**2. Background**

In 1990, the American Association of Medical Colleges (AAMC) initiated Project 3000 by 2000 which involved launching a national campaign to increase the annual matriculation number of underrepresented minority medical students from 1,485 to 3,000 by the year 2000. The goal of this project was to increase diversity

in healthcare in the US and create a culturally competent healthcare workforce that reflects the country's diverse population [3]. The AAMC also proposed a list of core competencies for students prior to entering medical school. This competency framework was intended to inform the medical school admissions processes and to deemphasize the importance of cognitive measures during admissions [4]. Similarly in 2009, the UK Government appointed a task force called the Panel on Fair Access to the Professions. The panel found that the individuals from non-privileged backgrounds had reduced access to various professions including healthcare [5]. This led to a program called Widening Access (WA). Similar to AAMC project, WA also encouraged increasing the fairness of the admissions process and providing more opportunities to students from lower socio-economic backgrounds entering medical school [6]. As a result of these projects, medical schools have witnessed a shift from knowledge-based admissions to holistic review of student applicants. Institutions have changed their admission policies to provide equal emphasis on skills and lived experiences. Measures such as situational judgment tests, multiple mini-interviews, and psychometric tests have been introduced to the admissions process to assess said competencies [7, 8].

These measures have widened the applicant pool which would otherwise have been limited due to grade-based admissions process. This resulted in a slight increase in students from underrepresented minority groups (URM) [9]. This has also opened up more opportunities for students who are non-science majors, have a lapse in education since graduation, or are of a higher age [10]. As more institutions embrace this movement towards widening access, predictably the medical student cohort will no longer be homogenous but would rather be comprise of unique individuals with diverse knowledge, skills, and abilities. As a result, institutions will have to make concerted efforts to support the appropriate progression of their students throughout the continuum of their medical education.

## **3. Supporting transition of matriculating medical students**

While great strides have been made to widen access, attrition of URM and their underrepresentation in medical workforce continues to be a challenge [11]. For example, in the UK, ethnic minority medical students as a group on average were found to perform worse when compared to their white colleagues during medical school and training [12]. Similarly, URM students were more likely than non-URM students to experience graduation delays and failure [13]. In addition to the stress associated with adjusting to the rigor of medical school, URM students were more likely to view themselves as "fraud" and doubt their abilities to succeed [14]. This phenomenon has found to be secondary to systemic problems associated with factors such as low socio-economic status or quality of undergraduate studies etc. [15].

Institutions have strived to address these challenges and support meaningful transitions of their medical students. There has been an rise in innovative pipeline programs to increase the academic preparedness of URM students [16]. Academic enrichment programs on science and pre-med courses, and academic support programs have also been introduced to meet the diverse needs of matriculating students and support their transition into medical school [17]. Mentoring programs have been established to provide social support vital to professional identity formation of URM students [18, 19]. Several institutions have introduced pre-matriculation courses to increase student awareness on academic preparedness for medical school. These programs supported student transition by introducing knowledge and skills required for medical school, integrating students into the learning environment and/or helping them immerse into the community [17]. Some institutions

#### *How to Support Student Academic Success DOI: http://dx.doi.org/10.5772/intechopen.100061*

have used these courses to proactively identify students who could potentially be at risk of academic difficulties during medical school [20]. Some have been designed to introduce the students to the rigors of the medical school curriculum. The goal of these programs were to "normalize the playing field" for students with diverse levels of pre-med knowledge and skills [21].

There were also several post matriculation remediation programs that were introduced to identify and support struggling medical students. These programs provided academic and emotional support, the outcomes of which were predominantly context dependent [22]. Due to the varying levels of success of these proactive and reactive approaches to supporting student success, institutions have grappled with the challenging question – how to support student academic success?

According to self-determination theory, student engagement in their own academic success is closely related to three basic psychological needs – autonomy, competence, and relatedness. Students who feel autonomous, competent and have a sense of belonging are typically more intrinsically motivated to maximize their potential [23]. The three psychological needs can be hindered by external pressures such as exceptionally challenging learning tasks, negative and disparaging feedback, judgments, threats, and punishments [24]. A learning environment that fails to address the three basic psychological needs of students could impact students' internal motivation and engagement in lifelong learning.

Therefore, the learning environment that is inherent to the traditional curriculum and its ability to support the progression of diverse group of students has come under scrutiny.


*5.1. Foraminifera Shell Weights Are Tracers of Past Oceanic Circulation*

The sieved-based weight analysis of *G. bulloides* shells from the South Atlantic core GeoB 1710-3 during the last 200 kyr was combined with two additional eastern Atlantic shell weight records and revealed reorganizations in the meridional circulation of the Atlantic Ocean. The measured foraminifera shell masses were converted to seawater density values using a lineal relationship that was calibrated for the Atlantic Ocean using geochemical data [17]. The mass-based reconstructed seawater densities from the three different eastern Atlantic localities describe their hydrography and unveil two occasions, SMCE I and SMCE II, when the seawater densities between these regions appear similar (Figure 3). Interhemispheric convergence of surface Atlantic densities denotes the absence of seawater density gradients across the basins and thus momentary cessation of the Atlantic Meridional Overturning Circulation (AMOC), which implies an increase in surface ocean stratification [49] and abrupt, large changes in climate [50].

The basin-scale reconstructions of seawater densities using planktonic foraminifera shell mass measurements have enabled the consideration of several aspects of the Atlantic hydrography. Figure 3 showed that planktonic foraminifera can alter their shell mass considerably and verifies that the degree of this alteration in time is a function of latitude [51] with no overall response to atmospheric *p*CO2. The water from the S. Atlantic site is generally found to be denser than the other two eastern areas. This illustrates the northward water movement towards less dense regions, which is known to feed the northern Atlantic latitudes with southern-sourced waters [52]. The high S. Atlantic densities of enhanced variability may be the result of the site's location offshore the Kalahari Desert, which as a hyper-arid area would favor the development of high salinity in the sea water, while pulses of leaking warmer and thus lighter Agulhas waters may contribute to abrupt density variabilities (see Section 5.2). Seawater densities at the tropical Atlantic site GeoB 8502-2 are stable throughout the studied interval and *G. bulloides* specimens were the lightest between records. As discussed in Zarkogiannis*,* et al. [40], this is a tropical region of insolation and climatic stability, under the influence of the ITCZ, which is a zone of enhanced precipitation and of low-density surface waters [53].

Planktonic foraminifera shell weights start recording the glacial/interglacial cyclicity signal at mid-latitudes or at latitudes that are more sensitive to insolation changes. That seawater densities are here reconstructed higher for the site at 23◦ S (GeoB 1710-3) than that of 57◦ N (ODP 982A) might imply that the overturning circulation and oceanic density gradients may not respond directly to the amount of summer insolation falling across northern high-latitude regions. They are possibly dictated by moisture fluxes from Hadley cells, driven by the Earth's latitudinal insolation gradient (LIG) [54] and the latitudinal temperature gradient (LTG) that it creates, which drives the poleward energy flux via the atmospheric and ocean circulation [55]. Site GeoB 1710-3, where the highest shell weights were recorded, is located directly at the descending limb of the Hadley cell. Furthermore, since the LGM is an arid period [56,57] and may have been more arid that the penultimate glacial maximum [58], the highest-density waters (of increased salinity and decreased

temperature) were to be expected in the Atlantic basins of the mid-latitudes (Figure 5a). The response of planktonic calcification to high-density waters is notably manifested in Figure 4i,j.

Furthermore, Figure 3 suggests that the Atlantic Ocean was slightly lighter during MIS 6 than the subsequent glaciation as it can been seen in all three records. The penultimate glacial, MIS 6, appears to have been approximately as extreme as the last ice age in terms of global ice volume and sea level [59,60]. Yet, unlike the last glacial interval, no major ice-rafted debris (IRD) deposits, known as Heinrich events [61,62] that suggest increased iceberg formation, were recorded prior to the penultimate deglaciation in the Atlantic [63,64], while on the Iberian margin, MIS 6 has been described as a warmer glacial interval compared with the last ice age [63,65]. Thus, for occupying the same volume at higher temperatures, its density should have been reduced. Except for this glacial interval, which raises arguments that the interocean salt leakage is not as straightforward as previously suggested [66], the South Atlantic has most of the time been the densest of the three basins as it is today [67]. Furthermore, its record appears to be "nervous" with increased variability.

