**3. Proteomic and peptidomic analysis: A new approach to study venoms**

Proteins are very large molecules formed by amino acids chains linked together as a poly‐ mer. Although biological systems uses only 20 amino acids to build their proteins, the differ‐ ent possible combinations among them is virtually infinite, resulting in tens of thousands different proteins, each one with a unique sequence, genetically defined, which determines its specific form and biological function. Furthermore, each protein may undergo a variety of post-translational modifications, which diversifies even more its form and function. Pro‐ teins are the main constituents of protoplasm of all cells. As the major components of cells metabolic pathways, proteins have vital functions in organism, such as: catalyze biochemical reactions (eg. enzymes), transmit messages (eg. neurotransmitters), regulate cellular repro‐ duction, influence growth and development of various tissues (eg. trophic factors), carry oxygen in the blood (eg. hemoglobin), defend the body against diseases (eg. antibodies), among countless other achievements. There is no metabolic reaction in which the participa‐ tion of at least one protein is dispensable.

The term "proteome" is derived from the junction of the word "PROTEin" with the word "genOME" and refers to the set of proteins expressed starting from a genome, i.e., all the proteins produced by an organism. Indeed, the word proteome is often be more related to the set of proteins expressed in a specific organ, or biological fluid, or cell, in a given state (eg. diseased cell). The proteome is therefore the complete complement of a genome, in‐ cluding the "makeup" that proteins receives after being synthesized, i.e., the post-transla‐ tional modifications, all of them absolutely relevant for that proteins perform their biological function. The proteome of a cell or fluid varies with time and conditions under which the organism is subjected. The human body, for example, can contain more than 2 million different proteins, each one exerting a distinct role. Unlike the genome, which is relatively static, the proteome is constantly changing in response to tens of thousands of intra and extracellular environmental signals. The proteome varies with the nature of each tissue or organ, the cell development stage, the stress conditions to which the organism is subjected, the organism health state, the effects of drug treatment, etc. As such, the pro‐ teome is often defined as the proteins present in a sample (tissue, organism, cell culture, biological fluid, etc.) at a given point in time.

However, this treatment can be effectively used only a limited number of times for a partic‐ ular person, since that person will develop antibodies to neutralize the exogenous animal's antibodies used to produce the antiserum (antibodies antiantibodies). Even if that person does not suffer a severe allergic reaction to the antiserum, his own immune system can de‐ stroy the antiserum even before the antiserum destroys the venom toxins. Most people will never need an antiserum treatment throughout their lives. However, others, who work or live in risk areas habited by snakes or other venomous animals, such as agricultural areas

An Integrated View of the Molecular Recognition and Toxinology - From Analytical Procedures to Biomedical

Some treatments are done not with antiserum, but herbal. *Aristolochia rugosa* and *Aristolochia trilobata*, or angelic, are medicinal plants used in Western India and in Central and South America against snake and scorpion bites [41]. Aristolochic acid, produced by those plants, inhibits inflammation induced by immune complexes and non-immunological agents (carra‐ geenan or croton oil). It also inhibits the activity of phospholipases present in snake venoms (PLA2], forming a 1:1 complex with the enzyme. Phospholipases play an important role in the reactions cascade that lead to inflammatory response and pain. Therefore, its inhibition

**3. Proteomic and peptidomic analysis: A new approach to study venoms**

Proteins are very large molecules formed by amino acids chains linked together as a poly‐ mer. Although biological systems uses only 20 amino acids to build their proteins, the differ‐ ent possible combinations among them is virtually infinite, resulting in tens of thousands different proteins, each one with a unique sequence, genetically defined, which determines its specific form and biological function. Furthermore, each protein may undergo a variety of post-translational modifications, which diversifies even more its form and function. Pro‐ teins are the main constituents of protoplasm of all cells. As the major components of cells metabolic pathways, proteins have vital functions in organism, such as: catalyze biochemical reactions (eg. enzymes), transmit messages (eg. neurotransmitters), regulate cellular repro‐ duction, influence growth and development of various tissues (eg. trophic factors), carry oxygen in the blood (eg. hemoglobin), defend the body against diseases (eg. antibodies), among countless other achievements. There is no metabolic reaction in which the participa‐

The term "proteome" is derived from the junction of the word "PROTEin" with the word "genOME" and refers to the set of proteins expressed starting from a genome, i.e., all the proteins produced by an organism. Indeed, the word proteome is often be more related to the set of proteins expressed in a specific organ, or biological fluid, or cell, in a given state (eg. diseased cell). The proteome is therefore the complete complement of a genome, in‐ cluding the "makeup" that proteins receives after being synthesized, i.e., the post-transla‐ tional modifications, all of them absolutely relevant for that proteins perform their biological function. The proteome of a cell or fluid varies with time and conditions under which the organism is subjected. The human body, for example, can contain more than 2

for example, need that this treatment is available in public health network.

may reduce problems of scorpionism, snakebite and loxoscelism.

tion of at least one protein is dispensable.

