*3.2.7 Cross-layered approach*

When compared to layered approaches, cross-layered approach in WSN is energy efficient. The protocol stack is considered as a single system instead of individual layers in the cross-layered approach. For interaction among the protocol layers, state information of the protocols is shared among all layers. Cross-layered protocol implementations significantly affect the system efficiency with respect to the energy and lifetime.

energy. However, the probabilistic CH selection process prompts unequal clusters

Periodic, event-driven, and query-based protocol (PEQ) and its variation, CPEQ, were proposed by Boukerche et al. [35] in 2006. PEQ is designed for achieving the following: low latency, high reliability, and broken path

reconfiguration. CPEQ is a cluster-based routing protocol. The publish/subscribe

Genetic algorithm-based clustering approach (LEACH-GA) was introduced in literature [36] to predict the optimal probability for electing an optimal number of CHs. This approach improved the network lifetime by achieving energy-efficient

Artificial bee colony (ABC)-based algorithm [37] has been proposed, where the CH selection is performed by adopting the ABC algorithm. ABC algorithm improves the clustering process by employing efficient and fast search feature to select the CHs. Both cluster members to CH, and CH to BS communication is performed by direct data communication. However, this protocol does not consider the coverage

Ant colony algorithm for data aggregation (DAACA) has been introduced by Chi

Lusheng Miao et al. [39] have introduced network coding to resolve the issues in gradient-based routing (GBR) scheme, such as broadcasting of interest messages by sink node which prompts duplication of packets, which causes more energy dissipation, and point-to-point message delivery forces more data retransmissions due to the unstable network environment in WSNs. The authors have proposed network coding for GBR (GBR-NC) to implement energy-efficient broadcasting algorithm which reduces network traffic. Further, the authors have presented two competing

In 2012, Rashmi Ranjan Rout et al. [40] proposed an energy-efficient triangular (regular) deployment strategy with directional antenna (ETDDA), where 2-connectivity pattern has been utilized. This pattern is accomplished by aligning the directional antenna beam of a sensor node in a specified direction toward the sink. Data forwarding depends on network coding for many-to-one traffic flow from sensor nodes to sink. The proposed approach ensures energy efficiency, robustness,

Ming Ma et al. [41] have put forward a mobility-based data-gathering mechanism for WSNs. A mobile data collector (M-collector), perhaps a mobile robot or a vehicle, is implemented with a transceiver and battery. The M-collector travels through a specific path and determines the sensor nodes, which comes within its communication range while traversing. Then, it collects the data from the sensor nodes in the single-hop communication and forward the data to the base station without delays. Hence, this mechanism improves the lifetime of the sensor nodes. The authors have primarily focused to reduce the length of each data-gathering tour

Lin et al. [38]. This approach comprises of three phases: initialization, packets transmissions, and operations on pheromones. In the transmission phase, the next hop is dynamically selected by determining the number of pheromones of neighbor nodes and the residual energy. Pheromones' adjustments are accomplished for every specified number of rounds of data transmissions. Besides, various pheromones' adjustment strategies such as basic-DAACA, elitist strategy-based DAACA (ES-DAACA), maximum- and minimum-based DAACA (MM-DAACA), and ant colony system-based DAACA (ACS-DAACA) are utilized to enhance the network lifetime. However, duplication packets are transmitted from sink nodes to initialize

the network, which causes higher energy depletion in the network.

algorithms such as GBRC and auto-adaptable GBR-C to minimize the data

and better connectivity in communicating data to the sink.

called as single-hop data-gathering problem (SHDGP).

mechanism is used to broadcast requests throughout the network.

of the CH and it prompts more energy dissipation.

which leads to more energy dissipation.

*Data Collection Protocols in Wireless Sensor Networks DOI: http://dx.doi.org/10.5772/intechopen.93659*

clustering.

retransmissions.

**91**

## **4. Existing routing techniques**

In WSN, so many techniques are proposed to achieve energy efficiency, longer lifetime, fault tolerance. Low latency by different researchers are briefly explained in this section. Most of these solutions are designed based on different techniques such as clustering, network coding, duty cycling, aggregation, directional antennas, sink mobility, and cross-layer solutions.

Low-energy adaptive clustering hierarchy (LEACH) routing strategy was proposed by Heinzelman et al. [29]. It is a cluster-based routing algorithm to decrease energy consumption and improve the network lifetime. In this protocol, the network is divided into clusters; each cluster contains a set of CMs and a leader called CH. The CMs send the data to its respective CH; CHs communicate the collected data to the BS and are elected in a random and distributed manner. Subsequently, LEACH was altered to LEACH-C [30], a centralized approach. The process of CH selection is performed based on the residual energy of the sensor nodes. However, due to dynamic cluster formation, the distance between CH and BS is faraway and some of the cluster nodes are also faraway from the CHs; it increases the communication cost. Later, a lot of modified LEACH protocols have been proposed to enhance the network lifetime and have been reviewed in [17].

LEACH protocol has been improved as power-efficient gathering in information systems (PEGASIS) [31], a multi-hop chain-based protocol, where every node aids in transmitting and/or receiving the data from its neighbor node by forming the chain. The collected data are aggregated and carried from node to node. One of the nodes in the chain is selected as a leader; the leader node transfers data to the BS. PEGASIS performs better than LEACH by minimizing the number of transmissions from sensor nodes to BS and clustering overhead. However, data transmission delay is higher due to the large chain length.

Threshold-sensitive energy-efficient sensor network protocol (TEEN) [32] is a homogenous reactive routing protocol. In this approach, the process of CH selection is performed similar to LEACH; the data transmission varies from LEACH. The workings of TEEN are based on the thresholds, namely, Hard threshold (*H*T) and soft threshold (*S*T). However, the CH selection process is random and the size of the clusters is unequal; it causes an unbalanced energy consumption among the clusters. Network throughput is also decreased due to the threshold mechanism.

Hybrid energy-efficient distributed (HEED) protocol [33] has been proposed by Younis and Fahmy. It is a homogenous cluster-based routing protocol; CH selection is accomplished based on the probability function of residual energy and node degree. Later, HEED protocol is extended as the heterogeneous HEED to manage the routing in the heterogeneous network field. This protocol utilizes fuzzy logic model for the CH selection process; the parameters considered in the fuzzy logic model are node degree, distance, and remaining energy. Finally, direct data transmission is carried out between the CM and CH and between the CH and BS.

Qing et al. [34] have presented distributed energy-efficient clustering scheme (DEEC), a heterogeneous data collection protocol. The sensor nodes possess varied energy levels. The selection of CHs is done based on the probability ratio between the residual energy of the nodes and average energy of the whole network. The possibility of evolving a CH is higher for the nodes which possess more residual

#### *Data Collection Protocols in Wireless Sensor Networks DOI: http://dx.doi.org/10.5772/intechopen.93659*

layers, state information of the protocols is shared among all layers. Cross-layered protocol implementations significantly affect the system efficiency with respect to

*Wireless Sensor Networks - Design, Deployment and Applications*

In WSN, so many techniques are proposed to achieve energy efficiency, longer lifetime, fault tolerance. Low latency by different researchers are briefly explained in this section. Most of these solutions are designed based on different techniques such as clustering, network coding, duty cycling, aggregation, directional antennas,

Low-energy adaptive clustering hierarchy (LEACH) routing strategy was proposed by Heinzelman et al. [29]. It is a cluster-based routing algorithm to decrease energy consumption and improve the network lifetime. In this protocol, the network is divided into clusters; each cluster contains a set of CMs and a leader called CH. The CMs send the data to its respective CH; CHs communicate the collected data to the BS and are elected in a random and distributed manner. Subsequently, LEACH was altered to LEACH-C [30], a centralized approach. The process of CH selection is performed based on the residual energy of the sensor nodes. However, due to dynamic cluster formation, the distance between CH and BS is faraway and some of the cluster nodes are also faraway from the CHs; it increases the communication cost. Later, a lot of modified LEACH protocols have been proposed to

LEACH protocol has been improved as power-efficient gathering in information systems (PEGASIS) [31], a multi-hop chain-based protocol, where every node aids in transmitting and/or receiving the data from its neighbor node by forming the chain. The collected data are aggregated and carried from node to node. One of the nodes in the chain is selected as a leader; the leader node transfers data to the BS. PEGASIS performs better than LEACH by minimizing the number of transmissions from sensor nodes to BS and clustering overhead. However, data transmission delay

Threshold-sensitive energy-efficient sensor network protocol (TEEN) [32] is a homogenous reactive routing protocol. In this approach, the process of CH selection is performed similar to LEACH; the data transmission varies from LEACH. The workings of TEEN are based on the thresholds, namely, Hard threshold (*H*T) and soft threshold (*S*T). However, the CH selection process is random and the size of the clusters is unequal; it causes an unbalanced energy consumption among the clusters. Network throughput is also decreased due to the threshold

Hybrid energy-efficient distributed (HEED) protocol [33] has been proposed by Younis and Fahmy. It is a homogenous cluster-based routing protocol; CH selection is accomplished based on the probability function of residual energy and node degree. Later, HEED protocol is extended as the heterogeneous HEED to manage the routing in the heterogeneous network field. This protocol utilizes fuzzy logic model for the CH selection process; the parameters considered in the fuzzy logic model are node degree, distance, and remaining energy. Finally, direct data transmission is carried out between the CM and CH and between the CH and BS.

Qing et al. [34] have presented distributed energy-efficient clustering scheme (DEEC), a heterogeneous data collection protocol. The sensor nodes possess varied energy levels. The selection of CHs is done based on the probability ratio between the residual energy of the nodes and average energy of the whole network. The possibility of evolving a CH is higher for the nodes which possess more residual

enhance the network lifetime and have been reviewed in [17].

the energy and lifetime.

**4. Existing routing techniques**

sink mobility, and cross-layer solutions.

is higher due to the large chain length.

mechanism.

**90**

energy. However, the probabilistic CH selection process prompts unequal clusters which leads to more energy dissipation.

Periodic, event-driven, and query-based protocol (PEQ) and its variation, CPEQ, were proposed by Boukerche et al. [35] in 2006. PEQ is designed for achieving the following: low latency, high reliability, and broken path reconfiguration. CPEQ is a cluster-based routing protocol. The publish/subscribe mechanism is used to broadcast requests throughout the network.

