age 2 is negative. One interpretation can be that the average age of the second drivers is lower than the average age of the first drivers. However, in Section 3, we saw that driver age 2 is not significantly different for policies with claims and policies without claims. The coefficients associated with Duration and Policy duration are both negative. This implies that more experienced policyholders make fewer claims and also the more stable a policy is, the lower the mean of the number of claims. The coefficient of subscription to MB is negative and therefore this variable reduces the mean of claims frequency. Perhaps those who are willing to be monitored by telematics technology are more confident about their driving behaviour. We saw in the previous section that payment frequency is not a significant variable. As we can see, their corresponding *p*-values for some categories in models 1 and 2 are not significant at 0.05 and therefore we have removed them from Model 3. However, we decided to keep the variable Usage, although not all categories are significant at 0.05, as we found in the previous section that it is effective on the number of claims. Among our three models, Model 2 has the lowest AIC and Model 3 has the lowest BIC. As we can see, the computation time for Model 2 is longer than the other two models. The reason is that the stepwise algorithm examines different models to find the one with the smallest AIC.

Table 5 presents three logistic models with their coefficients and the corresponding *p*-values. Similar to Table 4, Model 1 includes all variables, Model 2 is based on the stepwise algorithm and Model 3 only includes significant variables. The interpretation of the coefficients in logistic regression is similar to Poisson regression and as we can see, the signs of the coefficients are the same. The only difference is that in logistic regression we look at the impact of variables on the odds of the occurrence of claims. So, for example, the interpretation of the coefficient associated with Bonus is that, the greater the percentage of the full premium (adverse claims history) is, the higher the odds of the occurrence of the claims for the coefficient associated with professional usage; we can say that the odds of the occurrence of claims for policyholders with professional usage increases by exp(0.1691) = 1.18 as opposed to policyholders with work and private usage. For the negative coefficient associated with subscription to MB, we can say that the odds of the occurrence of claims fall for a policyholder who joins this scheme. Other variables can be similarly interpreted. Model 2 is built by examining different models and finding the one with the lowest AIC. All variables in this model are the same as the variables in stepwise Poisson regression except for duration which is not included in stepwise logistic regression. For Model 3 we again remove all variables with a *p*-value greater than 0.05. In addition, we do not include payment frequency as this has been proved to be insignificant in Section 3. As we can see, Model 2 has the smallest AIC and Model 3 has the smallest BIC. Further, the computation time for the stepwise algorithm is longer than the stepwise Poisson regression model.

When building a model, it is important to consider the underlying assumptions. For example, to fit a ZIP model to our data, we first need to test for the presence of over-dispersion. One approach is to fit a quasi-Poisson and to determine the dispersion parameter, i.e., *θ* in Var(*y*) = *θ* E[*y*]. In our case, using only significant variables from Tables 4 and 5, the dispersion parameter is 1.1. Alternatively, we can fit NB regression and compare our new model with Poisson regression. In our case, AIC and BIC for NB regression are 46,184 and 46,346, respectively, which are lower than AIC and BIC for the Poisson regression. Now, since we have the problem of over-dispersion and excess zeros, we can fit a ZIP model to our data. Table 6 shows the estimated coefficients and their *p*-values for the Poisson (count) part and zero-inflated part of three ZIP models. Model 1 is the full model where we consider the variables of the full model in Table 4 for the count part and the variables of the full model in Table 5 for the zero-inflated part. As we can see, most variables are not significantly different from zero. If we consider the significant level of 0.1, the coefficient associated with Age 1 is positive as in Table 4 and statistically significant in the count part. In addition, the coefficient associated with Age 2 is positive and significant in the zero-inflated part, but not in the count part. From Section 3, we know that the second divers are younger than the first drivers. Therefore, we can claim that in this group older drivers are more likely to have zero claims. The coefficient of situation duration in the count part is

negative and significant as in Table 4 with the same interpretation. The coefficients associated with coverage are significant at 0.01 in the count part with the identical signs as in Table 4, but they are not significant in the zero-inflated part. The interpretation is that the mean frequency of claims for policyholders covered under, for example, Mini coverage is less than the policyholders covered under Maxi coverage by exp(−1.0487) = 0.35.

The coefficient of fuel (gasoline) is positive and significant which indicates that the odds of zero claims for drivers of gasoline cars increases by exp(0.5066) = 1.66 as opposed to drivers of diesel cars. Further, in the zero-inflated part, the coefficient of Driver2? is negative and significant. Therefore, a policy with two drivers is less likely to have zero claims, in other words, a policy with the 2nd driver is more likely to be involved in an accident and to make a claim. The associated coefficient of vehicle age is positive and significantly different from zero in the zero-inflated part, which is in line with our findings for Poisson and logistic models that it is more likely for the owners of older cars to have zero claims. All other variables including subscription to MB are not significantly different from zero. The variables of Model 2 in the count and zero-inflated part come from the variables of stepwise models in Tables 4 and 5, respectively. The coefficients have the same sign and therefore similar interpretation as in Model 1. Again the coefficient of subscription to MB is not significantly different from zero. Model 3 can be built using the variables of the models that contain only significant variables in Tables 4 and 5. Coverage in the count part and Age 2, Driver2?, fuel and vehicle age in the zero-inflated part are all significantly different from zero. In Table 6 the signs of some of the coefficients do not conform to Tables 4 and 5. For example, subscription to MB is positive both in the count part and in the zero-inflated part. Since such coefficients are not statistically significant, we can conclude that they are not significantly different from zero. Comparing AIC and BIC of these three models, we can see that the smallest AIC can be obtained by Model 2 where the variables come from stepwise models in Tables 4 and 5 and the smallest BIC by Model 3. In addition, AIC has considerably improved for ZIP models compared to Poisson models in Table 4. In the next section, we show that the prediction of zero claims by ZIP is considerably better than Poisson regression.

**Table 5.** Regression coefficients of logistic models.

**Table 6.** Regression coefficients of zero-inflated Poisson (ZIP) models.

\* Model 1: full model; Model 2: based on the variables of stepwise models in Tables 4 and 5; Model 3: based on the variables of only significant models in Tables 4 and 5.