Applications

8

The term proteomics consists of comprehensive and systematic study of all proteins present in a given cell state, which was made possible by the huge development of mass spectrome‐ try techniques over the past two decades. Proteomics and genomics run parallel and are in‐ terdependent. Genomics without proteomics is only an "alphabet soup", because it can only make inferences about their products (proteins). Moreover, proteomics requires genomics to identify the proteins expressed in a particular cell state. Briefly, genomics provides a static information of the various ways in which a cell may use its proteins, while proteomics gives a dynamic panorama of molecular diversity, showing not only which proteins are more or less expressed (or is not even expressed), but also how these proteins were modified and how these modifications affect its role in the cell theater.

Proteomic technologies can play an important role in new drugs discovery, new diagnos‐ tics and molecular medicine, because it is the connection between genes, proteins and dis‐ eases. For example, the discovery of defective proteins that cause specific diseases can help develop new drugs that either alter the shape of a defective protein or mimic its ac‐ tion. Most of the most popular drugs today either have proteinaceous nature or have a protein target. Through proteomics, one can create "custom" drugs, i.e., drugs specially designed for specific individuals. Such drugs are supposed to be more effective and cause fewer side effects. Another field to which proteomic studies can contribute is the biomark‐ ers discovery for specific diseases, whose overexpression (or depletion) would indicate, quite early, the disease development. For example, serum levels of prostate specific anti‐ gen (PSA) is commonly used in the diagnosis of prostate cancer in men, which makes PSA a biomarker for cancer. Unfortunately, however, the diagnosis based on a single pro‐ tein biomarker is not very reliable. Proteomics may help scientists to develop diagnostic tests that simultaneously analyze the expression of multiple proteins in order to improve the specificity and sensitivity of these tests.

Over time, new study areas with the suffix "omics" have emerged, such as metabolomics, lipidomics, carbohydratomics, degradomics etc. The term venomics did not slow to appear, and today it is defined as the study of all components (protean or not protean) of a venom. The word peptidomics has also been proposed to set the study of the peptides (instead of proteins) of a cell type or a biological fluid, such as venom. According to Ivanov and Yatskin [42]: "structure and biologic function of the entire multitude of peptides circulating in living organisms, their organs, tissues, cells and fluids comprises the scope of peptidomics". For these authors, "these two multitudes of polypeptides (proteins and peptides) play a domi‐ nant role in the functioning of any cellular system, tissue or organ. They are intimately con‐

nected with each other and exist in equilibrium as an essential part of homeostasis (i.e., the normal state of any living organism and the basis of life itself)".

quence, the highly combinatorial nature of venom components and their underlying pharmacologic complexity have been progressively revealed by mass spectrometry. Cur‐ rently, major challenges remain on samples complexity, lack of biological material and data‐

Peptidomic Analysis of Animal Venoms http://dx.doi.org/10.5772/53773 11

Peptidomic analysis of a sample will consist of essentially four steps: (I) peptides extraction from the sample; (II) separation of these peptides — including their prior separation from other polypetidic components of the sample, i.e., proteins, defined as the protean compo‐ nents with molecular weight above 10 kDa —; (III) peptides detection — which is commonly performed by mass spectrometry —, (IV) and finally identification of the peptides — which usually involves fragmentation of those peptides in a tandem mass spectrometer (MS/MS). With respect to peptide sequencing for identification purposes, the technique traditionally used is Edman degradation-based sequencing [66, 67]. But nowadays this kind of sequenc‐ ing is increasingly being replaced by sequencing techniques based on mass spectrometry [68, 69]. This is due to the fact that mass spectrometry is much more rapid and sensitive than Edman sequencing and prenscinde of prior separation of the peptides, which means that peptides can be sucessfully analyzed and sequenced by mass spectrometry from a complex peptide matrix, which is impossible by Edman sequencing. This is only possible because the peptide of interest is selected (i.e., separated from others) in the first mass spectrometer. Then, this parent ion is fragmented in a collision chamber and the daughter ions are ana‐ lyzed in a second mass spectrometer (MS/MS). Figure 3 gives an example of peptide *de novo* sequencing by tandem mass spectrometry. For more details about this kind of polypeptide

