**Author details**

Vittorio Picchio1 , Vittoria Cammisotto1 , Francesca Pagano2 , Roberto Carnevale1,3 and Isotta Chimenti1,3\*

1 Department of Medical Surgical Sciences and Biotechnologies, Sapienza University, Italy

2 Institute of Biochemistry and Cell Biology, National Council of Research (IBBC-CNR), Italy

3 Mediterranea Cardiocentro, Napoli, Italy

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


**3.2 Hepatitis**

As far back as 2003 Greek investigators had determined that refugees living in Athens (especially those from Asia and Albania) had a high incidence of hepatitis B viral (HBV) infection. Of note, the incidence of hepatitis C viral (HCV) infection was low [27]. Refugee populations in Greece in the early 2000s were avoiding established shelters for the fear of being departed, therefore they lived in crowded conditions among their own immigrant groups [28]. Hepatitis A viral disease (HAV) in Greece has remained high at 17.1% among non-immunized children [29]. Recent data from the Greek Government demonstrated spikes in HAV disease from 2005 to 2008, after the migration of populations from the Middle East and Roma (Albanian and other Balkan Roma groups) populations. A second spike occurred

in 2016 and 2017 secondary to the current Syrian disaster. In December 2016, as the Syrian crisis was reaching a crescendo, refugees and asylum seekers residing in host facilities in Greece were demonstrating an increase, mostly in children under 15 years of age [30, 31].

#### **3.3 Leishmania**

More than one million refugees arrived in Greece between 2015 and 2016 from areas with endemic Leishmaniasis (Syria, Iraq, and Afghanistan). This disease has serious social and economic consequences in these areas [32]. Fotakis et al. uncovered an infection rate of Phlebotomus spp. sand flies in refugee camps that indicated an elevated risk to local populations [32]. A common-sense recommendation would be to provide refugees access to descent living conditions, good health education, effective vector control, and interdict local colonization of sand flies. Ongoing studies of refugee populations regarding epidemiology and disease transmission may be helpful.

#### **3.4 Shigella**

Shigella is endemic in many low-income countries. The massive influx of refugees to Greece puts local and incoming refugee populations at risk [33]. At a syndromic notification center in Athens, Greece in 2015/2016 a cluster of shigellosis cases was identified. All cases were multi-drug resistant, and a potential common source was not identified. All cases were typed; real-time typing is helpful for control methods and epidemiological inquiries.

The truth is simple, refugees are colonized by resistant organisms during their extended stays in refugee/migrant camps [33, 34]. There is a need for a European tracking system that can be used by all countries were diseases and syndromes are identified to allow documentation and prompt, effective intervention.

## **4. Mental health**

To say that refugees experience stress is an understatement. They must deal with war, migration, oppression, forced detention, violence, and witness death and destruction [35, 36]. They suffer abuse from smugglers, criminals, and governments [37]. In 2016, 5096 individuals perished at sea [37]. In view of the afore-mentioned, refugees have many psychological and somatic complaints [38]. To document this violence towards Syrian refugees and its effect, MSF has supported camps in Greece, conducted a quantitative and qualitative research investigation at sites in Greece (Ritsona camp near Athens, Katskikas camp near Ioannina, and Samos). The study aimed to determine the levels and type of violence experienced by refugees in their home communities, during their journey, and during their stay abroad. It also looked at the types of perpetrators, and the prevalence of anxiety and other mental disorders [35]. MSF used the Refugee Health Screener 15 (RHS-15) as their investigative tool. They found that over 92% of the participants screened positive for anxiety. Up to 75% experienced a violent act in Syria and over half experienced a violent act on their journey to Greece. The violence, as expected, decreased from Syria to Turkey and from Turkey to Greece. However, there were violent acts reported in Greece [39]. Most refugees felt oppressed by daily stressful events such as poverty, poor housing, isolation, societal marginalization, and changes in family structure [40–42].

**109**

*Health Security and the Refugee Crisis in Greece: The Refugee Perspective*

To further elucidate the plight of Syrian refugees in Greece, in particular, Poole et al. studied major depressive symptoms and risk factors [43]. It is of interest that most migrants are normally healthier than the host populations [44]; this is called the "healthy migrant effect." However, refugees/migrants fleeing conflict zones are not, and they face an increased prevalence of mental health problems [45]. Major depressive disorder (MDD) undermines individual and family functionality, which is imperative for survival, resettlement, and acculturation [46, 47]. MDDs occurred in 44% of the population studied. Women had significantly increased odds of MDD. Globally, women have 50% more MDDs than men [48]. The prevalence of MDD did not differ by age or educational level; however, increased time of displacement and time in the asylum process in Greece seemed to increase the likelihood of MDD. The odds of MDD increased by 15% for each additional month an individual was in the asylum process. The prevalence of MDD was 10× higher in Syrian refugees that in Syrians in pre-conflict times and generally across the globe [49, 50]. There is some evidence that MDD may lessen as the time since leaving the

The destruction done to individuals, families, and the mental health infrastructure of countries that accept refugees, is cataclysmic and ongoing. This is only compounded by a lack of information about legal procedures and an uncertain

The plight of refugee women is difficult and perilous [52, 53]. While most of the refugees coming to Greece and Europe from the Middle East were initially men, women have been making the difficult trip in increasing numbers since 2016 [54]. Global figures show that 80% of the refugees and internally displaced people are women and children [55]. The displacement of families because of war has led to insecurity and vulnerability. Women are subjected to violence in their conflictravaged countries, during migration out of their country, and after their arrival in camps and refugee centers at their destination [52, 53]. Sexual and gender-based

In war zones the terror is very straight forward. Bombs fall, soldiers from all sides of a conflict (whether from the Islamic State of Iraq and Syria (ISIS), the Syrian army proper, or Syrian rebels) rape women, kill family members, and steal possessions [52]. Violence during their journey of escape and migration comes, for the most part, from those who are supposed to help them, or claim to help them. Clearly, women traveling alone or with children are extremely vulnerable; however,

Frequently, women are first victimized at the hands of smugglers who offer to help them and their children get to Europe for a price that includes "transactional sex." If transit to the European Union (EU) becomes more difficult due to the closing of more border crossings (EU—Turkish agreement of March 2016) [9] or the bombing/destruction of smuggler's boats (as proposed by the United Nations for the transit of refugees) [56] it is "likely that the demand for smugglers, and the price that they ask for facilitating the passage into Europe will increase [52]." A second opportunity for violence occurs at the hands of Turkish police and coast guard as women and their families try to flee to Greece [52]. A third threat along the road of migration comes from fellow male travelers. Even after reaching refugee camps women are frequently frightened to leave their tents at night (or at any time) due to the threat of rape by men in the camp [52]. The stress of flight from a war zone

future in the countries in which they are encamped [35].

violence (SGBV) has become a significant burden to refugee women.

even women travelling with men also do not have absolute safety.

*DOI: http://dx.doi.org/10.5772/intechopen.91210*

area of conflict increases [51].

**5. Women's health**

#### *Health Security and the Refugee Crisis in Greece: The Refugee Perspective DOI: http://dx.doi.org/10.5772/intechopen.91210*

To further elucidate the plight of Syrian refugees in Greece, in particular, Poole et al. studied major depressive symptoms and risk factors [43]. It is of interest that most migrants are normally healthier than the host populations [44]; this is called the "healthy migrant effect." However, refugees/migrants fleeing conflict zones are not, and they face an increased prevalence of mental health problems [45]. Major depressive disorder (MDD) undermines individual and family functionality, which is imperative for survival, resettlement, and acculturation [46, 47]. MDDs occurred in 44% of the population studied. Women had significantly increased odds of MDD. Globally, women have 50% more MDDs than men [48]. The prevalence of MDD did not differ by age or educational level; however, increased time of displacement and time in the asylum process in Greece seemed to increase the likelihood of MDD. The odds of MDD increased by 15% for each additional month an individual was in the asylum process. The prevalence of MDD was 10× higher in Syrian refugees that in Syrians in pre-conflict times and generally across the globe [49, 50]. There is some evidence that MDD may lessen as the time since leaving the area of conflict increases [51].

The destruction done to individuals, families, and the mental health infrastructure of countries that accept refugees, is cataclysmic and ongoing. This is only compounded by a lack of information about legal procedures and an uncertain future in the countries in which they are encamped [35].

## **5. Women's health**

*Contemporary Developments and Perspectives in International Health Security - Volume 1*

years of age [30, 31].

transmission may be helpful.

control methods and epidemiological inquiries.

**3.3 Leishmania**

**3.4 Shigella**

**4. Mental health**

in 2016 and 2017 secondary to the current Syrian disaster. In December 2016, as the Syrian crisis was reaching a crescendo, refugees and asylum seekers residing in host facilities in Greece were demonstrating an increase, mostly in children under 15

More than one million refugees arrived in Greece between 2015 and 2016 from areas with endemic Leishmaniasis (Syria, Iraq, and Afghanistan). This disease has serious social and economic consequences in these areas [32]. Fotakis et al. uncovered an infection rate of Phlebotomus spp. sand flies in refugee camps that indicated an elevated risk to local populations [32]. A common-sense recommendation would be to provide refugees access to descent living conditions, good health education, effective vector control, and interdict local colonization of sand flies. Ongoing studies of refugee populations regarding epidemiology and disease

Shigella is endemic in many low-income countries. The massive influx of refugees to Greece puts local and incoming refugee populations at risk [33]. At a syndromic notification center in Athens, Greece in 2015/2016 a cluster of shigellosis cases was identified. All cases were multi-drug resistant, and a potential common source was not identified. All cases were typed; real-time typing is helpful for

The truth is simple, refugees are colonized by resistant organisms during their extended stays in refugee/migrant camps [33, 34]. There is a need for a European tracking system that can be used by all countries were diseases and syndromes are

To say that refugees experience stress is an understatement. They must deal with war, migration, oppression, forced detention, violence, and witness death and destruction [35, 36]. They suffer abuse from smugglers, criminals, and governments [37]. In 2016, 5096 individuals perished at sea [37]. In view of the afore-mentioned, refugees have many psychological and somatic complaints [38]. To document this violence towards Syrian refugees and its effect, MSF has supported camps in Greece, conducted a quantitative and qualitative research investigation at sites in Greece (Ritsona camp near Athens, Katskikas camp near Ioannina, and Samos). The study aimed to determine the levels and type of violence experienced by refugees in their home communities, during their journey, and during their stay abroad. It also looked at the types of perpetrators, and the prevalence of anxiety and other mental disorders [35]. MSF used the Refugee Health Screener 15 (RHS-15) as their investigative tool. They found that over 92% of the participants screened positive for anxiety. Up to 75% experienced a violent act in Syria and over half experienced a violent act on their journey to Greece. The violence, as expected, decreased from Syria to Turkey and from Turkey to Greece. However, there were violent acts reported in Greece [39]. Most refugees felt oppressed by daily stressful events such as poverty, poor housing, isolation, societal marginalization, and changes in family

identified to allow documentation and prompt, effective intervention.

