**6. Ca2+ signals during host-pathogen interactions**

Pathogenic bacteria have evolved various strategies to successfully colonize and cause infection in their hosts. Intracellular Ca2+ mobilization has been implicated as an important signaling event during bacterial adhesion, invasion and intracellular replication during infection [6]. Interestingly, some pathogens induce Ca2+ increases while others interfere with the Ca2+ signal to promote invasion [9, 94, 95]. However, despite the significant role of Ca2+ signaling during pathogenesis, the mechanisms underlying how bacterial cells and their virulent factors manipulate Ca2+ mobilization in host cells remains to be elucidated. This section will present some examples of the role of Ca2+ in host-pathogen interactions.

phagosmes or disrupt cell-cell junctions (Tran Van Nhieu [6]; Reboud et al. [102]). Interestingly, some pore-forming toxins such as *Listeria* listeriolysin O (LLO) induce Ca2+ oscillations as a result of a direct Ca2+ influx via the pore-forming toxin. An interesting feature of LLO is that pores open and close in a synchronized fashion leading to long lasting Ca2+ oscillating signaling provoking a broad spectrum of cellular responses during infection [6, 103]. Two other pore-forming toxins produced by the opportunistic pathogens *P. aeruginosa* (ExlA) and *Serratia marcescens* (ShlA), which share similar structural and functional aspects, have the capacity to trigger Ca2+ influx leading to disruption of cell-cell junctions of epithelial and endothelial cells. This influx of Ca2+ activates a metalloproteinase called 10(ADAM 10), which cleaves cadherin inducing cell-cell-junction breakdown and loss of tissue integrity [102].

Calcium Signaling in Prokaryotes

99

http://dx.doi.org/10.5772/intechopen.78546

There is a great diversity of Ca2+-dependent processes that pathogens utilize to cause infection. However, studies on bacterial induced Ca2+ signaling are limited. More research is needed in this filed to understand the mechanisms of how bacterial virulence factors regulate second

The role of Ca2+ in bacteria is a fascinating field that still remains unexplored. It is clear that evidence supporting the role of calcium as a regulator in prokaryotes is accumulating. However, the extent and significance remains unclear. A systematic assessment and careful

I thank Dr. Rossetta N. Reusch for agreeing to reproduce figures of her work and Samantha

Clinical Laboratory Science/Public Health, The University of Texas at El Paso, El Paso, Texas,

messengers such as Ca2+ and Ca2+-dependent events during the infectious processes.

analysis of the processes involving calcium warrants further analysis.

**7. Conclusion**

**Acknowledgements**

**Conflict of interest**

**Author details**

USA

Delfina C. Domínguez

Meza for assisting with the references.

The author has no conflict of interest.

Address all correspondence to<EMAIL_ADDRESS>
*Neisseria meningitidis* (meningococci) is the causative agent of bacterial meningitis. Pili are one of the major virulent factors of meningococci. Pili are bacterial structures that play an important role in adhesion to host cells. Analyzing the role of Ca2+ during *N. meningitides* infection, Asmat et al. [9] found that the meningococcal protein PilC1 triggered a significant increase of cytosolic Ca2+ in human brain microvascular endothelial cells (HBMEC), which was critical for adherence and subsequent internalization into host endothelial cells. Use of the Ca2+ chelator, BAPTA-AM, significantly reduced PilC1-mediated meningococcal adherence. Mutants deficient in PilC1 were not able to increase cytosolic Ca2+ in endothelial host cells. Pretreatment of host cells with the phospholipase inhibitor, U73122, indicated that the Ca2+ increase in endothelial cells was mediated by phospholipase C (PLC). Similar findings where Ca2+ mediated adherence to host cells occur through pili were reported in *P. aeruginosa* [96] and efficient internalization via PLC was reported in *Campylobacter jejuni* [97] and *Borrelia burgdorferi* [98].

*Shigella* is another pathogen that utilizes Ca2+ signaling during infection of epithelial cells. *Shigella* is the etiologic agent of bacillary dysentery. This pathogen invades the intestinal mucosa producing massive destruction of the colonic epithelium by eliciting a strong inflammatory response [6]. As early as 5 min after bacterial contact with epithelial cells *Shigella* induces local Ca2+ signals in the host cell, which remodel the cytoskeleton allowing bacterial entrance to the cells. Global Ca2+ signals are involved in later stages of infection promoting slow cell death as a result of plasma membrane permeabilization and increased cytosolic Ca2+. *Shigella* also manipulates the Ca2+ signal to interfere with immune responses and inflammation [99]. Global Ca2+ signals have also been associated with an induced decrease of sumoylation by *Shigella*. Sumoylation is a posttranslational modification by *S*mall *U*biquitin *Mo*difier (SUMO) proteins, which is an essential regulatory mechanism involved in several processes including protein stability, cell cycle, cell communication and gene expression [100]. At late time of postinfection, *Shigella* induces inhibition of sumoylation through activation of calpain proteases, which degrade SUMO proteins [101]. Inhibition of Ca2+ influx or calpain activity prevented shigella-induced loss of sumoylation. On the other hand Ca2+ treatment and inomycin resulted in sumoylation inhibition [101]. Knowledge of how pathogens interfere with SUMO enzymatic machinery is limited and remains to be characterized.

Several bacterial pathogens secrete potent virulence factors such as pore-forming toxins. These toxins perforate host cell membranes in order to deliver virulence factors, escape from phagosmes or disrupt cell-cell junctions (Tran Van Nhieu [6]; Reboud et al. [102]). Interestingly, some pore-forming toxins such as *Listeria* listeriolysin O (LLO) induce Ca2+ oscillations as a result of a direct Ca2+ influx via the pore-forming toxin. An interesting feature of LLO is that pores open and close in a synchronized fashion leading to long lasting Ca2+ oscillating signaling provoking a broad spectrum of cellular responses during infection [6, 103]. Two other pore-forming toxins produced by the opportunistic pathogens *P. aeruginosa* (ExlA) and *Serratia marcescens* (ShlA), which share similar structural and functional aspects, have the capacity to trigger Ca2+ influx leading to disruption of cell-cell junctions of epithelial and endothelial cells. This influx of Ca2+ activates a metalloproteinase called 10(ADAM 10), which cleaves cadherin inducing cell-cell-junction breakdown and loss of tissue integrity [102].

There is a great diversity of Ca2+-dependent processes that pathogens utilize to cause infection. However, studies on bacterial induced Ca2+ signaling are limited. More research is needed in this filed to understand the mechanisms of how bacterial virulence factors regulate second messengers such as Ca2+ and Ca2+-dependent events during the infectious processes.


**2. Polyaniline**

Polyaniline is probably the eldest known electroconducting polymer, since it was used for textile coloring one century ago (Sayed & Dinesan, 1991; Wallace et al., 2009).The great interest in research of polyaniline is connected to discovery of its conductivity in the form of emeraldine salt and existence of different oxidation forms (Inzelt, 2008; MacDiarmid et al., as cited in Wallace et al., 2009; Syed & Dinesan, 1991).


*Article* **An Entropy-Based Approach to Measurement of Stock Market Depth**

**Joanna Olbry´s \* and Krzysztof Ostrowski**

Faculty of Computer Science, Bialystok University of Technology, 15-351 Bialystok, Poland<EMAIL_ADDRESS>
**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** The aim of this study is to investigate market depth as a stock market liquidity dimension. A new methodology for market depth measurement exactly based on Shannon information entropy for high-frequency data is introduced and utilized. The proposed entropy-based market depth indicator is supported by an algorithm inferring the initiator of a trade. This new indicator seems to be a promising liquidity measure. Both market entropy and market liquidity can be directly measured by the new indicator. The findings of empirical experiments for real-data with a time stamp rounded to the nearest second from the Warsaw Stock Exchange (WSE) confirm that the new proxy enables us to effectively compare market depth and liquidity for different equities. Robustness tests and statistical analyses are conducted. Furthermore, an intra-day seasonality assessment is provided. Results indicate that the entropy-based approach can be considered as an auspicious market depth and liquidity proxy with an intuitive base for both theoretical and empirical analyses in financial markets.

**Keywords:** entropy; market microstructure; dimensions of market liquidity; market depth; high-frequency data; intra-day seasonality

#### **1. Introduction**

The original idea of entropy dates back to the fundamental Shannon's theory of communication and information [1]. Entropy was defined by Shannon as a measure of information, choice and uncertainty. The concept of entropy originates from thermodynamics, but it has been utilized in many research fields to characterize the complexity of a system and to investigate the information content of a probability distribution. Entropy is a general measure, and therefore, many definitions and applications of entropy have been proposed in the literature. Since the aim of this paper is to introduce and utilize a new entropy-based estimator of stock market depth as one of stock market liquidity dimensions, the brief literature review focuses on selected entropy-based applications in economics, finance, and management. Theoretical, empirical, and experimental aspects of entropy utilization are highlighted.