Genetic algorithm-based clustering approach (LEACH-GA) was introduced in literature [36] to predict the optimal probability for electing an optimal number of CHs. This approach improved the network lifetime by achieving energy-efficient clustering.

Artificial bee colony (ABC)-based algorithm [37] has been proposed, where the CH selection is performed by adopting the ABC algorithm. ABC algorithm improves the clustering process by employing efficient and fast search feature to select the CHs. Both cluster members to CH, and CH to BS communication is performed by direct data communication. However, this protocol does not consider the coverage of the CH and it prompts more energy dissipation.

Ant colony algorithm for data aggregation (DAACA) has been introduced by Chi Lin et al. [38]. This approach comprises of three phases: initialization, packets transmissions, and operations on pheromones. In the transmission phase, the next hop is dynamically selected by determining the number of pheromones of neighbor nodes and the residual energy. Pheromones' adjustments are accomplished for every specified number of rounds of data transmissions. Besides, various pheromones' adjustment strategies such as basic-DAACA, elitist strategy-based DAACA (ES-DAACA), maximum- and minimum-based DAACA (MM-DAACA), and ant colony system-based DAACA (ACS-DAACA) are utilized to enhance the network lifetime. However, duplication packets are transmitted from sink nodes to initialize the network, which causes higher energy depletion in the network.

Lusheng Miao et al. [39] have introduced network coding to resolve the issues in gradient-based routing (GBR) scheme, such as broadcasting of interest messages by sink node which prompts duplication of packets, which causes more energy dissipation, and point-to-point message delivery forces more data retransmissions due to the unstable network environment in WSNs. The authors have proposed network coding for GBR (GBR-NC) to implement energy-efficient broadcasting algorithm which reduces network traffic. Further, the authors have presented two competing algorithms such as GBRC and auto-adaptable GBR-C to minimize the data retransmissions.

In 2012, Rashmi Ranjan Rout et al. [40] proposed an energy-efficient triangular (regular) deployment strategy with directional antenna (ETDDA), where 2-connectivity pattern has been utilized. This pattern is accomplished by aligning the directional antenna beam of a sensor node in a specified direction toward the sink. Data forwarding depends on network coding for many-to-one traffic flow from sensor nodes to sink. The proposed approach ensures energy efficiency, robustness, and better connectivity in communicating data to the sink.

Ming Ma et al. [41] have put forward a mobility-based data-gathering mechanism for WSNs. A mobile data collector (M-collector), perhaps a mobile robot or a vehicle, is implemented with a transceiver and battery. The M-collector travels through a specific path and determines the sensor nodes, which comes within its communication range while traversing. Then, it collects the data from the sensor nodes in the single-hop communication and forward the data to the base station without delays. Hence, this mechanism improves the lifetime of the sensor nodes. The authors have primarily focused to reduce the length of each data-gathering tour called as single-hop data-gathering problem (SHDGP).

Roja Chandanala et al. [42] have presented a mechanism to preserve energy in flood-based WSNs by applying two techniques: network coding and duty cycling. Initially, the authors have proposed DutyCode, a cross-layer technique, where Random Low Power Listening MAC protocol was devised to implement packet streaming. The authors have applied flexible intervals for randomizing sleep cycles. Further, an enhanced coding scheme was proposed, which selects appropriate network coding schemes for nodes to remove redundant packet transmissions.

aggregates sensed data from the sensor nodes using compressive sensing. A random projection root node with compressive data-gathering aids to achieve a balanced energy consumption all over the network. Besides, eMSTP has been introduced which is the extended version of MSTP; the sink node in the eMSTP behaves like a

Ahmad et al. [49] proposed a protocol called Away Cluster Heads with Adaptive

A genetic algorithm-based approach [50] has been applied for binding the sensor nodes to the sink nodes, considering the balanced load among the sink nodes. The authors have presented a fitness function which takes into account the communication cost between the sensor node and sink node and the processing cost of the sink node. This approach dealt with the nodes which do not have any sink node in

In 2015, energy-aware routing (ERA) [51] has been proposed, where the residual

PSO-based approach for energy-efficient routing and clustering has been proposed in literature [55]. Routing path between the gateway to BS is determined using the PSO technique. This approach provides energy-efficient routing and energy-balanced clustering. This approach is fault tolerant when CHs failed. But, nodes that are not reachable to any gateway are left out from communication. Gravitational search algorithm for cluster head selection and routing (GSA-CHSR) [56] has been proposed. The authors have used GSA algorithm for deciding the optimal number of CH nodes and finding the optimal route between CH and BS. This approach improves performance parameters such as network lifetime, residual energy, and the number of packets received at BS. However, this approach incurs

Guravaiah and Leela Velusamy [57] proposed a routing protocol titled hybrid cluster communication using RFD (HCCRFD) based on clustering using river formation dynamics-based multi-hop routing protocol (RFDMRP) [58]. This protocol increases the network lifetime. However, load balancing among CHs is not considered and clustering overhead exists due to periodic CH selection. Further, the authors have proposed a balanced energy and adaptive cluster head selection algorithm (BEACH) [59]. They considered the parameters such as degree of the node, remaining energy of the node, the distance from BS to the sensor node, and the average transmission

energy of the CHs and the intra-cluster distance are the parameters taken into account for the process CH selection. However, the parameters such as the optimal number of CHs, network density, and cluster coverage are not considered in the CH selection process; hence this causes uneven energy consumption in every cluster. A GSA-based approach titled GSA-based energy-efficient clustering (GSA-EEC) was presented by literature [52]. For the fitness value calculation, the parameters considered are the distance between the sensor nodes and gateways, the distance between gateways and sink, and residual energy of gateways. This approach improves the network lifetime and total energy consumption. Further, they introduced a routing strategy titled gravitational search algorithm-based multi-sink placement (GSA-MSP) for placing multiple sinks on the sensor network [53]. Priority-based WSN clustering of multiple sink scenario using artificial bee colony [54] has been proposed. The fitness function in this approach considers the energy of the sink node and the sensor node, the distance between the sensor node

network lifetime. However, global node information is required for communicating data and the size of the clusters is also unequal. As the node distribution among the clusters is unequal, this approach prompts to variation in energy depletion ratio

) and this mechanism has been utilized for enhancing

root node for all MST.

Clustering Habit (ACH<sup>2</sup>

among clusters in the network.

*Data Collection Protocols in Wireless Sensor Networks DOI: http://dx.doi.org/10.5772/intechopen.93659*

their communication range.

to the sink node, and the priority of each sink.

clustering overhead for selecting the optimal set of CHs.

distance to its neighbors for achieving the load-balanced clustering.

**93**

Meikang Qiu et al. [43] have introduced informer homed routing (IHR), which is a novel energy-aware cluster-based fault-tolerance mechanism for WSN. IHR is the foremost variant of dual homed routing (DHR) fault-tolerance mechanism. In this mechanism, each sensor node is attached with two cluster heads called primary cluster head (PCH) and backup cluster head (BCH). Sensor nodes deliver the data to PCH rather than sending simultaneously to both PCH and BCH. In each round, BCH probes the PCH to identify whether the PCH is active or not using the beacon message. In three continuous rounds, if BCH cannot receive any beacon message from PCH, then BCH will declare that the PCH has failed and it informs to sensor nodes to transmit data to BCH. Hence, IHR provides an energy-efficient faulttolerance mechanism to prolong the lifetime of the network. However, cluster head selection process is containing more overhead.

A novel evolutionary approach for load-balanced clustering problem is presented in literature [44]. CH (gateway) formation is performed using a novel genetic algorithm. This algorithm differs from the traditional GA in the initial population and mutation phase. This approach balances the load among the gateways and it is energy efficient. However, sensor nodes that are not reachable to any gateway are left out from communication. Later, they extended a differential evolution-based approach [45] used for clustering the nodes with gateways (CHs) in a load-balanced way to ensure load balancing among the gateways and energy efficiency. But, this approach used single-hop communication between the gateway to BS and hence it may not be suitable for long-distance communication.

Flow partitioned unequal clustering (FPUC) algorithm has been proposed by Jian Peng et al. [46] to attain an enhanced network lifetime and coverage. FPUC has two phases: clustering and flow partition routing. In the clustering phase, cluster head is decided based on the higher residual energy and larger overlapping degree of sensor nodes. In the flow partition routing phase, cluster head collects the data from the member nodes and aggregates the data into a single packet; then it forwards the data to the sink through gateway nodes depending on residual energy The flow-partitioned routing phase has two subphases: dataflow partitioning phase and relaying phase. In the dataflow partitioning phase, the cluster head segments the dataflow into various smaller packets and then delivers these packets to its gateway nodes. In the relaying phase, gateways communicate the received data to the next hop with minimum cost.

An energy-efficient adaptive data aggregation strategy using network coding (ADANC) to attain improved energy efficiency in a cluster based duty-cycled WSN has been introduced by Rashmi Ranjan Rout et al. [47]. Network coding minimizes the network traffic inside a cluster and duty cycling scheme has been used in the cluster network to prolong network lifetime.

Dariush Ebrahimi and Chadi Assi [48] have presented a new compressive data gathering method. This method utilizes compressive sensing (CS) and random projection techniques to enhance the lifetime of large WSNs. The authors preferred the method to equally distribute the energy throughout the network rather than decreasing the overall network energy consumption. In the proposed data-gathering method, minimum spanning tree projection (MSTP) has been adopted. MSTP creates several minimum spanning trees (MSTs) and each root node of the tree

Roja Chandanala et al. [42] have presented a mechanism to preserve energy in flood-based WSNs by applying two techniques: network coding and duty cycling. Initially, the authors have proposed DutyCode, a cross-layer technique, where Random Low Power Listening MAC protocol was devised to implement packet streaming. The authors have applied flexible intervals for randomizing sleep cycles. Further, an enhanced coding scheme was proposed, which selects appropriate network coding schemes for nodes to remove redundant packet transmissions.