**108**

structure [40–42].

The plight of refugee women is difficult and perilous [52, 53]. While most of the refugees coming to Greece and Europe from the Middle East were initially men, women have been making the difficult trip in increasing numbers since 2016 [54]. Global figures show that 80% of the refugees and internally displaced people are women and children [55]. The displacement of families because of war has led to insecurity and vulnerability. Women are subjected to violence in their conflictravaged countries, during migration out of their country, and after their arrival in camps and refugee centers at their destination [52, 53]. Sexual and gender-based violence (SGBV) has become a significant burden to refugee women.

In war zones the terror is very straight forward. Bombs fall, soldiers from all sides of a conflict (whether from the Islamic State of Iraq and Syria (ISIS), the Syrian army proper, or Syrian rebels) rape women, kill family members, and steal possessions [52]. Violence during their journey of escape and migration comes, for the most part, from those who are supposed to help them, or claim to help them. Clearly, women traveling alone or with children are extremely vulnerable; however, even women travelling with men also do not have absolute safety.

Frequently, women are first victimized at the hands of smugglers who offer to help them and their children get to Europe for a price that includes "transactional sex." If transit to the European Union (EU) becomes more difficult due to the closing of more border crossings (EU—Turkish agreement of March 2016) [9] or the bombing/destruction of smuggler's boats (as proposed by the United Nations for the transit of refugees) [56] it is "likely that the demand for smugglers, and the price that they ask for facilitating the passage into Europe will increase [52]." A second opportunity for violence occurs at the hands of Turkish police and coast guard as women and their families try to flee to Greece [52]. A third threat along the road of migration comes from fellow male travelers. Even after reaching refugee camps women are frequently frightened to leave their tents at night (or at any time) due to the threat of rape by men in the camp [52]. The stress of flight from a war zone

and life in a refugee camp may lead to both verbal and violence from husbands. Psychological stress leads to SGBV and intimate partner violence [53]. This type of violence is a manner in which to eliminate feeling of helplessness and many refugee communities experience it [57]. It is of interest that SGBV is a reaction to something dangerous post immediate conflict [53, 58]. In 2015, the organization UN Women estimated that 35% of women are physically abuse or raped at some time in their lives [59].

Two other factors have exacerbated the plight of refugee women: (1) there are no clear policies at their first destination point in the EU (or for that matter, at any intermediate or final destination point) regarding whom to report physical or sexually abuse and (2), as alluded to above, the lack of an adequate accommodations increases their insecurity [52]. The above difficulties are all complicated by the fact that there are no legal, regular routes of transit for refugees.

Once asylum seeking women refugees (ASWR) reach a destination outside their country of origin there are considerable barriers to the provision of health care [60]. The first barrier is the legal barrier. ASWR (and men and children) will have limited access to national health systems. Specifically, the sexual and reproductive health (SRH) rights of ASWR are often compromised because of their lack of knowledge on what their rights are and how to navigate the health care system of their host country. This may be compounded by a deficit of knowledge on the part of those who try to provide services to them [60]. A second barrier is one of geography. Refugees can be moved from camp to camp and find it difficult to develop a sense of trust regarding relief workers. A lack of trust and a discontinuity of care compromise an ASWR's SRH. A third barrier involves the differing administrative rules and regulations in host countries. Even those providing the health care do not know all the rules and regulations regarding refugees and what they may be entitled to [60]. Another barrier of significance, involves the socio-cultural aspects affecting an ASWR. Some cultures have strict gender roles, and some ASWR do not want to be examined by a male health care provider. Even in a situation where the woman is willing, their husband or extended family may object [61]. Simply disrobing to any extent or assuming a particular position for a physical examination can be challenging [37, 62]. The general mistrust by the refugee community of the host country is accentuated by the health provider's lack of awareness regarding the socio-cultural mores of the refugees. Finally, the economic barriers cannot be discounted. ASWR may not be able to find work, or may not be allowed to work by their husbands or family [60, 63, 64]. Janssens et al. points out that the merely the need to purchase contraceptives may be beyond an ASWR's reach because of cost [60].

Therefore, the provision of care for ASWR is anything but systematic and organized [65]. Through their journeys, the barriers they encounter, and the woeful inadequacies they confront in their host countries, ASWR are left with unaddressed or inadequately addressed serious issues such as adequate perinatal care, controlling their sexuality, depression, anxiety, discrimination, unmet health service needs, and even female genital mutilation in their host destination perpetrated by their male dominant culture [65]. ASWR are a group that needs local, regional, and national assistance from the host country. Healthcare providers must understand position of refugee women from every perspective and must endeavor to overcome barriers to respect and meaningful care.

#### **6. Child health**

The international public health community is concerned about childhood morbidity in the refugee camps of Greece. Kampouras et al. was one of the first groups

**111**

breastfeeding [70].

*Health Security and the Refugee Crisis in Greece: The Refugee Perspective*

to investigate and report on the disease burden of camps among children [15]. They divided the illnesses that occurred over the winter of 2016–2017 into infectious and non-infectious categories. Children less than the age of 12 years were usually presented with infectious causes (nearly 81%). Infants, toddlers and children suffered from respiratory infections more frequently than adolescents and adults who tended to present with non-infectious diseases. The most common infections in younger patients included infections of the respiratory tract (67%), skin (23%), the gastrointestinal tract (6%), and the urinary tract (3%). Non-communicable diseases among the youngest were often due to disease of the gastrointestinal tract (20%), respiratory system (18%), surgical problems (13%), and allergies (10%). Infants had better health than children or toddlers. There was no association

There is no doubt that non-breastfed infants are at a higher risk for infection, hospitalization and death than those who are breastfed [66]. Significantly, while 75% of the babies arriving in Lesbos, Greece, were breastfed, only 25% of those leaving Lesvos were still being breastfed. The reason behind this may be related to some non-government organizations (NGOs) giving out infant formula indiscriminately. Because refugee camps have problems with overcrowding and many of the refugees/migrants arriving at these camps are already in poor health the general hygienic conditions of the camps are not very good [67–69]. Therefore, once the breast-feeding stops, not only is the mother's immunity no longer passed on to the infant, but the use of formula is plagued by a lack of hot, clean water, poor steriliza-

This leads to a general concern for the growth and development of refugee children [70]. Growth abnormalities have been identified among Syrian refugees in Jordan and Lebanon, where acute malnutrition is low, but stunting of growth is high [71–73]. Stunting, defined as low height for age, usually occurs because of prolonged undernutrition or malnutrition as well as poor living conditions [70]. In addition to stunting micronutrient deficiencies and a lack of adequate mineral and vitamin supplementation (such as zinc, iron, and calcium) in children is also associated with increased mortality [70]. In 2016 Walpole et al. carried out a project in Northern Greece to assess this situation among refugee children [70]. They found a high prevalence of stunting among the children from 0-5 years of age (including infants). Walpole et al. reported that "a high body mass index in stunted children was a common finding raising concerns over long-term health outcomes and risk of non-communicable disease." This is essentially caused by chronic malnutrition as opposed to acute malnutrition. The rates of stunting for children in camps in Northern Greece were twice as high as that found in Jordanian camps. The children were exposed to a high amount of carbohydrate and fat, and very little protein. Micronutrient deficiencies were likely attributable to factors such as inadequate dietary intake by pregnant and breastfeeding mothers. Because of this finding a recommendation has been made to the Greek government to supplement micronutrients to children under 5 years of age, pregnant women, and women who are

To avert important childhood diseases and decrease childhood morbidity an effective vaccination program must also be put into place. Until the spring of 2017, vaccination of refugee/migrant children was primarily accomplished by NGOs collaborating with the Greek Ministry of Health (MOH) [74]. Unfortunately, not all camps were equally covered by NGOs administering vaccines. This was particularly noted in camps that used hostels, hotels, and apartments for housing. In the spring of 2016, the General Directorate of Public Health of the MOH took over all vaccination activities under a program entitled "PHILOS-Emergency health response to refugee crisis." The program was implemented by the Hellenic Center for Disease

tion of bottles and nipples and an unreliable supply of milk types.

*DOI: http://dx.doi.org/10.5772/intechopen.91210*

between illness and gender [15].

#### *Health Security and the Refugee Crisis in Greece: The Refugee Perspective DOI: http://dx.doi.org/10.5772/intechopen.91210*

*Contemporary Developments and Perspectives in International Health Security - Volume 1*

and life in a refugee camp may lead to both verbal and violence from husbands. Psychological stress leads to SGBV and intimate partner violence [53]. This type of violence is a manner in which to eliminate feeling of helplessness and many refugee communities experience it [57]. It is of interest that SGBV is a reaction to something dangerous post immediate conflict [53, 58]. In 2015, the organization UN Women estimated that 35% of women are physically abuse or raped at some time in their

Two other factors have exacerbated the plight of refugee women: (1) there are no clear policies at their first destination point in the EU (or for that matter, at any intermediate or final destination point) regarding whom to report physical or sexually abuse and (2), as alluded to above, the lack of an adequate accommodations increases their insecurity [52]. The above difficulties are all complicated by the fact

Once asylum seeking women refugees (ASWR) reach a destination outside their

country of origin there are considerable barriers to the provision of health care [60]. The first barrier is the legal barrier. ASWR (and men and children) will have limited access to national health systems. Specifically, the sexual and reproductive health (SRH) rights of ASWR are often compromised because of their lack of knowledge on what their rights are and how to navigate the health care system of their host country. This may be compounded by a deficit of knowledge on the part of those who try to provide services to them [60]. A second barrier is one of geography. Refugees can be moved from camp to camp and find it difficult to develop a sense of trust regarding relief workers. A lack of trust and a discontinuity of care compromise an ASWR's SRH. A third barrier involves the differing administrative rules and regulations in host countries. Even those providing the health care do not know all the rules and regulations regarding refugees and what they may be entitled to [60]. Another barrier of significance, involves the socio-cultural aspects affecting an ASWR. Some cultures have strict gender roles, and some ASWR do not want to be examined by a male health care provider. Even in a situation where the woman is willing, their husband or extended family may object [61]. Simply disrobing to any extent or assuming a particular position for a physical examination can be challenging [37, 62]. The general mistrust by the refugee community of the host country is accentuated by the health provider's lack of awareness regarding the socio-cultural mores of the refugees. Finally, the economic barriers cannot be discounted. ASWR may not be able to find work, or may not be allowed to work by their husbands or family [60, 63, 64]. Janssens et al. points out that the merely the need to purchase

contraceptives may be beyond an ASWR's reach because of cost [60].

barriers to respect and meaningful care.