The most important outcome of Figure 3 in terms of abrupt Atlantic hydroclimate changes may however be the identification of intervals of surface seawater density convergence. Independent indications of a collapse of the Atlantic meridional circulation during SMCE I and SMCE II are provided by geochemical evidence of 231Pa/230Th records from N. Atlantic cores. 231Pa/230Th is a kinematic proxy for the meridional overturning circulation. For a given scavenging rate, lower rates of AMOC in the past would result in comparatively less 231Pa export from the Atlantic and in higher sedimentary 231Pa/230Th, reaching a maximum of 0.093 for a total cessation [68]. In the present study, the first instance of surface ocean density gradient attenuation is recorded at ~122.4 ka (SMCE II), shortly after the peak in the last interglacial (MIS 5.5) within a cold climatic phase [69,70]. During the same interval, the sedimentary record of core MD95-2037 from the north central Atlantic shows increased 231Pa/230Th values that also indicate cessation of the overturning circulation in the region (Figure 2 in [71]).

According to the density differences between the Atlantic regions of Figure 3 and in line with previous findings, the overturning rate at the ocean surface was weak during MIS 5e, and a change to a more vigorous circulation pattern occurred mostly during the glacial inception, i.e., the transition from MIS 5.5 to MIS 5.4 [71–73]. Hence, during the warm optimum of MIS 5.5, the structure of the AMOC was similar to the modern one (Figure 5b). The records are also in agreement for a sluggish Atlantic circulation at ~100 ka, since the weak density gradients that appear in Figure 3 are synchronous with an increase in the 231Pa/230Th records [71]. Nevertheless, the weight-based reconstructed density gradients show that the glacial Atlantic circulation mode started after 120,000 years ago with an increase in the overturning rate [71] and thus a more vigorous behavior of the AMOC [74,75] following the decrease in Northern Hemisphere summer insolation, which favored the initiation of ice-sheet growth [76].

**Figure 5.** The hydrographic properties of water parcels are strongly influenced by the atmosphere through air–sea interaction and once subducted from the surface layer the density (temperature and salinity) of a water parcel is conserved and remains constant since mixing across isopycnal surfaces is generally much weaker than mixing on isopycnal surfaces [77]. In oceanic regions of normal salinity conditions, the latitudinal temperature changes determine the density of the subducted waters. (**a**) During extreme glacial conditions, such as the LGM, enhanced atmospheric thermal gradients increase the number of seawater subduction zones that lead to enhanced oceanic density gradients (Figure 3) and thus more vigorous oceanic circulation; (**b**) during deglacial times of relaxed thermal gradients, surface ocean stratification prevails that can lead to the cessation of the oceanic circulation (SMCEs). Note the density difference between the glacial and interglacial ocean, which can be up to ~3.5 kg/m3 [78] due to ice cap buildup. However, the seawater density of tropical regions under the influence of the ITCZ is expected to be stable with perhaps only small glacial/interglacial variations.

The surface ocean density values during MIS 5e (~1026.8 kg/m3 ) were found to be remarkably similar to the values recorded for SMCE I during Termination I (~18.4 ka) and for most of the Holocene. 231Pa/230Th radiochemical data from sediment core OCE326- GGC5 from the western subtropical Atlantic also provide independent evidence of a collapse and rapid resumption of the AMOC [5]. In that 231Pa/230Th record, the circulation is found to momentarily cease at 17.5 kyr ago, during the H1 stadial. This is a few hundred years later than suggested from the convergence of the planktonic foraminifera shell weight records. This discrepancy may be due to the difference in the resolution of the records and/or because the response time of sediment 231Pa/230Th to changes in circulation is ∼500 yr [68,79]. Thus, the 231Pa/230Th profiles lag the information of surface ocean circulation changes that is provided by the foraminifera proxy.

The two records also agree in the duration of the shutdown of the AMOC, which appears to last 2000 yr by the 231Pa/230Th signal and 1600 to 2000 years in the foraminiferal records. The synchrony between changes in 231Pa/230Th and foraminifera weights suggests a connection between the AMOC and local surface hydrography, and the inferred nearcessation of AMOC during early deglaciation appears to be directly linked to the freshening and increased buoyancy of Northern Atlantic surface water during the H1 [80–82]. During this event, decreasing *G. bulloides* shell weights were recorded in three additional cores from

the N. Atlantic, all converging towards the beginning of the Holocene [43]. These findings thus support earlier suggestions that melt water associated with catastrophic iceberg discharge freshened the high-latitude surface ocean, stabilized the water column, and weakened the AMOC [83,84]. The results indicate that the effect was dramatic, resulting in a near-total collapse of the AMOC possibly during periods of substantial regional cooling.

Present planktonic foraminifera shell weight records reveal an attenuation of surface Atlantic density gradients after SMCE 1 (~18.4 ka), and this is supported by investigations that provide ample evidence for large-scale glacial and deglacial AMOC reorganizations [85–87]. While discrepancies remain between the different studies regarding the timing, overall tendency, and amplitude of circulation variations [88], there is a general consensus that AMOC variability was subdued during the Holocene compared with the last glacial termination [89,90]. This is also supported by the present record, where similar shell weight values are shown to characterize entire Holocene sections (14.1 ± 0.6 µg), suggesting no major changes in AMOC during at least the past 18 kyr (Figure 3). The slightly steeper gradients during the early Holocene imply a weakly increased rate of AMOC, supporting previous findings [5], but the convergence of shell mass values in the most recent sediment samples supports recent studies that suggest a decline in the AMOC strength during the past centuries [91–93]. However, these results must be confirmed with additional high-resolution analyses.


PC1 = 0.20 (QN1) + 0.06 (Gap energy) + 0.71 (Mor05u) − 68 (MlogP). (2)

From this equation, more active nitrofurans, in general, can be obtained when we have lower values for the QN1 combined with lower values for Gap energy and Mor05u and higher values for MlogP.

#### *<IP_ADDRESS> HCA model*

The results of the HCA model are displayed in the dendrogram in **Figure 9** and are similar to those of PCA model. The nitrofurans are fairly well grouped according to their activity. From this figure, the two clusters (+ and −) mirror the same two classes displayed by PCA model (**Figure 7**).

*Inhibitor concentration of 5 μM. b Growth inhibition ≥ 75, more active (MA)c , and growth inhibition < 75, less active (LA)c .*

#### **Table 2.**

*Values for the four most important descriptors which classify the studied nitrofuran compounds, in vitro T. cruzi growth inhibition (experimental data), activity, and correlation matrix.*

#### *<IP_ADDRESS> KNN model*

**Table 4** shows the results for the KNN models obtained with the KNN technique and constructed with one (1NN) to four (4NN) nearest neighbors. To all models the percentage of correct information was 100%. We used the model 4NN because the greater the number of the nearest neighbors, the better the reliability of the KNN technique, and the same was used for validation of the training set from **Figure 2**.

#### *<IP_ADDRESS> SDA model*

In the construction of the SDA model, the discrimination functions for groups more active and less active, respectively, are given below:

**61**

**Figure 7.**

**Figure 8.**

Group MA (more active):

Group LA (less active):

*Molecular Electrostatic Potential and Chemometric Techniques as Tools to Design Bioactive…*

0.51(QN1) + 0.43Gap energy + 3.05Mor05u − 1.5MlogP–0.62 (3)

*Loading vector plots of the first PCs, PC1 and PC2, for four variables responsible for the separation of the 23*

*nitrofurans (training set) into two classes: (+) more active and (−) less active against T. cruzi.*

*Score plots of the two first PCs, PC1 and PC2, responsible for the separation of the 23 nitrofurans (training set)*

−0.80QN1 − 0.67Gap energy − 4.75Mor05u + 2.34MlogP − 3.92 (4)

Also, through the discrimination functions, Eqs. (3) and (4), and of the value of each descriptor for the nitrofurans, we obtain the classification matrix by using all compounds from the training set (**Table 5**). The classification error was 0.00% resulting in a satisfactory separation of more active and less active compounds. From SDA model, the allocation rule was derived when the activity against *T. cruzi* of new nitrofurans is investigated: (a) initially calculate, for the new compound, the value of the most important descriptors obtained in the construction of the SDA model, (b) put these auto-scaled values in the two discrimination functions