Firstly, there are quite many entropy-based applications in portfolio selection, asset pricing, and risk management, including the entropy optimization approach. Zhou et al. [2] presents a comprehensive review of applications of entropy in finance. Both primary and recent studies are included. For instance, the pioneering work of Philippatos and Wilson [3] proposed the mean-entropy concept in the efficient portfolio selection problem. The main contribution of this primary research lies in the conclusions that mean-entropy portfolios are consistent with the Markowitz and Sharpe models.

In light of the recently growing literature on the entropy-based applications, the topic concerning portfolio selection is very popular. Among others, Usta and Kantar [4] present a multi-objective method based on a mean-variance-skewness-entropy portfolio selection model to generate a well-diversified portfolio. Zhang et al. [5] deal with a multi-period portfolio selection problem with fuzzy returns. In this paper, the diversification degree of a

**Citation:** Olbry´s, J.; Ostrowski, K. An Entropy-Based Approach to Measurement of Stock Market Depth. *Entropy* **2021**, *23*, 568. https://doi.org/10.3390/ e23050568

Academic Editors: Yong Deng and Stanisław Drozd˙ z˙

Received: 8 March 2021 Accepted: 1 May 2021 Published: 3 May 2021

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

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

portfolio is measured by the originally presented possibilistic entropy. Huang [6] proposes two types of credibility-based fuzzy mean-entropy models for fuzzy portfolio selection, and entropy is used as the measure of risk. Yu et al. [7] evaluate the performance of the portfolio models that are used to rebalance with short selling, considering transaction costs, minimizing portfolio risk, and utilizing entropy in modeling asset allocation. Zhou et al. [8] systematically explore the properties of six kinds of entropy-based risk measures, and develop and compare several portfolio models based on different risk measures. Yang and Qiu [9] extend the classical decision model under risk to a more general case. They propose an expected utility-entropy measure of risk and a decision-making model based on expected utility and entropy. Pele et al. [10] investigate relationship between the information entropy of the distribution of intraday returns, and intraday and daily proxies of financial market risk. They use Value-at-Risk and Expected Shortfall as risk measures for the EUR/JPY exchange rate. Gradojevic and Caric [11] concentrate on quantifying the behavioral aspects of systematic risk by utilizing a novel entropy-based approach. Their empirical results confirm the predictive usefulness of new entropy setting in stock market risk management.

In the mathematical finance literature, there are several papers dealing with entropy as an optimization criterion, especially in the context of asset and option pricing. For example, Fritelli [12] investigates the properties of the minimal entropy martingale measure, and shows that the minimization of relative entropy is equivalent to the maximization of expected exponential utility of wealth. Stutzer [13] proposes relative entropy minimization approach to derivation of a generalized Black-Scholes option pricing model. In their theoretical research concerning risk management, Geman et al. [14] use entropy maximization approach to recognize the uncertainty of asset distribution. Xu et al. [15] propose a continuous maximum entropy method to analyze the robust optimal portfolio selection problem in the case of the market with transaction costs and dividends. Brody and Hughston [16] introduce a new term structure calibration methodology based on maximization of entropy, and present some new models of interest rate. Gulko [17,18] applies the Entropy Pricing Theory to introduce new formulas for pricing European stock and bond options.

Another broad research field is information and entropy econometrics that directly or indirectly builds on the foundations of information theory and the principle of maximum entropy. Among other topics, Golan and Perloff [19] deeply investigate the generalized maximum entropy estimation method. Ullah [20] provides the uses of entropy and divergence measures for evaluating econometric approximations and inference. Kitamura and Stutzer [21] develop the relationship between entropic and linear projections in asset pricing estimation based on stochastic discount factor models. Maasoumi and Racine [22] examine the predictability of stock market returns by employing a new metric entropy measure and compare their results with a number of traditional measures. Bera and Park [23] use maximum entropy portfolio selection method in the optimal portfolio diversification problem, and their approach can be viewed as a shrinkage estimation of portfolio weights.

According to the literature, several studies propose entropy-based methods to investigate groups of stock markets in the world, especially in the context of various common features, relationships and interdependences between them. For instance, Billio et al. [24] use different entropy measures and new early warning indicator for banking crises to analyze the time evolution of systematic risk in Europe. They focus on the euro zone and analyze a total of 437 European financial institutions. Zhao et al. [25] propose copula entropy models to measure dependence in stock markets. The Authors provide an algorithm for the copula entropy approach to obtain the numerical results, and they approve the validity of the proposed method. Zunino et al. [26] introduce two quantifiers for a stock market inefficiency: the number of forbidden patterns and the normalized permutation entropy. The Authors analyze equity indexes and returns for 32 different stock exchanges. They point out that their empirical findings suggest that the proposed physical tools are helpful to discriminate the stage of stock market development.

Another promising strand of the literature concerns network entropy since Mantegna [27] first represented the financial market as a network. Financial markets are complex systems and can be represented as complex networks. Network entropy can be treated is a measure of information contained in the system [28,29].

It is worth noting that quite extensive studies consider the concepts of mutual information and transfer entropy. These tools enable us to investigate the information flow between time series and are especially useful in economic and financial applications [30–38].

The literature contains several theoretical, empirical, and experimental studies concerning entropy-based applications in market microstructure research. For instance, Liu et al. [39] use entropy-based measures to identify various types of trading behaviors. Albeit, the papers regarding dimensions of market liquidity are relatively scarce. For instance, McCauley [40] points out that interest in thermodynamic analogies in economics and finance is older than the idea of von Neumann to look for market entropy in liquidity. McCauley assumes that the definition of an asset's liquidity is analogous to this of stock market depth. However, he concludes that real financial markets cannot behave thermodynamically because they are unstable.

Order imbalance has a significant influence on stock illiquidity, considerably more important even than volume. In the recent paper, Lu et al. [41] proposed an indicator called polarity to investigate trading imbalance in Chinese stock market. This indicator is based on high-frequency transaction data. However, the definition of polarity is very similar to this of order ratio, which is well known and broadly used in the literature as an indicator of stock market depth and market illiquidity (see e.g., [42,43] and the references therein). Therefore, the aforementioned paper was our research inspiration and motivation for taking and exploring the subject of an entropy-based approach to measurement of stock market depth as one of market liquidity dimensions [44].

The aim of this study is to introduce a new entropy-based market depth proxy that is exactly based on the definition of Shannon information entropy [1]. Our proposition substantially differs from the entropy-based indicator of trading imbalance presented in [39] because we employ the Lee and Ready [45] algorithm inferring the initiator of a trade to distinguish between so-called buyer- and seller-initiated trades.

The value-added of this research derives both from the new methodology and novel empirical findings. There are some advantages of the proposed indicator. Firstly, it can be treated as a new measure of stock market liquidity. The values of the entropy-based market depth are decimal fractions that vary between zero and the exactly defined maximal value equal to one. Therefore, the entropy-based market depth values calculated for different equities can be effectively compared to each other.

Moreover, based on the Shannon entropy definition, the entropy-based market depth indicator can be used to summarize the information content of a probability distribution, and it can be treated as a measure of stock market efficiency according to the Efficient Market Hypothesis (EMH). High values of entropy are related to randomness in the evolution of stock prices [26]. Higher values of market entropy inform about higher market efficiency, and are coupled with higher values of stock liquidity. Therefore, both market entropy and market liquidity can be directly measured by the proposed new indicator.

Empirical experiments on financial markets depend on data availability. Therefore, the real-data experiments and statistical analyses are conducted for high-frequency data with a time stamp rounded to the nearest second from the Warsaw Stock Exchange (WSE). Stability and robustness tests are conducted. Moreover, an intra-day seasonality assessment is provided to recognize intra-day hourly patterns in new entropy-based market depth indicator. Results indicate that this indicator can be considered as an auspicious market depth measure with an intuitive base for both theoretical and empirical analyses in financial markets. The proposed entropy-based indictor can be successfully utilized using intraday data from other stock markets in the world, and the results could be interesting for investors.

The remainder of the study is organized as follows: Section 2 specifies the methodological background of measurement of market depth in the context of the broad topic concerning dimensions of stock market liquidity. Section 3 contains real-data description and presents the findings of some empirical experiments, statistical analyses, and robustness tests for high-frequency data. In Section 4, we discuss and conclude the results and propose several directions for further research.