In proteomics, the most widely used technique to separate protean components of a sample is the two-dimensional polyacrylamide gel electrophoresis (2D-PAGE). In peptidomics, however, techniques based on liquid chromatography coupled to mass spectrometry (LC-MS) appear to be more popular, since peptides are not well resolved by electrophoresis [70]. Despite this, capillary electrophoresis has also been used successfully in peptidomic analy‐ sis, mainly to analyze biological fluids for clinical applications, such as disease diagnosis

As an example, Valente and co-workers [71] ran a two-dimensional gel from the venom of *Bothrops insularis*, an endemic snake specie in Queimada Grande Island, Brazil. The result is shown in Figure 1. This is an example of venomics, i.e., the study of all protean components of a venom. Using the proteomic approach, the authors detected 494 spots in the gel using an image analysis software, from which 69 proteins were identified by current identification techniques, using mass spectrometry and heavy bioinformatics to interpret the mass spectra and also to make a comparative search of protein sequences deposited in databases. The identified proteins include metalloproteinases, serine proteinases, phospholipases A2, lec‐ tins, growth factors, L-amino acid oxidases, the developmental protein G10, a disintegrin, a nuclear protein of the BUD31 family, and putative novel bradykinin-potentiating peptides. In the same study, the authors also performed a peptidomic analysis of the venom, by direct analysis of the crude venom by MALDI-TOF-TOF and LC-ESI-Q-TOF. Many new peptides were partially or completely sequenced by both MALDI-MS/MS and LC-ESI-MS/MS. Using

bases absence to peptide and protein identification based on sequence information.

sequencing, see reference [69].

and response to therapy [46].

Peptidomic analysis has been proposed by several authors [43-55] as a way to access infor‐ mation relevant to clinical diagnosis and/or to monitor the patient biochemical profile dur‐ ing the therapy. The growing interest in peptidomic analysis led some scientists to develop new analytical technologies to improve peptidomic analysis, such as: use of capillary elec‐ trophoresis to separate the peptides [46]; use of size exclusion chromatography as a pre-frac‐ tionation step [53, 56]; new technologies and methods for sample pretreatment [57], such as methods for isolation rare amino acid-containing peptides, terminal peptides, PTM peptides and endogenous peptides, automated sample pretreatment technologies (automated sample injection and on-line digestion) [58]; development of a new target plate for MALDI-MS for one step electric transfer of analytes from a 1-dimensional electrophoresis gel directly to the target plate [59, 60]; etc. In recent years, in the face of the remarkable development on nano‐ technology, many researchers have produced different kind of nanoparticles, such as meso‐ porous silica nanoparticles [50, 51, 61, 62] and carbon nanotubes [52, 63], for selective peptide extraction (and, hence, its enrichment) from biological fluids for therapeutic purpos‐ es (clinical diagnosis and/or novel biomarker discovery).

In the case of animal venoms, however, peptidomics is a highly interesting area for differ‐ ent reasons, since most of the biologically active components of pharmacological interest are of peptidic nature [64]. For example, Biass and co-workers [12] studied the venom peptidomic profile of the cone snail-hunting fish, *Conus consors*, through approaches in‐ volving different sample preparation protocols and analysis by mass spectrometry. The cone snail was quoted in the television series *Animal Planet: The Most Extreme*, because it can quickly shoot a harpoon filled with deadly toxins. The conidia (Conidae) constitute a family of several shells divided into subfamilies. It is estimated that this genus produce more than 70,000 different pharmacologically active components, most of peptidic nature, whereas interspecies variations. It is a rich library of neuropharmacology and combinato‐ rial chemistry. Precisely for this reason, the 6th Framework Programme of the European Union funded with € 10.7 million the international project CONCO involving 20 partners and 13 countries [65], whose objective is to explore new molecules therapeutically rele‐ vant produced by venomous marine cone snails.


