On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity

The paper studies existence, uniqueness, and stability of large-amplitude periodic cycles arising in Hopf bifurcation at infinity of autonomous control systems with bounded nonlinear feedback. We consider systems with functional nonlinearities of Landesman-Lazer type and a class of systems with hysteresis nonlinearities. The method is based on the technique of parameter functionalization and methods of monotone concave and convex operators. (C) 2001 Academic Press.

Tide-induced water table fluctuations in coastal aquifers bounded by rhythmic shorelines

Previous studies on tidal water table dynamics in unconfined coastal aquifers have focused on the inland propagation of oceanic tides in the cross-shore direction based on the assumption of a straight coastline. Here, two-dimensional analytical solutions are derived to study the effects of rhythmic coastlines on tidal water table fluctuations. The computational results demonstrate that the alongshore variations of the coastline can affect the water table behavior significantly, especially in areas near the centers of the headland and embayment. With the coastline shape effects ignored, traditional analytical solutions may lead to large errors in predicting coastal water table fluctuations or in estimating the aquifer's properties based on these signals. The conditions under which the coastline shape needs to be considered are derived from the new analytical solution.

Energy efficient scheduling for cluster-tree wireless sensor networks with time-bounded data flows: application to IEEE 802.15.4/ZigBee

Cluster scheduling and collision avoidance are crucial issues in large-scale cluster-tree Wireless Sensor Networks (WSNs). The paper presents a methodology that provides a Time Division Cluster Scheduling (TDCS) mechanism based on the cyclic extension of RCPS/TC (Resource Constrained Project Scheduling with Temporal Constraints) problem for a cluster-tree WSN, assuming bounded communication errors. The objective is to meet all end-to-end deadlines of a predefined set of time-bounded data flows while minimizing the energy consumption of the nodes by setting the TDCS period as long as possible. Sinceeach cluster is active only once during the period, the end-to-end delay of a given flow may span over several periods when there are the flows with opposite direction. The scheduling tool enables system designers to efficiently configure all required parameters of the IEEE 802.15.4/ZigBee beaconenabled cluster-tree WSNs in the network design time. The performance evaluation of thescheduling tool shows that the problems with dozens of nodes can be solved while using optimal solvers.

Simulation study of energy efficient scheduling for IEEE 802.15.4/ZigBee cluster-treeWireless Sensor Networks with time-bounded data flows

The simulation analysis is important approach to developing and evaluating the systems in terms of development time and cost. This paper demonstrates the application of Time Division Cluster Scheduling (TDCS) tool for the configuration of IEEE 802.15.4/ZigBee beaconenabled cluster-tree WSNs using the simulation analysis, as an illustrative example that confirms the practical applicability of the tool. The simulation study analyses how the number of retransmissions impacts the reliability of data transmission, the energy consumption of the nodes and the end-to-end communication delay, based on the simulation model that was implemented in the Opnet Modeler. The configuration parameters of the network are obtained directly from the TDCS tool. The simulation results show that the number of retransmissions impacts the reliability, the energy consumption and the end-to-end delay, in a way that improving the one may degrade the others.

Delay-bounded medium access for unidirectional wireless links

Consider a wireless network where links may be unidirectional, that is, a computer node A can broadcast a message and computer node B will receive this message but if B broadcasts then A will not receive it. Assume that messages have deadlines. We propose a medium access control (MAC) protocol which replicates a message in time with carefully selected pauses between replicas, and in this way it guarantees that for every message at least one replica of that message is transmitted without collision. The protocol ensures this with no knowledge of the network topology and it requires neither synchronized clocks nor carrier sensing capabilities. We believe this result is significant because it is the only MAC protocol that offers an upper bound on the message queuing delay for unidirectional links without relying on synchronized clocks.

Time-bounded distributed QoS-aware service configuration in heterogeneous cooperative environments

The scarcity and diversity of resources among the devices of heterogeneous computing environments may affect their ability to perform services with specific Quality of Service constraints, particularly in dynamic distributed environments where the characteristics of the computational load cannot always be predicted in advance. Our work addresses this problem by allowing resource constrained devices to cooperate with more powerful neighbour nodes, opportunistically taking advantage of global distributed resources and processing power. Rather than assuming that the dynamic configuration of this cooperative service executes until it computes its optimal output, the paper proposes an anytime approach that has the ability to tradeoff deliberation time for the quality of the solution. Extensive simulations demonstrate that the proposed anytime algorithms are able to quickly find a good initial solution and effectively optimise the rate at which the quality of the current solution improves at each iteration, with an overhead that can be considered negligible.