#### **2. Methods**

#### *2.1. Depth as One of Stock Market Liquidity Dimensions*

Generally speaking, stock market liquidity is not a one-dimensional variable. The literature concerning the dimensions of market liquidity has continued to grow since Kyle [44] first distinguished between three dimensions: depth, tightness, and resiliency. Depth can be defined as the ability to buy or sell a certain amount of an asset without influence on the quoted price. In other words, the depth of market captures the relation between order flow and price changes. When demand (buy) and supply (sell) sides are quantitatively the same, the quoted price will not change (there is no impulse to price changes). The definition of tightness states that this is the ability to buy and to sell an asset at about the same price at the same time. One of definitions of market resiliency specifies that this is the ability to buy or to sell a certain amount of an asset with little influence on the quoted price. Theoretical and empirical findings of research on liquidity dimensions in several stock markets in the world are reported in [46–52].

It is pertinent to notice that the studies that explore depth, tightness, and resiliency as dimensions of stock market liquidity on the WSE are rather scarce. For instance, order imbalance as a measure of market depth is assessed in the papers [42,43,53]. Market tightness as the cost of turning around a position over a short period of time on the WSE is investigated in the works [42,43]. Moreover, two new methods for measurement of intraday stock market resiliency based on the Discrete Fourier Transform and Short-Time Fourier Transform approaches are introduced and utilized for high-frequency data from the WSE in the recent papers [54,55].

#### *2.2. Measuring Stock Market Depth*

Related literature proposes various proxies of stock market depth, and a comprehensive review of them is presented e.g., in [42]. In general, the measures of order imbalance are the most frequently used.

To introduce a new entropy-based method, firstly we propose a supporting modified version of the Order Ratio (OR) indicator as a refined proxy of market depth which accurately captures market order imbalance. It is defined by the following Equation (1):

$$OR = \frac{|\mathbb{C}TV\_b - \mathbb{C}TV\_s|}{\mathbb{C}TV\_b + \mathbb{C}TV\_s},\tag{1}$$

where *OR* ∈ [0, 1] and the sums *CTVb* ∑*m i*=1 *Vbuyi*, *CTVs* ∑*k j*=1 *Vsellj* denote the cumulated trading volume related to transactions classified as buyer- or seller-initiated trades, respectively. The modification lies in the denominator ∑*m*+*k n*=1 *Vn* = *CTVb* + *CTVs* which denotes the cumulated trading volume for all classified transactions within a particular period of time (in the frequently used version of the OR indicator, the denominator includes the cumulated trading volume for all transactions within an investigated period of time).

The OR indicator can be calculated within various time intervals, for example in 30-min, hourly or daily manner because the Formula (1) is the general one. The order ratio informs about imbalance in the market since it rises when the difference in the numerator rises, and therefore it measures illiquidity. High values of the order ratio indicate low market depth and low liquidity. Conversely, small values of this indicator denote high market depth and high liquidity. According to definition (1), the order ratio value is nonnegative and it is equal to zero when cumulated trading volumes related to transactions classified as buyer- or seller-initiated trades are equal within a particular time interval. The

order ratio value given by Equation (1) is not defined for the following two cases: (1) when all transactions within an analyzed time period are unclassified, and (2) an analyzed time period is a zero-volume period, which means the total lack of transactions. In such cases, the total trading volume in the denominator is equal to zero. The OR value is equal to one when all transactions within an analyzed time period are classified in the same manner (i.e., as only buyer- or only seller-initiated trades).

In the next step, the definitions of cumulated trading volumes related to transactions classified as buyer- or seller-initiated trades are used to define the probabilities and the entropy-based proxy of stock market depth. In light of the recently growing literature, entropy is a widely accepted measure of a generally understood diversity and disorder. In this context, an entropy-based indicator could represent the unevenness of buying and selling in trading decisions on a stock market [41]. Shannon [1] proves that quantities of the form *H* = −*K*· ∑*n i*=1 *pi*· log(*pi*), where *K* is a positive constant that amounts to a choice of a unit of measure, play a central role in information theory as measures of information, choice, and uncertainty. Exactly based on the definition of Shannon information entropy [1] (p. 394) we propose the following new Entropy-based Market Depth (EMD) indicator given by Equation (2):

$$EMD = \frac{-1}{\log(2)} \left( P\_{\text{buy}} \cdot \log \left( P\_{\text{buy}} \right) + P\_{\text{sell}} \cdot \log \left( P\_{\text{sell}} \right) \right), \tag{2}$$

where:

$$P\_{bny} = \frac{\mathbb{C}TV\_b}{\mathbb{C}TV\_b + \mathbb{C}TV\_s} \in [0, 1], \tag{3}$$

$$P\_{sell} = 1 - P\_{buy} = \frac{\mathcal{C}TV\_s}{\mathcal{C}TV\_b + \mathcal{C}TV\_s} \in [0, 1]. \tag{4}$$

According to the Shannon definition, the EMD indicator (2) measures the entropy in the case of two possibilities with probabilities defined by Equations (3) and (4). It is scaled to obtain the EMD values that belong to the [0; 1] interval (without the normalization, the maximal EMD value is equal to log(2) ≈ 0.301, and it is obvious based on the properties of the Shannon information entropy [1], p. 394). According to Equation (2), the EMD value is non-negative, and it is defined as equal to zero in the following two cases:

(1) If *CTVb* = 0 ⇔ *Pbuy* = 0 ⇔ *Psell* = 1 ⇔ log(*Psell*) = 0 ⇔ *EMD* = 0; (2) If *CTVs* = 0 ⇔ *Psell* = 0 ⇔ *Pbuy* = 1 ⇔ log- *Pbuy* = 0 ⇔ *EMD* = 0.

The EMD value given by Equation (2) is not defined for the following two cases: (1) when all transactions within an analyzed time period are unclassified, and (2) an analyzed time period is a zero-volume period, which means the total lack of transactions. In such cases, the total trading volume in the denominator in Equations (3) and (4) is equal to zero. Appendix A contains further justification for the EMD indicator in the context of the Shannon information entropy definition.

To calculate both the OR (1) and EMD (2) indicators using intraday data it is essential to recognize the side initiating a transaction. Although the WSE is a pure order-driven market with an electronic order book, information of the order book database is not publicly available. Thus, the side initiating a trade cannot be directly identified from a raw data set. Therefore, the Lee and Ready (LR) [43] algorithm inferring the initiator of a trade is used to distinguish between so-called buyer- and seller-initiated trades. Although several tradeside classification rules have been proposed in the literature, Olbry´s and Mursztyn [56] confirm that the LR algorithm performs better than other procedures on the Polish stock market. For details about the LR algorithm see Table A1, in Appendix B.

As the EMD is a new both market depth and market liquidity indicator which is indirectly connected (via the probabilities defined by Equations (3) and (4)) with the supporting modified version of the OR proxy, it would be useful and informative to compare the OR and EMD values. Table 1 presents simple illustrative examples of calculations of both indicators for four selected cases within the same time period. Example 1 shows that the

minimal OR value equal to zero is coupled with the maximal EMD value equal to one. In general, as the EMD values are decimal fractions that belong to the [0; 1] interval, the EMD values calculated for different equities can be easily compared to each other. Furthermore, Examples 2–3 illustrate that increasing values of the OR are coupled with decreasing values of the EMD indicator, and vice versa. Example 4 shows that the maximal OR value equal to one is coupled with the minimal EMD value equal to zero. It means that, on an intuitive base, the maximal value of trading imbalance indicates the lack of liquidity.

**Table 1.** Simple illustrative examples of the OR and EMD values for four selected cases and the same time period.

Figure 1 depicts the relationship between OR and EMD indicators. To sum up, the examples presented in Table 1 and Figure 1 show that low Order Ratio values are accompanied by high values of the Entropy-based Market Depth indicator. Otherwise, high ORs are accompanied by low values of the EMD indicator. This evidence is consistent with overall relations between these two depth estimates.

**Figure 1.** The relationship between the Entropy-based Market Depth (EMD) and Order Ratio (OR) indicators.

Table 2 briefly summarizes basic relationships between the indicators (1) and (2), market depth, market liquidity, and market entropy. As one can observe, the OR proxy is only a measure of depth and illiquidity, while the EMD can be treated as a measure of market depth, market liquidity and market entropy, which is the advantage of this new indicator.

**Table 2.** Overall relationships between two market depth indicators, market depth, market liquidity, and market entropy.

