*2.1. Reagents and Standards*

Ultrapure water was produced using a Milli-Q water purification system (Millipore, St. Louis, MA, USA). Methanol of LC-MS grade was purchased from Merck (Darmstadt, Germany). Acetonitrile, formic acid, and ammonium formate of LC–MS grade were purchased from Thermo Fisher Scientific (Waltham, MA, USA). All of the authentic standards used for qualification are listed in Table S1.


**7. References**

[4] Lozano-Perez, T. (1983). Robot Programming. *Proceedings of the IEEE*, Vol. 71, No. 7, pp. 821-841

92 Petri Nets – Manufacturing and Computer Science

**6. Conclusions**

**Author details**

Gen'ichi Yasuda

**7. References**

on the organization level in multiple robot systems.

*Magazine*, IEEE, Vol. 14, No. 12, pp. 82-96

*Nagasaki Institute of Applied Science, Japan*

The multi-robot controller accomplishes the specified task by executing the net model constructed above. Unit actions in a net model used for lowest level controllers are defined in a specified task space, where the action is executed. In the control software the position and orientation in the task space is transformed to the robot coordinate system using the homogeneous transformation matrix. The controller coordinates and supervises the individual controllers based on information explicitly represented by places, place parameters, transitions, arcs, and gates. That is, when a token enters a place that represents a subtask, immediately the controller defined by the control code is informed to execute the subtask with a specified data. Because of the proper nature of the Petri net, the designer can easily create a multi-robot task program which is free of logical errors. The method acts as a programming method on the coordination level and on the organization level [20]. That is, the Petri net is applied as a tool to the operator who plans the multi-robot task, and by executing the net model the individual hardware controllers are regulated and supervised. If, before moving the real robot, the outputs of the robot controller are linked with the graphic robot motion simulator, the whole task programmed can be tested off-line. When the task specification is required to be changed, the net model can be modified on-line.

It was confirmed that the multi-robot controller developed based on tasks programmed in the net form controls the equipment according to the programmed net model. The method provides concurrent movement of all robots and machines in the system, and it provides synchronization commands to allow coordination of their movements to accomplish user defined tasks. The commands used by this system are not based on any specific existing robot language. So, the method can be used in any real robot by translating it to the appropriate robot language, and it acts as a programming tool on the coordination level and

[1] Martinez, J., Muro, P. & Silva, M. (1987). Modeling, Validation and Software Implementation of Production Systems Using High Level Petri Nets, *Proceedings of IEEE*

[2] Sakane, S. (1993). Distributed Sensing System with 3D model-based agents, *Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems*, pp. 1157-1163 [3] Bonner, J. & Shin, K. G. (1982). A Comparative Study of Robot Languages. *Computer*

*International Conference on Robotics and Automation*,pp. 1180-1185

	- [19] Yasuda, G. & Tachibana, K. (1991). A Parallel Processing Control Approach to the Design of Autonomous Robotic Manufacturing Systems, *Proceedings of the XIth International Conference on Production Research*, pp. 445-449

**Chapter 5**

© 2012 Facchin and Sellitto, licensee InTech. This is an open access chapter 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.

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.

© 2012 Facchin and Sellitto, licensee InTech. This is a paper distributed under the terms of the Creative Commons

**Measurement of Work-in-Process**

**by Petri Nets Modeling and Throughput Diagram**

A proper planning and the search for better results in the production processes are important for the competitiveness that manufacturing can add to business operations. However, changes in manufacturing involve risks and uncertainties that may affect the company's operations. In this case, modeling and simulation of the production line can assist the decision-making process, avoiding unnecessary expenses and risks before making a decision. A model that can be simulated in the computer is a mechanism that turns input parameters, known and associated requirements of the process, into output parameters and performance metrics that have not yet happened in the real world (Law; Kelton, 1991).

Thereby, a line production model, which can be used in a computer simulation, can be a tool for decision support, because, before the results will crystallize in the real world

Inventory in process and throughput time that a production plan will generate are quantities that may be useful in decision making in manufacturing and can be predicted by computer simulation. The inventory process (work in process or WIP) consists of materials that have already been released for manufacture (have already left the warehouse or have been received from suppliers), but their orders still not been completed. Lead time is the time between release manufacture order and the product availability for shipment to the customer (Antunes et al., 2007). Some decisions in internal logistics of manufacturing may be related to these quantities: choosing alternatives for compliance with scheduled delivery dates, intermediate storage areas for processing of applications, equipment for internal movement; resources for tool changes and machinery preparation. The most important decision that can be supported by the proposed method is the definition of in-process

manufacturing, it can be predicted, with a given reliability, in virtual simulation.

**and Manufacturing Lead Time**

Tiago Facchin and Miguel Afonso Sellitto

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/50288

**1. Introduction**

[20] Graham, J. H. & Saridis, G. N. (1982). Linguistic Decision Structures for Hierarchical Systems. *IEEE Transaction on Systems, Man, and Cybernetics*, Vo. 12, No. 3, pp. 325-329

Tiago Facchin and Miguel Afonso Sellitto

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/50288


**6. Expanding professional competence and moral responsibility in advancing corporate sustainability**

Attempts to empower the corporate sustainability through professional and moral balance are in line with the strategic principles of oriented quality standard as the basis on expanding individual and social quality assurance [65, 66]. With the orientation of standard quality in achieving the nurturance of principles of corporate sustainability, the need to incorporate professional competence and moral responsibility should be taken into consideration in advancing the environmental concern in the worldwide. The wider attempts on achieving the standard quality in committing with the main principles of professional and moral engagement should bring along with continued learning procedure transformed into the mutual accountability in ensuring the proper solution with a wise approach basis [39, 67, 68]. As such, getting advance towards the appropriate solution of transmitting individual quality with the social responsibility refers to expand the progression in responding the challenging issues on the professional competence, such as lack of digital native towards information management, communication strategy for harmony, and also environmental concern. With this regard, the committed awareness in possessing the responsible engagement to determine the standard quality of firm' manufacturing process and production procedure should be wisely consolidated within the main principle as in the design plan [69, 70]. In this view, the continued assessment should be conducted properly in achieving the responsible continuance together with bringing professional and moral orientated procedure.

In line with expanding professional competence in advancing corporate responsibility, moral responsibility progression is determined as an essential element to bring along with considering the individual and social balance transmitted into the committed awareness. The subsequent orientation of gaining the extent of standard quality on the goal achievement refers to have a sufficient enhancement towards the overall production process together the service management performance [71–73]. It is important to take note that social and individual quality assurance should bring along looking into the whole context of purpose-based instruction strategy. Determining the main point of basic application on professional skills, the overall production process could incorporate with continuing experiential-based learning, referring to the service learning enhancement [19, 25, 30]. In this view, the real application basis assigned into taking the mutually beneficial value from the entire process of production instruction needs to potentially fit into the strategic purpose as in the plan decision. In enhancing the instructional purpose by bringing the commitment awareness on professional expertise and moral duty, having the mutual responsibility with particular attention on obtaining the appropriate

solution towards the certain challenging issues possibly emerged has to go through wisdom-basis. As such, this specific incorporation basis as the strategic way to look into the whole context of the particular issues could bring the particular means to find out the proper answer. It is sure to acknowledge that the extensive point of systematic approach will give insights in allowing the appropriate solution in giving the response on the challenging issues, for instance conflict between individual and social concern. With this regard, the corporate social responsibility (CSR) may play its role in giving the appropriate way in managing the multi-human with their unique diversity background within one venue in the certain firm.

In terms of intensifying the solving progression towards the certain problematic issues, the prominent element of knowledge skills referring to both professional and moral competence should bring along with designing the principles in line with the phase of production and service. As such, the particular attention on instructing the commitment on determining the goal achievement together with firms' procedural context has to go through balancing the alignment on taking benefit along with intensifying concern of personality and community in assisting the readiness into the firms' environmental basis [74–76]. With this regard, addressing the wider context of achieving the accessibility in assessing the profit assigned into the societal concern is potentially needed to have a sufficient measurement on the quality process and outcome. The certain standard quality in attempting to incorporate the solving problem towards the issues possibly occurred refers to expand a sufficient preparation in managing professional and moral responsibility within the social community [77–79]. Apart from this, the consolidation on transmitting into the production service needs to point out disseminating the principal requirement in achieving target through mentoring procedure in the form of dynamic approach. In the contextual basis, determining the societal approach with the balance between quality and duty amongst the firms' team should bring along with the committed awareness in maximising the appropriate manners actually comprehended in enabling what to do in line with right and responsibility in corporate sustainability [67, 80, 81]. In ensuring the sustainable development in continuing the process together with matching to the proper way, the procedural context in emphasising the strategic enhancement to cooperate into the entire process of firms should do with empowering the personal and social responsibility within the continued performances in achieving the planned aim together with providing them the solving-based strategy. Through maximising the knowledge-based comprehension together with actual practice incorporation, the basic systems in empowering the corporate sustainability is really linked into the problem-based management assigned into incorporating the stage of firms' objective plan to lead into the sustainable development.


**2. Methodology**

#### **2.1 Sampling**

During three two-week sampling campaigns (November 2003 and 2004, and March 2004), PM2.5 samples were collected at two sites with different land use. **Figure 1** shows the two sampling sites, along with the orographic characteristics of the Mexico City Metropolitan Area. La Merced (MER) is an important commercial site with a major food market, located approximately 0.2 km west of downtown; the site is near to moderately traveled paved streets. Xalostoc (XAL) is located in the northeast of the city, adjacent to heavily traveled paved and unpaved roads where old and new gasoline and diesel vehicles transit in an industrialized area; this site is 5 km west of the dry Lake Texcoco, thus resuspended dust from the dry lake bed may affect this site.

