Дисертації з теми "Operators of small groups"

This thesis is devoted to the study of operators on discrete structures. The operators are supposed to be self-adjoint and obey a certain translation invariance property. The discrete structures are given as Cayley graphs via finitely generated groups. Here, sofic groups and amenable groups are in the center of our considerations. Note that every finitely generated amenable group is sofic. We investigate the spectrum of a discrete self-adjoint operator by studying a sequence of finite dimensional analogues of these operators. In the setting of amenable groups we obtain these approximating operators by restricting the operator in question to finite subsets Qn , n ∈ N. These finite dimensional operators are self-adjoint and therefore admit a well-defined normalized eigenvalue counting function. The limit of the normalized eigenvalue counting functions when |Qn | → ∞ (if it exists) is called the integrated density of states (IDS). It is a distribution function of a probability measure encoding the distribution of the spectrum of the operator in question on the real axis. In this thesis, we prove the existence of the IDS in various geometric settings and for different types of operators. The models we consider include deterministic as well as random situations. Depending on the specific setting, we prove existence of the IDS as a weak limit of distribution functions or even as a uniform limit. Moreover, in certain situations we are able to express the IDS via a semi-explicit formula using the trace of the spectral projection of the original operator. This is sometimes referred to as the validity of the Pastur-Shubin trace formula. In the most general geometric setting we study, the operators are defined on Cayley graphs of sofic groups. Here we prove weak convergence of the eigenvalue counting functions and verify the validity of the Pastur-Shubin trace formula for random and non-random operators . These results apply to operators which not necessarily bounded or of finite hopping range. The methods are based on resolvent techniques. This theory is established without having an ergodic theorem for sofic groups at hand. Note that ergodic theory is the usual tool used in the proof of convergence results of this type. Specifying to operators on amenable groups we are able to prove stronger results. In the discrete case, we show that the IDS exists uniformly for a certain class of finite hopping range operators. This is obtained by using a Banach space-valued ergodic theorem. We show that this applies to eigenvalue counting functions, which implies their convergence with respect to the Banach space norm, in this case the supremum norm. Thus, the heart of this theory is the verification of the Banach space-valued ergodic theorem. Proceeding in two steps we first prove this result for so-called ST-amenable groups. Then, using results from the theory of ε-quasi tilings, we prove a version of the Banach space-valued ergodic theorem which is valid for all amenable groups. Focusing on random operators on amenable groups, we prove uniform existence of the IDS without the assumption that the operator needs to be of finite hopping range or bounded. Moreover, we verify the Pastur-Shubin trace formula. Here we present different techniques. First we show uniform convergence of the normalized eigenvalue counting functions adapting the technique of the Banach space-valued ergodic theorem from the deterministic setting. In a second approach we use weak convergence of the eigenvalue counting functions and additionally obtain control over the convergence at the jumps of the IDS. These ingredients are applied to verify uniform existence of the IDS. In both situations we employ results from the theory of large deviations, in order to deal with long-range interactions.

This book is devoted to the study of operators on discrete structures. The operators are supposed to be self-adjoint and obey a certain translation invariance property. The discrete structures are given as Cayley graphs via finitely generated groups. Here, sofic groups and amenable groups are in the center of our considerations. Note that every finitely generated amenable group is sofic. We investigate the spectrum of a discrete self-adjoint operator by studying a sequence of finite dimensional analogues of these operators. In the setting of amenable groups we obtain these approximating operators by restricting the operator in question to finite subsets Qn , n ∈ N. These finite dimensional operators are self-adjoint and therefore admit a well-defined normalized eigenvalue counting function. The limit of the normalized eigenvalue counting functions when |Qn | → ∞ (if it exists) is called the integrated density of states (IDS). It is a distribution function of a probability measure encoding the distribution of the spectrum of the operator in question on the real axis. We prove the existence of the IDS in various geometric settings and for different types of operators. The models we consider include deterministic as well as random situations. Depending on the specific setting, we prove existence of the IDS as a weak limit of distribution functions or even as a uniform limit. Moreover, in certain situations we are able to express the IDS via a semi-explicit formula using the trace of the spectral projection of the original operator. This is sometimes referred to as the validity of the Pastur-Shubin trace formula. In the most general geometric setting we study, the operators are defined on Cayley graphs of sofic groups. Here we prove weak convergence of the eigenvalue counting functions and verify the validity of the Pastur-Shubin trace formula for random and non-random operators . These results apply to operators which not necessarily bounded or of finite hopping range. The methods are based on resolvent techniques. This theory is established without having an ergodic theorem for sofic groups at hand. Note that ergodic theory is the usual tool used in the proof of convergence results of this type. Specifying to operators on amenable groups we are able to prove stronger results. In the discrete case, we show that the IDS exists uniformly for a certain class of finite hopping range operators. This is obtained by using a Banach space-valued ergodic theorem. We show that this applies to eigenvalue counting functions, which implies their convergence with respect to the Banach space norm, in this case the supremum norm. Thus, the heart of this theory is the verification of the Banach space-valued ergodic theorem. Proceeding in two steps we first prove this result for so-called ST-amenable groups. Then, using results from the theory of ε-quasi tilings, we prove a version of the Banach space-valued ergodic theorem which is valid for all amenable groups. Focusing on random operators on amenable groups, we prove uniform existence of the IDS without the assumption that the operator needs to be of finite hopping range or bounded. Moreover, we verify the Pastur-Shubin trace formula. Here we present different techniques. First we show uniform convergence of the normalized eigenvalue counting functions adapting the technique of the Banach space-valued ergodic theorem from the deterministic setting. In a second approach we use weak convergence of the eigenvalue counting functions and additionally obtain control over the convergence at the jumps of the IDS. These ingredients are applied to verify uniform existence of the IDS. In both situations we employ results from the theory of large deviations, in order to deal with long-range interactions.