*DOI: http://dx.doi.org/10.5772/intechopen.89113*

*into two classes: (+) more active and (−) less active against T. cruzi.*

*Molecular Electrostatic Potential and Chemometric Techniques as Tools to Design Bioactive… DOI: http://dx.doi.org/10.5772/intechopen.89113*

#### **Figure 7.**

*Cheminformatics and Its Applications*

**Nitrofurans QN1 Gap**

**energy (kcal/mol)**

− 0.201 220.9 −3.966 1.135 30 LA − 0.201 220.9 −2.938 1.708 20 LA − 0.165 220.9 −2.723 0.181 32 LA 4+ 0.165 226.5 −6.869 1.980 92.7 MA 5+ 0.165 225.3 −7.439 3.155 83.7 MA 6+ 0.169 229.7 −0.016 1.708 96.2 MA 7+ 0.164 208.3 −7.439 1.889 81.9 MA − 0.164 205.2 −4.854 0.334 26.7 LA − 0.166 215.9 −3.292 0.478 58 LA 10+ 0.166 215.9 −7.470 2.146 90 MA 11+ 0.164 208.3 −5.674 1.354 87.4 MA 12+ 0.164 208.3 −8.435 3.307 92.3 MA − 0.167 195.2 −4.338 0.751 12 LA − 0.161 203.3 −2.872 0.501 3 LA − 0.167 208.3 −4.217 0.411 30 LA − 0.167 225.3 −2.373 0.609 20 LA − 0.167 225.9 −4.054 1.063 6 LA 18+ 0.167 225.3 −6.339 2.001 75 MA − 0.166 225.3 −4.145 0.398 31 LA − 0.167 226.5 −4.786 0.667 35 LA − 0.167 225.3 −3.398 1.157 23 LA − 0.166 218.4 −3.876 0.802 14 LA 23+ 0.166 224.6 −6.314 3.014 90.5 MA

**Mor05u MlogP % in vitro**

*T. cruzi* **growth inhibitiona,b**

*, and growth inhibition < 75, less active*

**Activityc**

**60**

*a*

*(LA)c .*

**Table 2.**

*<IP_ADDRESS> KNN model*

Gap energy −0.171

*Inhibitor concentration of 5 μM. b*

Mor05u 0.27 −0.006

MlogP 0.026 −0.184 −0.785

*growth inhibition (experimental data), activity, and correlation matrix.*

*<IP_ADDRESS> SDA model*

**Table 4** shows the results for the KNN models obtained with the KNN technique and constructed with one (1NN) to four (4NN) nearest neighbors. To all models the percentage of correct information was 100%. We used the model 4NN because the greater the number of the nearest neighbors, the better the reliability of the KNN technique, and the same was used for validation of the training set from **Figure 2**.

*Growth inhibition ≥ 75, more active (MA)c*

*Values for the four most important descriptors which classify the studied nitrofuran compounds, in vitro T. cruzi*

In the construction of the SDA model, the discrimination functions for groups

more active and less active, respectively, are given below:

*Score plots of the two first PCs, PC1 and PC2, responsible for the separation of the 23 nitrofurans (training set) into two classes: (+) more active and (−) less active against T. cruzi.*

#### **Figure 8.**

*Loading vector plots of the first PCs, PC1 and PC2, for four variables responsible for the separation of the 23 nitrofurans (training set) into two classes: (+) more active and (−) less active against T. cruzi.*

Group MA (more active):

0.51(QN1) + 0.43Gap energy + 3.05Mor05u − 1.5MlogP–0.62 (3)

Group LA (less active):

$$-0.80 \text{QN1} \text{ - } 0.67 \text{Gap energy} \text{ - } 4.75 \text{Mor} \text{05u} \text{ + } 2.34 \text{MlogP} \text{ - } 3.92 \qquad \text{(4)}$$

Also, through the discrimination functions, Eqs. (3) and (4), and of the value of each descriptor for the nitrofurans, we obtain the classification matrix by using all compounds from the training set (**Table 5**). The classification error was 0.00% resulting in a satisfactory separation of more active and less active compounds. From SDA model, the allocation rule was derived when the activity against *T. cruzi* of new nitrofurans is investigated: (a) initially calculate, for the new compound, the value of the most important descriptors obtained in the construction of the SDA model, (b) put these auto-scaled values in the two discrimination functions

#### *Cheminformatics and Its Applications*

**Table 3.**

*Variables matrix for the first three principal components.*

#### **Figure 9.**

*Dendrogram obtained with HCA technique for the separation of the nitrofurans into two classes: (+) more active and (−) less active against T. cruzi.*

#### **Table 4.**

*Classification obtained with the KKN technique.*

performed in this work, and (c) check which discrimination function, Eq. (3) or Eq. (4), presents higher value. The new compound is more active if it is related to discrimination function of group more active and vice versa.

In order to check the reliability of the model, the "leave-one-out technique" was employed. One nitrofuran compound is excluded from the data set, and the remaining compounds are used in building the classification functions.

Subsequently, the removed analogue is classified according the generated classification functions. In the further step, the omitted compound is included, and a new nitrofuran is removed, and the procedure goes on until the last compound is removed. In **Table 6** the results obtained with the cross-validation model are summarized.

**63**

biological receptor.

*Molecular Electrostatic Potential and Chemometric Techniques as Tools to Design Bioactive…*

**Classification group or class Number of compounds More active Less active** Group (Class): more active 9 9 0 Group (Class): less active 14 0 14 Total 23 9 14 % Correct information — 100 100

**Classification group or class Number of compounds More active Less active** Group (class): more active 9 9 0 Group (class): less active 14 0 14 Total 23 9 14 % correct information — 100 100

**True group**

**True group**

The SIMCA model were built with the same descriptors as PCA, HCA, KNN, and SDA models and used two (2) PCs in the modeling of the two classes: more active nitrofurans (**4–7**, **10–12**, **18,** and **23**) and less active (**1–3, 8, 9, 13–17,** and **19–22**) nitrofurans. In **Table 7**, the obtained results for the SIMCA model are shown. In this case, the information percentage was also 100%. According to the PCA, HCA, KNN, SDA, and SIMCA models, we can also notice that the QN1, gap energy, Mor05u, and MlogP descriptors are key properties for explaining the anti-*T.*

*Classification matrix obtained by using SDA technique with cross-validation technique.*

As QN1, gap energy, Mor05u, and MlogP properties were selected in the chemometric modeling as the most important characteristics to describe the antitrypanosomal activity, some considerations about them may be relevant to the understanding of the behavior of more active nitrofurans. According to classical chemical theory, chemical interactions can be classified in two categories: electrostatic (polar) or orbital (covalent). Electrical charges in the molecule are indubitably the impelling cause of electrostatic interactions. It has been demonstrated that local electron densities or charges are important in many chemical reactions, physicochemical properties, and ligand–receptor interactions [89, 90]. Thus, charge-based parameters have been widely employed as chemical reactivity indices or as measures of weak intermolecular interactions. Many quantum–chemical descriptors are derived from the partial charge distribution in a molecule or from the electron densities on particular atoms [91]. From **Table 2**, we can observe that, in general, QN1 for more active analogues must present lower values than the less active ones. This is an indication that biological processes can occur through electrostatic interactions between the more active nitrofurans and an eventual

Gap energy is an important stability index. A large gap energy implies high stability for the molecule in the sense of its lower reactivity in chemical reactions.

*cruzi* activity of the nitrofurans training set (**Figure 2**).

*DOI: http://dx.doi.org/10.5772/intechopen.89113*

*Classification matrix obtained using SDA technique.*

*<IP_ADDRESS> SIMCA model*

**Table 5.**

**Table 6.**

*Molecular Electrostatic Potential and Chemometric Techniques as Tools to Design Bioactive… DOI: http://dx.doi.org/10.5772/intechopen.89113*

#### **Table 5.**

*Cheminformatics and Its Applications*

*Variables matrix for the first three principal components.*

**62**

summarized.

