**1. Introduction**

Extra virgin olive oil (EVOO)—which is considered an essential component of the Mediterranean diet, as well as its main source of fats—is appreciated all over the world for its nutritional value and associated health benefits [1,2]. When talking about EVOO, however, it should be considered that there is a wide variety of oils on the market that are often characterized by different quality standards and sensory profiles [3]. In recent years, the increasing demand for olive oil has led to the rapid spread of high-density and super-high-density olive plantations that, although only possible using a limited number of cultivars, maximize productivity and efficiency, providing a more standardized product with an affordable selling price [3–5]. At the same time, the main producing countries have vigorously implemented a policy of using as many local cultivars as possible, aiming to preserve olive tree biodiversity and diversify and promote sensory specificity and highquality local olive oil production [3,5]. This trend has also received the endorsement of the European Union (EU) that, as far back as 1992, introduced the quality trademark Protected Designation of Origin (PDO) to protect and promote typical foods with strong roots in a specific geographic region [6]. Conservation of biological diversity is, in fact, the best tool

**Citation:** Paciulli, M.; Difonzo, G.; Conte, P.; Flamminii, F.; Piscopo, A.; Chiavaro, E. Physical and Thermal Evaluation of Olive Oils from Minor Italian Cultivars. *Foods* **2021**, *10*, 1004. https://doi.org/10.3390/ foods10051004

Academic Editor: Anna Vallverdú-Queralt

Received: 2 April 2021 Accepted: 1 May 2021 Published: 4 May 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

to ensure species survival, through their adaptability to new environmental conditions and climate change and, in turn, to guarantee long-term sustainability of the entire supply chain [7]. In this scenario, Italy and its very rich olive germplasm—estimated to include about 800 cultivars—play a dominant role, not only in the preservation of olive biodiversity, but also in the production of high-quality olive oils with strong sensory specificity [8,9]. In recent years, several studies have focused on the rediscovery and valorization of minor local Italian cultivars in an attempt to provide valuable genetic resources to be used as strategic elements to increase the sustainability of the future of oil production, pursuing, at the same time, enrichment and diversification of EVOOs to be placed on the market [5,7,9–13].

The authentication of extra virgin olive oils represents a key strategy for their valorization and diversification. Traditionally the traceability of extra virgin olive oils involves their chemical characterization, which is influenced by genotype and different agronomic, environmental, and technological factors [14].

Closely related to chemical composition, but less debated in the literature, is the physical and thermal characterization of olive oils, which could be considered of large interest for consumers and industries.

Differential scanning calorimetry (DSC) has been proposed as an alternative and reproducible method for olive oils identification, through the study of their thermal behavior upon cooling and heating [15]. This technique has been successfully applied in the field of olive oil with the aim to discriminate between commercial categories [16], oxidative status [17], agronomic practices [18], or to detect fraudulent mixtures with other vegetable oils [19]. Some studies have also applied DSC to study the authentication and traceability of extra virgin olive oils by applying chemometric data processing. Chatziantoniou and co-workers [20] successfully determined the botanical origin and geographical origin of six monovarietal extra virgin olive oils originating from four geographical regions of Greece, by applying linear discriminant analysis (LDA) on the data obtained from DSC heating and cooling profiles. DSC in combination with principal component analysis (PCA) was applied to identify EVOO from different Mediterranean countries, revealing how the thermogram obtained upon heating contains important information for sample characterization [21]. An approach based on HPLC-DSC in combination with partial least-square (PLS) regression was used to clarify the influence of triacylglycerol composition on the shape of the cooling curves of EVOOs, to a subsequent authentication of the olive oils [22]. DSC exhibits some advantages compared to the classical analytical methods as it is rapid, does not require sample preparation or solvent utilization, and has a reduced environmental impact.

The measurement of oil viscosity is essential at an industrial level for the selection of proper equipment, such as settling and centrifugation devices, including pumps, pipes, filtration systems, etc. Moreover, from the sensorial point of view, the viscosity can be associated with the term 'fluidity', where oil with low viscosity means a higher fluidity. Although this subject is not included in the official method [23], the differences perceived between samples can be linked with the oil fatty acid composition [24].

Color is a basic criterion affecting consumer preferences, although the European Union does not require its measurement for the assessment of the virgin olive oil quality. [23] The green shades of olive oil are strictly related to the olive fruit pigments, especially chlorophylls, that are transferred to the oil during the extraction process [25]. Their composition changes during the olive ripening time, influencing both drupe and oils' color [26]. Olive oil pigments have also been proposed as markers of olive oil's genetic and environmental make-up [27].

The aim of this work was to analyze thermal profiles and color of thirteen monovarietal extra virgin olive oils, obtained from minor autochthonous Italian olive cultivars, at three different ripening stages, to evaluate the potentiality of these two fast and green methods to differentiate samples based on cultivar-environment-agronomic practice interaction, in relation to the FA and chlorophyll composition.

This approach can be strategic to create a unique and recognizable hallmark for authentication and traceability of extra virgin olive oils from minor Italian cultivars, with the final goal to pursue their valorization and preserve their biodiversity.

#### **2. Materials and Methods**

#### *2.1. Plant Material*

Drupes of 13 minor olive Italian cultivars, from 4 Italian regions, were harvested in the 2017 harvest seasons.

The selected cultivars were: Tortiglione (TOR), Dritta (DR) and Gentile dell'Aquila (GEN) from Abruzzo; Sivigliana da olio (SIV), Semidana (SEM) and Corsicana da olio (COR) from Sardinia; Cima di Melfi (CM), Oliva Rossa (OR) and Bambina (BAM) from Apulia; the two clones Ottobratica Cannavà (OTT) and Ottobratica Calipa (OTTC), Tonda di Filogaso (TDF), Ciciarello (CIC) from Calabria.

Temperature data from 2017, in each olive production area, are reported in Table 1.

**Table 1.** Temperatures (◦C) recorded in 2017 in the selected Italian provinces 1.

1 Source: Italian Ministry of Agriculture, Food and Forestry [28]. Tortiglione (TOR), Dritta (DR), Gentile dell'Aquila (GEN), Sivigliana da olio (SIV), Semidana (SEM), Corsicana da olio (COR), Cima di Melfi (CM), Oliva Rossa (OR), Bambina (BAM), Ottobratica Cannavà (OTT), Ottobratica Calipa (OTTC), Tonda di Filogaso (TDF), Ciciarello (CIC).