Particle samples were collected with battery-powered MiniVol portable PM2.5 samplers (Airmetrics) operating with a volume intake of air of 5 L/min for 24 h. Before sampling, the filtration volume of the samplers was previously calibrated at standard conditions of temperature and pressure. Teflon membranes were used to measure

mass by gravimetry. Details of the equipment and sampling procedures can be found elsewhere [9].

### **2.2 PM2.5 concentration and composition measurements**

PM2.5 mass was determined by duplicate samples collected on 47 mm Teflon filters, which were weighted in a microbalance prior to and after sampling.

Ions were collected on quartz filters and extracted in deionized water by sonication. Ions were analyzed by high-performance liquid chromatography. Nitrate, sulfate, and ammonium were analyzed by ion exchange chromatography. Organic carbon and elemental carbon were analyzed by thermal–optical reflectance.

#### **2.3 Stable nitrogen and carbon isotopes measurements**

Stable carbon and nitrogen isotopes of PM2.5 were collected in pre-combusted GF/F filters, which were placed in the MiniVol samplers. After sampling, filters were freeze-dried to remove any water or humidity in the sample, placed in aluminum vials, and inserted into a combustion column. Generated gases (CO2 and N2) were analyzed in a MAT-Finnigan 252 stable isotope mass spectrometer to quantify the 13C/12C and 15N/14N isotopes in each sample. Standards used for instrument calibration were acetanilide, methionine, and urea, all with a known isotopic value. An acetanilide substandard was run for every 10 samples. Carbon and nitrogen isotopes are referred to as VPDB and Vienna air nitrogen standards, respectively.

#### **2.4 Meteorological and ambient air data**

Ancillary ambient data were obtained from the RAMA and REDMET data sets. RAMA (Spanish acronym for automatic ambient monitoring network; [17]) measures criteria atmospheric pollutants (PM10, CO, CO2, NOx, NO2, SO2, and O3) at 15 locations within Mexico City on an hourly basis. At MER, PM2.5 hourly data are also measured by RAMA. Wind velocity and direction, relative humidity, and temperature measured on an hourly basis were obtained from the REDMET (meteorological network) database [17]. For each sampling period, the hourly data were averaged, except for wind direction where the hourly mode was used.


*2.8. Plant Inoculation*

A pot experiment was conducted in the greenhouse of the Botany Department, PMAS-AAUR, Rawalpindi. A complete randomized design was applied with three replications. Each selected halotolerant strain was grown overnight in LB media. To obtain a cell pellet, the supernatant was discarded after centrifugation at 3000 rpm for 3 min. The cell pellet was washed three times with autoclaved water and the absorbance was recorded with a spectrophotometer at 600 nm to obtain the desired concentration, i.e., 107 CFU. Ten sterilized seeds were sown in each pot (containing 10 kg of soil) in the greenhouse with the day 10 h/14 h night at a temperature of 21/15 ◦C. Soil moisture was maintained at 15 ± 1%. Four strains and their consortium were evaluated under two treatment controls and 150 mM NaCl stress. The salt level was maintained with EC of 4.0 dS m−1 (first irrigation) or 8.5 dS m−1 (second irrigation). Plants were harvested after 45 days of sowing. Fresh and dry biomass was recorded. Leaf area was measured with the help of a leaf area meter. All the samples were collected in zipper bags and stored at −20 ◦C freezer for further biochemical assays. The percent of water content was determined by measuring the ratio between the fresh and dry weight of the upper fully developed leaf by using the following formula [27]:

$$\text{RWC} = [\text{FW} - \text{DNV}] \text{[TW} - \text{DW]} \times 100 \tag{1}$$

#### *2.9. Electrolyte Leakage (%)*

Electrolyte leakage was determined by the method of Srairam [28]. Leaf discs weighing 0.1 g were heated in 10 mL of distilled water for 30 min at 40 ◦C and the electrical conductivity (C1) was recorded. The same discs were then heated at 100 ◦C and again electrical conductivity (C2) was recorded. Whereas, calculations were done by the following formula:

$$\text{MSI} = \left[1 - \text{(C1/C2)}\right] \times 100\tag{2}$$

#### *2.10. Chlorophyll and Carotenoid Content*

Leaf chlorophyll a, b, total chlorophyll, and carotenoid contents were estimated by the method of Arnon [29]. Fresh leaves (0.5 g) were ground in 10 mL of 80% acetone. The readings of the filtrate were measured at 470 nm, 663 nm, and 645 nm. Calculations were done by the following equations:

$$\text{Chla (mg/g)} = \left[ 12.7 \text{A}\_{663} - 2.69 \text{A}\_{645} \right] \left( \upsilon / w \right) \tag{3}$$

$$\text{Chllb (mg/g)} = \left[ 22.9 \text{A}\_{645} - 4.68 \text{A}\_{663} \right] \left( \upsilon / w \right) \tag{4}$$

$$\text{Total chlorophyll} \left(\text{mg/g}\right) = \left[\left(20.2 \text{A}\_{645} + 8.02 \text{A}\_{663}\right) \text{v/}w\right] \tag{5}$$

$$\text{Caroteroids content(mg/g)} = (1000 \text{ A}\_{470} - 1.8 \text{ Chl}\_{\text{a}} - 85.02 \text{ Chl}\_{\text{b}}) / 198 \tag{6}$$

where A is the optical density at a specific wavelength.

#### *2.11. Proline Content*

Proline contents were determined by following the protocols of Bates [30]. Fresh leaves (0.5 g) were homogenized with 10 mL of sulfosalicylic acid (3.0%). The solution was filtered, and the filtrate was mixed with equal amounts of glacial acetic acid and ninhydrin reagent. The mixture was heated for 1 h in a water bath at 90 ◦C and the reaction was stopped by transferring the mixture to ice. Toluene (1 mL) was added to the mixture and the solution was mixed and the solution separated into two layers. The upper layer was isolated in separate test tubes and the reading was measured at 520 nm. Proline was determined as follows:

$$\text{Proline} = \text{(Reading of sample} \times \text{Diluted concentration} \times \text{K value)/material weight} \tag{7}$$

#### *2.12. Total Soluble Sugar and Amino Acid*

Soluble sugars were estimated after the method of Dubois et al. [31]. Ground plant tissue (0.1 g) was mixed with 3 mL of 80% methanol. The solution was heated in a water bath for 30 min at 70 ◦C. An equal volume of extract (0.5 mL) and 5% phenol was mixed with concentrated sulphuric acid (1.5 mL) and was again incubated in the dark for 30 min. The absorbance of the sample was checked at 490 nm and the calculations were done by applying the following formula:

$$\text{Sugar } (\mu \text{g/mL}) = \text{Absorbance of sample} \times \text{Dilution factor} \times \text{K value} \tag{8}$$

Fresh tissue in grams.

The standard curve was prepared for glucose solution, which was used for the determination of the amount of sugar, expressed in mg g−1 fw−1.

The Ninhydrin method was used for the determination of free amino acids [32]. Leaf extract (1 mL) was mixed with the same volume of 0.2 M citrate buffer (pH-5) and 80% ethanol, and 2 mL of the ninhydrin reagent. The absorbance of the reaction mixture was taken to 570 nm. Amino acids were computed with the equation:

```
Amino acids = Absorption × volume × Diluted concentration/Sample weight × 1000.
```
The amino acid, leucine, was used for preparing the standard curve, and results were expressed in mg of amino acid per g of dry tissue.

#### *2.13. Total Protein Content*

The concentration of protein was quantified by the Bradford assay [33]. Bovine serum albumin was used as a standard. Proteins were extracted by dissolving 0.2 g of leaf samples in 4 mL of sodium phosphate buffer (pH 7), and 0.5 mL of the extract was mixed with 3 mL of Comassive bio red dye. The optical density of the solution was measured at 595 nm. Protein was determined by:

Protein = Reading of extract × Diluted concentration × value of K/sample weight (9)

#### *2.14. Antioxidant Enzyme Assay*

Enzyme extract was prepared by grinding one gram of leaf in liquid nitrogen. The obtained powder was added in 10 mL of 50 mM phosphate buffer (pH 7.0) and was mixed with 1 mM Ethylene Diamine Tetra Acetic acid (EDTA) and 1% polyvinylpyrrolidone (PVP). The whole mixture was centrifuged at 13,000× *g* for 20 min at 4 ◦C. The supernatant was used for the enzyme assay.

The catalase (CAT) content was estimated by observing the degradation of H2O2 at 240 nm [34]. Catalase activity (U mg protein−1) was calculated from the molar absorption coefficient of 40 mm−1cm−1for H2O2. Peroxidase dismutase (POD) was determined by following the procedure of Rao [35]. The reaction mixture consisted of 10 μL of crude enzyme extract, 20 μL of 100 mM guaiacol, 10 μL of 100 mM H2O2, and 160 μL of 50 mM sodium acetate (pH 5.0). Absorbance was recorded at 450 nm.

Superoxide dismutase (SOD) activity was done by using the procedure of Giannopolitis and Ries [36]. The composition of the reaction mixture was 50 mM sodium phosphate buffer (pH 7.8), 0.1 M tris-HCL, 14 mM methionine, 1.05 mM riboflavin, 0.03% TritonX-100, 50 mM nitroblue tetrazolium chloride (NBT), 100 mM EDTA, and 20 μL enzyme extracts. After adding riboflavin, the glass tubes were illuminated for 5 min, and reactions were stopped by turning off lights. The absorbance was recorded at 560 nm.

#### *2.15. Statistical Analysis*

Three replicates were used for the mean and standard deviation values of the data. The obtained data were further analyzed by Duncan's multiple range tests using MSTAT-C version 1.4.2. The correlation coefficient of the data was done using the software Statistix version 8.1. Mean values were compared by the least significant difference (LSD) at *p* ≤ 0.05 [37]. The heatmap for the correlation coefficient was prepared by using web tool clustvis (https://biit.cs.ut.ee/clustvis/).