**Figure 9.**

**Table 3.**

**Table 4.**

*active and (−) less active against T. cruzi.*

*Classification obtained with the KKN technique.*

performed in this work, and (c) check which discrimination function, Eq. (3) or Eq. (4), presents higher value. The new compound is more active if it is related to

*Dendrogram obtained with HCA technique for the separation of the nitrofurans into two classes: (+) more*

**Variable PC1 PC2 PC3** QN1 0.20 0.66 0.69 Gap energy 0.06 −0.70 0.70 Mor05u 0.71 0.11 −0.10 MlogP −0.68 0.26 0.17

**Category Number of compounds Compounds incorrectly classified**

Class:more active 9 0 0 0 0 Class: less active 14 0 0 0 0 Total 23 0 0 0 0 % Correct information 100 100 100 100

**1NN 2NN 3NN 4NN**

In order to check the reliability of the model, the "leave-one-out technique" was employed. One nitrofuran compound is excluded from the data set, and the remain-

Subsequently, the removed analogue is classified according the generated classification functions. In the further step, the omitted compound is included, and a new nitrofuran is removed, and the procedure goes on until the last compound is removed. In **Table 6** the results obtained with the cross-validation model are

discrimination function of group more active and vice versa.

ing compounds are used in building the classification functions.

*Classification matrix obtained using SDA technique.*

#### **Table 6.**

*Classification matrix obtained by using SDA technique with cross-validation technique.*


**5.3.1 Block adaptive weight adjustment**

Initially the classification was attempted by feeding cumulant slices of short ST segments of the order of 10 to 30 samples at 500 Hz sampling rate. This attempt was 80% successful as the network missed low profile petal patterns with low levels of signal-to-noise ratios in their vicinity as a result of short data segmentation. A function was introduced to strengthen the relative magnitude of the discriminant cumulant slice features. The function is sampled across the input layer and its parameters (,) can be adaptively changed for each cumulant slice fed during the training phase which usually takes up to 10 modified cumulant slices every 1000 cardiac cycles. Obviously the shape of function can be changed to cater for other types of abnormalities.

Detection and Classification of Adult and

1988).

control parameters.

**5.4 Experimental results**

invasively examined and confirmed.

Fetal ECG Using Recurrent Neural Networks, Embedded Volterra and Higher-Order Statistics 247

has become the most popular learning algorithm for multi-layer networks, its rate of convergence is often found to be too slow for practical applications. Well established methods have been adopted (Hush and Salas, 1988). In the modified back-propagation method, every weight wij in the network is given its own learning rate ij, and the training data set is divided into a number of epochs each containing K training patterns (training patterns are 1-d cumulants from overlapping segments of the ST region). The weight wij and learning rate ij are updated every time after an entire training epoch (10 cumulants) has been presented to the network. The weight and learning rate updating rules of the modified back-propagation algorithm can be summarized as follows (Hush and Salas,

> 1 ( 1) ( ) ( 1) ( ) ( ) ( 1) *K*

> >

*if S n D n*

, ( 1) ( ) 0

*otherwise*

*k k ij n D n*

*w n*

( 1) ( ) ( )

( ) ( ), ( 1) ( ) 0

1 ( ) ( ) ( ) *K*

The index n refers to the nth epoch in the training data; the index k refers to the kth pattern in an epoch containing K patterns; kj is the modulated error signal of neuron j with the kth pattern in an epoch; yki refers to the actual computed output of neuron I with the kth pattern in an epoch; k is the index performance to be minimised by the weight update rule with the kth input pattern; finally, , , and (all of which have values between 0 and 1) are the

Three orthogonal leads ECG were recorded from several subjects confirmed of having VT with a prior myocardial infarction (MI). Two subjects suspected of having MI but time- and frequency-domains analysis had not shown any abnormality, and several normal subjects. A total of 3,000 cardiac cycles for this pilot study. Their feature extraction and enhancement were performed. The parameter and of the exponential weight function applied across the input layer were chosen to fall in the region of 1-2 and 0.25 – 0.5 for and , respectively. The initial learning rates ij(0) were all chosen to be 0.06. The momentum factor, , was fixed at 0.09. The control parameters , and were chosen to be 0.03, 0.1 and 0.5 respectively. The classifier described here achieved very high (90%) classification rate. The remaining 10% failure mainly arose because the MI suspected cases were not

*n n if S n D n*

*ij n nn*

*ij ij* (5.2)

(5.4)

*Sn Dn Sn* ( ) (1 ) ( ) ( 1). (5.5)

(5.3)

(5.1)

*ij ij ij kj ki ij k w n w n n ny n w n*

0, *ij ij*

Fig. 5.1. Typical third-order cumulants and their 1-d diagonal and wall slices shown in insets (left, right) of (a) a normal subject and (b) a subject having infarction in the ventricular muscle.

Fig. 5.2. Architecture of the four-layerd neural network. (a) Neuron or processing unit in the network. (b) The four-layer neural network. Only 1-d slice of the weight function modifies the corresponding cumulant slice.

#### **5.3.2 Modification to the back-propagation algorithm**

The back propagation method (Hush and Salas, 1988) used in the supervised learning of a multi-layer neural network is basically a gradient descent method. Although this method has become the most popular learning algorithm for multi-layer networks, its rate of convergence is often found to be too slow for practical applications. Well established methods have been adopted (Hush and Salas, 1988). In the modified back-propagation method, every weight wij in the network is given its own learning rate ij, and the training data set is divided into a number of epochs each containing K training patterns (training patterns are 1-d cumulants from overlapping segments of the ST region). The weight wij and learning rate ij are updated every time after an entire training epoch (10 cumulants) has been presented to the network. The weight and learning rate updating rules of the modified back-propagation algorithm can be summarized as follows (Hush and Salas, 1988).

$$w\_{ij}(n+1) = w\_{ij}(n) + \eta\_{ij}(n+1) \sum\_{k=1}^{K} \delta\_{kj}(n) y\_{ki}(n) + \text{\textquotedbl{}l\textquotedbl{}} w\_{ij}(n-1) \tag{5.1}$$

$$
\eta\_{ij}(n+1) = \eta\_{ij}(n) + \Delta \eta\_{ij}(n) \tag{5.2}
$$

$$\Delta \eta\_{ij}(n) = \begin{vmatrix} \Omega\_{\prime} & \text{if } & S(n-1)D(n) > 0 \\ -\phi \eta\_{ij}(n) & \text{if } & S(n-1)D(n) < 0 \\ 0 & & \text{otherwise} \end{vmatrix} \tag{5.3}$$

$$D(n) = \sum\_{k=1}^{K} \frac{\partial \varepsilon\_k(n)}{\partial w\_{ij}(n)} \tag{5.4}$$

$$S(n) = (1 - \Theta)D(n) + \Theta S(n-1). \tag{5.5}$$

The index n refers to the nth epoch in the training data; the index k refers to the kth pattern in an epoch containing K patterns; kj is the modulated error signal of neuron j with the kth pattern in an epoch; yki refers to the actual computed output of neuron I with the kth pattern in an epoch; k is the index performance to be minimised by the weight update rule with the kth input pattern; finally, , , and (all of which have values between 0 and 1) are the control parameters.

### **5.4 Experimental results**

246 Recurrent Neural Networks and Soft Computing

(a) (b)

Fig. 5.1. Typical third-order cumulants and their 1-d diagonal and wall slices shown in insets (left, right) of (a) a normal subject and (b) a subject having infarction in the ventricular

Fig. 5.2. Architecture of the four-layerd neural network. (a) Neuron or processing unit in the network. (b) The four-layer neural network. Only 1-d slice of the weight function modifies

The back propagation method (Hush and Salas, 1988) used in the supervised learning of a multi-layer neural network is basically a gradient descent method. Although this method

muscle.

the corresponding cumulant slice.

**5.3.2 Modification to the back-propagation algorithm**

Three orthogonal leads ECG were recorded from several subjects confirmed of having VT with a prior myocardial infarction (MI). Two subjects suspected of having MI but time- and frequency-domains analysis had not shown any abnormality, and several normal subjects. A total of 3,000 cardiac cycles for this pilot study. Their feature extraction and enhancement were performed. The parameter and of the exponential weight function applied across the input layer were chosen to fall in the region of 1-2 and 0.25 – 0.5 for and , respectively. The initial learning rates ij(0) were all chosen to be 0.06. The momentum factor, , was fixed at 0.09. The control parameters , and were chosen to be 0.03, 0.1 and 0.5 respectively. The classifier described here achieved very high (90%) classification rate. The remaining 10% failure mainly arose because the MI suspected cases were not invasively examined and confirmed.

