*5.2. Assessing Atlantic Planktonic Foraminifera Shell Mass Records as Seawater Density and AMOC Proxies*

The use of planktonic foraminifera shell mass as a seawater paleodensity proxy has revealed changes in the circulation mode of the Atlantic Ocean and has provided estimates of absolute past density values of the seawater column at the depths where *G. bulloides* live when they attain a cell size of 300–355 µm. The average Atlantic Ocean density during the periods of quasi-total cessation of the AMOC was found to be ~1026.82 kg/m3 . This value is similar to 1026.72 kg/m3 , which is the average density reconstructed for the modern ocean by the three core top samples and refers to a depth of 130–170 m in the study area today [94]. Such depths are in the range of the calcification depths reported for *G. bulloides* for the southern Atlantic [95], the Indian [96] and Southern Ocean [97], and the Atlantic [98,99], although for the N. Atlantic shallower depths have also been reported [100]. Since calcification depths change with ontogeny and thus with size [99,101], it is reasonable to assume that specimens as large as 355 µm calcify at greater depths and so the proposed reconstructions are plausible. However, like many applications of transfer functions on fossil foraminifera to reconstruct past environments, the shell-weightbased seawater density reconstructions fundamentally rely on the assumption of stable environmental niches in both space and time. Niche stability in environmental space is found to be greatest for subpolar species such as *G. bulloides* across glacial and interglacial intervals [102].

Planktonic foraminifera shell mass biomineralization responds very differently to atmospheric *p*CO2 with latitude (Figure 2a,c) if at all (Figure 2b). Shell weight variability is greater at intermediate latitudes and especially at those related to the descending limb of the Hadley circulation, such as the region of core GeoB 1710-3. The increased shell masses recorded during the last glacial maximum could also have been attributed to enhanced upwelling, a wind-driven oceanic circulation, of denser water masses during the LGM but this is definitely not the case for core GeoB 8502-2, which is beneath one of the major upwelling areas in the Atlantic Ocean [30]. Furthermore, the intervals of shell weight convergence between the records would suggest an instantaneous decline in the wind-driven circulation and its attenuation of 18 ka for which no evidence exists. Alternatively, the shell weight variations are overall better explained by changes in the thermohaline circulation that match the 231Pa/230Th geochemical indications of AMOC cessation and thus increased shell masses are related to densification of the Atlantic waters. The geochemically reconstructed density estimates for SMCE II from GeoB 8502-2 in Table 2 agree within error (which is ± 1.73 kg/m3 [17]) with the weight-based density estimates;

however, more geochemical analyses of the present records are required to confirm the accuracy of the results.

#### **6. Conclusions**

Species-specific planktonic foraminifera shell weights have the potential to be a valuable tool for the determination of surface ocean paleoseawater circulation and thus a powerful proxy for physical paleoceanographic applications in paleoclimatology. The use of planktonic foraminifera shell weight as a direct seawater paleodensity proxy has revealed two intervals in the Atlantic Ocean during the past 200 kyr, when the meridional circulation may have been disrupted momentarily due to the absence of interhemispheric seawater density gradients in the Atlantic. Shell-weight-based seawater density values not only converge in the three studied cores within these extraordinary intervals but they also converge between both of these intervals to the same value, which also characterizes the modern Atlantic Ocean density at the same depth horizons. After the convergence at 18 ka, the Atlantic seawater density gradients alleviate and this weakening suggests a decline in the AMOC strength with only small variability thereafter.

Furthermore, it confirms that the surface South Atlantic has always been denser [67] and that, after the last convergence (at ~18.4 Ka) towards the Holocene, the interhemispheric surface Atlantic density gradients alleviate, possibly suggesting an attenuated AMOC thereafter.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/10 .3390/jmse9050519/s1, Table S1: *G. bulloides* sieve (300-355 µm) based shell weights from core GeoB 1710-3, Table S2: Biometric analyses of XµCT scanned *G. bulloides* specimens.

**Funding:** This research was published during my research fellowship at the University of Oxford funded by the Royal Society.

**Data Availability Statement:** The raw tomographic data from the XµCT scanning of *G. bulloides* specimens from core GeoB 8502-2 can be found at 10.6084/m9.figshare.14370959 and for core GeoB 1710-3 at 10.6084/m9.figshare.14397884.

**Acknowledgments:** I would like to thank the University of Bremen in Germany and the University of Cambridge in the United Kingdom for providing sample materials and resources. I would also like to thank the Maxwell Institute at the University of Cambridge for providing the X-ray facilities. This research was completed during my research fellowship in the University of Oxford, funded by the Royal Society under the Newton International Fellowships scheme.

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

#### **References**

*Article*


**2. Mechanical vibration**

#### **2.1 General characteristics**

Mechanical vibration is a physical agent of wave nature. It can be produced by different devices, such as a refrigerator engine, a motor vehicle engine, an air conditioner, and others. A vibrating platform is one of such examples. In all the examples provided, the device is outside the person's body, but if the person is in contact with it, the mechanical vibration is transmitted to the person [11, 12]. As shown in **Figure 1**, the waveforms of mechanical vibrations produced by different devices, can be deterministic (**Figure 1A**) or random in nature.

The mechanical vibration, that is generated in a vibrating platform [11, 12] or portable [10] devices, is characterized by the sinusoidal form, and this deterministic approach has particular interest for everything that will be covered in this book chapter on vibration therapy.

#### **2.2 Mechanical vibration as a daily stimulus**

It is very important to highlight that mechanical vibration is a natural stimulus that is part of the daily life of all living beings and is periodically added to the organism during movements [11, 12]. It is closely associated with the physiological responses of all organisms, including human being. The addition of mechanical vibration happens in a wide number of routine situations [11], such as walking, running, playing, being in a car or public transport, or doing a domestic activity, such as using a vacuum cleaner for cleaning or a fruit extractor while making a juice. Likewise, in professional activities such as driving a car, truck, train, or using dental equipment, mechanical vibration is transmitted to the individual that is in contact with the device that is producing the referred vibration [13, 14]. In addition, several structures of the human body naturally produce mechanical vibrations, such as the heart, digestive system, the shortening and stretching of muscle fibers, vessels of the vascular system, the vibrational energy of electrons in a chemical bond, or the vibration of molecules in the cellular metabolism. Likewise, many of the organic functions depend on mechanical vibrations at different levels of anatomical structures [12, 15, 16]. Of course, in general, this addition of mechanical vibration is

#### **Figure 1.**

*Different waveforms related to mechanical vibration.*

not fully perceived by the person, but when a movement is performed, mechanical vibration is added to the body. However, in some activities like walking or running, when the foot contacts the floor, mechanical vibration is more easily perceived. It may be relevant to consider that this addition of mechanical vibration would be the trigger for organic functions to take place and for the person to live with physical and mental health [12, 16].

When, for several reasons, the person cannot add mechanical vibration to the body, the mechanical vibration generated by a device can be transmitted to the person in contact with it. This procedure corresponds to a clinical intervention called vibration therapy [10–12].

#### **2.3 Biomechanical characteristics of mechanical vibration**

Vibration therapy, which is considered in this chapter, uses mechanical vibration, which is a physical agent that transports energy and is characterized by a displacement in relation to an equilibrium position with an oscillatory, sinusoidal, and deterministic movement, as shown in **Figure 2**.

In this case, biomechanical parameters such as frequency, amplitude, and peakto-peak displacement can be conveniently adjusted depending on the outcome to be achieved and the individual's clinical conditions. These parameters need to be considered when designing a vibration therapy intervention protocol [8].

Frequency (f) is expressed in Hertz (Hz) and represents the number of cycles in one unit of time, for example, the second. Peak-to-peak displacement (D) is the measure of the perpendicular extension between the largest and smallest displacement of mechanical vibration expressed in millimeters (mm). The amplitude represents half the peak-to-peak displacement and is also expressed in mm. These parameters are represented in **Figure 3**. The path of the mechanical stimulus between the successive points Z1 and Z2, defines the cycle developed by the vibration. The number of cycles performed in the unit of time is the frequency [8, 11, 12]. An important observation is that at Z2, the stimulus begins again to have the same characteristics as point Z1.

The distance comprised by the straight-line segment between points Z1 and Z2, measured, for example, in mm, is defined as the wavelength of the mechanical

**Figure 2.** *Sinusoidal waveforms related to mechanical vibration.*

**Figure 3.** *Representation of a sinusoidal mechanical vibration.*

stimulus. This corresponds to the projection of the entire cycle on the propagation plane. It is important to consider that in the International System of Measurements, the wavelength value would be expressed in meters. Considering the perpendicular measure between the highest point or the lowest point (x1) of the mechanical vibration and the propagation plane or the lowest point (x2) is the amplitude. The perpendicular of the point X1 up to the level of the x2 is the displacement peakto-peak. The value of the displacement peak-to-peak corresponds to twice the amplitude [17].

The peak acceleration (Ap) of mechanical vibration depends on the frequency and the peak-to-peak displacement and is normally expressed in multiples of gravity (xg). The peak acceleration can be determined using accelerometers, or according to the equation Ap = 2 x π2 x f2 x D [17]. Peak acceleration allows defining the intensity or magnitude of mechanical vibration and of the vibration therapy.