*Wireless Sensor Networks - Design, Deployment and Applications*

Meikang Qiu et al. [43] have introduced informer homed routing (IHR), which is a novel energy-aware cluster-based fault-tolerance mechanism for WSN. IHR is the foremost variant of dual homed routing (DHR) fault-tolerance mechanism. In this mechanism, each sensor node is attached with two cluster heads called primary cluster head (PCH) and backup cluster head (BCH). Sensor nodes deliver the data to PCH rather than sending simultaneously to both PCH and BCH. In each round, BCH probes the PCH to identify whether the PCH is active or not using the beacon message. In three continuous rounds, if BCH cannot receive any beacon message from PCH, then BCH will declare that the PCH has failed and it informs to sensor nodes to transmit data to BCH. Hence, IHR provides an energy-efficient faulttolerance mechanism to prolong the lifetime of the network. However, cluster head

A novel evolutionary approach for load-balanced clustering problem is presented in literature [44]. CH (gateway) formation is performed using a novel genetic algorithm. This algorithm differs from the traditional GA in the initial population and mutation phase. This approach balances the load among the gateways and it is energy efficient. However, sensor nodes that are not reachable to any gateway are left out from communication. Later, they extended a differential evolution-based approach [45] used for clustering the nodes with gateways (CHs) in a load-balanced way to ensure load balancing among the gateways and energy efficiency. But, this approach used single-hop communication between the gateway

to BS and hence it may not be suitable for long-distance communication.

Flow partitioned unequal clustering (FPUC) algorithm has been proposed by Jian Peng et al. [46] to attain an enhanced network lifetime and coverage. FPUC has two phases: clustering and flow partition routing. In the clustering phase, cluster head is decided based on the higher residual energy and larger overlapping degree of sensor nodes. In the flow partition routing phase, cluster head collects the data from the member nodes and aggregates the data into a single packet; then it forwards the data to the sink through gateway nodes depending on residual energy The flow-partitioned routing phase has two subphases: dataflow partitioning phase and relaying phase. In the dataflow partitioning phase, the cluster head segments the dataflow into various smaller packets and then delivers these packets to its gateway nodes. In the relaying phase, gateways communicate the received data to the next

An energy-efficient adaptive data aggregation strategy using network coding (ADANC) to attain improved energy efficiency in a cluster based duty-cycled WSN has been introduced by Rashmi Ranjan Rout et al. [47]. Network coding minimizes the network traffic inside a cluster and duty cycling scheme has been used in the

Dariush Ebrahimi and Chadi Assi [48] have presented a new compressive data gathering method. This method utilizes compressive sensing (CS) and random projection techniques to enhance the lifetime of large WSNs. The authors preferred the method to equally distribute the energy throughout the network rather than decreasing the overall network energy consumption. In the proposed data-gathering method, minimum spanning tree projection (MSTP) has been adopted. MSTP creates several minimum spanning trees (MSTs) and each root node of the tree

selection process is containing more overhead.

hop with minimum cost.

**92**

cluster network to prolong network lifetime.

aggregates sensed data from the sensor nodes using compressive sensing. A random projection root node with compressive data-gathering aids to achieve a balanced energy consumption all over the network. Besides, eMSTP has been introduced which is the extended version of MSTP; the sink node in the eMSTP behaves like a root node for all MST.

Ahmad et al. [49] proposed a protocol called Away Cluster Heads with Adaptive Clustering Habit (ACH<sup>2</sup> ) and this mechanism has been utilized for enhancing network lifetime. However, global node information is required for communicating data and the size of the clusters is also unequal. As the node distribution among the clusters is unequal, this approach prompts to variation in energy depletion ratio among clusters in the network.

A genetic algorithm-based approach [50] has been applied for binding the sensor nodes to the sink nodes, considering the balanced load among the sink nodes. The authors have presented a fitness function which takes into account the communication cost between the sensor node and sink node and the processing cost of the sink node. This approach dealt with the nodes which do not have any sink node in their communication range.

In 2015, energy-aware routing (ERA) [51] has been proposed, where the residual energy of the CHs and the intra-cluster distance are the parameters taken into account for the process CH selection. However, the parameters such as the optimal number of CHs, network density, and cluster coverage are not considered in the CH selection process; hence this causes uneven energy consumption in every cluster.

A GSA-based approach titled GSA-based energy-efficient clustering (GSA-EEC) was presented by literature [52]. For the fitness value calculation, the parameters considered are the distance between the sensor nodes and gateways, the distance between gateways and sink, and residual energy of gateways. This approach improves the network lifetime and total energy consumption. Further, they introduced a routing strategy titled gravitational search algorithm-based multi-sink placement (GSA-MSP) for placing multiple sinks on the sensor network [53].

Priority-based WSN clustering of multiple sink scenario using artificial bee colony [54] has been proposed. The fitness function in this approach considers the energy of the sink node and the sensor node, the distance between the sensor node to the sink node, and the priority of each sink.

PSO-based approach for energy-efficient routing and clustering has been proposed in literature [55]. Routing path between the gateway to BS is determined using the PSO technique. This approach provides energy-efficient routing and energy-balanced clustering. This approach is fault tolerant when CHs failed. But, nodes that are not reachable to any gateway are left out from communication.

Gravitational search algorithm for cluster head selection and routing (GSA-CHSR) [56] has been proposed. The authors have used GSA algorithm for deciding the optimal number of CH nodes and finding the optimal route between CH and BS. This approach improves performance parameters such as network lifetime, residual energy, and the number of packets received at BS. However, this approach incurs clustering overhead for selecting the optimal set of CHs.

Guravaiah and Leela Velusamy [57] proposed a routing protocol titled hybrid cluster communication using RFD (HCCRFD) based on clustering using river formation dynamics-based multi-hop routing protocol (RFDMRP) [58]. This protocol increases the network lifetime. However, load balancing among CHs is not considered and clustering overhead exists due to periodic CH selection. Further, the authors have proposed a balanced energy and adaptive cluster head selection algorithm (BEACH) [59]. They considered the parameters such as degree of the node, remaining energy of the node, the distance from BS to the sensor node, and the average transmission distance to its neighbors for achieving the load-balanced clustering.

An approach called LEACH-PSO [60] has been proposed for improving the network lifetime by selecting an optimum number of CHs in every round. In this work, the particle swarm optimization method is integrated with LEACH for

Energy efficiency,

FCR algorithm Energy efficiency Energy balancing is not ensured

reliable

**Sl. No. Algorithm Techniques used Metrics Drawbacks**

Clustering using genetic algorithm

Clustering (gateways) using

multi-hop GSA

LEACH, RFD

Cuckoo search algorithm

hop, spanning tree

PSO

23 GSA-CHSR [56] Clustering using

24 HCCRFD [57] Clustering using

28 MLBC [64] MOPSO, multi-

throughput

Clustering Energy efficiency, lifetime

25 BEACH [59] Clustering, RFD Energy efficiency CH selection overhead 26 GSA-EC [61] GSA, multi-hop Network lifetime Clustering overhead

21 GSA-EEC [52] Clustering, GSA Energy efficiency Load balancing among CHs not

Global node information for data transmission, cluster head selection overhead

Optimum number of CHs is not

any gateway are not considered

Nodes that are not reachable to any CH are not considered

Energy efficiency Single-hop communication

considered

considered

Energy efficiency Nodes that are not reachable to

Energy efficiency No load-balanced clustering

Energy efficiency Load balance among CHs not considered

Energy efficiency Clustering overhead

between sink and BS

18 ACH2 [49] Clustering Lifetime,

*Data Collection Protocols in Wireless Sensor Networks DOI: http://dx.doi.org/10.5772/intechopen.93659*

19 GA-based

20 Energy-aware routing (ERA) [51]

22 PSO-based routing [55]

27 Cuckoo and

29 Energy-efficient and delay-less routing [65]

*Existing protocols for data collection.*

harmony searchbased routing [63]

approach [50]

Energy-efficient CH-based GSA (GSA-EC) [61] for finding an optimal set of CHs using GSA has been proposed. To balance the energy consumption, one-hop clusters are formed using an optimal set of CHs. The authors have also proposed the hybrid approach of PSO and GSA. This approach increases network lifetime and network stability. However, this approach also incurs clustering overhead for selecting the optimal set of CHs. Later, Kavitha et al. [62] used GSA for assigning sensor nodes to an appropriate cluster head (CH) in a load-balanced way such that it reduces the energy consumption and hence enhances the lifetime of a network. Integrated clustering and routing protocol using cuckoo and harmony search has

been proposed in literature [63]. This approach has adopted the cuckoo search algorithm for CH selection. Residual energy, degree of a node, intra-cluster distance, and coverage ratio are the parameters for developing fitness function used in CH selection. The harmony search algorithm has been employed for routing from

forming the clusters.

**Table 2.**

**95**

*Data Collection Protocols in Wireless Sensor Networks DOI: http://dx.doi.org/10.5772/intechopen.93659*

#### **Table 2.**

**Sl. No. Algorithm Techniques used Metrics Drawbacks**

scalability

scalability

lifetime

energy

Energy, throughput, and low latency

Energy, low latency, scalability, and throughput

Fault tolerance and energy

Energy efficiency, lifetime

Energy, low latency, and lifetime

Energy, network lifetime

Fault tolerance, low latency, and energy

Network lifetime,

3 TEEN [32] Clustering Lifetime Same as LEACH, network

4 HEED [33] Clustering Lifetime Direct transmission,

Lifetime Network throughput decreased

consumption

consumption

round

calculations

collector

Energy Transition between active and

Energy efficiency Single-hop communication

Energy efficiency Single-hop communication

calculations

Traffic overhead

Not considering RE for CH selection, unbalanced energy

throughput decreased

heterogeneity is not considered

Direct transmission, unequal size of clusters, unbalanced energy

Bottleneck problem nearer to sink node, overhead in pheromones calculation at each

Overhead in optimal antenna pattern and transmission power

High control overhead to maintain the trajectory path, packet loss due to speed of data

sleep states overhead

reliability problems

between the CH to BS

between the CH and BS

CH selection overhead

Cluster maintenance overhead

Computational overhead in MST

Node unable to find CH, leads to

Transmission delays in competing algorithm

construction

*Wireless Sensor Networks - Design, Deployment and Applications*

2 LEACH [30] Clustering Lifetime,

5 DEEC [34] Clustering Lifetime,

Clustering and publish/subscribe mechanism

Network coding and multi-hop

antennas, network coding, and multi-

and single-hop

Network coding, duty cycling, and multi-hop

multi-hop

Clustering, genetic algorithm

Clustering using differential evolution

aggregation, and multi-hop

network coding, and duty cycling

using compressive

sensing

hop

7 DAACA [38] Clustering, ACA Energy, network

1 PEGASIS [31] Chain

6 PEQ and CPEQ [35]

8 GBR-NC, GBR-C, and autoadaptable GBR-C

[39]

11 DutyCode and ECS [42]

> evolutionary approach [44]

13 Novel

14 DE-based clustering algorithm [45]

**94**

9 ETD-DA [40] Directional

10 SHDGP [41] Mobile collectors

12 IHR [43] Clustering and

15 FPUC [46] Clustering, data

17 MSTP [48] Data aggregation

16 ADANC [47] Clustering,

*Existing protocols for data collection.*

An approach called LEACH-PSO [60] has been proposed for improving the network lifetime by selecting an optimum number of CHs in every round. In this work, the particle swarm optimization method is integrated with LEACH for forming the clusters.