Therefore, the provision of care for ASWR is anything but systematic and organized [65]. Through their journeys, the barriers they encounter, and the woeful inadequacies they confront in their host countries, ASWR are left with unaddressed or inadequately addressed serious issues such as adequate perinatal care, controlling their sexuality, depression, anxiety, discrimination, unmet health service needs, and even female genital mutilation in their host destination perpetrated by their male dominant culture [65]. ASWR are a group that needs local, regional, and national assistance from the host country. Healthcare providers must understand position of refugee women from every perspective and must endeavor to overcome

The international public health community is concerned about childhood morbidity in the refugee camps of Greece. Kampouras et al. was one of the first groups

that there are no legal, regular routes of transit for refugees.

**110**

**6. Child health**

lives [59].

to investigate and report on the disease burden of camps among children [15]. They divided the illnesses that occurred over the winter of 2016–2017 into infectious and non-infectious categories. Children less than the age of 12 years were usually presented with infectious causes (nearly 81%). Infants, toddlers and children suffered from respiratory infections more frequently than adolescents and adults who tended to present with non-infectious diseases. The most common infections in younger patients included infections of the respiratory tract (67%), skin (23%), the gastrointestinal tract (6%), and the urinary tract (3%). Non-communicable diseases among the youngest were often due to disease of the gastrointestinal tract (20%), respiratory system (18%), surgical problems (13%), and allergies (10%). Infants had better health than children or toddlers. There was no association between illness and gender [15].

There is no doubt that non-breastfed infants are at a higher risk for infection, hospitalization and death than those who are breastfed [66]. Significantly, while 75% of the babies arriving in Lesbos, Greece, were breastfed, only 25% of those leaving Lesvos were still being breastfed. The reason behind this may be related to some non-government organizations (NGOs) giving out infant formula indiscriminately. Because refugee camps have problems with overcrowding and many of the refugees/migrants arriving at these camps are already in poor health the general hygienic conditions of the camps are not very good [67–69]. Therefore, once the breast-feeding stops, not only is the mother's immunity no longer passed on to the infant, but the use of formula is plagued by a lack of hot, clean water, poor sterilization of bottles and nipples and an unreliable supply of milk types.

This leads to a general concern for the growth and development of refugee children [70]. Growth abnormalities have been identified among Syrian refugees in Jordan and Lebanon, where acute malnutrition is low, but stunting of growth is high [71–73]. Stunting, defined as low height for age, usually occurs because of prolonged undernutrition or malnutrition as well as poor living conditions [70]. In addition to stunting micronutrient deficiencies and a lack of adequate mineral and vitamin supplementation (such as zinc, iron, and calcium) in children is also associated with increased mortality [70]. In 2016 Walpole et al. carried out a project in Northern Greece to assess this situation among refugee children [70]. They found a high prevalence of stunting among the children from 0-5 years of age (including infants). Walpole et al. reported that "a high body mass index in stunted children was a common finding raising concerns over long-term health outcomes and risk of non-communicable disease." This is essentially caused by chronic malnutrition as opposed to acute malnutrition. The rates of stunting for children in camps in Northern Greece were twice as high as that found in Jordanian camps. The children were exposed to a high amount of carbohydrate and fat, and very little protein. Micronutrient deficiencies were likely attributable to factors such as inadequate dietary intake by pregnant and breastfeeding mothers. Because of this finding a recommendation has been made to the Greek government to supplement micronutrients to children under 5 years of age, pregnant women, and women who are breastfeeding [70].

To avert important childhood diseases and decrease childhood morbidity an effective vaccination program must also be put into place. Until the spring of 2017, vaccination of refugee/migrant children was primarily accomplished by NGOs collaborating with the Greek Ministry of Health (MOH) [74]. Unfortunately, not all camps were equally covered by NGOs administering vaccines. This was particularly noted in camps that used hostels, hotels, and apartments for housing. In the spring of 2016, the General Directorate of Public Health of the MOH took over all vaccination activities under a program entitled "PHILOS-Emergency health response to refugee crisis." The program was implemented by the Hellenic Center for Disease

Control and Prevention, and was funded by the Asylum, Migration and Integration Fund of the European Union's Directorate-General for the Migration and Home Affairs.

In a one-year period from 2017 to 2018, PHILOS performed 57,615 vaccinations. This included 21,031 vaccinations for measles-mumps-rubella (MMR), 7341 for diphtheria-tetanus-pertussis (DPT), 7652 for poliomyelitis, 5938 for pneumococcal disease, 7179 for Haemophilus influenza type b and 8474 for hepatitis B. Unfortunately, vaccination coverage was still not consistent, and subsequent vaccination often dropped off. The rate of vaccination for the first MMR dose was greater than 80%. However, the follow-up dose dropped by nearly one half. For all other vaccines the rates were even lower. The rate of 50% for children aged 0–4 years had follow-up vaccine coverage fall to less than 25% [31]. While numbers of those vaccinated are available, the denominator remains elusive. The lack of "cultural mediators" among the refugee community was a large problem in follow through. This was compounded by refugees being moved between locations as some camps closed and other camps opened. Vaccinating refugee children must be a priority, because refugees have low baseline rates of immunization and encounter obstacles to getting adequate healthcare. While PHILOS had developed standard operating procedures and improved coordination of vaccination implementation, much more needs to be done for the refugee children in Greece.

While we have addressed the SGBV women/girls suffer above. Here we need to address the topic of street children in Greece and the sexual exploitation of refugee boys. While the problem with street children in Greece has been a topic of concern since, but not extensively researched, since the late 20th century (1990s) [75], the sexual exploitation of refugee boys is a particular and growing concern in the face of the refugee crisis currently exacerbated by the Syrian refugee crisis [76].

What is the definition of street children? Determining this can be difficult because the action and locations of children "in the street" are difficult to ascertain and evaluate [75]. There have been attempts at defining this term by the United Nations (UN), and the Council of Europe (CE). However, according to Atlantis et al. there is agreement that the term refers to "children and young people who have early street experience and who usually spend most of their time in the streets, in the sense that they use that location as the principal place of some of their main daily activities (such as working, eating, and sleeping) [75]." However, let us review the two primary definitions as provided by the UN and the CE. The UN definition is as follows:

*"any boy or girl…for whom the street has become his/her abode and/or source of livelihood; and who is inadequately protected, supervised, or directed by responsible adults [77]."*

The CE has a similar, but somewhat different definition:

*"Street children are children under eighteen who, for longer or shorter periods, live in a street milieu. They are children who live wandering from place to place and who have their peer groups, and contacts in the street. Officially these children may have as their address their parents' home or an institution of social welfare. Most significantly, they have few or no contacts with those adults, parents, school, child welfare institutions, social services, with a duty toward them [78, 79]."*

Why are these children in this position? Before the current immigration/refugee crisis, this was usually this is due to "family breakdown, unemployment, poverty, membership of a minority group, armed conflict, and natural disasters [75]."

**113**

*Health Security and the Refugee Crisis in Greece: The Refugee Perspective*

While these reasons apply today, the vast majority of these days are due to armed conflict or threat of conflict and the above-mentioned reasons still apply, but are secondary to conflict. In 1986, world-wide estimates were as high as 80 million street children [79, 80]. The current crises in the Middle East and those of the Balkans in the 1990s, do not give hope to a lesser estimate from 30 years ago. Greece has an attraction for those fleeing the Middle East and Africa because of its location as a stepping stone into Europe, but it does not have the resources to adequately

In 1999–2002, most of the street children were male (75%) [75]. In the recent flood of refugees to Greece (2015), the situation has worsened (89%) [79, 80]. Freccero et al. enlighten us that the current immigration crisis "is increasingly defined by the unprecedented numbers of children crossing the Mediterranean Sea, many of whom are unaccompanied and separated children (UASCs) as defined by the United Nations High Commissioner for Refugees (UNHCR) and the Committee on the Rights of Children [81]." In 2015 90,000 UASCs applied for asylum in Europe, four times higher than the previous year, and in 2016 there were 63,000

This has been a particular problem in Greece where a majority UASCs are between 14 and 17 years of age and are inadequately housed and accommodated [83]. Frecerro et al. makes us aware that sexual exploitation is illegal in Greece and that Greece is a signatory of the Optional Protocol to the Convention on the Rights of the Child on the sale of Children, Child Prostitution and Child Pornography [76, 84]. Nonetheless, the high visibility of UASCs in public has led to increasing reports of teenage boys being exploited sexually by older men for money [84–88]. Young boys and teens are the majority of UASCs, and while institutions and governments have been appropriately concerned about girls and women, young male UASCs have been left without adequate responses to their plight. The Greeks have debated and given serious consideration to three approached to prevention of this dilemma for male UASCs: (1) the use of secure shelters for prevention of abuse and protection, (2) improving life skills to empower better decision-making, and (3) direct cash distribution to the individual [76]. There are positive aspects to these proposals, however, there still remains much work to be done on their implementation, need for funding sources, and the subsequent evaluation of their

Gender-based violence programs for women have been sorely needed and some have been implemented. However, these young, male, UASCs must not be overlooked. Shelter, tools for survival, and guidance are necessary to ensure their

Violence is on the increase in Greek refugee camps [89]. Gender-based violence has been addressed above. Disease, insects, cold, uncontrolled amounts of waste, impure water, congestion, and increased stressed have led to violence in the camps through short tempers [89]. There are frequent clashes, riots, and incidence of violence, compounded by only 72 people per toilet and 84 people per shower [90]. Furthermore, Greece is struggling with a new refugee/migrant influx of 10,000 in October of 2019 and the camps are always at the breaking point [91]. The situation is so dire that children as young as 10 years of age are attempting suicide [92]. These problems in the camps and the increasing number of refugees has been compounded by "A combination of right-wing, populist narratives, a sluggish Greek economy and lack of tourism" on once popular Greek islands "have also affected

*DOI: http://dx.doi.org/10.5772/intechopen.91210*

support the current flood of refugees.