Detection and Classification of Adult and

third-order cumulant method.

**7. Conclusion**

template.

Fetal ECG Using Recurrent Neural Networks, Embedded Volterra and Higher-Order Statistics 249

methods have AUC values of 0.731, 0.794, and 0.843, respectively. This suggests that the third-order cumulant is a better detection method than second-order statistics-based, and

Youden's index, defined as sensitivty + specificity – 1, has also been used for the detection methods. The second-order statistics-based methods have indices in the range of 0.42 to 0.55. The third-order cumulant method has an index of 0.72. The bispectral contour method has an index of 0.80. This suggests that the third-order cumulant is a better detection method than second-order statistics-based, and that the bispectral contour method outperforms the

Also, the Partial Area Under Curve (PAUC) measure has been used for a False-Positive Rate (FPR) of 10% and sensitivty larger than 75%. The second-order statistics-based method gives a PAUC of 0.043. The third-order cumulant method has a corresponding value of 0.125 whilst that of the bispectral contour method is 0.137. This suggests that the third-order cumulant is a better detection method than second-order statistics-based, and that the

The sensitivity, specificity and classification rate for the third-order slice cumulant matching hybrid system have been calculated . The technique has been evaluated for diagonal, wall, or arbitrary TOC slices, employing both the LMF-based quadratic and cubic Volterra filters. The results indicate that a linear combination of diagonal and wall slices of the TOC can improve the detection rate by up to 1% over and above the 77.8% obtainable using only either slice. Using two more arbitrary slices off-diagonal and off-wall would result in a further improvement of up to 1%. Using two slices instead of only one results in an two-fold increase in the CPU time of 1 msec using Unix WS. Further improvement of 6% to 8% is attainable with maternal transabdominal ECG signal linearisation employing second- and third-order Volterra synthesisers, respectively. Based on the first hybrid system using TOC slices for signal processing and subsequent single-hidden-layer classification, 100% and 86.16% classification rates have been achieved for maternal QRS-complex and fetal heartbeats, respectively. Note that the classification rates for coincident and non-coincident maternal and fetal QRS-complexes are 0% and 95.55%, respectively. The remaining undetected 13.84% fetal heartbeats include 9.8% overlap with the maternal QRS-complexes and 4% occur during depolarisation of the maternal T-waves. Those events unavoidably lead to significant distortion of the fetal TOCs. This means that the cumulant signatures will not be close to the TOC template signature stored in the database. Examples of false negatives and false positives have been found in the following cases, respectively, (i) a fetal heartbeat with maternal contribution TOC diagonal slice was wrongly matched to a QRSfree ECG TOC diagonal slice template, and (ii) a QRS-free ECG TOC diagonal slice was wrongly matched to a fetal heartbeat with maternal contribution TOC diagonal slice

Results obtained for the bispectral contour matching hybrid system from 30 cases using the non-invasive transabdominally-measured ECG signal, with the simultaneous fetal scalp electrode ECG signal as a reference, show that the method has a classification rate of 100% for normal, healthy maternal QRS-complexes and 90.12% for fetal heartbeats. It has been

that the bispectral contour method outperforms the third-order cumulant method.

bispectral contour method outperforms the third-order cumulant method.


**2. Water allocation model**

The water allocation model can be divided into the surface water model and the groundwa‐ ter model. The parts of the water allocation model are described in the sequel.

### **2.1. Surface water model**

largest account for about 90% of the total storage capacity of roughly 9x109 m³

**Figure 1.** Structure of the proposed decision support system (DSS) for the region of Beijing

timal water management approach are presented in section 5.

**2. Water allocation model**

A common approach for policy generation in this field of application is to use mathematical programming techniques based on a dynamic model of the essential elements of the water allocation and distribution system [3]. The great impact of the groundwater storage for the supply system at hand requires a more detailed description of the groundwater flow dy‐ namics compared to other known DSS implementations. Therefore a 3D Finite-Element model of the plain region has been developed. However, a direct integration of this 3D mod‐ el into an optimal control framework is not possible due to its computational costs. A trajec‐ tory based model reduction scheme is proposed, which guarantees a very fast response of

the DSS in combination with a specially tailored non-linear programming algorithm.

The chapter is organized as follows: In section 2 the essential models (surface and ground‐ water models) and the model reduction approach are described. While the formulation of the optimal control problem is subject of section 3, the numerical solution of the large scale structured non-linear programming problem is described in section 4. First results of the op‐

The water allocation model can be divided into the surface water model and the groundwa‐

ter model. The parts of the water allocation model are described in the sequel.

of a total length of about 400 km.

24 Water Supply System Analysis - Selected Topics

is distributed to the customers using rivers and artificial transport ways (channels, pipes)

. The water

The surface water model has to comprise all important elements for the allocation, storage and distribution of water within the considered region. The intended field of application of the decision support system under development embraces management and upgrading strategies for the mid and long term range. This implies a significant simplification for the process model, because the retention time along the different transport elements (river reaches, channel or pipelines) is less than the desired minimum time step for decision of one day. Therefore, a simple static approach for flow processes is sufficient and the use of so‐ phisticated models for the dynamics of wave propagation (like e. g. Saint-Venant-Equations) with respect to control decisions is avoided. In this case, the flow characteristics are repre‐ sented by simple lag elements of the first order combined with dead-time elements. Given *y* and *u* as an output and input, respectively. The following mathematical relationship indi‐ cates a lag element of the first order.

$$T\_1 \cdot \frac{dy}{dt} + y = u \tag{1}$$

where T1 is the only parameter and indicates the time lag; t indicates the time. The following relationship represents the dead-time element:

$$y = \mu(t - T\_t) \tag{2}$$

In this case the parameter is the dead-time *Tt* , which is thus the measure of the time taken for water to flow in a conduit over a known distance.

The surface water system is described as a directed graph. The edges characterize the trans‐ port elements and introduce only a variable for the discharge. The nodes represent reser‐ voirs, lakes, points of water supply or extraction and simple junction points. Every node constitutes a balance equation involving the edges linked with and possibly the storage vol‐ ume. The sole nonlinearity results from modeling the evaporation from the water surface of the storages (volume-area-curve), which is described by a piecewise polynomial approach. At time step *k*, the volume of a reservoir node evolves as follows:

$$V\_j^{k+1} = V\_j^k + \Delta t^k \left(\sum\_{i \in \mathcal{E}(j)} \mathcal{Q}\_i^k + A\_{O,j}^k q\_{\text{evpt},j}^k - q\_{\text{seep},j}^k + A\_{O \text{max}} q\_{\text{pre},j}^k\right) \tag{3}$$

where *AO*, *j k* = *f* (*Vj k* ), the storage volume is denoted by *V*, the discharge into and from the storage is denoted by *Q* and discrete time step is denoted by *Δt*. The total evaporation from the reservoir depends on the water surface *A0* and the potential evaporation *qevpot.* q*seep* de‐ notes the seepage from the reservoir to the groundwater and *qprec* specifies the precipitation.

Channels with a very low slope are modeled as water storage. The level dependent upper bound for the channel outflow is derived from a steady state level-flow relation like e.g. Chezy-Manning friction formula and is directly added as constraint to the optimization problem.

