Classification of immunotherapy.
\r\n\tThe fundamental research areas of Evolutionary Psychology can be divided into two broad categories: on the one hand, the basic cognitive processes, and the way they evolved within the species, and on the other, the adaptive social behaviors that derive from the theory of evolution itself: survival, mating, parenting, family and kinship, interactions with non-parents and cultural evolution. Indeed, Evolutionary Psychology explains at individual and group level the fundamental behaviors of social life, such as altruism, cooperation, competition, social exclusion, social support, etc. etc. Similar to the mechanisms of natural selection for physical characteristics, not only the mind follows biological laws, but also psychological abilities - such as the theory of mind, the ability to represent the intentions, thoughts, beliefs, and emotions of others - have had to adapt and must make themselves functional to the social life of individuals and groups. In addition, Sociology takes the same aspects into consideration, emphasizing the interaction, symbolic and otherwise, of individuals. The latter investigates the neural mechanisms underlying the same social behaviors that are of interest to evolutionary psychology. To study the neural correlates involved in such behaviors is necessary to understand the biological laws that underlie human behavior and brain functioning.
\r\n\r\n\tThis book aims to open a debate full of theoretical and experimental contributions among the different disciplines in social research, psychology, neuroscience, sociology, useful to give an innovative vision to the present research and future perspective on the topic.
",isbn:"978-1-83968-871-3",printIsbn:"978-1-83968-870-6",pdfIsbn:"978-1-83968-872-0",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"bd4df54e3fb185306ec3899db7044efb",bookSignature:"Dr. Rosalba Morese, Dr. Vincenzo Auriemma and Dr. Sara Palermo",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10450.jpg",keywords:"Evolutionary Psychology, Human Social Evolution, Human Social Behaviour, Social Cognition, Social Neuroscience, Functional Neuroimaging, Neuropsychology, Altruism, Cooperation, Social Exclusion, Social Support, Social Inclusion",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 18th 2020",dateEndSecondStepPublish:"December 21st 2020",dateEndThirdStepPublish:"February 24th 2021",dateEndFourthStepPublish:"May 15th 2021",dateEndFifthStepPublish:"July 14th 2021",remainingDaysToSecondStep:"a month",secondStepPassed:!0,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,biosketch:"Dr. Rosalba Morese is carrying out research in the framework of Neuroscience and Social Psychology. She currently works at the Institute of Public Health of Faculty of Biomedical Sciences and at the Faculty of Communication, Culture, and Society of Università Della Svizzera Italiana, Lugano, Switzerland.",coeditorOneBiosketch:"Dr. Vincenzo Auriemma's focus is on the study of empathy in human interactions. He studied at the University of Essex in England, the University of Pisa, Genoa, Rome in Italy, and the University of Italian Switzerland in Switzerland. He is the principal responsible for the 'PERSEO' research which analyzes the reasons for the 'drop-out' in psychology.",coeditorTwoBiosketch:"Researcher of the EUROPEAN INNOVATION PARTNERSHIP on Active and Healthy Ageing and Assistant Specialty Chief Editor for Frontiers in Psychology - Neuropsychology.",coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"214435",title:"Dr.",name:"Rosalba",middleName:null,surname:"Morese",slug:"rosalba-morese",fullName:"Rosalba Morese",profilePictureURL:"https://mts.intechopen.com/storage/users/214435/images/system/214435.jpg",biography:"Rosalba Morese obtained a degree in psychology at the University of Parma. She subsequently held various\nteaching positions at the Department of Psychology and the Faculty of Medicine and Surgery of the\nUniversity of Parma.\nHer training continued with the attainment of the title of PhD in Neuroscience at the University of Turin,\nduring which she acquired and developed interdisciplinary skills and point of view through the application\nof bioimaging and psychophysiological methods to investigate the neurophysiological mechanisms involved\nduring communication and social interactions.",institutionString:"Universita della Svizzera Italiana",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"6",totalChapterViews:"0",totalEditedBooks:"3",institution:{name:"Universita della Svizzera Italiana",institutionURL:null,country:{name:"Switzerland"}}}],coeditorOne:{id:"338363",title:"Dr.",name:"Vincenzo",middleName:null,surname:"Auriemma",slug:"vincenzo-auriemma",fullName:"Vincenzo Auriemma",profilePictureURL:"https://mts.intechopen.com/storage/users/no_image.jpg",biography:'He is pursuing a PhD in Sociology from the University of Salerno, Italy. He is a researcher of sociology and neurosociology at the University of Salerno, Italy. His focus is on the study of empathy in human interactions and he studied at the University of Essex in England, the University of Pisa, Genoa, Rome 3 in Italy and the University of Italian Switzerland in Switzerland. He has participated in national and international conferences with about 25 reports/communications. He is the principal responsible for the "PERSEO" research which analyzes the reasons for the "drop-out" in psychology, using the methodology of the Gounded Theory and analyzing empathy, fear and panic. He is Co-Editor for Frontiers. He is also a member of the Italian Society of Sociology (AIS).',institutionString:"University of Salerno",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"University of Salerno",institutionURL:null,country:{name:"Italy"}}},coeditorTwo:{id:"233998",title:"Dr.",name:"Sara",middleName:null,surname:"Palermo",slug:"sara-palermo",fullName:"Sara Palermo",profilePictureURL:"https://mts.intechopen.com/storage/users/233998/images/system/233998.jpeg",biography:"Sara Palermo is a MSc in Clinical Psychology and a PhD in Experimental Neuroscience. Moreover, she obtained the National Scientific Enabling Certificate for Associate Professorship in April 2017 (ASN-2017). She is an expert in experimental neuroscience, clinical neuropsychology and advance neuropsychological testing. Moreover, she performs multidimensional geriatric evaluation and basic neurological symptomatology detection in patients with neurodegenerative disorders. She is also engaged in Activation Likelihood Estimation meta-analysis of neuroimaging studies.\r\nShe worked as a postdoc research fellow at the Department of Neuroscience 'Rita Levi Montalcini” in Turin until July 2017. Since then she works as research fellow at the Department of Psychology in Turin. To date, she owns three research Group memberships at the University of Turin (Italy). She is a member of the 'Center for the Study of Movement Disorders” (research area: Neurology) and the 'Placebo Responses Mapping Group” (research area: Physiology) at the Department of Neuroscience, and a member of the 'Neuropsychology of cognitive impairment and central nervous system degenerative diseases Group” at the Department of Psychology (Research Area: Psychobiology and physiological psychology).\r\nThe main topics of her research are the study of awareness of illness, metacognitive-executive deficits in neuropsychiatric and neurological disorders, physical and cognitive frailty in the elderly, and placebo/nocebo phenomena. Interestingly, all of them may represent appealing perspectives from which to study how neuropsychological abnormalities can be explained in terms of brain activities and with the use of neuropsychiatric and neuropsychological batteries considering a neurocognitive approach. Given her research interests and scientific publications, she has been an ordinary member of the Italian Society of Neuropsychology (SINP), of the Italian Association of Psychogeriatrics (AIP), of the Italian Society of Neurology for Dementia (SiNdem), and – finally – of the international Society for Interdisciplinary Placebo Studies (SIPS). Importantly, she is a member of the European Innovation Partnership on Active and Healthy Aging (EIP on AHA), for which she is involved in the Action Group A3 Functional decline and frailty. \r\n\r\nSara Palermo is Panel Editor for 'EC Psychology and Psychiatry'. She was recently appointed as Specialty Chief Editor for 'Frontiers in Psychology - Neuropsychology'.",institutionString:"University of Turin",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"4",totalChapterViews:"0",totalEditedBooks:"3",institution:{name:"University of Turin",institutionURL:null,country:{name:"Italy"}}},coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"21",title:"Psychology",slug:"psychology"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"259492",firstName:"Sara",lastName:"Gojević-Zrnić",middleName:null,title:"Mrs.",imageUrl:"https://mts.intechopen.com/storage/users/259492/images/7469_n.png",email:"sara.p@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"5810",title:"Socialization",subtitle:"A Multidimensional Perspective",isOpenForSubmission:!1,hash:"bfac2e9c0ec2963193e9d15d617c6a01",slug:"socialization-a-multidimensional-perspective",bookSignature:"Rosalba Morese, Sara Palermo and Juri Nervo",coverURL:"https://cdn.intechopen.com/books/images_new/5810.jpg",editedByType:"Edited by",editors:[{id:"214435",title:"Dr.",name:"Rosalba",surname:"Morese",slug:"rosalba-morese",fullName:"Rosalba Morese"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"7818",title:"Social Isolation",subtitle:"An Interdisciplinary View",isOpenForSubmission:!1,hash:"db3b513d7d35476f333a0d4a3147935b",slug:"social-isolation-an-interdisciplinary-view",bookSignature:"Rosalba Morese, Sara Palermo and Raffaella Fiorella",coverURL:"https://cdn.intechopen.com/books/images_new/7818.jpg",editedByType:"Edited by",editors:[{id:"214435",title:"Dr.",name:"Rosalba",surname:"Morese",slug:"rosalba-morese",fullName:"Rosalba Morese"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"8262",title:"The New Forms of Social Exclusion",subtitle:null,isOpenForSubmission:!1,hash:"29bf235aa7659d3651183fe9ea49dc0d",slug:"the-new-forms-of-social-exclusion",bookSignature:"Rosalba Morese and Sara Palermo",coverURL:"https://cdn.intechopen.com/books/images_new/8262.jpg",editedByType:"Edited by",editors:[{id:"214435",title:"Dr.",name:"Rosalba",surname:"Morese",slug:"rosalba-morese",fullName:"Rosalba Morese"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"6494",title:"Behavior Analysis",subtitle:null,isOpenForSubmission:!1,hash:"72a81a7163705b2765f9eb0b21dec70e",slug:"behavior-analysis",bookSignature:"Huei-Tse Hou and Carolyn S. 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Max-algebra is\nan analogue of linear algebra developed on the pair of operations \nextended to matrices and vectors, where and for .\nThe system of equations and inequalities have each been studied in the literature. We will present necessary and sufficient conditions for the solvability of a system consisting of these two systems and also develop a polynomial algorithm for solving max-linear program whose constraints are max-linear equations and inequalities. Moreover, some solvability concepts of an inteval system of linear equations and inequalities will also be presented.