(89% being male) [79, 82].

effectiveness.

**7. Violence in Greek refugee camps**

welfare.

#### *Health Security and the Refugee Crisis in Greece: The Refugee Perspective DOI: http://dx.doi.org/10.5772/intechopen.91210*

*Contemporary Developments and Perspectives in International Health Security - Volume 1*

Control and Prevention, and was funded by the Asylum, Migration and Integration Fund of the European Union's Directorate-General for the Migration and Home

In a one-year period from 2017 to 2018, PHILOS performed 57,615 vaccinations. This included 21,031 vaccinations for measles-mumps-rubella (MMR), 7341 for diphtheria-tetanus-pertussis (DPT), 7652 for poliomyelitis, 5938 for pneumococcal disease, 7179 for Haemophilus influenza type b and 8474 for hepatitis B. Unfortunately, vaccination coverage was still not consistent, and subsequent vaccination often dropped off. The rate of vaccination for the first MMR dose was greater than 80%. However, the follow-up dose dropped by nearly one half. For all other vaccines the rates were even lower. The rate of 50% for children aged 0–4 years had follow-up vaccine coverage fall to less than 25% [31]. While numbers of those vaccinated are available, the denominator remains elusive. The lack of "cultural mediators" among the refugee community was a large problem in follow through. This was compounded by refugees being moved between locations as some camps closed and other camps opened. Vaccinating refugee children must be a priority, because refugees have low baseline rates of immunization and encounter obstacles to getting adequate healthcare. While PHILOS had developed standard operating procedures and improved coordination of vaccination implementation,

While we have addressed the SGBV women/girls suffer above. Here we need to address the topic of street children in Greece and the sexual exploitation of refugee boys. While the problem with street children in Greece has been a topic of concern since, but not extensively researched, since the late 20th century (1990s) [75], the sexual exploitation of refugee boys is a particular and growing concern in the face of the refugee crisis currently exacerbated by the Syrian refugee crisis [76]. What is the definition of street children? Determining this can be difficult because the action and locations of children "in the street" are difficult to ascertain and evaluate [75]. There have been attempts at defining this term by the United Nations (UN), and the Council of Europe (CE). However, according to Atlantis et al. there is agreement that the term refers to "children and young people who have early street experience and who usually spend most of their time in the streets, in the sense that they use that location as the principal place of some of their main daily activities (such as working, eating, and sleeping) [75]." However, let us review the two primary definitions as provided by the UN and the CE. The UN definition is

*"any boy or girl…for whom the street has become his/her abode and/or source of livelihood; and who is inadequately protected, supervised, or directed by respon-*

*"Street children are children under eighteen who, for longer or shorter periods, live in a street milieu. They are children who live wandering from place to place and who have their peer groups, and contacts in the street. Officially these children may have as their address their parents' home or an institution of social welfare. Most significantly, they have few or no contacts with those adults, parents, school, child*

Why are these children in this position? Before the current immigration/refugee crisis, this was usually this is due to "family breakdown, unemployment, poverty, membership of a minority group, armed conflict, and natural disasters [75]."

*welfare institutions, social services, with a duty toward them [78, 79]."*

The CE has a similar, but somewhat different definition:

much more needs to be done for the refugee children in Greece.

**112**

as follows:

*sible adults [77]."*

Affairs.

While these reasons apply today, the vast majority of these days are due to armed conflict or threat of conflict and the above-mentioned reasons still apply, but are secondary to conflict. In 1986, world-wide estimates were as high as 80 million street children [79, 80]. The current crises in the Middle East and those of the Balkans in the 1990s, do not give hope to a lesser estimate from 30 years ago. Greece has an attraction for those fleeing the Middle East and Africa because of its location as a stepping stone into Europe, but it does not have the resources to adequately support the current flood of refugees.

In 1999–2002, most of the street children were male (75%) [75]. In the recent flood of refugees to Greece (2015), the situation has worsened (89%) [79, 80]. Freccero et al. enlighten us that the current immigration crisis "is increasingly defined by the unprecedented numbers of children crossing the Mediterranean Sea, many of whom are unaccompanied and separated children (UASCs) as defined by the United Nations High Commissioner for Refugees (UNHCR) and the Committee on the Rights of Children [81]." In 2015 90,000 UASCs applied for asylum in Europe, four times higher than the previous year, and in 2016 there were 63,000 (89% being male) [79, 82].

This has been a particular problem in Greece where a majority UASCs are between 14 and 17 years of age and are inadequately housed and accommodated [83]. Frecerro et al. makes us aware that sexual exploitation is illegal in Greece and that Greece is a signatory of the Optional Protocol to the Convention on the Rights of the Child on the sale of Children, Child Prostitution and Child Pornography [76, 84]. Nonetheless, the high visibility of UASCs in public has led to increasing reports of teenage boys being exploited sexually by older men for money [84–88]. Young boys and teens are the majority of UASCs, and while institutions and governments have been appropriately concerned about girls and women, young male UASCs have been left without adequate responses to their plight. The Greeks have debated and given serious consideration to three approached to prevention of this dilemma for male UASCs: (1) the use of secure shelters for prevention of abuse and protection, (2) improving life skills to empower better decision-making, and (3) direct cash distribution to the individual [76]. There are positive aspects to these proposals, however, there still remains much work to be done on their implementation, need for funding sources, and the subsequent evaluation of their effectiveness.

Gender-based violence programs for women have been sorely needed and some have been implemented. However, these young, male, UASCs must not be overlooked. Shelter, tools for survival, and guidance are necessary to ensure their welfare.

### **7. Violence in Greek refugee camps**

Violence is on the increase in Greek refugee camps [89]. Gender-based violence has been addressed above. Disease, insects, cold, uncontrolled amounts of waste, impure water, congestion, and increased stressed have led to violence in the camps through short tempers [89]. There are frequent clashes, riots, and incidence of violence, compounded by only 72 people per toilet and 84 people per shower [90]. Furthermore, Greece is struggling with a new refugee/migrant influx of 10,000 in October of 2019 and the camps are always at the breaking point [91]. The situation is so dire that children as young as 10 years of age are attempting suicide [92]. These problems in the camps and the increasing number of refugees has been compounded by "A combination of right-wing, populist narratives, a sluggish Greek economy and lack of tourism" on once popular Greek islands "have also affected

the sentiment of the locals towards migrants and refugees." The communities that opened their doors in 2015 are no longer warm and receptive [91]. The possible of violence between refugees, between Greek citizens and refugees, and refugee suicide/suicide attempts remains disturbing. An international effort in support of the refugees and in support of the government of Greece is needed.

### **8. Human trafficking**

Many of the previous sections spoke to the topic of human trafficking, sexual or otherwise, involving men, women, children and smugglers/traffickers. Here we would like to emphatically point out that the trafficking of people as refugees leaving, not only poverty, but violence, abuse of all kinds, and seeking political asylum because of the fear of reprisal, is common, almost unstoppable, and a stain on the human effort for justice and on the instruments and institutions of government.

Another term for mass migration/exodus of refugees/migrants can be termed "irregular movement." In mass movements of migrants/refugees, there is little evidence as to when, why, and how such a susceptibility arises [93]. The reader may have noticed a "fluidity" in the terms of these different categories; there is neither a linear nor obvious trajectory between the identities of "migrant," "refugee," and "trafficking victim [93]." Trafficking could lead an individual to becoming a migrant/refugee, or sometimes migrants/refugees are trafficked in their flight from harm's way. There are different types of exploitation for trafficking and this includes: trafficking for sexual exploitation, trafficking for labor exploitation, trafficking for the removal of organs, trafficking for criminal activity, trafficking for forced marriage, and trafficking for sexual and labor exploitation [93]. Those who are trafficked have particular vulnerabilities as pointed out by Brunovskis and Surtees: a paucity of resources, no legal status, inadequate knowledge regarding laws, rights, and assistance, barriers to language, lack of humanitarian aid availability, work scenarios that can lead to exploitation and abuse, threats to safety of self and family, and exposure to violence and abuse with communities and families [93].

Populations moving irregularly and/or migrants/refuges encamped for prolonged stays are extremely vulnerable to being trafficked. There is no State organization or instrument that can provide proper protection from exploitation. Efforts to protect migrant/refugees requires a multi-agency approach between regional, national, and international organizations, including "criminal justice, judicial engagement, human rights and development [94]."

#### **9. Social determinants of disease**

It is evident from the above discourse that social determinants of disease effect refugees/migrants. A person's health is influenced by many factors, and these can be placed into five categories [95]. These categories include genetics, behavior, environmental and physical aspects, medical care, and social factors, i.e., social determinants of disease or health. In fact, migration, in and of itself, is a social determinant of disease [96]. Any meaningful endeavor to improve refugee health will depend on those who make policy and provide funding, as well as clinicians and public health officials and professionals. Movements of populations act as social determinants of disease of health in two ways. As previously stated, the first factor of just trying to get to safety or a better life through hostile areas presents a variety of health risks [97], and the second involves just being a refugee or migrant because this status "limits behavioral choices and, indeed, often directly impacts

**115**

*Health Security and the Refugee Crisis in Greece: The Refugee Perspective*

and significantly alters the effect of other social positioning such as race/ethnicity, gender, or socioeconomic status, because it places individuals in ambiguous and often hostile relationships to the state and its institutions, including health

The World Health Organization has created a Commission on the Social Determinants of Health in order to eliminate health inequities [95]. This commission wished to improve the daily life of populations, address the problems of distribution of power, money, and resources, and measure, evaluate, and act on these problems. This is a noble undertaking, however, if being a refugee or migrant is a social determinant of disease (and a significant one), then the policies and politics of war, religion, and genocide must be solved. This is a daunting, formidable, and

Many of the over one million refugees who have passed through Greece have been exposed to severe physical and mental trauma in their land of origin, on their routes of escape, and in the camps themselves. Their well-being necessitates physical security, food security, shelter, and a means of re-entering a safe society. More efforts are needed by the international community to ensure these necessities are put into place. More specifically, more attention must be directed to the security of women, girls, and male adolescents and their ultimate welfare, as well as encouraging refugees and migrants as to their rights as displaced people, services and legal options that are available to them. Furthermore, approaches to shelter, physical security, skill acquisition, and methods to assess and mitigate economic vulnerability must be pursued by institutions and governments. The dilemmas regarding the financial and manpower constraints of the Greek government in their ability to assist refugees and migrants must be addressed primarily by the EU and Middle Eastern nations in order to facilitate appropriate resolutions. These problems cannot simply be left at the doorstep of Greece. The ethics involving the plight of refugees and migrants in Greek camps require thoughtful and powerful approaches to

While the migrant/refugee problems related to Greece are highlighted here, it must be noted that there are still serious refugee matters in Syria (6.7 million refugees), Afghanistan (2.7 million refugees), South Sudan (2.3 million refugees), Myanmar (1.1 million refugees), and Somalia (0.9 million refugees), and these

The authors hope that serious efforts are made on behalf of the refugees and migrants to ensure their well-being, while at the same time allotting resources to the Greek government so that the tasks that the European Union, the United States, and others expect the Greeks to execute can be accomplished in an efficient and

migrant/refugees face the same unenviable circumstances [99].