#### **5. Validation**

In this section, we use our validation set to compare the predictability of the models discussed in Section 4. Table 7 presents the predicted number of zero and non-zero claims by our models in Section 4. In this table, individual 1 refers to an 85-year-old male policyholder with a maxi policy that pays biannually with the bonus (percentage of the full premium) of 0.5. He holds this policy for retired usage, for 29 years and has not signed to MB scheme. The policy was modified nine years ago. He owns a 10-year-old tourism car with gasoline, the din of 98 and max speed of 182. In year 0, this policyholder has not made any claim and the probability of zero claims predicted by Poisson regression according to full model is exp(−0.1036) where 0.1036 is the estimated parameter *λ* and the probability of zero claims predicted by logistic regression is 1 − 0.0903 where 0.0903 is the estimated *π* = Pr(*y* = 1). Prediction of zero claims by ZIP is 0.9104. Individual 2 is a male policyholder with a maxi policy. This policy covers two drivers aged 54 and 56 and has been held for six years and been modified two years ago with a bonus of 0.5 and monthly premium payment. The policyholder owns a two-year old tourism car with diesel for work and private purposes with the din of 75 and max speed of 163. The estimated parameter by Poisson regression is *λ* = 0.1794 and by logistic regression is *π* = 0.1525. As we can see, the count part of ZIP for the two policyholders is very close to the estimated value of Poisson regression. If we add the probability of zero claims in all these models, we can approximate the number of zero claims. Results show that ZIP models considerably outperform Poisson regression and logistic regression performs better than ZIP models in predicting zero claims. Further, we can see that there is a slight difference between predictions made by full models, stepwise models and the models with only significant variables.

\* Model 1: full model; Model 2: based on the variables of stepwise models in Tables 4 and 5; Model 3: based on the variables of only significant models in Tables 4 and 5. \*\* An 85-year-old male policyholder with biannual maxi coverage and bonus of 0.5 for retired usage. He had this policy for 29 years and changed it nine years ago. He has not registered for MB and owns a 10-year old tourism car with gasoline, the din of 98 and max speed of 182. \*\*\* A 54-year-old male with monthly maxi coverage and bonus of 0.5 for private usage. The 2nd driver is a 56-year-old female. The policy was written six years ago and was modified two years ago. It covers a two-year-old tourism car with diesel and din of 75 and max speed of 163. It is not part of MB scheme.

#### **6. Conclusions**

We have divided our dataset into training and validation sets. Using our training set, we have developed three models and compared our models according to their AIC and BIC values. We found that type of coverage, vehicle age and fuel are statistically significant in most of our models. We then validated our models and showed that a ZIP model can predict the frequency of claims better than a Poisson regression. Further, we have shown that if we are just concerned about the number of zero and non-zero claims, logistic regression can even outperform a ZIP model. In fact, logistic regression is a one layer neural network and there is a scope to extend our study to a more generalised form of logistic regression for future research. We saw that the policyholders who were willing to be monitored by telematics devices are less likely to make a claim. A thorough study of the policyholders' behaviour before and after being monitored by telematics devices can be another area of future research. Given the current concern regarding climate change and sustainability, the possibility of the inclusion of fuel consumption into a pricing model may be considered in the future (Tselentis et al. 2017).

**Funding:** This research received no external funding.

**Acknowledgments:** I am very grateful to the reviewers' comments and suggestions which were valuable to improve this paper.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **Appendix A**

```


*Edited by Mohammad Reza Pahlavani*

Quantum mechanics, shortly after invention, obtained applications in different area of human knowledge. Perhaps, the most attractive feature of quantum mechanics is its applications in such diverse area as, astrophysics, nuclear physics, atomic and molecular spectroscopy, solid state physics and nanotechnology, crystallography, chemistry, biotechnology, information theory, electronic engineering... This book is the result of an international attempt written by invited authors from over the world to response daily growing needs in this area. We do not believe that this book can cover all area of application of quantum mechanics but wish to be a good reference for graduate students and researchers.

ISBN 978-953-51-0059-1

Some Applications of Quantum Mechanics

Photo by LeeYiuTung / iStock


Meet the editors

Dr Diarte-Plata is a professor of research with an appointment candidate level in the SNI-CONACYT Mexico. He received his BSc degree in aquaculture at the Universidad Autónoma de Sinaloa, Mexico. He has his Masters degree in natural resources and environment from the Instituto Politécnico Nacional (IPN CI-IDIR-Sinaloa), Mexico. He is currently a professor at the Instituto Politécnico Nacional, Mexico (since 2006). He is also a researcher

of the Sinaloa System of Researchers and Technologists (SSIT-INAPI Sinaloa). He received his PhD in marine and coastal sciences at the Universidad Autónoma de Baja California Sur, Mexico. His research topics include investigations in marine, culture and ecology of molluscs and crustaceans. As a professor-researcher within the IPN CIIDIR-Sinaloa, he has participated in 48 research projects, given 11 seminars, 260 presentations at international and national conferences, written 5 book chapters, and 19 indexed articles. He teaches descriptive and multivariate statistics at the undergraduate level, and aquaculture at the postgraduate level. He has been the director of 15 undergraduate theses and 5 Masters and 2 Doctorates from various universities. He is the arbitrator in the revision of manuscripts sent to international journals (ISI-JCR).

Dr Escamilla-Montes received her doctorate in marine and coastal sciences with a specialty in aquaculture. She is an assistant technologist of the Sinaloa System of Researchers and Technologists. Her areas of study are cultivation and ecology of molluscs and crustacean. In the last five years, she has focused on the isolation and characterization of lactic acid bacteria, yeasts, and bacilli with probiotic potential and pathogenic bacteria such as *Vibrio*

*parahaemolyticus* and its effect on the growth, survival, and expression of genes of the immune system and stress of marine organisms. She has participated in 11 research projects, as well as presentations at national and international conferences, written 4 books, and 28 articles in ISI Thomson-JCR international journals. She is also the arbitrator in the revision of manuscripts sent to international journals (ISI-JCR).

Contents

**Section 1**

Crustacean

(Molina, 1782) *by Walter Reyes A.*

Marine Isopod

and Belize)

*and Oscar Frausto-Martínez*

*by Imad Mahmood Ghafor*

*by Selvaraj Kumaralingam*

The Robber Crab *Birgus latro* (Linnaeus, 1767)

*by Kari L. Lavalli, Ehud Spanier and Jason S. Goldstein*

Management of the Interaction and Cannibalism of Postlarvae and Adults of the Freshwater Shrimp *Cryphiops caementarius*

Bateman Gradients and Alternative Mating Strategies in a

*by Katharine M. Saunders and Stephen M. Shuster*

Scyllarid Lobster Biology and Ecology

**Preface III**

Biology and Ecology **1**

**Chapter 1 3**

**Chapter 2 21**

**Chapter 3 25**

**Chapter 4 51**

**Chapter 5 65**

**Chapter 6 77**

The Habitat Types of Freshwater Prawns (Palaemonidae: *Macrobrachium*) with Abbreviated Larval Development in Mesoamerica (Mexico, Guatemala

*by Luis M. Mejía-Ortíz, Jesús E. Cupul-Pool, Marilú López-Mejía,*

*Alfredo G. Baez-Meléndres, Juan C. Tejeda Mazariegos, Jair G. Valladarez, Keith A. Crandall, Marcos Pérez-Losada*

## Contents

## **Section 2**

Preface

Crustaceans form one of the most successful zoological groups, both for the number of registered living species (67,829) and for the diversity of habitats that they colonize (from the shallow coastline to the deep ocean basins). They are organisms that have various anatomical variations and dimensions ranging from a few millimeters (some copepods) to more than 4 m in length (spider crab). The variety of life strategies has allowed them to adapt to a wide variety of environments, first marine, then freshwater, and finally terrestrial. As for food, there are detritivores,

The importance of crustaceans not only lies at the food level, but they also provide multiple benefits to man: in the commercial field (through the exploitation of different species, which means significant economic income worldwide); in the pharmaceutical, food, and beverage industry; in water treatment; in agriculture; in medicine (chitosan is used, which is extracted from the main component of the shell that forms the body of organisms, chitin); and in the food and dye industry by the use of carotenoids (astaxanthin) extracted from the lobster exoskeleton (*Pleuroncodes planipes*) to give a reddish color to different foods. In the biological aspect, crustaceans are fundamental in the functioning of aquatic ecosystems; with their abundance and diversity they give structure to the macroinvertebrate communities. Because of the position they occupy in the food chains, as secondary consumers, they are responsible for the transformation of organic matter into energy and consumable proteins.