\nMax-algebraic linear systems were investigated in the first publications which deal with the introduction of algebraic structures called (max,+) algebras. Systems of equations with variables only on one side were considered in these publications [1], [2] and [3]. Other systems with a special structure were investigated in the context of solving eigenvalue problems in correspondence with algebraic structures or synchronisation of discrete event systems, see [4] and also [1] for additional information. Given a matrix , a vector of an appropriate size, using the notation , , the studied systems had one of the following forms: , \nor . An infinite dimensional generalisation can be found in\n[5].
\nIn [1] Cuninghame-Green showed that the problem can be solved using residuation [6]. That is the equality in be relaxed so that the set of its sub-solutions is studied. It was shown that the greatest solution of is given by where
\nThe equation is also solved using the above result as follows: The equation has solution if and only if . Also, Gaubert [7] proposed a method for solving the one-sided system using rational calculus.
\nZimmermann [3] developed a method for solving by set covering and also presented an algorithm for solving max-linear programs with one sided constraints. This method is proved to has a computational complexity of , where are the number of rows and columns of input matrices respectively. Akian, Gaubert and Kolokoltsov [5] extended Zimmermann\'s solution method by set covering to the case of functional Galois connections.
\nButkovic [8] developed a max-algebraic method for finding all solutions to a system of inequalities using generators. Using this method Butkovic [8] developed a pseudopolynomial algorithm which either finds a bounded mixed-integer solution, or decides that no such solution exists. Summary of these results can be found in [9] and [10]
\nCechlrova and Diko [11] proposed a method for resolving infeasibility of the system . The techniques presented in this method are to modify the right-hand side as little as possible or to omit some equations. It was shown that the problem of finding the minimum number of those equations is NP-complete.
\nIn this section we introduce max-algebra, give the essential definitions and show how the operations of max-algebra can be extended to matrices and vectors.
\nIn max-algebra, we replace addition and multiplication, the binary operations in conventional linear algebra, by maximum and addition respectively. For any problem that involves adding numbers together and taking the maximum of numbers, it may be possible to describe it in max-algebra. A problem that is nonlinear when described in conventional terms may be converted to a max-algebraic problem that is linear with respect to .
\nDefinition 1 The max-plus semiring is the set , equipped with the addition\n and multiplication denoted by and respectively. That is and .\nThe identity element for the addition (or zero) is , and the identity element for the multiplication (or unit) is 0.
\n\nDefinition 2 The min-plus semiring is the set , equipped with the addition\n and multiplication denoted by and respectively.\nThe zero is , and the unit is 0. The name tropical semiring is also used as a synonym of min-plus when the ground set is .
\n\nThe completed max-plus semiring is the set , equipped with the addition\n and multiplication , with the convention that .\nThe completed min-plus semiring is defined in the dual way.
\nProposition 1 The following properties hold for all :
\nThe statements follow from the definitions.
\nProposition 2 For all the following properties hold:
\nThe statements follow from definitions.\n\nThe pair of operations (,) is extended to matrices and vectors as in the conventional linear algebra as follows: For of compatible sizes and we have:
\nExample 1
\nExample 2
\nExample 3
\nProposition 3
\nFor of compatible sizes, the following properties hold:
\nThe statements follow from the definitions.
\nProposition 4
\nThe following hold for , of compatible sizes and :
\nThe statements follow from the definition of the pair of operations (,).
\nDefinition 3 Given real numbers , a max-algebraic diagonal matrix is defined as:
\nGiven a vector , the diagonal of the vector is denoted as .
\n\nDefinition 4 Max-algebraic identity matrix is a diagonal matrix with all diagonal entries zero. We denote by an identity matrix.\nTherefore, identity matrix .
\n\nIt is obvious that for any matrices and of compatible sizes.
\nDefinition 5 Any matrix that can be obtained from the identity matrix, , by permuting its rows and or columns is called a permutation matrix. A matrix arising as a product of a diagonal matrix and a permutation matrix is called a generalised permutation matrix [12].
\n\nDefinition 6 A matrix is invertible if there exists a matrix , such that . The matrix is unique and will be called the inverse of . We will henceforth denote by .
\nIt has been shown in [1] that a matrix is invertible if and only if it is a generalised permutation matrix.
\nIf we will denote , that is , in conventional notation.
\n\nExample 4
\nConsider the following matrices
\nThe matrix is an inverse of because,
\nGiven a matrix , the transpose of will be denoted by , that is . Structures of discrete-event dynamic systems may be represented by square matrices over the semiring:
\nThe system is embeddable in the self-dual system:
\nBasic algebraic properties for and are similar to those of and described earlier. These are obtained by swapping and . Extension of the pair to matrices and vectors is as follows:
\nGiven of compatible sizes and , we define the following:
\nAlso, properties of matrices for the pair are similar to those of , just swap and . For any matrix over , the conjugate matrix is obtained by negation and transposition, that is .
\nProposition 5 The following relations hold for any matrices\n over .
\nFollows from the definitions.
\nLinear equations and inequalities in max-algebra have a considerable number of applications, the model we present here\nis called the multiprocessor interactive system (MPIS) which is formulated as follows:
\nProducts are prepared using processors, every processor\ncontributing to the completion of each product by producing a partial product. It is assumed that every processor can work on all products simultaneously and that all these actions\non a processor start as soon as the processor is ready to work. Let be the duration of the work of the processor needed to complete the partial product for\n . Let us denote by the starting time of the processor . Then, all partial products for\n will be ready at time . If the completion times are given for each product then the starting times have to satisfy the following system of equations:
\nUsing the notation and for extended to matrices and vectors in the same way as in linear algebra, then this system can be written as
\nAny system of the form (▭) is called \'one-sided max-linear system\'. Also, if the requirement is that each product is to be produced on or before the completion times , then the starting times have to satisfy
\nwhich can also be written as
\nThe system of inequalities (▭) is called \'one-sided max-linear system of inequalities\'.