All the olive trees were located in commercial orchards and grown traditionally. Ten kilograms of drupes were sampled from ten different olive trees, every 15 days (Sampling 1 (t1); Sampling 2 (t2); Sampling 3 (t3)), starting around the middle of October (±one week) at the physiological maturity stage, defined at about 50–70% véraison of the fruits, according to the growers harvesting experience, and as confirmed by the maturity index assessment, as reported by Alamprese et al. [29], on the same olive samples. For each sampling, the drupes were divided into 3 aliquots (around 3 kg each), representing the biological replicates. For each harvesting time, the olive drupes were collected from the same trees and stored at refrigerated temperature overnight, before extraction. VOOs were extracted starting from each cultivar at each harvesting time.

For olive oil extraction, the drupes were milled with a hammer mill. The obtained paste was malaxated at a temperature below 20–25 ◦C for 30 min and pressed using a hydraulic press (pressure up to 200 bar) in a small olive oil press mill Mini 30 system (Agrimec Valpesana, Firenze, Italy). After centrifugation and filtration through paper, olive oils were then stored in dark glass bottles at room temperature [30].

#### *2.2. Fatty Acids Composition*

The fatty acid composition was determined after sample transesterification with KOH 2N in methanol [23,31] using a gas-chromatograph system composed of an Agilent Technologies 7890 (Agilent Technologies Inc., Santa Clara, CA, USA), equipped with an FID detector (set at 220 ◦C) and an SP™ 2340 fused silica capillary column (Supelco, Bellefonte, PA, USA), 60 m length × 0.25 mm i.d. and 0.20 μm film thickness. The temperature of the split injector was 210 ◦C, with a splitting ratio of 1:100; the detector temperature was 220 ◦C. The oven temperature was programmed as follows: at the very beginning, the temperature was set at 160 ◦C then gradually raised to 240 ◦C. Helium was used as the carrier gas at a flow of 1 mL min−1. The identification of each fatty acid was carried out by comparing the retention time with that of the corresponding standard methyl ester (Sigma-Aldrich, St. Louis, MO, USA). The amount of single fatty acids was expressed as area % with respect to the total area [23,31].

#### *2.3. Thermal Analysis*

EVOO samples (8–10 mg) were weighed in non-hermetic aluminum pans and analyzed by differential scanning calorimetry with a DSC Q100 (TA Instruments, New Castle, DE), following the method of Cerretani et al. [32]. Indium (melting temperature 156.6 ◦C, ΔHf = 28.45 J/g) and *n*-dodecane (melting temperature −9.65 ◦C, ΔHf = 216.73 J/g) were used to calibrate the instrument and an empty pan was used as reference. Oil samples were equilibrated at 30 ◦C for 8 min and then cooled at −80 ◦C at the rate of 2 ◦C/min, equilibrated at −80 ◦C for 8 min and then heated from −80 to 30 ◦C at 2 ◦C/min. Dry nitrogen was purged in the DSC cell at 50 cm3/min. DSC curves were analyzed with Universal Analysis Software (Version 3.9A, TA Instruments) to obtain the enthalpy change for transition (ΔH, J/g), onset temperature of transition (Ton,◦C), offset temperature of transition (Toff,◦C), and peak temperature at the maximum (Tp) for the main events of cooling and heating transitions (p1c and p2c, p1h, p2h, and p3h, ◦C). The range of transition was calculated as the temperature difference between Ton and Toff for both the cooling and heating transitions.

#### *2.4. Viscosity Measurement*

Measurements were made using an Advanced Rheometric Expansion System (ARES, Rheometrics (Co)). The viscosity value, in mPas, was calculated on the basis of the speed (100 s−1) and the geometry of the probe (Couette cell geometry). Temperature (25 ◦C) was controlled with a water bath connected to the rheometer. The experiment was carried out using 15 mL of sample. Shear stress was plotted as a function of shear rate using the Orchestrator™® software package and the viscosity (μ) value was obtained from Newton's law (Equation (1)).

$$
\sigma = \mu \dot{\mathbf{y}} \tag{1}
$$

where σ is shear stress (mPa), ˙y is the shear rate (1/s) and p is viscosity (mPa s).

#### *2.5. Chlorophyll Content*

Chlorophylls were determined according to Zago et al. [33]. The chlorophyll content was evaluated by the absorption spectrum according to the American Oil Chemists' Society [34] and expressed as mg of pheophytin a per kg of oil.

#### *2.6. Color*

The olive oil color was measured using the software package ImageJ, v.1.38x, fitted with the plugin Color Inspector 3D v. 2.3 [18]. Each time 20 mL of samples were put into a glass Petri dish. The images of each Petri dish were acquired with a scanner (Hewlett Packard, Palo Alto, CA, USA) at 600 dots per inch (dpi). Based on the CIELAB colorimetric system, the measured colorimetric parameters were *L\** (lightness); *-a\** (green shade); *b\** (yellowness).

### *2.7. Statistical Analysis*

Means and standard deviations were calculated with the SPSS (version 27.0 SPSS Inc., Chicago, IL, USA) statistical software package. SPSS was used to perform a oneway analysis of variance (ANOVA) and Tukey's honest significant difference test (HSD) at a 95% confidence level (*p* < 0.05) to identify differences between samples. Pearson correlation coefficients were calculated between the variables at 95% and 99% confidence levels (*p* < 0.05 and *p* < 0.01). Principal component analysis (PCA) was also performed, on normalized data, by means of the Statistica software package (version 8.0, Stat-Soft, Tulsa, OK, USA). PCA was used as a descriptive statistical technique by plotting the normalized independent variables (analytical parameters) versus all cases (samples) with the aim to identify the variables able to discriminate between the cases.


**8. Conclusion and recommendations on the cotton and textile industry in SSA**

Apparel manufacturing is particularly labour-intensive, with minimal start-up costs and readily transferable technologies. As a result, several nations with low labour costs, particularly in South and East Asia, have gained significant market share in the recent four decades.

Main policy recommendations for LIC governments, industry associations and clothing firms can be summarized as follows:

### **8.1 Big data analytics framework model for oilseeds and textile production in SSA**

From the concept of a Big Data strategy to the technical tools and capabilities that a company should have, there's a lot to consider. The following are the key advantages of using a Big Data framework:

The Big Data Framework's Structure.

When establishing a Big Data organization, organizations should consider the Big Data framework, which is a structured approach that comprises of six basic

*A Big Data Analytics Architecture Framework for the Production and International Trade… DOI: http://dx.doi.org/10.5772/intechopen.107225*

### **Figure 11.**

*Big data analytics framework model for oilseeds and textile production.*

capabilities. The following is a diagram of the Big Data Framework shown on **Figure 11**. The Hadoop Architecture layout is shown on **Figure 12**.