This book is made up of five sections. The first section is about **Biology and Ecology.** The first chapter is *Crustace*an, where aspects of all the animals of the phylum Arthropoda and Subphylum Crustacea are discussed. This group of animals are a very diverse group of invertebrate animals, which includes active animals such as crabs, lobsters, shrimp, krill, copepods, amphipods, and more sessile creatures like barnacles. It includes about 11,340,000 species in all habitats. This constitutes about 83% of all the known animal species on earth. The phylum is characterized by heteronomous metamerism, chitinous exoskeleton, and joined appendages. In very small crustaceans, the exchange of respiratory gases occurs through the general body surface. Large aquatic arthropods respire through gills and book gills, whereas

The chapter entitled *The robber crab Birgus latro (Linnaeus, 1767)* gives us information on the terrestrial hermit crab. It is the largest land-living arthropod in the world. In India, distribution of this crab is restricted to Great Nicobar Island and South Sentinel Island in Andaman and Nicobar Archipelago. This research is focused on aspects of ecology such as habitat, size, eating habits, behavior, life

In the chapter *Scyllarid Lobster Biology and Ecology,* the current available knowledge on the biology of scyllarids is presented. The author attempts to point out where questions remain to help focus further studies on these lobsters, while also mentioning that slipper lobsters are found in tropical and temperate habitats with hard or soft undercarriages and at different depths, and exhibit a wide array

terrestrial forms respire through trachea and book lungs.

cycle, and distribution on the Nicobar Islands, India.

herbivores, omnivores, carnivorous scavengers, and parasites.


*6.9.1 Build a sense of fulfillment through a higher purpose*

A clear purpose is essential to keep a team focused. It can also build a sense of fulfillment within colleagues. Leaders should have team members visualize *how* their individual contribution is part of a bigger mission. With everyone being on the same page, leaders can capitalize upon people's innate need to serve. Reminding the team of the purpose behind their responsibilities will help keep everyone's motivation high.


**3. Farm-forestry and smallholder farms**

In order to cope with extreme climate variation, many smallholder farmers are already implementing practices that maintain complex agrobiodiversity and a higher capacity of their production units to resist such risks [24, 25]. Yet the poor tree cover in agricultural land, world over, suggests poor adoption despite economic viability and environmental benefits of agroforestry systems [26]. Several issues plague the much-desired adoption level at farmers' end. The low adoption of agroforestry, despite huge potential, is explained, among others, by the lack of regulations and guidelines related to harvesting, transportation and marketing of agroforestry produce [27]. The smallholder farms, in particular, suffer from low quality infrastructure *viz.*, access to markets, financial assistance, disaster relief, technical assistance or government support [19] due to remote location in developing countries.

The long rotation of trees hinders their adoption on farms as forest policies in countries like India inhibit harvesting, transport and marketing of certain trees species declared as prohibited species. This discourages farmers in taking tree enterprise in their farms. The purpose of such policy is well intentioned but lacks in desired encouragement to stakeholders in large scale adoption of farm forestry.

Property rights, particularly land tenure, has been suggested to greatly affect adoption of agroforestry on smallholder farms. While longer gestation of tree enterprise along with the annual crop enhances profitability and environmental sustainability of farming, it warrants right to land to encourage farmer to invest in agroforestry, apart from other factors.

There are no supports for agroforestry-based land use practices, similar to those in crop production and inputs such as fertilizer, credit for smallholder farms, which discourages them going for tree-based crop production on their small holdings. In fact, the policy support for fertilizer encourages more fertilizer use rather than going for agroforestry which builds nutrients in the soil over a period of time.

The poor extension system in updating farmers' knowledge regarding sustainable tree-based land management also discourages farmers in larger adoption of agroforestry on their farms in developing countries. Farmers' traditional practice of growing trees on field boundaries does not support the farm profitability and environmental sustainability. Innovative and new ways of managing trees on farms (*e.g.* intercrop systems for soil health) are not yet known to the vast majority of farmers. The combination of suitable tree species with the cropping systems practiced by them needs scientific/technical backup not only about choice of tree species but also the desired silvicultural practices.

Although farm-forestry projects fail for a number of different reasons, one common factor is the inadequate attention given to socioeconomics in the development of systems and projects [28]. The socio-economic studies of agroforestry systems have revealed the vulnerability of farm profit in medium to longer term to output prices. With gestation period of more than a couple of years, the smallholder farmers are not convinced enough to adopt them. Because of higher initial establishment costs, the net capital inflow in the initial years, in agroforestry, is not favorable even for tree species of short duration. This is also true for agri-horticultural plantation where fruit bearing occurs some years later [29]. The right combination of crop and tree species is, therefore, crucial to win the faith of stakeholders.