#### **3. Empirical Experiments for High-Frequency Intraday Data**

As empirical experiments on financial markets depend on data availability, this section is devoted to the comparative and comprehensive investigation of the OR and EMD indicators on the Polish stock market. It presents findings of several empirical experiments and statistical analyses for high-frequency data from the Warsaw Stock Exchange. The database is large. It contains 21,010,718 records in total (see Table 3). Therefore, all computations were performed using a customized program (language C++, system: Linux, processor 3.6 GHz, RAM 4 GB).

**Table 3.** The averaged daily values of the Order Ratio (OR) and Entropy-based Market Depth (EMD) indicators within the whole sample period and three sub–periods for the group of 20 WSE–listed companies.

**Table 3.** *Cont.*

Notes: The 20 WSE–listed companies are labeled by ticker symbols and reported in decreasing order of the market value (MV) at the end of 2016. WS—the whole sample period 2 January 2005–30 December 2016; S1–the pre-crisis sub-period 6 September 2005–31 May 2007; S2—the crisis sub-period on the WSE 1 June 2007–27 February 2009; S3—the post-crisis sub-period 2 March 2009–19 November 2010. Standard deviations are given in parentheses.

#### *3.1. Real-Data Description*

The sample contains high-frequency data for 20 WSE-listed companies with the largest market capitalization (MV) at the end of 2016. Tick-by-tick transaction data is not publicly available for the WSE. Thus, in this research transaction prices and volume records with a time stamp rounded to the nearest second, for each security over one unit of time are used. The data comes from the Bank for Environmental Protection (BOS) brokerage house (available at http://bossa.pl; accessed date 5 January 2017). All stocks included in the database have been incessantly listed on the WSE through the whole sample period. This study is the continuation and extension of the research on dimensions of market liquidity on the WSE presented in the papers [54,55], and therefore the database is the same.

The sample period ranges from 2 January 2005 to 30 December 2016 (3005 trading days). To verify the robustness of the empirical findings, the calculations are provided both for the whole sample and over three consecutive sub-samples of equal length (436 trading days) [54]:

The crisis sub-period on the WSE connected to the 2007–2009 Global Financial Crisis (GFC) period was formally defined based on the paper [57], in which the statistical method for the quantitative identification of market states is used.

#### *3.2. Estimation Results of the Order Ratio and Entropy-Based Market Depth*

This subsection includes brief information on the group of 20 WSE-traded companies that are analyzed in this research (Table 3). The companies are labeled by ticker symbols and presented in decreasing order of the market value (MV) at the end of 2016. Table 3 reports the numbers of records in the database for each stock and the averaged daily values of the OR and EMD indicators. Standard deviations are given in parentheses. The evidence is that for the most liquid equities with the largest numbers of records in the database (namely PKN, PKO, PEO, KGH, OPL) the averaged daily values of the OR and EMD indicators and standard deviations of these values are stable in time. The findings confirm high market depth and high liquidity of these stocks as the averaged EMD proxy is approximately equal to one and accompanied by very low standard deviations. What is important, the experimental results reported in Table 3 show that the precise ranges of OR [0.17; 0.68] and EMD [0.47; 0.98] are equally broad (0.51 for OR and 0.51 for EMD).

Table 4 reports Pearson correlation coefficients calculated for series of daily market depth estimators given by Equations (1) and (2), for each asset separately. This table presents the results for the whole sample (WS) and three sub-samples S1, S2, S3. All correlations are significantly negative and their absolute values are very high. This evidence confirms that the information content of both market depth proxies is the same, while the main advantage of the EMD indicator is that it measures liquidity (not illiquidity, like the OR estimate). This evidence is consistent with the relationship presented in Figure 1.

**Table 4.** Pearson correlation coefficients between daily market depth values calculated using the alternative indicators (1) and (2).

Notes: Notation as in Table 3.

#### *3.3. Robustness Tests of Entropy-Based Market Depth*

Various robustness analyses are standard procedures for testing stability of stock market characteristics, especially in the context of crises periods, e.g., [24,41,54,55]. The existing studies indicate that the empirical results could be diverse and economic interpretations are needed in such cases. The Entropy-based Market Depth (EMD) indicator (2) is proposed as a new estimator of a stock market depth and market liquidity. Therefore, the stability of estimation results by time periods could be assessed. To address this issue, the robustness tests over the whole sample period and three sub-periods are provided. The goal is to investigate whether the mean results of stock depth and liquidity approximated by EMD within the analyzed periods (reported in Table 3) significantly differ between each other. The following two-tailed hypothesis is tested:

$$\begin{aligned} H\_0: \mu\_1 &= \mu\_2 \\ H\_1: \mu\_1 &\neq \mu\_2 \end{aligned} \tag{5}$$

where *μ*1, *μ*2 are the expected values of depth for each equity within the compared periods, and the null hypothesis assumes that two expected values are equal.

To verify the hypotheses, the Z-statistic for independent large sample means is used:

$$Z = \frac{\overline{X\_1} - \overline{X\_2}}{\sqrt{\frac{s\_1^2}{n\_1} + \frac{s\_2^2}{n\_2}}},\tag{6}$$

where *x*1, *x*2 are sample means, *s*2 1,*s*2 2 are sample variances, and *n*1, *n*2 denote a sample size, respectively. The numbers *n*1, *n*2 of trading days for each stock within each period are reported in Table A2, Appendix C. The average daily values of the EMD and standard deviations of these values are documented in Table 3. To address the multiple testing problem, the Bonferroni correction is used, and therefore the significance level is equal to *α* = 0.0025. The critical value of Z-statistic (6) at 0,25% significance level is equal to 3.03 for each test (we thank an anonymous referee for this suggestion).

Six pairs of periods are investigated, i.e., WS/S1, WS/S2, WS/S3, S2/S1, S2/S3, and S1/S3. Summarized findings for the whole group of companies are presented in Table 5 and they require some comments and economic interpretations. The hypothesis *H*0 indicates that the average EMD values are stable in time within compared periods. One can observe that for the companies PKN, OPL, ZWC, CAR, STP there are no reason to reject *H*0 for all six cases, for the KGH—for five cases, and for KTY—for four cases. However, for the remaining equities the results are more diverse. After deep investigation of the obtained results we can assert that there are three main reasons of this phenomenon.

**Table 5.** Summarized results of the significance test for the difference between two means of daily Entropy-based Market Depth (EMD) values for the group of 20 WSE–listed equities.

Notes: Notation as in Table 3. The critical value of Z-statistic at 0.25% significance level is equal to 3.03 for each test.

Firstly, although Table 3 documents that for the most liquid equities the averaged daily values of the EMD indicator are high and approximately the same, the values of standard deviation and the significantly diverse number of trading days within the analyzed periods (reported in Table A2, Appendix C) leads to rejection of the null hypothesis (5) for some isolated cases (for instance, for PKO and PEO).

Moreover, the results depend on the pair of the sub-periods. It is important to remind that the pre-crisis (S1), crisis (S2), and post-crisis (S3) periods on the WSE are investigated, and the crisis sub-period on the WSE is connected to the 2007–2009 Global Financial Crisis (GFC). Therefore, the findings inform whether the mean results of market depth and liquidity during the GFC period on the WSE significantly differ compared to the other periods. One can observe that in the case of the pairs: S2/S1 (crisis/pre-crisis), and S2/S3 (crisis/post-crisis), the hypothesis *H*0 is outweighed by the hypothesis *H*1 in 9 out of 20 and 5 out of 20 cases, respectively. Moreover, for the pair WS/S2 (whole sample/crisis) the number of *H*1 is equal to 10. Therefore, we can conclude that the visible influence of the GFC on market depth and liquidity was present for the following equities, including five banks: BZW, ING, MBK, LPP, BHW, MIL, SNS, BDX, GTC, ORB, ECH. In general, market depth and liquidity significantly differed during the crisis sub-period on the WSE for several analyzed companies, but not for all of them. The EMD values for the most liquid companies were much more stable. This evidence is consistent with the studies that have utilized other liquidity proxies to assess stock market liquidity dimensions on the WSE during the GFC (e.g., [42,43]).

Furthermore, the whole sample period (WS) is long (12 years), and it includes the years of substantial changes in market liquidity. The WSE was a medium-size emerging

stock market during this period. Especially, the level of liquidity within the pre-crisis period (S1) was lower compared to other periods for several companies, e.g., ING, MBK, LPP, BDX, ECH (see Table 3), while the level of liquidity during the post-crisis period (S3) was higher for many stocks. As a consequence, the hypothesis *H*0 is outweighed by the hypothesis *H*1 in 11 out of 20 (for the pair WS/S1) and 13 out of 20 cases (for the pair S1/S3). The total number of *H*1 is equal to 57 out of 120. In conclusion, the results reported in Table 5 are not homogenous but they can be explained based on the WSE liquidity behavior within the whole sample period and remaining sub-periods.

