**2.3 Effect of rice husk biochar on days to flowering of maize under drought stress**

Under drought conditions plant growth as well as days to flowering of maize was affected. Days to flowering of maize varied appreciably with different doses of biochar under drought conditions (**Figure 1**).

Under control condition (80% of FC), 60% of field capacity, and 40% of field capacity, lowest days to flowering of maize were 52, 57, and 61 days, respectively, when biochar was applied at 20 t/ha, and highest days to flowering of maize were 60, 62, and 63 days, respectively, when no biochar was applied. Drought stress affected plant physiological process and biochar helps to maintain physiological activities thereby flowering of plants, improved plant growth and influenced days to flowering. [25] observed that the mung bean plants grown in soil amended with 8.5% and 15.75% wood biochar started flowering, pod filling, and maturing 6 to 7 days earlier than those grown in unamended soil.


**7. Conclusions**

This study can be considered to be a basic contribution in terms of overcoming the generalization problem for human emotion recognition. The aim was to show the feasibility and the possibility of building such generalized models for relevant application contexts. Furthermore, this study examined the less intrusive sensors based on statistical analyses in real-life datasets and reviewed various state-of-the-art approaches to human emotion recognition in smart home environments.

Additionally, emotion recognition is a cornerstone of advanced intelligent systems for monitoring a subject's comfort. Thus, information on a subject's emotion and stress level is a key component for the future of smart AAL environments.

In our future work, we will focus on human emotion recognition using EDA with respect to different lab–settings, which means, we will try to build a generalized approach which should be trained using lab–settings X and tested using lab–settings Y. Additionally, we plan to combine Stacked Sparse Auto Encoders with CNN. Moreover, CNN essentially learns local (spatial) features. On the other side, RNN does in essence rather learn temporal features. Consequently, combining both neural network concepts will result in a neuro-processor which can learn both contextual dependencies (i.e., spatial and temporal) from inputted local features. As a result, such a combination does potentially improve the overall performance.

**Author Contributions:** F.A.M. and A.E. conceived and designed the approach; E.A.M. and M.A. performed the formal analysis; F.A.M., K.K. wrote the paper.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest. The authors ensure that there are no personal circumstances, interest or sponsors that may be perceived as inappropriately influencing the representation or interpretation of reported research results.


**2. The intensity of conditioning regimen**

The early data on myeloablative conditioning (MAC) regimen can be obtained from the transplant registries [8-12]. Cyclophosphamide (Cy) with total body irradiation (Cy-TBI) and busulfan with Cy were the mostly used conditioning regimens. Transplant-related mortality (TRM) rates ranged from 30% to 50%. Actuarial survival for the EBMT-registered patients was 28% at 7 years [9], 15 % for the Hutchinson Center–registered patients [10]. IBMTR data showed that the probabilities of survival at 4 years was 35% for patients with Karnofsky performance scores higher than 70 at pretransplantation and approximately 15% for patients with scores lower than 70 [11]. Thus, due to the exceedingly high TRM, myeloablative Allo-SCT was largely abandoned worldwide in the 1990s.

The use of reduced intensity conditioning (RIC) regimens in allo-SCT was introduced in an attempt to reduce the regimen-related toxicities while preserving an effect of graft versus tumor effect. First study was performed in a canine model conditioned with low-dose (2 Gy) total body irradiation (TBI) in combination of postgrafting mycofenolatemofetil (MMF) and cyclosporine (CSP). This approach permitted to stable engraftment with minimal toxicity [13, 14]. Seattle group introduced the strategy of autologous SCT followed by a RIC allo-SCT in 2-4 months with low-dose TBI as conditioning regimen [15]. Forty eight percent of 52 multiple myeloma patients had relapsed or refractory disease prior to SCT and the overall response rate was 81 % (51% CR + 29% PR). In this tandem modality, the 100-day TRM after the allo-RIC was 2%, progression free survival (PFS) and overall survival (OS) at 2 years were 48% and 69%, respectively. Preliminary clinical studies [15-25] were also encouraging with low TRM rates (Table1). Kröger, et al performed tandem auto/Allo-RIC in 17 myeloma patients using unrelated or mismatched related donors and fludarabine, melphalan, anti-thymocyte globulin (ATG) as conditioning regimen [16]. Early TRM (day 100) was reported as 11% and estimated 1-year disease free survival (DFS) and OS were 56% and 74%.