\nIn this section we will present a system of linear equation and inequalities in max-algebra. Solvability conditions for linear system and inequalities will each be presented. A system consisting of max-linear equations and inequalities will also be discussed and necessary and sufficient conditions for the solvability of this system will be presented.
\nIn this section we present a solution method for the system as given in [3], [1], [13] and also in the monograph [10]. Results concerning the existence and uniqueness of solution to the system will also be presented.
\nGiven and , a system of the form
\nis called a one-sided max-linear system, some times we may omit \'max-linear\' and say one-sided system. This system can be written using the conventional notation as follows
\nThe system in (▭) can be written after subtracting the right-hand sides constants as
\nA one-sided max-linear system whose all right hand side constants are zero is called normalised max-linear system or just normalised and the process of subtracting the right-hand side constants is called normalisation. Equivalently, normalisation is the process of multiplying the system (▭) by the matrix from the left. That is
\nwhere,
\nFor instance, consider the following one-sided system:
\nAfter normalisation, this system is equivalent to
\nThat is after multiplying the system (▭) by
\nConsider the first equation of the normalised system above, that is . This means that if \nis a solution to this system then ,, and at least one of these inequalities will be satisfied with equality. From the other equations of the system, we have for , , hence we have \nwhere is the column 1 maximum. It is clear that for all then , where is the column maximum. At the same time equality must be attained in some of these inequalities so that in every row there is at least one column maximum which is attained by . This observation was made in [3].
\nDefinition 7 A matrix is called doubly ℝ-astic [14], [15], if it has at least one finite element on each row and on each column.
\n\nWe introduce the following notations
\nWe now consider the cases when and/or . Suppose that . Then can simply be written as
\nTherefore if we have . Now, if and then . Thus, we may assume in this section that and . If for some then for any we have if , , as a result the equation could be removed from the system together with every column in the matrix where (if any), and set the corresponding . Consequently, we may assume without loss of generality that .
\nMoreover, if and has an row then . If there is an column in then may take on any value in a solution . Thus, in what follows we assume without loss of generality that is doubly and .
\nTheorem 1 Let be doubly and . Then if and only if
\nSuppose . Thus we have,
\nHence, .
\nNow that . Since we only need to show that . Let . Since for some and for every we have . Hence and .
\nSuppose that and . Let , . Then if . If then
\nTherefore . At the same time for some satisfying . For this both inequalities in (▭) are equalities and thus .\n\nThe following is a summary of prerequisites proved in [1] and [12]:
\nTheorem 2 \nLet be doubly and . The system has a solution if and only if is a solution.
\n\nFollows from Theorem ▭.
\nSince has played an important role in the solution of . This vector is called the principal solution to [1], and we will call it likewise. The principal solution will also be used when studying the systems and also when solving the one-sided system containing both equations and inequalities. The one-sided systems containing both equations and inequalities have been studied in [16] and the result will be presented later in this chapter.
\nNote that the principal solution may not be a solution to the system . More precisely, the following are observed in [12]:
\nCorollary 1 \nLet be doubly and . Then the following three statements are equivalent:
\nThe statements follow from Theorems ▭ and ▭.
\nFor the existence of a unique solution to the max-linear system we have the following corollary:
\nCorollary 2 \nLet be doubly and . Then if and only if
\nFollows from Theorem ▭.\n\nThe question of solvability and unique solvability of the system was linked to the set covering and minimal set covering problem of combinatorics in [12].
\nIn this section we show how a solution to the one-sided system of inequalities can be obtained.
\nLet and\n. A system of the form:
\nis called one-sided max-linear system of inequalities or just one-sided system of inequalities. The one-sided system of inequalities has received some attention in the past, see [3], [1] and [17] for more information. Here, we will only present a result which shows that the principal solution, is the greatest solution to (▭). That is if (▭) has a solution then is the greatest of all the solutions. We denote the solution set of (▭) by . That is
\nTheorem 3 \n if and only if .
\n\nSuppose . Then we have
\nand the proof is now complete.\n\nThe system of inequalities
\nwas discussed in [18] where the following result was presented.
\nLemma 1 A system of inequalities (▭) has a solution if and only if
\nIn this section a system containing both equations and inequalities will be presented, the results were taken from [16].\nLet , ,\n and .\nA one-sided max-linear system with both equations and inequalities is of the form:
\nWe shall use the following notation throughout this paper
\nWe also define the vector , where
\nand .
\nTheorem 4 \nLet , , and . Then the following three statements are equivalent:
\n. Let , therefore and\n. Since , it follows from Theorem ▭\nthat . Now that and also ,\nwe need to show that for all \n(that is ). Let then . Since\n we have and therefore\n thus . Hence,\n and by Theorem ▭ . This\nalso proves
\n. Suppose .\nSince we have . Also\n and gives\n. Hence\n, therefore and\n. Hence \n(that is ) and this also proves\n.
\nTheorem 5 \nLet , , and . Then if and only if
\n() Let , then and\n. Since \nwe have . Also, implies that .\nIt follows from Theorem ▭ that .
\n() Suppose that \nand . It follows from Theorem ▭ that\n, also by Theorem ▭ . Thus\n.
\nWe introduce the symbol which stands for the number of elements of the set .
\nLemma 2 \nLet , , and . If then .
\n\nSuppose , that is for an . Since we have and thus .\nFor contradiction, suppose . We need to check the following two cases:\n(i) and (ii) where , and show in each case that .
\nProof of Case (i), that is :\nSuppose that contains only one element say i.e .\nSince it follows from Theorem ▭that\n. That is
Proof of Case (ii), that is : Suppose that .\nThen we have . Suppose without loss of\ngenerality that such that . Then\n and also .\nThus, . Consequently, , and\n. Hence .
\nTheorem 6 \nLet , ,\n and\n. If then .
\n\nSuppose . It follows from Theorem ▭ that
Corollary 3 Let , ,\n and\n. If then\n.
\n\nThe statement follows from Theorem ▭ and Lemma ▭.
\nCorollary 4 \nLet , ,\n and\n. Then,\nthe following three statements are equivalent:
\nIt is immediate that and the statement now follows\nfrom Theorem ▭.
\nTheorem 7 \nLet , , and . If then is infinite .
\n\nSuppose . By Corollary ▭ we have ,\nfor some , (that is such that\n). Now and\n, Theorem ▭ implies that any vector\n of the form
\nis in , and the statement follows.
\nRemark 1 From Theorem ▭ we can say that the number of solutions to the\none-sided system containing both equations and inequalities can only be\n.
\n\nThe vector plays an important role in the solution of the one-sided system\ncontaining both equations and inequalities. This role is the same as that of the\nprincipal solution to the one-sided max-linear system , see [19] for more details.
\nSuppose that the vector is given. The\ntask of minimizing [maximizing]the function\n subject\nto (▭) is called max-linear program with one-sided equations and\ninequalities and will be denoted by and\n[]. We denote the sets of optimal solutions by\n and , respectively.\n
Lemma 3 Suppose and let be defined\non . Then,
\n(i) is max-linear, i.e.
\nfor\nevery .
\n(ii) is isotone, i.e. for every\n, .
\n\n(i) Let . Then we have
\nand the statement now follows.
\n(ii) Let such that . Since , we have
\n\nNote that it would be possible to convert equations to inequalities and conversely but\nthis would result in an increase of the number of constraints or variables and thus increasing the\ncomputational complexity. The method we present here does not require any new constraint or variable.
\nWe denote by
\nA variable will be called active if , for some .\nAlso, a variable will be called active on the constraint equation if the\nvalue is attained at the term respectively.\nIt follows from Theorem ▭ and Lemma ▭ that\n. We now present a polynomial algorithm which finds\n or recognizes that .\nDue to Theorem ▭ either or .\nTherefore, we assume in the following algorithm that and\nalso .\n
Find , , and , ;
If
then stop ()
Set small enough (so that it is not active on any equation or inequality)\nfor every
Go to 3
Theorem 8 The algorithm ONEMLP-EI is correct and its computational complexity is .