The surface water simulation model has been implemented in Matlab/Simulink using the toolbox "WaterLib" [5] and contains the most important elements of the drinking water sup‐ ply system of Beijing. The simulation model was developed to reach a sufficient accuracy as well as a high simulation speed. A one-year simulation is carried out in a simulation time of several seconds. This is a very important condition for using the model in the decision sup‐

The most important water resource in the considered area is groundwater that is modeled by a dynamic spatially distributed finite element groundwater model. The governing equa‐ tion for groundwater flow is Darcy's law [6] describing slow streams through unconfined aquifers. Combining Darcy's law with mass conservation yields the partial differential equa‐

In (4) denotes *h* the hydraulic head (which corresponds to the groundwater level) and *kf* the hydraulic conductivity that governs the hydrogeological properties of the soil. S0 denotes the specific storage coefficient. The terms on the right hand side of (4) summarize all sources and sinks that coincide with the time dependent groundwater exploitation due to industry, households and agriculture (Qexpl) and recharge e. g. due to precipitation and irrigation

The partial differential equation (4) is an initial-boundary value problem which has to be solved numerically for *h* in the 3 dimensional model domain Ω. The groundwater model has been implemented using FEFLOW, which is a Finite Element (FEM) software specialized on subsurface flow [7]. The initial condition is h (Ω,t0) (groundwater surface) at the initial time t0. The inflow/outflow is described by Dirichlet boundary conditions, i.e. h (∂Ω) at the boun‐ dary ∂Ω and by well boundary conditions, that define a particular volume rate into or out of Ω. The advantage of the latter one is that they are scalable. The 3D FEM model consists of more than 150,000 nodes, distributed on 25 layers (cf. Fig. 3). Huge computational costs re‐ sult from this high resolution. The simulation of 5 years needs ~15 Minutes on an Intel Core 2 Duo CPU (2.5 GHz). Hence it is very time consuming to calculate optimal water allocation strategies with the 3D FEM groundwater model. This is the motivation for model reduction

The main task with respect to the groundwater model is the parameterization of the largescaled model covering an area of 6,300 km². On the one hand the time independent soil pa‐

of measured values. On the other hand the source / sink terms Qexpl, Qrech have to be calculat‐ ed time dependent. For these calculations time dependent maps of precipitation and water demand are needed. The water demand is splitted into the three user groups households,

, S0 have to be estimated and generalized for the whole domain Ω by a (small) set

0 ( *f rech l* ) exp *Sh k h Q Q* -Ñ× Ñ = - & (4)

Model Based Sustainable Management of Regional Water Supply Systems

http://dx.doi.org/10.5772/51973

27

port system.

(Qrech) in Ω.

(see subsection 2.3).

rameters kf

**2.2. Groundwater water model**

tion (4) which is a diffusion equation.

The Structure of the Beijing water supply system is shown in Fig. 2. Firstly, there are the four main reservoirs Miyun, Huairou, Baihebao and Guanting. Further sources are groundwater storages and water transfers. Secondly, there are the water transportation systems such as channels and rivers. Miyun reservoir and Huairou reservoir are connect‐ ed to Beijing by the Miyun-Beijing water diversion. In the simulation model the arrows describe hydraulic behavior of water flow. Baihebao and Guanting reservoir are connect‐ ed by tunnel and river Guishui. From Guanting water runs into the Yongding river wa‐ ter diversion system to Beijing. Existing retention areas for flood control are also considered in the simulation model.

The surface water from channels and rivers is delivered to the customers in different ways, directly or through the surface waterworks. Groundwater is distributed to the customers through ground waterworks as well as motor-pumped wells. Therefore, the waterworks build the third part of the Beijing water supply system. The last category is made up of all the customer groups (agriculture, industry, households and environment). To complete up the cycle, catchments area models are integrated in the system to take into account precipita‐ tion and evapotranspiration.

**Figure 2.** Structure of the Beijing water supply system

The surface water simulation model has been implemented in Matlab/Simulink using the toolbox "WaterLib" [5] and contains the most important elements of the drinking water sup‐ ply system of Beijing. The simulation model was developed to reach a sufficient accuracy as well as a high simulation speed. A one-year simulation is carried out in a simulation time of several seconds. This is a very important condition for using the model in the decision sup‐ port system.


**5. Neuro–EM and neuro-k mean clustering approach for VLSI design partitioning**

This section is focused in use of clustering methods k-means (J. B. MacQueen, 1967) and Expectation-Maximization (EM) methodology (Kaban & Girolami, 2000).

#### **5.1 Neuro-EM model**

The system consists of three parts each dealing with data extraction, Learning stage and recognition stage. In data extraction, a circuit is bipartite and partitions it into 10 clusters, a user-defined value, by using K-means (J. B. MacQueen, 1967) and EM methodology (Kaban & Girolami, 2000), respectively. In recognition stage the parameters, that is, centroid and probability are fed into generalized delta rule algorithm separately and train the network to recognize sub-circuits with lowest amount of interconnections between them. Block diagram of model to recognize sub-circuits with lowest amount of interconnections between them using two techniques K-means and EM methodology with neural network are shown in Fig.6 and Fig.7.

In recognition stage the parameters, that is, centroid and probability are fed into generalized delta rule algorithm separately and train the network to recognize sub circuit with minimum interconnection between them. Block diagram of model for Partitioning a Circuit are depicted in Fig. 8.

Algorithms for CAD Tools VLSI Design 141

Sub circuit 1 A, B, C total edges = 7, Sub circuit 2 D, E, F total edges =10

Cell No of edges Bipartition

A 2 1

B 2 1

C 3 1

D 3 0

E 3 0

F 4 0

The EM algorithm was explained and given its name in a classic 1977 paper by Arthur Dempster, Nan Laird, and Donald Rubin in the Journal of the Royal Statistical Society (Arthur et al.,1997). They pointed out that method had been "proposed many times in special circumstances" by other authors, but the 1977 paper generalized the method and

Fig. 10. Bipartition Circuit

Table 1. Bipartation Matrix

Sub circuit2 (D, E, F) 0011 0011 0100

developed the theory behind it.

**5.3 Expectation Maximization algorithms**

Data representation: Sub circuit1 (A, B, C) 0010 0010 0011,

Fig. 6. Block diagram of K-means with neural network

Fig. 7. Block diagram of EM methodology with neural network

Fig. 8. Block Diagram of Model for Partitioning a Circuit

### **5.2 Sample data set**

A sample example representation is shown in Fig.9 and Fig 10

Fig. 9. Sample Circuit

**Classifier Neural Network**

> **Classifier Neural Network**

**Recognition Result**

**Recognition Result**

Fig. 6. Block diagram of K-means with neural network

1. Circuit is bipartite and data represented

2. Applying K-means 3. Applying EM methodology 4. centroid and probability 5. Neural network 6. Recognition Result

**A circuit is bipartite**

> **A circuit is bipartite**

**5.2 Sample data set**

Fig. 9. Sample Circuit

Fig. 7. Block diagram of EM methodology with neural network

**Probability extracted by EM clustering method**

**Centroid extracted by K-means clustering method**

Fig. 8. Block Diagram of Model for Partitioning a Circuit

A sample example representation is shown in Fig.9 and Fig 10

Fig. 10. Bipartition Circuit Sub circuit 1 A, B, C total edges = 7, Sub circuit 2 D, E, F total edges =10

Table 1. Bipartation Matrix Data representation: Sub circuit1 (A, B, C) 0010 0010 0011, Sub circuit2 (D, E, F) 0011 0011 0100

#### **5.3 Expectation Maximization algorithms**

The EM algorithm was explained and given its name in a classic 1977 paper by Arthur Dempster, Nan Laird, and Donald Rubin in the Journal of the Royal Statistical Society (Arthur et al.,1997). They pointed out that method had been "proposed many times in special circumstances" by other authors, but the 1977 paper generalized the method and developed the theory behind it.

Algorithms for CAD Tools VLSI Design 143

iii. Classification probabilities instead of classifications. The results of EM clustering are different from those computed by k-means clustering. The latter will assign observations to clusters to maximize the distances between clusters. The EM algorithm does not compute actual assignments of observations to clusters, but classification probabilities. In other words, each observation belongs to each cluster with a certain probability. Of course, as a final result one can usually review an actual assignment of observations to

clusters, based on the (largest) classification probability (Gyllenberg et al., 2000).

The algorithm is similar to the K-means procedure in that a set of parameters are recomputed until a desired convergence value is achieved. The parameters are recomputed until a desired convergence value is achieved. The finite mixtures model assumes all

A mixture is a set of *N* probability distributions where each distribution represents a cluster. An individual instance is assigned a probability that it would have a certain set of attribute values given it was a member of a specific cluster. In the simplest case N=2 the probability distributes are assumed to be normal and data instances consist of a single real-valued attribute. Using the scenario, the job of the algorithm is to determine the value of five

2. Use the probability density function for a normal distribution to compute the cluster probability for each instance. In the case of a single independent variable with mean

1 ( )

*f x*

1. Use the probability scores to re-estimate the five parameters.

(2 )

In the two-cluster case, there are two probability distribution formulae each having differing

The algorithm terminates when a formula that measures cluster quality no longer shows significant increases. One measure of cluster quality is the likelihood that the data came from the dataset determined by the clustering. The likelihood computation is simply the multiplication of the sum of the probabilities for each of the instances. With two clusters *A*

.5 ( | ) .5 ( | ) .5 ( | ) .5 ( | ) ... .5 ( | ) .5 ( | ) *Px A Px B Px A Px B Px A Px B* 1 12 2 *n n* (11)

and *B* containing instances x1, x2, … xn where PA = PB = 0.5 the computation is:

*e*

2 2 (? ) 2

(10)

3. The sampling probability *P* for cluster 1 (the probability for cluster 2 is 1-*P*)

clusters (Kim, 2002).

parameters specifically,

attributes to be independent random variables.