When establishing a Big Data organization, organizations should consider the Big Data framework, which is a structured approach that comprises of six basic capabilities. It's a people business when it comes to big data. Even with the world's most modern computers and processors, businesses will fail if they lack the necessary knowledge and skills. As a result, the Big Data Framework strives to broaden the expertise of everybody interested in Big Data. The modular method, as well as the supporting certification scheme, attempts to create Big Data knowledge in a similar

**Figure 12.** *Hadoop's architecture.*

organized manner. The Big Data framework is a comprehensive approach to Big Data. It examines the numerous elements that businesses should consider when establishing a Big Data company. Every component of the framework is as important, and organizations can only progress if they give all components of the Big Data framework similar attention and effort.


**4.2. Provision of employment opportunities**

Council forests provide local employment opportunities. As Cuny [9] notes, about 85% of council forests employees are local indigenes. The contribution of the case study council forests to local employment and in terms of average monthly income is depicted in **Figures 2** and **3**, respectively. Apart from the Dimako council forest where almost all the logging operations are carried out by people directly employed by the council, most of the other councils have contracted their forest to large-scale logging companies for the purpose of timber extraction.

1 2,484,000 FCFA is almost equal to 5000 USD.

**Figure 2.** Number of people working with the case study council forests.

**Figure 3.** Average monthly wages for people working with the case study council forests.


*4.3. Experimental Validation*

In order to validate the results of the calculations, a sample was extracted from the center of the welded blanks at *z* ≈ 125 mm. This sample was embedded, ground, polished, and prepared for metallographic investigations by means of an optical microscope. The merged micrograph of the entire weld cross-section (both unetched and etched using Barker's reagent) is shown in Figure 10. As marked in Figure 10a, three sections of the bonding interface between the weld seam and the steel sheet can be distinguished: (i) the top section, (ii) the side section, and (iii) the bottom section. The surrounding micrographs illustrate the varying thickness of the IM layer (dark grey seam between the

light grey aluminum weld and the medium grey steel sheet) at different positions on the three sections of the bonding interface.

**Figure 10.** Weld seam cross-section of sample 63, (**a**) unetched and (**b**) etched with Barker's reagent. The surrounding micrographs illustrate the thickness variations of the IM layer.

According to the micrographs shown in Figure 10, the mean thickness of the intermetallic layer was 10.9 μm (*SD* = 4.2 μm) at the top section, 4.8 μm (*SD* = 2.1 μm) at the side section, and 7.8 μm (*SD* = 2.2 μm) at the bottom section. The maximum thickness of approximately 20 μm was found close to the weld butt, at the position where the peak temperatures occurred and where the majority of the filler was deposited. From this point, the thickness of the IM layer decreased bidirectionally: just slightly toward the cutting edge of the steel sheet, but markedly toward the base corner of the weld seam. This was also predicted by the numerical model, as visualized in Figures 8 and 9. However, lack of fusion—which was not included in the present numerical model—occurred at the base corners of the weld seam. The etched micrograph shown in Figure 10b allowed identification of the width of the fusion zone (i.e., the width of the weld pool) between the aluminum sheet and the steel sheet. This width was about 2 mm.


*2.1. Materials*

The experiments were carried out with fresh blueberries of the Huertos de Chile brand (variety *Vaccinium corymbosum*), which were bought at a local market. Blueberries with a diameter of 14–15 mm were selected.

#### *2.2. Blueberry Characterization and Freezing*

The blueberry fruits used as raw material to carry out a set of experimental treatments were characterized to ensure a homogeneous quality of said material. Total Soluble Solids (TSS), or ◦Brix, was selected for this purpose as it is one of the main quality indicators of the blueberry fruit [29]. To determine ◦Brix, blueberry fruits were weighed using a RADWAG balance (AS 220/C/2, Radom, Poland) and then crushed and homogenized for 5 min with 10 mL of distilled water until a homogeneous juice was obtained. The resulting juice was filtered, and aliquots were taken for ◦Brix analysis with a HI 96,680 digital refractometer (Hanna instruments, Rothe Island, USA).

Blueberries to be used in the set of experimental treatments were first frozen in a convection freezer (MT05, Alaska, Minas Gerias city, Brasil) at −40 ◦C for 2 h to obtain a product temperature equal to or less than −35 ◦C.

A series of experiments, divided into two steps, was carried out in order to achieve the research objectives:

	- a. Whole, without any treatment.
	- b. Cut in half.
	- c. With 1, 3, 6, and 9 CO2-laser microperforations.

The Pressure Increase Test (PIT) was performed to estimate the treatment effect on primary drying time, and the MTM method was applied to evaluate the mass transfer phenomena, as affected by blueberry characteristics (skin, A, RT) and the busting process. The final fraction of busted blueberries was also evaluated. Table 1 depicts a summary of the experimental setup, showing its two steps—visual observation/evaluation of the busting process of whole blueberries and a total of 6 treatments to evaluate the effect of CO2-laser microperforations on primary drying time and quality.

> **Table 1.** Description of the experimental setup.


**4. The concept of three-way destination safety solution to crisis management (TWaDeSS model)**

Three-way destination safety solution otherwise known as TWaDeSS model is a new concept in destination management that is proposed for tackling crisis arising from safety issues at rural tourism destinations. This model is product of long-term field/research experience on rural tourism development in Nigeria. It is anchored on three variables of host community, tourism resources and tourists/visitors to guarantee sustainable crisis management in rural tourism destinations. The TWaDeSS model is expected to be conducted by the developer/investors at the various stages of the rural tourism project. The model has three major stages that are to be followed accordingly by the developers/investors of tourism projects in rural areas to yield expected positive results (**Figure 1**).