\n\nThe correctness follows from Theorem ▭ and the computational\ncomplexity is computed as follows. In Step 1 is , while ,\n and can be determined in , and respectively.\nThe loop 3-7 can be repeated at most times, since the number of elements in is\nat most and in Step 4 at least one element will be removed at a time. Step 3 is , Step 6 is and Step 7 is . Hence loop 3-7 is .
\nConsider the following system max-linear program in which ,
\nWe now make a record run of Algorithm ONEMLP-EI. , ,\n, and , , and\n. and and . We also have\n and . Then set (say) and\n. Now and .\nSince set (say) and we have .\nNow and . Since then we stop and an\noptimal solution is and .
\nSuppose \nand are given matrices and vectors. The system
\nis called non-homogeneous two-sided max-linear system and the set of solutions\nof this system will be denoted by . Two-sided max-linear systems have been\nstudied in [20], [21], [22] and [23].
\nOptimization problems whose objective function is max-linear and constraint (▭)\nare called max-linear programs (MLP). Max-linear programs are studied in [24]\nand solution methods for both minimization and maximization problems were developed. The methods are proved\nto be pseudopolynomial if all entries are integer. Also non-linear programs with max-linear constraints were dealt with in [25], where\nheuristic methods were develeoped and tested for a number of instances.
\nConsider max-linear programs with two-sided constraints (minimization),\n
\nwhere , , and are given matrices and vectors. We introduce the following:
\nmeans a diagonal matrix whose diagonal elements are and\noff diagonal elements are . It therefore follows from (▭) that
\nHence, by substituting (▭) and (▭) into (▭) we have
\nwhere is transpose of the zero vector, \nand
\nTherefore we assume without loss of generality that and hence (▭) is\nequivalent to
\nThe set of feasible solutions for (▭) will be denoted by \nand the set of optimal solutions by . A vector is called constant if all its components are equal.\nThat is a vector is constant if .\nFor any we define the set .\nWe introduce the following notation of matrices. Let\n, and\n. Then,
\nwhere, , . Similar notation is used for\nvectors .\nGiven with , we define the following sets
\nWe also define the following matrices:
\nAn easily solvable case arises when there is a constant vector such that the set . This constant vector satisfies the following equations and inequalities
\nwhere , and are defined in (▭).\nThe one-sided system of equation and inequalities (▭) can be written as
\nwhere,
\nRecall that is the set of solutions for (▭).
\nTheorem 9 \nLet for some constant vector .\nIf then .
\n\nLet . Suppose and\n. This implies that . Therefore we have,\n, . Consequently, and\n for all . Since, and .
\nCorollary 5 If for some constant vector then .
\n\nThe statement follows from Theorem ▭.
\nSystem of max-separable linear equations and inequalities arise frequently in several branches of Applied Mathematics: for instance in the description of discrete-event dynamic system [4], [1] and machine scheduling [10]. However, choosing unsuitable values for the matrix entries and right-handside vectors may lead to unsolvable systems. Therefore, methods for restoring solvability suggested in the literature could be employed. These methods include modifying the input data [11], [26] or dropping some equations [11]. Another possibility is to replace each entry by an interval of possible values. In doing so, our question will be shifted to asking about weak solvability, strong solvability and control solvability.
\nInterval mathematics was championed by Moore [27] as a tool for bounding errors in computer programs. The area has now been developed in to a general methodology for investigating numerical uncertainty in several problems. System of interval equations and inequalities in max-algebra have each been studied in the literature. In [26] weak and strong solvability of interval equations were discussed, control sovability, weak control solvability and universal solvability have been dealt with in [28]. In [29] a system of linear inequality with interval coefficients was discussed. In this section we consider a system consisting of interval linear equations and inequalities and present solvability concepts for such system.
\nAn algebraic structure with two binary operations and is called max-plus algebra if
\nfor any .
\nLet be given positive integers and , we use throughout the paper the notation and . The set of all , matrices over is denoted by and respectively. The set of all -dimensional vectors is denoted by . Then for each matrix and vector the product is define as
\nFor a given matrix interval with and given vector interval with the notation
\nrepresents an interval system of linear max-separable equations of the form
\nSimilarly, for a given matrix interval with and given vector interval with the notation
\nrepresents an interval system of linear max-separable inequalities of the form
\nInterval system of linear max-separable equations and inequalities have each been studied in the literature, for more information the reader is reffered to . The following notation
\nrepresents an interval system of linear max-separable equations and inequalities of the form
\nwhere and .
\nThe aim of this section is to consider a system consisting of max-separable linear equations and inequalities and presents some solvability conditions of such system. Note that it is possible to convert equations to inequalities and conversely, but this would result in an increase in the number of equations and inequalities or an increase in the number of unknowns thus increasing the computational complexity when testing the solvability conditions.\nEach system of the form (▭) is said to be a subsystem of (▭). An interval system (▭) has constant matrices if and . Similarly, an interval system has constant right hand side if and . In what follows we will consider and .
\nDefinition 8 A vector is a weak solution to an interval system (▭) if there exists and such that
\nTheorem 10 A vector is a weak solution of (▭) if and only if
\nand
\nLet be an arbitrary chosen index and fixed. If then is isotone and we have
\nHence, is a weak solution if and only if
\nSimilarly, if then is obviously a weak solution to
\nThat is
\nAlso from (▭) is a weak solution if and only if
\nThat is
\nDefinition 9 An interval system (▭) is weakly solvable if there exists and such that (▭) is solvable.
\n\nTheorem 11 An interval system (▭) with constant matrix , is weakly solvable if and only if
\nThe (if) part follows from the definition. Conversely, Let
\nbe solvable subsystem for . Then we have
\nDefinition 10 A vector is a strong solution to an interval system (▭) if for each and each there is an such that (▭) holds.
\n\nTheorem 12 a vector is a strong solution to (▭) if and only if it is a solution to
\nwhere
\nIf is a strong solution of (▭), it obviously satisfies (▭). Conversely, suppose satisfies (▭) and let such that and . Then such that either or and . Therefore, , and and the theorem statement follows.
\nThe author is grateful to the Kano University of Science and Technology, Wudil for paying the publication fee.
\nUnderstanding the immune system and its components may enlighten future potential treatments to generate disease progression such as cancer. For almost 30 years, by targeting the immune system by therapeutics brought a totally new point of view in the field of cancer treatment. Accordingly, besides the commonly preferred cancer treatments, the treatments developed specifically for the patient and the diseases come to the forefront. To date, immunotherapy is a method developed as an alternative to conventional cancer treatments [1, 2]. The immune system which is an awareness system based on distinguishing between “self” and “non-self” works in harmony with cells, related tissues, and organs respectively to protect the organisms. The main goal of the immune system is to defense to battle against “enemies”. There are two types of immune responses; humoral and cellular immunity. Humoral immunity is primarily mediated by B and T lymphocytes and their products. It is also characterized by a weak response and a strong immunological memory. Cellular immunity components are natural killer (NK) cells, eosinophils, macrophages, and lymphocytes (B and T cells). Cellular immunity works faster than humoral immunity via activation and proliferation of B cells and activation of antigen-presenting cells (APCs). Cellular immunity can recognize tumors immediately, but it does not provide long-term immunity. Specifically, B and T cells primarily mediate the antitumor response. The CD4+ T cells pretend as “helper cells” and excrete cytokines relying on their profile either Th1 or Th2. Humoral and cellular immunity plays a crucial role in antitumor response [3, 4].