This study identified factors and variables of informal leadership in small groups with different gender composition (Men, women and mixed groups) and goal orientation (competition and cooperation). Behavioral dominance patterns (Information Sheet, pencil, decision sheet) and number of verbal interventions were compared to the main informal leadership factors identified in the groups. There were 24 participants (12 men and 12 women). Among the main variables and factors identified, there were some that had a higher possibility to appear than other. There was no significant difference of the factors and variables between women and men. Communication variables were more likely to be present in groups with the goal of cooperation as for the goal of competition. Guidance variables were more likely to be present in women groups than in men groups and mixed groups. There was a significant correlation between the factor’s Communication, Character and Guidance with the number of interventions and behavioral dominance patterns.

For a finite group \(G\), the Hurwitz space \(H\)\(^i\)\(_r\)\(_,\)\(^n\)\(_g\) (\(G\)) is the space of genus \(g\) covers of the Riemann sphere with \(r\) branch points and the monodromy group \(G\). Let ε\(_r\)(\(G\)) = {(\(x\)\(_1\),...,\(x\)\(_r\)) : \(G\) = \(\langle\)\(x\)\(_1\),...,\(x\)\(_r\)\(\rangle\), Π\(^r\)\(_i\)\(_=\)\(_1\) \(x\)\(_i\) = 1, \(x\)\(_i\) ϵ \(G\)#, \(i\) = 1,...,\(r\)}. The connected components of \(H\)\(^i\)\(_r\)\(_,\)\(^n\)\(_g\)(\(G\)) are in bijection with braid orbits on ε\(_r\)(\(G\)). In this thesis we enumerate the connected components of \(H\)\(^i\)\(_r\)\(_,\)\(^n\)\(_g\)(\(G\)) in the cases where \(g\) \(\leq\) 2 and \(G\) is a primitive affine group. Our approach uses a combination of theoretical and computational tools. To handle the most computationally challenging cases we develop a new algorithm which we call the Projection-Fiber algorithm.

This dissertation advances our understanding of the structure of social relations between small groups and the larger organizations within which such groups are situated. Specifically, I examine structures of leadership and authority to gain an in-depth understanding of group organization in one nondenominational and one Southern Baptist megachurch. Methods include in-depth interviews with church clergy, staff, and group leaders; participant observation in groups and other church activities; and a written survey for group leaders. Using this combination of methods, I investigate how small groups are structured in terms of their connections to the megachurches within which they reside. I examine the extent to which the church staff provides oversight and exerts control over groups, and I connect variation on this dimension to how groups relate to their members and to the outside world.My findings include, first, that market metaphors permeate the organization of groups in these two megachurch organizations. The diffusion of ideas and practices from other institutional realms is notable in these two sites, and this may be true for megachurches more generally. Second, I argue that understanding strictness in religious groups is at least as much about the structure of relations between church leadership and membership as it is about beliefs. Third, small groups in megachurches look very much like small groups in American religion more generally, and church oversight may not make much difference in solving problems in small groups identified in previous research. Finally, I find that the level of oversight and control exerted by church leadership on the organization of groups may have a critical influence on the function of groups. Loose and tight connections appear to encourage a more outward and inward focus, respectively.Sociologists studying religious strictness or small groups in any setting should pay particular attention to the structure of relations connecting groups to the larger organizations within which they reside. Religious leaders interested in organizing groups of members should understand that the structure they create to connect with group leaders is at least as important as beliefs they teach leaders, in terms of influencing the focus of the groups.

Let (X, μ) be a measure space, and let L1, . . . ,Ln be (possibly unbounded) selfadjoint operators on L2(X, μ), which commute strongly pairwise, i.e., which admit a joint spectral resolution E on Rn. A joint functional calculus is then defined via spectral integration: for every Borel function m : Rn → C, m(L) = m(L1, . . . ,Ln) = ∫ Rn m(λ) dE(λ) is a normal operator on L2(X, μ), which is bounded if and only if m - called the joint spectral multiplier associated to m(L) - is (E-essentially) bounded. However, the abstract theory of spectral integrals does not tackle the following problem: to find conditions on the multiplier m ensuring the boundedness of m(L) on Lp(X, μ) for some p ≠ 2. We are interested in this problem when the measure space is a connected Lie group G with a right Haar measure, and L1, . . . ,Ln are left-invariant differential operators on G. In fact, the question has been studied quite extensively in the case of a single operator, namely, a sublaplacian or a higher-order analogue. On the other hand, for multiple operators, only specific classes of groups and specific choices of operators have been considered in the literature. Suppose that L1, . . . ,Ln are formally self-adjoint, left-invariant differential operators on a connected Lie group G, which commute pairwise (as operators on smooth functions). Under the assumption that the algebra generated by L1, . . . ,Ln contains a weighted subcoercive operator --- a notion due to [ER98], including positive elliptic operators, sublaplacians and Rockland operators---we prove that L1, . . . ,Ln are (essentially) self-adjoint and strongly commuting on L2(G). Moreover, we perform an abstract study of such a system of operators, in connection with the algebraic structure and the representation theory of G, similarly as what is done in the literature for the algebras of differential operators associated with Gelfand pairs. Under the additional assumption that G has polynomial volume growth, weighted L1 estimates are obtained for the convolution kernel of the operator m(L) corresponding to a compactly supported multiplier m satisfying some smoothness condition. The order of smoothness which we require on m is related to the degree of polynomial growth of G. Some techniques are presented, which allow, for some specific groups and operators, to lower the smoothness requirement on the multiplier. In the case G is a homogeneous Lie group and L1, . . . ,Ln are homogeneous operators, a multiplier theorem of Mihlin-H\"ormander type is proved, extending the result for a single operator of [Chr91] and [MM90]. Further, a product theory is developed, by considering several homogeneous groups Gj , each of which with its own system of operators; a non-conventional use of transference techniques then yields a multiplier theorem of Marcinkiewicz type, not only on the direct product of the Gj , but also on other (possibly non-homogeneous) groups, containing homomorphic images of the Gj . Consequently, for certain non-nilpotent groups of polynomial growth and for some distinguished sublaplacians, we are able to improve the general result of [Ale94].