#### *3.4. Intra-Day Seasonality in Entropy-Based Market Depth*

The aim of this subsection is to assess intra-day seasonality and recognize intra-day hourly patterns in the EMD indicator of market depth. According to the literature, there are some possible shapes of intra-day patterns in various stock market characteristics such as volumes, depths, spreads, returns, transaction costs, order flows, market resiliency, etc. (see e.g., [55,58–68] and the references therein). Goodhart and O'Hara [58] emphasize that a fundamental property of high-frequency data is that observations can occur at varying time intervals. Therefore, trades are not equally spaced over the day, which may result in intra-day 'seasonal' patterns in stock market activity. Empirical investigation and visualization of these patterns may be a useful tool for decision-making process and can help an investor to state how particular characteristics vary over a session. Some shapes of intra-day patterns in stock market are possible but it is not surprising that perfectly shaped visual patterns rarely appear. There are several attributes that help to differentiate the most important shapes such as: M-similar, U-similar, W-similar, inverted-U, J-similar, and inverted-J patterns [55].

To explore intra-day patterns in the EMD indicator, the average hourly values of this indicator are calculated for each equity within the whole sample period (WS) and three sub-periods (S1, S2, S3). The WSE is an order-driven market with an electronic order book. Therefore, liquidity is provided only by limit orders submitted by investors and there are no market makers who support liquidity. Table 6 presents short market trading schedule on the WSE and the notation concerning the trading hours (*H*1–*H*8).

**Table 6.** Market trading schedule on the WSE equities–continuous trading system.

ource: The WSE website (https://gpw.pl/session-details; accessed date 15 February 2021).

Figure 2 illustrates hourly patterns in the EMD values within the whole sample period. The EMD intra-day behavior during remaining periods is presented in Figures A2–A4, Appendix D. Table 7 reports summarized findings of hourly patterns in the EMD indicator for the whole group of 20 WSE–listed equities investigated in this research. The trading hours *H*1–*H*8 based on Table 6.

*Entropy* **2021**, *23*, 568

Notes: Notation as in Table 3. Based on Figures 2 and A2, Figures A3 and A4 (Appendix

It is important to notice that the results are homogenous. Except for isolated cases (e.g., LPP, ZWC), the M-similar and U-similar (with a decrease during the last hour H8) patterns dominate for the vast majority of stocks.

The M-shaped pattern depicts lower EMD values during the beginning and the ending of a session with the highest values slightly after the beginning and before the end. It is also marked by distinctively low value in the middle of a session.

The U-shaped pattern means that the value of the EMD decreases after the first hour. It then stays more or less constant, and increases during the last hour. In this context, the evidence concerning the U-similar pattern with a visible increase within the hour H7 and a pronounced decrease during the last hour H8 requires some explanations. It seems that this pattern is common for the most equities on the WSE. After deep investigation of the obtained empirical findings we can assert that the main reason of this phenomenon lies in the trade side classification results. Based on the Lee-Ready procedure presented in Appendix B (Table A1), two possible cases dominate within the last hour H8 on the WSE:

Based on the summarized findings presented in Table 7 one can observe that, in general, the M-similar pattern dominates within the sub-periods S1 (pre-crisis) and S2 (crisis), while the U-similar pattern appears for vast majority of equities during the whole sample period and the sub-period S3 (post-crisis). In our opinion, the main reason of this phenomenon can be a higher level of market liquidity on the WSE after the GFC period.

It is worthwhile to emphasize that our results concerning intra-day behavior of the EMD indictor as a measure of liquidity are consistent with the literature. For instance, Jain and Joh [60] study joint characteristics of hourly common stock trading volume and returns and they find the U-shaped pattern in volume over the trading day on the New York Stock Exchange (NYSE). They emphasize that average volume as a liquidity proxy reveals significant hour of the day effect. McInish and Wood [62] show that number of shares traded as a liquidity estimate has a U-shaped intra-day pattern for all stocks listed on the Toronto Stock Exchange. Vo [64] also assess the intra-day behavior of market activity on the Canadian stock exchange in Toronto. The results confirm that spread follows Ushaped pattern, while volume is low at the open, stable during the day, and increases at the close. Ahn and Cheung [67] investigate the Stock Exchange of Hong Kong which is a pure electronic order-driven market without market makers.

The authors find the U-shaped patterns in spread and trading volume. As for the Polish stock market, Olbry´s and Oleszczak [68] conduct empirical experiments for real-data from the WSE and they document that intra-day trading volume reveals U-similar or Msimilar hourly patterns in the case of all investigated equities and for all analyzed periods.

#### **4. Discussion and Conclusions**

Concept of market depth focuses on the volume which can be observed at the current price level [49]. From investors' and stock market analysts' point o view, market depth is crucial because it can be treated as quantity dimension of market liquidity [51]. Harris [69] points out that the topic concerning dimensions of liquidity is especially interesting for practitioners as they often think about liquidity quite intuitively. Thinking about liquidity, investors usually think about trading quickly, trading large size, or trading at low costs.

According to the literature related to the microstructure of markets, several proxies of market depth are proposed: (1) depth as a number of units offered at the ask price plus a number of units at the bid price (e.g., [46,51,52]), (2) dollar depth calculated in currency terms (e.g., [70]), (3) an average depth of the ask and the bid (e.g., [71]), (4) an average dollar depth measured in currency terms (e.g., [71]), (5) various versions of order ratio as a proxy of realized market depth (e.g., [43,49,51–53]). The vast majority of these depth proxies require information about ask and bid prices.

However, although the WSE is a pure order-driven market with an electronic order book, information about ask and bid prices is not publicly available. Therefore, the side initiating a transaction cannot be directly identified from a data set. This problem concerns many emerging markets in the world, and a procedure inferring the initiator of a trade is needed in such cases.

Taking the above into consideration, this research contributes to the existing literature regarding dimensions of market liquidity by introducing and utilizing a new methodology for estimation of market depth and liquidity with the EMD indicator based on the Shannon entropy and supported by an algorithm inferring the initiator of a trade. The advantage of the EMD is that it measures liquidity, and the min and max values are in accordance with an investor's intuition, i.e., EMD = 0 in the case of total illiquidity and EMD = 1 in the case of total liquidity. Hence, depth and liquidity calculated using the EMD for different stocks can be easily interpret and compared to each other. Moreover, the EMD can be treated as a measure of both market liquidity and market entropy. This is the advantage of this new indicator because higher values of entropy inform about higher market efficiency (in the sense of the EMH), and are coupled with higher values of stock liquidity.

Furthermore, intra-day behavior of the EMD indicator has been assessed and empirical findings concerning intra-day seasonal patterns in the EMD are homogenous and consistent with the existing studies on other liquidity proxies.

It is well documented in the literature that market depth varies with spread, volume, transactions, and volatility (see e.g., [49,51,70]). Therefore, one possible direction for future study could be an extensive econometric analysis of relationships between various stock market characteristics using the new EMD indicator as market depth proxy. Subject to data availability provision, the proposed entropy-based indictor could be utilized using highfrequency data from other stock markets in the world, and the results might be interesting for practitioners.

Another promising direction for further research might be to perform a theoretical analysis of the new entropy-based indictor from the perspective of the properties of extropy [72]. As the entropy and the extropy of a binary distribution are identical, the EMD indicator can be regarded also as an extropy measure (we would like to thank an anonymous referee for this valuable suggestion.).

**Author Contributions:** Conceptualization, J.O.; methodology, J.O.; software, K.O.; validation, J.O.; formal analysis, J.O. and K.O.; investigation, J.O. and K.O.; resources, J.O. and K.O.; data curation, J.O. and K.O.; writing—original draft preparation, J.O.; writing—review and editing, J.O.; visualization, K.O. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the grant WZ/WI/1/2019 from Bialystok University of Technology and founded by the Ministry of Education and Science.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available at http://bossa.pl since 4 January 2021.