Two mechanical vibrations, with the same frequency, with displacement with correspondences in points X1 and x2, are said to be in phase. On the other hand, when these coincidences do not occur, the two stimuli are out of phase. These considerations are relevant, in the same way, the stimulus generated in the platform has its own amplitude, the medium being crossed also presents mechanical vibration.


*2.3.5 Measured result*

The prototype fabrication and measurement verify the proposed filter design using the Vector Network Analyzer (VNA). The photographic view of the structure for the top plane and ground plane is illustrated in **Figures 36** and **37**, respectively. It is found in **Figure 38** that simulation and measured S-parameter results are in good agreement. **Figure 39** shows the measured phase response almost linear in the passband region.

**Figure 35.** *Surface electric and Magnetic current distribution at 5.16 GHz.*

**Figure 36.**

*Photographic view of the Top plane of the Split-ring DGS with Open-stub.*


**1. Introduction**

The metabolism can be defined as the sum of all the biochemical reactions carried out by an organism. Metabolites are the intermediates and products of metabolism and are usually restricted to small molecules. The term "secondary" introduced by A. Kossel in 1891 implies that while primary metabolites are present in every living cell capable of dividing, the secondary metabolites are present only incidentally and are not of paramount significance for organism's life. Though secondary metabolites are derived from primary metabolism, they do not make up basic molecular skeleton of the organism. Its absence does not immediately curtail the life of an organism, a feature contrary to primary metabolite, but survival of the organism is impaired to a larger extent. Its presence and synthesis are observed in ecologically disadvantaged species within a phylogenetic group [1].

The difference between primary and secondary metabolite is ambiguous since many of the intermediates in primary metabolism is overlapping with the intermediates of secondary metabolites [2]. Amino acids though considered a product of primary metabolite are definitely secondary metabolite too. Contrary to the observation that sterols are secondary metabolites that are indispensable part of many structural framework of a cell. The mosaic nature of an intermediate indicates common biochemical pathway being shared by primary and secondary metabolism [3]. The secondary metabolites serve as a buffering zone into which excess C and N can be shunted into to form inactive part of primary metabolism. The stored C and N can revert back to primary metabolite by the metabolic disintegration of secondary metabolite when on demand. There is dynamism and a delicate balance between the activities of the primary and secondary metabolism (**Figure 1**) being influenced by growth, tissue differentiation and development of the cell or body, and also external pressures [4].

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

have different variety of unrelated structures, while steroids have a common tetracyclic carbon skeleton and are modified terpenoids that are biosynthesized from the triterpene lanosterol.

An Introductory Chapter: Secondary Metabolites http://dx.doi.org/10.5772/intechopen.79766 5

There are over 12,000 known compounds of alkaloids, and their basic structures consist of

Around 10,000 compounds are identified and are biosynthesized from simple acyl precursors

These amino acids derived compounds are biologically synthesized by a multifunctional

(i) competitive weapons against other livings such as animals, plants, insects, and

The other functions include interference in spore formation (not obligatory) and germination [5]. Predominantly, the secondary metabolites are used for variety of biological activities like antimicrobial and antiparasitic agents, enzyme inhibitors and antitumor agent, immunosup-

The major sources of secondary metabolites are plants (80% of secondary metabolite), bacteria, fungi, and many marine organisms (sponges, tunicates, corals, and snails) (**Table 1**) [8].

basic amine group and are derived biosynthetically from amino acids.

Enzyme cofactors are nonprotein, low-molecular enzyme component [6].

The major functions of the secondary metabolites including antibiotics are:

**2.3. Fatty acid-derived substances and polyketides**

enzyme complex without direct RNA transcription.

**3. Functions of secondary metabolites**

(iii) agents for symbiotic relation with other organisms

(vi) agents of communication between organisms

**4. Sources of secondary metabolites**

**2.4. Nonribosomal polypeptides**

**2.5. Enzyme cofactors**

microorganisms

(ii) metal transporting agents

(iv) reproductive agent and (v) differentiation effectors

pressive agents, etc. [7].

such as propionyl CoA, acetyl CoA, and methylmalonyl CoA.

**2.2. Alkaloids**

**Figure 1.** Schematic diagram representing integration of primary and secondary metabolism.

Hence, secondary metabolites or natural products can be defined as a heterogeneous group of natural metabolic products that are not essential for vegetative growth of the producing organisms, but they are considered differentiation compounds conferring adaptive roles, for example, by functioning as defense compounds or signaling molecules in ecological interactions, symbiosis, metal transport, competition, and so on [5]. The multitude of secondary metabolite secretions is harvested by human kind to improve their health (antibiotics, enzyme inhibitors, immunomodulators, antitumor agents, and growth promoters of animals and plants), widen the pyramid of healthy nutrition (pigments and nutraceuticals), enhancing agricultural productivity (pesticides, insecticides, effectors of ecological competition and symbiosis and pheromones), and hence impacting economics our society in a certain positive way. They are a source of antibiotics.


**Author details**

Miroslav Verbič

342 Nonlinearity, Bifurcation and Chaos – Theory and Applications

In a market with fundamentalists and contrarians the fundamental steady state is the unique steady state of the system, which arises for low values of intensity of choice. Memory affects neither the position of this steady state nor its stability. For increasing intensity of choice a primary bifurcation, i.e. a period doubling bifurcation occurs; the steady state becomes unstable and a stable period two-cycle appears. Both the primary bifurcation value and the position of the period two-cycle are independent of the memory. For further increasing intensity of choice a secondary bifurcation, i.e. a supercritical Hopf bifurcation, occurs; the period two-cycle becomes unstable and an attractor appears consisting of two invariant circles around each of the two (unstable) period two-points, one lying above and the other one below the fundamental. For high intensity of choice chaotic asset price dynamics occurs, interspersed with many stable period cycles. Such a bifurcation route to chaos is often called

In case of strong contrarians and high intensity of choice it is reasonable to expect that we will obtain a system that is close to having a homoclinic intersection between the stable and unstable manifolds of the fundamental steady state, which indicates the occurrence of chaos. There exists a certain limited interval of memory strength values, for which at a given intensity of choice we are more likely to obtain such a system with more additional memory in the model. A rational choice between fundamentalists' and contrarians' beliefs triggers situations that do not reach fruition due to practical considerations and are thus unattainable, 'castles in the air', as Brock and Hommes (1998, p. 1258) would put it. As a consequence we obtain market instability, characterized by irregular up and down oscillations around the unstable efficient market hypothesis fundamental price. Additional memory lengthens on average the period of this irregular cycle and mainly appears to be

In a market with fundamentalists and opposite biases the fundamental steady state is also the unique steady state of the system, arising for low values of intensity of choice. Memory does not affect the position of this steady state, but does affect its stability. For increasing intensity of choice a supercritical Hopf bifurcation occurs; the steady state becomes unstable and an attractor appears. Memory affects the emergence of this bifurcation; the higher the memory strength, the higher the bifurcation value. More memory thus has a stabilizing effect on dynamics. For high intensity of choice the dynamic behaviour is more complex. However, irrespective of the amount of additional memory such a route to complicated dynamics is different from that in the presence of contrarians, for after the bifurcation value only regular (quasi-)periodic fluctuations around the unstable fundamental steady state occur. Consequently, an important finding is that the predominating quasi-periodic

After the incidence of the bifurcation the higher value of the memory strength parameter causes the dynamics to be less periodic and more quasi-periodic; the dynamics therefore converges on purely quasi-periodic behaviour with increasing memory strength. Opposite biases may cause perpetual oscillations around the fundamental, even without costs for fundamentalists, but can not lead to chaotic movements. Furthermore, in a three-type world,

**5. Concluding remarks**

the rational route to randomness.

stabilizing with regard to asset prices.

dynamics does not seem to evolve to chaotic dynamics.

*Faculty of Economics, University of Ljubljana, Slovenia & Institute for Economic Research, Ljubljana, Slovenia*


**1. Introduction**

Nowadays, the continuous development of the cement-based materials industry, fueled by unflagging demand, is a cause for concern due to the large amount of CO2 and NOx emitted during the production process. One of the most effective ways to reduce the negative environmental impact of the cement industry is the use of so-called supplementary cementitious materials (SCMs). The most commonly used SCMs are fly ash and groundgranulated blast furnace slag. However, their availability will continue to decline, thus increasing the need for alternative sources of SCMs. One of the most promising alternative sources are calcined clays, which are abundant and widely available [1–3]. Among the most well-known material to be used as a calcined clay in cement and concrete technology is metakaolin. Metakaolin is a pozzolanic material obtained by calcination of kaolinitic clay, and it has been shown to considerably enhance the mechanical and chemical properties of concrete [1]. Calcined clays other than metakaolin are rarely used as SCMs due to the complex composition of clay minerals, such as the calcite impurities in clays containing kaolinite and insufficient knowledge of the basic reaction mechanisms [2–4]. Additionally, although there is an increasing interest in demonstrating the effectiveness of various treatments that can lead to improvements in the reactivity of clays with respect to their usage as an SCM [3], issues such as the required quality control procedures and the acceptance criteria also need to be taken into account [1].