**Figure 1.** *The flow chart for TWaDeSS model and its application.*

*Public Sector Crisis Management*

tourism resources in a deplorable state.

legal litigations from outside the community, among others.

among others.

traditional dances, notable festivals, masquerading, attractive ceremonies, food typologies, belief systems and ritual practices and traditional outfits or attire,

However, some of these rural communities have harnessed some of their tourism resources for meaningful tourism development that would improve their standard of living. While some of these communities have actualized their rural tourism base and transform their respective communities to *rural tourist destinations*, their counterparts have not been able to achieve similar heights, thereby leaving their

Crisis has been defined as "…negative changes in the security, economic, political, societal, or environmental affairs, especially when they occur abruptly, with little or no warning" ([15], p. 3). In tourism studies or management, crisis can be said to be unwanted circumstance that come with huge negativities on the tourist destination, host community, tourists, visitors, tourist attractions and tourism schemes or project in a given area. The consequences are better imagined than witnessed as it might lead to the closure or abandonment of tourism projects or schemes in a given area. In most cases huge capital investments and natural resources are lost to this situation. The causes could either intrinsic or extrinsic depending on the nature of the crisis. Intrinsic has to do with those crises that are caused from within the tourism project circle, i.e. the stakeholders and/or natural factors. The stakeholders may include members of the host community, visitors/tourists, tourism project managers, tourism project developers and tourism resources (developed or undeveloped), among others. The natural factors has to do with some unforeseen natural occurrences like earthquakes, erosion, heavy rains, weather conditions, volcanoes, land movements and some other similar natural occurrences that are not within the control of man. Then the extrinsic factors have to do with some other factors that could cause crisis that are not within the list given above. It could be persons outside of the defined stakeholders, intercommunal crisis, invaded criminal activities and

Crisis management on other hand has been defined as "…the overall coordination of an organisation's response to a crisis, in an effective, timely manner, with the goal of avoiding or minimizing damage to the organisation's profitability, reputation, or ability to operate and often involves the need to make quick decisions on the basis of uncertain or incomplete information" ([15], p. 3). In tourism management, crisis management can be said to be programmes designed and implemented to check possible crisis in tourist destinations or on tourism projects with the aim of either avoiding the crisis and its consequences or managing or controlling the consequences of both expected and unexpected crisis at tourist destinations. This view was supported by Colpofer [15] in the following lines:

*CM includes the development of plans, based upon an integral approach with internal and external organizations to reduce the risk of a crisis occurring and to deal with any crises that do arise, and the implementation of these plans so as to minimize the impact of crisis and assist the organization to recover from them and*

However, safety issues has been identified as among the major sources of crisis at rural tourism destinations [6, 11, 14, 16–19]. Rural tourism projects in Nigeria of recent have been faced with multiplicity of crisis arising from safety issues. Poorly managed safety issues have given rise to high safety and risk perceptions among major actors in rural tourism projects in Nigeria and in some other sub-Saharan countries. This has sandwiched rural tourism projects in a

*restart its normal activities as quickly as possible. ([15], p. 3).*

**126**


**7. Management of interstitial pneumonia associated with connective tissue disease**

Because of the wide variation in manifestations of ILD in the autoimmune disease of CTD, no simple management strategy is adequate for every possible clinical setting. While a part of patients with CTD-associated ILD have limited and stable disease, not always requiring treatment, the significant proportions have severe and progressive disease which necessitates prompt and appropriate treatment. Essentially, nevertheless, general therapeutic principles in CTDs can be applied to many situations including acute and chronic disease. These include use of corticosteroids, azathioprine (AZA), cyclophosphamide (CYC), methotrexate (MTX), mycophenolate mofetil (MMF), and calcineurin inhibitors [13]. Although there are no specific guidelines for the management of CTD-ILD, general strategies recommended for IPF of IIP are also often applied in some cases of CTD-ILD. Emerging treatments with effects in IPF, e.g., Pirfenidone (a pyridine showing both anti-inflammatory and anti-fibrotic effects) and Nintedanib (a small-molecule tyrosine kinase inhibitor targeting VEGF-, FGF-, PDGFreceptors) may offer additional treatment options, though the efficacy has not been evaluated in CTD-ILD [166]. Basically, in contrast to the dismal prognosis in IPF/UIP of IIP with a median survival since diagnosis of 2–3 years, clinical experience in managing patients has taught us that immunosuppressive drugs in CTD-associated ILDs are capable of benefiting a significant proportion of patients, particularly those with certain histological patterns of disease.

With regard to the clinical study, there have been only two randomized placebo-controlled trials investigating the effect of immunosuppressive treatment in SSc-associated ILD. Briefly, the Scleroderma Lung Study (SLS) and the Fibrosing Alveolitis Scleroderma Trial (FAST), evaluated CYC (given orally at 2 mg/kg for 1 year in SLS and intravenously at a dose of 600 mg/m2 monthly for 6 months, followed by oral AZA for the following 6 months in FAST) for SSc-ILD [72, 73]. Both studies found a slower decline in forced vital capacity (FVC) in the CYC group compared with placebo. Intravenous CYC elicited a lower rate of bone marrow toxicity, severe infections, and gonadal failure compared to oral administration, likely due to higher cumulative dose acquired by daily oral administration [167]. Six months after quitting of immunosuppressant, the recovery in FVC fell into baseline, suggesting the requirement of prolonged immunosuppression therapy to maintain stability of lung function [168]. However, it should be noted that, despite studies supporting the benefit of CYC therapy in preventing deterioration in the lung function and premature death in patients with SSc–ILD, recent systematic review and meta-analysis of RCTs and observational prospective cohort studies failed to validate any clinically significant improvement in pulmonary function in SSc patients treated with CYC [169, 170].

of the pathogenic antigens, which may potentially lead to the development of antigen-specific, molecular-targeted therapies, such as the induction of anergy by peptide analogues similar in

Thus, as a result, the T cell receptor (TCR) repertoire study combined with histological analysis demonstrated substantial CD3+ T cell lung infiltrates with specific oligoclonal TCR usage that differed from those in PBL, suggesting a pivotal role for T cells in the pathogenesis of

**7. Management of interstitial pneumonia associated with connective**

proportion of patients, particularly those with certain histological patterns of disease.

With regard to the clinical study, there have been only two randomized placebo-controlled trials investigating the effect of immunosuppressive treatment in SSc-associated ILD. Briefly, the Scleroderma Lung Study (SLS) and the Fibrosing Alveolitis Scleroderma Trial (FAST), evaluated CYC (given orally at 2 mg/kg for 1 year in SLS and intravenously at a dose of

for SSc-ILD [72, 73]. Both studies found a slower decline in forced vital capacity (FVC) in the CYC group compared with placebo. Intravenous CYC elicited a lower rate of bone marrow toxicity, severe infections, and gonadal failure compared to oral administration, likely due to higher cumulative dose acquired by daily oral administration [167]. Six months after quitting of immunosuppressant, the recovery in FVC fell into baseline, suggesting the requirement of prolonged immunosuppression therapy to maintain stability of lung function [168]. However, it should be noted that, despite studies supporting the benefit of CYC therapy in preventing deterioration in the lung function and premature death in patients with SSc–ILD,

monthly for 6 months, followed by oral AZA for the following 6 months in FAST)

