\r\n\tGlobalization does not represent a pure and generous process for humanity or other species, but rather it implies social exclusion and also provokes situations of vulnerability in groups of people, forced exclusion, and apartheid: poor job opportunities, lack of access to education, worse socio-sanitary conditions. Specifically, it can be said that social segregation entails the apartheid of social groups of different ages, genders, and ethnicities; these groups live a reality manifested through the deepening of poverty, in terms of increased vulnerability of the poor and groups with little economic, social, cultural, labor and health stability.
\r\n\r\n\tThis book aims to talk about some topics that are neglected in the discourses of academic communities and political elites. The inequality process is deeply rooted among humans and is part of many people's lives in the form of modern apartheid, gender segregation, lack of health access, and cultural gap. All those structural inequality processes are the product of the biopower perpetuated and produced in the macrosystem, exosystem, mesosystem, and microsystem. For many people from the academy, the information-consuming public, and the society in general, it is a problem to talk about these processes, since they have either lost interest or have normalized the structural and social inequity. For this reason, we see it as transcendental to explain how this situation occurs from the most internal fibers to the most evident processes, intending to make it more visible and thus expose the situation for possible solutions.
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A typical feature of many of these problems is that evolution of interaction Hamiltonians takes significantly longer than the time required to generate local unitary transformations (unitary transformations that effect individual spins only). In NMR spectroscopy [2, 3], local unitary transformations on spins are obtained by application of rf-pulses, whose strength may be orders of magnitude larger than the couplings between the spins. Given the Schróedinger equation for unitary evolution
\nwhere \n
The Hamiltonian of a spin \n
Note
\nwhere \n
The Hamiltonian for a system of two coupled spins takes the general form
\nwhere \n
is the coupling or interaction Hamiltonian and operates on both the spins.
\nThe following notation is therefore common place in the NMR literature.
\nThe operators \n
The unitary transformations of the kind
\nobtained by evolution of the local Hamiltonians are called local unitary transformations.
\nThe coupling Hamiltonian can be written as
\nWritten explicitly, some of these matrices take the form
\nand
\nThe \n
for \n
The Lie algebra \n
Here \n
This decomposition of a real semi-simple Lie algebra \n
This special structure of Cartan decomposition arising in dynamics of two coupled spins in Eq. (1), motivates study of a broader class of time optimal control problems.
\nConsider the following canonical problems. Given the evolution
\nwhere \n
We assume \n
In general, \n
Given the Cartan decomposition \n
The special structure of this problem helps in complete description of the reachable set [27]. The elements of the reachable set at time \n
where \n
This reachable set can be understood as follows. The Cartan decomposition of the Lie algebra \n
Then, any arbitrary element of the group \n
for some \n
The results in this chapter suggest that \n
Written as evolution
\nwhere \n
The chapter is organized as follows. In Section 2, we study the \n
Given Lie algebra \n
where \n
To understand the reachable set of this system we make a change of coordinates \n
If we understand reachable set of \n
and \n
For \n
By KAK, \n
where, \n
Observe
\nWe equate \n
Multiplying both sides with \n
where, \n
We evaluate \n
such that \n
Given \n
with \n
With this choice of \n
Consider the case, when \n
where \n
Consider the decomposition
\nwhere \n
where \n
Then we write
\nwhere in Eq. (24) we can solve for \n
Let \n
where \n
is a diagonal matrix. Let \n
where
\n\n\n
Note \n
as \n
Now using \n
where the above expression can be written as
\nwhere \n
Let \n
Choose an ordering of \n
\n\n
By Schur convexity,
\nwhere \n
Therefore,
\nThe difference
\nis regulated by size of \n
For each point \n
A. Collection of overlapping neighborhoods forming the finite subcover. B. Depiction of
Then we get the following recursive relations.