#### **3. Results**

#### *3.1. Soil Analysis*

Analysis of the rhizospheric soil samples of all four plants showed the soil was sandy clay loam with an EC range of 0.76–0.85 dSm−1, pH in the range of 7.99–8.12, high Na/K ratio, and a low concentration of nutrients (Table 1).

**Table1.**Physiochemicalpropertiesoftherhizospheresoilandrhizobacterialpopulation.

#### *3.2. Isolation and Screening of Salt-Tolerant PGPR Strains*

A total of 50 isolates were obtained from the rhizospheric soil of four halophytic plants. Among all isolates, 90% of colonies were round, creamy, and had entire margins (Supplementary Materials Table S1). Further, 78% of isolates were Gram-negative and rod-shaped (Supplementary Materials Table S2).

In the halotolerant assay, 70% of strains were able to grow up to 6%, 20% strains showed tolerance at 10%, while four strains SR1, SR2, SR3, and SR4 were able to grow at 15% NaCl (Supplementary Materials Table S2). These four strains also showed positive results for phosphorous solubilization, hydrogen cyanide, and siderophore production (Supplementary Materials Table S3).

#### *3.3. E*ff*ect of Bacterial Isolates on Germination of Wheat*

Salt stress resulted in a considerable reduction in the germination parameters of the wheat seeds. Under salt-stressed conditions, the seedling vigor index and germination index showed a 12.5% and 31% decrease compared to the control. Though most of the strains showed a significant increase in seed germination, four strains SR1, SR2, SR3, and SR4 showed prominent results (14.28%, 35%, 42%, and 55%), respectively, as compared to the non-inoculated control under the salt stress condition (Supplementary Materials Table S4).

#### *3.4. Identification of Isolates*

Initially, the four strains were identified based on the C/N source utilization pattern (Supplementary Materials Table S5). Molecular identification of the screened halotolerant strains was done based on 16S rRNA sequences and on the comparison of the 1500-bp sequence of 16S rRNA gene subjected to BLAST to confirm the relatedness with other bacterial strains. The isolate SR1 (1485 base pair) was closely related (98% nucleotide identity) to sequences of bacteria annotated as *Bacillus* strain JQ 926435 in the GenBank database. The sequence of SR2 (1480 base pairs) was 99% identical to *Azospirillum brasilense* DQ 288686.1, SR3 (1482 base pairs), and 96% identical to strain *Azospirillum lipoferum* accession no. M. 5906.1. Furthermore, the isolated strain SR4 showed a 99% homology with *Pseudomonas stutzeri* JQ 926435. The accession numbers of the identified strains were obtained from NCBI and are given in Table 2.

**Table 2.** Molecular identification of the isolates based on partial 16S rDNA analysis.

Further phylogenetic analysis of the identified bacteria was conducted in MEGA4 software to determine their affiliation [38]. The evolutionary history was inferred using the maximum parsimony method [26]. The results are shown in Supplementary Materials Figures S1–S4.

#### *3.5. Production of Phytohormones*

Based on the halotolerance assays, PGP traits, and germination assay results, four isolates were selected for further analysis. All the halotolerant PGPR strains showed the production of phytohormones in liquid culture (Figure 1). Halotolerant PGPR strains were able to produce IAA (0.5–2.1 μg mL−1), gibberellic acid (1.5–2.5 μg mL−1), CK (0.39–0.64 μg mL−1), and ABA (1.9–3.4 μg mL−1). The PGPR strains SR2 and SR3 produced higher concentrations of phytohormones than those of SR1 and SR4; however, the bacterial consortium produced maximum concentrations of IAA (2.1 μg mL−1), gibberellic acid (2.5 μg mL−1), CK (0.64 μg mL−1), and ABA (3.4 μg mL−1).

**Figure 1.** Production of phytohormones (Indole Acetic Acid (IAA), Gibberellic Acid (GA), Cytokinin (CK), and Abscisic Acid (ABA) by PGPR strains and their consortium in culture media. (SR1: Inocualted with *Bacillus* sp; SR2: Inocualted with *Azospirillum brasilense*; SR3: Inocualted with *Azospirillum lipoferum*; SR4: Inocualted with *Pseudomonas stutzeri*; Consortium is a combination of all four strains *Bacillus* sp, *Azospirillum brasilense, Azospirillum lipoferum, Pseudomonas stutzeri*). This data displays the means and standard deviation (*n* = 3). Different letters show significant differences between treatments (*p* < 0.05).

#### *3.6. Production of Compatible Solutes*

A considerable amount of proline was produced by all the screened halotolerant strains when subjected to different salinity levels. Production of proline by SR2 and SR3 was the highest in the 10% saline condition than the control. The maximum amount of proline (12.1 μg mg−1) was produced by the bacterial consortium, which was 23% greater than SR2 and SR3. For the carbohydrate contents, a significant amount of soluble sugars was recorded by all the strains (Figure 2). The production of soluble sugars was more pronounced at different salinity levels than the control. The bacterial strains SR2 and SR3 produced a greater amount of (89–111 μg mg−1) soluble sugar as compared to the control, but the consortium of bacterial isolates recorded the maximum values at 10% NaCl (222 μg mg−1) (Figure 3).

**Figure 2.** Production of proline by PGPR strains and their consortium in culture media supplemented with different concentrations of NaCl (2%, 4%, 6%, 8%, and 10%). The treatment details are the same as in Table 3. This data displays the means and standard deviation (*n* = 3). Different letters show significant differences between treatments (*p* < 0.05).

**Figure 3.** Production of total soluble sugar by PGPR strains and their consortium in culture media supplemented with different concentrations of NaCl (2%, 4%, 6%, 8%, and 10%). The treatment details are the same as in Table 3. This data displays the means and standard deviation (*n* = 3). Different letters show significant differences between treatments (*p* < 0.05).


**3. Meat and dairy products as a functional agent**

#### **3.1 Dairy Products**

Authors have considered different traditional dairy products such as yogurt, milk and cheese as a functional products as these are rich source of various vitamins and minerals and other constituents that can be used as functional agents [84]. Such as conjugated linoleic acid (CLA) and Selenium, that play an important role in lowering the serum cholesterol level thus preventing the atherosclerosis and other cardiovascular diseases also having antioxidant functions in the body [85].

Yogurt is a traditional dairy product that was prescribed by physicians in Middle East as a treatment of gastrointestinal diseases [86]. Yogurt is manufactured using *Streptococcus thermophilus and Lactobacillus bulgaricus* which both work in synergism. Health benefits of yogurt can be enhanced by the addition of probiotic bacteria in yogurt such as *Bifidobacterium, Lactobacillus acidophilus* and *L. rhamnosus* [87]. Yogurt has been used a food source consisting of probiotic organism throughout the world.

A wide variety of fermented milks have also been developed and various health benefits were linked with the consumption of fermented milks such as lowering of cholesterol. They also contain the important probiotics strains that are involved in improving the health [88].

Probiotic cheeses are available in soft as well as hard varieties. Various Probiotic Strains such as *Bifidobacterium and L. rhamnosus* are readily used in such cheeses and these cheeses can be beneficial source of Probiotics [89].

#### **3.2 Meat products**

Meat products are good source of protein and fat along with water and other vitamins which are highly bioavailable. Meat products can be made highly beneficial for health either by incorporating any ingredient in it that is considered healthy or eliminating or reducing any component that can be considered harmful [90].

Fatty acid and cholesterol level of meat can be modified by selecting different breeds, modifying the feed patterns, addition of some feed additives and several interventions regarding animal metabolism [91].

Similarly addition of olive oil to variety of meat products was thought to be associated with the high biological value and decrease onset of breast cancer and heart diseases [92].

Soy protein can also be added into the meat products. In 1999, US FDA stated that any product low in saturated fats and cholesterol containing 25 g of soy proteins may be helpful in preventing the cardiovascular diseases [93].

Lipid oxidation is the major issue in meat products thus instead of using synthetic antioxidants that pose toxicity and other harmful effects can be replaced by the antioxidants from the plat source such as rosemary, tea, etc. Green tea is associated with reducing the level of Cholesterol in body as well as increasing the portion of High density Lipoproteins and decreased the oxidation of lipoproteins [90, 94, 95].

Addition of salt for the preservation purpose can lead to high percentage of salt intake and can lead to the development of hypertension. Several substitutes were assessed and one of the best substitute was the addition of calcium ascorbate. This substitute causes higher acidification due to the fermentation by lactic acid bacteria. Replacement of salt with Calcium ascorbate helped in reducing the sodium chloride level as well enriching the meat with nutrition [96].

**15**

*Therapeutic Potential of Probiotics and Prebiotics DOI: http://dx.doi.org/10.5772/intechopen.86762*

compare to chemical treatment.

**4.1 Mode of action of prebiotics**

resident microbes.

• They produce bateriocins.

carbohydrates.

Important modes of action of prebiotics are:

• Prebiotics do cause intestinal homeostasis.

• Host surface receptors are coated by prebiotics.

Prebiotics are the food that is not digested in the human gut but food ingredients

• These are non-digestible carbohydrates that are not digested by the upper gastrointestinal tract and travel in the ileum and colon where fermented by the

• Favorable bacteria produce short chain fatty acids with the help of non-digestible

Fermentation of resistant starches and dietary fiber caused by bacteria in colon release short chain fatty acid metabolites (SCFA). SCFA are well known for gut health as well as their part in provision of supplementary energy to the host in fatness is in debate. On contrary, 10% of entire energy in humans is provided by SCFA. According to energy yield hypothesis, dysbioticmicrobiomes have an amplified capacity to remove energy from the food, so that the bacterial conversion of non-digestible carbohydrates and dietary fiber to SCFAs could give additional energy to the host and result fatness of individual over time. Likewise, G-protein coupled receptors (GPR) can sense SCFAs that tie them with lipid and glucose breakdown. SCFAs activate the two major proteins, GPR41 and GPR43 which are expressed on adipocytes and enter endocrine L cells. Peptide YY is released by stimulation of intestinal GPR41 which enhances gut passage time and increase satiety. Inflammation lessens by activation of intestinal GPR43 as well as it simulates glucagon-like peptide (GLP), a hormone which contributes in regulation of insulin secretion. Enteroendocrine L cells express GLP-1 as well as secrete the gut-trophic

• Short-chain fatty acids are the energy source of epithelial cells.