One of the possible applications of calcined clays, making use of their composition and pozzolanic properties, is as an additive to cement or concrete with the objective of

**Citation:** Jó ´zwiak-Nied ´zwiedzka, D.; Jaskulski, R.; Dziedzic, K.; Antolik, A. Effect of Low-Quality Calcined Clay on the Suppression of the Alkali–Silica Reaction. *Mater. Proc.* **2023**, *13*, 15. https://doi.org/ 10.3390/materproc2023013015

Academic Editors: Katarzyna Mróz, Tomasz Tracz, Tomasz Zdeb and Izabela Hager

Published: 14 February 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

reducing the expansion induced by an alkali silica reaction [5,6]. However, previous studies have mostly focused on the application of metakaolin [7–9], thus overlooking the fact that the efficacy of calcined clays in mitigating ASR can vary significantly due to differences in quality and sources [5]. As a result, the information on the efficacy of ASR mitigation of calcined clays obtained from various sources and of different quality is still limited [6].

The research presented in this paper is focused on the effectiveness of locally available low-quality calcined clay with respect to its ability to control the expansion due to the alkali–silica reaction. The scope of experimental work includes a characterization of the raw and calcined clay, an assessment of the effectiveness of the calcined clay in mitigation according to ASTM C1567 [10] and a microstructural analysis. Although a different clay was tested than that used in [6], similar assumptions were made. One calcination temperature (850 ◦C) was used because the highest pozzolanic reactivity was reached when the clay was calcined at 800 ◦C [11,12], and the strength performance was maximized for raw clays calcined at temperatures up to 850 ◦C [3]. In the conducted research, the main factor, which is the replacement level, was taken into consideration.


Approaches and New Methods

## **Chapter 5**

## A New Approach of Power Transformations in Functional Non-Parametric Temperature Time Series

*Haithem Taha Mohammed Ali and Sameera Abdulsalam Othman*

## **Abstract**

In nonparametric analyses, many authors indicate that the kernel density functions work well when the variable is close to the Gaussian shape. This chapter interest is on the improvement the forecastability of the functional nonparametric time series by using a new approach of the parametric power transformation. The choice of the power parameter in this approach is based on minimizing the mean integrated square error of kernel estimation. Many authors have used this criterion in estimating density under the assumption that the original data follow a known probability distribution. In this chapter, the authors assumed that the original data were of unknown distribution and set the theoretical framework to derive a criterion for estimating the power parameter and proposed an application algorithm in two-time series of temperature monthly averages.

**Keywords:** functional non-parametric time series, power transformation, Kernel density function, Mean Integrated Square Error

## **1. Introduction**

One of the most common approaches for studying forecasting models is the Nonparametric functional regression method, which has been successfully applied in time series analysis. In this chapter, a new approach of power transformation is proposed to improve time series prediction when using functional nonparametric techniques. Although the nonparametric regression estimation under dependence is a useful tool for forecasting in time series [1], the functional and nonparametric approaches does not work well in certain circumstances.

Regarding the functional approach, The functional data (FD) analysis treats with the observations as a functions [2] without the need for fully parametric and non-parametric modeling conditions. In other words, FD analysis reduces the size of the data by clarifying the correlations between a large number of variables by a small number of factors or functions [3]. This transformation of the data structure into a linear combination of a

few functions (curves) is equivalent to structural regression models. A number of useful semi-metrics families can be used to measure the proximities between the curves of the functional variables. One of these ways, for example, the Functional Principle Components Analysis (FPCA) [4, 5]. In some data sets with the time dependence of observations, FPCA may lead to weak estimates and that this problem may be exacerbated in some time series data sets especially those characterized by the presence of seasonal changes [6] (See also [7] who pointed out that the standard PCA may not be the suitable technique to apply when the data distribution is skewed or there are outliers).

As for the nonparametric approach to estimating kernel density functions (KDF) or predictions in regression and time series models, although this approach is a Distribution-Free method, the symmetricity of the data is an important issue in order to obtain efficient estimators [8, 9].

As for time series and the goal of improving forecastability, it is known that the time series data sets in practical applications are rarely adapted for statistical analysis due to their instability in variance, trend, and seasonal variations [10].

Based on the aforementioned requirements of importance that precede the analysis and inference in the functional nonparametric time series analysis, it can be said that the power transformation (PT) provide a novel corrective framework of the predictive modeling.

The rest of the chapter is organized as follows: The second section includes some explanations and clarifications of some traditional approaches of PT and their uses in KDF. In the third section, the authors present their proposal which contains a new approach for Transforming of KDS. Section four includes the algorithm for applying the proposed method. While the fifth section includes an applications of the proposed method to two temperature time series datasets. Finally, the sixth section included the conclusions and some future recommendations.

## **2. The traditional approaches of transformations in KDF**

There is a long tradition of applying PT models in statistical applications. In 1952, Finney [11] used the PT model *Ψ*ð Þ¼ *Z Zλ* when *λ* ¼6 **0** and *Ψ*ð Þ¼ *Z log z*ð Þ when *λ* ¼ **0**, where Z represents the original dose variable in the biological assay. The purpose of using transformation in dose response relationship was to achieve the monotonous and linear characteristics for the Intrinsically nonlinear models. In 1964, Box and Cox [12] proposed the following general class of transformation of the response variable in the multiple linear regression model,

$$\Psi(\mathbf{Z}) = \begin{cases} \mathbf{Z}^{\lambda} - \mathbf{1} & \text{if } \lambda \neq \mathbf{0} \\ \frac{\lambda}{\log \left( x \right)} & \text{if } \lambda = \mathbf{0} \end{cases} \tag{1}$$

to achieve a linear relationship with normality errors. In 1977, Tukey [13] describes an orderly way of re-expressing variables using the following model in order to preserve the order of the variable after the PT is used,

$$\Psi(\mathbf{Z}) = \begin{cases} \begin{array}{c} Z^{\lambda} \ \text{if } \lambda > \mathbf{0} \\ \log\left(\mathbf{z}\right) \ \text{if } \lambda = \mathbf{0} \\ -Z^{\lambda} \ \text{if } \lambda < \mathbf{0} \end{array} \tag{2}$$

*A New Approach of Power Transformations in Functional Non-Parametric Temperature Time… DOI: http://dx.doi.org/10.5772/intechopen.105832*

to make the relationship as close to a straight line as possible. As for the nonparametric estimates, many authors refer to the usefulness of PT in reducing the bias of KDF when the data is clearly skewed or heavy tailed [14], (For more details see, [15–17]).

Regarding the transformation parameter estimation issues, most transformation methodologies have a common analytical path, which is the choice of the PT model and proposing an algorithm for estimating the power parameters in parallel with the mechanisms of estimating traditional model parameters. As for the approach of transforming the probability density function (PDF) of all or some model variables before proposing an algorithm estimation, there are at least two common methodologies of data transformation. The first in chronological order is the Box Cox transformation (BCT) methodology of data transforming to normality of response variable in parametric multiple regression models [12]. The common decision rule for selecting power parameter estimator in this approach is the maximization of log likelihood function of the PDF of original data. In some cases, the Bayesian estimating method is used and many other methods included in the subject literature can also be used to choose the transformation parameter. The second methodology is proposed by Wand, Marron and Ruppert in 1991 [8] to transform the KDF to a symmetrical shape in density function. In this methodology, the decision rule for selecting optimal estimator of density power parameter is the minimization of the Mean Integrated Square Error (MISE) of KDF estimator. Both transformation ways are used the distribution approach of transformed data and therefor defining the original data distribution as a "back-transformed" of change-of-variable technique. Mathematically, in the case of the univariate random variable *Z*, Box and Cox [12] assumes that there exist a parametric PT function *ψ*ð Þ*:* of the random variable *Z* such that *ψ*ð Þ¼ *z Z*ð Þ*λ* � *N μ*, *σ***2** � � under the assumption that the original data is of unknown distribution. Therefore, the PDF of the original variable is given by,

$$f\_Z(\mathbf{z}) = f\_{\varphi(\mathbf{z})}(\varphi(\mathbf{z}\_i); \boldsymbol{\mu}, \sigma^2). \left| \frac{d\boldsymbol{\mu}(\mathbf{z})}{d\mathbf{z}\_i} \right| \tag{3}$$

While the second methodology [8], Wand, Marron, and Ruppert assumes the estimated KDF of the transformed variable *ψ*ð Þ*z* that is close to the symmetrical shape is given by,

$$f\_{\boldsymbol{\Psi}^{(\mathbf{z})}}(\boldsymbol{\Psi}(\mathbf{z});\lambda) = \boldsymbol{f}\_Z\left\{\boldsymbol{\Psi}^{-1}(\mathbf{z})\right\}\left(\boldsymbol{\Psi}^{-1}\right)'(\boldsymbol{\Psi}(\mathbf{z})) \tag{4}$$

Such that the estimated KDF of the original variable *Z* is the back-transform of (Eq. (4)) and given by,

$$\hat{f}\_{\mathbf{z}}(\mathbf{z}; \mathbf{h}, \lambda) = \mathfrak{n}^{-1} \sum \mathfrak{y}'(\mathbf{z}) k\_{\mathbf{h}} \{\mathfrak{y}(\mathbf{z}) - \mathfrak{y}(\mathbf{Z}\_i)\} \tag{5}$$

Where h is the bandwidth and the kernel K is a density. In brief terms, the first methodology aims in the parametric models to improve the efficiency of the statistical inference based on the data normality, and the second methodology aims to improve the kernel estimator at least on the basis of symmetrical data. And in the same context, the literatures recommend the use of transformations as long as they can improve interpretation of effect sizes between variables [13] or given the fact that model parameters are not easily interpreted in terms of the original response [14], (For more details, see [15–17]).