Today, non-communicable diseases are held accountable as the leading cause of death worldwide. Among these diseases, cancer is predicted as one of the most important disease in the world that causes deaths and reduces the life quality [5]. Soon, it is thought that the number of cancer patients and cancer-related deaths will increase [6]. The definition of cancer for the first time in 3000 BC was used in inscriptions called the Edwin Smith Papyrus, the part of an ancient Egyptian textbook on trauma surgery. Cancer is generally characterized by the growth of abnormal cells beyond their normal limits. Cancer disease can affect almost any part of the body and has many anatomical and molecular subtypes, each of which requires specific treatment strategies. The main factors causing cancer are as follows; ionizing radiation, ultraviolet rays, age, inadequate physical activity, smoking and alcohol consumption, nutrition and diet, chemicals, microorganisms, and genetic factors. It is known that environmental factors are much more effective in the formation of the disease than hereditary factors. The most important reason is stated as mutations that occur in genes. Most cancers are caused by a series of mutations that allow cells to divide faster, escape internal and external controls, and prevent programmed cell death. As the cells continue to divide under the influence of mutations in solid tissue such as organ, bone or muscle the resulting mass is called tumor. Solid tumors are classified as; benign (noncancerous) and malignant (cancerous). Benign tumors do not have the ability to metastasize; they can only grow where they are located. On the other hand, malignant tumors have the ability to spread to neighboring tissues and organs from where they are formed. Many types of cancer initially show no symptoms. The main symptoms observed can be given as; unexplained, and rapid weight loss, fever, malaise, pain, swelling and bleeding. However, each type of cancer has its own specific symptoms, so the treatment method of each cancer type differs. Figure 1 shows a schematic representation of tumor cells progression.
Schematic representation of tumor cells progression (created with BioRender.com).
Cancer is an individual disease; hence treatment methods vary from patient to patient. The method of treatment should be chosen by considering the degree and course of the disease, age and health situation of the patient. Generally, most of the patients have the combination of treatment methods. Surgical intervention, radiation therapy, chemotherapy, and hormone therapy are defined as traditional cancer treatments in the literature [2]. In recent years, immunotherapy has also been the increasingly used method in cancer treatment.
Surgical intervention, a local treatment method, can also be used in the combination of other treatment methods. It is applied in tumors without metastasis that only exist in one area such as solid tumors; but not effective in leukemia and cancer types that spread. Also, surgical intervention is preferred when the tumor is in an untreatable part of the body by other treatment methods such as radiation therapy or chemotherapy (cannot reach the brain). In order to remove the tumor without damaging the neighboring healthy cells, the size of the tumor can be reduced by other methods. The surgical intervention method works against cancer in three ways; eradicating the entire tumor, debulking a tumor, and palliate the disease symptoms. Only eradicating the entire tumor may cure the patients if the cancer cells are located in small area at one place. Debulking a tumor is used to reduce the tumors size while surgery is combined with other treatment methods. Palliate the symptoms, the last way in surgical intervention, is to remove the tumor to reduce the pain or pressure caused by the tumor. There are some disadvantages of surgical intervention such as the possibility of leaving microscopic residues around the tumor after surgery, the health status of the patients, and the success of the surgery [7, 8].
Radiation therapy or radiotherapy (RT) is based on the principle of using a fairly high dose of radiation to shrink the tumor by killing the cancer cells. There are various types of radiotherapy depends on the general state of the patient and disease. The principle of radiation therapy is to destroy cancer cells as possible without damaging healthy cells. Because, in the late 20th century, scientist discovered that radiation therapy not only cures cancer cells but also may be the cause of cancer itself. The notable side effect, it can kill and harm healthy cells significantly. Thereby it has side effects such as hair loss, vomiting, and loss of appetite that will affect your daily life. The choice of the exact type of radiation therapy relies on several circumstances such as the type, stage, size and location of cancer, and medical history of the patients. Reducing the tumor mass by radiation therapy is helpful to decrease the pressure of tumor on the nearest healthy cells. Additionally, it is used before surgical intervention to shrink tumor mass to make it suitable for surgery and after surgery; the microscopic residues on the edge of the tumor can be removed much more easily. Also, this method of therapy is very suitable for making systemic therapy [9, 10].
Chemotherapy (CT), also as chemo, is the most commonly used method in cancer treatment. The aim is to kill cancer cells using chemotherapeutic agents. This method is developed in the late 20th century and combined with surgery and/or radiation therapy. Over the years, many chemotherapeutic drugs showed great impact and gained success for the treatment of many types of cancer. The aim of the treatment can be stated as reducing the size of the tumor, reducing the effects of the symptoms seen in the patient, preventing metastasis, and reducing the total number of tumor cells in the body. The drugs used in chemotherapy direct the cell to death by stopping or decelerating the cancer cell proliferation. Some of these drugs are natural and some of them are synthetic. Hair loss, vomiting, loss of appetite, fever, diarrhea and fatigue are temporary side effects of the drugs that end after the treatment [11, 12].
Hormones, in the classical sense, are organic compounds that are synthesized in ductless glands such as the pituitary gland, adrenal gland, thyroid gland, and parathyroid gland, which are known as endocrine organs, and act on certain target tissue that is carried by the blood. All cells communicate with each other via hormones. In the human body, hormones either can be small proteins (insulin, etc.) or stimulator for a cell to generate new proteins or cease making products. One possible featured outcome is cell growth and proliferation. Even though cancer cells are abnormal, they still keep the ability to react to signals of hormones. The main idea of hormone-based treatments is to deprive cancer cells of hormone signals. Otherwise, they would be stimulating to continue dividing. The main theme of the drugs that are used in this method relies on preventing the activity of hormone within the target cell or blocking the production of the related hormone. Hormone therapy is often preferred for the treatment of prostate and breast cancer. Generally, hormone therapy is combined with other treatment methods depending on the cancer type. Hormone therapy is very suitable for adjuvant and neoadjuvant therapy to reduce tumor mass. The term adjuvant therapy is about reducing the risk of cancer recurrence after major cancer treatment. Hormone therapy is also appropriate for the removal of cancer cells that spread to different parts of the body. Like all other methods, hormone therapy has common side effects. But these effects depend on the body’s response to the therapy and the type of hormone therapy. Side effects are influenced by different terms such as patients’ sex and type of hormone that is used. Hot flashes, weakened bones, nausea, and fatigue are common side effects for men. Menstrual irregularities for women who are not menopausal and vaginal dryness are seen in addition to the common side effects. To date, there are several hormone based drugs based on the hormonal signals, but their principles are diverse from each other. They all attack different parts of the pathways to decelerate to the growth of cancer [13].
Nowadays, cancer treatment is moving from non-specific methods to specific methods. Although success is achieved in the destruction of tumors with surgery and radiotherapy, cancer may recur due to cancerous cell debris in the damaged area. Cancer immunotherapy, an individualized method, is referred to as the “fifth step” of the treatment following the traditional methods mentioned above [14]. The immunotherapy method; boost the immune system to fight against cancer, train the immune system component’s to memory, attack the cancer cells, and heighten the immune response via biological substances. For the last decades, immunotherapy becomes a promising method to fight against cancer. Immunotherapy can be applied using either external substances or their body cells [4].
It is common knowledge that many cases of regression of tumor growth after high fever attacks or infectious diseases have been reported throughout history from Ancient Egypt to the 18th century. However, the relationship between the immune system and cancer was noticed in the middle of the 18th century with the developing technology. In the mid-18th century, two German doctors, Busch and Fehleisen, independently reported cases of tumor regressions of patients after erysipelas infection (Streptococcus pyogenes infection). In the literature, the first systematic immunotherapy study for the treatment of malignant tumors was conducted in 1891 by William B. Coley, a surgical oncologist. Coley injected the heat-inactivated Streptococcus pyogenes and Serratia marcescens organisms into the patient to stimulate the patient’s immune system. After the project that he initiated, Coley has seen a regression in the tumor in more than 1000 sarcoma patients who cannot undergo surgical intervention. In a very short time, humanity evaluated this mixture as a great invention, “Coley Toxins”. However, the word “toxin” was an unfortunate choice; the more acceptable name for the treatment was “mixed bacteria vaccine”. Although the bacteria had some side effects such as fever and malaise, it is not as toxic as chemotherapy or radiotherapy and does not destroy the immune system [15, 16]. Coley’s life-long cancer immunotherapy studies that will spearhead for many scientists have started after this project. In 1900, Paul Ehrlich stated that the first findings of the treatment, which would later be called antibody-mediated passive immunotherapy, had an important place in the treatment of tumors. In 1975, George Köhler and Cesar Milstein developed hybridoma technology for monoclonal antibody production. This was followed by the first successful use of monoclonal adults in human neoplasia in 1982 and the FDA (US Food and Drug Administration) approval of muromonab-CD3 (Orthoclone OKT3) in 1986. In 1997, both the first humanized monoclonal antibody, daclizumab (Zenapax), and the first monoclonal antibody for malignancy, rituximab (Rituxan), were approved by the FDA. This was followed by the FDA approval of gemtuzumab ozogamicin (Mylotarg) in 2000, the first toxin-bound monoclonal antibody, and ibritumomab tiuxetan (Zevalin) in 2002, the first radionuclide-bound monoclonal antibody [17].