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

#### **Appendix A**

Entropy is a measure that is used to summarize the information content of a probability distribution. Specifically, the Shannon information entropy quantifies the expected value of information contained in a discrete distribution [10]. The entropy in the case of two possibilities with probabilities *p* and 1 − *p* can be represented as a function of *p* [1] (p. 394). Given the probabilities defined by Equations (3) and (4), we can set *Pbuy* = *p*

and *Psell* = 1 − *p*, and then the EMD indicator (2) can be directly written as the function of probability *p* = *Pbuy*:

$$\begin{array}{l}EMD = \frac{-1}{\log(2)} \left( P\_{hyy} \cdot \log \left( P\_{hyy} \right) + P\_{selll} \cdot \log \left( P\_{selll} \right) \right) \\ = \frac{-1}{\log(2)} \left( p \log(p) + (1-p) \log(1-p) \right) = f(p) \end{array} \tag{A1}$$

By analogy with the Shannon entropy, the *f*(*p*) function (A1) has several important properties which substantiate it as a reasonable measure of choice or information, and all of them are documented in [1]. In this paper, we focus on some basic properties, especially in the context of a binary distribution, and most of them are analyzed in Section 2.2. However, it is crucial to add that the *f*(*p*) function (A1) is non-negative, continuous and differentiable at each point in its domain. For instance, these properties allow us to assess the sensitivity of the EMD to changes in probability *p* as the argument of function *f*(*p*). The results could be interesting for practitioners as, from an investor's point of view, it is important to know how do changes in probability *p* = *Pbuy* (connected with cumulated trading volume) affect the EMD value (it could be a possible direction for further investigation).

Figure A1 illustrates the plot of the EMD as the function of probability *p* = *Pbuy*. It is important to notice that the EMD plot is identical with the plot of entropy presented in the Shannon's seminal paper [1] (p. 394), and it confirms that the EMD measures both market liquidity and market entropy.

**Figure A1.** The Entropy-based Market Depth (EMD) as the function of probability *p* = *Pbuy*.

#### **Appendix B**

Table A1 presents the Lee and Ready [45] algorithm inferring the initiator of a trade. The midpoint price *Pmid t* at time t is calculated as the arithmetic mean of the low price *PL t* and the high price *PH t* at time t, i.e., *Pmid t* = *PL t* +*PH t* 2 . The transaction price *Pt* at time t is approximated by the closing price. The opening trade is treated as being unclassified according to the LR procedure.

**Table A1.** The Lee-Ready algorithm inferring the initiator of a trade.

Source: [56] (p. 6).

#### **Appendix C**

Table A2 reports the number of trading days for each company and investigated period excluding the days when all of the transactions within a day are unclassified based on the Lee and Ready [45] algorithm inferring the initiator of a trade. These numbers are necessary to test the hypothesis (5) as the OR and EMD indicators are not defined when: (1) all transactions within an analyzed time period are unclassified, and (2) an analyzed time period is a zero-volume period, which means the total lack of transactions. Additionally, one can observe that for the most liquid companies (namely PKN, PKO, PEO, ING, KGH, MBK, BHW, OPL, MIL, SNS, GTC) the numbers of days reported in Table A2 are equal (or almost equal) to the particular sample size, respectively.

**Table A2.** The number of trading days excluding the days when: (1) all of the transactions within a day are unclassified, and (2) total daily trading volume is equal to zero.

Notes: Notation as in Table 3. The sample size: WS (3005 trading days); S1, S2, S3 (436 trading days).

#### **Appendix D**

Figures A2–A4 illustrate intra-day seasonality results within three sub-periods S1, S2, S3 for the whole group of 20 WSE–listed companies investigated in this study. Notation as in Table 3. Information about trading hours *H*1–*H*8 based on Table 6.

**Figure A2.** Intra-day hourly patterns of the EMD indicator within the pre-crisis period (S1) for the whole group of 20 WSE–listed stocks. Notation as in Tables 3 and 6.

**Figure A3.** Intra-day hourly patterns of the EMD indicator within the crisis period (S2) for the whole group of 20 WSE–listed stocks. Notation as in Tables 3 and 6.

**Figure A4.** Intra-day hourly patterns of the EMD indicator within the post-crisis period (S3) for the whole group of 20 WSE–listed stocks. Notation as in Tables 3 and 6.

#### **References**


**OXIDATIVE STRESS – ENVIRONMENTAL INDUCTION AND DIETARY ANTIOXIDANTS**

Edited by **Volodymyr I. Lushchak**

http://dx.doi.org/10.5772/2536 Edited by Volodymyr I. Lushchak

#### **Contributors**

Vladimir Jakovljevic, Dejan Cubrilo, Dusica Djordjevic, Vladimir Zivkovic, Dragan Djuric, Fahmy Gad Elsaid, Baitullah Alipoor, Aziz Homayouni Rad, Elnaz Vaghef Mehrabany, Humberto Antonio Lopez-Delgado, Martha Elena Mora-Herrera, Ernestina Valadez-Moctezuma, Ian M Scoot, Tayeb Wafa, Katrin Engelmann, Robert Ebel, Tiiu Kullisaar, Epp Songisepp, Mihkel Zilmer, Hiroshi Sugiya, Ken Okabayashi, Takanori Narita, Yu Takahashi, Rajagopalan Vijayaraghavan, Anshoo Gautam, Pınar Tatlı Seven, Seval Yılmaz, İsmail Seven, Guluzar Tuna Kelestemur, Hitomi Ohta, Kenji Akita, Tsunetaka Ohta, Warin Sangkitikomol, Jean-Max Rouanet, Sylvie Gaillet, Dominique Lacan, Maria Angelova, Nedelina Kostadinova, Ekaterina Krumova, Tsvetanka Stefanova, Vladislava Dishlijska, Volodymyr I Lushchak, Oksana Stoliar

#### **© The Editor(s) and the Author(s) 2012**

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#### **Notice**

Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book.

First published in Croatia, 2012 by INTECH d.o.o. eBook (PDF) Published by IN TECH d.o.o. Place and year of publication of eBook (PDF): Rijeka, 2019. IntechOpen is the global imprint of IN TECH d.o.o. Printed in Croatia

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Tectonics and Seismicity

**3**

**Chapter 1**

**Abstract**

Tentative Intracontinental Seismic

Overwhelming majority of minor, strong and major earthquakes in south Siberia and Russian Far East coincide with relatively narrow intracontinental zones on the boundaries of blocks and lithosphere plates. The geodynamic activity of these zones connects, besides the plate interaction, with deep lithosphere structure and anomalies of the different geophysical fields as well as with blocks' kinematics. Authors' located areas of the seismic centers origin and the possible manifestations of the high seismicity based on the distribution of the maximal volumes of releasing seismic energy. We established these areas, with certain care, in the northeast Altai and adjacent part of the west Sayany, in the west of the east Sayany, around the Baikal Lake and in northwest Transbaikalia, in the east of Transbaikalia between the Vitim River and upper stream of the Aldan River, and in the north of the Sakhalin Island. The majority of minor and strong, rarely major, earthquakes took place in these areas. Deep and near surface structural peculiarities influence on these areas' geodynamics and allow establishing possible levels of seismic energy releasing. We draw areas of intensive seismic energy releasing with its calculating for each from investigated regions. They gravitate towards interblock zones, which separate crust blocks and the North Eurasian Lithosphere Plate. The fulfilled investigation allows establishing specific areas of the increased seismicity in south Siberia, Russian Far East and adjacent territories.

**Keywords:** seismic active zone, strong and major earthquakes, seismic energy, area of origin of seismic centers, active fault, block, interblock zone, lithosphere plate,

In 2013–2018, authors analyzed at the relatively small scale the structure and seismicity of intracontinental interblock zones within the Asiatic part of Russia and adjacent countries together with calculation of the releasing seismic energy and construction of their dissipation graphs as well as the deep seismic sections [1, 2]. The results of this analyzing allowed selecting the most active seismic zones, including overwhelming majority of minor and strong earthquakes' epicenters, and examined in detail the lithosphere deep structure under them and not far of them with establishing the possible connection of these zones with the geodynamic activity and anomalies of different geophysical fields. With special attention, we considered kinematics of blocks and main lithosphere plates as well as the connection with them active processes in interblock zones. All blocks considered in our paper are delineated by active

Activity in South Siberia and

Russian Far East

deep structure, geophysical field

**1. Introduction**

*Yuriy Gatinsky and Tatiana Prokhorova*


*Article* **Chitosan-Based Green Pea (***Pisum sativum* **L.) Pod Extract Gel Film: Characterization and Application in Food Packaging**

**Essam Mohamed Elsebaie 1,\*, Mona Metwally Mousa 2 , Samah Amin Abulmeaty 2 , Heba Ali Yousef Shaat 2 , Soher Abd-Elfttah Elmeslamy 2 , Galila Ali Asker 2 , Asmaa Antar Faramawy 3 , Hala Ali Yousef Shaat 2 , Wesam Mohammed Abd Elrahman 3 , Hanan Salah Eldeen Eldamaty 3 , Amira Lotfy Abd Allah 3 and Mohamed Reda Badr 4**