\nwhere \n
Adding the above equations,
\nwhere \n
where \n
Note, \n
where \n
From Theorem 1, we have \n
We can synthesize \n
The transformation maps the algebra \n
where \n
Multiplying both sides with \n
where \n
Note \n
where \n
Furthermore \n
\n\n
Consider the product
\nwhere \n
Observe \n
Multiplying both sides with \n
which we can write as
\nwhere using \n
Furthermore \n
\n\n
\n\n
Let
\n\n\n
\n\n
The range of \n
where \n
\n\n
Let \n
then by one to one property of \n
Given a sequence \n
Let \n
if \n
as \n
where \n
where \n
and show that
\nwhere for \n
where \n
To show Eq. (46), we show there exists \n
where \n
Given \n
where \n
We bound the largest element (absolute value) of \n
where \n
Given decomposition of \n
Given
\nwhere \n
We describe an iterative procedure
\nwhere \n
where \n
Note \n
Where, using bound in \n
This gives, \n
For \n
Similarly,
\nNote, \n
where \n
The above exercise was illustrative. Now we use an iterative procedure as above to show Eq. (47).
\nWriting
\nwhere \n
We refer to Remark 5, Eq. (45). Given \n
\n\n
which gives \n
we obtain
\nwhere \n
where \n
where, using bounds derived above \n
which gives \n
We can decompose, \n
This gives
\nFor \n
Using \n
Similarly,
\nNote, \n
where \n
The above iterative procedure generates \n
where \n
such that \n
This follows because the orthogonal part of \n
(\n
where \n
\n\n
This implies \n
We have shown existence of \n
Applying the theorem again to
\nwhere \n
where, \n
Using Lemma 1 and 2, we can express
\nLetting \n
Hence the proof of theorem.
In this chapter, we studied some control problems that derive from time optimal control of coupled spin dynamics in NMR spectroscopy and quantum information and computation. We saw how dynamics was decomposed into fast generators \n
If you are associated with any of the institutions in our list below, you can apply to receive OA publication funds by following the instructions provided in the links.
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The term “culture”, which diversifies in each community and so is experienced differently, also affects the way individuals perceive the phenomena such as health, illness, happiness, sadness and the manner these emotions are experienced. The term health, whose nature and meaning is highly variable across different cultures requires care involving cultural recognition, valueing and practice. The nursing profession, which plays an important role in the health team, is often based on a cultural phenomenon. The cultural values, beliefs and practices of the patient are an integral part of holistic nursing care. The aim of nursing is to provide a wholly caring and humanistic service respecting people’s cultural values and lifestyles. Nurses should offer an acceptable and affordable care for the individuals under the conditions of the day. 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He is a full professor of signal processing and pattern recognition and is head of the Signals and Communications Department at ULPGC, teaching from 2001 on subjects on signal processing and learning theory. His research lines are biometrics, biomedical signals and images, data mining, classification system, signal and image processing, machine learning, and environmental intelligence. He has researched in 52 international and Spanish research projects, some of them as head researcher. He is co-author of 4 books, co-editor of 27 proceedings books, guest editor for 8 JCR-ISI international journals, and up to 24 book chapters. He has over 450 papers published in international journals and conferences (81 of them indexed on JCR – ISI - Web of Science). He has published seven patents in the Spanish Patent and Trademark Office. He has been a supervisor on 8 Ph.D. theses (11 more are under supervision), and 130 master theses. He is the founder of The IEEE IWOBI conference series and the president of its Steering Committee, as well as the founder of both the InnoEducaTIC and APPIS conference series. He is an evaluator of project proposals for the European Union (H2020), Medical Research Council (MRC, UK), Spanish Government (ANECA, Spain), Research National Agency (ANR, France), DAAD (Germany), Argentinian Government, and the Colombian Institutions. He has been a reviewer in different indexed international journals (<70) and conferences (<250) since 2001. 