Another area that cancer immunotherapy has advanced was using the patient’s body cells. In the 1960s, the tumor immune surveillance hypothesis was put forward by Burnet. Since 1995, persuasive studies on effective tumor-specific immunity have attracted great interest. In particular, many studies show the ability of dendritic cells to elicit tumor-specific T cell immunity has led to this situation. Following preclinical researches, many studies involving various types of cancer have been conducted in patients. Recent studies have also made the immunosurveillance hypothesis quite popular [18, 19]. Immunotherapy studies have increased their importance in the 21st century with the licensing of clinical studies carried out with developing technology and methods [20]. Immunotherapy was declared as “breakthrough of the year” by Science magazine in 2013 after the clinical success achieved and has become even more prominent. Also, in 2018 James Allison and Tasuku Honjo received the Nobel Prize in Physiology and Medicine for their work based on the use of the immune system to destroy cancer cells. In the past two decades, great strides have been made in cancer immunotherapy. With all these spectacular developments, the number of cancer immunotherapy studies is increasing day by day [21, 22]. There are certain categories in cancer immunotherapy applications. These are the mechanism of innate and acquired immune resistance, internal and external resistance to immunotherapy, self-neutralization of tumor cells and antigen- presenting cells, inhibition of immunity by exosome release mechanisms, the response of tumor cells to therapy. Like all other methods, cancer immunotherapy has several advantages and disadvantages. Higher precision and specificity, long-term survival rate, fewer side effects than traditional treatment methods, removing residual tumor cells and microscopic lesions that remain in the body after treatment and improving the body’s immune function are the advantages of immunotherapy. Also, it can control and kill more than one tumor type and it uses the body’s immune system to increase immune response. Higher treatment costs, various non-specific toxic side effects after treatment are the disadvantages of immunotherapy. There is a high selectivity for patients in treatment. When the tumor type is “immunosuppressant type” or “immune exclusion type”, the effect of immunotherapy treatment is considerably weak. Additionally, in particular, the use of immune checkpoint inhibitors can have adverse consequences leading to autoimmune diseases and even death [23].
Cancer immunotherapy is generally classified in three ways; passive, active and combination immunotherapy depending on the mechanism of the therapeutic agent and the state of the patient’s immune system. Classification of passive and active cancer immunotherapy studies is shown in Table 1.
Passive immunotherapy | Active immunotherapy | |
---|---|---|
NON-SPECIFIC | Adoptive Cell Therapy | Cytokines Immune Checkpoint Inhibitors |
SPECIFIC | Monoclonal Antibodies | Cancer Vaccines Oncolytic Viruses |
Classification of immunotherapy.
The main purpose of passive immunotherapy is to increase the current anti-tumor response by using therapeutics that can be produced under laboratory conditions. It is preferred to use the treatment in patients with weak or dysfunctional immune systems. It is designed to attack tumor cells independently by modifying the components of the immune system in the laboratory. Monoclonal antibodies and adoptive cell therapy are frequently used passive immunotherapy methods [4, 20, 24].
For the past 20 years, monoclonal antibodies are the most commonly used FDA approved treatment in clinical immunotherapy studies. They are large artificial proteins with high antigen specificity produced by particular B cells. Due to their antigen specificity, their capacity to bind to epitopes on the surface of the tumor cell is high [25]. So, antibodies specific to antigens of cancer cells are produced in ex vivo conditions and transferred to the patient to increase the immune response. Antibodies in these targeted therapies are guided directly to the antigen on the surface of cancer cells. Different signaling functions can be created by the interaction of monoclonal antibodies and receptors on the surface of malignant tumors. Antibodies are used in treatment can be classified as naked, conjugated, radiolabeled, chemically labeled, and bispecific monoclonal antibodies. Naked monoclonal antibodies are most commonly used in cancer immunotherapy and bind directly to the antigen without any radioactive markers or drugs. Conjugated monoclonal antibodies are used to transfer chemotherapeutic drugs or radiolabeled particles to cancer cells. Radiolabeled monoclonal antibodies are created by adding radioactive particles to naked antibodies. Chemically labeled antibodies are monoclonal antibodies with a high chemotherapeutic effect. Radioactive or chemically labeled monoclonal antibodies aim to destroy the target cell with the toxins they contain or the radiation they emit. Bispecific antibodies carry two types of antibodies in their structure and can bind to two different antigens that are receptors for these two antibodies at the same time [18, 26, 27]. The first drug including monoclonal antibodies approved by the FDA was rituximab (Rituxan, Genentech) was used in the clinic at 1997. Today, with developing technology, many new drugs have emerged for the treatment of different types of cancer [25].
It gathered speed with the studies carried out in the 20th century about the discovery of tumor-specific antigens located not on healthy cells but just on the tumor cells. Thus the importance of adoptive T cell transfer has been understood. Adoptive cell therapy is the transfer of natural or genetically modified T cells to patients in ex vivo conditions instead of stimulating the immune system. The transferred cells can be autologous or allogeneic targeted to a particular antigen in the host cell. It was pointed out that the stage of an immune response in the host is skipped directly by this step. To create a targeted immune response, autologous cells can recognize tumor antigens, move towards the tumor and exit the circulation. The transfer of T cells to destroy tumor cells is carried out in two ways; the infiltrating (TIL) of tumor specific T cells from existing tumor cells and the use of genetically modified T cells to specifically identify tumor cells. In both methods, the T cell is processed ex vivo and then transferred back to the patient [28]. The first successful cellular therapy in history was performed on an advanced melanoma patient with autologous TIL. The specific T cell receptor (TCR) is obtained by genetically modifying T cells. T cells and tumor-specific antigens are matched with HLA recognition by TCR technology. A minimal cytotoxic effect occurs by this natural pairing. TCRs also have disadvantages such as the low expression on the surface and short lifespan of T cells in vivo. Although the first studies ended up with disappointment, today, the other genetically modified T cell is chimeric antigen receptors, CAR. Many studies are conducted around the world on CAR-T technology and it is believed that positive results will be achieved in the near future [29, 30].
Active immunotherapy aims to destroy cancer cells by stimulating the immune system by vaccination, immunomodulation, or targeting specific antigen receptors. The method is carried out employing cancer vaccines, oncolytic viruses, immune checkpoint inhibitors, and cytokines [20].
The purpose of vaccination is to create an immune response to detect and destroy cancer cells. Cancer vaccines, containing whole, part, or purified antigens of tumor cells, can be peptide-based, immune cell or dendritic cell-based, or tumor cell-based. After the tumor cells are removed from the body, the patient is vaccinated and an immune response is created against the tumor cells that may remain in the body. Variable antigen expression, low immune response, diminishing the immune response in the tumor microenvironment and a decrease in activity over time are the restrictions of the cancer vaccine applications [4, 25].
Peptide-based vaccines are designed to create an immune response against tumor antigens that interact with HLA molecules on the surface of tumor cells. Their toxic effects on healthy cells are low due to their antigen-specific design, but tumor antigen peptides and the patient’s HLA type should be well characterized [31].
Immune or dendritic cell-based vaccines consist of the use of tumor-associated antigens or autologous tumor cells and dendritic cells (DC) obtained from monocyte cells in early-stage cancer vaccines. In 2010, the drug called Sipuleucel-T (Provenge, Dendreon Corp.) is the first DC-based cancer vaccine was approved by the FDA for the treatment of prostate cancer. DC-based vaccines today use innovative in vitro culturing techniques enriched with cytokines, enhancing immunogenicity and improving DC function. DC-based cancer vaccines can be designed differently for both ex vivo and in vivo applications for various cancer types [4].