1. The mean and standard deviation for cluster 1 2. The mean and standard deviation for cluster 2

1. Guess initial values for the five parameters.

and standard deviation , the formula is:

the general procedure is given below,

mean and standard deviation values.

2. Return to Step 2

refined (adjusted) to maximize the likelihood of the data given the specified number of

The EM algorithm for clustering is described in detail in Witten and Frank (2001) (Witten & Frank, 2005). The Expectation-Maximization (EM) algorithm is part of the Weka clustering package. EM is a statistical model that makes use of the finite Gaussian mixtures model. The basic approach and logic of this clustering method is as follows. Suppose a single continuous variable in a large sample of observations is measured. Further, suppose that the sample consists of two clusters of observations with different means (and perhaps different standard deviations) within each sample, the distribution of values for the continuous variable follows the normal distribution. The resulting distribution of values (in the population) may look as shown in Fig.11.

Fig. 11. Two normal distributions of EM Algorithm (Screen Shot)

i. Mixtures of distributions. The illustration in Fig 5.12 shows two normal distributions with different means and different standard deviations and the sum of the two distributions. Only the mixture (sum) of the two normal distributions (with different means and standard deviations) would be observed. The goal of EM clustering is to estimate the means and standard deviations for each cluster so as to maximize the likelihood of the observed data (distribution). Put another way, the EM algorithm attempts to approximate the observed distributions of values based on mixtures of different distributions in different clusters.

With the implementation of the EM algorithm in some computer programs, one may be able to select (for continuous variables) different distributions such as the normal, lognormal, and Poisson distributions (Karlis, 2003) and can select different distributions for different variables, thus derive clusters for mixtures of different types of distributions.

ii. Categorical variables. The EM algorithm can also accommodate categorical variables. The method will at first randomly assign different probabilities (weights, to be precise) to each class or category, for each cluster. In successive iterations, these probabilities are

The EM algorithm for clustering is described in detail in Witten and Frank (2001) (Witten & Frank, 2005). The Expectation-Maximization (EM) algorithm is part of the Weka clustering package. EM is a statistical model that makes use of the finite Gaussian mixtures model. The basic approach and logic of this clustering method is as follows. Suppose a single continuous variable in a large sample of observations is measured. Further, suppose that the sample consists of two clusters of observations with different means (and perhaps different standard deviations) within each sample, the distribution of values for the continuous variable follows the normal distribution. The resulting distribution of values (in the

population) may look as shown in Fig.11.

Fig. 11. Two normal distributions of EM Algorithm (Screen Shot)

different distributions in different clusters.

i. Mixtures of distributions. The illustration in Fig 5.12 shows two normal distributions with different means and different standard deviations and the sum of the two distributions. Only the mixture (sum) of the two normal distributions (with different means and standard deviations) would be observed. The goal of EM clustering is to estimate the means and standard deviations for each cluster so as to maximize the likelihood of the observed data (distribution). Put another way, the EM algorithm attempts to approximate the observed distributions of values based on mixtures of

With the implementation of the EM algorithm in some computer programs, one may be able to select (for continuous variables) different distributions such as the normal, lognormal, and Poisson distributions (Karlis, 2003) and can select different distributions for different variables, thus derive clusters for mixtures of different types of distributions. ii. Categorical variables. The EM algorithm can also accommodate categorical variables. The method will at first randomly assign different probabilities (weights, to be precise) to each class or category, for each cluster. In successive iterations, these probabilities are refined (adjusted) to maximize the likelihood of the data given the specified number of clusters (Kim, 2002).

iii. Classification probabilities instead of classifications. The results of EM clustering are different from those computed by k-means clustering. The latter will assign observations to clusters to maximize the distances between clusters. The EM algorithm does not compute actual assignments of observations to clusters, but classification probabilities. In other words, each observation belongs to each cluster with a certain probability. Of course, as a final result one can usually review an actual assignment of observations to clusters, based on the (largest) classification probability (Gyllenberg et al., 2000).

The algorithm is similar to the K-means procedure in that a set of parameters are recomputed until a desired convergence value is achieved. The parameters are recomputed until a desired convergence value is achieved. The finite mixtures model assumes all attributes to be independent random variables.

A mixture is a set of *N* probability distributions where each distribution represents a cluster. An individual instance is assigned a probability that it would have a certain set of attribute values given it was a member of a specific cluster. In the simplest case N=2 the probability distributes are assumed to be normal and data instances consist of a single real-valued attribute. Using the scenario, the job of the algorithm is to determine the value of five parameters specifically,

the general procedure is given below,

$$f(\mathbf{x}) = \frac{1}{\sqrt{2\pi}\sigma\sigma\right)e^{\frac{-(\mathbf{?}-\mu)^2}{2\sigma^2}}}\tag{10}$$

In the two-cluster case, there are two probability distribution formulae each having differing mean and standard deviation values.

The algorithm terminates when a formula that measures cluster quality no longer shows significant increases. One measure of cluster quality is the likelihood that the data came from the dataset determined by the clustering. The likelihood computation is simply the multiplication of the sum of the probabilities for each of the instances. With two clusters *A* and *B* containing instances x1, x2, … xn where PA = PB = 0.5 the computation is:

$$\left[\left.5P(\mathbf{x}\_{1}\,\middle|\,A) + \left.5P(\mathbf{x}\_{1}\,\middle|\,B)\right\|\right] \left[\left.5P(\mathbf{x}\_{2}\,\middle|\,A) + \left.5P(\mathbf{x}\_{2}\,\middle|\,B)\right] \dots \left[\left.5P(\mathbf{x}\_{n}\,\middle|\,A) + \left.5P(\mathbf{x}\_{n}\,\middle|\,B)\right]\right] \right.\tag{11}$$

Algorithms for CAD Tools VLSI Design 145

Step 3. Initialize the weight for network. Each weight should be set to a random value

Step 6. Compares the actual output with desired outputs and finds a measure of error.

Step 7. After comparison it finds in which direction (+ or -) to change each weight in order to

Step 8. Find the amount by which to change each weight. It applies the corrections to the weight and repeat all above steps with all training vectors until the error for all the vectors

**6. Evaluation of fuzzy ARTMAP with DBSCAN in VLSI partition application**

This section describes a new model for partitioning a circuit using DBSCAN and fuzzy

The basic ART system is an unsupervised learning model. It typically consists of a comparison field and a recognition field composed of neurons, a vigilance parameter, and a reset module. The vigilance parameter has considerable influence on the system, higher vigilance produces highly detailed memories (many, fine-grained categories), while lower vigilance results in more general memories (fewer, more-general categories). The comparison field takes an input vector (a one-dimensional array of values) and transfers it to its best match in the recognition field. Its best match is the single neuron whose set of weights (weight vector) most closely matches the input vector. Each recognition field neuron outputs a negative signal (proportional to that neuron's quality of match to the input vector) to each of the other recognition field neurons and inhibits their output accordingly. In this way the recognition field exhibits lateral inhibition, allowing each neuron in it, to represent a category to which input vectors they are classified. After the input vector is classified, the reset module compares the strength of the recognition match to the vigilance parameter. If the vigilance threshold is met, training commences. Otherwise, if the match level does not meet the vigilance parameter, the firing recognition neuron is inhibited until a new input vector is applied. The training commences only upon completion of a search procedure. In the search procedure, recognition neurons are disabled one by one, by the reset function until the vigilance parameter is satisfied by a recognition match. If no

1 xJh=g( xpn)= 1 ( xpn) *wjkh e wjkh* (12)

1 xio=g( xjh)= 1( xjh) *wjko e wijo* (13)

between –0.1 to 1.

reduce error.

