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Background: Microglia and macrophages (MMs) are the largest component of the inflammatory infiltrate in glioblastoma (GBM). However, whether there are immunophenotypic differences in isocitrate dehydrogenase (IDH)-mutated and -wildtype GBMs is unknown. Studies on specimens of untreated IDH-mutant GBMs are rare given they comprise 10% of all GBMs and often receive treatment at lower grades that can drastically alter MM phenotypes. Methods: We obtained large samples of untreated IDH-mutant and -wildtype GBMs. Using immunofluorescence techniques with single-cell automated segmentation, and comparison between single-cell RNA-sequencing (scRNA-seq) databases of human GBM, we discerned dissimilarities between GBM-associated MMs (GAMMs). Results: There are significantly fewer but more pro-inflammatory GAMMs in IDH-mutant GBMs, suggesting this contributes to the better prognosis of these tumors. Our pro-inflammatory score which combines the expression of inflammatory markers (CD68/HLA-A, -B, -C/TNF/CD163/IL10/TGFB2), Iba1 intensity, and GAMM surface area also indicates more pro-inflammatory GAMMs are associated with longer overall survival independent of IDH status. scRNA-seq analysis demonstrates microglia in IDH-mutants are mainly pro-inflammatory, while anti-inflammatory macrophages that upregulate genes such as FCER1G and TYROBP predominate in IDH-wildtype GBM. Conclusions: Taken together, these observations are the first head-to-head comparison of GAMMs in treatment-naïve IDH-mutant versus -wildtype GBMs that highlight biological disparities that can be exploited for therapeutic purposes.
This paper describes a model of electron energization and cyclotron-maser emission applicable to astrophysical magnetized collisionless shocks. It is motivated by the work of Begelman, Ergun and Rees [Astrophys. J. 625, 51 (2005)] who argued that the cyclotron-maser instability occurs in localized magnetized collisionless shocks such as those expected in blazar jets. We report on recent research carried out to investigate electron acceleration at collisionless shocks and maser radiation associated with the accelerated electrons. We describe how electrons accelerated by lower-hybrid waves at collisionless shocks generate cyclotron-maser radiation when the accelerated electrons move into regions of stronger magnetic fields. The electrons are accelerated along the magnetic field and magnetically compressed leading to the formation of an electron velocity distribution having a horseshoe shape due to conservation of the electron magnetic moment. Under certain conditions the horseshoe electron velocity distribution function is unstable to the cyclotron-maser instability [Bingham and Cairns, Phys. Plasmas 7, 3089 (2000); Melrose, Rev. Mod. Plasma Phys. 1, 5 (2017)].
Let
$q\geq 1$
be any integer and let
$\unicode[STIX]{x1D716}\in [\frac{1}{11},\frac{1}{2})$
be a given real number. We prove that for all primes
$p$
satisfying
Background: CNS innate immune cells, microglia and macrophages (MMs), are the largest component of the inflammatory infiltrate in glioblastoma (GBM). They initially participate in tumor surveillance, but are co-opted by GBM to further angiogenesis and invasion. There are no effective immunotherapies against GBM in part because GBM-associated MMs are not well understood. We hypothesized that the extent and inflammatory phenotype of MM infiltration into GBM is variable between patients. This variability could have important implications on immunotherapy selection and treatment outcomes. Methods: Using automated quantitation of fluorescently labeled human GBMs, flow cytometry/live cell sorting, collection of conditioned GBM-associated MM media, and corroboration with TCGA and previously published scRNA-seq data, we have uncovered there is surprisingly marked variation in the amount of MM infiltration between tumors. Results: MM infiltration can range from almost non-existent, to comprising ~70% of GBM cells. By detecting cell surface markers and secreted cytokines, we determined that a mixture of pro- and anti-inflammatory MMs are found in each tumor. The overall inflammatory phenotype did not depend on the amount of infiltration. Interestingly, IDH-mutant GBM-associated MMs are more pro-inflammatory and less heterogeneous than IDH-wildtype GBMs. Conclusions: Taken together, the highly variable immunologic status of GBMs suggests the success of immunotherapies hinges on selecting appropriately vulnerable tumors.