Energy-efficient CH-based GSA (GSA-EC) [61] for finding an optimal set of CHs using GSA has been proposed. To balance the energy consumption, one-hop clusters are formed using an optimal set of CHs. The authors have also proposed the hybrid approach of PSO and GSA. This approach increases network lifetime and network stability. However, this approach also incurs clustering overhead for selecting the optimal set of CHs. Later, Kavitha et al. [62] used GSA for assigning sensor nodes to an appropriate cluster head (CH) in a load-balanced way such that it reduces the energy consumption and hence enhances the lifetime of a network.

Integrated clustering and routing protocol using cuckoo and harmony search has been proposed in literature [63]. This approach has adopted the cuckoo search algorithm for CH selection. Residual energy, degree of a node, intra-cluster distance, and coverage ratio are the parameters for developing fitness function used in CH selection. The harmony search algorithm has been employed for routing from

CH to BS. It is energy efficient and balances the energy consumption of the network. Further, it minimizes the un-cluster nodes, that is, nodes that are not within the communication range of any CH are minimized. But, load balancing among CHs is not considered.

range in large size (area) cluster and faraway nodes consume more energy in

• The sizes of the clusters formed in the existing protocols are not equal. This

• Density of network was not considered as a parameter in CH selection process. This impacts the formation of unequal sized clusters and leads to uneven

• Uneven distribution of load on CH and the intra- and inter-communication

• Security is the major parameter need to be considered in military applications.

• In recent years, more popularity gain is deterministic rather than probabilistic-

• Heterogeneous network in WSN is also an important problem due to different

In this chapter, classification of data collection routing protocols in WSN has been thoroughly discussed. Various techniques such as clustering, duty cycling, aggregation, network coding, sink mobility, and cross-layered solutions, and directional antennas have been utilized by data collection routing protocols for attaining long lifetime, energy efficiency, fault tolerance, and low latency. These techniques are reviewed briefly in this chapter. Finally, this chapter demonstrates a paramount comparison among the existing approaches applicable on data collection process in WSN. Future directions of routing protocols are presented at the end of

Considering security, energy efficiency is still challenging issues.

based clustering due to reliability. However, CH selection and other

computational complexity are still a challenging area.

communication and processing capabilities.

leads to unbalanced energy consumption among the clusters.

large size (area) cluster.

*Data Collection Protocols in Wireless Sensor Networks DOI: http://dx.doi.org/10.5772/intechopen.93659*

distribution of load to CH.

path length is more.

**6. Conclusions**

this chapter.

**97**

Multi-objective load-balancing clustering technique (MLBC) [64] has been proposed for clustering in WSN by adopting multi-objective PSO (MOPSO) strategy which is used for CH selection. The shortest-path tree (SPT) for loop-free routing is created using Dijkstra's algorithm. It is energy efficient and reliable. But, the nodes that are not reachable to any CH are not considered.

In energy-efficient and delay-less routing [65], CH selection is performed using firefly with cyclic randomization (FCR) algorithm. This approach reduces transmission delay in the network. But, this approach has not considered energy balancing.

Overall comparison of above routing protocols are shown in **Table 2** with the techniques used, metrics considered, and drawbacks of each solution.


**1. Introduction**

Titanium dioxide (TiO2) is one of the main food additives used for its coloring and opacifying properties to improve the appearance and taste of processed foods. Food-grade TiO2 is found in over 900 food products such as pastries, sauces, ice-creams, candies, chocolates, and chewing gum. In foods, TiO2 is commonly reported as E171. It is also referred to as CI 77891 when used in cosmetics and toothpaste as a white colorant [1]. E171 consists of a wide range of particle TiO2 sizes and can contain up to 36% nanosized TiO2 particles, i.e., less than 100 nm in diameter [2,3]. Compared with their macroscopic counterparts, nanoparticles (NPs) can easier pass through the body's cells and then into the bloodstream and internal organs such as liver, kidney, and lung tissues. Daily, the human

**Citation:** Rinninella, E.; Cintoni, M.; Raoul, P.; Mora, V.; Gasbarrini, A.; Mele, M.C. Impact of Food Additive Titanium Dioxide on Gut Microbiota Composition, Microbiota-Associated Functions, and Gut Barrier: A Systematic Review of In Vivo Animal Studies. *Int. J. Environ. Res. Public Health* **2021**, *18*, 2008. https:// doi.org/10.3390/ijerph18042008

Academic Editors: Diana María Cardona Mena and Pablo Roman

Received: 26 December 2020 Accepted: 13 February 2021 Published: 19 February 2021

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

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

dietary exposure dose of TiO2 NPs can reach one to four micrograms per kilogram body weight per day (μg per kg bw per day) [3]. In 1966, the Food and Drug Administration (FDA) approved the use of food-grade TiO2 referred to as INS171, specifying that the quantity of TiO2 must not exceed one percent by weight of the food [4]. In Europe, in 2006, the European Food Safety Authority (EFSA) authorized the use of E171 in food concluding that E171 is safe for consumers, having margins of safety (MoS) of 2.25 mg per kg bw per day [5,6]. However, TiO2 NPs raise health concerns among the scientific community and governments given their potential to cross the gut barrier and distribute to other organs eliciting immunological response. In June 2018, the EFSA evaluated four new in vivo and in vitro studies [7–10] assessing potential toxicities and reaffirmed the safety of E171 [11]. In April 2019, the French Agency for Food, Environmental and Occupational Health and Safety (ANSES) published a review suggesting a genotoxic and carcinogenic potential even if further in vivo mammalian studies are warranted to confirm or rule out these hypotheses [12]. As requested by the European Commission, EFSA provided urgent scientific and technical review regarding the opinion issued by ANSES [13]. The EFSA concluded that the latest ANSES opinion does not identify any major new findings that would overrule the conclusions made in the previous two scientific opinions in 2016 and 2018. The latest ANSES opinion reiterated the previously identified uncertainties and emphasized that there was still not enough data available to carry out a proper assessment of the risks associated with the food use of E171. EFSA considered this recommendation should be revisited once the ongoing work on the physicochemical characterization of E171 will be completed. In January 2020, France has adopted a decree to ban the use of E171 in foods as a precautionary measure to protect consumers' health.

In a scientific context of "microbiota revolution", potential health risks of TiO2 NPs and their impact on the intestinal tract and the gut microbiota are increasingly being studied. Gut microbiota is composed of millions of bacterial species that bi-directionally interact with the host in the intestinal tract, regulating the development of immune cells. Alterations in the abundance and composition of intestinal microbiota, known as dysbiosis, are associated with host health such as brain function, lipid metabolism, immune responses, and development of diseases [14]. Recent studies reported adverse effects of in vitro exposure of intestinal epithelial cells to E171 [9,15,16]. Indeed, TiO2 NPs could damage microvilli structure and alter epithelial integrity [17,18]. TiO2 NPs can be internalized and can cross the epithelial barrier to enter the bloodstream and potentially affect the function of distant organs, such as the liver [19]. Moreover, in vitro, NPs have the potential to negatively affect intestinal functions and gut homeostasis associated with gut microbiota [20]. New evidence from numerous recent animal studies has emerged highlighting the effects of various physiological doses of TiO2 NPs on gut microbiota composition and gut homeostasis. Such evidence has not yet been systematically reviewed. Hence, we sought to systematically review current evidence from in vivo animal models to disentangle the TiO2 effects on the gut microbiome composition and functions.


**2. The autophagy process**

Eukaryotic cells digest their cytoplasmic content through different processes that come under the general term autophagy (from the Greek words *auto* meaning "self" and *paghein* meaning "to eat"). Autophagy includes different forms of digestive pathways such as macroautophagy, microautophagy, chaperone-mediated autophagy, and noncanonical autophagy. Generally, the term autophagy refers to macroautophagy, and this process depends on specialized autophagy-related proteins (ATGs) to digest different targets, such as organelles, large aggregates of proteins, and microorganisms. Autophagy also plays a key role in direct microorganisms and virus clearance, in the control of inflammation through the inhibition of inflammasome, in antigen presentation, in regulating T cell homeostasis, and the secretion of immune mediators [6]. It is worth nothing that autophagy impairment plays a crucial role in several diseases, in particular proteopathies, such as Parkinson's [7] and Huntington's disease [8].

As analytically described by Codogno et al. [9], there are four types of autophagy:

To date, several autophagy-related genes (*ATG*s) have been described and exert a finely coordinated function at different stages of the pathway. It is widely accepted that autophagy consists of six sequential steps: (1) initiation; (2) nucleation or phagophore formation; (3) ATG5-ATG12 conjugation, interaction with ATG16L, and multimerization at the phagophore; (4) LC3 processing and insertion into the nascent autophagosome; (5) capture of random/selective targets for degradation; and (6) fusion of the autophagosome with the lysosome.

**57**

disease complications.