### **4. Policy reforms promoting agroforestry/farm-forestry**

The policy reforms directly targeting the expansion of agroforestry have experienced good success world over (**Table 3**). The re-interpretation and

**83**

**Table 3.**

*Farm-Forestry, Smallholder Farms and Policy Support – The Way Ahead*

**Country Programme Ministry Activities**

Ministry of Environment

Ministry of Agriculture and Farmers Welfare

Ministry of Agriculture and Livestock

Ministry of Environment

Ministry of Food and Agriculture

Ministry of Agrarian Development

Agriculture and Rural Development Ministry of member

U S Department of Agriculture

Ministry of Agriculture and Livestock Development

Roadmap for promoting leadership and synergies in agroforestry

Providing a platform for converging the various tree planting programs outside of forest

Facilitates stakeholder linkages within and among national, regional, and international agroforestry and watershed

Strengthening on-farm tree access, reduced punitive punishment for tree cutting, discussion on acess

Supporting research (adaptive trials and demonstration), training

Refining financing mechanisms, enhancing training of extension

Capital investments, grants to businesses and training for improvement of agriculture, forest

Supporting research, tools and information for adoption of

and forestry products

agroforestry

and extension education

Site specific appropriate agroforestry systems and species, availability of planting material, credit and insurance for agroforestry plantation

areas

networks

rights

agents

implementation of the Forest Code in Niger leading to expansion in farmer managed natural regeneration to over 5 million hectares of land [34] is good example. Similarly, granting communities the long-term rights to forest land in return for environmental stewardship of the land (HKM programme), in Indonesia, created a village forest concept (HutanDesa) providing villages rights to benefits of carbon or other environmental services [35]. In response to deforestation, increase in agricultural land area and to motivate farmers for planting trees, the Government of Kenya, in 2009 enacted new Farm Forestry rules requiring farmers to cover 10% of all farms with trees. Guatemala simplified the Forest Act, 1966 regarding procedures for timber harvesting in agroforestry systems resulting in diversification of land use by farmers in their farms as another source of income [36]. Several other countries developed or modified the agroforestry policies. Brazil refreshed agroforestry policy of 1997. The United States Department of Agriculture (USDA) developed an Agroforestry Strategic Framework 2011–2016 [37]. France passed an agroforestry policy, in 2010, to establish agroforestry as a legal agricultural land

states

*DOI: http://dx.doi.org/10.5772/intechopen.96942*

action plan 2018–2027

Agroforestry Policy 2014

Rwanda Rwanda agroforestry and

India The India National

Ethiopia Ethiopian National

Niger Reinterpretation and

Ghana National Agroforestry Policy 1986

Nepal National Agroforestry Policy 2019

Brazil The National Program

Farming 2003

EU Rural Development Policy 2007–2013

USA Agroforestry Strategic

*Agroforestry policy and reforms.*

for Strengthening Family

Framework 2019–2024

*Source: Bernard* et al*, 2019; Chavan et al., 2010; USDA, 2019; Smith, 2010 [13, 30–33].*

Watershed and Agroforestry Multistakeholder Platform

implementation of the Forest Code

*Farm-Forestry, Smallholder Farms and Policy Support – The Way Ahead DOI: http://dx.doi.org/10.5772/intechopen.96942*

#### **Table 3.**

*Agroforestry - Small Landholder's Tool for Climate Change Resiliency and Mitigation*

or government support [19] due to remote location in developing countries.

The long rotation of trees hinders their adoption on farms as forest policies in countries like India inhibit harvesting, transport and marketing of certain trees species declared as prohibited species. This discourages farmers in taking tree enterprise in their farms. The purpose of such policy is well intentioned but lacks in desired encouragement to stakeholders in large scale adoption of farm forestry. Property rights, particularly land tenure, has been suggested to greatly affect adoption of agroforestry on smallholder farms. While longer gestation of tree enterprise along with the annual crop enhances profitability and environmental sustainability of farming, it warrants right to land to encourage farmer to invest in

There are no supports for agroforestry-based land use practices, similar to those in crop production and inputs such as fertilizer, credit for smallholder farms, which discourages them going for tree-based crop production on their small holdings. In fact, the policy support for fertilizer encourages more fertilizer use rather than going for agroforestry which builds nutrients in the soil over a period of time.

The poor extension system in updating farmers' knowledge regarding sustainable tree-based land management also discourages farmers in larger adoption of agroforestry on their farms in developing countries. Farmers' traditional practice of growing trees on field boundaries does not support the farm profitability and environmental sustainability. Innovative and new ways of managing trees on farms (*e.g.* intercrop systems for soil health) are not yet known to the vast majority of farmers. The combination of suitable tree species with the cropping systems practiced by them needs scientific/technical backup not only about choice of tree species but also

Although farm-forestry projects fail for a number of different reasons, one common factor is the inadequate attention given to socioeconomics in the development of systems and projects [28]. The socio-economic studies of agroforestry systems have revealed the vulnerability of farm profit in medium to longer term to output prices. With gestation period of more than a couple of years, the smallholder farmers are not convinced enough to adopt them. Because of higher initial establishment costs, the net capital inflow in the initial years, in agroforestry, is not favorable even for tree species of short duration. This is also true for agri-horticultural plantation where fruit bearing occurs some years later [29]. The right combination of crop and

tree species is, therefore, crucial to win the faith of stakeholders.

**4. Policy reforms promoting agroforestry/farm-forestry**

The policy reforms directly targeting the expansion of agroforestry have experienced good success world over (**Table 3**). The re-interpretation and

In order to cope with extreme climate variation, many smallholder farmers are already implementing practices that maintain complex agrobiodiversity and a higher capacity of their production units to resist such risks [24, 25]. Yet the poor tree cover in agricultural land, world over, suggests poor adoption despite economic viability and environmental benefits of agroforestry systems [26]. Several issues plague the much-desired adoption level at farmers' end. The low adoption of agroforestry, despite huge potential, is explained, among others, by the lack of regulations and guidelines related to harvesting, transportation and marketing of agroforestry produce [27]. The smallholder farms, in particular, suffer from low quality infrastructure *viz.*, access to markets, financial assistance, disaster relief, technical assistance

**3. Farm-forestry and smallholder farms**

agroforestry, apart from other factors.

the desired silvicultural practices.

**82**

*Agroforestry policy and reforms.*

implementation of the Forest Code in Niger leading to expansion in farmer managed natural regeneration to over 5 million hectares of land [34] is good example. Similarly, granting communities the long-term rights to forest land in return for environmental stewardship of the land (HKM programme), in Indonesia, created a village forest concept (HutanDesa) providing villages rights to benefits of carbon or other environmental services [35]. In response to deforestation, increase in agricultural land area and to motivate farmers for planting trees, the Government of Kenya, in 2009 enacted new Farm Forestry rules requiring farmers to cover 10% of all farms with trees. Guatemala simplified the Forest Act, 1966 regarding procedures for timber harvesting in agroforestry systems resulting in diversification of land use by farmers in their farms as another source of income [36]. Several other countries developed or modified the agroforestry policies. Brazil refreshed agroforestry policy of 1997. The United States Department of Agriculture (USDA) developed an Agroforestry Strategic Framework 2011–2016 [37]. France passed an agroforestry policy, in 2010, to establish agroforestry as a legal agricultural land

use qualifying for European Commission agricultural subsidies in the framework of the common agricultural policy (CAP). This helped farmers receive investment support for the establishment of the agroforestry systems on agricultural lands [38]. Asian countries like China (Grain for Green) and India (Greening India) have also embarked on ambitious programs to increase tree cover outside of forests, including some attention to smallholder agroforestry by providing necessary support such as providing market and/or establishing floor price for agroforestry product.