A total of 45 strains of Vibrio cholerae O1 isolated from 10 different places in India where they were associated with cases of cholera between the years 2007 and 2008 were examined by molecular methods. With the help of phenotypic and genotypic tests the strains were confirmed to be O1 El Tor biotype strains with classical ctxB gene. Polymerase chain reaction (PCR) analysis by double – mismatch amplification mutation assay PCR showed 16 of these strains carried the ctxB-7 allele reported in Haitian strains. Sequencing of the ctxB gene in all the 45 strains revealed that in 16 strains the histidine at the 20th amino acid position had been replaced by asparagine and this single nucleotide polymorphism did not affect cholera toxin production as revealed by beads enzyme-linked immunosorbent assay. This study shows that the new ctxB gene sequence was circulating in different places in India. Seven representatives of these 45 strains analysed by pulsed – field gel electrophoresis showed four distinct Not I digested profiles showing that multiple clones were causing cholera in 2007 and 2008.
Preliminary evidence suggests that direct poultry contact may play a lesser role in transmission of avian influenza A(H7N9) than A(H5N1) to humans. To better understand differences in risk factors, we quantified the degree of poultry contact reported by H5N1 and H7N9 World Health Organization-confirmed cases. We used publicly available data to classify cases by their degree of poultry contact, including direct and indirect. To account for potential data limitations, we used two methods: (1) case population method in which all cases were classified using a range of sources; and (2) case subset method in which only cases with detailed contact information from published research literature were classified. In the case population, detailed exposure information was unavailable for a large proportion of cases (H5N1, 54%; H7N9, 86%). In the case subset, direct contact proportions were higher in H5N1 cases (70·3%) than H7N9 cases (40·0%) (χ2 = 18·5, P < 0·001), and indirect contact proportions were higher in H7N9 cases (44·6%) than H5N1 cases (19·4%) (χ2 = 15·5, P < 0·001). Together with emerging evidence, our descriptive analysis suggests direct poultry contact is a clearer risk factor for H5N1 than for H7N9, and that other risk factors should also be considered for H7N9.
Diarrhoeal diseases are major causes of morbidity and mortality in developing countries. This longitudinal study aimed to identify controllable environmental drivers of intestinal infections amidst a highly contaminated drinking water supply in urban slums and villages of Vellore, Tamil Nadu in southern India. Three hundred households with children (<5 years) residing in two semi-urban slums and three villages were visited weekly for 12–18 months to monitor gastrointestinal morbidity. Households were surveyed at baseline to obtain information on environmental and behavioural factors relevant to diarrhoea. There were 258 diarrhoeal episodes during the follow-up period, resulting in an overall incidence rate of 0·12 episodes/person-year. Incidence and longitudinal prevalence rates of diarrhoea were twofold higher in the slums compared to rural communities (P < 0·0002). Regardless of study site, diarrhoeal incidence was highest in infants (<1 year) at 1·07 episodes/person-year, and decreased gradually with increasing age. Increasing diarrhoeal rates were associated with presence of children (<5 years), domesticated animals and low socioeconomic status. In rural communities, open-field defecation was associated with diarrhoea in young children. This study demonstrates the contribution of site-specific environmental and behavioural factors in influencing endemic rates of urban and rural diarrhoea in a region with highly contaminated drinking water.
The measurement of voting power is a very important topic in social sciences. It is concerned with the power of a member of a voting body or a board that makes yes-or-no decisions on a proposed resolution (or bill) by votes according to some unambiguous criterion. Examples of such decision-making bodies are the United Nations Security Council, the International Monetary Fund, the Council of Ministers in the European Union and the governing body of any corporate house etc.
The voting process of any collective decision-making body is governed by its own constitution, which prescribes the decision-making rule for the body. The individual votes are aggregated using the decision rule to determine the decision of the body as whole. Generally, when a proposal is presented before a voting body, its members are asked to vote either for the proposal (‘yes’) or against it (‘no’). (The more general case when abstention is allowed is discussed later in Section 7.6.) The individual votes are then transformed into a collective decision of the body using the laid down rules.
By voting power of an individual voter, we mean his capability to alter the outcome of the voting procedure by changing his position on the proposed bill. It is an indicator of the extent to which a voter has control over the decision of the voting body. It should rely on the voter's importance in casting the deciding vote. To illustrate this, consider a voting situation where there are three voters, namely a, b and c. These three voters are distinguished by the characteristic that the numbers of votes they have are respectively 9, 4 and 2. Also suppose that the decision rule imposes the condition that at least 12 votes are necessary for any resolution to get through. Now, we may be tempted to conclude that since the number of votes of a is more than two times that of b, the power of a must be greater than that of b. Also since c has a positive number of votes, c should have some positive power.
The objectives of game theory are to model and analyze interdependent decision-making circumstances. A distinction is made in the literature between cooperative and non-cooperative games in the sense that while for the former, obligatory contracts between the participants, referred to as players, is possible, such a possibility is ruled out for the latter.