Because of the wide variation in manifestations of ILD in the autoimmune disease of CTD, no simple management strategy is adequate for every possible clinical setting. While a part of patients with CTD-associated ILD have limited and stable disease, not always requiring treatment, the significant proportions have severe and progressive disease which necessitates prompt and appropriate treatment. Essentially, nevertheless, general therapeutic principles in CTDs can be applied to many situations including acute and chronic disease. These include use of corticosteroids, azathioprine (AZA), cyclophosphamide (CYC), methotrexate (MTX), mycophenolate mofetil (MMF), and calcineurin inhibitors [13]. Although there are no specific guidelines for the management of CTD-ILD, general strategies recommended for IPF of IIP are also often applied in some cases of CTD-ILD. Emerging treatments with effects in IPF, e.g., Pirfenidone (a pyridine showing both anti-inflammatory and anti-fibrotic effects) and Nintedanib (a small-molecule tyrosine kinase inhibitor targeting VEGF-, FGF-, PDGFreceptors) may offer additional treatment options, though the efficacy has not been evaluated in CTD-ILD [166]. Basically, in contrast to the dismal prognosis in IPF/UIP of IIP with a median survival since diagnosis of 2–3 years, clinical experience in managing patients has taught us that immunosuppressive drugs in CTD-associated ILDs are capable of benefiting a significant

structure to culprit antigens [164, 165].

172 Contemporary Topics of Pneumonia

**tissue disease**

600 mg/m2

PM-associated IP via antigen-driven immune mechanisms.

In PM/DM-associated ILD, high-dose steroid is often the first-line drug, although no definite therapeutic recommendation for the disease has been established yet. The other drugs most frequently used are AZA, MMF, hydroxychloroquine, MTX, CYC, and calcineurin inhibitors, e.g., cyclosporine A (CSA) and tacrolimus (TAC). Rituximab, anti-CD20 monoclonal antibody therapy, has lately emerged as a promising remedy of biologics in patients who have failed conventional immunosuppression treatments [171, 172]. Among a variety of immunosuppressants, the efficacy of calcineurin inhibitors for the treatment of PM/DM-associated ILD should be highlighted. CSA, which inhibits T cell proliferation and T cell-mediated cytokine productions at the transcriptional level, has begun to be used for PM/DM-ILD since the 1980s [173–175]. In 1998, the first nation-wide survey for the treatment with CSA in IP associated with CTDs was conducted in Japan, and the efficacy of a combination therapy with CSA and corticosteroids in PM/DM associated IP was indicated [176]. A number of retrospective and open-label studies have supported the benefit of CSA for the treatment of ILD with PM/DM [177–181]. Takada et al. published a retrospective multicenter study of 38 cases with acute ILD with PM/ DM, whereas it was shown that the combination therapy with CSA and corticosteroids started from the early phase of ILD is superior to corticosteroid monotherapy [178]. Today, calcineurin inhibitors are widely used especially in Japan as both an induction and maintenance therapy for PM/DM-ILD, generally resulting in favorable prognostic outcomes. The appropriate serum concentration of CSA to ensure a maximal effect as well as to avoid toxicity in patients with PM/DM-ILD should reach approximately 150 ng/mL and1000 ng/mL, at trough and at 2 hours after administration, respectively [179]. Another calcineurin inhibitor, TAC, which is a 100 fold potent T cell inhibitor compared to CSA, was also introduced into the treatment for PM/ DM-ILD, and its efficacy and tolerability have been demonstrated in retrospective studies and case series since the report by Oddis et al. in 1999 [182–185]. Ochi, et al. described a superior effect of TAC used in two myositis patients with progressive ILD who failed CYC and corticosteroid treatment but successfully recovered with TAC, showing significant improvement in symptoms and radiologic changes [183]. The appropriate tacrolimus trough level for the treatment of ILD in PM/DM patients have not been established by clinical trials, but it is usually set as 5–20 ng/mL on the basis of data from renal and bone marrow transplantation [186].

Given the treatment-effect heterogeneity of the lung disease observed in PM/DM, it is important to prepare novel therapeutics for the challenging cases of ILD which are refractory to conventional formulas. Recently, Suda et al. reported the effectiveness of multitarget therapy for the ILD in two cases of anti-MDA5 antibody-positive DM which is known to be associated with progressive ILD and sometimes has a lethal outcome despite strong immunosuppressive therapy including CYC [187]. They used TAC and mizoribine (MZR, an inosine monophosphate dehydrogenase inhibitor) in combination with corticosteroids. MZR is a nucleoside of the imidazole class, with the same mechanism as MMF: selective inhibition of lymphocyte proliferation by blocking inosine monophosphate dehydrogenase [188]. The safety and steroid-sparing effects of MZR have been shown in various CTDs, and the efficacy of multitarget therapy using TAC and MZR was reported for systemic lupus erythematosus [189, 190].


**1.2 Applications of solid polymer electrolytes**

SPEs are of great interests in the technology field, especially the area of electrical power generation and storage systems. It is primarily due to their wider range of applications, ranging from small scale production of commercial secondary lithium ion batteries (also known as the rechargeable batteries) to advanced high energy electrochemical devices, such as chemical sensors, fuel cells, electrochromic windows (ECWs), solid state reference electrode systems, supercapacitors, thermoelectric generators, analog memory devices and solar cells (Gray, 1991; Rajendran et al., 2004). As for the commercial promises of lithium rechargeable batteries, there is a wide range of applications which ranges from portable electronic and personal communication devices such as laptop, mobile phone, MP3 player, PDA to hybrid electrical vehicle (EV) and start–light–ignition (SLI) which serves as traction power source for electricity (Gray, 1997a; Ahmad et al., 2005).

#### **1.3 Advantages of solid polymer electrolytes**

A force had been driven in the development of SPEs to replace conventional liquid electrolytes due to its attractive advantages. These features include the elimination of the problems of corrosive solvent leakage and harmful gas production, ease of processability due to elimination of liquid component, and suppression of lithium dendrite growth as well (Rajendran et al., 2004; Ramesh et al., 2010). Besides safety performance, SPE is also a promising candidate because of its intrinsic characteristics, such as ease to configure in any shape due to its high flexibility of polymer matrix, high automation potential for electrode application and no new technology requirement as well as light in weight (Xu and Ye, 2005; Gray, 1991). The other advantages of SPEs are viz., negligible vapor pressure, ease of handling and manufacturing, wide operating temperature range, low volatility, high energy density and high ionic conductivity at ambient temperature (Baskaran et al., 2007; Rajendran et al., 2004). In addition, they exhibit excellent electrochemical, structural, thermal, photochemical and chemical stabilities without the combustible reaction products at the electrode surface by comparing with conventional liquid electrolyte (Adebahr et al., 2003; Nicotera et al., 2006; Stephan, 2006). Moreover, they produce miniaturized structures via fabrication methods and provide longer shelf–lives with no internal shorting (Gray, 1997a; Stephan, 2006).