Development programs, such as National Adaptation Programs of Action (NAPAs) and Nationally Appropriate Mitigation Actions (NAMAs), as a result of increased attention to climate change, have helped advance agroforestry in some countries. Agroforestry has been recommended to make agricultural production and income more resilient to climate change and variability, transformations in the management of natural resources (*e.g.* land, water, soil nutrients, and genetic resources), resulting in higher efficiency in the use of these resources and inputs for production. Agroforestry, for climate-smart agriculture, is now considered as one of the strategies along with institutional and policy options to promote the transition to climate-smart agriculture at the smallholder farms [39]. The Comprehensive African Agricultural Development Programme (CAADP) endorsed an agriculture climate change adaptation and mitigation framework highlighting agroforestry in 2010. The United Nations Framework Convention on Climate Change (UNFCCC), similarly, recognized agroforestry as a key climate mitigation method within agriculture [40]. The African ministers of agriculture, in the same manner, endorsed wide scaling up of agroforestry to address climate change adaptation and mitigation objectives in agriculture in 2009.

The recognition of agroforestry in development programs and the reforms enacted highlight the good intention of the planners and policy makers world over. There are several case studies corroborating the resultant impact of the reforms and strengthening the belief on agroforestry production system, yet the evidences fall short of universal replicability due to poor adoption by and large. The climatic and bio-physical constraints, apart from socio-economic constrains, still hinder the desired spread of the successful models across the globe. The region-specific approach to address the issues need further studies to understand the constraints,

*1 Scale: 1 = most important barrier, 2 = important barrier, 3 = less important barrier, 4 = least important barrier, 5 = not a barrier. Source: Faulkner* et al*, 2014 [41].*

**85**

mass movement.

in the Philippines and Indonesia.

*Farm-Forestry, Smallholder Farms and Policy Support – The Way Ahead*

reforms, yet these are crucial for success of agroforestry reforms.

yet some broad consensus on general issues, based on the literature, have been extensively highlighted for limited farmers such as smallholders (**Table 4**).

Policy reforms in agroforestry has played an important role in promoting agroforestry in different regions/countries differently. The policy reforms have helped promote agroforestry, at macro level, in facilitating adoption and expansion, yet there remains some concern related to, among others, tree germplasm multiplication and dissemination, long term private property rights over land and trees, recognition of agroforestry as an attractive investment area within agricultural institutions and programme. Some of these are outside the domain of agroforestry

High quality seedlings production and supply across the farms which need quality trees is crucial. There is good involvement by governments in many instances. In some countries, governments have directly involved in providing seed and seedlings for tree planting efforts in non-agricultural areas to provide watershed protection services. The Ethiopian government, for example, has played an active role in all facets of upscaling tree planting including the establishment of government nurseries and sales at subsidized rates. The Kenyan government has, similarly, supported agroforestry tree seed and seedling supply to meet the newly enacted regulation that all farms must have 10% tree cover. Timber and fruit seedlings are being produced and sold by private sector nurseries, yet seed and seedling systems for tree systems are still not well privatized. The efforts still lack the up-scaling required to provide quality seed and seedlings to different agro-climatic regions. The efforts for local production and supply chain development is warranted with larger role at community and private level. Incentivization and technical back up of such units meeting requirements of region-specific demand of tree species needs a

The likelihood of farmers' ability to adopt and reap benefits from agroforestry enhances with long-term tenure security to land [42] due to longer time periods required in testing, adapting and eventually adopting the agroforestry technologies and practices. Trees require lengthy periods to mature, and, therefore, the goods and services produced can affect the incentives for adoption, distribution of benefits, and the impacts leading to poor incentivization of the agroforestry production programme [43]. Absence of land secure rights have poorly impacted even the development of Payment for Ecosystem Services schemes [44], a selfsustaining model to promote agroforestry. Therefore, there is much to be done on this in several regions. While insufficient long-term rights to land have demotivated long term investment on land including agroforestry, this has also manifest itself as conflict between state and smallholder land users within *de jure* forest land such as

Agroforestry is getting recognition in agricultural strategies, but often merely in a list of options for addressing sustainability. The capacity for agroforestry to generate income is hardly ever recognized in policy documents and, therefore, the associated policy support for its profitability at farms, particularly, smallholder is not quite evident. The micro studies conducted on agroforestry profitability provide ample evidence in favor of market linkage in general and price in particular. The long gestation period of tree harvest postpones the positive net returns flow because of higher initial costs of tree establishment. Smallholder farmers are quite susceptible to initial cash inflow and outflow in sustaining the production enterprise.

*DOI: http://dx.doi.org/10.5772/intechopen.96942*

**5. Policy reforms implications**

#### **Table 4.**

*Barriers to adoption of agroforestry technologies.*

yet some broad consensus on general issues, based on the literature, have been extensively highlighted for limited farmers such as smallholders (**Table 4**).


**2.2 Northwestern African or Saharan cheetah**

*Acinonyx jubatus hecki*, historically found in Northwest Africa in Egypt, Algeria, Tunisia, Morocco, Niger, Mauritania, Mali and in some western African countries, including Benin, Burkina Faso, Senegal and Ghana [38]. Today, small populations remain in Algeria, Niger, Benin, and Burkina Faso [28]. Most are in the central western region of the Saharan desert and the Sahel. Unique in appearance, this subspecies in critically endangered with only approximately 250 individuals remaining. Saharan cheetahs are extremely pale, almost white in color. Their coloring provides them with a natural defense against detection in the desert environment. Sometimes there are no spots on its face and its tear marks appear to be missing. In general, they are smaller than the other subspecies. This may be a product of their desert environment, where there is less prey for them to hunt.

### **2.3 Eastern African or Sudan cheetah**

*Acinonyx jubatus soemmeringii*, was historically found in Sudan, Djibouti, Cameroon, Niger, Nigeria, Chad, Ethiopia and Somalia [38]. Today, small populations are in Chad Ethiopia, Somali, Somaliland, and South Sudan [28]. This subspecies is the richly colored.

### **2.4 Southern African cheetah**

*Acinonyx jubatus jubatus*, originally found throughout Namibia, Botswana, South Africa, Zambia, Angola, Mozambique, Malawi, and Democratic Republic of Congo and Zimbabwe [38]. Today, over 50% of the remaining cheetahs are found in Namibia and Botswana, with small populations in Angola, South Africa Mozambique, Zambia and Zimbabwe [28], and the new classification of those from Kenya, Tanzania and Uganda [4]. They have large home ranges that can encompass hundreds of square kilometers.