**4. Non-dietary therapies**

*The Emerging Role of the Autophagy Process in Children with Celiac Disease: Current Status…*

Autophagy plays a crucial role in the pathogenesis of several autoimmune diseases. In particular, in Crohn's disease, an inflammatory bowel disease is caused by a combination of environmental, immune, and bacterial factors in genetically susceptible individuals. It has been demonstrated that genetic polymorphisms in the *ATG16L* and *IRGM* autophagy-related genes lead to a strong predisposition for the development of Crohn's disease [10]. Despite this significant association, the role played by the ATG16L protein in the disease pathogenesis is still under debate. In particular, the ATG16L protein is known to suppress the inflammatory process, as demonstrated in Atg16L-deficient mice, which were find to be highly susceptible to colitis induced by dextran sulfate sodium. Subsequently the symptoms developed by these mice were effectively treated with injections of anti-IL-1β and IL-18 antibodies [11]. Recently, nucleotide polymorphisms within the key regulatory autophagy gene *ULK1* have been shown to increase susceptibility to Crohn's disease, thus demonstrating that autophagy might contribute to the pathogenesis of this disease [12]. Similarly, the ATG5 protein, another essential component of the autophagic machinery, is implicated in the development of systemic lupus erythematosus (SLE), multiple sclerosis (MS), and rheumatoid arthritis (RA). SLE is an autoimmune disease in which the patient's immune system attacks healthy tissues. Different single nucleotide polymorphisms (SNPs), identified near and within the *ATG5* locus, are associated with SLE initiation and/or development, although the pathogenetic mechanisms involved are still unknown. In another study, it was demonstrated that T cells in SLE patients are autoreactive and autophagy promotes their survival and contributes to their persistence in autoimmune conditions [13]. MS is a demyelinating disease that affects the brain and the spinal cord. Changes in the expression of the ATG5 protein correlates also with immune-mediated myelin injury in MS-derived mice and in affected patients. Specifically, ATG5 is overexpressed in circulating T cells of relapsing–remitting MS patients compared with healthy controls. ATG5 altered expression seems to extend T cell survival and proliferation during active disease; moreover, ATG5 expression profiles correlate with the severity of the disease in mice models [14]. In RA, anti-citrullinated protein antibodies are the most powerful biomarkers in the diagnosis of this disease. During inflammation, the arginine residues of self-proteins are converted to citrulline (a nonessential alpha amino acid) by the peptidylarginine deiminase enzyme, in a process known as citrullination, thus leading to an altered immune response. Presentation of these peptides is blocked after treatment with 3-methyladenine, an autophagy modulator drug, or by reducing ATG5 protein expres-

*DOI: http://dx.doi.org/10.5772/intechopen.80692*

**3. Autophagy and autoimmune diseases**

sion, confirming a key role of autophagy in RA pathogenesis [15].

treatment (versus gluten-free diet) or GFD adjuvant.

is to offer a better quality of life to celiac patients.

The clinical spectrum of celiac disease is broad, and often it may be not so easy to discern between poor compliance, difficult acceptance of therapy, or presence of

It is important to emphasize experimental therapies, in terms of alternative

Recent advances in the "non-dietary" treatment of CD include engineering gluten-free grains, degrading immunodominant gliadin peptides, decreasing intestinal permeability, and inducing oral tolerance to gluten with a therapeutic vaccine.

As outlined above, there are many reasons behind the need to identify new therapeutic options for celiac disease, especially non-dietary therapies. The purpose *The Emerging Role of the Autophagy Process in Children with Celiac Disease: Current Status… DOI: http://dx.doi.org/10.5772/intechopen.80692*


Preface

In this book, *Neuromorphic Computing*, we embark on a captivating journey through the cutting-edge realm of brain-inspired computing systems that are revolutionizing the landscape of artificial intelligence and computational paradigms.

Neuromorphic computing, inspired by the intricate workings of the human brain, represents a groundbreaking approach to computational architectures. With an emphasis on mimicking the brain's neural networks, this emerging field has shown remarkable promise in addressing the inherent limitations of traditional computing systems. By harnessing the power of neural networks and synaptic connections, neuromorphic computing opens up new vistas of possibilities in data processing, pattern recognition, decision-making, and beyond.

This book is a comprehensive guide to understanding the principles, methodologies, and applications of neuromorphic computing. This book is for a diverse audience eager to explore the boundless potentials of brain-inspired computing.

Key features of this book include 1) foundational concepts, 2) neuromorphic circuits and systems; 3) emerging devices for neuromorphic computing; 4) deep learning, unsupervised learning, and sparse learning, 5) spiking neural network, recurrent neural network, and temporal neural network, and 6) memory computing.

In crafting this book, our goal is to provide readers with a comprehensive and insightful journey into the realm of neuromorphic computing. We have endeavored to make the content accessible to both beginners and experts, ensuring an enriching experience for everyone.

We extend our heartfelt gratitude to the researchers, scientists, and engineers who have contributed to the field of neuromorphic computing, pushing the boundaries of innovation. Their work continues to inspire and shape the landscape of artificial intelligence and computing systems.

> **Yang (Cindy) Yi** Bradley Department of Electrical and Computer Engineering, College of Engineering, Virginia Tech, Blacksburg, VA, USA


**5. Conclusions**

**Author Contributions:** Conceptualization, A.-M.G., M.J. and P.R.; Methodology, R.S., M.J. and P.R.; Validation, P.R., R.S. and M.J.; Formal Analysis, P.R., R.S. and M.J.; Investigation, P.R., R.S. and M.J.; Data Curation, P.R., R.S. and M.J.; Writing—Original Draft Preparation, P.R.; Writing—Review and Editing, A.-M.G., M.J., R.S. and P.R.; Visualization, P.R.; Supervision, A.-M.G. and P.R.; Project Administration, A.-M.G. and P.R.; Funding Acquisition, A.-M.G. All authors have read and agreed to the published version of the manuscript.

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

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** This study was financially supported by the IRT Jules Verne (Nantes, France) as part of the ADUSCOR research program.

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


**4. Frames and fusion frames in stroboscopic tomography. Generalizations to subalgebras**

As we have seen the concepts of frames and fusion frames appear in stroboscopic tomography in natural way. The conclusion is based on the discussed above polynomial representations of semigroups which describe evolutions of open systems. The possibility to represent the semigroup Φ(*t*) = exp(*t* **L**) in the form

$$\Phi(t) = \sum\_{k=0}^{\mu - 1} a\_k(t) \mathbb{L}^k,\tag{52}$$

where *μ* stands for the degree of the minimal polynomial of the superoperator **L** and *αk*(*t*), *k* = 0..., *μ* − 1, denote some functions of the eigenvalues of **L** gives the equality (32) as a sufficient condition for stroboscopic tomography. On the other hand, this equality means that the Krylov subspaces K*μ*(**L**, *Qi*), *i* = 1, . . . ,*r*, constitute a fusion frame in the Hilbert-Schmidt space B∗(H) of all observables. Moreover, this also means that the collection of vectors

$$f\_{jk} := \mathbb{L}^k \mathbb{Q}\_{j\nu} \tag{53}$$

for *j* = 1, . . . ,*r* and *k* = 0, 1, . . . , *μ* − 1, constitute a frame in B∗(H) and the system in question is (*Q*1,..., *Qr*)-reconstructible. In this case every element *Q* of the space B∗(H) can be represented as

$$Q = \sum\_{j,k} \langle F^{-1} f\_{jk} | Q \rangle f\_{jk} = \sum\_{j,k} \langle f\_{jk} | Q \rangle F^{-1} f\_{jk} \tag{54}$$

where *F* denotes the frame operator of the collection of vectors (53). One can say even more. If *Q* ∈ B∗(H) also has another representation *Q* = ∑*j*,*k cjk fjk* for some scalar coefficients *cjk*,

Quantum Systems 15

Fusion Frames and Dynamics of Open Quantum Systems 81

whole algebra B(H). In other words, we want to determine whether every element in B(H) can be represented in the form *π*(*Q*1,..., *Qr*), where *π* is a polynomial in noncommutative

Let us observe that according to the *fundamental theorem* if A is a subalgebra of the full complex

If a set of generators of A is known, then the above inequality can be verified by a finite number of arithmetic operations. The procedures possessing such property are called *effective*. A very important example of an effective procedure can be formulated when we discuss the problem of the existence a common one-dimensional invariant subspace for a pair of operators *Q*1, *Q*2. In other words, we ask about a common eigenvector for two operators *Q*1, *Q*2. An answer to this question is given by the following procedure. Let the symbol [*Q*1, *Q*2] denote, as usual, the commutator of the operators *Q*1, *Q*2. Then a common eigenvector for *Q*1 and *Q*2

dim A < dim B(H). (58)

2] , (59)

2], (61)

algebra B(H), then a nontrivial invariant subspace in H exists if and only if

K :=

*N* −1 *j*=1 *k*=1

Ker[*Qj*

where *N* = dim H, satisfies the condition dim K > 0 (this is the so-called Shemesh criterion

First of all, let us observe that if |*ψ*� is a common eigenvector of the operators *Q*1 and *Q*2, i.e.,

dim K > 0 means that the gist of the Shemesh condition is in observation that the subspace K is invariant under *Q*1 and *Q*2. Indeed, if |*ψ*� belongs to K, then by the definition of subspaces

and extend it to a basis in H. We then observe that there exists a nonsingular matrix *S* such that matrices *SQ*1*S*−1 and *SQ*2*S*−1 have block-triangular forms and the submatrices which correspond to subspace K commute. This means that these submatrices have a common eigenvector and therefore the same is true for *Q*1 and *Q*2. D. Shemesh observed that the

2] one can check that *Q*1|*ψ*�∈K and *Q*2|*ψ*�∈K. Now, let us choose a basis for K

1, *Qk*

*Q*1|*ψ*� = *α*|*ψ*� and *Q*2|*ψ*� = *β*|*ψ*�, (60)

2] for all *j*, *k* greater then 1. This fact and the inequality

exists if and only if the subspace K of H defined by

then |*ψ*� belongs to Ker[*Qj*

Ker[*Qj*

1, *Qk*

(Shemesh, 1984)). A short proof of this condition is possible.

1, *Qk*

condition dim K > 0 is equivalent to the singularity of the matrix

**M** :=

*N*−1 ∑ *j*=1 *k*=1

[*Qj* 1, *Qk* 2] ∗[*Qj* 1, *Qk*

where \* denotes complex conjugate transpose. For our purposes, on the basis of Burnside's theorem, more interesting is the case when matrices *Q*1, *Q*2 do not have common eigenvectors and the algebra *A*(*Q*1, *Q*2) generated by them coincides with B(H). This situation may be

variables.