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Papakostas has received a diploma in Electrical and Computer Engineering in 1999 and the M.Sc. and Ph.D. degrees in Electrical and Computer Engineering in 2002 and 2007, respectively, from the Democritus University of Thrace (DUTH), Greece. Dr. Papakostas serves as a Tenured Full Professor at the Department of Computer Science, International Hellenic University, Greece. Dr. Papakostas has 10 years of experience in large-scale systems design as a senior software engineer and technical manager, and 20 years of research experience in the field of Artificial Intelligence. Currently, he is the Head of the “Visual Computing” division of HUman-MAchines INteraction Laboratory (HUMAIN-Lab) and the Director of the MPhil program “Advanced Technologies in Informatics and Computers” hosted by the Department of Computer Science, International Hellenic University. He has (co)authored more than 150 publications in indexed journals, international conferences and book chapters, 1 book (in Greek), 3 edited books, and 5 journal special issues. His publications have more than 2100 citations with h-index 27 (GoogleScholar). His research interests include computer/machine vision, machine learning, pattern recognition, computational intelligence. \nDr. Papakostas served as a reviewer in numerous journals, as a program\ncommittee member in international conferences and he is a member of the IAENG, MIR Labs, EUCogIII, INSTICC and the Technical Chamber of Greece (TEE).",institutionString:null,institution:{name:"International Hellenic University",institutionURL:null,country:{name:"Greece"}}},editorTwo:null,editorThree:null},{id:"25",title:"Evolutionary Computation",coverUrl:"https://cdn.intechopen.com/series_topics/covers/25.jpg",isOpenForSubmission:!0,editor:{id:"136112",title:"Dr.",name:"Sebastian",middleName:null,surname:"Ventura Soto",slug:"sebastian-ventura-soto",fullName:"Sebastian Ventura Soto",profilePictureURL:"https://mts.intechopen.com/storage/users/136112/images/system/136112.png",biography:"Sebastian Ventura is a Spanish researcher, a full professor with the Department of Computer Science and Numerical Analysis, University of Córdoba. Dr Ventura also holds the positions of Affiliated Professor at Virginia Commonwealth University (Richmond, USA) and Distinguished Adjunct Professor at King Abdulaziz University (Jeddah, Saudi Arabia). Additionally, he is deputy director of the Andalusian Research Institute in Data Science and Computational Intelligence (DaSCI) and heads the Knowledge Discovery and Intelligent Systems Research Laboratory. He has published more than ten books and over 300 articles in journals and scientific conferences. Currently, his work has received over 18,000 citations according to Google Scholar, including more than 2200 citations in 2020. In the last five years, he has published more than 60 papers in international journals indexed in the JCR (around 70% of them belonging to first quartile journals) and he has edited some Springer books “Supervised Descriptive Pattern Mining” (2018), “Multiple Instance Learning - Foundations and Algorithms” (2016), and “Pattern Mining with Evolutionary Algorithms” (2016). He has also been involved in more than 20 research projects supported by the Spanish and Andalusian governments and the European Union. He currently belongs to the editorial board of PeerJ Computer Science, Information Fusion and Engineering Applications of Artificial Intelligence journals, being also associate editor of Applied Computational Intelligence and Soft Computing and IEEE Transactions on Cybernetics. Finally, he is editor-in-chief of Progress in Artificial Intelligence. He is a Senior Member of the IEEE Computer, the IEEE Computational Intelligence, and the IEEE Systems, Man, and Cybernetics Societies, and the Association of Computing Machinery (ACM). Finally, his main research interests include data science, computational intelligence, and their applications.",institutionString:null,institution:{name:"University of Córdoba",institutionURL:null,country:{name:"Spain"}}},editorTwo:null,editorThree:null},{id:"26",title:"Machine Learning and Data Mining",coverUrl:"https://cdn.intechopen.com/series_topics/covers/26.jpg",isOpenForSubmission:!0,editor:{id:"24555",title:"Dr.",name:"Marco Antonio",middleName:null,surname:"Aceves Fernandez",slug:"marco-antonio-aceves-fernandez",fullName:"Marco Antonio Aceves Fernandez",profilePictureURL:"https://mts.intechopen.com/storage/users/24555/images/system/24555.jpg",biography:"Dr. Marco Antonio Aceves Fernandez obtained his B.Sc. (Eng.) in Telematics from the Universidad de Colima, Mexico. 