*3.3. The BDCDO Solving Framework Combined with SRIRMD and STOR*

By integrating the SRIRMD sampling strategy and the STOR termination criterion proposed in this work into the BDCDO solving framework, a new BDCDO solving method, named SRIRMD-STOR, is generated as depicted in Figure 3. The input and output of the SRIRMD-STOR method are shown in Table 1, and the specific realization of the SRIRMD-STOR method is listed in Table 2.

**Table 1.** Input and output of the SRIRMD-STOR method.

**Figure 3.** The flowchart of the BDCDO solving framework SRIRMD-STOR.

**Table 2.** The specific realization of the SRIRMD-STOR method.


**3.1 What is juvenile crime committed with malware apps?**

There are lots of juvenile crimes and many reasons that may lure or encourage young children to commit crimes with malware apps [10]. The bottom line of these issues is that any act of infringement by juvenile with malware apps is a crime in this respect. Infringement can be defined as an act of violation or misdemeanor and such act usually disregards ethical agreement or moral uprightness. For examples, a child that uses malware apps to unlawfully break into the telephone or computer system of another person, or steal, corrupt, modify or update the information in the electronic device(s) of another person can be alleged of crimes committed with malware apps.  In addition,


*4.1. Animal Experiments*

Male Sprague–Dawley rats (Charles River) weighing 180 g to 250 g were housed in a facility with 1:1 light/dark cycle. The animals were acclimated for at least 7 days and had free access to food and water. The well-established model of puromycin aminonucleoside nephropathy (PAN) was achieved by injecting puromycin aminoglycoside dissolved in 0.9% saline (125 mg/kg body weight i.p.). Rats injected with 0.9% saline served as controls. Eight days later, renal afferent lymphatic vessels were harvested for pressure myography. In a separate subset of PAN and control rats, renal lymph was collected using a glass pipette. The animal protocol was approved by Vanderbilt University Medical Center Institutional Animal Care and Use Committee in accordance with National Institutes of Health guidelines.


*Article* **Experimental Study of Supercavitation Bubble Development over Bodies in a Duct Flow**

#### **Lotan Arad Ludar \* and Alon Gany**

Faculty of Aerospace Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel<EMAIL_ADDRESS>
**\*** Correspondence<EMAIL_ADDRESS>
Received: 18 December 2019; Accepted: 6 January 2020; Published: 8 January 2020

**Abstract:** Understanding the development and geometry of a supercavitation bubble is essential for the design of supercavitational vehicles as well as for prediction of bubble formation within machinery-related duct flows. The role of the cavitator (nose) of a body within the flow is significant as well. This research studied experimentally supercavitation bubble development and characteristics within a duct flow. Tests were conducted on cylindrical slender bodies (3 mm diameter) within a duct (about 20 mm diameter) at different water flow velocities. A comparison of supercavitation bubbles, developing on bodies with different nose geometries, was made. The comparison referred to the conditions of the bubbles' creation and collapse, as well as to their shape and development. Various stages of the bubble development were examined for different cavitators (flat, spherical, and conical nose). It was found that the different cavitators produced similar bubble geometries, although at different flow velocities. The bubble appeared at the lowest velocity for the flat nose, then for the spherical nose, and at the highest velocity for the conical cavitator. In addition, a hysteresis phenomenon was observed, showing different bubble development paths for increasing versus decreasing the water flow velocity.

**Keywords:** supercavitation; supercavities; cavitator; hysteresis

#### **1. Introduction**

The geometry of supercavitation bubbles has been studied for decades, using diverse tools and methods, because of its significance for the design of supercavitation vehicles and applications. In particular, comprehensive studies have examined axisymmetric supercavitation bubbles, proposing methods of calculation and presenting relations between the bubble dimensions and the flow conditions [1–5]. Other studies have analyzed the wall effect in channels on the bubble dimensions as well as the values of the cavitation number of fully developed cavitation bubbles [6]. Some experimental works showed the development of axially symmetric supercavities in bounded and unbounded flows and examined the bubble characteristics relating to natural and artificial supercavitation [7,8]. These studies are significant for hydraulic machinery in which the appearance and development of cavitation play a key role in the performance of the system. One of the most significant topics in the field is the role of the cavitator in determining the bubble shape and size. This has been examined analytically for 2D flows [9] and numerically for 3D flows for more accurate results and for specific geometries [10]. Numerical results have shown that the bubble dimensions are dependent on the cavitator shape [11]. In addition, some estimations and predictions have been done, mainly for unbounded bubbles [12–18]. Other experimental investigations have described the bubbles formed on different bodies, examining the gravitation effect, the closing modes, the separation point, etc. Many of them were summarized by Franc and Michel (2004) [19].

The objective of the present study was to investigate supercavitation bubble development over bodies in a duct water flow. We examined experimentally the influence of different cavitator geometries on axisymmetric cylindrical bodies, finding the relations between the dimensions of the bubble and the cavitation number. We also revealed and investigated a hysteresis phenomenon in naturally developed supercavitation bubbles. Previous studies have discussed this phenomenon for ventilated (artificial) bubbles. Semenenko (2001) [3] examined hysteresis found in bubbles closing on a solid body, investigating the angle of the bubble closure on the solid surface as well as the required gas supply to the bubble for maintaining its size. Wosnik and Arndt (2009) [20] examined hysteresis for different bodies in ventilated bubbles. In our research, we observed hysteresis in naturally formed bubbles that do not close on a solid body.

#### **2. Problem Description**

We considered axisymmetric supercavitation bubbles developing along a cylindrical object in a uniform flow of water within a convergent-divergent nozzle. Slender cylindrical bodies with different nose (cavitator) geometries were examined. The front edge nose causes velocity change, flow separation, and pressure drop. When the pressure decreases below the equilibrium vapor pressure of the liquid, the water starts to evaporate, developing a supercavitation bubble over the body. As the flow velocity increases, the pressure decreases, and the bubble grows and can envelope the entire body (see Figure 1). The geometry of the body, and especially its front edge, is the main factor that determines the flow field and the supercavitation bubble creation and development.

**Figure 1.** A scheme of the physical problem.

#### **3. The Experimental System and Flow Conditions**

The experimental system included a converging–diverging nozzle (converging angle 6.5◦, diverging angle 2◦), connected to a straight pipe from which the water flowed uniformly in a constant temperature of about 20 ◦C (Figure 2). The nozzle accelerated the flow to the appropriate speed in which cavitation could be created. A valve was used to adjust the water flow rate. The supercavitation body was placed right after the nozzle throat (Figure 3). Three slender cylindrical bodies of 2.97 mm diameter with different cavitators (noses) were tested: a flat cavitator, a spherical cavitator, and a conical cavitator with an angle of 15◦ (Figure 4). The bubble created over the body was examined while increasing the water flow rate. Seven pressure measurement taps were placed along the wall: one at the wall of the pipe before the entrance to the nozzle; two at the converging section of the nozzle; one at the nozzle throat, where the cavitator nose was placed (the location where the initial creation of the cavitation bubble was expected); and three additional gauges at the diverging section, along the supercavitation bubble (see again Figure 3). The Reynolds number of the flow, calculated with a relation to the object as well as the duct, was higher than 30,000 for all flow-rates tested.