Let G be a complex semisimple Lie Group with parabolic subgroup P, so that G/P is a generalized flag manifold. An algebraic construction of invariant differential operators between sections of homogeneous bundles over such spaces is given and it is shown how this leads to the classification of all such operators. As an example of a process which naturally generates such operators, the algebraic Penrose transform between generalized flag manifolds is given and computed for several cases, extending standard results in Twistor Theory to higher dimensions. It is then shown how to adapt the homogeneous construction to manifolds with a certain class of tangent bundle structure, including conformal manifolds. This leads to a natural definition of invariant differential operators on such manifolds, and an algebraic method for their construction. A curved analogue of the Penrose transform is given.

The notion of a categorical semidirect product was introduced by Bourn and Janelidze as a generalization of the classical semidirect product in the category of groups. The main aim of this work is to study the general properties of semidirect products of groups with operators, describe them in various classical varieties of such algebraic structures and apply the results to homological algebra and related areas of modern algebra. The context in which the study is done is a semiabelian category (that is, a pointed, Barr-exact and Bourn-protomodular category). The main result in the thesis is the construction of the semidirect product in a variety -RLoop of right -loops as the product of underlying sets equipped with the -algebra structure. A variety of right -loops is a variety that is pointed, has a binary + (not necessarily associative or commutative) and a binary satisfying the identities 0 + x = x, x + 0 = x, (x + y) y = x and (x - y) + y = x. Thus, -RLoop is a generalization of the variety of -groups introduced by Higgins and the results obtained are valid for varieties of -loops. We also describe precrossed and crossed modules in the variety -RLoop. The theory of crossed modules developed is independent of that developed by Janelidze for crossed modules in an arbitrary semiabelian category and gives simplified explicit formulae for crossed modules in -RLoop. Finally, we mention that our constructions agree with the known ones in the familiar algebraic categories, specifically the categories of groups, rings and Lie algebras.

International Telemetering Conference Proceedings / October 22-25, 2001 / Riviera Hotel and Convention Center, Las Vegas, Nevada<br>Reducing spacecraft ground system operations costs are a major goal in all missions. The Fast Auroral Snapshot (FAST) flight operations team at the NASA/Goddard Spacecraft Flight Center developed in-house scripts and procedures to automate monitoring of critical spacecraft functions. The initial staffing profile of 16x7 was reduced first to 8x5 and then to “lights out”. Operations functions became an offline review of system performance and the generation of future science plans for subsequent upload to the spacecraft. Lessons learned will be applied to the challenging Triana mission, where 24x7 contact with the spacecraft will be necessary at all times.