Now, assuming that *U* ¼ *ψ*ð Þ*z* , The optimum value of the PT parameter *λ* is the one that corresponds to the lowest possible value of MISE of the estimated density (Eq. (5)) and given by,

$$\text{MISE}\_Z(\hbar,\lambda) = \mathbf{E}\left[\left\{\hat{f}\_Z(\mathbf{z};\hbar,\lambda) - f\_Z(\mathbf{z})\right\}^2 \mathbf{d}\mathbf{z}\right] \tag{6}$$

Assume that the first and second derivatives of the function *fZ*ð Þ*z* exist, as well as that *K***1** ¼ Ð *Z***2** *K Z*ð Þ *dz, K***2** ¼ Ð *K***2**ð Þ *Z dz* so

$$\text{MISE}\_Z(h,\lambda) = \text{AMISE}\_Z(h,\lambda) + \mathcal{O}\left(h^4 + n^{-1}h^{-1}\right) \tag{7}$$

Where:

$$\text{AMISE}\_{Z}(h,\lambda) = h^{4}\left(\mathbf{K}\_{1}^{2}/4\right) \left[\boldsymbol{\psi}^{\prime}\left\{\boldsymbol{\psi}^{-1}(u)\right\} \boldsymbol{f}\_{\boldsymbol{U}}^{\prime}(u;\lambda)^{2} du + n^{-1} h^{-1} \mathbf{K}\_{2} \to \boldsymbol{\psi}^{\prime}(\boldsymbol{x})\right] \tag{8}$$

and the minimized window width for any value of **λ** is given by,

$$\boldsymbol{h}\_{\boldsymbol{\lambda},\boldsymbol{x}}^{\*} = \left[\frac{\boldsymbol{K}\_{2}\boldsymbol{E}\,\boldsymbol{\Psi}'(\boldsymbol{x})}{\boldsymbol{K}\_{1}^{2}\left[\boldsymbol{\Psi}'\left\{\boldsymbol{\Psi}^{-1}(\boldsymbol{u})\right\}\boldsymbol{f}\_{\boldsymbol{U}}''(\boldsymbol{u};\boldsymbol{\lambda})^{2}\boldsymbol{d}\boldsymbol{u}\right]}\right]^{1/5}\boldsymbol{\mathcal{n}}^{-1/5}\tag{9}$$

and it contains less **AMISEz**ð Þ *:*, **λ** for each constant value of **λ** that equals,

$$\inf\_{h>0} \text{AMISE}\_{\mathbf{z}}(h,\lambda) = (\mathbf{5}/4) \left(\mathbf{K}\_1 \mathbf{K}\_2^2\right)^{2/5} \mathbf{J}\_{\mathbf{z}}(\lambda) \mathfrak{n}^{-4/5} \tag{10}$$

Where,

$$J\_{\mathfrak{z}}(\lambda) = \left[ \left\{ E \,\upmu'(\mathfrak{z}) \right\}^4 \int \limits \bigu{\mu'} \left\{ \left\langle \upmu^{-1}(u) \right\rangle f\_U''(u;\lambda)^2 du \right\}^{1/5} \tag{11}$$

The last two equations (Eqs. (10) and (11)) represent a measure of the transformation's *ψ*ð Þ*z* influence on minimizing the error associated with estimating the function of the original data ^*f z*ð Þ *:*; *h*, *λ* . Therefore, the optimal value of λ can be known as the one that minimizes: *Inf h >* **0** *AMISEz*ð Þ *h*, *λ .*

By the same decision rules logic *AMISEz*ð Þ *h*, *λ* , derived from the density estimation of the transformed variable **Z**, the optimal asymptotical window width for each **λ** according to the original random variable is:

$$h^\*\_{\lambda, u} = \left[\frac{K\_2}{K\_1^2 J\_u(\lambda) n}\right]^{1/5} \tag{12}$$

Asymptotically, the optimal choice of **λ** minimizes

$$\inf\_{h>0} \text{AMISE}\_{\mathfrak{u}}(h,\lambda) = (\mathfrak{F}/\mathfrak{A}) \left(\mathbf{K}\_1 \mathbf{K}\_2^2\right)^{2/5} \mathbf{J}\_{\mathfrak{u}}(\lambda) n^{-4/5} \tag{13}$$

*A New Approach of Power Transformations in Functional Non-Parametric Temperature Time… DOI: http://dx.doi.org/10.5772/intechopen.105832*

Where:

$$J\_{\mathfrak{u}}(\lambda) = \left[ \int f\_{U}^{\prime\prime}(\mathfrak{u}; \lambda)^{2} d\mathfrak{u} \right]^{1/5} \tag{14}$$

In other words, it can be said that the minimization of *Jz*ð Þ*λ* and *Ju*ð Þ*λ* are the sufficient condition to prove the optimization of *λ* since Eq. (11) and Eq. (14) represents the variable parts of Eq. (10) and Eq. (13) respectively.

Finally, the relationship between *MISEu*ð Þ *h*, *λ* and *MISEz*ð Þ *h*, *λ* can be determined according to the equations:

$$\text{MISE}\_{\mathfrak{x}}(\mathfrak{h},\mathfrak{\lambda}) = E\left[ \left\{ \hat{f}\_{\mathfrak{u}}(\mathfrak{u}) - f\_{\mathfrak{u}}(\mathfrak{u}) \right\}^2 \mathfrak{y}' \left\{ \mathfrak{y}^{-1}(\mathfrak{u}) \right\} du \tag{15}$$

$$\text{MISE}\_{\mathfrak{u}}(\mathfrak{h}, \lambda) = E\left[ \left\{ \hat{f}\_{\mathfrak{z}}(\mathfrak{u}) - f\_{\mathfrak{z}}(\mathfrak{u}) \right\}^2 \Psi^{-1} \right] \langle \Psi(\mathfrak{z}) \rangle d\mathfrak{z}.\tag{16}$$

Both error functions yield the same results, whether in terms of the original variable or of the transformed variable.

## **3. A new approach of transformations in KDS**

Unlike BCT methodology, which assumes that the original data is of unknown distribution, PTs' in KDF estimation are used to shifted the random variables with a known distribution into symmetric shapes to obtain an efficient kernel density estimation. The statistical literature in nonparametric estimation suggested the use of MISE indicator as a decision rule for power parameter estimation for a number of distributions such as Lognormal [8, 18], gamma [8], Cauchy [9], Pareto [18] and heavy-tailed distributions [19, 20].

Now, similar to the BCT approach, the primary hypothesis of the new approach in this chapter is that the data do not have a definite distribution. We will use the power transformation to transform the data to a normal shape and use MISE as a decision rule to choose the optimal value of the power parameter. Later in the sections 4 and 5 we will use this approach in the functional nonparametric time series analysis.

Let us assume that we have the random variable *Z* with unknown distribution and *U* ¼ *ψ*ð Þ*z* represents a PT model. Let, for Finney transformation (FT), suppose *U* ¼ *zλ* follows the normal distribution with mean **μ** and variance **σ2**. Therefore, according to the Eq. (3), the PDF of the original variable *Z* is given by *fZ*ð Þ¼ *z ψ*0 ð Þ*z f U ψ*ð Þ *zi* ; *μ*, *σ***2** � �.

In our proposed approach, the assumption of the normality of the transformed data when the original data is of unknown distribution provides uncomplicated options for estimating the power parameter so that Eq. (14) can be used as the simplest alternative to Eq. (11). In our assumption, we have,

$$f\_{\,\,U}(u;\lambda) = \frac{1}{\sqrt{2\pi\sigma^2}} \, e^{\frac{-(u-\rho)^2}{2\sigma^2}}, \mathcal{U} \in \mathcal{R} \tag{17}$$

So, the square of the second derivative of Eq. (17) is,

$$\left(f^{\prime\prime}(u;\lambda)\right)^{2} = \left(\sqrt{2\pi\sigma^{2}}\right)^{-2} \exp\left(\frac{-\left(u-\mu\right)^{2}}{\sigma^{2}}\right) \left[\frac{1}{\sigma^{4}} + \frac{-2}{\sigma^{2}}\frac{\left(u-\mu\right)^{2}}{\sigma^{4}} + \frac{\left(u-\mu\right)^{4}}{\sigma^{8}}\right] \tag{18}$$

By inserting the integration factor, we get,

$$\int f^{\prime\prime}(u;\lambda)^2 du = \sigma^{-8} \left(\sqrt{2\pi\sigma^2}\right)^{-1} \left[\int \sigma^4 \left(\sqrt{2\pi\sigma^2}\right)^{-1} e^{\frac{-(u-\mu)^2}{\sigma^2}} du\right.\tag{19}$$

$$-\int 2\sigma^2 (u-\mu)^2 \left(\sqrt{2\pi\sigma^2}\right)^{-1} e^{\frac{-(u-\mu)^2}{\sigma^2}} du$$

$$+\int (u-\mu)^4 \left(\sqrt{2\pi\sigma^2}\right)^{-1} e^{\frac{-(u-\mu)^2}{\sigma^2}} du\right]$$