Tumor cell-based cancer vaccines use the entire tumor cell to create an immune response. Unlike peptide-based vaccines, tumor cells are not specific to antigens on their surface, but the range of epitopes to which they can bind is wider. These vaccines can be prepared using the patient’s cells (autologous) or using another patient’s tumor cells (allogeneic). Tumor cell-based vaccines such as M-Vax (AVAX Technologies) can be used in the treatment of many different types of cancer in clinical studies [25].
These are called genetically altered viruses that can naturally penetrate only cancer cells and kill them. Talimogene laherparepvec (T-Vec) is the first oncolytic virus-based drug, approved by the FDA, that the protection mechanisms developed against viral infections are impaired in most cancer cells. By taking advantage of this degradation, viruses can reproduce more intensely in cancer cells than healthy cells. Recently, replication specific to cancer cells was obtained and a reovirus variant called Reolysin (exhibiting oncolytic behavior in cells with activated Ras signaling pathway) has been developed. In 1991, positive results were gained in the treatment of brain cancer with a mutation in a genetically modified type 1 herpes simplex virus [32].
Several inhibitory receptors and ligands expressed on T cells, antigen-presenting cells, and tumor cells have recently been important elements of immunosuppression in the tumor microenvironment. Because of their biological role as regulators of T cell activation, these receptor/ligand pairs have been termed “immune checkpoints”. Immune checkpoints are cell membrane proteins involved in the regulation of the immune response. Multiple controls or “checkpoints” are present or activated to ensure that the immune-inflammatory response is not continuously activated after tumor antigens have generated a response. Immune checkpoints are signals that can halt an existing immune response. The over -expression of these signals by tumor cells affects tumor cell-specific T-cell immunity in the cancer microenvironment. The aim of treatments involving inhibition of the immune checkpoint is to use and strengthen the immune system by disrupting the negative immune system. In 2011, the drug called Ipilimumab was used in clinical use for melanoma patients by using immune control point drugs. As of March 2019, 7 immunotherapy drugs based on checkpoints are used in clinical practice. Monoclonal antibodies that bind to immune checkpoints bind with cytotoxic T lymphocyte-associated molecule-4 (CTLA-4), programmed cell death protein 1 (PD-1), and programmed cell death ligand (PDL-1) [33].
PD-1/PDL-1, under normal circumstances, PD-1 has two ligands; PD-L1 and PD-L2. Blocking the interaction between PD-1 and PDL-1 with antibodies enhances the immune response against cancer cells, “releases the brakes” in the immune system and allows for the attack of tumor cells that express PDL-1. Nivolumab and Pembrolizumab are the first two drugs approved by the FDA in 2014 [34].
CTLA-4 inhibition increases the activation of cytotoxic T cells. Thus, immune blockade due to Treg cells is inhibited and antitumor activation is observed. Ipilimumab is the first drug approved by the FDA for CTLA-4 treatment in 2011 [35].
They are the main regulators of innate and adaptive immune systems that allow cells of the immune system to communicate in paracrine and autocrine systems over short distances. Unlike other therapeutic agents, these molecules directly stimulate immune cells, for example Interleukin-21 (IL-21) can act as agents involved in active immunotherapy [36]. The use of cytokines in cancer immunotherapy showed tumor regression, prevention of metastasis formation, improvement of immunological memory and decrease in risk of disease recurrence with increased survival. The use of cytokine (IL-2, GM-CSF, IFN-α) -based biological therapy in combination with conventional therapies is under clinical development [37]. In 1986, IFN-α became the first FDA approved cytokine for the treatment of leukemia. Subsequently, IL-2 was approved by the FDA in 1992 for metastatic kidney cancer and 1998 for advanced melanoma treatment [36].
Combinational immunotherapy refers the use of a different anticancer agent for treatments of cancer. Conjugation of IL-2 and HER-2 monoclonal antibody proved to be a very forceful combination in immunotherapy. Lately, PD-1 and CTLA-4 conjugation has been examined. The results revealed that the combined system was safe and had no significant toxic effect [38].
Nanoparticle-based biomaterials have a critical role in cancer immunotherapy compared with conventional drugs [39]. Immunotherapy often targets tumor cells, immune and stromal cells in the tumor microenvironment [40]. Additionally, side reactions occurring due to the interactions between nanoparticles (NPs) and cells can be adjusted by modifications of nanoparticles [41]. Nanoparticle-based drug delivery systems can improve the solubility, in vivo stability, and pharmacokinetic profile. Also, they protect drugs from premature release and degradation in the living system. These systems can be designed according to the microenvironment of the target such as pH, redox potential or enzymes, and external dynamics such as light, electrical and magnetic fields. Targeted delivery with NPs can also reduce toxicity and immune-related side effects [2]. The size and the shape of the NP are very effective in therapeutic efficacy by changing its pharmacokinetics, transportation, and cellular uptake [42]. Recent advances in nanoparticle formulations have generated a wide range of other shapes like rods, prisms, cubes, stars, and discs out of spherical. It is considered as non-spherical particles have higher blood circulation periods, prolonged margination effects, and higher penetration capacities within solid tissues and tumors [43]. The charge of NP has great priority in the transition of it into cells. Besides, NP-ligand coupling conditions and the elasticity of NP upgrade transportation and accumulation of NP in the living system [44, 45]. Generally, it is well known that cationic NPs create a higher immune response than neutral or anionic NPs [43]. The size, shape, elasticity, optical, magnetic, and electrical properties of nanoparticles can be modified to increase the usage of NPs in cancer therapy as a carrier [2, 41, 46]. High specificity, efficacy, diagnosing, imaging, and therapeutic properties make NPs candidates in immunotherapy for effective cancer treatment. Liposomes, micelles, polymeric, metallic, and inorganic NPs have a wide range of usage in cancer immunotherapy [44].
The nanoparticles are generally categorized into tree class as organic, inorganic, and carbon-based. Dendrimers, micelles, and liposomes are the most widely known organic nanoparticles. These biodegradable, non-toxic, and capsule-shaped nanoparticles appear to be an ideal choice for drug delivery due to their sensitivity to thermal and electromagnetic radiation. Inorganic nanoparticles, metal, and metal oxide-based NPs do not contain carbon in their structure. Aluminum, cadmium, cobalt, copper, gold, iron, lead, silver, and zinc can be used to fabricate metallic NPs in 10 to 100 nm size range. Carbon-based nanoparticles, fullerenes, graphene, carbon nanotubes (CNT), and carbon nanofibers, are build up from carbon in nanosize [47].
It can be viewed two different ways to synthesize nanoparticles; bottom-up and top-down methods (Table 2). These techniques also can be divided as chemical and physical methods. Although both methods have positive and negative features, the chemical one has more disadvantages due to the wet reaction steps it has [48].
Top-down approach | Bottom-up approach | ||
---|---|---|---|
Physical processing methods | Physical and chemical processing methods | ||
Physical techniques | |||
Mechanical methods: | Cutting, etching, grinding | Physical Vapor Deposition (PVD): | Evaporation (thermal, e-beam) |
Ball milling | Sputtering | ||
Lithographic techniques: | Photo Lithography | Plasma Arching | |
Electron Beam Lithography | Laser Ablation | ||
Chemical techniques | |||
Chemical Vapor Deposition (CVD): | Plasma enhanced CVD (PECVD) | ||
Self Assembling | Electronic deposition, sol-gel method, emulsion, pyrolysis |
Techniques in Top-Down and Bottom-Up approaches.
It is also known as a constructive method like building-up of material from an atom. Sol–gel, spinning, chemical vapor deposition (CVD), pyrolysis, and biosynthesis are the foremost methods in this technique. Nanoparticles, nanoshells, and nanotubes with narrow size distribution can be synthesized by this approach. Besides, in this method deposition parameters can be controlled. However large scale production is difficult and chemical purification is needed.