Cooperative game theory has become very influential in social sciences in the recent years. This book discusses some highly important issues in cooperative game theory with examples from economics, business and sometimes from politics. The book is divided into two parts. Part 1 is composed of Chapters 1—9. Foundations of game theory and a description of the Chapters 2—13 are presented in Chapter 1. Cooperative games with transferable utility are discussed in Chapters 2—6. Chapter 2 explains some basic concepts, definitions and preliminaries. Chapter 3 analyzes set-valued solution concepts like the core, the dominance core, stable sets and different core catchers. An extensive discussion on the relations between alternative solution concepts is also made in this chapter. Two additional set-valued solution concepts, the bargaining set and the kernel that rely on a coalition structure, are presented in Chapter 4. This chapter also discusses the nucleolus, a one-point solution concept, which has interesting relations with the bargaining set and the kernel. In Chapter 5, we consider a well-known one-point solution concept, the Shapley value. A particular type of transferable-utility cooperative game with some especially attractive properties is a convex game, which has been examined in Chapter 6. Relations between the Weber set, an alternative set-valued solution concept, the core and the Shapley value for such games are also reviewed in detail in this chapter. Chapter 7 presents a systematic analysis of voting games that often arise in interactive decision-making situations. The subject of Chapter 8 is stable matching. We discuss the Gale—Shapley basic model of matching men to women or vice-versa, the concept of stable matching, matching problems in two-sided markets, matching problems when participants from one side do not have preferences and housing exchange problems. An investigation of nontransferable utility games is carried out in Chapter 9.
This chapter is devoted to the analysis of a two-sided matching market that consists of two sets of non-overlapping agents. The major objective here is to discuss the possibility of matching a set of agents with another set of agents. For instance, in a marriage problem, a set of men and a set of women need to be matched in pairs.
Such a market differs from a standard commodity market in which market price determines whether a person is a buyer or a seller. For example, a person may be a buyer of a good at some price and a seller of another good at some other price—the market is not two-sided. Additional examples of matching problems include: firms have to be matched with workers, hospitals have to be matched with interns, colleges have to admit students and football players require matching with clubs. ‘The term matching refers to the bilateral nature of exchange in these markets—for example, if I work for some firm, then that firm employs me’ (Roth and Sotomayor 1990, p.1). These markets are definitely different from markets for goods in which a person may be buyer of one good (say, potato) and a seller of another good (say, rice).
The matching theory is a leading area in economic theory because of its importance and also because of the difficulties involved in the allocation of indivisible resources. The appropriate tools for analysis are linear programming and combinatorics. In recent years, it has become quite popular because of applications game theory to study matching problems.
One very important problem in the analysis of matching problems is stability. The problem is to find a stable matching between two sets of agents given a set of preferences for each agent. An allocation where no person will make any gain from a further exchange is called stable. In their pioneering contribution, Gale and Shapley (1962) defined a matching problem and the concept of stable matching. They also showed that stable matchings always exist and suggested an algorithm for computing stable matchings.
The class of weighted majority games is a special case of the class of simple voting games. Both weighted majority games and simple voting games have been discussed in an earlier chapter. One of the key issues for such games is to measure the power of an individual. Several such measures have been introduced and studied in literature. The question that concerns us in this chapter is the following. Given a weighted majority game, is it possible to actually compute the values of the different power indices for this game? We are interested in efficient algorithms and more generally, in the computational complexity of the problem. Before getting into the algorithmic details, we briefly recapitulate some of the basic notions related to weighted majority games.
Recall that a weighted majority game, which we write as v = (w, q) is given by a set of n players N; a list of weights w = (w1, …, wn) ∈ ℜn, one weight for each player in N; and a quota q. Given a subset S of N, its weight is defined to be w(S) = Σi∈Swi. As mentioned earlier, the subset S is said to be a winning coalition if w(S) ≥ q and a losing coalition otherwise. A minimal winning coalition is a winning coalition S such that if any player is dropped from S, it turns into a losing coalition, i.e., w(S) ≥ q and w(Ti) < q for every i ∈ S with Ti = S \ {i}.
Given a game, the total number of winning coalitions in it and the total number of minimal winning coalitions in it are of interest. For a player i, recall that MWi is the set of all minimal winning coalitions S such that i ∈ S. For the Deegan—Packel index, it is required to obtain the distribution of the cardinalities of the sets in MWi.