2.5.1. DNA Isolation

The isolation of genomic DNA was performed using the Genomic Mini AX Bacteria Spin kit (A&A Biotechnology, Gda ´nsk, Poland). All isolation steps were conducted according to the protocol provided by the manufacturer. The samples were taken after 168 h of the biodegradation process. The isolation efficiency was controlled by the fluorimetric method on the Qbit 3.0 device, using the Qubit™ dsDNA HS Assay Kit (ThermoFisher Scientific, Waltham, MA, USA). For each sample, three DNA extractions were carried out. Lastly, samples were mixed together, after a positive quantification.

## 2.5.2. NGS Sequencing

For microbial population taxonomy analysis, the V4 region of the 16SrRNA was amplified, based on the 515F-806R primers designed by Caporaso et al. (2012) [28]. The PCR details were optimized, and described in a previous publication [8].

Sequencing of the obtained amplicons was performed on the MiSeq platform (Illumina, CA, USA). The construction of amplicons and libraries normalization protocol is described in a previous work [26].

#### 2.5.3. Bioinformatic Analysis

The output sequencing data were analyzed using the CLC Genomics Workbench 8.5, with the CLC Microbial Genomics Module 1.2 software (Qiagen, Hilden, Germany). Readings were trimmed, demultiplexed, and paired ends were joined. Then, the chimeric readings were identified and removed. The data were clustered independently against two reference databases at 97% similarity of operational taxonomic units (OTU). The SILVA v119 database [29] was used for taxonomy annotation and biodiversity analysis, and the Green-Genes 13.5 database [30] was used for PICRUSt analysis. Selected biodiversity indices were determined: OTU number, Simpson's index, and phylogenetic diversity. Raw sequence data were deposited in the Sequence Read Archive (SRA) as project no. PRJNA831882.

In order to better characterize the analyzed microbiome, a linear discriminant analysis (LDA) effect size (LEfSe) [31] was performed. It allowed for the identification and selection of the most differentially abundant taxa. The microbial biomarkers that best describe the differences between the groups differing in the level of supplementation with nitrogen compounds were assessed. The following groups were determined: deficiency of nitrogen compounds: variants NP0 and NP1; and no deficiency (sufficient level: variants NP2 and NP3). LDA was coupled with effect size measurements: a non-parametric Kruskal–Wallis rank-sum test (*p* < 0.05), and the Wilcoxon rank-sum test (*p* < 0.05). A threshold of 3.5 for the logarithmic LDA score for discriminative attributes was established as the cut-off value.

#### 2.5.4. PICRUSt Analysis

In order to evaluate the bacterial functional composition in the analyzed samples, the bioinformatic tool PICRUSt v. 1.1.1 was used. This algorithm is widely used in environmental studies to analyze functional assessment of bacteria communities in different environments (soil, sediments, wastewater etc.) [32–38]. The predictions of functional composition of metagenomes were performed on the basis of sequencing data clustered against GreenGenes 13.5, and reference bacterial genomes deposited in the IMG database. The detailed algorithm's mode of action is described in a publication of its authors [39]. Based on the analysis, data on the predicted prevalence of 6009 KEGG Orthology IDs (KO IDs) participating in the degradation of polycyclic, aromatic hydrocarbons were obtained. It was assessed which OTU contributed to particular functions. Quality control of the PICRUSt prediction was performed according to the algorithm authors advices. The genome coverage was calculated for all samples using a weighted-Nearest Sequenced Taxon Index (NSTI) score [39].


**1. Introduction**

Dendrite is an important component of solidification structure, whose morphological characteristics directly affect the performance of an alloy. Therefore, studying the growth of dendrite is helpful for researchers to optimize the process parameters and improve the performance of alloys. Experimental methods for obtaining the microstructure during solidification have been proposed, such as the electronic probe [1], synchrotron X-ray [2,3], etc. that have been developed, but cannot be applied to product at a large scale due to the expensive cost and harsh environment. Moreover, these methods are unable to show the dynamic evolution process of dendrite growth.