One of the largest data related to a RIC-allograft in myeloma was published by the EBMT in which the outcome of 229 patients with MM from 33 centers was reported [18]. One-year TRM was 22%, the 3-year estimated PFS and OS were 41% and 21%, respectively. The adverse outcomes were seen in chemo-resistant disease prior to allo-SCT, transplantation to the pair of male recipient- female donor, no-chronic GvHD and the use of alemtuzumab.

The EBMT has also retrospectively compared 320 patients allografted a RIC regimen with 196 received a MAC regimen in multiple myeloma. They have reported markedly lower non relapse mortality in RIC than MAC setting (24% vs 32%, p<.002) [19]. However PFS and OS were not affected by the intensity of conditioning regimen. This was attributed to higher relapse rates in RIC group than the MAC group. Progressive disease at transplantation was associated with an adverse effect on non-relapse mortality, PFS and OS. T cell depletion with alemtuzumab or other(s) led to high relapse rates as well.

In this chapter, we discussed the role of allo-HCT in MM patients, and also we tried to clarify the issues as the intensity of conditioning regimen, the timing of the transplantation, and post-

The early data on myeloablative conditioning (MAC) regimen can be obtained from the transplant registries [8-12]. Cyclophosphamide (Cy) with total body irradiation (Cy-TBI) and busulfan with Cy were the mostly used conditioning regimens. Transplant-related mortality (TRM) rates ranged from 30% to 50%. Actuarial survival for the EBMT-registered patients was 28% at 7 years [9], 15 % for the Hutchinson Center–registered patients [10]. IBMTR data showed that the probabilities of survival at 4 years was 35% for patients with Karnofsky performance scores higher than 70 at pretransplantation and approximately 15% for patients with scores lower than 70 [11]. Thus, due to the exceedingly high TRM, myeloablative Allo-SCT was largely

The use of reduced intensity conditioning (RIC) regimens in allo-SCT was introduced in an attempt to reduce the regimen-related toxicities while preserving an effect of graft versus tumor effect. First study was performed in a canine model conditioned with low-dose (2 Gy) total body irradiation (TBI) in combination of postgrafting mycofenolatemofetil (MMF) and cyclosporine (CSP). This approach permitted to stable engraftment with minimal toxicity [13, 14]. Seattle group introduced the strategy of autologous SCT followed by a RIC allo-SCT in 2-4 months with low-dose TBI as conditioning regimen [15]. Forty eight percent of 52 multiple myeloma patients had relapsed or refractory disease prior to SCT and the overall response rate was 81 % (51% CR + 29% PR). In this tandem modality, the 100-day TRM after the allo-RIC was 2%, progression free survival (PFS) and overall survival (OS) at 2 years were 48% and 69%, respectively. Preliminary clinical studies [15-25] were also encouraging with low TRM rates (Table1). Kröger, et al performed tandem auto/Allo-RIC in 17 myeloma patients using unrelated or mismatched related donors and fludarabine, melphalan, anti-thymocyte globulin (ATG) as conditioning regimen [16]. Early TRM (day 100) was reported as 11% and estimated

One of the largest data related to a RIC-allograft in myeloma was published by the EBMT in which the outcome of 229 patients with MM from 33 centers was reported [18]. One-year TRM was 22%, the 3-year estimated PFS and OS were 41% and 21%, respectively. The adverse outcomes were seen in chemo-resistant disease prior to allo-SCT, transplantation to the pair

The EBMT has also retrospectively compared 320 patients allografted a RIC regimen with 196 received a MAC regimen in multiple myeloma. They have reported markedly lower non relapse mortality in RIC than MAC setting (24% vs 32%, p<.002) [19]. However PFS and OS were not affected by the intensity of conditioning regimen. This was attributed to higher relapse rates in RIC group than the MAC group. Progressive disease at transplantation was

of male recipient- female donor, no-chronic GvHD and the use of alemtuzumab.

transplantation approaches in relapse or refractory patients.