This PhD thesis is about incentives in the presence of agents who interact in small groups. It is composed by three chapters, each corresponding to a self-contained paper, applying different methodologies (theoretical and empirical) and different perspectives. I refer to groups not as collection of independently acting individuals, but, in line with Arrow, McGrath, and Berdahl (2000), as "adaptive, dynamic systems that are driven by interactions both among group members and between the group and its embedding contexts''. Following such point of view, I focus on groups in which individuals' each actions revoke responses by another individuals. While the first chapter considers purely rational individuals, abstracting from other-regarding preferences such as reciprocity, inequity aversion, and fairness considerations (Dufwenberg, Heidhues, Kirchsteiger, Riedel, and Sobel, 2008; Sobel, 2005; Fehr and Schmidt, 1999; Bolton and Ockenfels, 2000; Charness and Rabin, 2002), in the other two chapters I include such behavioral aspects, which lead to the emergence of new strategic behaviors with respect to the case in which such preferences are not taken into account. Hence, the aim of this thesis is not only to understand the working and reasoning behind incentivized decision making, to be able to explain observable phenomena in economic and social interaction, but also to study mechanisms that may restore incentives in cases in which efficiency needs to be increased, and, when possible, establish optimal incentives. While the first chapter contains a theoretical model dealing with an optimal mechanism, considering the interaction among several agents or firms on the market, the second chapter treats with a mechanism dealing with agents inside an organization, applying experimental methodology. Instead of suggesting a new mechanism, as the first chapter does, the second chapter tries to understand the mechanisms behind the observable phenomena of having mediocre agents in organizations. Finally, the last chapter tries to explain the reasoning behind the delegating of decisions, which may play a role either inside a firm (when a manager delegates to his subordinate) or outside (when two firms negotiate). More in detail, the first chapter deals with the aspect of incentivizing a firm to take the optimal investment decision when simple complete contracts cannot be written as to induce the desired outcome, or, more precisely, the hold-up problem is present (Hart and Moore, 1999). The principal interacts with two or more agents, where agent may be understood as an individual player or as well as firm. More specifically, the case I consider is a seller vending identical products to two buyers that have a common interest in inducing the seller to make a quality enhancing investment. I show that a trilateral contract may provide the correct incentives to restore efficiency, in a setting in which two bilateral contracts would have failed to provide such incentives. Because there is more than one buyer, the purchasing decision can be transformed from a contemporaneous to a sequential problem. This allows to condition the exchange of an extra payment on verifiable previous transactions. The contract induces a coalition proof Nash equilibrium and holds under complete as well as incomplete information. The presence of two or more agents is important, since it is the sequentiality with which payments of the two agents are exchanged with the principal that resolve the issue of incentive compatibility. With one agent, this sequentiality could not be made use of. The number of agents may be easily extended to more than two buyers. The second chapter applies economic experimental methodology to study the incentives behind employing mediocre agents in organizations, and its focus is individual decision taking. Me and my coauthors Natalia Montinari and Antonio Nicolò run a decision making experiment in which a principal selects one agent to perform a task for a fixed compensation. Agents' productivity depends on two components, a non contractible ex-post effort and an exogenous ex-ante productivity. The principal chooses between two agents with different ex-ante productivity, in a setting with common information. Once the principal has selected one agent, this agent chooses a level of costly non-contractible effort. We run three different treatments: one treatment with communication, in which the principal can send a message to the selected agent; one treatment without communication, and a control treatment where the agent is selected by a random device. Our results are the following: in treatments where the principal selects the agent, a significant share of principals employ the agent who has the ex-ante lowest productivity. In the communication treatment, the selected agents with lowest ex-ante productivity exert a significantly higher effort compared to the agents with ex-ante highest productivity. The higher effort overcompensates the low ex-ante productivity, and principals who have chosen low ex-ante productive agents gain on average 40% more than principals who hired high ex-ante productive agents. In the no-communication treatment and in the control treatment the average effort exerted by the ex-ante low productive and ex-ante high productive agents does not differ significantly. Our experiment provides a rationale for the selection of mediocre (ex-ante less productive) workers in organizations. Agents who are ex-ante less entitled to fill a position reciprocate more than individuals who are ex-ante more competent, and exert a higher non contractible effort ex-post when principals are able to inspire mediocre agents to feel indebted towards them. It follows that principals may find it profitable to hire agents who ex-ante can be viewed as less qualified. We suggest that this is a prominent characteristic in organizations, like civil service, where i) reciprocity cannot be induced by means of higher wages and ii) non-contractible effort is a relevant component of the employer's production function. The third chapter presents again a laboratory experiment, with which me and my coauthor Zachary Grossman investigate the incentives behind the delegation of a decision. Beyond the classical reasons of efficiency, commitment, the distribution of information, or incentive provision, a person may also delegate decision rights so as to avoid blame for an unpopular or immoral decision. Extending the results of Bartling and Fischbacher (2011), we show that by delegating to an intermediary, a dictator facing an allocation decision can effectively shift moral responsibility onto the delegee even when doing so necessarily eliminates the possibility of a fair outcome. Dictators choosing selfishly via an intermediary are punished less and earn greater profits than those who do so directly. Despite being powerless to influence the fairness of the outcome, an intermediary given the choice between two unfair outcomes is punished more than when the dictator chooses one directly. This is not the case when the intermediary merely can initiate the random selection of one of the outcomes. Our findings reinforce and clarify the usefulness of agency as a tool to evade perceived culpability, addresses the limits of blame shifting, and makes an interesting contribution to the emerging literature on the delegation of responsibility.<br>Questa tesi analizza gli incentivi in presenza di agenti che interagiscono tra loro in piccoli gruppi. Questo lavoro è un compendio di tre articoli tra loro indipendenti che applicano metodologie diverse, sia teoriche che empiriche, e impiegano diverse prospettive. Arrow, McGrath e Berdahl (2000) descrivono i gruppi come sistemi adattivi e dinamici, che sono guidati da interazioni sia tra i componenti dei gruppi, sia tra i gruppi stessi e il loro contesto - e non come un insieme di individui che si comportano in modo indipendente gli uni dagli altri. Partendo da questo punto di vista, in questa tesi mi focalizzo su piccoli gruppi in cui gli individui interagiscono tra di loro e ciascuna azione dei singoli provoca una risposta degli altri componenti del gruppo. Nel primo capitolo vengono analizzati i comportamenti di individui puramente razionali mentre nei capitoli successivi si considerano anche aspetti comportamentali tra i quali la reciprocità, avversione alla disuguaglianza, il senso di giustizia (Dufwenberg, Heidhues, Kirchsteiger, Riedel, e Sobel, 2008; Sobel, 2005; Fehr e Schmidt, 1999; Bolton e Ockenfels, 2000; Charness e Rabin, 2002), che inducono comportamenti strategici diversi rispetto a quando non si considerano le preferenze sociali. L'obiettivo di questo lavoro è, quindi, non solo di analizzare i meccanismi di funzionamento dei processi decisionali, ma anche di studiare come sia possibile generare degli incentivi in grado di migliorare il livello di efficienza, che è lo scopo ultimo dello sviluppo economico. Il primo e il secondo capitolo si concentrano sulla definizione di schemi di incentivi in contesti specifici. In particolare, il primo capitolo presenta un modello teorico che analizza gli incentivi ottimali considerando l'interazione tra diversi agenti o aziende presenti nel mercato. Mentre il primo capitolo assume che gli aspetti comportamentali non siano rilevanti, gli ultimi due capitoli introducono aspetti comportamentali nell'interazione degli agenti all'interno di un'organizzazione. Il primo capitolo definisce un nuovo sistema di incentivi , mentre nel secondo si analizzano degli aspetti comportamentali che spiegano la presenza di lavoratori mediocri nelle organizzazioni. Infine, l'ultimo capitolo si pone l'obiettivo di spiegare un meccanismo alla base del processo di delega decisionale, che si rivela di notevole importanza sia all'interno dell'azienda (quando, ad esempio, un manager delega la decisione ad un subordinato), sia tra aziende (quando due aziende negoziano tra loro). Più in dettaglio, il primo capitolo affronta attraverso un modello teorico, come incentivare un'organizzazione a prendere delle decisioni ottimali quando non possono essere stipulati dei semplici contratti bilaterali ottimali (Hart e Moore, 1999), o, più precisamente, quando sia presente il problema di "hold-up''. Il principale interagisce con due (o più) agenti, dove per agente si intende sia un individuo singolo o un'azienda. Più specificamente, il caso considerato è quello di un'impresa che vende dei prodotti identici a due diversi acquirenti, che hanno un interesse comune ad indurre il venditore a fare un investimento che aumenta la possibilità che il prodotto sia di alta qualità. Attraverso un'analisi teorica si dimostra che un contratto trilaterale può fornire gli incentivi adatti a ripristinare l'efficienza, in un ambiente in cui due contratti bilaterali falliscono in questo compito. Data l'esistenza di una molteplicità di acquirenti, la decisione di acquisto può essere trasformata da una decisione simultanea ad un problema sequenziale. La sequenzialità permette di subordinare lo scambio di un pagamento addizionale alla verifica delle transazioni precedenti. Il contratto induce un equilibrio "coalition proof Nash'' di decisione sequenziale, sia sotto l'ipotesi di informazione completa che incompleta. La presenza di due agenti è rilevante, dato che la sequenzialità con la quale i pagamenti dei due agenti sono stati versati al principale risolve il problema della compatibilità degli incentivi. Con un solo agente, infatti, non si potrebbe far uso di questa sequenzialità. A partire da questo risultato, il numero di agenti, può essere esteso facilmente a più di due. Il secondo capitolo applica la metodologia sperimentale per studiare gli incentivi che motivano l'impiego di agenti mediocri nelle organizzazione, focalizzandosi sul meccanismo decisionale degli individui. Insieme a Natalia Montinari e Antonio Nicolò abbiamo realizzato un esperimento di laboratorio, in cui incentiviamo gli individui a prendere una decisione in cui un principale sceglie un agente per eseguire un compito, pagandogli un compenso fisso. La produttività dell'agente dipende da due componenti: uno sforzo non contrattabile a posteriori, ed una produttività esogena a priori. Il principale sceglie tra due agenti che hanno diversi livelli di produttività a priori. Una volta scelto un agente, questo sceglie un livello di sforzo costoso non contrattabile. Eseguiamo, quindi, tre trattamenti diversi: uno con comunicazione, in cui un principale può mandare un messaggio all'agente selezionato; uno senza comunicazione, ed infine un trattamento di controllo in cui l'agente viene selezionato in modo casuale. I risultati dell'esperimento sono i seguenti. Nei trattamenti nei quali il principale seleziona l'agente, una quota significativa dei principali impiega l'agente che ha a priori la produttività più bassa. Nel trattamento con comunicazione, gli agenti con la produttività a priori più bassa esercitano uno sforzo significativamente più alto rispetto agli agenti con la produttività a priori più alta. Lo sforzo più alto compensa in maniera più che proporzionale la produttività più bassa e i principali che scelgono l'agente a priori meno produttivo guadagnano in media il 40% di più rispetto ai principali che assumono un agente a priori più produttivo. Nel trattamento senza comunicazione e nel trattamento di controllo, non c'è evidenza dell'esistenza di uno sforzo più alto da parte dei dipendenti di produttività bassa. Dunque, il nostro esperimento fornisce una spiegazione razionale per la selezione di individui mediocri (cioè quelli che sono meno produttivi a priori) nelle organizzazioni. Coloro che sono scelti nonostante abbiano la consapevolezza di avere minori capacità reciprocano di più rispetto agli individui che sono più competenti a priori ed esercitano uno sforzo non-contrattabile più alto quando i principali sono in grado di far percepire agli agenti mediocri la loro condizione di inferiorità. Pertanto, i principali possono trovare remunerativo: assumere un agente che a priori può essere considerato meno qualificato. Suggeriamo che questa è una caratteristica importante specie nelle organizzazioni dove i) la reciprocità non può essere indotta tramite salari più alti, e ii) lo sforzo non contrattabile è una componente rilevante nella funzione di produttività del datore di lavoro (si pensi, per esempio, alle organizzazioni della pubblica amministrazione). Anche il terzo capitolo, scritto a due mani con Zachary Grossman, presenta un esperimento di laboratorio. L'obiettivo del capitolo è di indagare gli incentivi che sottostanno alla delega di una decisione. Oltre ai tradizionali incentivi alla scelta di delegare una decisione identificati in letteratura, come l'efficienza, l'impegno, la distribuzione di informazione o la trasmissione di incentivi, studi recenti hanno suggerito che anche la volontà di evitare di addossarsi la colpa per una decisione impopolare o immorale possa motivare un agente a delegare. Bartling e Fischbacher (2011) hanno dimostrato che, tramite la delega di una decisione ad un intermediario, un dittatore che è di fronte a una decisione di allocazione può effettivamente spostare la responsabilità morale sulla persona che poi prende la decisione (il delegato). Grazie al nostro esperimento si dimostra che questo meccanismo di trasferimento della responsabilità funziona anche se la scelta di delegare comporta necessariamente l'implementazione di una scelta ingiusta. I dittatori che scelgono l'allocazione ingiusta sono puniti di meno e guadagnano di più se utilizzano un intermediario rispetto a quelli che prendono questa decisione senza delegare. Pur non essendo in grado di influenzare il risultato, un intermediario che ha la scelta tra due allocazioni inique viene punito di più rispetto a quando quella stessa scelta sia presa direttamente dal dittatore. Questo non avviene quando l'intermediario può soltanto iniziare il processo di selezione casuale tra le due allocazioni, ma non scegliere direttamente tra queste due allocazioni inique. I nostri risultati rafforzano e chiariscono l'utilità di utilizzare un intermediario come mezzo per deviare l'attribuzione di responsabilità. Grazie al confronto tra il caso in cui l'intermediario può scegliere rispetto a quando può solo iniziare il processo di scelta casuale, il nostro lavoro contribuisce alla crescente letteratura sulla delegazione della responsabilità.