*DOI: http://dx.doi.org/10.5772/intechopen.91210*

seemingly insurmountable task at this time.

services [98]."

**10. Conclusions**

resolve these difficult matters.

empathetic fashion.

*Health Security and the Refugee Crisis in Greece: The Refugee Perspective DOI: http://dx.doi.org/10.5772/intechopen.91210*

and significantly alters the effect of other social positioning such as race/ethnicity, gender, or socioeconomic status, because it places individuals in ambiguous and often hostile relationships to the state and its institutions, including health services [98]."

The World Health Organization has created a Commission on the Social Determinants of Health in order to eliminate health inequities [95]. This commission wished to improve the daily life of populations, address the problems of distribution of power, money, and resources, and measure, evaluate, and act on these problems. This is a noble undertaking, however, if being a refugee or migrant is a social determinant of disease (and a significant one), then the policies and politics of war, religion, and genocide must be solved. This is a daunting, formidable, and seemingly insurmountable task at this time.

### **10. Conclusions**

*Contemporary Developments and Perspectives in International Health Security - Volume 1*

the refugees and in support of the government of Greece is needed.

engagement, human rights and development [94]."

**9. Social determinants of disease**

**8. Human trafficking**

the sentiment of the locals towards migrants and refugees." The communities that opened their doors in 2015 are no longer warm and receptive [91]. The possible of violence between refugees, between Greek citizens and refugees, and refugee suicide/suicide attempts remains disturbing. An international effort in support of

Many of the previous sections spoke to the topic of human trafficking, sexual or otherwise, involving men, women, children and smugglers/traffickers. Here we would like to emphatically point out that the trafficking of people as refugees leaving, not only poverty, but violence, abuse of all kinds, and seeking political asylum because of the fear of reprisal, is common, almost unstoppable, and a stain on the human effort for justice and on the instruments and institutions of government. Another term for mass migration/exodus of refugees/migrants can be termed "irregular movement." In mass movements of migrants/refugees, there is little evidence as to when, why, and how such a susceptibility arises [93]. The reader may have noticed a "fluidity" in the terms of these different categories; there is neither a linear nor obvious trajectory between the identities of "migrant," "refugee," and "trafficking victim [93]." Trafficking could lead an individual to becoming a migrant/refugee, or sometimes migrants/refugees are trafficked in their flight from harm's way. There are different types of exploitation for trafficking and this includes: trafficking for sexual exploitation, trafficking for labor exploitation, trafficking for the removal of organs, trafficking for criminal activity, trafficking for forced marriage, and trafficking for sexual and labor exploitation [93]. Those who are trafficked have particular vulnerabilities as pointed out by Brunovskis and Surtees: a paucity of resources, no legal status, inadequate knowledge regarding laws, rights, and assistance, barriers to language, lack of humanitarian aid availability, work scenarios that can lead to exploitation and abuse, threats to safety of self and family, and exposure to violence and abuse with communities and families [93]. Populations moving irregularly and/or migrants/refuges encamped for prolonged stays are extremely vulnerable to being trafficked. There is no State organization or instrument that can provide proper protection from exploitation. Efforts to protect migrant/refugees requires a multi-agency approach between regional, national, and international organizations, including "criminal justice, judicial

It is evident from the above discourse that social determinants of disease effect refugees/migrants. A person's health is influenced by many factors, and these can be placed into five categories [95]. These categories include genetics, behavior, environmental and physical aspects, medical care, and social factors, i.e., social determinants of disease or health. In fact, migration, in and of itself, is a social determinant of disease [96]. Any meaningful endeavor to improve refugee health will depend on those who make policy and provide funding, as well as clinicians and public health officials and professionals. Movements of populations act as social determinants of disease of health in two ways. As previously stated, the first factor of just trying to get to safety or a better life through hostile areas presents a variety of health risks [97], and the second involves just being a refugee or migrant because this status "limits behavioral choices and, indeed, often directly impacts

**114**

Many of the over one million refugees who have passed through Greece have been exposed to severe physical and mental trauma in their land of origin, on their routes of escape, and in the camps themselves. Their well-being necessitates physical security, food security, shelter, and a means of re-entering a safe society. More efforts are needed by the international community to ensure these necessities are put into place. More specifically, more attention must be directed to the security of women, girls, and male adolescents and their ultimate welfare, as well as encouraging refugees and migrants as to their rights as displaced people, services and legal options that are available to them. Furthermore, approaches to shelter, physical security, skill acquisition, and methods to assess and mitigate economic vulnerability must be pursued by institutions and governments. The dilemmas regarding the financial and manpower constraints of the Greek government in their ability to assist refugees and migrants must be addressed primarily by the EU and Middle Eastern nations in order to facilitate appropriate resolutions. These problems cannot simply be left at the doorstep of Greece. The ethics involving the plight of refugees and migrants in Greek camps require thoughtful and powerful approaches to resolve these difficult matters.

While the migrant/refugee problems related to Greece are highlighted here, it must be noted that there are still serious refugee matters in Syria (6.7 million refugees), Afghanistan (2.7 million refugees), South Sudan (2.3 million refugees), Myanmar (1.1 million refugees), and Somalia (0.9 million refugees), and these migrant/refugees face the same unenviable circumstances [99].

The authors hope that serious efforts are made on behalf of the refugees and migrants to ensure their well-being, while at the same time allotting resources to the Greek government so that the tasks that the European Union, the United States, and others expect the Greeks to execute can be accomplished in an efficient and empathetic fashion.


Effect of Microbiota on Health and Disease

*Edited by Hoda El-Sayed*

Published in London, United Kingdom

Effect of Microbiota on Health and Disease http://dx.doi.org/10.5772/intechopen.100893 Edited by Hoda El-Sayed

#### Contributors

Bahareh Vakili, Parisa Shoaei, Seyed Davar Siadat, Zahra Esfandiari, Basavaraju M., Gunashree B.S., Srinath B.S., Kishwer Fatima Sherwani, Dill Ara Abbas Bukhari, Ana Maria Calderon de la Barca, Maria-Esther Mejia-Leon, Alejandra Argüelles-Lopez, Paulina. Briseño-Sahagun, Sandra V. Aguayo Patrón, Subha Bhassu, Gayatri Thergarajan, Shahzad Irfan, Haseeb Anwar, Humaira Muazaffar, Farhat Jabeen, Arslan Ahmad, Sakhawat Riaz, Muhammad Tanveer

#### © The Editor(s) and the Author(s) 2022

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First published in London, United Kingdom, 2022 by IntechOpen IntechOpen is the global imprint of INTECHOPEN LIMITED, registered in England and Wales, registration number: 11086078, 5 Princes Gate Court, London, SW7 2QJ, United Kingdom

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**4. Equivalent decomposition model of MIMO system**

In the previous section, the concepts of SVD, EVD and the significance of eigenvalues have been discussed. As aforementioned, the receiver and transmitter symbols relies on precoding and combining matrices obtained from channel

*Performance Analysis of Multiple Antenna Systems with New Capacity Improvement Algorithm… DOI: http://dx.doi.org/10.5772/intechopen.98883*

decomposition [1]. In this section, the basic structure of the channel and importance of channel state information are explained.

In the **Figure 2**, *H* ¼ *U*Σ*VH* is the channel matrix, the columns of U and V are the unitary matrices and diagonal matrix Σ is a *NR* � *NT* dimension with singular values σk, where *σk* is the kth singular value of the Σ ordered decreasingly (*σ*1 >*σ*2 > … >*σr*) and rank 'r' of the matrix. For a input *s* ¼ *V*~*s* using precoder at transmitter is sent in the channel and received at receiver as

$$r = \sqrt{\frac{E\_s}{N\_T}} \\ \text{Hs} + n = \sqrt{\frac{E\_s}{N\_T}} \\ U\Sigma V^H V\tilde{s} + \tilde{n}$$

also expressed as,

$$r = \sqrt{\frac{E\_s}{N\_T}} U \Sigma \bar{s} + \bar{n}$$

The output of channel is multiplied by UH at receiver, resulting in

$$
\tilde{r} = \sqrt{\frac{E\_t}{N\_T}} U^H U \Sigma \tilde{s} + U^H \tilde{n} = \sqrt{\frac{E\_s}{N\_T}} \Sigma \tilde{s} + \tilde{n} \tag{14}
$$

further expressed as,

$$r\_i = \sqrt{\frac{E\_s}{N\_T}} \sigma\_i s\_i + \tilde{n}\_i = \sqrt{\frac{E\_s}{N\_T}} \sqrt{\lambda\_i} s\_i + \tilde{n}\_i \tag{15}$$

where *σi* ¼ ffiffiffiffi *λi* p , *λi* is the eigenvalue.

$$\text{trace } \text{of } R\_{\mathfrak{s}} = Tr(R\_{\mathfrak{s}}) = N\_T \text{ and } E(\tilde{n}\tilde{n}^H) = \sigma\_n^2 I\_r$$

From the above expression the number of non-zero elements in the diagonal matrix Σ corresponds to the number of independent channels. The processing of U matrix to the noise elements is not going to change the variance in the noise components *UHn*~ ¼ *n*~. In order to find U and V matrices, the channel matrix H is needed i.e. to do transmit precoding CSI at transmitter (CSIT) and CSIR for receiver shaping is needed [8].