**Optimized Scalable Wavelet-Based Codec Designs for Semi-Regular 3D Meshes**

Shahid M. Satti, Leon Denis, Ruxandra Florea, Jan Cornelis, Peter Schelkens and Adrian Munteanu *Department of Electronics and Informatics (ETRO) Vrije Universiteit Brussel-IBBT, Brussels, Belgium*


**Author details**

Roghayeh Imani1 and Guillermo Huerta Cuellar2,3\*

1 Department of Engineering Sciences and Mathematics, Luleå University of Technology, Luleå, Sweden

2 Dynamical Systems Laboratory, Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno, Jalisco, Mexico

3 Applied Mathematics Division, Instituto Potosino de Investigación Científica y Tecnológica (IPICYT), San Luis Potosí, Mexico

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Introductory Chapter: Optical Fibers DOI: http://dx.doi.org/10.5772/intechopen.91397*


*3.2. Material Properties*

The mechanical response of both timber and steel components is described with the support of constitutive laws and material models available in the ABAQUS library. An isotropic, elastic-plastic Von Mises constitutive law is used for carbon steel screws (10.9 the nominal resistance class), with *E* = 210 GPa and ν = 0.3 as nominal modulus of elasticity (MoE) and Poisson' ratio. Based on [6], the yielding/ultimate stress values are set in *f* y = *f* u = 940.3 MPa. An ultimate strain δu = 0.5% is considered. At the same time, an orthotropic constitutive law is used for spruce [21]. To ensure more realistic behaviours for the timber members, this constitutive law is integrated with a Hill plastic criterion and a brittle failure parameter. The Hill criterion allows to account for different resistance values in the principal directions of timber, and thus for different potential critical mechanisms for the examined PO setup. The additional brittle failure law, moreover, is used to include possible crushing phenomena in the timber close to the fasteners. Once attained the ultimate resistance *f* c,90, a linear propagation of compressive damage is taken into account for timber. Due to lack of more detailed experimental feedback, this material degradation is set to maximize at a failure deformation of δu = 4mm. This value is adapted from [20], where C24 timber members have been investigated, based on the similarity in the resistance parameters for GL24h spruce. The final input parameters for timber are listed in Table 1, based on the nominal mechanical properties for GL24h strength class [24,25].

**Table 1.** Input mechanical properties for GL24h strength class timber (ABAQUS/Explicit).

Finally, the equivalent soft layer in Figure 5 is mechanically characterized in accordance with [20,21], in the form of an indefinitely linear elastic material with GL24h input properties (Table 2).

**Table 2.** Input mechanical properties for the soft layer and for the CZM contact interaction (ABAQUS/Explicit).


**2. AgNP synthesis methods**

Various techniques are utilized in the production of silver nanoparticles, encompassing physical, chemical, and biological methods. It is noteworthy that every approach possesses its own set of merits and demerits. In the process of biogenic synthesis of silver nanoparticles, the biological entity functions as a capping, reducing, or stabilizing agent, thereby facilitating the reduction of Ag+ to Ag0 [22]. In recent years, there has been a surge in the popularity of biological methods that rely on natural products derived from microorganisms and plants. This can be attributed to their low cost, high yields, and minimal toxicity to both the environment and human health [23]. The subsequent sections outline various techniques employed in the synthesis of silver nanoparticles.


**3. Petri nets with variable arc weights**

470 Petri Nets – Manufacturing and Computer Science

systems.

such systems.

tracking technology, most of the studies related to PBS systems in the literature have focused on their history, development and some practical advises [9]-[31]-[39]. There are, however, relatively few studies addressing strategic and operational issues that arise in such

About strategic issues, Lin and Yang (2011) [22] and Lin et al., (2011) [23] address the strategic problem of finding optimal stations using mathematical programming techniques. The problem is formulated as a hub location inventory model. The key design decisions considered are: the number and locations of bicycle stations in the system, the creation of bicycle lanes between bicycle stations, the selection of paths of users between origins and destinations, and the inventory levels of sharing bicycles to be held at the bicycle stations. The design decisions are made with consideration for both total cost and service levels. Dell'Olio et al. (2011) [7] present a complete methodology for the design and implementing of bicycle sharing systems based on demand estimates considering the stations and the fares. Vogel et al. (2011) [38] develop a methodology for strategic and operational planning using data mining. A case study shows how Data Mining applied to operational data offers insight into typical usage patterns of bike-sharing systems and is used to forecast bike demand with the aim of supporting and improving strategic and operational planning.

Regarding operational issues, besides the work presented in [38], the static balancing problem studying the repositioning of bicycles among bicycle stations where the customer demand is assumed to be negligible is addressed in [5]-[30]. Several mathematical formulations of the problem can be found in [30] and an exact algorithm based on column generation and a suitable pricing algorithm based on dynamic programming are given by Chemla et al.; (2011) [5]. From an OR perspective, the bicycle repositioning problem bears great similarities to some other routing problems which have been largely studied in the literature. As an example from this point of view, Forma et al. (2010) [12] consider the bicycle repositioning problem as a variation of the Pickup and Delivery problem (PDP). Naturally, some similarities between bicycle-sharing and car-sharing systems can be explored in order to adapt some existing results in this field (see, for example [26]-[36]).

Besides OR approaches developed, particularly by using mathematical programming techniques [5]-[12]-[22]-[23]-[30] to support decision making in the design and management of PBS systems, Data Mining techniques receives attention in academia as well as in practice. Data Mining is particularly suitable to analyze and to predict the dynamics of a PBS system. By exploring and analyzing the temporal and geographic human mobility data in an urban area using the amount of available bicycles in the stations of a PBS system [3], statistical and prediction models can be developed [13]-[16] for tactical and operational management of

As noted in [37], although extensive analysis of bicycle data or customer surveys can be applied to predict future bicycle demand at stations, the demand still has to be considered stochastic and not deterministic. Moreover various points in time have to be incorporated in a suitable mathematical optimization models. Such a stochastic and dynamic model can be computational intractable. In addition, customer behavior cannot be modelled in these

In its basic form, a Petri net may be defined as a particular bipartite directed graph consisting of places, transitions, and arcs. Input arcs are ones connecting a place to a transition, whereas output arcs are ones connecting a transition to a place. A positive weight may be assigned to each arc. A place may contain tokens and the current state (the marking)

#### 472 Petri Nets – Manufacturing and Computer Science

of the modelled system is specified by the number of tokens in each place. Each transition usually models an activity whose occurrence is represented by its firing. A transition can be fired only if it is enabled, which means that all preconditions for the corresponding activity are fulfilled (there are enough tokens available in the input places of the transition). When the transition is fired, tokens will be removed from its input places and added to its output places. The number of tokens removed/added is determined by the weight of the arc connecting the transition with the corresponding place. Graphically, places are represented by circles, transitions by bars or thin rectangles (filled or not filled), tokens by dots. For a comprehensive introduction of Petri nets, see for example [27].