Assume **σ2** ¼ **2δ2** , then the first term of Eq. (19),

$$\int \sigma^4 \frac{\mathbf{1}}{\sqrt{2\pi 2\delta^2}} e^{\frac{-(u-\mu)^2}{2\delta^2}} \, du = \frac{\sigma^4}{\sqrt{2}} \left[ \frac{\mathbf{1}}{\sqrt{2\pi \delta^2}} e^{\frac{-(u-\mu)^2}{2\delta^2}} \, du = \frac{\sigma^4}{\sqrt{2}} \right] \tag{20}$$

and the second term of Eq. (19),

$$\begin{split} \int \left[ 2\sigma^{2} (\boldsymbol{u} - \boldsymbol{\mu})^{2} \left( \sqrt{2\pi\sigma^{2}} \right)^{-1} \boldsymbol{e}^{\frac{-(\boldsymbol{u}-\boldsymbol{\mu})^{2}}{\sigma^{2}}} d\boldsymbol{u} \right. &= \frac{2\sigma^{2}}{\sqrt{2}} \Big[ (\boldsymbol{u} - \boldsymbol{\mu})^{2} \left( \sqrt{2\pi\delta^{2}} \right)^{-1} \boldsymbol{e}^{\frac{-(\boldsymbol{u}-\boldsymbol{\mu})^{2}}{2\delta^{2}}} d\boldsymbol{u} \\ &= \frac{2\sigma^{2}}{\sqrt{2}} \boldsymbol{E} (\boldsymbol{U} - \boldsymbol{\mu})^{2} = \frac{\sigma^{4}}{\sqrt{2}} \end{split} \tag{21}$$

and the third term of Eq. (19),

$$\begin{split} \int (u - \mu)^4 \left(\sqrt{2\pi\sigma^2}\right)^{-1} e^{\frac{-(u-\mu)^2}{\sigma^2}} du &= \frac{1}{\sqrt{2}} \int (u - \mu)^4 \left(\sqrt{2\pi\delta^2}\right)^{-1} e^{\frac{-(u-\mu)^2}{2\delta^2}} du \\ &= \frac{1}{\sqrt{2}} \operatorname{E} (U - \mu)^4 \end{split} \tag{22}$$

by using the central moments equation of the real-valued random variable *U*, *E U*ð Þ � *μ n* ¼ *E* P*n j*¼**0***Cn j* ð Þ �**1** *n*�*j Uj μn*�*j* then,

$$\mathbf{E}(\mathbf{U} - \boldsymbol{\mu})^4 = \mathbf{E}(\mathbf{U}^4) - \mathbf{4}\,\mu\,\mathbf{E}(\mathbf{U}^3) + \mathbf{6}\,\mu^2\mathbf{E}(\mathbf{U}^2) - \mathbf{4}\,\mu^3\,\mathbf{E}(\mathbf{U}) + (\mu^4) \tag{23}$$

Based on the moments equation,

$$\begin{aligned} \text{Hess } \mathbf{e}\_1 &= \mathbf{E}(\mathbf{U}^k), \text{get,} \\ \mathbf{E}(\mathbf{U} - \boldsymbol{\mu})^4 &= \boldsymbol{\mu}\_4 - \mathbf{4}\,\boldsymbol{\mu}\_3\,\boldsymbol{\mu} + \mathbf{6}\,\boldsymbol{\mu}\_2\,\boldsymbol{\mu}^2 - \mathbf{4}\,\boldsymbol{\mu}\,\boldsymbol{\mu}^3 + \boldsymbol{\mu}^4 \end{aligned} \tag{24}$$

Substitute the three parts defined by Eq. (20), Eq. (21) and (Eq. (22) into Eq. (19) get,

$$J\_U(\lambda) = \left[\frac{\mathbf{1}}{\sigma^8} \left(\sqrt{2\pi\sigma^2}\right)^{-1} \left(\frac{\mathbf{1}}{\sqrt{2}} \left(\mu\_4 - 4\mu\_3\mu + 6\mu\_2\mu^2 - 4\mu\mu^3 + \mu^4\right)\right]^{1/5} \tag{25}$$

Eq. (25) is the end of the derivation. The optimal power parameter value is the one that minimizes the value of *JU*ð Þ*λ* . In the practical application, the estimators of the maximum likelihood method were used for the moments about zero *μ*^*k* ¼ P*n i*¼**1***uk i =n* and the central moments *μ*^*k* ¼ Pð Þ *ui* � *u k =n*.

*A New Approach of Power Transformations in Functional Non-Parametric Temperature Time… DOI: http://dx.doi.org/10.5772/intechopen.105832*

## **4. Proposed application algorithm**

For the univariate time series *{Zt*,*t R*g, assume that the sample is divided into ð Þ *p* þ **1** ) statistical samples of size ð Þ *n* ¼ *N* � *s* � *p* þ **1** so that the time series data set can be defined as a functional data *Xi* f g ð Þ , *Yi i*¼**1**,*::*,*n*. The regression model,

$$\mathbf{Y} = \mathbf{m}(\mathbf{X}) + \mathbf{e} \tag{26}$$

represents the relationship between the smooth functional data *m X*ð Þ and scalar response *Yi* ¼ *Zi*þ*s*, *i* ¼ *p*, , *N* � *s*. The white noise **ε** is a sequence of independent identically distributed functions in such *E*ð Þ¼ *ε=X* **0***. X***1**, *X***2**, … *:*, *Xn* are identically distributed as the functional random variable *Xi* ¼ *Zi*�*p*þ**1**, … ,*Zi* � �*.* Assume **N** ¼ **nτ** for some *n ϵ N* and some *τ >* **0** to get a statistical sample of curves *Xi* ¼ f g *Z t*ð Þ,ð Þ *i* � **1** *τ < t iτ* of size ð Þ *n* � **1** and the response *Yi* ¼ *Z i*ð Þ *τ* þ *s* , *i* ¼ **1**, … , *n* � **1** [5]. The kernel regression estimator evaluated at a given function *m X*ð Þ in Eq. (26) by:

$$\hat{m}(\mathbf{X}) = \frac{\sum\_{i=1}^{n} \mathbf{Y}\_i \mathbf{K}\left(\boldsymbol{h}^{-1} \, d\left(\mathbf{X}, \mathbf{X}\_i\right)\right)}{\sum\_{i=1}^{n} \mathbf{K}\left(\boldsymbol{h}^{-1} \, d\left(\mathbf{X}, \mathbf{X}\_i\right)\right)} \tag{27}$$

Where K is a kernel function and, h (depending on n) are a positive real bandwidth and *d X*ð Þ , *Xi* denotes any semi-metric index of proximity between the observed curves based on the functional principal components [5, 6, 21]. Many authors have proposed a number of methods for measuring the proximity such as, the method of FPCA in which, *d X*ð Þ , *Xi* is measuring by the square root of the quantity

Ð *Xi*ð Þ� *t Xj*ð Þ*t* � �**2** *dt* or the quantity Ð *X*ð Þ **2** *i* ð Þ� *t X*ð Þ **2** *j* ð Þ*t* � �**2** *dt* (for more details, see [4, 21–25]).

The application methodology includes estimating the smooth functional data *m X*ð Þ in the regression equation Eq. (26) according to the kernel estimator Eq. (27) after transforming the time series dataset. So, the following proposed application algorithm of the nonparametric estimation of transformed functional time series according to the proposed new approach for transforming the kernel density were as follows:

Step 1: Choosing the common range *Λ* ¼ �f g **3**, **3** for the power parameter **λ** Step 2: Calculate the value of *Jψ*ð Þ *Z* ð Þ*λ* according to Eq. (14).

Step 3: Transform the original response variable *Z* according the Finney [11] PT model, *Ψ*ð Þ¼ *Z Zλ* when *λ* 6¼ **0** and BCT model Eq. (1) to get the explanatory functional matrices *Ψλ*ð Þ¼ *X* ½ � *Ψλ*ð Þ*z nxτ* (for more about the matrices file organizing in the R program, see [5, 21]".

Step 4: Redefining the functional data of the regression model *Xi* f g ð Þ , *Yi i*¼**1**,*::*,*n* so that the statistical sample of curves *Xi* ¼ f g *Z t*ð Þ,ð Þ *i* � **1** *τ < t iτ* is defined as follows,

$$\Psi\_{\lambda}(\mathbf{X}\_{i}) = \{\Psi\_{\lambda}(\mathbf{Z}(\mathbf{t})), (i - \mathbf{1})\mathbf{r} < \mathbf{t} \le i\pi\} \tag{28}$$

and the response *Yi* ¼ *Z i*ð Þ *τ* þ *s* , *i* ¼ **1**, … , *n* � **1** is defined as follows,

$$\Psi\_{\lambda}(\mathbf{Y}\_{i}) = \Psi\_{\lambda}(\mathbf{Z}(i\mathbf{r} + \mathbf{s})) \tag{29}$$

Step 5: Defining the Eq. (28) and Eq. (29) in which **τ** equal the seasonal length. Step 6: Estimate the explanatory function regression *Ψλ*ð Þ¼ *Yi m*ð Þþ *Ψλ*ð Þ *X ε*, (where)

$$\hat{m}(\boldsymbol{\Psi}\_{\boldsymbol{\lambda}}(\mathbf{X})) = \frac{\sum\_{i=1}^{n} \boldsymbol{\Psi}\_{\boldsymbol{\lambda}}(\mathbf{Y}\_{i}) \mathbf{K} \left(\boldsymbol{h}^{-1} \boldsymbol{d} \left(\boldsymbol{\Psi}\_{\boldsymbol{\lambda}}(\mathbf{X}), \boldsymbol{\Psi}\_{\boldsymbol{\lambda}}(\mathbf{X}\_{i})\right)\right)}{\sum\_{i=1}^{n} \boldsymbol{\K} \left(\boldsymbol{h}^{-1} \boldsymbol{d} \left(\boldsymbol{\Psi}\_{\boldsymbol{\lambda}}(\mathbf{X}), \boldsymbol{\Psi}\_{\boldsymbol{\lambda}}(\mathbf{X}\_{i})\right)\right)} \tag{30}$$

by using the Nadaraya–Watson regression estimator for functional data. Step 7: Perform the steps 2 through 6 for all **λ ∈ Λ**.