**4.2 Targets for prebiotics: gut microbiota and intestinal health**

• They regulate metabolic function and modulate immune system [98].

boost the growth and activity of bacteria that are good for our intestine, consequently they balance the intestine of an organism [97]. The most commonly used bacteria that are good for our health is amplified by prebiotics comprise of genus *Bifidobacterium* and *Lactobacillus,* which control the growth of harmful bacteria. Most commonly used prebiotics are mannan-oligosaccharides, galactoglucomannans, lactose, inulin and oligofructose. Short chain carbohydrates used as prebiotics consist of three to ten sugar units derived from the cell wall of yeast and plants. Prebiotics functionality are not alter by any food processing treatment and require little or no regulatory requirements, hence making their consumption more easy as

**4. Prebiotics**


*2.2. Terrain Classification Methodology*

In robot navigation, terrain recognition can essentially be supposed as surface texture recognition. Terrain recognition based on local features is the most popular because of its robustness to illumination and weather and high recognition rate.

The terrain classification system proposed in this paper is depicted in Figure 2. The Kinect is installed on top of the robot to collect information on terrain (color, depth, and infrared images) and an obstacle detection module is established to detect obstacles in the front. If there are no obstacles, the information will be directly transmitted to the terrain classifier. Otherwise, the module will locate obstacles and identify their size. Meanwhile, a color image of the terrain is processed by the image infilling method to decrease the influence of obstacles on terrain identification. After classification, the confidence scores of each terrain are summarized into a pie chart. The analysis of the pie chart shows whether the terrain is mixed or not. If the terrain is mixed, the color image would be subjected to image segmentation and infilling. Then, the processed color image will be classified by the terrain classifier again, which provides an accurate identification of multiple areas of complex terrain. Finally, all terrain types can be predicted accurately, thus good performance by the robot is guaranteed. The function modules are described in detail in the following section.

**Figure 2.** Terrain classification system.

#### 2.2.1. Obstacle Detection Module

Detecting and localizing obstacles are important to realize autonomous motion and path planning. The sensors used for traditional obstacle detection mainly include laser radar sensors, ultrasonic sensors, infrared sensors, visual equipment, etc. [24]. In this paper, a fast and accurate detection method based on depth and infrared information is used [25]. The image is segmented by the mean-shift algorithm and the pixel gradient of the foreground is calculated. After pretreatment of edge detection

and morphological operation, the depth and infrared information are fused. The characteristics of depth and infrared images are used for edge detection. Thus, the false rate of detection is reduced and detection precision is improved. Since depth images cannot be affected by natural sunlight, the influence of light intensity and shadow on obstacle recognition is effectively eliminated and the robustness of the algorithm is improved. This method can accurately identify the position and size of obstacles. In this paper, the results obtained by obstacle detection with this method are used as the input of the terrain image infilling method.


Preface

This book provides an overview of current environmental issues and sustainable solutions. Nowadays, both developed and developing countries are paying much attention to environmental management practices. This book is a resource for students, researchers, and decision-makers in the field of environmental management. It consists of twenty-three chapters, each focusing on a certain environmental issue. The chapters are developed across five themes: natural resources, waste management, climate change, sustainability, and pollution management.

Section 1 – "Natural Resources"

Chapter 1 presents a case study on developing the capabilities needed to adapt to freshwater shortages and enhance prospects for human security in Panchkahl Municipality, Kathmandu, Nepal. Data from the study suggest the need for further system transformation to promote adaptation.

Chapter 2 addresses microfinance practices and value-added, non-wood forest products for a sustainable environment, using a state in India as an example. This study reveals opportunities for using natural resources sustainably and encourages forest dwellers to become micro-entrepreneurs.

Chapter 3 addresses the consequences of different processes in the grassland ecosystem in the shola forest and grassland mosaic of the Nilgiri Biosphere Reserve (NBR), South India.

Chapter 4 describes the effects of climatic variability on harmful algal blooms, providing systematic knowledge to manage and mitigate their impacts.

Chapter 5 addresses the need to improve models for effective communication and to answer policy-relevant questions. Study findings reveal that there is a need to improve communication between decision-makers and the public to advance knowledge and understanding of results at the appropriate decision-making hub and the associated community.

Chapter 6 discusses the rights and responsibilities of forest fringe communities in Ghana and Collaborative Forest Management (CFM) in the northern region. It explores the levels of awareness of communities of these rights and responsibilities.

Section 2 – "Waste Management"

Chapter 7 elaborates on microbial fuel cell technology and its application for dairy wastewater treatment. It provides useful insight for integrating this technology with existing conventional wastewater treatment methods to achieve the degradation of various dairy pollutants, including emerging micropollutants.

Chapter 8 is a study of municipal solid waste generation in Dir City, District Dir Upper Khyber Pakhtunkhwa (KP), Pakistan. The study finds that the spatial

distribution of waste generation varies across the city. For example, a high rate of generation was found in the Rehankot and Shaow areas, whereas low generation rates were found in fringe areas.

Chapter 9 provides a review of RS waste management strategies, highlighting applications for removing contaminants from wastewater in single and multi-component systems, and in static or continuous operation modes.

Chapter 10 discusses hazardous wastes and their management.

Chapter 11 reviews the structure and dynamics of organic soils and explains their creation, evolution, and ultimate fate. It focuses on degraded peatland net primary productivity because of potential forthcoming differences attributed to rainfall, temperature, vegetation, hydrology, and permafrost disappearance.

Section 3 – "Climate Change"

Chapter 12 addresses multiple deleterious consequences of climate change. It talks about the causes of climate change and its effect on the planet, environment, plants, animals, and humans. It also discusses climate change adaptation and preventive strategies.

Chapter 13 is a review distinguishing the levels of vulnerability and resilience between the people who live in high potential zones and low potential zones in Tanzania. Study findings suggest that farmers with weak adaptive capacity should be carefully and immediately attended to, otherwise their livelihood options can destroy the environment further.

Chapter 14 is a study assessing the potential impact of climate change under a range of scenarios on intercrops of maize and improved pigeon pea varieties developed and released in Kenya.

Section 4 – "Sustainability"

Chapter 15 discusses how the spatial carrying capacity of cities, river basins, and regional transformation adapt to environmental changes, as well as the direction of carrying capacity improvement.

Chapter 16 discusses non-timber forest products and the associated economic activities. It also relates habitat management aspects along with commercial invasion, which have become detrimental to the environment.

Chapter 17 describes the methodology for designing sustainable structures with examples of control systems for promoting sustainable structure design and the process of producing and revising sustainable structure design guidelines.

Section 5 – "Pollution Management"

Chapter 18 is an experimental study describing the encapsulation of the polluting gases NO3, NO2, CO2, and N2 by the calix[4]arene molecule. Study results clearly explain the charge distribution reactivity.

**VII**

Chapter 19 describes the development of solid pellet technology for molten salt in heat transport processing. The apatite phosphate, molten salt in slime-salt bath mixes was investigated under microwave radiation heating, resulting in insoluble sorbent fines dissolved in a porous basket. Study findings are helpful for advanced fuel energy storage with favorable economic potential and intrinsic properties.

Chapter 20 provides a detailed and comprehensive account of the numerical

as well as their main strengths and weaknesses and simulation capabilities.

a discussion of preventive strategies to minimize exposure to EDCs.

the efficiency of an individual process.

environmental management.

Chapter 21 reviews how advanced oxidation processes (AOPs) help in removing pharmaceutically active compounds (PhACs) in which hydroxyl radicals (HO) act as common oxidants to improve the biodegradability of further treatments. The chapter concludes that treatment with AOPs increases efficiency when compared to

Finally, Chapter 22 describes the human health consequences of endocrine-disrupting chemicals (EDCs). It provides information on routes of exposure, metabolism, and mechanisms of action of EDCs. It also discusses the main consequences of EDCs, including obesity, diabetes, reproductive disorders, and cancer. The chapter ends with

Overall, this book enhances understanding of various environmental issues, changes, and sustainable solutions. The information contained herein will help to improve the skills of environmental scientists and decision-makers. It also contributes to the exchange of best practices for developing and implementing methods for

**Suriyanarayanan Sarvajayakesavalu**

Vinayaka Missions Kirupanandavariyar Arts and Science College, Vinayaka Missions Research Foundation Deemed to be University,

SCOPE – India (*Scientific Committee of Problems of the Environment*),

Director of Ph.D. and Master Programmes in Environmental Science,

JSS Academy of Higher Education and Research (JSSAHER),

Director of Master Programme in Intellectual Property

and Innovation Management Graduate School,

Professor,

Salem, India

Mysuru, Karnataka, India

**Pisit Chareonsudjai, Ph.D.**

Department of Environmental Science,

Faculty of Science,

Khon Kaen University, Khon Kaen, Thailand

approaches proposed to analyze the fouling phenomenon that occurs inside exhaust gas systems. It examines in detail the main characteristics of each numerical model

Chapter 19 describes the development of solid pellet technology for molten salt in heat transport processing. The apatite phosphate, molten salt in slime-salt bath mixes was investigated under microwave radiation heating, resulting in insoluble sorbent fines dissolved in a porous basket. Study findings are helpful for advanced fuel energy storage with favorable economic potential and intrinsic properties.

Chapter 20 provides a detailed and comprehensive account of the numerical approaches proposed to analyze the fouling phenomenon that occurs inside exhaust gas systems. It examines in detail the main characteristics of each numerical model as well as their main strengths and weaknesses and simulation capabilities.