#### **4.1 CSI at receiver (CSIR)**

It has all the channel coefficients i.e. transmitted from transmitter to receiver. It is estimated by using pilot symbols insertion in the signal sent from the transmitter. It is assumed that the receiver is having perfect CSI to do receiver shaping. In open loop MIMO system the CSI is available only at the receiver but not at the transmitter.

**Figure 2.** *MIMO system decomposition model for perfect CSIT.*


*Article* **Thermodynamic Curvature of the Binary van der Waals Fluid**

## **George Ruppeiner 1,\* and Alex Seftas 2**

Received: 28 September 2020; Accepted: 22 October 2020; Published: 26 October 2020

**Abstract:** The thermodynamic Ricci curvature scalar *R* has been applied in a number of contexts, mostly for systems characterized by 2D thermodynamic geometries. Calculations of *R* in thermodynamic geometries of dimension three or greater have been very few, especially in the fluid regime. In this paper, we calculate *R* for two examples involving binary fluid mixtures: a binary mixture of a van der Waals (vdW) fluid with only repulsive interactions, and a binary vdW mixture with attractive interactions added. In both of these examples, we evaluate *R* for full 3D thermodynamic geometries. Our finding is that basic physical patterns found for *R* in the pure fluid are reproduced to a large extent for the binary fluid.

**Keywords:** information geometry of thermodynamics; thermodynamic curvature; critical phenomena; binary fluids; van der Waals equation

## **1. Introduction**

The thermodynamic Ricci curvature scalar *R* has yielded a number of interesting results in the study of fluids [1]. However, to this point, the great majority of the calculations of *R* have been made for pure fluids. Much less examined has been *R* for binary fluids. Pure fluids offer many research topics in a relatively simple thermodynamic geometric scenario. One element of this simplicity is that pure fluids may be represented by a two-dimensional (2D) thermodynamic Riemannian geometry, where just the scalar *R* gives the full curvature picture.

The dimension of the thermodynamic phase space grows by one for each added fluid component, and, as the dimension grows, the curvature rapidly becomes more complicated. For example, the binary fluid corresponds to a three-dimensional (3D) phase space, where there are six independent components of the full Riemannian curvature tensor [2]. Which of these components do we focus on for physical interpretation? In this paper, our results suggest that the curvature scalar *R* remains the fundamental physical quantity. (We offer no rigorous proof, but we do note that classical general relativity, based on four-dimensional Riemannian geometry, may be expressed as a variational principle based on the Hilbert action, with *R* as the Lagrangian [2]. This variational principle is certainly not in play in this paper, but we do hope that this significance for *R* translates to the thermodynamic scenario as well).

We calculate *R* for two thermodynamic examples represented by a 3D thermodynamic geometry: (1) a binary van der Waals (vdW) fluid with just repulsive interactions, and (2) a binary vdW fluid with attractive interactions added. To add conceptual structure to our presentation, we discuss to what extent the 3D results for *R* follow the same physical principles as the 2D ones. As we show, there is a great deal of correspondence. (Scenarios with a thermodynamic geometric dimension greater than two have also been considered for black hole thermodynamics; see Sahay for a brief review [3]. This theme is beyond the scope of this paper.)

A few cases have been worked out for *R* for the full 3D thermodynamic geometry. Ruppeiner and Davis [4] worked out *R* for the multicomponent ideal gas, with an arbitrary number of components. Kaviani and Dalafi-Rezaie [5] worked out *R* for the paramagnetic ideal gas, where, in addition to the temperature and the density, there is an external organizing magnetic field. Erdem [6] worked out *R* for the antiferromagnetic Ising model with a temperature and two ordering fields, with special attention to the critical phenomena near the Neel point.

One may also approach 3D thermodynamic geometries by working out *R* over 2D slices of the full 3D thermodynamic geometry. This has physical relevance if, for example, one of the independent variables is irrelevant to a phase transition. Ginoza [7] considered the binary fluid mixture in generality, and calculated *R* 2D along surfaces of constant *T*. Jaramillo-Gutiérrez et al. [8] calculated a constrained *R* 2D by fixing the sum of the mole numbers. These authors made several comments about how their constrained *R* relates to that of the pure fluid. Generally, the calculation is simplified in 2D, but, in an age of powerful mathematics software, considerations of simplicity should maybe no longer be so much of a driving force.

## **2. Expectations for 3D Outcomes for** *R*

For guidance as to what 3D thermodynamic geometry might tell us, let us pose some questions motivated by findings in the pure fluid [9–12]: (a) In the ideal gas limit, is |*R*| either zero or small? "Small" means |*R*|*ρ* < 1, with *ρ* the number density. In this event, the volume measured by |*R*| is less than the average volume occupied by a single particle, and we are under the low |*R*| limit [10,11]. Thermodynamics is challenged at such a size scale, and a precise physical interpretation for *R* is harder to come by (though researchers do try if the opportunity arises). (b) As a critical point is approached, does |*R*| diverge in proportion to the correlation volume *ξ*3? (c) Near a critical point, is the sign of *R* negative? A negative sign is consistent with effectively attractive interactions. (d) Are the values of *R* in two coexisting phases equal to each other near a critical point? (e) Are there interesting regimes of positive *R*? A positive sign is consistent with effectively repulsive interactions. (f) Does the binary repulsive fluid have instances of anomalous negative *R*, such as is present for the hard-sphere pure fluid [13]?

We find considerable physical correspondence between *R* for the pure fluid and for the binary fluid.

## **3. Thermodynamic Geometry of a Binary Fluid**

For a binary fluid, the Helmholtz free energy per volume may be written in terms of its appropriate coordinates [4,14],

$$f = f(T, \rho\_1, \rho\_2),\tag{1}$$

where *T* is the temperature, and *ρ*1 = *n*1/*V* and *ρ*2 = *n*2/*V* are the molar densities of the two components 1 and 2. Here, *n*1 and *n*2 are the mole numbers of the components, and *V* is the volume.

The thermodynamic entropy metric originates from the thermodynamic fluctuation theory [1,15]. Consider a finite open subsystem A*V*, with fixed volume *V*, of an infinite closed thermodynamic fluid system A; see Figure 1. The thermodynamic state (*T*, *ρ*1, *ρ*2) of A*V*, fluctuates in time about the state of A. The Gaussian fluctuation probability density is proportional to

$$\exp\left[-\frac{V}{2}(\Lambda\ell)^2\right],\tag{2}$$

where the entropy metric is [1]

$$
\Delta (\Delta \ell)^2 = \frac{1}{k\_B T} \left( \frac{\partial \mathbf{s}}{\partial T} \right) (\Delta T)^2 + \frac{1}{k\_B T} \sum\_{i,j=1}^2 \left( \frac{\partial \mu\_i}{\partial \rho\_j} \right) \Delta \rho\_i \Delta \rho\_j. \tag{3}
$$

Here, the entropy per volume of A*V* is

$$s = -\frac{\partial f}{\partial T}'\tag{4}$$

and the chemical potentials of the two fluid components are

$$
\mu\_i = \frac{\partial f}{\partial \rho\_i}.\tag{5}
$$

Δ*T*, Δ*ρ*1, and Δ*ρ*2 are the differences in the temperature and density coordinates of A*V* and A. In addition, *kB* is Boltzmann's constant. The thermodynamic metric is employed here in fluctuation theory. It has also been used in finite time thermodynamics [16] as a measure of dissipation.

**Figure 1.** A standard structure in thermodynamic fluctuation theory, a single open subsystem A*V*, with fixed volume *V*, of an infinite closed environment A.

Let us emphasize a point not always appreciated in the metric geometry of thermodynamic fluctuations. A major project in this geometry is to calculate the thermodynamic curvature *R*. We want *R* to tell us something about the intrinsic properties of the material comprising the system A. This goal naturally requires the use of an open subsystem A*V*, so as to leave particles free to move in or out of A*V*, unimpeded by any surrounding artificial wall or membrane. Such a physical constraint would change the value of *R* in a way involving more than just the properties of the particles; this should be avoided. As emphasized by Callen [14], fluid thermodynamics requires us to set one of the thermodynamic variables aside as the fixed subsystem scale. For an open system, this scale is the volume *V*. We recommend that authors always work with open subsystems for calculating *R*.

In the coordinates (*T*, *ρ*1, *ρ*2), the metric tensor **g** is composed of five nonzero elements, which can be read off from Equation (3):

$$\mathbf{g} = \frac{1}{k\_B T} \begin{pmatrix} -\frac{\partial^2 f}{\partial T^2} & 0 & 0\\ 0 & \frac{\partial^2 f}{\partial \rho\_1^2} & \frac{\partial^2 f}{\partial \rho\_1 \partial \rho\_2} \\\ 0 & \frac{\partial^2 f}{\partial \rho\_2 \partial \rho\_1} & \frac{\partial^2 f}{\partial \rho\_2^2} \end{pmatrix} . \tag{6}$$

The fourth-rank curvature tensor has elements [2]

$$R^{a}\_{\beta\gamma\delta} = \Gamma^{a}\_{\beta\gamma,\delta} - \Gamma^{a}\_{\beta\delta,\gamma} + \Gamma^{\mu}\_{\beta\gamma}\Gamma^{a}\_{\delta\mu} - \Gamma^{\mu}\_{\beta\delta}\Gamma^{a}\_{\gamma\mu\star} \tag{7}$$

where the Greek indices range from 1, 2, 3, and denote the coordinates (*T*, *ρ*1, *ρ*2), respectively. The Christoffel symbols are defined as

$$
\Gamma^{\mathfrak{g}}\_{\hat{\mathcal{P}}\gamma} = \frac{1}{2} g^{a\mu} (g\_{\mu\gamma,\mathfrak{g}} + g\_{\mu\mathfrak{f},\gamma} - g\_{\mathfrak{f}\gamma,\mu}),
\tag{8}
$$

where *gαβ* denotes the elements of the inverse of the metric **g** with elements *gαβ*. We use the comma notation (e.g., , *β*) to denote the partial derivative with respect to some specific coordinate. Repeated indices are summed over. The second-rank Ricci tensor is given by

$$R\_{\alpha\beta} = R\_{\alpha\mu\beta'}^{\mu} \tag{9}$$

and the Ricci curvature scalar is

$$R = \mathcal{g}^{\mu\nu} R\_{\mu\nu}.\tag{10}$$

It is straightforward to show that *R* has units of volume per particle for the binary fluid, the same units as for the pure fluid. These units alone label *R* as a measure of some sort of size scale within the system. The definition of the Riemannian curvature tensor is ambiguous with respect to a sign, and we use the sign convention of Weinberg [17], where the two spheres have negative *R*.