1-year disease free survival (DFS) and OS were 56% and 74%.

**2. The intensity of conditioning regimen**

166 Multiple Myeloma - A Quick Reflection on the Fast Progress

abandoned worldwide in the 1990s.

Long-term follow-up data was reported in a RIC allo-graft for salvage setting of relapse and/or refractory myeloma patients (Table 1). These data showed that long term remission can be feasible for a subset of myeloma patients with allo-RIC performed in the salvage setting [21]. Seattle group reported the long term comparison data of RIC and MAC regimens [23]. Although the intensity of regimens changed time dependently, RIC regimens resulted in significantly lower overall mortality, improved PFS and much lower TRM.

**Abbreviations:** ASCT: Autologous Stem Cell Transplantation; GvHD: Graft versus Host Disease; TRM: Transplant-Related Mortality; NRM: Non-Relapse Mortality; CR: Complete Remission; PFS. Progression-Free Survival; OS: Overall Survival; TBI: Total Body Irradiation; ATG: Anti-Thymocyte Globulin; CSP: Cyclosporine; MMF: Mycofenolate Mofetif; TAC: Tacrolimus; MTX: Methotrexate; MP: Methyl-Prednisolone; URD: Unrelated Donor; MRD: Matched Related Donor

**Table 1.** Reduced intensity allogeneic transplantation alone or following autogous-SCT

A prospective multicenter study by the Gruppo ItalianoTrapianti di Midollo Osseo (GITMO) enrolled 100 newly diagnosed multiple myeloma patients who were < 65 years of age and who had a sibling donor [24]. Allo-RIC transplantation was performed 2 to 4 months after ASCT in 96 patients. Disease sensitivity at the transplantation was significantly associated with longer OS and event-free survival (EFS). Overall survival were not significantly affected by the presence of del(13q) whereas EFS was better in patients without del(13q). Similarly, the Eastern Cooperative Oncology Group (ECOG) performed a trial of ASCT followed by RIC-allo from matched sibling donor to provide maximal tumor cytoreduction to allow for a subsequent graft versus myeloma (GvM) effect [25]. With a median follow up of 4.6 years from registration, 23 patients who completed both transplantations had a median PFS of 3.6 years and a 2-year survival rate of 78%. Cumulative non-relapse mortality on day 100 was 8.7%. In contrast to Italian study, plateau in PFS or OS was not observed with this treatment approach even in patients achieving CR.

**Auto/auto vs**

**Conditioning for allo- RIC**

busulfan, ATG

80 vs 82 Low-dose TBI 26 vs 55

Melphalan

366 vs156 Low-dose TBI 13 vs 9

46 vs58 Low-dose TBI 26 vs 55

**Table 2.** Double transplantation comparing tandem ASCT with auto/allo RIC

the patients received double ASCT (p=.002).

**CR (%) (auto/auto vs**

p=.004

40 vs 11 p=.001

p=.0004

p=.003

TRM: Transplant-Related Mortalitiy; TBI: Total Body Irradiation; ATG: Anti-Thymocyte Globulin

**auto/allo RIC)**

**PFS/EFS (months) (auto/auto vs**

**OS (months) (auto/auto vs**

Allogeneic Hematopoetic Cell Transplantation in Multiple Myeloma

**auto/allo RIC)**

57 vs 41 p=.08

80 vs 54 p=.01

3 years 80% vs 77% P:0.19

5.3 years vs not reached P=.02

60% vs 61.8% (5y) p=.9

**TRM % P(auto/auto**

**auto/allo RIC)**

169

Not evaluated

46 pts. vs 58pts. P=.09

5 vs 16 p=.09

Not evaluated

16 vs 2

**vs**

http://dx.doi.org/10.5772/54762

**auto/allo RIC)**

p=.88

35 vs 29 p=.02

p=.08 26 vs 19.6 p=.4

46% vs 43% (3 y) p=.7

33 vs39 p=0.02

**Abbreviations:** CR: Complete Remission; PFS: Progression-Free Survival; EFS: Event-Free Survival; OS: Overall Survival;