Chapter 21 reviews how advanced oxidation processes (AOPs) help in removing pharmaceutically active compounds (PhACs) in which hydroxyl radicals (HO) act as common oxidants to improve the biodegradability of further treatments. The chapter concludes that treatment with AOPs increases efficiency when compared to the efficiency of an individual process.

Finally, Chapter 22 describes the human health consequences of endocrine-disrupting chemicals (EDCs). It provides information on routes of exposure, metabolism, and mechanisms of action of EDCs. It also discusses the main consequences of EDCs, including obesity, diabetes, reproductive disorders, and cancer. The chapter ends with a discussion of preventive strategies to minimize exposure to EDCs.

Overall, this book enhances understanding of various environmental issues, changes, and sustainable solutions. The information contained herein will help to improve the skills of environmental scientists and decision-makers. It also contributes to the exchange of best practices for developing and implementing methods for environmental management.

## **Suriyanarayanan Sarvajayakesavalu**

Professor, Vinayaka Missions Kirupanandavariyar Arts and Science College, Vinayaka Missions Research Foundation Deemed to be University, Salem, India

SCOPE – India (*Scientific Committee of Problems of the Environment*), JSS Academy of Higher Education and Research (JSSAHER), Mysuru, Karnataka, India

#### **Pisit Chareonsudjai, Ph.D.**

Faculty of Science, Department of Environmental Science, Director of Ph.D. and Master Programmes in Environmental Science, Director of Master Programme in Intellectual Property and Innovation Management Graduate School, Khon Kaen University, Khon Kaen, Thailand

**VI**

distribution of waste generation varies across the city. For example, a high rate of generation was found in the Rehankot and Shaow areas, whereas low generation

Chapter 9 provides a review of RS waste management strategies, highlighting applications for removing contaminants from wastewater in single and multi-component

Chapter 11 reviews the structure and dynamics of organic soils and explains their creation, evolution, and ultimate fate. It focuses on degraded peatland net primary productivity because of potential forthcoming differences attributed to rainfall,

Chapter 12 addresses multiple deleterious consequences of climate change. It talks about the causes of climate change and its effect on the planet, environment, plants, animals, and humans. It also discusses climate change adaptation and preventive

Chapter 13 is a review distinguishing the levels of vulnerability and resilience between the people who live in high potential zones and low potential zones in Tanzania. Study findings suggest that farmers with weak adaptive capacity should be carefully and immediately attended to, otherwise their livelihood options can

Chapter 14 is a study assessing the potential impact of climate change under a range of scenarios on intercrops of maize and improved pigeon pea varieties developed

Chapter 15 discusses how the spatial carrying capacity of cities, river basins, and regional transformation adapt to environmental changes, as well as the direction of

Chapter 16 discusses non-timber forest products and the associated economic

Chapter 17 describes the methodology for designing sustainable structures with examples of control systems for promoting sustainable structure design and the process of producing and revising sustainable structure design guidelines.

Chapter 18 is an experimental study describing the encapsulation of the polluting gases NO3, NO2, CO2, and N2 by the calix[4]arene molecule. Study results clearly

activities. It also relates habitat management aspects along with commercial invasion,

rates were found in fringe areas.

Section 3 – "Climate Change"

destroy the environment further.

and released in Kenya.

Section 4 – "Sustainability"

carrying capacity improvement.

Section 5 – "Pollution Management"

explain the charge distribution reactivity.

which have become detrimental to the environment.

strategies.

systems, and in static or continuous operation modes.

Chapter 10 discusses hazardous wastes and their management.

temperature, vegetation, hydrology, and permafrost disappearance.

**1**

Section 1

Natural Resources


*5.1. The Urban Value Index (Ivu)*

Urban quality and building quality are multidimensional concepts that can be interpreted from different points of view and perspectives [37]. One possible definition refers to the analysis of real estate values, to some degree a synthesis, effect and overall measure of these phenomena. The assumption is that the willingness to pay different prices suggests a greater or lesser appreciation of assets, not only in relation to their intrinsic characteristics, but also to the qualities expressed by the urban contexts in which they are located. This latter approach was used to construct the urban values index.

The starting point is defined by the OMI Zone (acronym for the Revenue Agency's *Osservatorio del Mercato Immobiliare*, Real Estate Market Observatory): a "continuous portion of the municipal territory that reflects a homogeneous sector of the local real estate market, with a uniform appreciation of economic and socio-environmental conditions". This uniformity is translated into a homogeneity of characteristics related to position, urban planning, historical-environmental and socio-economic qualities of settled areas, and the offering of urban services and infrastructures. The territorial delimitation of a homogenous market area thus passes through the analysis of the homogeneity of socio-environmental and economic conditions and location: first and foremost the requisite of centrality in terms of the presence of functions, accessibility to public and private facilities and services of varying degrees and levels, the level of urban and suburban transportation services, vehicular connections, the presence of schools, healthcare and sport facilities, shops, tertiary services, etc.

The index defines the distance (in terms of real estate values and therefore of market appreciation) between different urban contexts; it is calculated based on the maximum OMI market value on a municipal basis (for residential buildings in good condition) and the OMI market value where the property is located, according to the following formula:

$$I\_{\rm vu} = \
a V\_{\rm OMI} - q\_{\prime} \tag{1}$$

### *5.2. The Use Index (Iut)*

The use index represents the yield (or measure of its efficiency) tied to the use of an asset in relation to its occupancy. The index consists of two parameters describing both the actual degree of use in terms of surface area, and the ability of occupants to pay property management/utility costs (electricity, water, gas as well as services such as waste collection taxes, etc.).

The first parameter is linked to the management of spaces: parameter P1 expresses the relationship between the total building area and the portion occupied. This aspect indicates the degree of use of the property, or its underutilisation which permits the allocation of other activities (instrumental to the organisation of the Institution as well as social and/or cultural).

The second parameter, P2, expresses the capacity of the asset to achieve financial autonomy under current conditions of use. This parameter was envisaged as many public buildings are often granted (to non-profit associations) free of charge, meaning that users do not contribute to utility costs.

The index is expressed as follows:

$$I\_{\rm ult} = \left\{ \frac{P\_1 + P\_2}{2} \right\} = \left\{ \frac{\left(\frac{S\_{\rm acc}}{S\_{\rm trt}}\right) + \left(\frac{K\_{\rm acc}}{K\_{\rm att}}\right)}{2} \right\} \tag{2}$$

Structured in this way, the index will have a value of 1 when the building is completely occupied and when utility costs are fully paid by occupants. An index of 0.5 generally refers to intermediate situations, such as total occupancy but no payment of utility costs by occupants (buildings rented free of charge), or situations in which the building is only partially occupied (suggesting better strategies for organising spaces) and utility costs are not covered entirely by occupants.


*2.3. Challenges and Opportunities for Measuring SDGs in the Construction Industry*

As discussed above, there is evidence of an increasing interest, and in some cases demand, for promoting SDG measurement in the construction industry [19,20], with one report [14] that surveyed 325 engineers having a 95% demand from practitioners, who said that this was "very important" to them, with only 30% stating that they had adequate tools, processes and systems to measure them at project level. The survey [14] indicated four primary shortfalls for measuring SDGs on infrastructure projects, namely, leadership (1), tools and methods (2), engineers' business skills in measuring SDG impact (3) and how project success is too narrowly defined as outputs (such as time, cost and scope) and not outcomes (longer-term local impacts and stakeholder value) (4). This highlights that there are several challenges that impede the practical measurement of SDGs on projects, which need to be fully acknowledged.

Whilst there is still a limited body of research on the limitations of SDG measurement, there is much that can be learned from the measurement of sustainability on projects, and this is transferable to the SDG research. For example, Arif et al. [28] identified that there is often limited sustainability knowledge, especially amongst senior leaders, and this results in weaker understanding and impact assessments of related themes, such as poverty, environmental issues, supply chain adherence to sustainability best practice, cultural evaluation, technological deficiencies and limitations of research in depth and breadth, all of which have a negative influence on the valuation of sustainability, both as an

investment lens and a delivery approach. A further barrier to the use of SDGs, which potentially mirrors sustainable construction, is what some authors have suggested is a lack of capacity and capability to implement effective and efficient sustainability [29]. Considering the aforementioned literature, it is possible to synthesise the third proposition related to SDGs in the context of the challenges and opportunities for measuring SDGs in the construction industry as follows.

**Proposition 3 (P3).** *Although there is knowledge of the importance of sustainability on infrastructure projects, there is a lack of awareness of how to measure the performance of infrastructure against the SDGs.*


**6. Discussion**

An important exploration of the development of construction waste recycling systems is the study of the game interaction between the government agency and different recyclers, as well as the evolutionary trajectory of participants. Due to the lack of effective management strategies in the past, construction waste recycling has brought significant impacts on the environment and human health [7,32]. To improve environmental quality, many countries' governments have enacted a variety of environmental incentive policies [1]. However, there are multiple parties involved in the construction waste recycling system, and the existence of conflicts of interest makes it difficult to effectively implement environmental incentive policies. In particular, the existence of uncertainty in the external environment, makes the behavior of participants in the construction waste recycling system more complicated [15]. Under the premise of bounded rationality, the stochastic evolutionary game model is built to analyze the complex behavior of participants, in which the Gaussian white noise is introduced to describe the impacts of uncertainty factors on stakeholders' decision evolution trajectories. Balancing the interests of participants is the key to improving the quality of construction waste recycling. For example, China established a Processing Fund for Waste Electrical and Electronic Products in 2012 to assist the formal recycling sectors of the electronic waste dismantling industry. The dismantling fund has lost \$8 billion since its establishment, with the fund already stagnant in 2017. As a result, the management of e-waste recycling cannot rely solely on subsidies, but also on corresponding punitive measures, which is consistent with previous research [33] and also useful for construction waste recycling. According to Andrew et al. [34], different policies must be implemented based on the characteristics of different countries in order to improve governance quality. Furthermore, environmental uncertainty is a significant factor that must be considered during the decision-making process. The random interference factors can influence the equilibrium strategy's trajectory [16]. In addition, certain critical values are determined so that the system behaves chaotically.