Step 8: Choose the optimal value that corresponds to the lowest value of *JU*ð Þ*λ* . Step 9: Calculate the estimator of mean square errors of the last curve *MSE X*ð Þ¼ *n* ð Þ **1***=s* P*s j*¼**1** ^*zj* � *zj* � �**2** , where, ^*zj* and **zj** are the j-th estimated and real values respectively in the last curve. ^*zj*values denoted to, they are computed from the back transform of *ψ*ð Þ¼ *z z***λ** *i* .

**Figure 1.** *Plots of the monthly temperature averages series: (a) TSN; (b) TST [21].*

*A New Approach of Power Transformations in Functional Non-Parametric Temperature Time… DOI: http://dx.doi.org/10.5772/intechopen.105832*

In all PT methodologies, the decision rule for choosing the optimal power parameter, always leads to what we might call the area of feasible solutions. For example, the argumentative question in BCT is: Does the optimal parameter that results from minimizing MLE method for the original response function achieve the normality of the transformed variable in practice? The authors believe that this problem is due to the nature of the data. In the proposed approach, the optimal power parameter that corresponds to the lowest *JU*ð Þ*λ* , we have the challenge of complexity in the feasible solutions area that we suppose to achieve: The transformed response normality in practical application that provides quality conditions for both functional and nonparametric analyzes approaches in nonstationary seasonal time series (For more see [26, 27] that point to other challenges related to the use of PT and the quality of the power parameter estimation).

## **5. Applications**

The PT models indicated in the proposed application algorithm have been applied to two examples of nonstationary time series of monthly temperature averages [21]. The first has a size of 200 observations of Nineveh City in Iraq (TSN) for the period 1976 to 2000 (**Figure 1a**). The second has a size of 300 observations of Tunisia (TST) of the period 1991 to 2015 (**Figure 1b**). R software was used to analyze the data. The data is available at https://climateknowledgeporta l.worldbank.org.

**Figure 2.**

*The curves of the ordered pairs* **λ**^*i*,*Ju*ð Þ*λ of the transformed responses of the two time series data sets using FT: (a) TSN. (b) TST.*

Returning to the ideas of the of feasible solutions area, we must verify the results of choosing the optimal PT value according to the proposed density transformation approach and its contribution to achieving the analysis efficiency requirements: the concavity of *Ju*ð Þ*λ* , the normality of the transformed response, and the reduction of the prediction error in the functional nonparametric time series analysis.

Mathematically, *Ju*ð Þ*λ* is a concave function, but a number of authors state the possibility that there is no mini-point or is not unique [8, 18]. This conclusion may depend on the success in choosing the appropriate PT model [20]. The plots in **Figures 2** and **3** show the curves of the ordered pairs **λ***i* ,*Ju*ð Þ*λ* of Eq. (14).

In **Figure 2**, it can be seen that the curves of the two time series data sets using FT has a concavity point in the range ð Þ �**3**, **0** , while the *Ju*ð Þ*λ* values tends to zero in which the curves fades towards the horizontal line in the range ð Þ **0**, **3** .

While when applying BCT, it becomes clear from **Figure 3** that there is no point of concavity in the curves of *Ju*ð Þ*λ* as its value goes to zero whenever the value of *λ* goes to �3. Therefore, it is not possible to obtain an optimal value for *λ*.

As for the normality of the transformed data, **Table 1** shows for the two examples, that the response variable data in its original and transformed states are not normal. Both optimal values of *λ* corresponding to the minimum values of *Ju*ð Þ*λ* did not shift the data to the normal shape. But on the other hand, the improvement in the forecastability of the two-time series was evident through the estimates of mean square errors of the last curve (**Table 2**).

#### **Figure 3.**

*The curves of the ordered pairs* **λ**^*i*,*Ju*ð Þ*λ of the transformed responses of the two time series data sets using BCT: (a) TSN. (b) TST.*

*A New Approach of Power Transformations in Functional Non-Parametric Temperature Time… DOI: http://dx.doi.org/10.5772/intechopen.105832*

#### **Table 1.**

*The data normality tests of the original and transformed responses in the two examples using FT model.*

**Table 2.**

*The MSE estimates of the last curve* **Xn** *of the two-time series datasets.*

## **6. Conclusions**

In the analysis of parametric and non-parametric time series, like any statistical modeling process that requires the availability of certain conditions so that the results of statistical inference are reliable, which contributes to improving the forecastability.

Data is rarely ready for statistical analysis, which necessitates the use of power transformation to improve the required output. In this chapter, power transformation has been used with a new methodology to improve the outputs of the analysis with the following three directions: time series, nonparametric estimation and functional analysis. Therefore, the authors faced the challenge of choosing the optimal power parameter estimation method in accordance with the conditions of the feasible solutions area for the three directions. Using MISE as a criterion for choosing the power parameter in the proposed method did not achieve the normality of the data but it enhanced the forcasetibility of the time series.

By applying the FT and BCT models, the first was applicable and fulfilled the concavity condition for the transformation effect measurement function *Ju*ð Þ*λ* , while the function curve was divergent at both ends of the power parameter range using the second model.

In the future, we recommend developing the proposed methodology using other transformation models and looking into the possibility of using it in other shapes of time series.

*Time Series Analysis - New Insights*

## **Author details**

Haithem Taha Mohammed Ali1,2 and Sameera Abdulsalam Othman3 \*

1 Department of Economic Sciences, University of Zakho, Kurdistan Region, Iraq

2 Department of Economic, Nawroz University, Kurdistan Region, Iraq

3 Department of Mathematics, College of Basic Education, University of Duhok, Kurdistan Region, Iraq

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*A New Approach of Power Transformations in Functional Non-Parametric Temperature Time… DOI: http://dx.doi.org/10.5772/intechopen.105832*

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Section 6


**Author details**

Farida Hanna Campbell Epidaurus Telemedical, Leiden, The Netherlands

\*Address all correspondence to<EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*The Need for XR-Measurement of Decision-Making Decline and Conscious-State Transition… DOI: http://dx.doi.org/10.5772/intechopen.97384*


*Editorial* **Special Issue: Valorization of Material Waste for Environmental, Energetic, and Biomedical Applications**

**Antonio Gil**

INAMAT2 Science Department, Campus of Arrosadia, Public University of Navarra, Building Los Acebos, 31006 Pamplona, Spain<EMAIL_ADDRESS>
#### **Preface**

Waste management and its recovery to provide it with added value are increasingly important lines of research that fall within the concept of a *Circular Economy*. Reducing the amount of waste that is generated is no longer only the objective; at present and in the future it is necessary to achieve a utility for this waste that contributes effectively to the scarcity of raw materials, as well as the impossibility of storing any type of waste.

The development of materials and products from industrial waste has attracted the attention of the research community for years. The physicochemical characteristics have specific impacts on the material properties and the materials and products are applied in environmental, energetic, and biomedical areas such as pollutant removal, CO2 capture, energy storage, catalytic oxidation and reduction processes, conversion of biomass to biofuels, and drug delivery. Examples of materials are activated carbons, clays, and zeolites, among others. The aim of this Special Issue is to compile the recent advances and progress in relation to valorized materials from industrial waste and their applications in environmental, energetic, and biomedical areas.

This book contains up to eight papers published by several authors interested in the valorization of materials and in the concept of a *Circular Economy*. Voultsos et al. [1] evaluate the energetic and environmental performance of a cogeneration biomass gasification plant, situated in Thessaly, Greece, via a methodology combining process simulation and Life Cycle Assessment (LCA). Initially in the work, the gasification process of the most common agricultural residues found in the Thessaly region is simulated to establish the effect of technical parameters such as gasification temperature, equivalence ratio, and raw biomass moisture content. The gasifier model is up-scaled by the authors, achieving the operation of a 1 MWel and 2.25 MWth cogeneration plant. The LCA of the operation of the cogeneration unit is conducted using the performance data from the process simulation as input. Global Warming Potential and the Cumulative Demand of Non-Renewable Fossil Energy results suggest that the component which had the major share in both impact categories is the self-consumption of electricity of the plant. The results obtained by the authors suggest that plant operation in all examined conditions leads to GHG mitigation and non-renewable energy savings of approximately 0.6 kg CO2eq/kWhel and 10 MJ/kWhel, respectively.