**Figure 2.** The experimental system.

**Figure 3.** The nozzle geometry and the pressure measurement locations.

**Figure 4.** The supercavitation bodies.

#### **4. Results**

#### *4.1. Stages of Bubble Development*

The different stages in the bubble development along the body with increasing flow velocity are presented in Figure 5 for the flat cavitator. The observed geometries of the bubbles were practically similar for the three different cavitators. In every stage of the flow, the bubble did not close on the body, and it remained open in its back edge. At low velocities, the geometry of the bubble surface could be expressed by the function described in Equation (1):

$$f\_a = \frac{d}{2} \left( 1 + \frac{6}{d} z \right)^{\frac{1}{3}} \tag{1}$$

where *d* is the cavitator diameter. *z* is the coordinate of the axis of symmetry expressed with the same length units as *d*. This expression of the bubble geometry was used by Semenenko (2001) [3] based on Logvinovich empiric results (1973) [16].

**Figure 5.** Stages of the bubble development for a flat cavitator.

When increasing the velocity, the function convexity changed, and the geometry of the bubble surface could be expressed by the function described in Equation (2):

$$f\_b = \frac{d}{2} \left( 1 + \frac{a}{d}z \right)^{\frac{1}{2}} \tag{2}$$

where *a* is a constant factor, depending on the geometry of the nozzle and of the body. When the velocity was further increased, the geometry of the bubble surface could almost be described as an open cone, with the function in Equation (3):

$$f\_{\mathbb{C}} = \frac{d}{2} \left( 1 + \frac{a}{d} z \right) \tag{3}$$

In general, the convexity of the bubble decreases as the velocity increases in its front and in its back edges together. The two last functions, describing the bubble geometries in the later stages of development, are presented in Figure 6, revealing practically the same shape for all three cavitators.

Although the stages of development are similar for all three cavitators, the velocity at which the bubble starts as well as the characteristic velocity for each stage of development are different for the different cavitators. Table 1 presents the velocities of the flow at the front edge of the cavitator for the three cavitators in the six stages of the bubble development presented in Figure 5. The velocities were calculated from the water volume flow rate divided by the flow cross-section just before the cavitator.

**Figure 6.** The geometries of the supercavitation bubble for three different cavitators.

**Table 1.** Flow velocity at the front edge of the cavitator in Stages 1–6 of the bubble development for the three cavitators.

#### *4.2. The Pressure Field*

The change in the pressure was measured on the nozzle walls. The pressure decreases moderately with the increase of the flow velocity for each of the cavitators. A rapid decrease was detected when the cavitation bubble grew and extended, reaching the section of the gauge. Similar to the order that the beginning of the bubble creation appeared, the process took place at the lowest velocity for the flat cavitator, then for the spherical cavitator, and finally at the highest velocity for the conical cavitator (see measurements of P5 located at the divergent part of the nozzle where the bubble is extending in Figure 7).

**Figure 7.** The wall pressure in P5 vs. the velocity in this section for the three cavitators 1.

The results of the measurements of P5 show that there are pressure fluctuations in the system. The largest fluctuations occur for the conical cavitator, where the system is the least stable; the slender body undergoes mechanical vibrations caused by the high flow rate in the pipe required for the creation and development of the supercavitation bubble. The lowest fluctuations in the graph appear for the flat cavitator, in which the bubble is created and developed at the lowest flow velocities. The lowest static wall pressure (the same for the three cavitators) measured by P4 and P5 was 0.065 and 0.07 bar (with an uncertainty of ±0.025 bar), respectively. These values were somewhat higher than the theoretical equilibrium vapor pressure (0.023 bar at 20 ◦C), presumably existing within the cavitation bubble. The magnitude of the pressure drop was similar for all cavitators. In addition, the pressure change was similar in all cavitators for every stage of the bubble development.

#### *4.3. Comparison of Results with Theoretical Analysis*

A control volume analysis was done (Figure 8) to calculate the pressure at a cross section *i* with relation to the conditions at the nozzle throat *t* (where the front edge of the cavitator is placed), assuming a one-dimensional flow with negligible viscosity effects. The theoretical calculation was compared with the experimental data. From conservation of mass, one can find the relation between the velocities at *i* and *t* cross-sections:

$$u\_i = u\_t \frac{A\_t}{A\_i} \tag{4}$$

where *ui* and *Ai* are the flow velocity and cross-section area, respectively, at the location of gauge *Pi*, and *ut*, *At* are the corresponding values at the nozzle throat. Using Bernoulli equation on a flow streamline at the wall between the throat and a cross section *i* of the gauge and substituting Equation (4), we derive the pressure difference between section *i* and the nozzle throat:

$$
\Delta P = P\_i - P\_t = \frac{1}{2} \rho u\_t^2 \left( 1 - \left(\frac{A\_t}{A\_i}\right)^2 \right) - \rho g h \tag{5}
$$

where *Pi*, *Pt* are the pressures in section *i* and in the nozzle throat, correspondingly, *g* is the gravitational acceleration, ρ is the density of the water, and *h* is the height difference calculated in Equation (6) for the divergence angle of 2◦:

$$h = z \tan 2^{\circ} \tag{6}$$

where *z* is the distance from the throat cross-section to section *i* of gauge *Pi*. As the height contribution is three orders of magnitude smaller than the dynamic pressure, ρ*gh*/1 2ρ*u*2 ∼ *O*(10−3), this term in Equation (5) can be neglected.

**Figure 8.** Control volume for theoretical analyses. (**a**) the cavitation does not reach the cross-section (**b**) the cavitation reaches the cross-section.

1 Note that the velocities in Figure 7 describe the velocities in gauge P5 section, thus they are smaller than the velocities at the nozzle throat and those in Table 1 due to a mass conservation.

Figure 8a,b presents a situation where the cavitation bubble has not reached cross-section *i* and a situation where cross-section *i* is already within the bubble domain, respectively. In the former, the cross-section for the water flow at *i* is *Ai* = π - *di* 2 − *d*2 /4, whereas the cross section for the water flow at *t* is *Ai* = π - *dt* 2 − *d*2 /4. The theoretical pressure difference between *i* and *t* cross-sections, Δ*P* = *Pi* − *Pt*, should be derived from Equation (5). Figure 9 shows the theoretical line and experimental points versus the water flow velocity at cross section *t* for such a case, revealing very good agreement to within ±0.05 bar.