## **4. Thermodynamic Stability**

Fluctuations must satisfy thermodynamic stability, requiring maximum entropy of A in equilibrium. This is obtained if the line element in Equation (3) is positive definite for all fluctuations. A necessary and sufficient condition for thermodynamic stability is that the metric coefficients in Equation (6) satisfy the three following conditions [1,18]:

$$
\log\_{11} > 0,\tag{11}
$$

$$\left| \begin{array}{cc} \mathcal{G}11 & \mathcal{G}12 \\ \mathcal{G}21 & \mathcal{G}22 \end{array} \right| > 0, \tag{12}$$

and

$$
\begin{vmatrix}
\mathcal{S}11 & \mathcal{S}12 & \mathcal{S}13 \\
\mathcal{S}21 & \mathcal{S}22 & \mathcal{S}23 \\
\mathcal{S}31 & \mathcal{S}32 & \mathcal{S}33
\end{vmatrix} > 0.\tag{13}
$$

We tested frequently for stability.

#### **5. Helmholtz Free Energy for Binary van der Waals**

We take the Helmholtz free energy per mole for binary vdW from Konynenburg and Scott [19]:

$$\begin{split} A\_{\mathfrak{m}} &= \mathfrak{e}(T) - \mathcal{R} \, T \log \left( \frac{V\_{\mathfrak{m}} - b}{V\_{\mathfrak{m}0}} \right) \\ &\quad + \mathcal{R} \, T \left[ (1 - \mathfrak{x}) \log(1 - \mathfrak{x}) + \mathfrak{x} \log(\mathfrak{x}) \right] - \frac{a}{V\_{\mathfrak{m}}} \end{split} \tag{14}$$

where

$$
\sigma(T) = -\frac{3}{2}\mathcal{R}\,T\ln\left(\frac{T}{T\_0}\right) + \epsilon \tag{15}
$$

is the purely thermal part of the ideal gas contribution, R is the universal gas constant, *Vm* = *V*/(*n*1 + *n*2) is the molar volume, *Vm*0, *T*0, and are constants that do not appear in *R*, and *x* is the concentration

$$\mathbf{x} = \frac{n\_2}{n\_1 + n\_2}.\tag{16}$$

The quantities *a* and *b* are functions of *x* reflecting the purely attractive and repulsive parts of the interparticle interactions, respectively:

$$a(\mathbf{x}) = (1 - \mathbf{x})^2 a\_{11} + 2\mathbf{x}(1 - \mathbf{x}) \, a\_{12} + \mathbf{x}^2 a\_{22},\tag{17}$$

and

$$b(\mathbf{x}) = (1 - \mathbf{x}) \, b\_{11} + \mathbf{x} \, b\_{22}, \tag{18}$$

with *a*11, *a*12, *a*22, *b*11, and *b*22 as the five independent vdW coefficients.

The full (extensive) Helmholtz free energy is

$$A(T, n\_1, n\_2, V) = (n\_1 + n\_2)A\_{m\_1} \tag{19}$$

and the Helmholtz free energy per volume is

$$f(T, \rho\_1, \rho\_2) = \frac{A(T, n\_1, n\_2, V)}{V}.\tag{20}$$

For the pure fluid, vdW simplifies by using scaled units [15]. For binary vdW, scaling cannot be done in a natural way. One possibility is to scale in terms of the van der Waals coefficients of one of the fluid components [19], but this seems somewhat artificial. In this paper, we avoid scaled units, and simply adopt real units when needed.

## **6. Repulsive Binary van der Waals**

First consider the case with only repulsive interactions, with zero *a* coefficients, *b*11 = *b*1, and *b*22 = *b*2. By Equation (20), we have

$$\begin{split} f(T, \rho\_1, \rho\_2) &= -k\_B T (\rho\_1 + \rho\_2) \log \left[ \frac{1 - b\_1 \rho\_1 - b\_2 \rho\_2}{V\_{m0}} \right] + k\_B T \rho\_1 \log \left( \rho\_1 \right) \\ &+ k\_B T \rho\_2 \log \left( \rho\_2 \right) - \frac{3}{2} k\_B T (\rho\_1 + \rho\_2) \log \left( \frac{T}{T\_0} \right) + \varepsilon (\rho\_1 + \rho\_2), \end{split} \tag{21}$$

where we send R → *kB* to convert *ρ*1 and *ρ*2 to units of particles per volume.

By using Equation (21), and the process described in Section 3, we find:

$$\begin{split} R = \frac{1}{2\left(\rho\_1 + \rho\_2\right)} \left[1 - 2b\_2\rho\_1 - 2b\_1\rho\_2 - 4b\_1\rho\_1 - 4b\_2\rho\_2 + 5b\_1^2\rho\_1\rho\_2 \\ \quad + 5b\_2^2\rho\_1\rho\_2 + 5b\_1^2\rho\_1^2 + 5b\_2^2\rho\_2^2\right]. \end{split} \tag{22}$$

Note, *R* for repulsive vdW has no dependence on *T*, nor does it depend on the constants in Equation (21), other than the *b*'s.

Since *R* has units of volume per particle, *R* × (*ρ*1 + *ρ*2) is dimensionless. Setting *b*1 = *b*2 = *b* yields

$$R \times \left(\rho\_1 + \rho\_2\right) = \frac{1}{2} \left[1 - b\left(\rho\_1 + \rho\_2\right)\right] \left[1 - 5b\left(\rho\_1 + \rho\_2\right)\right].\tag{23}$$

If *b* → 0, this expression agrees with Ruppeiner and Davis [4] for the binary ideal gas with the thermal contribution in Equation (15). *R* × (*ρ*1 + *ρ*2) is shown as a contour graph in Figure 2.

With only the *b* coefficients nonzero, we would naively expect *R* > 0, consistent with repulsive interactions. Cases with *R* < 0 clearly occur, mirroring the situation in the pure fluid where, for example, the gas of hard-spheres has negative *R* [13]. Such anomalous results might be dismissed as aberrations since we are below the low |*R*| limit. However, it is interesting that the negative sign persists from the pure fluid into the binary fluid. This consistency contributes to the need for a more nuanced interpretation for the sign of *R*.

**Figure 2.** The contour graph of *R* × (*ρ*1 + *ρ*2). On approaching the bold red line from below, the pressure *P* → +∞. Above the line *P* is negative. The physical regime is below the line, where *R* has both positive and negative values, with a minimum of *R* × (*ρ*1 + *ρ*2) = −0.4. In the physical regime, values of *R* × (*ρ*1 + *ρ*2) are all less than the low |*R*| limit. The value at the origin is 1/2.

## **7. Attractive Binary van der Waals**

Now turn on the attractive interactions in binary vdW. In this scenario, Konynenburg and Scott [19] classified nine distinct possibilities, depending on the values of the vdW *a* and *b* coefficients. We consider here only an instance of their Type I possibility, with a single curve of critical points continuously connecting the critical points of the pure fluid components *x* = 0 and *x* = 1. Our example has vdW coefficients *a*11 = 0.002, *a*22 = 0.005, *a*12 = 0.004, and *b*11 = *b*22 = 0.00002. (In MKS units, the units of the *a*'s are Joules meters3/mole2 , and the units of the *b*'s are meters3/mole. These vdW coefficients produce critical points very roughly in the zone of normal fluid Helium.)

To structure the discussion, note that if *T* is high, the attraction between the particles has little effect, and we expect no phase transitions. Now consider lowering *T* slowly, with the particle numbers and the volume held fixed. We might move along such an isochore in a laboratory *PVT* experiment; see Figure 3. As *T* decreases, attractive interatomic interactions become more effective, and the binary fluid could eventually break into two phases.

**Figure 3.** The binary fluid inside a closed container fixing the number of particles and the volume. As the temperature is lowered, the kinetic energy decreases, and the fluid generally breaks into two phases at some temperature. The phases have different *x*'s.

These phase transitions have associated second-order curves of critical points [19]. For Type 1, every *x* has a single critical point with critical coordinates *T* = *Tc*, *P* = *Pc*, and *Vm* = *Vmc*. In their

Appendix A, Konynenburg and Scott [19] describe an explicit procedure *x* → (*Tc*, *Pc*, *Vmc*) for locating these critical points.

The critical curve is shown in Figure 4. The det(**g**) switches signs upon crossing this critical curve, with the thermodynamics stable above the curve and unstable below it, according to Equations (11)–(13). *R* diverges to negative infinity on the critical curve.

**Figure 4.** The critical parameters (*Tc*, *Pc*, *Vmc*) as functions of *x* (**a**–**c**). On crossing the critical curve, det(**g**) switches sign, as shown in (d), with *g* = det(**g**) calculated along critical isochores (*x*, *T*, *Vmc*). The thermodynamics is thus stable above the critical curve and unstable below it. *R* diverges to negative infinity on the critical curve.

The theoretical expectations on approaching the critical curve are well-known. A general physical argument was given by Widom [20] in the context of the hyperscaling critical exponent relation

$$d\,\nu = 2 - a,\tag{24}$$

where *d* is the spatial dimension (*d* = 3 here), *α* is the heat capacity critical exponent (*α* = 0 here), and *ν* is the correlation length critical exponent. On approaching the critical curve from above along a critical isochore with fixed *x*, fixed *Vm* = *Vmc*, and decreasing *T*, the correlation length is expected to diverge according to:

$$
\zeta^d \propto \left(\frac{T - T\_c}{T\_c}\right)^{a-2}.\tag{25}
$$

A key finding in previous research is that |*R*| ∝ *ξd* near a critical point [1,21–23], (The constant of proportionality between *R* and *ξ*3 calculated for both fluid and magnetic systems in distinct spatial dimensions appears to be −1/2: −1 2*R* = *ξd*; see [23] for a brief review.) and so we expect

$$|R| \propto \left(\frac{T - T\_{\hat{c}}}{T\_{\hat{c}}}\right)^{-2} \tag{26}$$

along a critical isochore.