Corruption is a structural and a moral problem of modern societies. It undermines social development, democracy and people's wealth. The cost of corruption is about $1 trillion per year, and it is often paid by the poorest groups in society. To study corruption is, therefore, not only a scientific challenge but also a necessity in the search for social justice and in the context of improving quality of life. ( In fighting corruption, policy makers often have to decide whether to shape an in- tervention based on the individual or on the individual's perception of their environ- ment. Moreover, campaigns against corruption need to be tailored to the social context in which they will be implemented. Policies to be designed to counteract corruption can, therefore, benefit of a tool to differ social settings wit3respect to corruption. The current literature on corruption lacks a theoretical framework as well as tools for shedding light on the subject matter outlined above. The following research attempts to fill this. Qualitative and quantitative research evidence is used to identify social regularities brought about by corruption and, based on those observations, a set of social mechanisms are put forward. These are then used to design a model and a tool to gather first hand data. Finally, a new set of analytic techniques to grasp the degree to which groups affect individuals' decisions complete the methodology. Moreover, to show the strong empirical link between the model and the data gathering method, a data collection exercise with 16 participants is illustrated. This study proposes a new methodology for understanding how corruption emerges in small groups. More specifically, the extent to which group features affect individu- als' decisions as to whether or not to uphold corrupt practices is addressed in the context of limited public resources. The main result of this study is the development of the methodology itself, producing a set of values which are then interpreted to provide a measure of corruption. Such a measure quantifies the extent to which individuals' decisions are affected by their group. This contribution is particularly relevant for policy making, especially when it comes to deciding whether to design initiatives tailored to the individual or to the individuals perception of society. Key words: Agent-Based Modelling, Computational Sociology, Corruption, Role-Playing Game, Cultural Dimensions, Emergence, Validation, Calibration