Sol–gel method: It is a simple, wet chemical process based on hydrolysis and polycondensation reactions [49]. This process indicates the chemical transformation of a system from a “sol” phase, a colloidal solution of solids suspended in a liquid phase, into a “gel” phase, a solid macromolecule submerged in a solvent [50]. The chemical and physical properties of the materials as high surface area and the stability can be obtained by the method via modifying experimental conditions. Metal oxide and chloride precursors are used in sol–gel process, and then a liquid and a solid phase separation occur after removing precursors either by shaking, stirring, or sonication. Nanoparticles are acquired in this phase separation by sedimentation, filtration, or centrifugation [47].
Spinning disc processing (SDP): The method consists of a rotating disc inside a reactor generally filled with nitrogen or other inert gases to remove oxygen inside and avoid chemical reactions. The purpose of spinning is to merge atoms or molecules. The parameters of this process such as the liquid flow rate, disc rotation speed, liquid/precursor ratio, location of feed, and disc surface may vary for different systems and determine the characteristics of NPs [51].
Chemical vapor deposition (CVD): It is the deposition technique of thin films of gaseous reactants onto a substrate. Gaseous reactants can be elemental and compound semiconductors, metal alloys, and amorphous or crystalline compounds. In the CVD process, a volatile material (chemically reactive) is coming together with other gases to produce a nonvolatile solid material that deposit at the atomic level on a suitable substrate. This is a well-organized process that some kind of reactors should be used depending on the type of precursors, deposition conditions, and the forms of the energy introduced to the system to stimulate the planned chemical reaction. Metal–organic, plasma-enhanced, low-pressure, laser-assisted, and aerosol-assisted CVDs are the most accepted methods [52]. The deposition is carried out in a reaction chamber at the temperature suitable for the reaction, the substrate is heated and the chemical reaction occurs when the heated substrate contact with the combined gas. The substrate temperature is an important parameter for this method to gain pure, uniform, hard, and strong nanoparticles [47, 53].
Spray pyrolysis: It is a method often used in industry for large scale production of NPs. Generally, nanometals and metal oxides are produced by this simple, reproducible, size controllable and low-cost method [54]. This process consists of a precursor with flame where the precursor solution is sprayed or injected using a nanoporous nebulizer onto the hot substrate into the furnace at high pressure to form a droplet. The precursor can be either liquid or vapor. After evaporation, the precursor decomposes to recover nanoparticles or films on the substrate. Some of the furnaces have laser or plasma to produce high temperature to facilitate evaporation [55].
Biosynthesis: It is an alternative to conventional physical and chemical nanoparticle synthesizing methods. Plants are preferred in this green and environmentally friendly cost-effective technique to prepare non-toxic and biodegradable nanoparticles [56]. In this method, several microorganisms as bacteria, fungus, and yeasts, etc. are used along with the precursors to produce nanoparticle for bioreduction and capping purposes. The biosynthesized nanoparticles have unique and enhanced properties that find a wide range of applications in drug delivery systems [57].
This method is also known as a destructive method due to the reduction of bulk material to nanometric scale particles. Contrary to bottom-up, large-scale production is possible and chemical purification is unnecessary in the top-down method. Broad size distribution (10–1000 nm), varied particle shapes, control over deposition parameters and reaction costs are disadvantages of this method. There are many techniques in this method, but mechanical milling, nanolithography, laser ablation and sputtering are among the most frequently used ones.
Mechanical milling: This process has been used for a long time in mineral, ceramic processing, and powder metallurgy industries. The aim of mechanical milling of materials consists of minimizing particle size, blending, changing particle shapes, and synthesizing nanoparticles in a high energy mill with a convenient medium. At nanoparticle synthesis elements are granulated in an inert atmosphere. Mechanical milling is an economical method for nanosize production of large quantities [58]. The dynamics of mechanical milling vary according to energy transfer to the material from the balls [59]. Type of mill, the powder supplied to drive the milling chamber, milling speed, size and size distribution of the balls, dry or wet milling, the temperature of milling and the duration of milling are the factors that affect the energy transfer. Also, deformations, fractures, and the type of welding cause variations in particle shape and size [58].
Nanolithography: This is the fabrication of molecules in a nanometric size range of 1 to 100 nm. Lithography is a combination of deposition and etching to have high-resolution topography. There are two main methods called as masked and maskless lithography. These 2 methods contain many techniques inside. While a mask or a mold is needed in masked lithography to fabricate patterns, maskless lithography produces unstable patterns without the use of mask. Photolithography, soft lithography, and nanoimprint lithography are the main techniques in masked lithography. Maskless lithography consists of electron beam lithography, ion beam lithography, and scanning probe lithography [60].
The process is about printing material in a required shape or structure on a light- sensitive material. The main advantage of nanolithography is to make several copies with the desired shape and size from a single nanoparticle. On the other hand, the necessity of some equipment and their costs are the disadvantages of nanolithography [61].
Laser ablation (LA): The laser irradiates the surface of the sample with a changeable wavelength of the laser and the refractive index of the solid or liquid target material in this complex PVD process. The laser removes electrons from the target material in a high electric field and those scattered electrons meet with the atoms of the bulk sample, where the energy transfer occurs. This leads to the heating of the surface and vaporization. The material is converted to a plasma state at high laser flux. There are some different applications in this method such as welding, cladding, cutting, cleaning, and generation of nanoparticles. During applications environmental conditions such as vacuum, air, gas and liquid can be changed. Pulsed-laser ablation types of solid target materials have great potential in the fields of laser-material microprocessing, nanotechnology and device fabrication. Besides, Laser Ablation Synthesis in Solution (LASiS) is a common and reliable top-down method that provides an alternative solution to the conventional chemical synthesis of metal-based nanoparticles. Also, organic solvents and water can be used in LASiS for NP synthesis and the method can be called as a ‘green’ process [62, 63].
Sputtering: The principle of this physical process is to use the energy of plasma on the surface of a material, to arrange the atoms of the material and deposit them on the substrate with energetic ions. After the bombardment with ions, the ejection of atoms from the target occurs and then they deposit onto a substrate in the vacuum sputtering chamber. This high vacuum-based coating technique is included in the group of PVD processes. The shape, size, and composition of the nanoparticles vary with the layer thickness, temperature, and annealing time and substrate type [64].
The application of polymeric NPs in cancer therapy has been studied for decades. Poly(lactic-co-glycolic acid) (PLGA), chitosan, and polyethylene glycol (PEG) are the most common, FDA-approved polymeric carriers for drug and bio-agent delivery. PLGA and chitosan contain hydrophobic domains which also capable of activating immune cells by their adjuvant character. In general, PLGA-based NPs for cancer immunotherapy is based on targeting dendritic cells. Micelles and liposomes are also convenient for the delivery of therapeutics and antigens. Recently, immunomodulatory nanoliposomes with 1oo nm size were designed to deliver cancer antigens. The researches continued until today has indicated the importance of NPs in cancer immunotherapy. The antigen-NP conjugated systems help to introduce the immune-therapeutic agent to antigen-presenting cells efficiently. A high immune effect occurs with the presence of immunotherapeutic agent-loaded nano delivery systems in comparison to free immunotherapeutic agents. Prolongation, antigenicity, adjuvant selection, and inflammation are the most critical parameters for designing and engineering NPs.
On the other hand, there are still some issues to be solved in cancer immunotherapy. In some cases, insufficient information about cancer cells causes drugs not to present the expected effect. Scientists are unable to have precise information about the behavior of nanoparticles in the living system. In addition to these, there are difficulties in adjusting the toxicity, characterization, and monitoring behavior of nanomaterials in biochemical pathways. Moreover, failure to comply with the rules in drug use in such practices makes the work of the researchers even more difficult.
Besides, nanotechnology is promising for oncological applications for precise diagnoses and struggles with cancer cells. In light of the information mentioned in the literature, it is seen that interdisciplinary approaches and researches about the design and development of nanoparticle-based cancer immunotherapy are promising. Nanotechnology-based studies enable a therapeutic efficacy with a low dose of therapeutics, avoid cytotoxicity, and not to destroy the healthy cells of the patient. The quality and duration of cancer patients’ lives can be improved by developing new methodologies in cancer immunotherapy based on nanoparticles.
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