An interesting contrast to binary vdW is offered by pure fluid vdW, where *R* is computed with 2D thermodynamic geometry. It was shown [1] that the asymptotic divergence of *R* for the pure vdW fluid, with the thermal ideal gas contribution as in Equation (15), along the critical isochore is

$$R = -b\left(\frac{T - T\_c}{T\_c}\right)^{-2}\,\_{\prime} \tag{27}$$

independent of the vdW constant *a*. Here, *b* = *b*11 if *x* = 0 and *b* = *b*22 if *x* = 1.

Physically, *ξ*3 should be the same for a binary fluid in the limits *x* → 0 or *x* → 1 as for the corresponding pure fluids. Since *R* in the critical region is a measure of *ξ*3, we might then physically expect the limiting *R* 3D's to be at least approximately equal to the corresponding *R* 2D's. Remarkably, this limiting correspondence holds very well, even though the 2D and 3D formulas for *R* are quite different.

We computed *R* along four critical isochores in 3D thermodynamic geometry, *x* = 0.2, 0.4, 0.6, and 0.8. Results near the critical point are shown in Figure 5. The four curves clearly overlap each other very closely, and show very little dependence on *x*. The asymptotic *R* is always negative, in accordance with expectations for effectively attractive interactions. The critical curves have asymptotic power law divergences, in accordance with Equation (26). The critical exponents of the four curves are all within better than 0.3% of the expected value 2, with the power law fits done over the full range of the data shown in Figure 5. Erdem [6] got similar 3D power law behavior in the Ising antiferromagnet. Note as well that the smallest values of |*R*| in Figure 5 are about 4 nm3/atom, so values near the particle level are on the asymptotic power law line. Such a large span of the critical regime was seen also in magnetic systems [23].

**Figure 5.** −*R* computed with the *R* 3D formula versus the reduced temperature for four critical isochores in the critical region. Points all fall nearly on the same straight line with slope −2. The values of *R* are all negative. Additionally shown is −*R* computed with the *R* 2D formula for the two pure fluids *x* = 0 and 1 along the critical isochores. Somewhat remarkably, these points also fall on the common line.

Additionally shown in Figure 5 is −*R* for the pure fluids *x* = 0 and 1 calculated with the 2D thermodynamic geometry. Asymptotically, we expect these curves to obey Equation (27), and we found that they do. The *R* 2D curves are in excellent agreement with the corresponding *R* 3D curves.

Next, we consider letting the binary fluid expand into the binary ideal gas state, which has the dimensionless quantity [4]

$$R \times (\rho\_1 + \rho\_2) = \frac{1}{2}.\tag{28}$$

We approached the binary ideal gas limit for four fixed values of *x* by starting at (*Tc*, *Vmc*) for each *x*, and increasing *Vm* at constant *T* = *Tc*. Results of this expansion are shown in Figure 6. Clearly, for each *x*, *R* × (*ρ*1 + *ρ*2) → 1/2, in accord with Equation (28).

**Figure 6.** The approach to the ideal gas limit. For each fixed *x*, we proceed at constant *T* = *Tc* by increasing *Vm*, starting from *Vmc*. This leads to the ideal gas where we expect *R* × (*ρ*1 + *ρ*2) = 1/2.

## **8. Conclusions**

We have made a start in calculating the full three-dimensional thermodynamic Ricci curvature scalar *R* in an interacting binary fluid system. Our main finding is that the physical interpretation of *R* for the pure fluid extends very naturally to the binary fluid. The emerging physical picture for the thermodynamic *R* is thus quite robust. We calculated *R* for two scenarios involving the van der Waals model for the binary fluid. The first had exclusively repulsive interactions, and the second added attractive interactions, and critical phenomena.

Let us place our results in the context of the expectations in Section 2. (a) In the binary ideal gas limit, we expect *R* × (*ρ*1 + *ρ*2) = 1/2 from an earlier exact calculation. Figure 6 clearly shows this known limit. This limit is also shown at the origin of Figure 2. Both these figures (in the ideal gas limit) have |*R*| smaller than the low |*R*| limit, and so the results here are not as strong as those in the critical regime, where |*R*| is much larger. (b) Near critical points, |*R*| was found to diverge with the expected critical exponent of 2, as shown in Figure 5. In the limits as the binary fluid goes to the pure fluid, we found excellent concordance with the pure fluid results calculated with the 2D thermodynamic geometry. These critical point results are the strongest that we present in this paper. (c) Near critical points, *R* was found to be negative, as shown in Figure 5. This negative sign is expected when interactions are effectively attractive. (d) Evaluating *R* along coexistence curves was beyond the scope of our paper. (e) Our regimes of positive *R* were all more or less expected, with values all under the low |*R*| limit. A more systematic search of the thermodynamic phase space for more interesting cases (above the low |*R*| limit) was beyond the scope of our paper. (f) We found that the repulsive vdW was negative at large densities, in accord with the anomaly found by Bra ´nka et al., for the hard sphere [13]; see Figure 2. That this anomaly translates from the 2D to the 3D thermodynamic geometry is interesting.

**Author Contributions:** Formal analysis, G.R. and A.S.; Project administration, G.R.; Writing—original draft, G.R. and A.S.; Writing—review & editing, G.R. and A.S. All authors have read and agreed to the published version of the manuscript.

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

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

## **References**

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© 2020 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 (http://creativecommons.org/licenses/by/4.0/).


*2.3. Sampling*

After collecting blood samples, according to the approved working protocol, the chicks (6 chicks/group) were electrically stunned and subsequently slaughtered by cervical dislocation. After bleeding and evisceration, thigh and breast meat samples were collected (6 breast and 6 thigh meat samples per group). From each of the samples collected, samples were taken to determine the proximate composition (dry matter—DM, crude protein—CP, ether extractives—EE, ash) and to determine the color, texture, and pH parameters. Until analysis, the samples were stored in plastic bags at −20 ◦C.

**Table 1.** Nutrient composition of experimental basal diets (%).

1 kg of A1 premix contains 1,100,000 IU/kg vitamin A; 200,000 IU/kg vitamin D3; 2700 IU/kg vitamin E; 300 mg/kg vitamin K; 200 mg/kg Vit. B1; 400 mg/kg vitamin B2; 1485 mg/kg pantothenic acid; 2700 mg/kg nicotinic acid; 300 mg/kg vitamin B6; 4 mg/kg Vit. B7; 100 mg/kg vitamin B9; 1.8 mg/kg vitamin B12; 2000 mg/kg vitamin C; 8000 mg/kg manganese; 8000 mg/kg iron; 500 mg/kg copper; 6000 mg/kg zinc; 37 mg/kg cobalt; 152 mg/kg iodine; 18 mg/kg selenium. C: control diet; E1: experimental diet supplemented with 200 μg/kg diet CrPic + 0.25 g vitamin C (VC)/kg diet; E2: experimental diet supplemented with 200 μg/kg diet CrPic +0.025 g Zn/kg diet; E3: experimental diet supplemented with 200 μg/kg diet CrPic +10 g creeping wood sorrel powder (CWS)/kg diet. 1 Diet structure published previously by Saracila et al. [14]. 2 A1 premix + 20 mg CrPic/kg premix + 25 g vit. C/kg premix; 3 A1 premix + 20 mg CrPic/kg premix + 2.5 g Zn/kg premix; 4 A1 premix + 20 mg CrPic/kg premix + 1% creeping wood sorrel powder.


4. Caesium (Cs) "consumption"

It is currently estimated that Cs will need to be injected into each ion source at a rate of ≈20 mg/h in order to reach the required extracted negative ion current. With quasi-continuous operation and that Cs injection rate, >1 kg will have been injected into each source every 6 years. It has been found that most of the injected Cs remains in the ion source and significantly less than 1 kg of Cs is almost certain to cause operational problems. There are three possible ways to overcome this problem:


**15. BRAF plus MEK inhibitors**

Therapy with a MEK inhibitor in combination with a BRAF inhibitor is more effective and less toxic than treatment with a BRAF inhibitor alone, and has become the standard of care for patients with BRAF-mutated melanoma. Trametinib, the first MEK inhibitor was approved for the treatment of BRAF-mutated metastatic melanoma not previously treated with BRAF inhibitors, and is also approved in combination with the BRAF inhibitor dabrafenib [68].

The clinical study about combination dabrafenib and trametinib versus dabrafenib monotherapy in BRAF V600E/K–mutant metastatic melanoma demonstrated improved progression-free survival and overall survival. Phase III clinical study enrolled previously untreated patients with BRAF V600E/K–mutant unresectable stage IIIC or stage IV melanoma. Patients were randomized to receive dabrafenib, 150 mg twice daily, plus trametinib, 2 mg once daily, or dabrafenib plus placebo. The primary endpoint was progression-free survival; secondary endpoints were overall response, duration of response, pharmacokinetics and safety. Results showed that 423 of 947 screened patients were randomly assigned to receive dabrafenib plus trametinib (n = 211) or dabrafenib monotherapy (n = 212). At data cutoff, outcomes remained superior with the combination: 3-year progression-free was 22% with dabrafenib plus trametinib versus 12% with monotherapy, and 3-year overall response was 44 versus 32%, respectively. Twenty-five patients receiving monotherapy crossed over to combination therapy, with continued follow-up under the monotherapy arm. Of combination-arm patients alive at 3 years, 58% remained on dabrafenib plus trametinib. Three-year overall response with the combination reached 62% in the most favorable subgroup (normal lactate dehydrogenase) versus only 25% in the unfavorable subgroup (elevated lactate dehydrogenase). The dabrafenib plus trametinib safety profile was consistent with previous clinical trial observations, and no new safety signals were detected with long-term use. These data demonstrate that durable survival is achievable with dabrafenib plus trametinib in patients with BRAF V600–mutant metastatic melanoma [69].

The optimal timing and sequence of combination therapy (in particular targeted therapy in combination with immunotherapy) is currently in progress and cannot be precisely predicted for all patients with melanoma. Due to the existence of many potential targets in the immune system many critical questions arise, e.g. which therapy combinations should move forward in development and which patients will benefit from these treatments [70].


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