Petri Nets Models for Analysis and Control of Public Bicycle-Sharing Systems 473

. The weight *w(i, j)* is assumed to take a positive

(4)

t1

*Customers*

The firing of transitions in a Petri net model corresponds to the occurrence of events that changes the state of the modelled system. This change of state can be due to (*i*) the completion of some activity or/and (*ii*) the verification of some logical condition in the system. Since transitions are often used to model activities (production, delivery, order…), transition enabling durations correspond to activity executions and transition firings correspond to activity completions. Hence, deterministic or stochastic temporal

In addition of the concept of time and the introduction of inhibitor arcs, which are not given in the original definition of Petri nets, the modelling of the complex dynamic of a PBS system requires the use of Petri nets models with "*variable arc weights depending on its marking"* and possibly on some decision parameters of the system. The same modelling concept is introduced for modelling inventory control systems and supply chains in [17]-[6]. Precisely, the Petri net model of an inventory control system whose inventory replenishment decision is based on the inventory position of the stock and the reorder and order-up-to-level parameters. Similarly, in the case of a PBS system, the redistribution operation of the bicycles between stations depends on the number of the available bicycles

By allowing the weights of some arcs of a Petri net to depend on its marking, control policies of the stations can be easily described in the PBS model. Therefore, we consider in this chapter that for any arc (*i, j*), its weight *w(i, j)* is now defined as a linear function of the

> (,) *i i ij ij i P p P*

To understand the mathematical and intuitive meaning of this concept, consider the Petri

 *M p*

*Stock*

p1

*Replenishment Delivery*

*Order outstanding orders*

*On-hand inventory plus*

 and

**10-M(p2)**

t3

**10-M(p2)**

p p2 3

**4**

**Figure 5.** Illustration of a Petri net with variable arc weights depending on its marking

*wij*

t2

specifications can be naturally associated with transitions [24].

in each station when controlled.

marking *M* with integer coefficients

net shown in Figure 5.

*Outstanding orders*

value.

*Suppliers*

Formally, a Petri net can be defined as *PN* = (*P, T, Pré, Post, Inhib, M0*), where: *P = {p1, p2, …, pn}* is a finite and non-empty set of places; *T = {t1, t2, …, tm}* is a finite and non-empty set of transitions; *Pre*: (*PT*) *N* is an input function that defines directed weighted arcs from places to transitions, where *N* is a set of nonnegative integers; *Post*: *(PT) N* is an output function which defines directed weighted arcs from transitions to places*; Inhib: (PT) N* is an inhibitor function which defines inhibitor weighted arcs (circle-headed weighted arcs) from places to transitions*;* and *M0* is called initial marking (initial distribution of the tokens in the places). A place connected with a transition by an arc is referred to as input, output, and inhibitor place, depending on the type of the arc. The set of input places, the set of output places, and the set of inhibitor places of a transition *t* are denoted by *t*, *t* , and *t*, respectively. The weights of the input arc from a place *p* to a transition *t*, of the output arc from *t* to *p*, and of the inhibitor arc from *p* to *t* are denoted by *Pre(p, t)*, *Post(p, t)*, and *Inhib(p, t)*, respectively.

The behavior of many systems can be described in terms of system states and their changes. In order to simulate the dynamic behavior of a system, a state or marking in a Petri net is changed according to the following transition rules:

 A transition *t* is said to be enabled if each of its input places contains at least a number of tokens equal to the weight of the corresponding input arc, and each of its inhibitor places contains tokens less than the weight of its corresponding inhibitor arcs.

Formally:

$$\forall p \in \textsuperscript{\bullet}{}^{\bullet}t,\ M(p) \ge \textit{Pre}(p,t) \tag{1}$$

$$\forall p \in \textsuperscript{\circ}{}^{\circ}t,\ M(p) < \textit{Inhib}(p,t) \tag{2}$$

 An enabled transition *t* fires by removing from each of its input places a number of tokens corresponding to the weight of the corresponding input arc, and adding a number of tokens in each of its output places corresponding to the weight of the corresponding output arc.

Formally:

$$\forall p \in P, M'(p) = M(p) - \text{Pre}(p, t) + \text{Post}(p, t) \tag{3}$$

The firing of transitions in a Petri net model corresponds to the occurrence of events that changes the state of the modelled system. This change of state can be due to (*i*) the completion of some activity or/and (*ii*) the verification of some logical condition in the system. Since transitions are often used to model activities (production, delivery, order…), transition enabling durations correspond to activity executions and transition firings correspond to activity completions. Hence, deterministic or stochastic temporal specifications can be naturally associated with transitions [24].

472 Petri Nets – Manufacturing and Computer Science

*t)*, respectively.

Formally:

Formally:

comprehensive introduction of Petri nets, see for example [27].

changed according to the following transition rules:

corresponding output arc.

places to transitions, where *N* is a set of nonnegative integers; *Post*: *(P*

function which defines directed weighted arcs from transitions to places*; Inhib: (P*

output places, and the set of inhibitor places of a transition *t* are denoted by

of the modelled system is specified by the number of tokens in each place. Each transition usually models an activity whose occurrence is represented by its firing. A transition can be fired only if it is enabled, which means that all preconditions for the corresponding activity are fulfilled (there are enough tokens available in the input places of the transition). When the transition is fired, tokens will be removed from its input places and added to its output places. The number of tokens removed/added is determined by the weight of the arc connecting the transition with the corresponding place. Graphically, places are represented by circles, transitions by bars or thin rectangles (filled or not filled), tokens by dots. For a