There are also some limitations in this paper. There are differences in construction recycling management and environment incentive policies in different countries. This paper built a stochastic evolutionary game model for a case study of China, which would be greater applicability by considering different environmental incentive policies in different countries. In addition, this paper only considers the government agencies, waste producers, and waste recyclers, and introduce Gaussian white noise, China's dual government systems also play an important role in construction waste recycling. More practical conclusions would be obtained by considering the combination of political concentration and economic decentralization of dual government systems.

Base on above analysis, some implications are proposed as follows:


Appendix

In this appendix, we use two examples to illustrate how to implement smoothing spline ANOVA (SSANOVA) models in R. The gss package in R, which can be downloaded on the CRAN https://cran.r-project.org/, is utilized.

We now load the gss package:

library(gss)

Example I: Apply the smoothing spline to a simulated dataset.

Suppose that the predictor x follows a uniform distribution on 0½ � ; 1 , and the response y is generated based on y ¼ 5 þ 2 cos 3ð Þþ πx e, where e � Nð Þ 0; 1 .

x<-runif(100);y<-5+2\*cos(3\*pi\*x)+rnorm(x)

Then, fit cubic smoothing spline model:

cubic.fit<-ssanova(y˜ x)

To evaluate the predicted values, one uses:

new<-data.frame(x=seq(min(x),max(x),len=50))

est<-predict(cubic.fit,new,se=TRUE)

The se.fit parameter indicates if one can get the pointwise standard errors for the predicted values. The predicted values and Bayesian confidence interval, shown in Figure 4, are generated by:

```
plot(x,y,col=1)
lines(new$x,est$fit,col=2)
lines(new$x,est$fit+1.96*est$se,col=3)
lines(new$x,est$fit-1.96*est$se,col=3)
```
Example II: Apply the SSANOVA model to a real dataset.

In this example, we illustrate how to implement the SSANOVA model using the gss package. The data is from an experiment in which a single-cylinder engine is run with ethanol to see how the nox concentration nox in the exhaust depends on the compression ratio comp and the equivalence ratio equi. The fitted model contains two predictors (comp and equi) and one interaction term.

```
data(nox)
```
Section 3, we discussed the models under the big data settings. When the volume of data grows, fitting the models is computing-intensive [11]. The adaptive basis selection algorithm [14] and rounding algorithm [15] we presented can significantly reduce the computational cost.

This work is partially supported by the NIH grants R01 GM122080 and R01 GM113242; NSF

The authors whose names are listed immediately below certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers' bureaus; membership, employment, consultancies, stock ownership, or other equity interests; and expert testimony or patent-licensing arrangements) or nonfinancial interest (such as personal or professional relationships, affiliations, knowledge, or beliefs) in the subject matter or materials discussed in this manuscript.

In this appendix, we use two examples to illustrate how to implement smoothing spline ANOVA (SSANOVA) models in R. The gss package in R, which can be downloaded on the

Suppose that the predictor x follows a uniform distribution on 0½ � ; 1 , and the response y is

grants DMS-1222718, DMS-1438957, and DMS-1228288; and NSFC grant 71331005.

Acknowledgements

78 Topics in Splines and Applications

Conflict of interest

Appendix

library(gss)

CRAN https://cran.r-project.org/, is utilized.

Then, fit cubic smoothing spline model:

To evaluate the predicted values, one uses:

est<-predict(cubic.fit,new,se=TRUE)

cubic.fit<-ssanova(y˜

Example I: Apply the smoothing spline to a simulated dataset.

generated based on y ¼ 5 þ 2 cos 3ð Þþ πx e, where e � Nð Þ 0; 1 .

x<-runif(100);y<-5+2\*cos(3\*pi\*x)+rnorm(x)

x)

new<-data.frame(x=seq(min(x),max(x),len=50))

We now load the gss package:

```
nox.fit <- ssanova(log10(nox)˜
                              comp*equi,data=nox)
```
The predicted values are shown in Figure 5.

```
x=seq(min(nox$comp),max(nox$comp),len=50)
```
y=seq(min(nox\$equi),max(nox\$equi),len=50)

temp <- function(x, y){

Figure 4. The solid red line represents the fitted values. The green lines represent the 95% Bayesian confidence interval. The raw data are shown as the circles.

[3] Friedman JH, Grosse E, Stuetzle W. Multidimensional additive spline approximation.

Smoothing Spline ANOVA Models and their Applications in Complex and Massive Datasets

http://dx.doi.org/10.5772/intechopen.75861

81

[4] Hastie TJ. Generalized additive models. In: Statistical Models in S. Routledge; 2017. pp.

[5] Stone CJ. Additive regression and other nonparametric models. The Annals of Statistics.

[6] Stone CJ. The dimensionality reduction principle for generalized additive models. The

[7] Barry D et al. Nonparametric bayesian regression. The Annals of Statistics. 1986;14(3):934-

[9] Gu C, Wahba G. Minimizing GCV/GML scores with multiple smoothing parameters via the Newton method. SIAM Journal on Scientific and Statistical Computing. 1991;12(2):383-398

[10] Wahba G. Partial and Interaction Splines for the Semiparametric Estimation of Functions

[11] Gu C, Smoothing Spline ANOVA. Models, Volume 297. In: Springer Science & Business

[14] Ma P, Huang JZ, Zhang N. Efficient computation of smoothing splines via adaptive basis

[15] Helwig NE, Ma P. Smoothing spline ANOVA for super-large samples: Scalable computation via rounding parameters. Statistics and Its Interface, Special Issue on Statistical and

[16] Green PJ, Silverman BW. Nonparametric Regression and Generalized Linear Models: A

[17] Kimeldorf GS, Wahba G. A correspondence between Bayesian estimation on stochastic processes and smoothing by splines. The Annals of Mathematical Statistics. 1970;41(2):

[18] Kimeldorf GS, Wahba G. Spline functions and stochastic processes. Sankhya: The Indian

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[20] Wahba G, Wang Y, Gu C, Klein R, Klein B. Smoothing spline ANOVA for exponential families, with application to the Wisconsin epidemiological study of diabetic retinopathy.

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Figure 5. The x-axis, y-axis, and z-axis represent the compression ratio, the equivalence ratio, and the predicted values, respectively.

```
new=data.frame(comp=x,equi=y)
return(predict(nox.fit,new,se=FALSE))
}
z=outer(x, y, temp)
persp(x,y,z,theta = 30).
```


Contents

Preface

The banking and finance industry plays a significant role in the economy of a nation. As such, it demands continuous research and up-to-date feeds for it to stay competitive and resilient. Due to its revolving and dynamic nature as well as its significance and interlinkages with other industries, a well-functioning banking and finance system is vital in safeguarding the interest of all stakeholders. The hard lessons and experiences learned from the financial crises of 1997/1998 and 2008/2009, as well as the recent COVID-19 pandemic, have instigated extensive postmortems and re-evaluations of the banking and financial system among related players in the field to improve and perhaps share and adopt best practices of every

Realizing the significant impacts of this industry, this book, Banking and Finance, highlights major issues related to banking and finance and puts forth recent empirical evidence, scientific research, best practices, and recommendations. This book discusses all major areas of banking and finance. With the wide range of topics highlighted and discussed, together with recent scientific research and findings using advanced econometrical approaches, this book not only enriches the literature but also offers policy implications that will benefit all players including

The book contains sixteen chapters by thirty-one authors divided into two sections.

In the banking section, Aysa Siddika and Razali Haron provide a concise overview of capital adequacy regulation and the importance and evolution of regulation. They further explain how several banking crises and banks' defaults motivated the Basel Committee on Banking Supervision (BCBS) to provide a comprehensive

Ellis Kofi Akwaa-Sekyi explores a qualitative self-regulation approach to address a major risk facing banks using the BCBS framework of internal controls. The chapter specifically examines the effect of the qualitative principles of the BCBS internal control framework on credit risk covering banks from selected EU countries. The author provides evidence on the significant relationship between board functions and activities, board structure and board monitoring, and credit risk and concludes that investment in high-risk assets, bank profitability, and the board chair being a

Naji Mansour Nomran and Razali Haron examine the impact of governance mechanisms on the performance of Islamic banks (IBs) in eighteen countries during the financial crisis of 2008. The study provides justifications on Shariah Supervisory Board effectiveness in improving IBs' performance even during the crisis periods. They conclude on the importance of IBs to adopt appropriate governance structures

academicians and practitioners in the field of banking and finance.

The first section discusses banking while the second covers finance.

aspect in the industry.

guideline in managing bank capital.

to sustain future performance.

former CEO increases credit risk in European banking.


**1.4 Fingerprint-based classifiers**

Informatic analysis has led to a new paradigm for classification known as fingerprinting or pattern matching. In this paradigm, individuals are classified based upon a particular pattern of intensities [Petricoin et al., 2003]. If an untested individual has the same pattern as a known individual, then these two have the same classification. The simplest fingerprintbased classifier is a decision tree (Figure 1). In all known applications of a decision tree to produce a classifier using spectral data [Ho et al., 2006; Liu et al., 2005; Yang et al., 2005; Yu

map.