Au cours de la dernière décennie, un nouveau domaine de recherche multidisciplinaire appelé traitement des signaux sociaux (SSP) a émergé. Il vise à permettre aux machines de détecter, reconnaître et afficher les signaux sociaux humains. L'analyse automatisée des interactions de groupe est l'une des tâches les plus complexes abordée par ce domaine de recherche. Récemment, une attention particulière s'est portée sur l'étude automatisée des états émergents. En effet, ceux-ci jouent un rôle important dans les dynamiques d'un groupe car ils résultent des interactions entre ses membres. Dans cette Thèse, nous abordons l'analyse automatique de la cohésion dans les interactions de petits groupes. La cohésion est un état émergent affectif multidimensionnel qui peut être défini comme un processus dynamique, reflété par la tendance d'un groupe à rester ensemble pour poursuivre des objectifs et/ou des besoins affectifs. Malgré la riche littérature disponible sur la cohésion du point de vue des Sciences Sociales, l'analyse automatique de la cohésion en est encore à ses débuts. En s'inspirant de connaissances tirées des Sciences Sociales, cette thèse vise à développer des modèles informatiques de cohésion suivant quatre axes de recherche, en s'appuyant sur des techniques d'apprentissage automatique et d'apprentissage profond. Ces modèles doivent en effet tenir compte de la nature temporelle de la cohésion, de sa multidimensionnalité, de la façon de modéliser la cohésion du point de vue des individus et du groupe, d'intégrer les relations entre ses dimensions et leur évolution dans le temps, ainsi que de tenir compte des relations entre la cohésion et d'autres processus de groupe. De plus, face à un manque de données disponibles publiquement, cette thèse a contribué à la collecte d'une base de données multimodales spécifiquement conçue pour étudier la cohésion, et pour contrôler explicitement ses variations dans le temps. Une telle base de données permet, entre autres, de développer des modèles informatiques intégrant la cohésion perçue par les membres du groupe et/ou par des points de vue externes. Nos résultats montrent la pertinence de s'inspirer des théories tirées des Sciences Sociales pour développer de nouveaux modèles computationnels de cohésion et confirment les avantages d'explorer chacun des quatre axes de recherche<br>Over the last decade, a new multidisciplinary research domain named Social Signal Processing (SSP) emerged. It is aimed at enabling machines to sense, recognize, and display human social signals. One of the challenging tasks addressed by SSP is the automated group interaction analysis. Recently, a particular emphasis is given to the automated study of emergent states as they play an important role in group dynamics. These are social processes that develop throughout group members' interactions.In this Thesis, we address the automated analysis of cohesion in small groups interactions. Cohesion is a multidimensional affective emergent state that can be defined as a dynamic process reflected by the tendency of a group to stick together to pursue goals and/or affective needs. Despite the rich literature available on cohesion from a Social Sciences perspective, its automated analysis is still in its infancy. Grounding on Social Sciences' insights, this Thesis aims to develop computational models of cohesion following four axes research axes, leveraging Machine Learning and Deep Learning techniques. Computational models of cohesion, indeed, should account for the temporal nature of cohesion, the multidimensionality of this group process, take into account how to model cohesion from both individuals and group perspectives, integrate the relationships between its dimensions and their development over time, and take heed of the relationships between cohesion and other group processes.In addition, facing a lack of publicly available data, this Thesis contributed to the collection of a multimodal dataset specifically designed for studying group cohesion and for explicitly controlling its variations over time. Such a dataset enables, among other perspectives, further development of computational models integrating the perceived cohesion from group members and/or external points of view. Our results show the relevance of leveraging Social Sciences' insights to develop new computational models of cohesion and confirm the benefits of exploring each of the four research axes