Let G = (U, V, E) be a bipartite graph with |U| = |V| = n and the edges in E have one end-point in U and the other end-point in V. A matching μ in G is a set of vertex disjoint edges, i.e., μ is a set of edges such that no two edges are co-incident on the same vertex. Since the edges in a matching have to be vertex disjoint, no matching can have more than n edges. A perfect matching is a matching containing n edges. There are well-known algorithms to find a perfect matching (if one exists).
In this section, we will address a different matching problem. An instance still consists of two sets U and V, but, the constraints are different. Let U = {u1, …, un} and V = {v1, …, vn}. Let π1, …, πn be permutations of the set V and let σ1, …, σn be permutations of the set U. The problem instance is given by the following relations. For 1 ≤ i ≤ n and 1 ≤ j ≤ n,
ui ↦ πi; vj ↦ σj.
The permutation πi is a linear ordering of the vertices in V and similarly, the permutation σj is a linear ordering of the vertices in U. Consider the vertices in U to represent n distinct men and the vertices in V to represent n distinct women. The permutation πi represents the ranking of the n women by the man ui; similarly, the permutation σj represents the ranking of the n men by the woman vj.
A matching μ is a pairing of a man and a woman and can be thought of as a marriage. Let the partner of the man ui be denoted by μ(ui) and the partner of woman vj be denoted by μ(vj). Suppose there is a man ui and a woman vj such that πi(vj) precedes πi(μ(ui)) and σj(ui) precedes σj(μ(vj)).
This is an innocuous looking question with a deep answer. We will not attempt to explore the question in its full generality (We refer the reader to Aho, Hopcroft and Ullman (1974) for a comprehensive discussion.). Instead, a high level view will be adopted. An intuitive answer is that an algorithm is a finite sequence of elementary operations with the objective of performing some (computational) task. Let us take this as an acceptable answer and consider several aspects of it in more detail.
Elementary operations: A natural question to ask is how elementary is ‘elementary’? The idea of Turing machines formalises an elementary operation as simply reading or writing a symbol and/or moving a tape head one cell to the left or writing on an infinite tape divided into cells where it is possible to write one symbol on any cell. It is possible to start from this simple notion and obtain algorithms for very complex tasks. In fact, it is a hypothesis that Turing machines capture the exact notion of algorithms. We, however, will not work with the Turing machine model. The reason is that the simplicity of the model makes it quite cumbersome to express higher level ideas. Instead, the elementary operations that we will consider will be at a higher level and include arithmetic and logical operations. This is also the usual practice in the study of algorithms. One works at a higher level knowing that, in theory, all algorithms can be reduced to the Turing machine model.
Finite sequence: The finiteness condition of an algorithm implies that it must always halt. Procedures which continue indefinitely will not be considered as algorithms. The notion of Turing machines can be extended to cover such procedures, but, we will not need to consider them here. A word about the sequence of operations in an algorithm will also be in order.
As we have seen in the discussion of the profit-sharing game in Chapter 1, if all the players in a game decide to work together, there arises a natural question concerning the division of profit among themselves. We have also observed that if some of the players in a coalition object to a proposed allocation, they can decide to leave the coalition. In order to understand this formally, a rigorous treatment of the worth of different coalitions of players and the marginal contribution of a player to a coalition is necessary. Often, some structural assumptions about a game, for instance, whether the game is additive, super-additive or sub-additive, make the analysis convenient. Moreover, in some situations, study of issues like equivalence between two games becomes relevant. This chapter makes a formal presentation of such preliminary concepts and analyzes their implications.
Preliminaries
In this section, we present and explain some preliminary concepts and look at their implications. We assume that N = {A1, A2, …, An} is a finite set of players, where n ≥ 2 is a positive integer. The players are decision makers in the game and we will call any subset S of N, a coalition. The entire set of players N is called the grand coalition. The collection of all coalitions of N is denoted by 2N; each coalition has certain strategies which it can employ. Each coalition also knows how best to use these strategies in order to maximize the amount of pay-off received by all its members. For any coalition S, the complement of S in N, which is denoted by N \ S, is the set of all players who are in N but not in S. For any coalition S, |S| stands for the number of players in S.
An n-person cooperative game assigns to each coalition S, the pay-off that it can achieve without the help of other players. It is a convention to define the pay-off of the empty coalition Ø as zero.