A Comparison of Biomarker and Fingerprint-Based Classifiers of Disease 183

Srinivasan et al., 2006; Stone et al., 2005]. While these authors stated that their algorithm was quite similar to a Self-Organizing Map (SOM), their algorithm, as they described it, has virtually nothing in common with a SOM. In a SOM [Kohonen, 1988], the layout of the cells is determined *a priori*, as are the number of features, *n*, used in the separation. In general, the cells are placed in a rectangular or hexagonal pattern, with a maximum of four or six adjacent cells, respectively. The cells are seeded with random centroids that represent the *n*dimensional coordinates of each cell. The first training sample is assigned to the cell with the closest centroid and the centroids of this and all the other cells are significantly shifted towards this sample. This procedure is repeated for all samples. Once all samples have been processed, the algorithm repetitively cycles through the list of training samples. In each subsequent cycle, the extent to which the centroid of the cell it is assigned to shifts towards that sample decreases, as does the extent to which the other centroids are affected. This shift becomes significantly smaller for cells that are further from the selected cell, as defined by the initial mapping. When finished, all samples are assigned to cells and each centroid represents an approximate average of the *n* features for all samples in that cell, and the distance between centroids increases as the cells become further apart in the pre-defined

In contrast, the algorithm used in the references cited above places the first training sample as the center of the first cell, and this cell is classified as the category of this sample. Since it is sample-centered, each cell has a medoid not a centroid. Each cell is given a constant trust radius, *r*. If the second sample has a distance that is larger than *r* from the first, it is assigned to a second cell and that cell is classified by its category; otherwise it is assigned to the first

Therefore, a SOM has a fixed number of cells, each cell is described by a centroid, and the algorithm cycles through the training data many times to adjust the centroid's coordinates. The algorithm used by the groups of Petricoin and Liotta has an undefined number of cells,

Also grouped within the class of fingerprint-based classifiers are Support Vector Machines and Linear Discriminant Analysis. A Support Vector Machine (SVM) [Boser et al., 1992; Vapnik, 1998] is a kernel-based learning system. SVM searches for the optimal hyperplane that maximizes the margin of separation between the hyperplane and the closest data points on both sides of the hyperplane. Linear Discriminant Analysis (LDA) [Fukunaga, 1990] is a supervised learning algorithm. LDA finds the linear combination of features that maximize the between-class scatter and simultaneously minimize the within-class scatter to achieve maximum discrimination in a dataset. The within-class scatter matrix may become singular if the sample size is smaller than the dimensionality of the search space (number of

An example if a state-specific marker is shown in Figure 2. Each "+" represents, for example, the blood concentration of a particular biochemical. The individuals in the left column are in a specific disease state, while those in the right column are not and are therefore considered to be in a healthy state, at least with respect to this disease. Individuals in each state have different blood concentrations of this biochemical due to genetic and environmental

cell. This process continues until all training samples have been analyzed.

features), but several techniques are available to handle this situation.

**1.5 Biomarker-based classifiers**

each described by a single sample, and the training data is only processed once.

et al., 2005], a single scoring metric (e.g. Gini Index, entropy gain, etc.) was used to determine the cut point at a given node so that the two daughter nodes were as homogeneous as possible for one or more categories (e.g. diseased versus healthy). Given the general structure of a decision tree in Figure 1, the root node (Node 1) would contain all training samples and an *m/z* value, or feature, and its cut point would be selected that best separates diseased and healthy individuals between Nodes 2 and 3. If there was still enough of a mixture in Node 2, for example, a second feature would be chosen based on the same metric that would separate the individuals into Nodes 4 and 5. The same process would be used for all heterogeneous nodes until there was a sufficient domination of one category over another.

Fig. 1. Example of a 7-node decision tree.

Decision Support also uses decision trees, but an independent question is asked at each level in the tree. For example, Node 1 may be used to separate the individuals by gender, race, or other genetic difference, and then different features may be used to separate samples obtained from affected and healthy patients at a given level of stratification. Since the stratifying variables are not known ahead of time, there is no way to know the proper metric that should initially separate the training set. Therefore, the procedure used here is to construct unconstrained decision trees that best classify the training individuals.

The medoid classification algorithm is a best attempt at reproducing the algorithm used in many of the studies conducted in the laboratories of Emmanuel Petricoin and Lance Liotta [Browers et al., 2005; Conrads et al., 2004; Ornstein et al., 2004; Petricoin et al., 2004;

et al., 2005], a single scoring metric (e.g. Gini Index, entropy gain, etc.) was used to determine the cut point at a given node so that the two daughter nodes were as homogeneous as possible for one or more categories (e.g. diseased versus healthy). Given the general structure of a decision tree in Figure 1, the root node (Node 1) would contain all training samples and an *m/z* value, or feature, and its cut point would be selected that best separates diseased and healthy individuals between Nodes 2 and 3. If there was still enough of a mixture in Node 2, for example, a second feature would be chosen based on the same metric that would separate the individuals into Nodes 4 and 5. The same process would be used for all heterogeneous nodes until there was a sufficient domination of one category

Decision Support also uses decision trees, but an independent question is asked at each level in the tree. For example, Node 1 may be used to separate the individuals by gender, race, or other genetic difference, and then different features may be used to separate samples obtained from affected and healthy patients at a given level of stratification. Since the stratifying variables are not known ahead of time, there is no way to know the proper metric that should initially separate the training set. Therefore, the procedure used here is to

The medoid classification algorithm is a best attempt at reproducing the algorithm used in many of the studies conducted in the laboratories of Emmanuel Petricoin and Lance Liotta [Browers et al., 2005; Conrads et al., 2004; Ornstein et al., 2004; Petricoin et al., 2004;

construct unconstrained decision trees that best classify the training individuals.

over another.

Fig. 1. Example of a 7-node decision tree.

Srinivasan et al., 2006; Stone et al., 2005]. While these authors stated that their algorithm was quite similar to a Self-Organizing Map (SOM), their algorithm, as they described it, has virtually nothing in common with a SOM. In a SOM [Kohonen, 1988], the layout of the cells is determined *a priori*, as are the number of features, *n*, used in the separation. In general, the cells are placed in a rectangular or hexagonal pattern, with a maximum of four or six adjacent cells, respectively. The cells are seeded with random centroids that represent the *n*dimensional coordinates of each cell. The first training sample is assigned to the cell with the closest centroid and the centroids of this and all the other cells are significantly shifted towards this sample. This procedure is repeated for all samples. Once all samples have been processed, the algorithm repetitively cycles through the list of training samples. In each subsequent cycle, the extent to which the centroid of the cell it is assigned to shifts towards that sample decreases, as does the extent to which the other centroids are affected. This shift becomes significantly smaller for cells that are further from the selected cell, as defined by the initial mapping. When finished, all samples are assigned to cells and each centroid represents an approximate average of the *n* features for all samples in that cell, and the distance between centroids increases as the cells become further apart in the pre-defined map.

In contrast, the algorithm used in the references cited above places the first training sample as the center of the first cell, and this cell is classified as the category of this sample. Since it is sample-centered, each cell has a medoid not a centroid. Each cell is given a constant trust radius, *r*. If the second sample has a distance that is larger than *r* from the first, it is assigned to a second cell and that cell is classified by its category; otherwise it is assigned to the first cell. This process continues until all training samples have been analyzed.

Therefore, a SOM has a fixed number of cells, each cell is described by a centroid, and the algorithm cycles through the training data many times to adjust the centroid's coordinates. The algorithm used by the groups of Petricoin and Liotta has an undefined number of cells, each described by a single sample, and the training data is only processed once.

Also grouped within the class of fingerprint-based classifiers are Support Vector Machines and Linear Discriminant Analysis. A Support Vector Machine (SVM) [Boser et al., 1992; Vapnik, 1998] is a kernel-based learning system. SVM searches for the optimal hyperplane that maximizes the margin of separation between the hyperplane and the closest data points on both sides of the hyperplane. Linear Discriminant Analysis (LDA) [Fukunaga, 1990] is a supervised learning algorithm. LDA finds the linear combination of features that maximize the between-class scatter and simultaneously minimize the within-class scatter to achieve maximum discrimination in a dataset. The within-class scatter matrix may become singular if the sample size is smaller than the dimensionality of the search space (number of features), but several techniques are available to handle this situation.


**4. Risk factors of radiation-induced ulcers**

There are some risk factors associated with the development of radiation dermatitis.

#### **4.1 Radiotherapy-related factors**

Higher total dose and higher irradiated volume are possibly related to a higher risk of skin injury [22–24]. Several articles revealed that hypofractionated RT contributed to a lower risk of radiation-induced skin injuries [25, 26]. However, a conflict result was shown as a hyperfractionated regime resulting in preferable outcomes [27]. Besides, intensity-modulated radiotherapy (IMRT) could lead to a reduction of skin reactions compared to 2D radiotherapy [28, 29].

Concurrent chemotherapy (i.g. cetuximab) or concurrent targeted therapy might result in a higher risk of skin injuries induced by RT as well [30–32].

#### **4.2 Patient-related factors**

Some regions of the body that are more sensitive to radiation such as the scalp, face, neck, extremities, chest, and abdomen, may be prone to develop skin reactions in patients receiving RT [33]. Patients who are obese (BMI > 30), contract connective tissue diseases, or have skin disorders also have a higher risk of developing radiation burns [34–36]. In addition, there are some genetic polymorphisms that were supposed to increase incidences of radiation dermatitis. They included polymorphisms in ABCA1 and IL12RB2, stefinA3, and S100A8 genes [37, 38].


**4. Heuristics**

The mathematical model presented in Section 3 can be solved through off-the-shelf solvers for mixed-integer linear programming to obtain an optimal solution for a given FQRP-G instance, i.e., the minimum number of rows that allows collision-free nonstop Manhattan paths to route vehicles on, together with the paths themselves. However, due to the computational complexity of integer linear programming, we expect that the efficiency of the model, in terms of time to obtain the optimal solution, degrades with the size of the instance to handle, as in fact our computational experiments, presented in Section 5, ascertain. We thus propose two heuristics to solve FQRP-G. The first one, called Heuristic

A, is a reinterpretation of the CaR algorithm given by Cenci et al. in [7], but it is much simpler and improves the computational complexity, as will be stated in Proposition 4. It uses the C-conflict directed graph to generate vehicle routes that are simple Manhattan paths and it is able to always provide a feasible solution to FQRP-G. The second one, called Heuristic B, is more flexible in choosing Manhattan paths and attempts to determine the vehicle routes by giving priority to the horizontal moves of vehicles ranked on the basis of measures obtained from the C-conflict directed graph.