The Italian group enrolled 162 consecutive younger patients ≤ 65 years of age with newly diagnosed myeloma who had at least one sibling [29]. Patients with an HLA-identical sibling donor received NMA TBI (2Gy) and stem cells median 94 days after ASCT (n=58). Patients without an HLA-identical sibling received tandem ASCT with high-dose melphalan (n=46). The rate of complete remission was significantly higher in the auto-allograft group (55% vs 26%, p=.004). Treatment-related mortality was similar (p=.009) but disease-related mortality was significantly higher in the double ASCT group (43% vs 7%, p<.001). There was a trend of higher EFS in auto-allograft arm (p=.07) while survival in the auto-allo setting was superior to

Another prospective study has been performed by the Spanish PETHEMA group [30]. They enrolled 110 patients with newly diagnosed failing to achieve at least near-CR after a 1st ASCT were scheduled to receive either 2nd ASCT (n=85) or allo-RIC (n=25), depending on the

31 vs not reached

**Auto/allo RIC**

166 vs 46 Fludarabine,

85 vs 25 Fludarabine,

**(n)**

Moreau [28]

Bruno [29]

Rosinol [30]

Krishnan [31]

Giaccone [32]

Another prospective study for myeloma as part of first-line therapy, a donor versus no-donor analysis was performed of the patients treated in the HOVON-50 study [26]. This study allowed the patients with an HLA-identical sibling donor to proceed to the HOVON-54 study of allo-RIC between 2 and 6 months after ACST. Their results did not support allo-SCT as a frontline therapy.


**Acknowledgements**

The authors acknowledge Ms. Shalini P. Etukuri and Dr. Govind Sharma at Alabama A&M University for reviewing this book chapter. Also, authors would like to thank anonymous reviewers and editor for their efforts in improving this book chapter. The authors acknowledge the funding support by the Capacity Building grant #2020-38821-31103 from the USDA National Institute of Food and Agriculture.


**3.2. Control of frequency transmission**

An approach to schedule a real time distributed system based upon modifications on frequency transmission of individual components in the system is presented in [4], this shows that scheduling of a distributed system can be accomplished through modifications on transmission frequencies into a region where the system performance is not affected. A linear time invariant model in which the coefficients of the state matrix are the relations between the transmission frequencies of each agent and through a feedback controller to modify transmission frequencies bounded between maximum and minimum values of transmission. This approach drives the frequency transmission based on three parameters: minimum frequency (*fm*), maximum frequency (*fh*) and real frequency (*fr*). Frequency transmission dynamics can be modeled as a linear time-invariant subsystem which state variables are transmission frequencies of the sensor nodes involved on the system. Note that for each primary task of a sensor *Si*, *i* = 1, ..., *m* frequency can be expressed as *fi* = 1/*pi*. There is a relationship between nodes' frequencies an external input frequencies which serves as coefficients of the linear system. Therefore it is possible to control the NCS through the input vector *u* such that the outputs *y* are nodes' frequencies into a region *L* bounded by maximum and minimum transmission frequencies, see Fig. 2.

**Figure 2.** Transmission frequencies bounded by a schedulability region

6 Will-be-set-by-IN-TECH

(Token Bus), FDMA, TDMA (TTP), Switched Ethernet, WLAN (802.11b), and ZigBee (802.15.4) are some types of network supported [2]. The network blocks are mainly configured using blocks dialogs. Some parameters common to all types of networks are bit rate, the minimum frame size, and the network interface delay. For each type of network there are some parameters that specifie the number of nodes, data rate (bits/s), preprocessing delay, minimum frame size, maximum frame size, frame overhead, etc. The network blocks may be used having one kernel block for each node in the network. The tasks into the kernels can send and receive arbitrary Matlab structure arrays over the network using ttSendMsg and ttGetMsg kernel primitives. This way is to quite flexible but requires to program some routines to configure the system. An useful network scheduler viewer shows the network activity for all nodes involved. An overview of all Truetime's primitives can be found on [12].