**Abstract:** This work focuses on studying the preparation, characterization (physical, mechanical, optical, and morphological properties as well as antioxidant and antimicrobial activities) and packaging application of chitosan (CH)-based gel films containing varying empty green pea pod extract (EPPE) concentrations (0, 1, 3, and 5% *w*/*w*). The experiments revealed that adding EPPE to CH increased the thickness (from 0.132 ± 0.08 to 0.216 ± 0.08 mm), density (from 1.13 ± 0.02 to 1.94 ± 0.02 g/cm3 ), and opacity (from 0.71 ± 0.02 to 1.23 ± 0.04), while decreasing the water vapour permeability, water solubility, oil absorption ratio, and whiteness index from 2.34 to 1.08 × 10−10 g −1 s −1 pa−1 , from 29.40 ± 1.23 to 18.75 ± 1.94%, from 0.31 ± 0.006 to 0.08 ± 0.001%, and from 88.10 ± 0.43 to 77.53 ± 0.48, respectively. The EPPE films had better tensile strength (maximum of 26.87 ± 1.38 MPa), elongation percentage (maximum of 58.64 ± 3.00%), biodegradability (maximum of 48.61% after 3 weeks), and migration percentages than the pure CH-gel film. With the addition of EPPE, the antioxidant and antibacterial activity of the film improved. SEM revealed that as EPPE concentration increased, agglomerates formed within the films. Moreover, compared to control samples, packing corn oil in CH-based EPPE gel films slowed the rise of thiobarbituric acid and peroxide values. As an industrial application, CH-based EPPE films have the potential to be beneficial in food packaging.

**Keywords:** green pea pods; corn oil; chitosan; films; gel


*Article* **Environmental Assessment of Latent Heat Thermal Energy Storage Technology System with Phase Change Material for Domestic Heating Applications**

**Daniel Chocontá Bernal 1, Edmundo Muñoz 2, Giovanni Manente 3, Adriano Sciacovelli 3, Hossein Ameli 4 and Alejandro Gallego-Schmid 5,\***

**Abstract:** The emissions generated by the space and water heating of UK homes need to be reduced to meet the goal of becoming carbon neutral by 2050. The combination of solar (S) collectors with latent heat thermal energy storage (LHTES) technologies with phase change materials (PCM) can potentially help to achieve this goal. However, there is limited understanding of the environmental sustainability of LHTES technologies from a full life cycle perspective. This study assesses for the first time 18 environmental impacts of a full S-LHTES-PCM system from a cradle to grave perspective and compares the results with the most common sources of heat in UK homes. The results show that the system's main environmental hotspots are the solar collector, the PCM, the PCM tank, and the heat exchanger. The main cause of most of the impacts is the extensive consumption of electricity and heat during the production of raw materials for these components. The comparison with other sources of household heat (biomass, heat pump, and natural gas) indicates that the S-LHTES-PCM system generates the highest environmental impact in 11 of 18 categories. However, a sensitivity analysis based on the lifetime of the S-LHTES-PCM systems shows that, when the lifetime increases to 40 years, almost all the impacts are significantly reduced. In fact, a 40-year S-LHTES-PCM system has a lower global warming potential than natural gas.

**Keywords:** thermal energy storage (TES); latent heat thermal energy storage (LHTES); circular economy; environmental sustainability; life cycle assessment (LCA); climate change


**Abstract**

Mychorrizae are indigenous soil fungi that are found associated symbiotically with plant root system. They promote growth of the root system by protecting the plant from pathogen attack, acting directly or indirectly as biocontrol agents and offering plant resistance. These group of rhizosphere fungi also benefit from various biosynthetic substances produced by the root of the plant (root exudates). In this chapter, attempt is being made to present a balanced account of the various roles these fungi play in plant protection. This will give our cherish readers the opportunity to appreciate the mycorrhizal fungi as potential biocontrol agents or bioprotectants of soilborne plant pathogens.

**Keywords:** mycorrhizae, mycorrhizal fungi, bioprotectant, biocontrol agents, rhizosphere fungi


**Abstract**

Thyroid cancer incidence has rapidly increased in high-income countries for the past 30 years. The increase in thyroid cancer cases may be due to improved diagnostic methods or exposure to unknown risk factors. Even though new thyroid cancer cases have increased, the mortality rate is relatively stable. Most thyroid cancer is differentiated thyroid cancer (DTC). Conventional management of DTC consists of near-total thyroidectomy followed by ablation therapy with radioiodine-131 (RAI). RAI was first used nearly 80 years ago to treat thyroid cancer and still plays a pivotal role in managing DTC. There are three RAI therapy options: remnant ablation, adjuvant therapy, and known disease treatments. After thyroid resection, radioactive Iodine-131 (RAI) is recommended for patients with intermediate to high risk of recurrent disease or distant metastases. Long-term follow-up is needed to detect a persistence or recurrence of the disease after initial RAI administration. RAI effectively improves treatment efficiency and reduces the risk of cancer recurrence and metastasis post-thyroid resection. Clinical outcome prediction is ultimately defined by appropriate management. This article will review some factors to consider when planning RAI therapy for DTC and subsequent surveillance after the therapy.

**Keywords:** adjuvant therapy, remnant ablation, refractory thyroid, risk- stratification, serum thyroglobulin, whole body scan


**2.2 Water permeability and juice recovery (%)**

Before each MF process, the membrane water permeability was measured at transmembrane pressures of 0.5, 1.0 and 2.0 Bar, respectively, to verify its recovery, according to the following formula:

Organic Acid Lime (*Citrus Latifolia* Tanaka) Clarified by Microfiltration 305

299

percentage of peels in the BLJ samples. However, a yield of 47% was previously reported by Pedrão et al. (1999) for conventional lime juice, cv. *Tahiti*. Other factors may affect juice yield such as crops with high concentrations of nitrogen and potassium, leading to increased peel thickness, as well as relative humidity, and ambient temperature (Chitarra et al., 1990). The maturity stage of the fruit also influences the yields of acid lime juice that have been

Mean water permeability flux was 1,241.95 L.m2.h (± 0.48) in the three processes using the

In order to determine the best operating transmembrane pressure for all MF processes, 8.0 L of CLJ were initially used in the feed, resulting in 6.0 L (75%) of clarified juice. The mean fluxes obtained at transmembrane pressures of 0.5, 1.0 and 2.0 bar were 49; 47 and 35 L.m2.h, respectively (Fig.2). A slight difference was observed between the fluxes at the applied transmembrane pressures during the first twenty minutes of the process, but after this time there was a significant flux decline for processes operated at 1.0 and 2.0 Bar, demonstrating that concentration polarization was the result of polarization on the membrane surface and/or fouling, providing a decrease in the clarified juice flux over time (60 minutes) in all cases, which was more pronounced at 2.0 Bar. For both UF and MF processes, flux decline is high even when the water permeability of the membrane is completely recovered by

observed, ranging from 55.60% in green fruit and 59.40% in ripe fruit (Ziena, 2000).

Fig. 2. Effect of process mechanism on the permeate flux at 0.5, 1.0 and 2.0 Bar

declined gradually declined until the end of the process, probably due to fouling.

Thus a 0.5 Bar transmembrane pressure for 60 minutes was adopted to process BLJ by MF, resulting in a mean volume of 6.0 L of clarified juice from a 8.15 L feed and yields of 73, 76 and 54% of clarified juice in the first, second and third processes, respectively (Fig. 3). In the first and third process, after the first 20 minutes there was a decrease in the flux that

transmembrane pressures with conventional lime juice.

**3.2 Water permeability and permeate fluxes**

0.3 μm membrane.

washing (Oliveira et al., 2006).

$$\text{Flux} \left( \text{L.m}^2 \,\text{.h} \right) = \frac{\left( \text{L} \,\text{/h} \right) \times \text{P} \left( \text{Bar} \right)}{0.05 \,\text{m}^2}$$

Where: 0.05 m2 = total membrane area; P = applied transmembrane pressure

The water permeability (L.m2.h) was measured with a chronometer, at 10 minutes intervals. Cleanup procedures (alkaline and chlorine-alkaline) were performed before and after each process, aiming to recover water permeability of the membrane.

Membrane alkaline cleaning was performed by adding 80 mL of a NaOH solution (Tedia, Rio de Janeiro, Brazil) (1N/pH 11) to 10 L of distilled water at 40 ºC, and re-circulating the solution in the system for 30 minutes. The solution was then discarded, using 80 L of distilled water. Chlorine-alkaline-cleaning was performed by using 40 mL of NaOH (1N/pH 11) and 130 mL of NaClO (Tedia, Rio de Janeiro, Brazil) (6% sodium hypochloride) diluted in 10 L of distilled water at 40 ºC, with recirculation in the system for 30 minutes, followed by washing with 80 L distilled water. After each cleanup, pH was checked.