### *4.1. Heuristic A*

Heuristic A is based on the C-conflict directed graph *F*. As from Proposition 1, each connected component of *F* is an oriented arborescence. Any such arborescence has a root, and its nodes can be partitioned according to their depth. The root has zero depth. The depth of any node is equal to the length of the unique path in *F* from the root to that node. For each node, we also define its height as the length of the longest path in *F* from that node to any of the leaves. The height of a connected component is equal to the length of the longest path from its root, i.e., the height of the root itself. Vehicles in *S*, as well as any vehicle that is not involved in C-conflicts, are isolated nodes in *F*, and have both height and depth equal to 0. The root of any non-trivial arborescence is either in *L* or in *R*.

We now state Heuristic A and, then, we discuss its correctness and properties. Given an instance of FQRP-G, in terms of the number of columns *n*, set of vehicles and related origins *α* and destinations *ω*, Heuristic A runs through the following steps:

**Proposition 2.** *The vehicle routes given by Heuristic A are nonstop collision-free simple Manhattan paths.*

 solution.

**Proof.** In the output of Heuristic A, all the horizontal moves performed at any level have the same direction. Indeed, each path in *F* is a C-conflict path and, hence, it alternates vehicles in *R* and in *L*. If follows that, under the assumption that the maximum height is related to an arborescence rooted in *R* (the case in *L* is similar) all vehicles in *R* move horizontally on an odd row, and all vehicles in *L* on an even row. This corresponds to having one-way horizontal lanes, which prevents collisions related to edge conflicts from occurring. We observe that, trivially, Heuristic A outputs simple Manhattan paths, as each vehicle performs consecutively all its horizontal moves on the same level. This, together with one-way lanes, avoids collisions related to B-conflicts.

For each pair of vehicles *p* and *q* such that *q* has a C-conflict with *p*, the directed graph *F* contains the arc (*p*, *q*), and *lq* = *lp* + 1 holds. Therefore, vehicle *p* performs its horizontal moves on a lower level than *q* does, and the route of *p* is below the one of *q* in column *ω*(*q*), as required to avoid collisions related to C-conflicts.

Notice that, if Heuristic A is applied to a single connected component of *F*, then the number of grid levels used by the output solution is equal to one plus the height of that component. Therefore, given any instance, the number of grid levels needed by Heuristic A is equal the height of the highest connected component of *F*, added by 2. The term "+2" comes from the case in which the forest *F* contains two (or more) highest components, of which, one rooted in *R* and another in *L*. This proves the following

**Proposition 3.** *Given an instance of FQRP-G and its C-conflict direct graph, let m*¯ *R and m*¯ *L be the maximum height of an arborescence rooted in R and, respectively L. The number of levels required by Heuristic A is* max{*m*¯ *R*, *m*¯ *L*} + *a, where a* = 1 *if m*¯ *R* = *m*¯ *L, a* = 2 *otherwise.*

The number of required levels is equal to the one stated for algorithm CaR proposed by Cenci et al. in [7]: as shown in [7], CaR optimally solves FQRP-G if the set of vehicle routes is restricted to simple Manhattan paths and under the hypothesis of one-way horizontal lanes. We thus have the following

**Corollary 1.** *Heuristic A finds the optimal solution of FQRP-G restricted to simple Manhattan paths and one-way horizontal lanes.*

In fact, as already stated above, Heuristic A is a reinterpretation of the CaR algorithm that improves its computational complexity (we recall that CaR runs in O(*n*)3).

**Proposition 4.** *Given an instance of FQRP-G on a grid network with n columns, the computational complexity of Heuristic A is* O(*n*)*.*

**Proof.** In order to detect all C-conflicts, O(*n*) calculations are sufficient. Indeed, for any vehicle *k* ∈ *R* (resp. in *L*), we only have to check if there is another vehicle moving from position (2 *ω*(*k*) − *α*(*k*), 1) and having its destination on the left (resp. on the right) of column *ω*(*k*); in such case, vehicle *k* has a C-conflict with the other vehicle. All the arcs of *F* can be thus detected in at most *n* (a bound on the number of vehicles) operations, and *F* built in O(*n*). All the data required by Heuristic A can be collected during a depth-first visit of *F*, which allows computing the depth and the height of any node in O(*n*). This shows that Step 1 takes O(*n*) operations. Concerning Steps 2 to 4, they simply assign the horizontal level to each vehicle, which can still be done in O(*n*).

### *4.2. Heuristic B*

Heuristic B aims at calling non-simple Manhattan paths conveniently into play. The underlying idea is to find an appropriate order of the vehicles and, then, to sequentially route each vehicle on the "lowest" Manhattan path possible, i.e., a Manhattan path obtained by choosing a horizontal step whenever this is compatible with previously assigned paths.

Vehicles are sorted according to a measure of how critical it is to route them. For example, an order of the vehicles could provide a feasible set of routes only if, for any pair of vehicles *k*1, *k*2 such that *k*2 has a C-conflict with *k*1 on column *ω*(*k*2), vehicle *k*1 precedes *k*2 in the order, since otherwise *k*2 would have precedence in the horizontal move to reach the conflict column and stay below *k*1 on it, which means that the C-conflict cannot be resolved (see Section 3.1). It follows that vehicles belonging to a C-conflict path should be sorted in the increasing order of their depth in the C-conflict directed graph *F*, which again plays an important role in prioritizing vehicles. We also observe that, in general, the assigned Manhattan paths are not simple and each level can be run in opposite directions; therefore, both edge conflicts and B-conflicts may actually generate collisions and have to be taken into account.

For each vehicle *k*, the following measures are considered:

•*lk*: the depth of *k* in *F*;

• *γk*: length of the longest C-conflict path *k* belongs to. Notice that, if *lk* and *hk* are, respectively, the depth and the height of *k* in *F*, *γk* = *lk* + *hk*, and, in particular, *γk* = 0 if *k* is not involved in any C-conflict;

Given an instance of FQRP-G, in terms of number of columns *n*, set of vehicles and related origins *α* and destinations *ω*, Heuristic B runs through the following steps:

	- (a) let (*i*, *j*) be the actual position of vehicle *k* in the grid (initially set to (*α*(*k*), 1));
	- (b) if *i* = *ω*(*k*) and *j* = *m*, then output "feasible path for *k* found" and consider the next vehicle;
	- (c) if *i* = *ω*(*k*) and all vehicles up to *k* in a C-conflict path are not involved in further conflicts, then *k* performs a vertical move;
	- (d) otherwise, if *i* = *ω*(*k*), then check if the horizontal move to node (*i* + 1, *j*) involves any collision with previously assigned paths (this could be related to a node-conflict if, after a unit of time, another vehicle will be in node (*i* + 1, *j*), or an edge conflict if another vehicle is performing the opposite move from (*i* +1, *j*) to (*i*, *j*) at the same time); if the answer is "no conflict", then *k* performs the horizontal move to node (*i* + 1, *j*);
	- (e) otherwise, check if the vertical move to (*i*, *j* + 1) involves any conflict with previously assigned paths (this could be a node-conflict if, after a unit of time, another vehicle will be in node (*i*, *j* + 1)); if the answer is "no conflict", then *k* vertically moves to node (*i*, *j* + 1);
	- (f) otherwise, output "no feasible path for *k* found" and stop.

With reference to Step 4c, we remark that, since vehicles are sorted by non-decreasing *lk*, collisions related to C-conflicts are avoided, as for any arc (*k*1, *k*2) of *F*, the path of vehicle *k*1 is set before the path of *k*2. These are the only collisions associated with vertical moves on the destination columns, so that, in the case specified by Step 4c, checking their occurrence is redundant.

While, in the above case, C-conflicts are solved by appropriately ordering the vehicles in the first phase of the algorithm, remaining node-conflicts and edge conflicts are tentatively solved during Steps 4d–4e. However, we have no guarantee to avoid related collisions and, indeed, Heuristic B may get stuck if both horizontal and vertical moves of a vehicle at a given node are forbidden. Nevertheless, if Heuristic B is successful, the required number of levels is not bounded from below by the length of the longest C-conflict path, as it is the case for Heuristic A: we thus aim to empirically evaluate the probability of getting stuck and, if this is not the case, the ability of Heuristic B to provide better results than Heuristic A.

The actual performance of Heuristic B depends on the specific sorting adopted by Step 3. We propose two alternatives giving rise to:

We now discuss the computational complexity of Heuristic B.

**Proposition 5.** *Given an instance of FQRP-G on a grid graph with n columns, the computational complexity of Heuristic B is* O(*n*2 *m*)*.*

**Proof.** Step 1 to determine *m* can be done in O(*n*). The measures required by the sorting step can be computed by building and depth-first visiting the C-conflict directed graph *F*, which can be done in O(*n*) (as discussed in proof of Proposition 4). The sorting Step 3 takes O(*n* log *n*). Since the number of moves in a Manhattan path is bounded by *n* + *m*, and the number of vehicles by *n*, the complexity of Step 4, and of overall Heuristic B, is O(*n*2 *m*).


**5.2 Origin and distribution**

*Ceiba pentandra* is native primarily in West Africa where it is found in rainforests typically at elevations of 900 to 1200 meters [138]. It is widely distributed in South America—Brazil, Venezuela, Ecuador, Peru, Bolivia, Colombia, the Guyanas; North through Central America to Mexico; Caribbean; West tropical Africa [75]. Kapok is a multipurpose tree with numerous uses for the local populace where it is grown. It is highly valued for its fiber, and it also provides food, medicines and other products.

Kapok is widely grown in the tropics for its medicinal value and fiber, the plant exists naturally in many areas [139]. It has long been planted around buildings in villages for food, medicine, beautification purpose and other uses. However, the floss is harmful as it causes irritation to the eye and nose, so the tree is not suitable for town planting. Commercially, kapok is grown for the fiber from the pod in Java [75].