Over the past few decades, a considerable number of numerical models have grown up around the theme of simulating the evolution process of dendrite morphology during solidification, such as level set [4], monte carlo (MC) [5], cellular automata (CA) [6–8], phase field (PF) [9], etc. Among them, the phase field model (PF) and CA model are the most widely used. Due to complex physical equations and massive calculations, the PF model is only applied to small-scale simulations. Whereas the CA model can perform large-scale simulations and reveal the evolution of micro-mesoscopic dendrites, such as the transformation of columnar crystals into equiaxed crystals (CET) [10], the behavior of dendrite deflection in fluids [6–8], and the formation of silicon facet dendrite [11]. Influenced by grid layout and capture rules, the traditional CA model can only simulate dendrites that grow along the x axis or 45◦ with the x axis. However, during the actual solidification process of the alloy, dendrites grow with different preferred orientations, which is caused by the solute profile and can lead to macro-segregation in the cast product [12]. Therefore, it is very important for the model to be able to simulate the dendrite with different orientations. Researchers have proposed various methods to achieve multi-orient dendrite simulation, such

**Citation:** Wang, J.; Meng, H.; Yang, J.; Xie, Z. GPU-Based Cellular Automata Model for Multi-Orient Dendrite Growth and the Application on Binary Alloy. *Crystals* **2023**, *13*, 105. https://doi.org/10.3390/ cryst13010105

Academic Editor: Yuying Wu

Received: 27 November 2022 Revised: 25 December 2022 Accepted: 31 December 2022 Published: 6 January 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/).

as defining block cells [13], establishing random ZigZag neighbor cell capture rules [14], etc. These methods can only simulate a dendrite with the same orientation at the same time due to complex algorithms. Hence, Rappaz and Gandin developed the decentered square algorithm (DCSA) [15], which can simulate dendrites with different orientations simultaneously, and it has been widely used to simulate the growth of columnar and equiaxed dendrites [16–19]. However, these models suffered from velocity anisotropy, which means velocities along different orientations are asymmetrical and have multiple interfaces. Then, Luo et al. [20] modified the velocity of the interface cell through the local solute equilibrium and improved the phenomenon of multiple interfaces. Wang et al. [21]. determined the length of the square half diagonal by the preferred orientation to ensure sharpness of the interface and introduced GF to reduce velocity anisotropy.

However, the DCSA rule dynamically determines the capture position and condition by tracking the dendrite tip, which is very complex. Massive calculations of the CA model incorporating the DCSA rule make large-scale simulations very time-consuming. It is, therefore, necessary to speed up the calculation. Some methods have attempted to improve calculation efficiency, such as adaptive meshes [22,23], parallelizing the computer program using MPI technology [24], and parallel computing technology based on serial arithmetic [25]. These accelerators are CPU-based, so the speedup is not good enough for the number of cores, being limited by the hardware architecture. Unlike the CPU, GPU is characterized by integrating thousands of computer cores inside, which makes it the most effective way to achieve acceleration. With the development of GPU in general purpose computing, it has been used in various fields [26,27]. Over the past two decades, the GPUbased acceleration method has become a hotspot in computational and material science [28–30] and has made great progress in dendrite growth simulation [31–34]. However, most of these contributions focused on the PF model, which is still unable to simulate dendrite growth at large scale, even when accelerated by using GPU.

This paper proposes a high-performance CA model incorporating the DCSA capture rule to simulate dendrite growth with different orientations more efficiently. To make full use of the hardware resources and improve the calculation efficiency, parallel algorithms and a task scheduling scheme using multi-stream are proposed. Compared to the traditional CPU-CA model, this model can achieve great acceleration with a speedup of 158×. In addition, the steady-state tip velocity predicted by this work shows great agreement with the analytical value of the LGK model. The simulation results of the binary alloy by this model not only show dendrites with different orientations, but also agree well with the experimental result in situ. This model will be a promising tool for studying the dendrite growth during the large-scale solidification.

The following chapters will cover the establishment, solution, and verification of the model in detail.

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

*2.1. Description of Numerical Model*

#### 2.1.1. Heat Transfer Model

Equation (1) is used to describe heat transfer during alloy solidification.

$$p c\_p \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} \left( \lambda \frac{\partial T}{\partial x} \right) + \frac{\partial}{\partial y} \left( \lambda \frac{\partial T}{\partial y} \right) \tag{1}$$

where *T* is the temperature, *fs* is the solid fraction, *ρ* is the density, *cp* is the equivalent specific heat, and *L* is the latent heat.

#### 2.1.2. Solute Distribution Model

The solute distribution model consists of solute redistribution at the interface and solute diffusion across the entire domain. For one thing, the solute redistribution is determined by Equations (2) and (3) according to local equilibrium.

$$\mathbb{C}\_s = k \mathbb{C}\_l \tag{2}$$

$$d\mathbb{C} = \mathbb{C}\_l (1 - k)\Delta f\_s \tag{3}$$

where *dC* is the residual solute expelled by the interface cell, and *k* is the coefficient of equilibrium solute partition (*k* < 1 in the present work).