**Figure 9.** Comparison between the theoretical and experimental values of Δ*P* = *P*5 − *Pt* vs. the velocity at the nozzle throat for the different cavitators.

Figure 8b shows a further developed bubble, exceeding section *i.* One can assume that the pressure within the naturally developed supercavitation bubble is equal to the equilibrium vapor pressure throughout the bubble. We can further assume that the pressure in a cross-section is more or less constant (meaning that, along the bubble, the pressure field is uniform and practically equal to the vapor pressure). Bernoulli equation implies that, to keep a uniform pressure along the flow path, the flow velocity should be constant, meaning the available cross section for the water flow should be constant. With the assumption that the water bypasses the contour of the vapor bubble, we obtain:

$$d\_{\mathcal{E}} = \sqrt{d\_1^2 - d\_l^2 + d\_l^2} \tag{7}$$

where, in our case, the nozzle divergence angle is 2◦, *dc* is the cavitation bubble diameter, and

$$d\_l = d\_l + 2z \tan 2^{\circ} \tag{8}$$

Equation (7) means that the shape of the bubble in a bounded duct (nozzle) is dictated by the shape of the nozzle to practically keep a constant cross-section for the water flow between the supercavitation bubble boundary and the nozzle walls. It explains the finding in this research that the different cavitators (of different nose shape, but the same diameter) exhibited the same bubble shape. The function describing the bubble geometry was obtained as:

$$f(z) = \frac{d\_c}{2} = \frac{d}{2} \left( 1 + \frac{(2m)^2/d}{d} z \left(\frac{d\_t}{m} + z\right) \right)^{1/2} \tag{9}$$

where *m* = tan 2◦. For small *z*, Equation (9) narrows to Equation (2) with the geometric factor:

$$a = 4m \left(\frac{d\_t}{d}\right) \tag{10}$$

A comparison between the bubble geometry predicted in Equation (9) and the experimental results for all three cavitators is described in Figure 10, showing agreement within about 3%. The experimental results are related to Stage 5 of the bubble development.

**Figure 10.** Comparison between the theoretical prediction and experimental results of the bubble geometry for the three cavitators.

#### *4.4. The Bubble Dimensions*

Based on the experiments, a relation between the supercavitation bubble dimensions and the cavitation number of the flow was deduced for all three cavitators (Figure 11), according to Equation (11):

$$l/c = A\sigma^n\tag{11}$$

where *l* is the bubble length; *c* is the diameter of the body; *A*, *n* are constants depending on the flow conditions, bubble position, and form; and σ is the cavitation number of the flow calculated according to Equation (12):

$$
\sigma = \frac{p\_a - p\_v}{\frac{1}{2}\rho v^2} \tag{12}
$$

where *pa* is the atmospheric pressure, *pv* is the vapor pressure of the water, ρ is the water density, and *v* is the water velocity.

**Figure 11.** The measured supercavitation bubble dimension ratio vs. the cavitation number for the three cavitators.

All curves reveal the same general trend of decreasing the ratio of the bubble length to body diameter when increasing the cavitation number. The two cavitators with the gradually changing front shape, namely, the conical and spherical cavitators, exhibit very similar curves, both in slope and in magnitude. This could be expected as they generated similar bubble shapes at only slightly different flow velocities. The flat cavitator, however, showed bubble formation and development at substantially lower flow velocities, causing different slope and level of the curve. One may assume that the reason should be flow separation due to the abrupt change from the flat nose to the cylindrical body shape.

#### **5. "Hysteresis"**

Increasing the flow rate, the bubble grew and extended along the body until it reached the rear edge of the nozzle, which was open to the atmosphere. When opening to the atmosphere, the pressure measured at the wall grew rapidly becoming equal to the outside pressure (one atmosphere). Further increase of the flow rate did not change the pressure. Examining the situation when gradually decreasing the water flow rate revealed that initially the pressure stayed constant and the bubble had the same size and shape. Further decrease in the flow rate, dropping the flow velocity much below the value that initially caused the bubble creation, led to a sudden collapse of the bubble. Detecting the bubble size and shape as well as the wall pressure during the process, one could see a hysteresis-like phenomenon, although the physical processes were not utterly reversed. Figure 12 shows the different paths of P5 and P6 wall pressure variation for the spherical cavitator, for the two parts of the experiment (a velocity increase followed by a velocity decrease). The first part of the experiment revealed a gradual pressure decrease followed by a substantial drop, when the bubble reached the gauge section (as described in Section 4.2), and then an abrupt increase to the atmospheric pressure when reaching the nozzle exit. In the second part of the experiment, when decreasing the flow velocity, the bubble and the pressure remained steady until the bubble collapsed (with only a slight change in pressure). The hysteresis that we observed is for a naturally developed vapor bubble, which was influenced by the opening of the bubble to the atmosphere. At that stage, the bubble contained a mixture of water vapors and atmospheric air. It showed a similar behavior to that of an artificial cavity resulting from a gas supply.

**Figure 12.** Wall pressure at the diverging part of the nozzle vs. the velocity for the spherical cavitator during a cycle including an increase followed a decrease of the flow velocity.

#### **6. Conclusions**

In a duct water flow, the wall has a significant influence on the flow regime and on the development of a supercavitation bubble on an object within the flow. The cavitator role in determining the bubble shape and dimensions becomes significantly smaller and its main impact is on the conditions (flow rate and velocity) of the bubble creation and collapse. It was found that different cavitators could produce similar bubble geometries, although at somewhat different flow velocities. Testing three different cavitators at the same flow conditions and examining the bubble development for each of the cavitators, one observes that a supercavitation bubble is created at the lowest flow velocity by a cavitator generating the largest disturbance in the flow, implying a more rapid change in the flow regime. This was the flat cavitator for which the bubble was created at a flow velocity of only 9.9 m/s. A bubble was created at the highest flow velocity for the cavitator causing the least and more moderate disturbance in the flow. This was the conical cavitator, for which the bubble was created at a velocity of 14.8 m/s (50% larger than for the flat cavitator). Another phenomenon observed was hysteresis. When increasing and decreasing the flow rates, the bubble as well as the pressure variations of growth and decrease underwent different paths. Supercavitation is a fluid dynamics phenomenon, depending mainly on the flow and pressure fields. The water quality, such as salt concentration (seawater vs. tap water), may have a small effect through the dependence of the vapor pressure. The vapor pressure of saline water is slightly lower than for pure water. For instance, at 20 ◦C, vapor pressure of pure water is 0.0234 bar, and that of seawater is 0.0229 bar. This small difference would practically not change the results but might cause a slight change in the velocity value for each stage of supercavitation bubble development.

**Author Contributions:** This academic research was conducted in full collaboration and involvement of both authors, as is commonly done by a PhD student (L.A.L.) and thesis Advisor (A.G.), with regards to conceptualization, evaluation, and presentation of the results. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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