Step 9: End.

ARTMAP neural network.

**6.1 Overview of art map**

Step 4. Calculates activation of hidden nodes

Step 5. Calculate the output from output layers

in training set is reduced to an acceptable value.

Algorithm is similar to K-mean procedure, in that sets of parameters are re-computed until desired convergence value is achieved. General procedure is

The tool shed output of this algorithm would be the probability for each cluster. EM assigns a probability distribution to each instance, which indicates the probability of it belonging to each of the clusters.

In the context of recognizing the sub circuit from circuit with minimum interconnections between them, artificial neurons is structured into three normal types of layers input, hidden and output which can create artificial neural networks. The layers of input neuron are responsible for inputting a feature vectors that is, centroid and probability, which are extracted from K-means and EM algorithms respectively. The number of neurons in this output layer is determined by size of set of desired output, with each possible output being represented by separate neuron. Between these two layers there can be many hidden layers. These internal layers contain many of the neuron in various interconnected structures.


**1. Introduction**

Removing gangue from raw coal is conducive to improving the efficiency of coal utilization and reducing environmental pollution. Therefore, the identification of gangue and coal blocks is a necessary step for the efficient removal of coal gangue in coal production, which is of great significance for environmental protection [1,2]. Because of its obvious advantages of resource saving, low cost, the simple processing system and convenient maintenance, image recognition technology for the separation of coal gangue has been widely studied and applied in the literature [3–7]. Researchers have developed a variety of image recognition methods for coal gangue image recognition, which contribute to research into coal gangue separation technology based on image recognition and have laid a foundation for further research. However, these methods have their shortcomings. For example, in [3], the proposed method resulted in a waste of computing resources and low time efficiency because it calculated 15 eigenvalues at the same time, although only the best five eigenvalues were actually used. In the study by Zhou et al. [4], the new method adopted a deep convolution neural network to address the task of online accurate and rapid identification of coal gangue, which required extensive computation. In other studies [5,6], although the recognition rate of the methods used was high, the artificially set threshold parameters played a decisive role in the intermediate calculation link, which depended on an extensive experimental statistical analysis or experience, resulting in the calculation being complex. The stability of performance was questionable, and the generalized ability to recognize coal gangue images with different characteristics in different regions was not

1 R & D Department, Zhuhai Xinhe Technology Co., Ltd., Zhuhai 519600, China; or

necessarily high. The authors of [7], proposed a method that required a large number of samples generated by the introduction of the transfer learning method, suggesting that the method's generalization and universality are questionable and may be limited when the sample size is small.

Since it was proposed by the team of Rumelhart and McClelland in 1986, the BP (back propagation) neural network has been widely used in the field of image recognition [8] because of its simple structure and high calculation efficiency, such as in [9]. To solve the problem of remote sensing image classification, the authors established an improved BP neural network and set the dynamic training intensity to improve the learning speed and classification accuracy of the BP neural network classifier. However, determining the optimal training intensity consumes a large amount of computing resources; moreover, the sample set classification problems of different fields have different optimal training intensities due to the large differences in the sample characteristics, so the generalizability is questionable, probably resulting in this method being unsuitable for image coal gangue classification with a wide area and many sources. In another study [10], a small image recognition and classification method based on GA-BP was proposed, in which the combination of a genetic algorithm and the BP neural network gave full play to the nonlinear mapping ability of the neural network, resulting in strong learning ability and fast convergence speed. The experimental results showed that the new method had higher recognition accuracy and better performance than the traditional BP algorithm and the GA-BP algorithm. The authors of [11] adopted a hybrid algorithm combining a genetic algorithm and a back propagation algorithm, and the experimental results showed that this GA-BP algorithm had higher efficiency, robustness and practicability. The researchers in [12] proposed an epilepsy diagnosis method based on an improved genetic algorithm– optimized back propagation (IGA-BP) neural network and used this method to detect clinical epilepsy quickly and effectively. Liu et al. [13] used a genetic algorithm (GA) to construct a classification model based on the BP neural network to automatically identify the correlations in a multi-mode blog, and the experimental results showed that the classification model based on GA-BP was better than the traditional BP neural network. Yu et al. [14] considered the problem that a BP algorithm based on a gradient descent principle falls into the local minima, and thus, the classification of multispectral remote sensing images using spectral information cannot obtain ideal results. Yu et al. developed a new method combining feature texture knowledge with a BP neural network trained by particle swarm optimization (PSO). The experimental results showed that this method had improved classification accuracy. Ying et al. [15] proposed a method combining a random loss algorithm and particle swarm optimization (PSO-BP) for the recognition and classification of small images, which corrected the weights of the PSO algorithm based on the error back propagation adjustment of the traditional BP algorithm to establish the PSO-BP network model. The hidden layer unit of the PSO-BP network was improved by using the random loss algorithm, thus achieving faster operation speeds. The authors of [16,17] proposed variants of the PSO-BP combining a BP neural network and PSO to address the task of supervised classification of synthetic aperture radar (SAR) images and the problems of low accuracy and efficiency in traditional part classification methods. This kind of BP neural network method based on GA or PSO optimization has a certain reference value for coal gangue image classification. Unfortunately, the accuracy of image coal gangue classification was still not high, as shown by a comparative experiment in a follow-up paper. In addition, the BP neural network has also been applied in other fields. For example, in [18], the researchers proposed a metal surface defect classification method based on an improved bat algorithm to optimize the BP neural network, which was used to classify images of defects with different characteristics. The researchers in [19] proposed an automatic recognition method of cloud and precipitation particle shapes based on a BP neural network to solve the problem that the shape of cloud particle images measured by airborne cloud imaging probes (CIPs) cannot be automatically recognized.

Although these methods have some shortcomings, they have still contributed to the research into coal gangue separation technology based on image recognition and laid a foundation for further research. In 2007, Yang and his coauthors proposed a new swarm intelligence algorithm [20], which simulates the predation process of wolves to solve complex nonlinear optimization problems. Due to its superior performance, it has been widely used in various fields and has been continuously developed and improved. For example, in [21], the author proposed a novel and effective opposite wolf pack algorithm to estimate the parameters of a Lorenz chaotic system. In another study [22], the improved wolf pack search algorithm was used to calculate the quasi-optimal trajectory of a rotor UAV in complex three-dimensional space. Moreover, in [23], the wolf pack algorithm was used to find the root of the polynomial equation of the problem accurately and quickly. Similarly, in [24], Zhou Qiang and others proposed a wolf pack search algorithm based on the leader strategy (LWCA). The researchers in [25] designed an adaptive shrinking grid search chaos wolf optimization algorithm (ASGS-CWOA) using adaptive standard deviation updating to achieve better performance, which included new regeneration rules, a new raid strategy, a new siege strategy and a new siege adaptive step size. Inspired by the good optimization ability of the wolf pack intelligent optimization algorithm and the excellent classification performance of the BP neural network, this article proposes a coal gangue image recognition method based on ASGS-CWOA and the BP neural network.

The remainder of this article is organized as follows. Section 2 presents a description of "*Encircle–City Feature*", a combination of ASGS-CWOA and the BP neural network and an overview of new method. In Section 3, we present comparative experiments to show the effectiveness of the proposed approach. The conclusion is given in Section 4.


**5. Conclusion**

In this chapter, a stochastically perturbed particle swarm optimization algorithm (SPPSO) is proposed for identical parallel machine scheduling (PMS) problems. The SPPSO has all major characteristics of the classical PSO. However, the search strategy of SPPSO is different. The algorithm is applied to (PMS) problem and compared with two recent PSO algorithms. The algorithms are kept standard and not extended by embedding any local search. It is concluded that SPPSO produced better results than DPSO and PSOspv in terms of number of optimum solutions obtained. In terms of average relative percent deviation, there is no significant difference between SPPSO and PSOspv. However, they are better than DPSO.

It also should be noted that, since PSOspv considers each particle based on three key vectors; position (Xi), velocity (Vi), and permutation (Πi), it consumes more memory than SPPSO. In addition, since DPSO uses one and two cut crossover operators in every iteration, implementation of DPSO to combinatorial optimization problems is rather cumbersome. The proposed algorithm can be applied to other combinatorial optimization problems such as flow shop scheduling, job shop scheduling etc. as future work.