'Game theory can be defined as the study of mathematical models of conflict and cooperation between intelligent rational decision makers. Game theory provides general mathematical techniques for analyzing situations in which two or more individuals make decisions that will influence one another's welfare' (Myerson 1997, p.1). The underlying idea here is that the decisions of the concerned individuals, who behave rationally, will influence each other's interests/pay-offs. No single person alone can determine the outcome completely. Each person's success depends on the actions of the other concerned individuals as well his own actions. Thus, loosely speaking, game theory deals with the mathematical formulation of a decision-making problem in which the analysis of a competitive situation is developed to determine an optimal course of action for a set of concerned individuals. Aumann (1987; 2008) suggested the alternative term ‘interactive decision theory’ for this discipline. However, Binmore (1992) argued that a game is played in a situation where rational individuals interact with each other. For instance, price, output, etc. of a firm will be determined by its actions as a decision maker. Game theory here describes how the firm will frame its actions and how these actions will determine the values of the concerned variable. Likewise, when two or more firms collude to gain more power for controlling the market, it is a game.
To understand this more clearly, consider a set of firms in an oligopolistic industry producing a common output. Each firm must not only be concerned with how its own output affects the market price directly; it must also take into consideration how variations in its output will affect the price through its effect on the decisions taken by other firms. Thus, strategic behaviour becomes an essential ingredient of the analysis. A tool that economists employ for modelling this type of situation is non-cooperative game theory.
As a second example, consider a landowner who owns a large piece of land on which some peasants work. The landowner does not work and requires at least one peasant to work on the piece of land to produce some output.
As a solution concept to cooperative games, the core consists of a set of imputations without distinguishing one element of the set from another. It is a useful indicator of stability. However, the core may be quite large or even empty. A more comprehensive solution to cooperative games is the stable set or the von Neumann—Morgenstern solution. However, here also no single point solution exists so that we can associate a single point vector to a coalition form game. These solution concepts cannot predict a unique expected pay-off corresponding to a given game. If an arbiter's objective is the assignment of a unique outcome, which may be decided by the arbiter in a fair and impartial manner, then these solution concepts are inappropriate.
In an axiomatic approach, Shapley (1953) characterized a unique solution using a set of intuitively reasonable axioms. Shapley's solution is popularly known as the Shapley value. The central idea underlying the Shapley value is that each player should be given his marginal contribution to a coalition, if we consider all possible permutations for forming the grand coalition. Therefore, in a sense, the player is paid out his fair share of the value from the coalition for having joined the coalition. The Shapley value of a player is the expected value of the marginal contributions of the player over all possible orderings.
In the next section of the chapter, the Shapley value is defined by an axiomatic approach. The characterization theorem is explained in Section 5.3. Section 5.4 presents a discussion on Young's (1985; 1988) alternative characterization of the Shapley value using an axiom involving monotonicity of the marginal contributions. This section also analyzes the Shapley value using the potential function introduced by Hart and Mas-Colell (1989). Finally, some applications of the Shapley value are discussed in Section 5.5.
The Formal Framework: Definitions and Axioms
In different orders of grand coalition formation, a player's marginal contributions are likely to vary. These marginal contributions indicate how important the player in the overall cooperation is. A natural question here is what pay-off can a player reasonably expect from his cooperation. The Shapley value provides an answer to this.
The coalition games we have analyzed in the earlier chapters are transferable utility (TU) games. In such games, each coalition is assigned a pay-off (utility) represented by a real number with the interpretation that the members of the coalition can divide this pay-off in an unambiguous manner. In contrast, for non-transferable utility (NTU) games, the pay-offs for each coalition are represented by a set of pay-off (utility) vectors indexed by the members of the coalition. Transferability of utility is a simplifying assumption which makes the analysis quite convenient. However, the transferability assumption may be undesirable in many applications. To illustrate this, consider a bilateral monopoly, a market situation in which a single seller confronts a single buyer. For concreteness, assume that a monopsonistic supplier of a rare metal, which is needed to produce an alloy, faces a monopolistic buyer, the only producer of the alloy. That is, a monopoly supplier of an input faces a monopoly demander of the input. It is known that in such a situation, the market outcome is indeterminate and the outcome must be settled through bargaining. If the producer ceases production, the supplier will not be able to sell the metal. On the other hand, if the supplier refuses to sell the metal, there will be no production of the alloy. In either case, no positive pay-off will be created for each of them. On the other hand, if the two parties decide to cooperate and come to a settlement, some positive pay-off will be created for each of them. However, the settlement does not involve any transfer of pay-off between the two parties. The settlement between the parties is the outcome of an NTU cooperative game. A unique solution to this bargaining problem emerges if the Nash (1950) bargaining model is adopted.
Extensive studies on NTU games were started only in the 1960s and the literature is not very voluminous. A large part of the literature is devoted to the analysis of bargaining games in which only the individual players and the grand coalition play a role.