In this section a formal definition of task model is provided and it gives an overview of the control of frequency transmission in a distributed systems and how it impacts over quality

Chen *et al.* [3] gives a formal definition of system model of a typical distributed systems consisting of a set of processors and a set of tasks. A distributed system are characterized as follows. A set of processors Ω = {*S*1, *S*2, ..., *Sm*} where Ω is the processor set, *Si* is the *i* − *th* processor and *m* is the total number of processors. In this model, all processors are assumed to be identical to assure same execution time for each task on different processors. It is also supposed that enough processors are provided. A set of primary copy of real-time tasks Φ = {*τ*1, *τ*2, ..., *τn*}, where *τi* = {*ci*, *pi*} , *i* = {1, 2, ..., *n*}. Here Φ is the set of tasks, *τi* is the *i* − *th* task, *n* is the number of tasks which are periodic, independent and preemptive, *ci*

An approach to schedule a real time distributed system based upon modifications on frequency transmission of individual components in the system is presented in [4], this shows that scheduling of a distributed system can be accomplished through modifications on transmission frequencies into a region where the system performance is not affected. A linear time invariant model in which the coefficients of the state matrix are the relations between the transmission frequencies of each agent and through a feedback controller to modify transmission frequencies bounded between maximum and minimum values of transmission. This approach drives the frequency transmission based on three parameters: minimum frequency (*fm*), maximum frequency (*fh*) and real frequency (*fr*). Frequency transmission dynamics can be modeled as a linear time-invariant subsystem which state variables are transmission frequencies of the sensor nodes involved on the system. Note that for each primary task of a sensor *Si*, *i* = 1, ..., *m* frequency can be expressed as *fi* = 1/*pi*. There is a relationship between nodes' frequencies an external input frequencies which serves as coefficients of the linear system. Therefore it is possible to control the NCS through the input vector *u* such that the outputs *y* are nodes' frequencies into a region *L* bounded by maximum

**3. Frequency transmission scheduling**

denotes the execution time of *τi*, *pi* denotes the period of task *τi*.

**3.2. Control of frequency transmission**

and minimum transmission frequencies, see Fig. 2.

performance.

**3.1. Task model**

The objective of controlling the frequency is to achieve coordination through the convergence of values. Each sensor *Si* knows its minimum and maximum frequencies based upon messages sent to controller and it could be estimated its own real transmission frequency. Let a NCS with a set Ω = {*S*1, *S*2, ..., *Sl*} nodes that performs a set of task *τi* = {*ci*, *pi*} for *i* = {1, 2, , *n*}, a subset of Ω is sensor nodes subset Ω*s* = {*S*1, *S*2, ..., *Sm*}.

### **3.3. Network scheduling based on frequency transmission**

An approach that modifies the frequency transmission uses *fm*, *fr*, *fx* frequencies. RTDS dynamics, is modeled as a linear time-invariant system, whose state variables are frequencies transmission rates of the *n* nodes that compose the RTDS [4]. Frequency rates of a node are affected by some external input frequency rates, minimal frequencies of all nodes and particular ratios serve as coefficients of the linear system. So, it is possible to control the NCS using the input vector *u*, such that the output vector *y* contains the frequency rates of all nodes within a nonlinear region *L*, bounded by the maximum and minimum transmission frequency rates. Let we assume that there is a relationship amongst real frequencies *f* 1 *r* , *f* 2 *r* , ..., *f m r* and external input frequencies *u*1, *u*2, ..., *um* which serve as coefficients of the linear system:

$$\begin{aligned} \mathbf{x}\_{k+1} &= A\mathbf{x}\_k + Bu\_{k\prime} \\ y\_k &= \mathbf{C}\mathbf{x}\_k. \end{aligned} \tag{1}$$