*j* = 1, . . . ,*r* and *k* = 0, 1, . . . , *μ* − 1, then

$$\sum\_{j\mathbf{k}} |c\_{j\mathbf{k}}|^2 = \sum\_{j\mathbf{k}} |\langle F^{-1} f\_{j\mathbf{k}} | Q \rangle|^2 + \sum\_{j, \mathbf{k}} |c\_{j\mathbf{k}} - \langle F^{-1} f\_{j\mathbf{k}} | Q \rangle|^2. \tag{55}$$

It is obvious that every frame in finite-dimensional space contains a subset that is a basis. As a conclusion we can say that if { *fjk*} is a frame but not a basis, then there exists a set of scalars {*djk*} such that ∑*j*,*k djk fjk* = 0. Therefore, any fixed element *Q* of B∗(H) can also be represented as

$$Q = \sum\_{j,k} \left( \langle F^{-1} f\_{jk} | Q \rangle + d\_{jk} \right) f\_{jk}. \tag{56}$$

The above equality means that every *Q* ∈ B∗(H) has many representations as superpositions of elements from the set (53). But according to equality (55) among all scalar coefficients {*cjk*} for which

$$Q = \sum\_{j,k} c\_{jk} f\_{jk\prime} \tag{57}$$

the sequence {�*F*−1 *fjk*|*Q*�} has minimal norm. This is a general method in frame theory (Christensen, 2008) and at the same time the main observation connected with the idea of stroboscopic tomography.

In conclusion, one can say that the Krylov subspaces K*μ*(**L**, *Qi*) in the space B∗(H) generated by the superoperator **L** can be used in an effective way for procedures of stroboscopic tomography if they constitute appropriate fusion frames in this space.

#### **4.1 Generalizations to subalgebras**

Now, we will discuss some problems of reconstruction of quantum states when the Krylov subspaces playing such important role in the stroboscopic tomography are replaced by some subalgebras of the Hilbert-Schmidt space B(H). Just as the fundamental theorem of algebra ensures that every linear operator acting on a finite dimensional complex Hilbert space has a nontrivial invariant subspace, the *fundamental theorem of noncommutative algebra* asserts the existence of invariant subspaces of H for some families of operators from B(H). It is an obvious observation that an algebra generated by any fixed operator Q and the identity on H can not be equal to B(H). This statement is based on the Hamilton-Cayley theorem. However, already for two operators *Q*1, *Q*2 and the identity we can have Alg(*I*, *Q*1, *Q*2) =B(H) (for details cf. below).

In general, the famous Burnside's theorem states (cf. e.g. (Farenick, 2001)) that an operator algebra on a finite-dimensional vector space with no nontrivial subspaces must be the algebra of *all* linear operators. In the sequel we will use the following version of this theorem:

*Fundamental theorem of noncommutative algebras*. If A is a proper subalgebra of B(H) containing identity, and the dimension of the Hilbert space H is greater or equal to 2, then A has a proper nonzero invariant subspace in H (i.e., the subspace is invariant for all members Q of the algebra A).

We will apply the above theorem for the following problem. Given a set F = {*Q*1,..., *Qr*} of observables, we would like to establish conditions, when the operators *Q*1,..., *Qr* generate the 14 Will-be-set-by-IN-TECH

It is obvious that every frame in finite-dimensional space contains a subset that is a basis. As a conclusion we can say that if { *fjk*} is a frame but not a basis, then there exists a set of scalars {*djk*} such that ∑*j*,*k djk fjk* = 0. Therefore, any fixed element *Q* of B∗(H) can also be

�*F*−1 *fjk*|*Q*� + *djk*

The above equality means that every *Q* ∈ B∗(H) has many representations as superpositions of elements from the set (53). But according to equality (55) among all scalar coefficients {*cjk*}

the sequence {�*F*−1 *fjk*|*Q*�} has minimal norm. This is a general method in frame theory (Christensen, 2008) and at the same time the main observation connected with the idea of

In conclusion, one can say that the Krylov subspaces K*μ*(**L**, *Qi*) in the space B∗(H) generated by the superoperator **L** can be used in an effective way for procedures of stroboscopic

Now, we will discuss some problems of reconstruction of quantum states when the Krylov subspaces playing such important role in the stroboscopic tomography are replaced by some subalgebras of the Hilbert-Schmidt space B(H). Just as the fundamental theorem of algebra ensures that every linear operator acting on a finite dimensional complex Hilbert space has a nontrivial invariant subspace, the *fundamental theorem of noncommutative algebra* asserts the existence of invariant subspaces of H for some families of operators from B(H). It is an obvious observation that an algebra generated by any fixed operator Q and the identity on H can not be equal to B(H). This statement is based on the Hamilton-Cayley theorem. However, already for two operators *Q*1, *Q*2 and the identity we can have Alg(*I*, *Q*1, *Q*2)

In general, the famous Burnside's theorem states (cf. e.g. (Farenick, 2001)) that an operator algebra on a finite-dimensional vector space with no nontrivial subspaces must be the algebra

*Fundamental theorem of noncommutative algebras*. If A is a proper subalgebra of B(H) containing identity, and the dimension of the Hilbert space H is greater or equal to 2, then A has a proper nonzero invariant subspace in H (i.e., the subspace is invariant for all members Q

We will apply the above theorem for the following problem. Given a set F = {*Q*1,..., *Qr*} of observables, we would like to establish conditions, when the operators *Q*1,..., *Qr* generate the

of *all* linear operators. In the sequel we will use the following version of this theorem:

*Q* = ∑ *j*,*k*

*j*,*k*

|*cjk* − �*F*−1 *fjk*|*Q*�|2. (55)

*fjk*. (56)

*cjk fjk*, (57)

*j* = 1, . . . ,*r* and *k* = 0, 1, . . . , *μ* − 1, then

represented as

for which

stroboscopic tomography.

**4.1 Generalizations to subalgebras**

=B(H) (for details cf. below).

of the algebra A).

∑ *jk* |*cjk*|

2 = ∑ *jk*

> *Q* = ∑ *j*,*k*

tomography if they constitute appropriate fusion frames in this space.

whole algebra B(H). In other words, we want to determine whether every element in B(H) can be represented in the form *π*(*Q*1,..., *Qr*), where *π* is a polynomial in noncommutative variables.

Let us observe that according to the *fundamental theorem* if A is a subalgebra of the full complex algebra B(H), then a nontrivial invariant subspace in H exists if and only if

$$
\dim \mathcal{A} < \dim \mathcal{B}(\mathcal{H}).\tag{58}
$$

If a set of generators of A is known, then the above inequality can be verified by a finite number of arithmetic operations. The procedures possessing such property are called *effective*. A very important example of an effective procedure can be formulated when we discuss the problem of the existence a common one-dimensional invariant subspace for a pair of operators *Q*1, *Q*2. In other words, we ask about a common eigenvector for two operators *Q*1, *Q*2. An answer to this question is given by the following procedure. Let the symbol [*Q*1, *Q*2] denote, as usual, the commutator of the operators *Q*1, *Q*2. Then a common eigenvector for *Q*1 and *Q*2 exists if and only if the subspace K of H defined by

$$\mathcal{K} := \bigcap\_{\substack{j=1 \\ k=1}}^{N-1} \text{Ker} [\mathbb{Q}\_{1'}^j, \mathbb{Q}\_2^k] \, , \tag{59}$$

where *N* = dim H, satisfies the condition dim K > 0 (this is the so-called Shemesh criterion (Shemesh, 1984)). A short proof of this condition is possible.

First of all, let us observe that if |*ψ*� is a common eigenvector of the operators *Q*1 and *Q*2, i.e.,

$$Q\_1|\psi\rangle = \alpha|\psi\rangle \quad \text{and} \quad Q\_2|\psi\rangle = \beta|\psi\rangle,\tag{60}$$

then |*ψ*� belongs to Ker[*Qj* 1, *Qk* 2] for all *j*, *k* greater then 1. This fact and the inequality dim K > 0 means that the gist of the Shemesh condition is in observation that the subspace K is invariant under *Q*1 and *Q*2. Indeed, if |*ψ*� belongs to K, then by the definition of subspaces Ker[*Qj* 1, *Qk* 2] one can check that *Q*1|*ψ*�∈K and *Q*2|*ψ*�∈K. Now, let us choose a basis for K and extend it to a basis in H. We then observe that there exists a nonsingular matrix *S* such that matrices *SQ*1*S*−1 and *SQ*2*S*−1 have block-triangular forms and the submatrices which correspond to subspace K commute. This means that these submatrices have a common eigenvector and therefore the same is true for *Q*1 and *Q*2. D. Shemesh observed that the condition dim K > 0 is equivalent to the singularity of the matrix

$$\mathbf{M} := \sum\_{\substack{j=1\\k=1}}^{N-1} [\mathbb{Q}\_1^j, \mathbb{Q}\_2^k]^\* [\mathbb{Q}\_1^j, \mathbb{Q}\_2^k]\_{\prime} \tag{61}$$

where \* denotes complex conjugate transpose. For our purposes, on the basis of Burnside's theorem, more interesting is the case when matrices *Q*1, *Q*2 do not have common eigenvectors and the algebra *A*(*Q*1, *Q*2) generated by them coincides with B(H). This situation may be

Quantum Systems 17

Fusion Frames and Dynamics of Open Quantum Systems 83

In the case of qutrits, that is for a three-dimensional Hilbert space, one can show by direct calculation that if [*Q*1, *Q*2] is invertible and *ω*([*Q*1, *Q*2]) �= 0, where for *Q* ∈ B(H) the symbol *ω*(*Q*) denotes the linear term in the characteristic polynomial of *Q*, then one can construct an explicit basis for B(H). Indeed, if *Q*1, *Q*2 belong to B(H), and (dim H) = 3, then the determinant of the 9-dimensional matrix Ω build from vec transformations of

2, *Q*1*Q*2, *Q*2*Q*1, [*Q*1, [*Q*1, *Q*2]], [*Q*2, [*Q*2, *Q*1]] satisfies the equality

That is, if det([*Q*1, *Q*2]) �= 0 and *ω*(*Q*) �= 0, then the columns of the matrix Ω correspond to a

Of course, one can also use the Shemesh criterion to characterize pairs of generators for B(H),

Papers written by mathematicians are usually focused on characterization of various properties of discussed objects and search for necessary and sufficient conditions for desired conclusion to hold. Concrete constructions offen play a minor role. The problems of frames and fusion frames are no exceptions. The main purpose of this paper was to discuss properties of some Krylov subspaces in a given Hilbert space as a natural examples of fusion frames and

their applications in reconstruction of trajectories of open quantum systems.