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Possible contributions can address (but are not limited to) the following research topics: Bioinspired design and control of exoskeletons, orthoses, and prostheses; Experimental evaluation of the effect of assistive devices (e.g., influence on gait, balance, and neuromuscular system); Bioinspired technologies for rehabilitation, including clinical studies reporting evaluations; Application of neuromuscular and biomechanical models to the development of bioinspired technology.',annualVolume:11404,isOpenForSubmission:!0,coverUrl:"https://cdn.intechopen.com/series_topics/covers/8.jpg",editor:{id:"144937",title:"Prof.",name:"Adriano",middleName:"De Oliveira",surname:"Andrade",fullName:"Adriano Andrade",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRC8QQAW/Profile_Picture_1625219101815",institutionString:null,institution:{name:"Federal University of Uberlândia",institutionURL:null,country:{name:"Brazil"}}},editorTwo:null,editorThree:null,editorialBoard:[{id:"49517",title:"Prof.",name:"Hitoshi",middleName:null,surname:"Tsunashima",fullName:"Hitoshi Tsunashima",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002aYTP4QAO/Profile_Picture_1625819726528",institutionString:null,institution:{name:"Nihon University",institutionURL:null,country:{name:"Japan"}}},{id:"425354",title:"Dr.",name:"Marcus",middleName:"Fraga",surname:"Vieira",fullName:"Marcus Vieira",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0033Y00003BJSgIQAX/Profile_Picture_1627904687309",institutionString:null,institution:{name:"Universidade Federal de Goiás",institutionURL:null,country:{name:"Brazil"}}},{id:"196746",title:"Dr.",name:"Ramana",middleName:null,surname:"Vinjamuri",fullName:"Ramana Vinjamuri",profilePictureURL:"https://mts.intechopen.com/storage/users/196746/images/system/196746.jpeg",institutionString:"University of Maryland, Baltimore County",institution:{name:"University of Maryland, Baltimore County",institutionURL:null,country:{name:"United States of America"}}}]},{id:"9",title:"Biotechnology - Biosensors, Biomaterials and Tissue Engineering",keywords:"Biotechnology, Biosensors, Biomaterials, Tissue Engineering",scope:"The Biotechnology - Biosensors, Biomaterials and Tissue Engineering topic within the Biomedical Engineering Series aims to rapidly publish contributions on all aspects of biotechnology, biosensors, biomaterial and tissue engineering. We encourage the submission of manuscripts that provide novel and mechanistic insights that report significant advances in the fields. Topics can include but are not limited to: Biotechnology such as biotechnological products and process engineering; Biotechnologically relevant enzymes and proteins; Bioenergy and biofuels; Applied genetics and molecular biotechnology; Genomics, transcriptomics, proteomics; Applied microbial and cell physiology; Environmental biotechnology; Methods and protocols. Moreover, topics in biosensor technology, like sensors that incorporate enzymes, antibodies, nucleic acids, whole cells, tissues and organelles, and other biological or biologically inspired components will be considered, and topics exploring transducers, including those based on electrochemical and optical piezoelectric, thermal, magnetic, and micromechanical elements. Chapters exploring biomaterial approaches such as polymer synthesis and characterization, drug and gene vector design, biocompatibility, immunology and toxicology, and self-assembly at the nanoscale, are welcome. Finally, the tissue engineering subcategory will support topics such as the fundamentals of stem cells and progenitor cells and their proliferation, differentiation, bioreactors for three-dimensional culture and studies of phenotypic changes, stem and progenitor cells, both short and long term, ex vivo and in vivo implantation both in preclinical models and also in clinical trials.",annualVolume:11405,isOpenForSubmission:!0,coverUrl:"https://cdn.intechopen.com/series_topics/covers/9.jpg",editor:{id:"126286",title:"Dr.",name:"Luis",middleName:"Jesús",surname:"Villarreal-Gómez",fullName:"Luis Villarreal-Gómez",profilePictureURL:"https://mts.intechopen.com/storage/users/126286/images/system/126286.jpg",institutionString:null,institution:{name:"Autonomous University of Baja California",institutionURL:null,country:{name:"Mexico"}}},editorTwo:null,editorThree:null,editorialBoard:[{id:"35539",title:"Dr.",name:"Cecilia",middleName:null,surname:"Cristea",fullName:"Cecilia Cristea",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002aYQ65QAG/Profile_Picture_1621007741527",institutionString:null,institution:{name:"Iuliu Hațieganu University of Medicine and Pharmacy",institutionURL:null,country:{name:"Romania"}}},{id:"40735",title:"Dr.",name:"Gil",middleName:"Alberto Batista",surname:"Gonçalves",fullName:"Gil Gonçalves",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002aYRLGQA4/Profile_Picture_1628492612759",institutionString:null,institution:{name:"University of Aveiro",institutionURL:null,country:{name:"Portugal"}}},{id:"211725",title:"Associate Prof.",name:"Johann F.",middleName:null,surname:"Osma",fullName:"Johann F. 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