First, the expelled solute will be discharged into the remaining liquid of the current cell. Then, the current *Cl* will be compared to the equilibrium solute concentration *Cl* ∗; the part beyond *Cl* ∗ will be discharged to adjacent liquid cells. *Cl* ∗ is calculated by Equation (4).

$$\mathbb{C}\_{l}^{\*} = \mathbb{C}\_{0} + \frac{T - T\_{0}}{m\_{l}} + \frac{\Gamma Ka(\hbar)}{m\_{l}} \tag{4}$$

where *T* is the actual temperature, *T*0 is the initial temperature, *C*0 is the initial solute concentration, *ml* is the liquidus slope, and *a*(*n*ˆ) is the function of interface anisotropy.

If the current cell is completely solidified, then all the excluded solute will be discharged to the adjacent liquid cells. How much solute will be discharged into an adjacent liquid cell is designed by weight, as shown in Equation (5).

$$w\_i = \frac{\mathbf{C}\_i^0 - \mathbf{C}\_I}{\sum\_{j=0}^N (\mathbf{C}\_j^0 - \mathbf{C}\_I)} \tag{5}$$

where *Ci* 0 − *Cl* is the solute difference between the interface cell and the adjacent liquid cell *i*, *N* is the number of liquid neighbours.

For another, the solute diffusion coefficient in liquid is three to four orders of magnitude larger than that in solid, so diffusion in solid phase is neglected in this paper. Equation (6) shows the diffusion of a solute in liquid and interface.

$$\frac{\partial \mathbf{C}\_{l}}{\partial t} = \frac{\partial}{\partial \mathbf{x}} \left( D\_{i} \frac{\partial \mathbf{C}\_{l}}{\partial \mathbf{x}} \right) + \frac{\partial}{\partial y} \left( D\_{i} \frac{\partial \mathbf{C}\_{l}}{\partial y} \right) \tag{6}$$

where *Di* is the solute diffusion coefficient, which is governed by Equation (7).

$$D\_l = f\_5 D\_s + (1 - f\_5) D\_l \tag{7}$$

where *Dl* and *Ds* are the diffusion coefficient in liquid and solid, respectively.

#### 2.1.3. CA Model

In the traditional CA model, only fully solidified cells (*fs* = 1) can capture their liquid neighbors. This capture rule is severely affected by the grid layout, so it can only simulate dendrites growing along the x axis and 45◦ with the x axis. However, the growth orientation of dendrite is chaotic in the actual solidification process of the alloy. In order to simulate dendrite growth closer to reality, the decentered square rule for capturing has been adopted by the present CA model. As shown in Figure 1, the key to the improved algorithms is dynamically calculating the nucleation position and nucleation conditions, according to the position where the interface cell (parent cell) reaches the liquid cell. All cells in the entire computing domain are initialized to liquid (*fs* = 0). As the temperature decreases, the one who receives the nucleation conditions will receive the chance to nucleate. The nucleation probability is calculated by Equation (8) combined with random probability.

$$\frac{dn}{d\Delta T} = \frac{n\_{\text{max}}}{\sqrt{2}\exp\left[-\frac{1}{2}\left(\frac{\Delta T - \Delta T\_N}{\Delta T\_V}\right)\right]}\tag{8}$$

where Δ*T* is the undercooling, *nmax* is the maximum density of nuclei given by the integral of undercooling (from 0 to Δ*T*) of Equation (8), Δ*TN* is the average nucleation undercooling, and Δ*Tσ* is the standard deviation. Once a cell is nucleated, its solid fraction will be changed from 0 to 1, and a decentered square with an angle *θ* between diagonal and x axis will be located at its center. Additionally, four corners of this square penetrate the nearest liquid neighbors, capturing them in the corners and changing them into interface cells. Captured cells will inherit the growth properties of the parent cell and grow along the diagonal to capture its liquid neighbors until it is completely solidified.