This thesis focuses on the subject of varieties for modules for elementary abelian p-groups. Given a homogeneous polynomial over an algebraically closed field of char- acteristic 2 we will give constructions for modules of small dimension having that polynomial as variety. This is similar to an earlier construction given by Jon Carlson but our modules will in general be of considerably smaller dimension. We also investigate the connection between the variety of a module and its Loewy length. We show that working over an algebraically closed field of characteristic 2 with modules of Loewy length 2 allows us to find modules with any hypersurface as their variety. On the other hand we also demonstrate that in odd characteristic p, with modules of Loewy length p, the only possible varieties are finite unions of linear hypersurfaces.

This dissertation uses social movement theory to analyze the emergence, activities and development of subcultures and small groups. The manuscript is comprised of an Introduction followed by three journal articles and one book chapter.  The introduction discusses: 1) the concept of theoretical extension whereby a theory developed for one purpose is adapted to another; 2) it identifies the social movement theories used to analyze subcultures and small groups; 3) it describes the data used in the analyses included here. The data for this work derives from two distinct research projects conducted by the author between 2002 and 2012 and relies on multiple sources of qualitative data. Data collection techniques used include fieldwork, archival research, and secondary data. Paper I uses resource mobilization (RM) theory to analyze the origin, development, and function of White Power music in relation to the broader White Power Movement (WPM). The research identifies three roles played by White Power music: (1) recruit new adherents, (2) frame issues and ideology for the construction of collective identity, (3) obtain financial resources. Paper II gives an overview of the subculture of Freestyle BMX, discussing its origins and developments—both internationally as a wider subcultural phenomenon, and locally, through a three-year ethnographic case study of a subcultural BMX scene known as “Pro Town USA.” Paper III conceptualizes BMX as a social movement using RM theory to identify and explain three different forms of commercialization within this lifestyle sport in “Pro Town.” The work sheds light on the complex process of commercialization within lifestyle sports by identifying three distinct forms of commercialization: paraphernalia, movement, and mass market, and analyses different impacts that each had on the on the development of the local scene.  Findings reveal that lifestyle-sport insiders actively collaborate in each form of commercialization, especially movement commercialization which has the potential to build alternative lifestyle-sport institutions and resist adverse commercial influences. Paper IV refines the small group theory of collaborative circles by: (1) further clarifying its concepts and relationships, (2) integrating the concepts of flow and idioculture, and (3) introducing a more nuanced concept of resources from RM. The paper concludes by demonstrating that circle development was aided by specific locational, human, moral, and material resources as well as by complementary social-psychological characteristics of its members.

The results of a laboratory investigation into the behaviour of small groups of up to five granular columns, in soft clay, loaded by various foundation configurations under rapid undrained conditions is presented. Columns with a constant layer length to diameter ratio in both floating and end-bearing conditions are considered. Electronic instrumentation was developed to record boundary stresses and displacements and radiographic techniques were employed to measure internal displacements and strains in the columns and clay. Extensive use of interactive mainframe and mini computers was made in collecting, storing and processing the laboratory data. The improvement in bearing capacity and reduction in settlement was found to be strongly dependent on the relative column and clay areas in contact with a foundation. The column end-bearing condition was also a contributory factor. The mechanism of column and clay deformation was observed as being dependent on the boundary conditions. Column yield occurred as a general shear failure or a local shear failure depending on the relative sizes of the clay and column areas. Laboratory results showed that direct analogy with conventional piles or pile groups cannot be made. An empirical relationship for estimating the improvement in bearing capacity and settlement is proposed.