Daubechies, I., Grossman. A., and Meyer, Y. (1986). *J. Math. Phys.* 27, 1271.

Farenick, D.R. (2001), *Algebras of Linear Transformations*, New York, Springer.

C. I. Byrnes and A. Lindquist, Amsterdam: Elsevier, p. 347.

Kovaˇcevi´c, J. and Chebira, A. (2008). *An Introduction to Frames*, Boston-Delft, NOW.

Jamiołkowski, A. (2010), *Journal of Physics: Conference Series* 213, 012002.

Hauseholder, A.S. (2009). *The Theory of Matrices in Numerical Analysis*, Dover Books. Heil, Ch. (Ed.) (2006). *Harmonic Analysis and Applications*, Boston, Birkhäuser.

Jamiołkowski, A. (1982). *On Observability of Classical and Quantum Stochastic Systems*, Toru ´n,

Jamiołkowski, A. (1986). *Frequency Domain and State Space Methods for Linear Systems*, Eds.

Casazza, P. G. & Kutyniok, G. (2004). Frames of subspaces, *Contemp. Math.* 345, 87.

Aslaksen, H. & Sletsjøe, A.B. (2009). *Lin. Algebra Appl.* 430, 1.

Casazza, P. G. et al. (2008). *Appl. Comput. Harmon. Anal.* 25, 114. Christensen, O. (2008). *Frames and Bases*, Boston, Birkhäuser.

Duffin, R. J. & Schaeffer, A. C. (1952). *Transactions AMS* 72, 341.

Fan, H., Hu, L. (2009) *Optics Comm.* 282, 932.

Gorini, V et al. (1976) *J. Math. Phys.* 17, 149.

Jamiołkowski, A. (1974). *Rep. Math. Phys.* 5, 415.

Jamiołkowski, A. (2000). *Rep. Math. Phys.* 46, 469.

Kossakowski, A. (1972) *Rep.Math. Phys.* 3, 247.

N. Copernicus Univ. Press, (in Polish). Jamiołkowski, A. (1983). *Internat. J. Theoret. Phys.* 22, 369.

det Ω = 9 det([*Q*1, *Q*2])*ω*([*Q*1, *Q*2]). (67)

**I**, *Q*1, *Q*2, *Q*2

basis for B(H).

where dim H = 3.

**5. Conclusions**

**6. References**

1, *Q*2

expressed by the following inequality

$$\det \mathbb{M} > 0,\tag{62}$$

which can be checked by an effective procedure, that is, by a finite number of arithmetic operations. It is obvious, that the matrix **M** is in general semipositive definite, and the above condition means the strict positivity of **M**.

#### **4.2 Examples**

In order to illustrate algebraic methods in reconstruction problems, we will discuss some algebraic procedures in low dimensional cases. For quantum systems of qubits and qutrits one can formulate an explicit form of some conditions in a matrix form which is sometimes more transparent then the general operator form. We will use the so-called *vec operator* procedure which transforms a matrix into a vector by stacking its columns one underneath the other. It is well known, that the tensor product of matrices and the vec operator are intimately connected. If *A* denotes a *N* × *N* matrix and *aj* its *j*-th column, then vec *A* is the *N*2-dimensional vector constructed from *a*1,..., *aN*. Moreover if *A*, *B*, *C* are three matrices such that the matrix product *ABC* is well defined, then

$$\text{vec}(ABC) = (\mathbb{C}^T \otimes A)\text{vec}\,B.\tag{63}$$

In the above formula *CT* denotes the transposition of the matrix *C*. In particular we have

$$\text{vec}\,A = (\mathbb{I} \otimes A)\,\text{vec}\,\mathbb{I} = (A^T \otimes \mathbb{I})\,\text{vec}\,\mathbb{I}.\tag{64}$$

Let us agree that when we say that a set of matrices generates the set B(H), we are thinking about B(H) as an algebra, while when we say that a set of matrices forms a basis for B(H), we are talking about B(H) as a vector space (here we identify B(H) with the set of all matrices on H = **C***N*).

For qubits, that is for two-dimensional Hilbert space, one can show by a direct computation that

$$\det(\text{vec}\,\mathbb{I}, \text{vec}\,Q\_1, \text{vec}\,Q\_2, \text{vec}(Q\_1Q\_2)) = \det([Q\_1, Q\_2])\tag{65}$$

and

$$\det(\text{vec}\,\mathbb{I}, \text{vec}\,Q\_1, \text{vec}\,Q\_2, \text{vec}[Q\_1, Q\_2]) = 2\det([Q\_1, Q\_2]),\tag{66}$$

where on the left hand side we have the determinants of the 4 × 4 matrices and on the right hand sides [*Q*1, *Q*2] denotes the commutator of the two 2 × 2 matrices.

From the last equality it follows, that if matrices **I**, *Q*1, *Q*2 and [*Q*1, *Q*2] are linearly independent, then the algebra which is spanned by them has the dimension 4, so *Q*1, *Q*2 and **I** generate B(H). In other words, two operators *Q*1, *Q*2 and the identity generate B(H) if and only if the matrix [*Q*1, *Q*2] has the determinant different from zero. In a similar way one can show that the matrices *Q*1, *Q*2, *Q*3, such that *no* two of them generate B(H), can generate B(H) if and only if the double commutator [*Q*1, [*Q*2, *Q*3]] is invertible. In general, the matrices *Q*1,..., *Qr* generate B(H) iff at least one of the commutators [*Qi*, *Qj*] or double commutators [*Qi*, [*Qj*, *Qk*]] is invertible (Aslaksen & Sletsjøe, 2009).

In the case of qutrits, that is for a three-dimensional Hilbert space, one can show by direct calculation that if [*Q*1, *Q*2] is invertible and *ω*([*Q*1, *Q*2]) �= 0, where for *Q* ∈ B(H) the symbol *ω*(*Q*) denotes the linear term in the characteristic polynomial of *Q*, then one can construct an explicit basis for B(H). Indeed, if *Q*1, *Q*2 belong to B(H), and (dim H) = 3, then the determinant of the 9-dimensional matrix Ω build from vec transformations of **I**, *Q*1, *Q*2, *Q*2 1, *Q*2 2, *Q*1*Q*2, *Q*2*Q*1, [*Q*1, [*Q*1, *Q*2]], [*Q*2, [*Q*2, *Q*1]] satisfies the equality

$$\det \Omega = 9 \det([Q\_1, Q\_2]) \omega([Q\_1, Q\_2]). \tag{67}$$

That is, if det([*Q*1, *Q*2]) �= 0 and *ω*(*Q*) �= 0, then the columns of the matrix Ω correspond to a basis for B(H).

Of course, one can also use the Shemesh criterion to characterize pairs of generators for B(H), where dim H = 3.

## **5. Conclusions**

16 Will-be-set-by-IN-TECH

which can be checked by an effective procedure, that is, by a finite number of arithmetic operations. It is obvious, that the matrix **M** is in general semipositive definite, and the above

In order to illustrate algebraic methods in reconstruction problems, we will discuss some algebraic procedures in low dimensional cases. For quantum systems of qubits and qutrits one can formulate an explicit form of some conditions in a matrix form which is sometimes more transparent then the general operator form. We will use the so-called *vec operator* procedure which transforms a matrix into a vector by stacking its columns one underneath the other. It is well known, that the tensor product of matrices and the vec operator are intimately connected. If *A* denotes a *N* × *N* matrix and *aj* its *j*-th column, then vec *A* is the *N*2-dimensional vector constructed from *a*1,..., *aN*. Moreover if *A*, *B*, *C* are three matrices such that the matrix

In the above formula *CT* denotes the transposition of the matrix *C*. In particular we have

Let us agree that when we say that a set of matrices generates the set B(H), we are thinking about B(H) as an algebra, while when we say that a set of matrices forms a basis for B(H), we are talking about B(H) as a vector space (here we identify B(H) with the set of all matrices

For qubits, that is for two-dimensional Hilbert space, one can show by a direct computation

where on the left hand side we have the determinants of the 4 × 4 matrices and on the right

From the last equality it follows, that if matrices **I**, *Q*1, *Q*2 and [*Q*1, *Q*2] are linearly independent, then the algebra which is spanned by them has the dimension 4, so *Q*1, *Q*2 and **I** generate B(H). In other words, two operators *Q*1, *Q*2 and the identity generate B(H) if and only if the matrix [*Q*1, *Q*2] has the determinant different from zero. In a similar way one can show that the matrices *Q*1, *Q*2, *Q*3, such that *no* two of them generate B(H), can generate B(H) if and only if the double commutator [*Q*1, [*Q*2, *Q*3]] is invertible. In general, the matrices *Q*1,..., *Qr* generate B(H) iff at least one of the commutators [*Qi*, *Qj*] or double commutators

hand sides [*Q*1, *Q*2] denotes the commutator of the two 2 × 2 matrices.

[*Qi*, [*Qj*, *Qk*]] is invertible (Aslaksen & Sletsjøe, 2009).

det**M** > 0, (62)

vec(*ABC*)=(*CT* ⊗ *A*) vec *B*. (63)

vec *A* = (**I** ⊗ *A*) vec **I** = (*AT* ⊗ **I**) vec **I**. (64)

det(vec **I**, vec *Q*1, vec *Q*2, vec(*Q*1*Q*2)) = det([*Q*1, *Q*2]) (65)

det(vec **I**, vec *Q*1, vec *Q*2, vec[*Q*1, *Q*2]) = 2 det([*Q*1, *Q*2]), (66)

expressed by the following inequality

condition means the strict positivity of **M**.

product *ABC* is well defined, then

**4.2 Examples**

on H = **C***N*).

that

and

Papers written by mathematicians are usually focused on characterization of various properties of discussed objects and search for necessary and sufficient conditions for desired conclusion to hold. Concrete constructions offen play a minor role. The problems of frames and fusion frames are no exceptions. The main purpose of this paper was to discuss properties of some Krylov subspaces in a given Hilbert space as a natural examples of fusion frames and their applications in reconstruction of trajectories of open quantum systems.