**Figure 1.** The diagram of the decentered algorithm (*θ* is the angle between diagonal and x axis).

In order to simulate the dendrite morphology in detail, the local level rule method is used to calculate the increment of the solid fraction [35], wherein Δ*fs* of each time step is determined by Equation (9). The length of the primary arm of the dendrite is updated by Equation (10).

$$
\Delta f\_s = \frac{\left(\mathbf{C}\_l^\* - \mathbf{C}\_l\right)}{\left(\mathbf{C}\_l^\*(1-k)\right)} GF \tag{9}
$$

$$l(t + \Delta t) = l(t) + \Delta f\_s l\_{\max} \tag{10}$$

*lmax* is the maximum half-diagonal length determined by Equation (11).

$$l\_{\max} = l \left(\frac{\Delta x}{\max(\sin \theta, \cos \theta)}\right) \tag{11}$$

Δ*x* is the size of the cell, and *GF* [36] is the geometry factor related to the state of neighbors, which is introduced to avoid multiple interfaces and is limited to no more than 1.

$$GF = \min\left\{1, G\left(\sum\_{m=1}^{4} S\_m^\mathrm{I} + \sqrt{2}\sum\_{m=1}^{4} S\_m^\mathrm{II}\right)\right\} \tag{12}$$

where *G* is an adjustable factor, *sm*I and *sm*II are the state of the nearest neighbor and the second nearest neighbor, respectively, and both of them have two values, as shown in Equation (13).

$$\mathbf{S}\_{m'}^{\mathrm{I}} \mathbf{S}\_{m}^{\mathrm{II}} = \begin{cases} \mathbf{0}, \, f\_{\mathrm{s}} < 1 \\ \mathbf{1}, \, f\_{\mathrm{s}} = 1 \end{cases} \tag{13}$$

#### *2.2. Parallel Solver Based on GPUq*

To simulate the morphology of dendrite with clequeqear secondary arms, the cell size is generally divided into 1~2 μm. There will be huge calculations when conducting large-scale simulations, which is time-consuming using CPU. In addition, the purpose of the simulation is to optimize the process parameters by performing many groups of experiments. Therefore, it is necessary to accelerate the calculation. This paper designs a GPU-based parallel solver for acceleration.


**3. Concept**

This section of the chapter represents the results of the ROs for the TBP. First, the overall system architecture will be represented. Afterward, the concept for the CQPs and the adaptive playout will be described. Finally, in the last subsection, the concept for the usage of DSTs will be described in more detail. Except for subsection 3.2, which is placed in Moodle, all other components described in the other subsections are within the KM-EP.


*3.1. In-Situ Records*

The long term monthly precipitation data that were collected from 20 meteorological stations over the Punjab region were acquired from Pakistan Meteorological Department (PMD) (Figure 1). The in-situ records were investigated during the study periods from 1979 to 2017 and from 2003 to 2017 as reference data for the assessment of GB and SB precipitation products, respectively. The selection of the gauges depends on their maximum availability and completeness of data series. The GPPs were evaluated against the in-situ records on an annual, winter, and summer monsoon season. The winter and summer monsoon seasons are the primary drivers of the annual hydrological cycle with major influence of Asian monsoon (summer monsoon season) over the study region [28]. The GB and SB GPPs were developed while using quality-controlled procedures and algorithms. However, the stations data are generally considered as standard measurements for the evaluation of GPPs [37,38]. Moreover, the standard quality-controlled procedures were adopted for the better accuracy assessment of GB and SB GPPs. For quality assurance, station data series were thoroughly checked and outliers were fixed with neighboring gauge records [39]. Gaps were filled using a time-based interpolation approach [40]. Several post-processing techniques have been developed to identify the consistency and homogeneity's in the station records [41]. The double-mass curve was applied to observe the inhomogeneity in the station records [42]. The curve of all the stations showed a straight line with no evident break points, which confirms a temporal consistency and uniformity in the time series records.

After quality control process in the reference data series, the thin-plate splines (TPS) interpolation method was introduced to convert the station data into products relative spatial grid sizes for the assessment of GB and SB GPPs on spatial scale. The original TPS method is defined by [43], whereas [44] provides a detailed description of its application for different climate indicators. The TPS scheme is applicable and robust in regions where stations density is low and prior estimation of the spatial auto-covariance is not required [44]. The time series autocorrelation method was applied prior to estimate the trend significance, magnitude, and abrupt turning point to ensure the occurrence of significant autocorrelation in the reference data series [1]. The presence of significant autocorrelation in the reference data series could influence the outcome of Mann–Kendall (MK), Sen's Slope (SS), and Mann–Kendall abrupt change analysis [45]. Therefore, the significance of autocorrelation should be checked before applying the trend tests [46]. The analysis revealed no significant autocorrelation in the reference data series of annual, winter, and summer monsoon seasons. Therefore, the in-situ records are completely independent, and the MK test is applicable to the original gauge records. The detailed description for autocorrelation method is reported by [47].