The methods to treat kinetic data for the biodegradation of various plastic materials are comparatively discussed in the work by Rossetti et al. [2]. Several samples of commercial formulates were tested for aerobic biodegradation in compost, following the standard ISO14855. Starting from the raw data, the conversion vs. time entries were elaborated using relatively simple kinetic models, such as integrated kinetic equations of zero, first, and second order; the Wilkinson model; or the Michaelis Menten approach.

Tam et al. [3] report that Q9 is widely used in industries handling flammable fluids and is central to explosion risk assessment (ERA). Q9 transforms complex flammable clouds from pressurized releases to simple cuboids with uniform stoichiometric concentration, drastically reducing the time and resources needed by ERA. Q9 is commonly believed in the industry to be conservative, but two studies on Q9 gave conflicting conclusions. This

**Citation:** Gil, A. Special Issue: Valorization of Material Waste for Environmental, Energetic, and Biomedical Applications. *Eng* **2022**, *3*, 24–26. https://doi.org/10.3390/ eng3010003

Received: 24 November 2021 Accepted: 22 December 2021 Published: 29 December 2021

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

efficacy issue is important, as impacts of Q9 have real life consequences, such as inadequate engineering design and risk management, risk underestimation, etc. The authors review published data and describe additional assessment on Q9 using the largescale experimental dataset from Blast and Fire for Topside Structure joint industry (BFTSS) Phase 3B project, which was designed to address this type of scenario. The presented results show that Q9 systematically under-predicts this dataset. Finally, the authors make several observations and recommendations.

Bächle et al. [4] also report that for solid–liquid separation, filter meshes are still used across large areas today, as they offer a cost-effective alternative, for example, compared to membranes. However, particle interaction leads to a continuous blocking of the pores, which lowers the flow rate of the mesh and reduces its lifetime. This can be remedied by filter aids. In precoat filtration, these provide an already fully formed filter cake on the fabric, which acts as a surface and depth filter. This prevents interaction of the particles to be separated with the mesh and thus increases the service life of the mesh. In the work, the effect of a precoat layer with fiber lengths of cellulose on the filtration behavior is investigated.

In the following, the authors indicate that the dispersion of vapor of liquefied natural gas (LNG) is generally assumed to be from a liquid spill on the ground in hazard and risk analysis [5]. The authors also explain that the cold vapor could be discharged at a certain height through cold venting. While there is similarity to the situation where a heavier-than-air gas (e.g., CO2) is discharged through tall vent stacks, LNG vapor is cold and induces phase change of ambient moisture, leading to changes in the thermodynamics as the vapor disperses.

Beltran-Siñani and Gil [6] present that waste generation is one of the multiple factors affecting the environment and human health that increases directly with growing population and social and economic development. The municipal solid waste disposal sites and their management create climate challenges worldwide, with one of the main problems being high biowaste content, which has direct repercussions for greenhouse gas (GHG) emissions. In the case of Bolivia, as in most developing countries, dumps are the main disposal sites for solid waste. These places are usually non-engineered and poorly implemented due to social, technical, institutional, and financial limitations. Composting plants for the treatment of biowaste appear to be an alternative solution to the problem. In this way, municipalities have implemented pilot projects with successful social results; however, access to economic and financial resources for this alternative are limited. The authors compile and summarize the Intergovernmental Panel on Climate Change (IPCC) guidelines methodology and some experimental procedures for the accounting of greenhouse gase emissions during the biowaste composting process as an alternative to its deposition in a dump or landfill.

Conventional water treatment technologies are not capable of removing estradiol from water, as indicated Pérez-González et al. [7]. Their study aims to assess a method that combines physicochemical and biological strategies to remove estradiol even when there are other compounds present in the water matrix. Na-montmorillonite, Ca-montmorillonite, and zeolite were used to remove estradiol in a medium with sulfamethoxazole, triclosan, and nicotine using a Plackett–Burman experimental design. Each treatment was followed by biological filtration with Daphnia magna. The most significant factors for estradiol adsorption were the presence of nicotine and triclosan, which favored the adsorption; the use of Ca-montmorillonite, Zeolite, and time did not favor the adsorption of estradiol.

In the final manuscript, Riley et al. [8] present a work where the extraction of Cu from mixed-metal acidic solutions by the thiourea-functionalized resin Puromet MTS9140 was studied. Despite being originally manufactured for precious metal recovery, a high selectivity towards Cu was observed over other first-row transition metals (>90% removal), highlighting the potential for Puromet MTS9140 in base metal recovery circuits. Resin behavior was characterized in batch mode under a range of pH and sulphate concentrations and as a function of flow rate in a fixed-bed setup. In each instance, a high selectivity

and capacity towards Cu was observed and was unaffected by changes in solution chemistry. The work is the first detailed study of a thiourea-functionalized resin being used to selectively target Cu from a complex multi-metal solution.

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

#### **References**

#### **Short Biography of Author**

**Antonio Gil** (Full Professor of Chemical Engineering, Universidad Pública de Navarra, Spain): Professor Gil earned his BS and MS in Chemistry at University of Basque Country (San Sebastián), and his PhD in Chemical Engineering at University of Basque Country (San Sebastián). He did postdoctoral research at the Université catholique de Louvain (Belgium) working on Spillover and Mobility of Species on Catalyst Surfaces.

The research interests of Professor Gil can be summarized as: Evaluation of the porous and surface properties of solids. Pillared clays. Gas adsorption. Energy and CO2 storage. Pollutants adsorption. Environmental technologies. Environmental management. Preparation, characterization and catalytic performance of metal supported nanocatalysts. Industrial waste valorization.


**Acknowledgements**

This work was supported by a grant from the National Research Foundation of Korea (NRF) funded by the Korea government (MSIP) (NRF-2018R1A2B6006199) and a grant from the Korea Health Technology R&D Project through the Korea Health Industry Development Institute (KHIDI), funded by the Ministry of Health & Welfare, Republic of Korea (HI16C0992).


**2. Methodology**

The community of vegans constitutes a multitude of bodies whose diversity and mobility make it difficult to locate their contours and borders. Veganism is a conglomerate of worlds, with different economic, social, and territorial contexts. To approach it, I carried out a three-year multi-situated ethnography of the community of vegans who live in the metropolitan area of Puebla, including the analysis of their social networks. I selected the Facebook group "Vegans and Vegetarians of Puebla," a virtual community representative of local veganism where most of its members live in the cities of Puebla, Cholula, and Atlixco. The case of Puebla is relevant for the following reasons: (1) it is an average city in Mexico that, not being the capital of the country, serves to exemplify the case of many other Latin American cities with similar situations. (2) Rapid urban and economic development has led Puebla to become an aspiring global city. (3) The rich cultural life of Puebla has favored the proliferation of groups with global tendencies with different philosophies and projects like the vegan movement.

I conceive the corpus of study based on a rhizomatic model or multiple networks, inspired by Deleuze and Guattari. The center or starting point is the multisituated critical ethnography of the Facebook group to follow from there its ramifications that arise both virtually (online) and face-to-face (offline). Research has been structured and reoriented by the various paths that the movement undertakes, recording its evolution and manifestations, the spaces it appropriates, the practices it inaugurates, and the connections it establishes. My ethnography pursues a logic of encounters and affects which become evident in "critical events," like fairs or *tianguis* days in which the vegans congregate, as well as their interactions on the Internet.

**100**

**Chapter**

**Abstract**

**1. Introduction**

*Victor Fonseca López*

Revolutionary Veganism

doxically enough, constitute a truly revolutionary quality.

**Keywords:** veganism, posthegemony, critical ethnography, Puebla

This dissertation analyzes the development of the vegan movement in Puebla and its potential to trigger political and social changes in the context of contemporary neoliberal capitalism. Through critic ethnography research, the study puts into question the emergence of a so-called Vegan Revolution examining the formation of a globalized social movement and community networks with specific habits and values, the different perceptions about veganism, and affective bodily interactions among its members. From dialog with posthegemony theory (Beasley-Murray), it propels the notion of a bio- and micropolitical transformation (Deleuze and Guattari) instead of a more traditional revolution concept to account the processes in which a multitude of bodies—beyond diverse ideologies—meet, share, and affect each other in daily life, which shapes alternative models of society and forms of community to the cultural and political programs of neoliberalism, which, para-

Coinciding with the arrival of the twenty-first century, the entry of veganism into cultural mainstream has been announced—mainly on the Internet—with a "Revolution" label. For some critics, veganism tries to settle some debts regarding the exploitation of animals that remained pending in the agenda of the countercultural movement of the 1960s and 1970s. Just as the *hippies* and the *beatniks* rose against the Vietnam War and social inequalities, modern *hipsters* and vegans demand for a change denouncing ecological deterioration and mistreatment of animals. Headlines such as "The 'boom' of veganism and vegetarian diet reveal the new ecological awareness of the world" associate vegan practices with a transformation of consciousness that is expressed more in a lifestyle than with traditional revolutionary actions. Even so, the "revolution" tag remains (it is sticky). Social and political revolution traditionally refers to the exertion of violence which aims to overthrow—or at least radically change—a certain order or system of oppression. Historically, since the eighteenth century, the term has been linked to nationalist processes, where peoples or nations rise up in arms to defeat a government whose dictatorship or tyranny is necessary to dismiss. In his Communist Manifesto, Marx wrote that the class struggle "each time ended either in a revolutionary re-constitution of society at large, or in the common ruin of the contending classes" [1]. But in the twenty-first century, political and social conditions have reduced the ideological conflict to its minimum expression. However, the decay of ideology does not mean that it has completely disappeared, nor does the restlessness or longing for revolution. Instead, a shift is taking place from ideological discourse to pulsing affects which posthegemony theory tries to acknowledge.