Formally, a Petri net can be defined as *PN* = (*P, T, Pré, Post, Inhib, M0*), where: *P = {p1, p2, …, pn}* is a finite and non-empty set of places; *T = {t1, t2, …, tm}* is a finite and non-empty set of transitions; *Pre*: (*PT*) *N* is an input function that defines directed weighted arcs from

an inhibitor function which defines inhibitor weighted arcs (circle-headed weighted arcs) from places to transitions*;* and *M0* is called initial marking (initial distribution of the tokens in the places). A place connected with a transition by an arc is referred to as input, output, and inhibitor place, depending on the type of the arc. The set of input places, the set of

respectively. The weights of the input arc from a place *p* to a transition *t*, of the output arc from *t* to *p*, and of the inhibitor arc from *p* to *t* are denoted by *Pre(p, t)*, *Post(p, t)*, and *Inhib(p,*

The behavior of many systems can be described in terms of system states and their changes. In order to simulate the dynamic behavior of a system, a state or marking in a Petri net is

 A transition *t* is said to be enabled if each of its input places contains at least a number of tokens equal to the weight of the corresponding input arc, and each of its inhibitor

 An enabled transition *t* fires by removing from each of its input places a number of tokens corresponding to the weight of the corresponding input arc, and adding a number of tokens in each of its output places corresponding to the weight of the

places contains tokens less than the weight of its corresponding inhibitor arcs.

*T)*

*p t Mp pt* , ( ) Pre( , ) (1)

*p t M p Inhib p t* , ( ) ( , ) (2)

*p P M p M p p t Post p t* , '( ) ( ) Pre( , ) ( , ) (3)

 *N* is an output

*T) N* is

*t*, *t* , and *t*, In addition of the concept of time and the introduction of inhibitor arcs, which are not given in the original definition of Petri nets, the modelling of the complex dynamic of a PBS system requires the use of Petri nets models with "*variable arc weights depending on its marking"* and possibly on some decision parameters of the system. The same modelling concept is introduced for modelling inventory control systems and supply chains in [17]-[6]. Precisely, the Petri net model of an inventory control system whose inventory replenishment decision is based on the inventory position of the stock and the reorder and order-up-to-level parameters. Similarly, in the case of a PBS system, the redistribution operation of the bicycles between stations depends on the number of the available bicycles in each station when controlled.

By allowing the weights of some arcs of a Petri net to depend on its marking, control policies of the stations can be easily described in the PBS model. Therefore, we consider in this chapter that for any arc (*i, j*), its weight *w(i, j)* is now defined as a linear function of the marking *M* with integer coefficients and . The weight *w(i, j)* is assumed to take a positive value.

$$\text{cov}(i, j) = \alpha\_{ij} + \sum\_{p\_i \in P} \left(\beta\_{ij}\right)\_{P\_i} \cdot M\left(p\_i\right) \tag{4}$$

To understand the mathematical and intuitive meaning of this concept, consider the Petri net shown in Figure 5.

**Figure 5.** Illustration of a Petri net with variable arc weights depending on its marking

#### 474 Petri Nets – Manufacturing and Computer Science

The model represents an inventory control system with continue review (*s, S*) policy (here *s* = *4* and *S* = *10*) [17]. The different operations of the system are modelled by using a set of transitions: generation of replenishment orders (*t3*); inventory replenishment (*t2*); and order delivery (*t1*). In the model, the weights of the arcs (*t3, p2*), (*t3, p3*) are variable and depend on the parameters s and *S* of the system and on the marking of the model (*S - M(p2); s*).

Petri Nets Models for Analysis and Control of Public Bicycle-Sharing Systems 475

model of the system. A closer look at the Petri net model shows three subnets (modules) representing three different functions named as follows: (*1*) the "station control" subnet; (*2*) the "bicycle flows" subnet; and (*3*) the "redistribution circuit" subnet. The main function of

 The "bicycle flows" subnet represents the bicycle traffic flows between the different stations of the network. A customer uses a bicycle to travel from one station to another. In other words, a bicycle can be taken out from any station and returned to the same or

 The "station control" subnet represents the control function of the stations to ensure bicycles are available for pick up and vacant berths available for bicycle drop off at every station *Si*. The purpose of this function is two-fold: First, the control of the state of the station in terms of the number of bicycles available for new users; and second, according to the state of the controlled station, take one decision among three alternatives: (*i*) Add bicycles in the station, or (*ii*) Remove bicycles from the station, or

 The "redistribution circuit" subnet represents the path (circuit) to be followed by the redistribution vehicle in order to visit the different stations of the network. Its objective is to rebalance bicycles between stations that are emptying out and those that are filling up.

*PSi* Represents a station *Si*. Its marking *M(PSi)* correspond to the number of

vehicle when the station *Si* is visited in order to be controlled. *POi* Specify whether the number of bicycles in a station *Si* is greater than the

*PCi* Specify the end of the control of a station *Si* by the redistribution vehicle.

that the redistribution vehicle is liberated to go to the next station.

*TOi* Test if the number of bicycles available in a station *Si* is greater than the

*TSi* Remove bicycles from a station *Si* if the number of bicycles available in this

*TEi* Test if the number of bicycles available in a station *Si* is equal to the reorder

reorder point *Ri*. It is indicated when *M(POi) = 1*.

*PRi* Represents a redistribution vehicle used to regulate the stations. Its marking

*M(PRi)* correspond to the number of bicycles available in this redistribution

*M(PCi) = 1* means that the control of the station *Si* is completed and indicates

any other station, provided that there is an available locking berth.

*Place Interpretation*

bicycles available in the station *Si*.

*Transition Interpretation*

*TRi* Test and add (if necessary) bicycles into a station *Si*.

station is judged less than the reorder point *Ri*

**Table 3.** Interpretation of places of the PN model

reorder point *Ri*.

**Table 4.** Interpretation of transitions of the PN model

point *Ri*

each subnet is described in the following:

(*iii*) Take no action.

 According to the current marking *Mi* = (*2, 2, 0*) of the net, the transition *t3* is enabled, since the following condition is satisfied:

$$M(p\_2) = 2 < Inhib(p\_2, t\_3) = 4$$

 After the firing of *t3*, 10 - *M(p2) =* 10–2 = 8 tokens are added into the places *p2* and *p3*. In other words, the firing of the transition *t3* from the initial marking *Mi* leads to a new marking *Mf* = (*2, 10, 8*) as the following:

$$\begin{aligned} M\_f(p\_2) &= M\_i(p\_2) + \left[ 10 - M\_i(p\_2) \right] = 2 + \left[ 10 - 2 \right] = 10. \\\\ M\_f(p\_3) &= M\_i(p\_3) + \left[ 10 - M\_i(p\_3) \right] = 0 + \left[ 10 - 2 \right] = 8. \end{aligned}$$