3.4.4. Analysis on the Adjustment of Efficiency Input in Western China

In Table 3, the production efficiency of greenhouse tomatoes in Inner Mongolia, Shaanxi, Gansu and Qinghai is not effective in western China. The adjustment range is shown in Figure 5b. The adjustment ranges of six input factors of greenhouse tomatoes in Inner Mongolia are 65.11%, 65.11%, 36.47%, 65.11%, 48.38%, and 60.68%, respectively, including material and service cost, number of working days, seed cost, fertilizer cost, farmyard manure cost, and pesticide cost. The adjustment ranges of six input factors of greenhouse tomatoes in Shaanxi Province are 84.85%, 84.85%, 43.66%, 84.85%, 61.10%, and 58.36%, respectively. The adjustment ranges of six input factors of greenhouse tomatoes in Gansu Province are 69.24%, 70.53%, 77.70%, 78.09%, 78.09%, and 78.09%, respectively. The adjustment ranges of six input factors of greenhouse tomatoes in Qinghai Province are 62.05%, 72.32%, 88.69%, 87.12%, 28.83%, and 95.84%, respectively.

In general, there exist some problems of excessive investment in Inner Mongolia, Shaanxi, Qinghai, and Gansu, resulting in waste of energy and environmental pollution. In the western region, the excessive input of pesticides in Shaanxi Province is 41.64%. The excessive input of fertilizers in Inner Mongolia is 39.32%, while the excessive input of pesticides is 34.89%.

#### **4. Conclusions and Policy Implication**

This paper uses a DEA model to analyze the overall technical efficiency (OTE), pure technical efficiency (PTE), and scale efficiency (SE) of greenhouse tomatoes, greenhouse cucumbers, greenhouse eggplants, and greenhouse peppers from the perspective of greenhouse vegetable production efficiency. According to different efficiency values of greenhouse vegetables, we put forward some suggestions to adjust the different production efficiency. The main conclusions are as follows:

• In the production of greenhouse tomatoes and cucumbers in China, the loss of PTE may lead to inefficiency in most provinces. For greenhouse tomatoes, among the 17 inefficient provinces, the PTE of 11 provinces is lower than the SE. For greenhouse cucumbers, among the 14 inefficient provinces, the PTE of 9 provinces is lower than the SE. The results show that the government should pay more attention to the improvement of the PTE of greenhouse tomatoes and cucumbers.

Based on the above analysis, we put forward some suggestions for the different characteristics of the efficiency of greenhouse vegetables in different provinces. The suggestions are as follows:

In the next study, we plan to study the change of greenhouse vegetable production efficiency from the perspective of time series and space in China. It is planned to use the DEA model and Tobit model to explore the influencing factors of greenhouse vegetable production efficiency, in order to make a contribution to the development of green and sustainable agriculture.

**Author Contributions:** All authors contributed to this study. J.R. and Y.L. formulated the study design. J.R., Y.S., Y.L., and Y.W. conceived and designed the research methodology. X.J., J.R., and Y.L. collected and analyzed the data. J.R. and Y.L. finalized the paper.

**Funding:** This work was supported in part by the National Natural Science Foundation of China under Grants 71703122, 71973106, and 71531002, the China Ministry of Education Social Sciences and Humanities Research Youth Fund Project under Grant 16YJC630102, the Science and Technology Plan Projects of Yangling Demonstration Zone under Grant 2016RKX-04, the Fundamental Research Funds for the Central Universities under Grant 2018RWSK02, the Key Research and Development Program of Shaanxi under Grant 2019ZDLNY07-02-01, and the National College Students' Innovation and Entrepreneurship Training Program under Grant<PHONE_NUMBER>75.

**Acknowledgments:** We thank the National Nature Science Foundation of China, China Ministry of Education Social Sciences and Humanities Research Youth Fund Project, Natural Science Basic Research Project in Shaanxi Province, Science and Technology Plan Projects of Yangling Demonstration Zone, Fundamental Research Funds for the Central Universities, Key Research and Development Program of Shaanxi and National College Students' Innovation and Entrepreneurship Training Program for funding the research.

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