This thesis is focussed on the role differentiationhypothesis as it relates to small groups (Bales, 1958). The hypothesis is systematically examined, both conceptually and empirically, in the light of the Equilibrium Hypothesis (Bales, 1953) and the Negotiated Order Theory of leadership (e.g. Hosking, 1988). Chapter 1 sketches in a context for the research,which was stimulated by attempts during the 60s and 70s to organise small groups without leaders (the leaderless group, based on isocratic principles). Chapter 2 gives a conceptual and developmental overview of Bales' work, concentrating on the Equilibrium Hypothesis. It is argued that Bales' conceptual approach, if developed, can potentially integrate the disparate small groups and leadership literatures. Chapters 3 and 4 examine the concepts `group', `leader' and `leadership' in terms of the Negotiated Order perspective. In chapter 3 it is argued that two aspects of the concept group need to be taken separately into account; physical attributes and social psychological aspects (the metaphysical glue). It is further argued that a collection of people becomes a group only when they begin to establish a shared sense of social order. In chapter 4 it is argued that leadership is best viewed as a process of negotiation between those who influence and those who are influenced, in the context of shared values about means and ends. It is further argued that leadership is the process by which a shared sense of social order is established and maintained, thus linking the concepts `leadership' and `group' in a single formulation. The correspondences with Bales' approach are discussed at the end of the chapter. Chapters 5 to 8 present a detailed critical description and evaluation of the empirical work which claims to show role differentiation or test the hypothesis, both Bales original work and subsequent studies. It is argued here, that the measurement and analytical procedures adopted by Bales and others, in particular the use of simple means as summaries of group structures, are fundamentally flawed, and that role differentiation in relation to particular identifiable groups has not been demonstrated clearly anywhere in the literature. Chapters 9 to 13 present the empirical work conducted for the thesis. 18 small groups are examined systematically for evidence of role differentiation using an approach based on early sociometry (Moreno, 1934). The results suggest that role differentiation, as described by Bales, does not occur as often as is implied in the literature, and not equivocally in any case. In particular structures derived from Liking are typically distributed or weak. This suggests that one of Bales' principal findings, that Liking varies independently of his other main dimensions, is the product of statistical artifact. Chapter 14 presents a general summary of results and presents some considerations about future research.

Applied Linguistics<br>Ph.D.<br>Small groups are integral for many activities in the foreign language classroom and their pedagogical importance is well established. Despite the widespread use of groups in foreign language education, there is a dearth of research investigating group processes and the impact of emergent leaders within these groups. This mixed-methods, longitudinal study was designed to first establish the presence of emergent leaders within an SLA context, and then to investigate the factors influencing who will emerge as the leader, and the impact they have on the views and performance of the group. First-year students majoring in science at a private university in western Japan were placed into three English Communication classes depending on their major within the school, and further randomly assigned to small groups of three to four people within each class. Students worked together in these groups for the first semester spanning 14 weeks and were required to take part in group presentations and group discussions. Measures of aural and general English ability, English communication self-efficacy, and the Big Five dimensions of personality were used to predict who would emerge as leaders within each group, and group and individual change was tracked using measures of self- and collective-efficacy. Participant and video observation, and interview data were used to provide rich description of the intra-group processes. In the second semester the students were allowed to self-select their groups, which were then fixed for the 14-week course. The first finding of the study was that leaders emerged in the small groups in this context, and proficiency in English was found to be the only consistent predictor of group leader emergence, with extroversion predicting initial perceptions of leadership only. The second finding of the study was that individuals' perceived leadership was relatively stable when in the same group, but that when the group makeup was changed there were large differences in the perceived leadership scores, suggesting that leadership behavior depends on the group in which students are in, and that group makeup influences individual student behavior. The third finding was that different types of leader were found to exist, with visible leaders who were easily identified by the teacher, and invisible leaders who were recognized by group members to be leader, but not clear to the teacher. The fourth finding was that collective-efficacy was existed as a group-level construct in this context, and growth models showed that self-efficacy increased for students in both the first and second semesters, and that the group experiences in the first semester seemed to influence rates of change in self-efficacy in the second semester, suggesting that the products of previous group experiences carry into subsequent group work and affect attitudes and behavior. The fifth finding was that students select group members based on friendship, but that students had mixed preferences with regard the choice between random group formation and self-selection into groups. Students almost universally felt that changing group members at regular intervals of several weeks was beneficial. Overall the study highlighted the importance of group makeup, and particularly leadership in this context, and showed that behavior in the language classroom was heavily influenced by group members.<br>Temple University--Theses

<p> Simple environmental features can shape complex behavior. Identifying key aspects of the environment (e.g., temperature, structure, toxins) that lead to widespread consequences is of central importance in a changing world. The primary objective of my dissertation is to investigate how relatively simple aspects of the environment can influence small groups of animals in profound and complex ways. In the first three chapters, I report on experiments showing how small changes in the environment can affect the expression of behavior at different points in development and can have important physiological consequences for litters of mouse pups. I then report on two sets of experiments showing how subtle changes in the environment can dramatically affect spacing patterns and social dynamics of small groups of adult zebrafish. Together, my results emphasize the ways that subtle changes in the environment can have profound impacts on individuals and small groups. In both lines of work, I have found that a more accurate characterization of the phenomena, infant rodent development and zebrafish social behavior, requires the use of individual and group measures and that temperature, density, and pollutants can have a powerful effect on group responses. These results are important because they show that the physical environment can have profound effects on the phenotype, and that with a changing physical environment or anthropogenic change, dramatic differences may be observed in the behavior of groups.</p>