#### **6. References**

Aslaksen, H. & Sletsjøe, A.B. (2009). *Lin. Algebra Appl.* 430, 1. Casazza, P. G. & Kutyniok, G. (2004). Frames of subspaces, *Contemp. Math.* 345, 87. Casazza, P. G. et al. (2008). *Appl. Comput. Harmon. Anal.* 25, 114. Christensen, O. (2008). *Frames and Bases*, Boston, Birkhäuser. Daubechies, I., Grossman. A., and Meyer, Y. (1986). *J. Math. Phys.* 27, 1271. Duffin, R. J. & Schaeffer, A. C. (1952). *Transactions AMS* 72, 341. Fan, H., Hu, L. (2009) *Optics Comm.* 282, 932. Farenick, D.R. (2001), *Algebras of Linear Transformations*, New York, Springer. Gorini, V et al. (1976) *J. Math. Phys.* 17, 149. Hauseholder, A.S. (2009). *The Theory of Matrices in Numerical Analysis*, Dover Books. Heil, Ch. (Ed.) (2006). *Harmonic Analysis and Applications*, Boston, Birkhäuser. Jamiołkowski, A. (1974). *Rep. Math. Phys.* 5, 415. Jamiołkowski, A. (1982). *On Observability of Classical and Quantum Stochastic Systems*, Toru ´n, N. Copernicus Univ. Press, (in Polish). Jamiołkowski, A. (1983). *Internat. J. Theoret. Phys.* 22, 369. Jamiołkowski, A. (1986). *Frequency Domain and State Space Methods for Linear Systems*, Eds. C. I. Byrnes and A. Lindquist, Amsterdam: Elsevier, p. 347. Jamiołkowski, A. (2000). *Rep. Math. Phys.* 46, 469. Jamiołkowski, A. (2010), *Journal of Physics: Conference Series* 213, 012002. Kossakowski, A. (1972) *Rep.Math. Phys.* 3, 247. Kovaˇcevi´c, J. and Chebira, A. (2008). *An Introduction to Frames*, Boston-Delft, NOW.

**Part 2**

**Quantum Phenomena with Laser Radiation**


**5. Recycling capability of magnesium alloys**

Recycling metals is critical to their overall sustainability. Magnesium retains most of the necessary physical integrity when recycled if it is not contaminated. Remelting and forming of ingots are the main energy requirement for recycling, but generally, secondary production of magnesium ingots requires substantially less energy than primary production [32]. Otherwise, this process's greenhouse gas emission mainly depends on the selected cover gas; generally, a cumulative 3.6 kgCO2eq/kg of secondary magnesium produced could be released [33].

Today the recycling of magnesium is technologically feasible. Currently, the primary source of magnesium alloy scrap comes from the magnesium die-casting industry (the most common method of fabricating new magnesium alloys parts). Die casting foundries can manage the amount of process scrap in three different ways:

On the other hand, the processing of end-of-life vehicles is today still not easily practicable and needs technological improvement. Shredded magnesium can be contaminated with iron, nickel, and copper from coatings and fasteners, all of which are detrimental to the corrosion resistance of the metal. Although the lowvalue markets mentioned above (aluminum alloys and steel desulphurization) can absorb low-quality post-consumer magnesium, options for separating it from other metals are necessary for magnesium structural alloys applications. The main viable option is melting magnesium in contact with molten salt to remove oxides from the liquid metal. This process is today not fully capable of separating magnesium from other metals. Another possibility is metal vapor distillation: due to higher vapor pressure and low boiling point of magnesium compared to aluminum and many other metals.

On the other hand, a too high magnesium-aluminum chemical affinity results in poor separation. A much more viable route is collecting and separating magnesium from the high-quality scraps made of aluminum-magnesium alloys: the beverage can stock (e.g., the aluminum 3xxx series alloys employed for the body, the aluminum 5xxxs series used for edge), and the aluminum 5xxxs series today preferred for body panels of automobiles. To separate magnesium, chlorine gas bubbling through the liquid alloyed metal can remove magnesium by reaction, but such a hydrometallurgy process requires large amounts of chlorine and energy. Further recent advancements in magnesium separation from aluminum alloy scraps focus on electrorefining. It is a process in which metals are purified in an electrolytic cell where the anode is the impure metal, and the cathode is a very pure sample of the metal [36]. To summarize, an efficient recycling route for magnesium by automotive scraps is still an issue. Broad approaches based on the design for corrosion-free assembling and easy disassembling of magnesium parts in the multi-material structure are on track.

*Magnesium Alloys for Sustainable Weight-Saving Approach: A Brief Market Overview, New… DOI: http://dx.doi.org/10.5772/intechopen.102777*


**2. Laboratory determination of hair cortisol concentration (HCC)**

Different laboratories use similar methods to measure HCC with minor variations in experimental procedures. Usually, the proximal 3 cm of hair which represents the last 3 months of cortisol production, is collected [8, 9]. Using the most proximal segments reduces the potential for a 'wash-out effect' which relates to a decline in cortisol levels in distal segments due to ultraviolet radiation and hair care practices [8]. The hair sample is carefully sectioned into segment lengths that approximate the period of interest, for example, cut into 1 cm fragments, or whole hair samples are used. Hair grows approximately 1 cm per month, so this is a convenient approximation of changes in HCC each month [9].

The hair is then either finely minced with scissors or pulverized with a ball mill. The mass of hair used for analysis varies between studies, with a range of 2.5–50 mg for ELISA and 1.25–20 mg for LCMS [10]. Next, the samples are incubated in a solvent such as methanol for a set period to extract the cortisol. The extraction medium is evaporated to dryness and the extracted cortisol is reconstituted in a solution such as phosphate-buffered saline or distilled water. HCC is typically measured using two types of analyses: immunoassays or mass spectrometry [9, 10]. Immunoassays used for the analysis include enzyme-linked immunosorbent assay (ELISA), immunoassay with chemiluminescence detection (CLIA), and radioimmunoassay (RIA).

*The Association of Hair Cortisol and Cardiometabolic Risk Factors in Cardiovascular… DOI: http://dx.doi.org/10.5772/intechopen.108356*

Alternatively, liquid chromatography-mass spectrometry (LCMS) is used to determine HCC. Typically, the inter- and intra-assay coefficients of variability (cvs) are reported to indicate variability between measurements using different plates or tests and between duplicate samples on the same plate, respectively [10].

As the clinical utilization of HCC increases, it is important to establish an international benchmark [8, 9, 11]. Russell *et al.* conducted a study comparing the cortisol testing protocols of four leading laboratories, which include four ELISA methods and two LCMS methods, by analyzing the same hair samples representing the low, intermediate, and high ranges of hair cortisol concentrations (HCC) [9]. This study showed significant positive correlations between the four different immunoassay methods, while the results for the LCMS methods were almost identical. Further, the study concluded that laboratories using immunoassays could use a correction factor to convert results into standard LCMS equivalents.

## **3. The role of long-term hair cortisol levels in CVD risk**

Stress can be defined as any stimuli that can alter homeostasis and causes physical, emotional, or psychological strain. It impairs both physical and physiological health [6], resulting in a higher risk for obesity, type 2 diabetes mellitus, and cardiovascular diseases [5, 6]. Stress can be the result of psychosocial factors like anxiety, social isolation, and traumatic life events. Although some stress is beneficial and helps the body cope (e.g., with inflammation), excessive/prolonged stress can be harmful [12–15]. The response to stress is mediated by the "stress hormone" cortisol, which is released in higher doses under an excessive amount of stress [12]. Cortisol is a lipid-soluble glucocorticoid hormone that regulates a wide range of basal processes throughout the body, including metabolism, and immune response, and, most importantly, it helps the body to respond to stress and to maintain homeostasis. Cortisol does this by increasing blood sugar through gluconeogenesis, suppressing the immune system, and increasing the metabolism of fat, glucose, protein, and carbohydrates [13]. The production of cortisol is housed in the cortex of the adrenal glands and then released into the bloodstream, which transports it throughout the body [12]. Cortisol is an end product of the Hypothalamic-Pituitary-Adrenal (HPA) axis; its secretion in response to biochemical stress may influence health and cognitive events [12, 13].

The hypothalamic-pituitary-adrenal (HPA) axis is a crucial stress response system in the human body [12]. The primary function of the HPA axis is to maintain homeostasis and facilitate successful adaption to the surrounding environment through an intricate cascade of hormonal reactions. The stress response initiates when a stressor triggers the hypothalamus, releasing corticotropin-releasing factor (CRF) and vasopressin (AVP). These hormones stimulate the production of adrenocorticotropic hormone (ACTH) from the pituitary gland, eliciting the release of glucocorticoids, most notably cortisol, from the adrenal glands (**Figure 2**). Chronic stress has been well-documented as increasing the risk of cardiovascular disease through sustained exposure to increased levels of endogenous cortisol [6, 13]. The elevation of plasma cortisol levels is one of the best-studied components of the stress response, and this hormone is one of the best indicators of acute stress in humans.

Elevated cortisol leads to downregulation of the glucocorticoid receptor and potently affects lipid and carbohydrate metabolism [6]. Repeated or chronic stress can result in HPA axis dysfunction and cortisol remaining at high levels [12]. Clinical and population studies have shown that excessive cortisol levels are associated with

#### **Figure 2.**

*The HPA axis response to stress resulting in elevated cortisol, increased cardiometabolic risk (CMR), and cardiovascular disease (CVD).*

*The Association of Hair Cortisol and Cardiometabolic Risk Factors in Cardiovascular… DOI: http://dx.doi.org/10.5772/intechopen.108356*

developing central adiposity, insulin resistance and hyperglycemia, hypertension, and dyslipidemia [14, 15]. Traditionally these studies measured cortisol levels in body fluids, including saliva, blood, and urine [16]. While blood and saliva samples provide a cortisol measurement of a single timepoint, urine reflects the total exposure to bioactive cortisol over 12 or 24 hours. In contrast, hair allows for retrospective assessment of long-term cortisol concentrations over weeks, months, and even years [11, 17], potentially providing a better measure of an individual's long-term exposure to stress. HCC is increasingly important in establishing and providing significant insight into cardiovascular disease prognosis, diagnosis, and management [13]. Elevated cortisol has been shown to be associated with an increased risk of cardiovascular diseases (9). Also, several cross-sectional studies found positive associations of hair cortisol with adverse cardiometabolic outcomes, including higher systolic blood pressure [18], diabetes, metabolic syndrome [18], and adiposity [18, 19].