**3.1. Adsorbent developments**

Intensifying the heat transfer of an adsorbent depends mainly on increasing its thermal conductivity where the conduction is the major way to transfer the heat through the adsorbent. Consolidating the adsorbent or using additives with good thermal conductivity into the adsorbent are the common approaches used to enhance the heat transfer in the adsorbent [50, 51]. However, such approaches always decrease the permeability of the adsorbent leading to a decrease in inter-particle mass transfer. The overall performance of the bed will be affected by this contradiction between *heat transfer* and *mass transfer* in the adsorbent. Thus, it should be considered that the increase in thermal conductivity 20-fold, for example, does not mean a similar great enhancement in the overall performance due to the reduction in mass transfer. On microscopic level, the distribution of micro layers inside the samples of an adsorbent affects both the thermal conductivity and permeability, and then investigation can be applied for enhancing both of them as made in Ref. [52]. Therefore, sample preparation and filling techniques can be optimized to enhance both heat and mass transfer. Testing adsorbents in various forms and sizes is also an effective way to investigate the best HMT performance of the adsorber. Developments of the composite adsorbents are another active area used to enhance refrigerant uptake of the pure adsorbents and their stability. More recently, there are two trends: coating the adsorbent over the heat transfer metal surfaces of adsorbers, aiming at the elimination both of thermal contact resistances and large inter-particle voids, or using the new metal-organic frameworks (MOFs) materials which provide attractive adsorption characteristics compared to common adsorbents.

#### *3.1.1. Adsorbent coatings*

From the standpoint that loose grains and consolidated adsorbent beds have poor heat transfer and mass transfer properties, respectively, the concept of coated adsorber has been developed to introduce adsorbers with efficient heat and mass transfer. Applying direct synthesis, or using a binder for deposition a layer of adsorbent over walls of the metal heat exchangers are two common technologies of adsorbent coatings. Different approaches have been reported and discussed in Ref.s [53, 54] as for illustrated in **Figure 8** [55].

### **3.2. Optimization of the adsorber design and cycle modes**

not sufficiently hydrophilic materials like HKUST-1 or MIL-101(Cr), respectively, or for low

kinetics and that heat and mass transfer could be optimized by various shaping procedures.

Enhancing the heat and mass transfer (HMT) of the adsorber is the most crucial part in developing ARSs. For a given cooling capacity, higher specific cooling capacity (SCC) means smaller amount of adsorbent to be used, and that can be a direct result of improving the heat and mass transfer performance of the adsorber. Besides, a lighter weight and smaller volume are existed in such case. As the adsorption system consumes less heat during regeneration modes, the COP is increased. Two methods are commonly used to increase the HMT: one is the development of adsorbents and the second is the optimization of the adsorber designs

Intensifying the heat transfer of an adsorbent depends mainly on increasing its thermal conductivity where the conduction is the major way to transfer the heat through the adsorbent. Consolidating the adsorbent or using additives with good thermal conductivity into the adsorbent are the common approaches used to enhance the heat transfer in the adsorbent [50, 51]. However, such approaches always decrease the permeability of the adsorbent leading to a decrease in inter-particle mass transfer. The overall performance of the bed will be affected by this contradiction between *heat transfer* and *mass transfer* in the adsorbent. Thus, it should be considered that the increase in thermal conductivity 20-fold, for example, does not mean a similar great enhancement in the overall performance due to the reduction in mass transfer. On microscopic level, the distribution of micro layers inside the samples of an adsorbent affects both the thermal conductivity and permeability, and then investigation can be applied for enhancing both of them as made in Ref. [52]. Therefore, sample preparation and filling techniques can be optimized to enhance both heat and mass transfer. Testing adsorbents in various forms and sizes is also an effective way to investigate the best HMT performance of the adsorber. Developments of the composite adsorbents are another active area used to enhance refrigerant uptake of the pure adsorbents and their stability. More recently, there are two trends: coating the adsorbent over the heat transfer metal surfaces of adsorbers, aiming at the elimination both of thermal contact resistances and large inter-particle voids, or using the new metal-organic frameworks (MOFs) materials which provide attractive adsorption

From the standpoint that loose grains and consolidated adsorbent beds have poor heat transfer and mass transfer properties, respectively, the concept of coated adsorber has been developed

O is not sufficient for acceptable

temperature applications, where the vapor pressure of H2

**3. Heat and mass transfer enhancements**

characteristics compared to common adsorbents.

*3.1.1. Adsorbent coatings*

and cycle modes.

**3.1. Adsorbent developments**

84 Sustainable Air Conditioning Systems

Optimized parameters and sophisticated designs of adsorber configurations can help in enhancing the inter-particle mass transfer in the adsorbent domain, along with facilitating the heat transfer between the adsorbent and heat transfer fluid HTF. Extended metal surfaces 'fins' are commonly used to intensify the heat transfer and overcome the low thermal conductivity of the adsorbent materials. However, the COP of an adsorption system is strongly affected by the metal-adsorbent mass ratio [56]. Therefore, the net effects of the fins parameters such as fin spacing, height and thickness should be investigated carefully to optimize the overall system performance [57–60].

In the same context, operational control parameters, such as adsorber modes' durations and fluid flow rates, influence considerably the ARSs' performance and need to be also optimized. Basically, in view of the fact that the diffusion of mass within the adsorbent particles is better with higher temperatures, therefore, the desorption process is carried out faster than the adsorption process. That explains why the differences between equilibrium and instantaneous amount of adsorbate (Weq–*w*) in desorption and adsorption modes are not identical during the cyclic steady state. A larger difference is required during an adsorption mode to adsorb the same total amount desorbed during a desorption mode for making cyclic steady state. Increasing the cooling water velocity and/or adsorption duration over heating water velocity and/or desorption mode are the common ways to reach steady state cycle. And that increases need to be optimized for maximizing the adsorption system performance, as by adsorption/ desorption times reallocation, [61]. Operating under low pressures is another challenge as in the case of water and methanol as refrigerants. In this case, the poor mass transfer in adsorbers can lessen greatly the difference in the refrigerant uptakes during the cycle. That requires more developed designs for such adsorbers to improve their performances. It is important to mention that studying the net effect of any operating parameter on the adsorption kinetic during only one mode (adsorption or desorption) based on given initial conditions may lead to inaccurate predictions for the overall performance.


**Author details**

J. Kenny Acuña Villavicencio\* and Georgina Vázquez Moreno Autonomous University of Guerrero, Mexico

\*Address all correspondence to<EMAIL_ADDRESS>
© 2023 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.

*Perspective Chapter: Internal Forced Displacement and Accumulation by Dispossession in Sierra... DOI: http://dx.doi.org/10.5772/intechopen.110263*


**Author details**

*New Innovations in Engineering Education and Naval Engineering*

Low involvement of issues in

and physical science phenomena

Element to assembly design approach (down-up)

Content MED as extension of Engineering Science

Humanities

Modelling Simplified mathematical models

Learning Study of independent machine elements

Emphasis Engineering and scientific novelty

**Traditional Proposed**

Outputs Engineering drawings Working models and/or prototypes

*Summary of differences between the current and proposed MED teaching approaches.*

MED as new body of knowledge, using GEPs\*

Mathematical and non-math models to deal with science and non-science constraints in design

Less time on independent elements, but more on

Assembly to element design approach (top-down)

Problem solution as simply, safely and economically

their interdependence in an assembly

Design codes, catalogues, standards, etc. Elements from Humanities primarily drive most of

MED and even, regulate it

optimization

as possible

,

The work in case No. 1 was funded by Cape Peninsula University of Technology

The author's interest in this, and other related work, is driven by an insatiable desire to make students realise that by their last year of undergraduate study, they can already have an inner ability to start contributing to make their societies live

The author thanks his student, Riel Haupt, for his drive and courage even after the almost fatal accident. Special thanks go to Riel's parents for supporting him.

**Acknowledgements**

*Good engineering practice principles*

Design process

*\**

**Table 4.**

**Conflict of interest**

**Thanks**

Research Fund, through research account RK23.

better now, and not wait for tomorrow.

**84**

Kant Kanyarusoke Cape Peninsula University of Technology, Cape Town, South Africa

\*Address all correspondence to<EMAIL_ADDRESS>
© 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, provided the original work is properly cited.