## **3. Results**

I propose that vegan activists are fed by a belief system that embraces the ideals of the revolution, but this revolution is simply the counterpart of the modern project of civilization. For this reason, from a posthegemonic perspective, it cannot be conceived as an authentic revolution: it does not break with the same social and epistemic categories of modernity. On the other side, merchants, who are not interested in a traditional, leftist revolution, are those who, through their habits and affections, carry out more effective or "revolutionary" transformation processes.

To qualify as a revolution in the traditional Marxist sense, the vegan movement would have to have a greater hierarchical organization (with leaders and militants), a more formal and constant type of membership, a political agenda with defined goals, and a more complex communication system. But perhaps most importantly, it would require objectives and actions aimed at mobilizing a social uprising—ready to assume the use of violence—against an imperial or state regime. The relatively small number of members of the vegan movement, their nonviolent strategies, and their nongovernmental political positioning distance them from the singularities of the revolution. The anti-speciesism vegan movements want a radical change mainly in ethical and consumer habits, and they do not seek to overthrow an economic or political system.

In this way, the vegan revolution may not qualify as a revolution for two main reasons: (1) the changes it intends to establish are situated in the same linear historicism. Vegan ideology considers the movement to be an engine of progress in a linear vision of history. For some activists, the "Vegan revolution" makes sense as a project of evolution and civilization that follows the colonialist logic. For others, it is the continuation of the utopian struggle of the 1960s counterculture that still believes in the overthrow of capitalism. But the shift to a vegan diet does not alter the economic system, only exchanges one element of the equation for another, leaving the capitalist mode of production untouched, and (2) they do not abandon the paradigm of modernity. Following Deleuze, "modern societies have replaced inoperative codes by a univocal overcodification, and lost territorialities by a specific territorialization" [4]. Hence, the implantation of veganism resorts to overcoding and segmentation by means of binary separation (vegans-non-vegans). The binary conflict is part of the modern paradigm, in which one party tries to defeat the other, in order to impose itself on the top of civilization. Since its inception, veganism has placed its participants in a tension with its otherness. For instance, pro-animal organizations act by defining binary subjectivities, "we" and "they," or "defenders," those who support charity and protection of animal rights, and "enemies," supermarket chains and distributors of meat products and its final consumers, carnivores themselves.

In its posthegemonic version, veganism calls into question the universal, anthropocentric humanism, rational capacity, the Truth, the History or other great narratives. It does not believe in pre-constituted objects or subjects, pre-existing unitary actors or final purposes, only "contingent foundations." There is no certainty of being. Instead of thinking rationally, in binary form (opposites "nature-culture"), it becomes "relational," looking for connections. In fact, posthegemonic veganism is not interested in the concept of revolution (unless it functions as a commercial slogan). The multitude of vegans does not have a defined project of society. For the multitude, a revolution would be understood as alternating flows that combine to form currents of invention. The actual transformation carried out by affective and habitual means is not called revolution. Revolution implies an ideological tradition, while veganism does not fit in the parameters of the communism or other theoretical constructions. It is not a class struggle, and it is the biopolitical change of the multitude toward other ways of seeing the world, an altermodernity. This approach consists not in attacking the ruling powers but in reshaping production,

**103**

*Revolutionary Veganism*

kinds of animal species.

**4. Conclusions**

**Author details**

Victor Fonseca López

*DOI: http://dx.doi.org/10.5772/intechopen.83691*

distribution, and consumption processes. Ethnographic results show that vegan groups do not have a center, and they work globally, having subsidiaries or counterparts in several cities of the world—small cells that replicate global patterns with local tonalities. It is not about changing cities but networks of bodies. Veganism as immaterial work can only be conducted in common, inventing new independent networks of cooperation. That said, it is preferable to refer to veganism not as a revolution (in any case biopolitic), but as a movement toward political emancipation through collective action. It is an abolitionist, liberation movement, but what sets veganism apart is that what is at stake is life itself not only human life, but of all

The vegan collective has woven its own networks, both virtual (mainly on Facebook) and face-to-face. It is these networks that give strength and sustain the economy of veganism: its ability to appropriate spaces, its mobility and flexibility to spread, and its parameters of inclusion and exclusion, making vegan groups appear within the cartography of biopower. When Puebla vegan sellers and distributors organize *tianguis* and fairs, they are demarcating their own topologies, moving throughout territories of the city and appropriating spaces to interact affectively. The bodies attracted to vegan events revolve around environments that arouse emotions that originate resonances of different intensities. The combination of these elements produces a pattern or assembly. The broader and more solid the networks of this assembly are, the more will increase the share of power and social influence of the vegan collective. And so, the "Vegan Revolution," an ideological burden—a discursive strategy that refers to an unattainable utopia—would give way to a seri-

provided the original work is properly cited.

San Andrés Cholula, Puebla, Mexico

\*Address all correspondence to<EMAIL_ADDRESS>
ous social transformation, always in process.

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

School of Arts and Humanities, Universidad de las Américas Puebla,

### *Revolutionary Veganism DOI: http://dx.doi.org/10.5772/intechopen.83691*

distribution, and consumption processes. Ethnographic results show that vegan groups do not have a center, and they work globally, having subsidiaries or counterparts in several cities of the world—small cells that replicate global patterns with local tonalities. It is not about changing cities but networks of bodies. Veganism as immaterial work can only be conducted in common, inventing new independent networks of cooperation. That said, it is preferable to refer to veganism not as a revolution (in any case biopolitic), but as a movement toward political emancipation through collective action. It is an abolitionist, liberation movement, but what sets veganism apart is that what is at stake is life itself not only human life, but of all kinds of animal species.


*2.10. Research on Greenery Elements*

The preliminary analyses related to the study area provoked a number of questions, one of which is concerned with the lack of the appropriate development plan for Podolski Boulevard. The detailed assessment of the existing condition revealed that an intended space of historical commemoration was to be the Boulevard of Allied Forces Pilots (Bulwar Lotników Alianckich). Today, this area is still wasteland (Figure 10) (overgrown with grass and high greenery) despite the fact that nearby there are new apartment buildings and the Andrzej Frycz Modrzewski Higher School in Cracow. Only a plaque with the boulevard name stresses the significance of the area. Because of the fact that Zabłocie is characterised by the high-density housing development of the city centre, and yet does not have a payable parking zone, today the boulevard is often used as a "wild" car park.

**Figure 10.** Plots constituting the main part of the development of the design of a multi-functional complex with objects and sites under the conservation (photo by E. Latusek).


*3.6. Shoots Diameter*

Plants of poplar AF2 were, on average, of the greatest shoot diameter (113.5 mm).  Siberian elm and silver maple had the lowest shoot diameter of 41.8 mm both (Table 2). Geyer, Argent, and Walawender [18] found 7-year-old Siberian elm to have, on average, stems of diameter of 109 mm at 10 cm. Walle et al. [11] found that shoots diameter (at 30 cm) of 4-year-old poplar (*Populus trichocarpa* × *deltoids*) (336 mm) and maple (*Acer pseudoplatanus* L.) (310 mm) were lower than shoot diameter of birch (*Betula pendula* Roth) (493 mm). These authors conducted research on other clones/species of trees in different habitat conditions than in presented study; however, differences in results show the importance of the selection of appropriate species/cultivars and proper density of planting to make the best use of habitat conditions ensuring high biomass accumulation.

Shoot diameter for all tested species was positively correlated with their green and dry mass and shoot diameter. For all tested species, a negative correlation with the planting density was found (Table 3). Shoot diameter of all tested plant species were decreasing with increasing planting density, but the strength of this reaction varied between species (Figure 7). The decrease in stem diameter is a common response to increasing planting density [18,26–28], which can also be modified by species genotype (clone) [29].

**Figure 7.** Relationship between plants shoot diameter (mm) and planting density (plants ha−1).

#### *3.7. Higher Heating Value*

Tested energy sources differed significantly in higher heating value (HHV). White birch and boxelder maple had the highest average HHV value (19,509 and 19,158 J g−1 o, respectively). The lowest HHV was observed for poplar AF2 (17,908 J g−1 o). Dry mass of Siberian elm, black alder, and silver maple had a similar HHV value of around 18,500 J g−1 o (Table 2). Geyer, Argent, and Walawender [18] found that HHV of 7-year-old Siberian was between 18,900 and 20,200 J g−1 (19,700 J g−1 on average), which is a higher HHV value than in the presented. Study stand density had no effect on most species' HHV. A statistically significant negative correlation of HHV with the plant density was found only for poplar AF2 and white birch (Table 3, Figure 8). In the case of other species, no relationship between HHV and planting density was found. Literature study shows that HHV is highly variable and depends on both genetic factors (species, cultivars) [15,30,31] and cultivation conditions (soil quality, management methods) [30,32] or even plant age [33].

**Figure 8.** Relation of higher heating value (J g−1) and planting density (plants ha−1).