*A*, *B*, *C* are matrices with appropriate dimensions. *A* is the matrix of relationships between frequencies of sensor nodes, *B* is the scale frequencies matrix, *C* is the matrix with frequencies ordered, *xk*+1 is a real frequencies vector in time *t* = *k* + 1, *yk* is the vector of output frequencies. The input *uk* is a function of reference frequencies and real frequencies of the nodes in the distributed system, hence *u* = *K*(*fm* − *fr*) where *fm*, *fr* are vectors. Then, the state vector in equation (1) can be written as:

$$\begin{array}{l} \mathbf{x}\_{k+1} = A\mathbf{x}\_{k} + Bu\_{k\prime} \\ \mathbf{x}\_{k+1} = Af\_{rk} + B\left(K(f\_{mk} - f\_{rk})\right) \end{array} \tag{2}$$

#### 8 Will-be-set-by-IN-TECH 56 Numerical Simulation – From Theory to Industry Issues on Communication Network Control System Based Upon Scheduling Strategy Using Numerical Simulations 9

Note that *K* is the control gain defined as the basics of a LQR algorithm. Matrices *A*, *B* and *C* has the proper dimensions and matrix *A* include the following restriction [11]:

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

*xc* is a real execution time and *xr*

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ *x*1 *k*+1 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ Λ *f* 1 *m f* 2 *m f* 1 *m f* 3 *m f* 1 *m f* 4 *m f* 1 *m* 0

*f* 1 *m f* 2 *m* Λ *f* 2 *m f* 3 *m f* 2 *m f* 4 *m f* 2 *m* 0

*f* 1 *m f* 3 *m f* 2 *m f* 3 *m* Λ *f* 3 *m f* 4 *m f* 3 *m* 0

*f* 1 *m f* 4 *m f* 2 *m f* 4 *m f* 3 *m f* 4 *m* Λ *f* 4 *m* 0

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ *c*1 *c*2 *c*3 *c*4 1

*K*1 *f* 1 *h* (*f* 1 *m* − *f* 1 *r* )

*K*2 *f* 2 *h* (*f* 2 *m* − *f* 2 *r* )

*K*3 *f* 3 *h* (*f* 3 *m* − *f* 3 *r* )

*K*4 *f* 4 *h* (*f* 4 *m* − *f* 4 *r* )

*r* ) + *K*2(*f* 2

*r* ) + *K*4(*f* 4

*c* − *xr*)

⎤ ⎥ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ *f* 1 *r f* 2 *r f* 3 *r f* 4 *r xc* ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ .

*m* − *f* 2 *r* )+

*m* − *f* 4 *r* )+

*m* − *f* 1

*m* − *f* 3

*Kc*(*xr*

=

+

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ *y*1 *k y*2 *k y*3 *k y*4 *k y*5 *k*

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

=

⎡ ⎢ ⎢ ⎢ ⎢ ⎣

*K*1(*f* 1

*K*3(*f* 3

*x*2 *k*+1

*x*3 *k*+1

*x*4 *k*+1

*x*5 *k*+1

Thus

*y*1 *k y*2 *k y*3 *k y*4 *k y*5 *k*

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

=

⎡ ⎢ ⎢ ⎢ ⎢ ⎣

*c* is a reference execution time.

⎤ ⎥ ⎥ ⎥ ⎥ ⎦

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ *f* 1 *r*

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

*f* 2 *r*

*f* 3 *r f n r*

*xc*

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

,

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ *f* 1 *r f* 2 *r f* 3 *r f* 4 *r xc* ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ .

Issues on Communication Network Control System Based Upon Scheduling Strategy Using Numerical Simulations

57

$$U = \sum\_{i=1}^{n} c\_i / p\_i \le 1,$$

as a new state of the system (1). For simplicity, frequency transition model will be described using a sensor node subset Ω*s* = {*S*1, *S*2, *S*3, *S*4}. The elements of the matrices for system 2 are defined as follows:

$$
\overline{a}\_{ij} = \begin{cases}
\frac{\Lambda\left(f\_m^1 f\_m^2 f\_m^3 f\_m^4\right)}{f\_m^1} & i = j \\
\\ \frac{f\_m^j}{f\_m^i} & i \neq j
\end{cases}
$$

$$
\overline{b}\_{ij} = \begin{cases}
f\_{li}^j & i = j \\
0 & i \neq j
\end{cases}
$$

$$
\overline{c}\_{ij} = \begin{cases}
1 & i = j \\
0 & i \neq j
\end{cases}
$$

Note that Λ � *f* 1 *m*, *f* 2 *m*, *f* 3 *m*, *f* 4 *m* � is the greatest common divisor of minimum frequencies, that is the planning cycle Γ expressed in terms of frequencies of the backup task, for shortening, it will be written only as Λ. *fm*, *fh*, and *fr* are vectors of respective frequencies.

 Thus

> ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

8 Will-be-set-by-IN-TECH

Note that *K* is the control gain defined as the basics of a LQR algorithm. Matrices *A*, *B* and *C*

as a new state of the system (1). For simplicity, frequency transition model will be described using a sensor node subset Ω*s* = {*S*1, *S*2, *S*3, *S*4}. The elements of the matrices for system 2

> *f i m*

> *f j m f i m*

*f i h i* = *j*

0 *i* �= *j*

1 *i* = *j*

0 *i* �= *j*

the planning cycle Γ expressed in terms of frequencies of the backup task, for shortening, it

Considering the execution time *ci* of each task executing in respective sensor nodes in Ω*s* as

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ *f* 1 *r*

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

*f* 2 *r*

*f* 3 *r f n r*

+

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ *f* 1

0 *f* 2

0 0 *f* 3

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ *f* 1 *r f* 2 *r f* 3 *r f n r xc* ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ ⎞

⎞

⎟⎟⎟⎟⎠ ,

⎟⎟⎟⎟⎠

000 *f n*

1 1 1 11

*h* 0 0 00

*h* 0 00

*h* 0 0

*h* 0

⎤ ⎥ ⎥ ⎥ ⎥ ⎦

*xc*

⎤ ⎥ ⎥ ⎥ ⎥ ⎦ ⎛

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ *f* 1 *m f* 2 *m f* 3 *m f* 4 *m xr c*

⎤ ⎥ ⎥ ⎥ ⎥ ⎦ −

⎜⎜⎜⎜⎝

⎧ ⎨ ⎩

> ⎧ ⎨ ⎩

*i* = *j*

,

is the greatest common divisor of minimum frequencies, that is

*i* �= *j*

,

.

*ci*/*pi* ≤ 1,

*n* ∑ *i*=1

has the proper dimensions and matrix *A* include the following restriction [11]:

*U* =

*aij* =

⎧ ⎪⎪⎨ Λ(*f* 1 *m*, *f* 2 *m*, *f* 3 *m*, *f* 4 *m*)

⎪⎪⎩

*bij* =

*cij* =

will be written only as Λ. *fm*, *fh*, and *fr* are vectors of respective frequencies.

are defined as follows:

Note that Λ �

*f* 1 *m*, *f* 2 *m*, *f* 3 *m*, *f* 4 *m* �

an additional state, we can rewrite (2) as follows:

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

Λ *f* 1 *m f* 2 *m f* 1 *m f* 3 *m f* 1 *m f* 4 *m f* 1 *m* 0

*f* 1 *m f* 2 *m* Λ *f* 2 *m f* 3 *m f* 2 *m f* 4 *m f* 2 *m* 0

*f* 1 *m f* 3 *m f* 2 *m f* 3 *m* Λ *f* 3 *m f* 4 *m f* 3 *m* 0

*f* 1 *m f* 4 *m f* 2 *m f* 4 *m f* 3 *m f* 4 *m* Λ *f* 4 *m* 0

*c*1 *c*2 *c*3 *c*4 1

*K*1 0000 0 *K*2 000 0 0 *K*3 0 0 000 *K*4 0 0000 *Kc*

=

·

⎛

⎡ ⎢ ⎢ ⎢ ⎢ ⎣

⎜⎜⎜⎜⎝

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ *x*1 *k*+1

*x*2 *k*+1

*x*3 *k*+1

*x*4 *k*+1

*x*5 *k*+1

*x*1 *k*+1 *x*2 *k*+1 *x*3 *k*+1 *x*4 *k*+1 *x*5 *k*+1 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ Λ *f* 1 *m f* 2 *m f* 1 *m f* 3 *m f* 1 *m f* 4 *m f* 1 *m* 0 *f* 1 *m f* 2 *m* Λ *f* 2 *m f* 3 *m f* 2 *m f* 4 *m f* 2 *m* 0 *f* 1 *m f* 3 *m f* 2 *m f* 3 *m* Λ *f* 3 *m f* 4 *m f* 3 *m* 0 *f* 1 *m f* 4 *m f* 2 *m f* 4 *m f* 3 *m f* 4 *m* Λ *f* 4 *m* 0 *c*1 *c*2 *c*3 *c*4 1 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ *f* 1 *r f* 2 *r f* 3 *r f n r xc* ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ + ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ *K*1 *f* 1 *h* (*f* 1 *m* − *f* 1 *r* ) *K*2 *f* 2 *h* (*f* 2 *m* − *f* 2 *r* ) *K*3 *f* 3 *h* (*f* 3 *m* − *f* 3 *r* ) *K*4 *f* 4 *h* (*f* 4 *m* − *f* 4 *r* ) *K*1(*f* 1 *m* − *f* 1 *r* ) + *K*2(*f* 2 *m* − *f* 2 *r* )+ *K*3(*f* 3 *m* − *f* 3 *r* ) + *K*4(*f* 4 *m* − *f* 4 *r* )+ *Kc*(*xr c* − *xr*) ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ *y*1 *k* ⎤ ⎥

*k*


**5. Conclusions**

In summary, this study reports the first extensive study regarding the prevalence and molecular characterization of ESBL genes and the epidemiology of ESBL-producing *E. coli* and ESBL-producing *K. pneumoniae* isolates causing infections in Trinidad and Tobago that was specifically and clearly delineated by the use of the PFGE method.


**3.3 Results of variable selection**

Here we select a subset of variables from 35 variables of Expectation data focusing on the loss of proportion *P*. Suppose we want to keep it under 1%, *q* ¼ 25 which is assigned from **Table 3** and **Figure 1**. The selected variables are marked by � in the right column of **Table 1**. As far as looking at the variables deleted from each block, two variables {8, 9} from 11 variables in "fashion" block, three variables {12, 16, 20} from 12 variables in "brand" block, and five variables {25, 27, 30, 32, 34} from 12 variables in "shop staff" block are deleted. That is, nine variables are selected from the first two blocks and seven from the third block. It can be stated that the proposed method selects a reasonable subset of variables. Comparing the number of deleted variables in the three blocks, a slightly larger number of variables are removed from the third block, so it is thought that questions on "shop staff" have little information rather than those in the other two blocks and some of them have less significance on the prediction efficiency. From this point of view, we can evaluate the usefulness of each question in the questionnaire.

To evaluate the significance of variables, we observe how many times each variable is selected through the selection for *q* ¼ 35, … , 5. Extracting the variables selected over 2*=*3 times (24 or more), for example, in the "fashion" block, variables {1, 6, 10, 11} were selected. Given the fact that the close-up questions are located close to each other (1 to 3, recognition on fashion, 4 to 7—consciousness on fashion, 8 to 11 activity on fashion), it is generally clear that NL.M.PCA using the proportion *P* selects variables well-balanced from the close-up questions. Similarly, if the most frequently selected variables (such as the above four items) are considered as the most important questions, they should be involved in future surveys. If variables are selected a few times, they should not be involved in the future. In such a way, there is a possibility to use the selection results to evaluate the questionnaire itself.