Essays on bounded rationality: Individual decision and strategic interaction

Economics is a social science which, therefore, focuses on people and on the decisions they make, be it in an individual context, or in group situations. It studies human choices, in face of needs to be fulfilled, and a limited amount of resources to fulfill them. For a long time, there was a convergence between the normative and positive views of human behavior, in that the ideal and predicted decisions of agents in economic models were entangled in one single concept. That is, it was assumed that the best that could be done in each situation was exactly the choice that would prevail. Or, at least, that the facts that economics needed to explain could be understood in the light of models in which individual agents act as if they are able to make ideal decisions. However, in the last decades, the complexity of the environment in which economic decisions are made and the limits on the ability of agents to deal with it have been recognized, and incorporated into models of decision making in what came to be known as the bounded rationality paradigm. This was triggered by the incapacity of the unboundedly rationality paradigm to explain observed phenomena and behavior. This thesis contributes to the literature in three different ways. Chapter 1 is a survey on bounded rationality, which gathers and organizes the contributions to the field since Simon (1955) first recognized the necessity to account for the limits on human rationality. The focus of the survey is on theoretical work rather than the experimental literature which presents evidence of actual behavior that differs from what classic rationality predicts. The general framework is as follows. Given a set of exogenous variables, the economic agent needs to choose an element from the choice set that is avail- able to him, in order to optimize the expected value of an objective function (assuming his preferences are representable by such a function). If this problem is too complex for the agent to deal with, one or more of its elements is simplified. Each bounded rationality theory is categorized according to the most relevant element it simplifes. Chapter 2 proposes a novel theory of bounded rationality. Much in the same fashion as Conlisk (1980) and Gabaix (2014), we assume that thinking is costly in the sense that agents have to pay a cost for performing mental operations. In our model, if they choose not to think, such cost is avoided, but they are left with a single alternative, labeled the default choice. We exemplify the idea with a very simple model of consumer choice and identify the concept of isofin curves, i.e., sets of default choices which generate the same utility net of thinking cost. Then, we apply the idea to a linear symmetric Cournot duopoly, in which the default choice can be interpreted as the most natural quantity to be produced in the market. We find that, as the thinking cost increases, the number of firms thinking in equilibrium decreases. More interestingly, for intermediate levels of thinking cost, an equilibrium in which one of the firms chooses the default quantity and the other best responds to it exists, generating asymmetric choices in a symmetric model. Our model is able to explain well-known regularities identified in the Cournot experimental literature, such as the adoption of different strategies by players (Huck et al. , 1999), the inter temporal rigidity of choices (Bosch-Dom enech & Vriend, 2003) and the dispersion of quantities in the context of di cult decision making (Bosch-Dom enech & Vriend, 2003). Chapter 3 applies a model of bounded rationality in a game-theoretic set- ting to the well-known turnout paradox in large elections, pivotal probabilities vanish very quickly and no one should vote, in sharp contrast with the ob- served high levels of turnout. Inspired by the concept of rhizomatic thinking, introduced by Bravo-Furtado & Côrte-Real (2009a), we assume that each per- son is self-delusional in the sense that, when making a decision, she believes that a fraction of the people who support the same party decides alike, even if no communication is established between them. This kind of belief simplifies the decision of the agent, as it reduces the number of players he believes to be playing against { it is thus a bounded rationality approach. Studying a two-party first-past-the-post election with a continuum of self-delusional agents, we show that the turnout rate is positive in all the possible equilibria, and that it can be as high as 100%. The game displays multiple equilibria, at least one of which entails a victory of the bigger party. The smaller one may also win, provided its relative size is not too small; more self-delusional voters in the minority party decreases this threshold size. Our model is able to explain some empirical facts, such as the possibility that a close election leads to low turnout (Geys, 2006), a lower margin of victory when turnout is higher (Geys, 2006) and high turnout rates favoring the minority (Bernhagen & Marsh, 1997).

The Barcelonnettes: an example of network-entrepreneurs in XIX century Mexico. An explanation based on a theory of bounded rational choice with social embeddedness

A theory of network-entrepreneurs or "spin-off system" is presented in this paper for the creation of firms based on the community’s social governance. It is argued that firm’s capacity for accumulation depends on the presence of employees belonging to the same social/ethnic group with expectations of "inheriting" the firm and becoming entrepreneurs once they have been selected for their merits and loyalty towards their patrons. Such accumulation is possible because of the credibility of the patrons’ promises of supporting newcomers due to high social cohesion and specific social norms prevailing in the community. This theory is exemplified through the case of the Barcelonnettes, a group of immigrants from the Alps in the South of France (Provence) who came to Mexico in the XIX Century.

Does bounded rationality lead to individual heterogeneity? The impact of the experimentation process and of memory constraints

In this paper we explore the effect of bounded rationality on the convergence of individual behavior toward equilibrium. In the context of a Cournot game with a unique and symmetric Nash equilibrium, firms are modeled as adaptive economic agents through a genetic algorithm. Computational experiments show that (1) there is remarkable heterogeneity across identical but boundedly rational agents; (2) such individual heterogeneity is not simply a consequence of the random elements contained in the genetic algorithm; (3) the more rational agents are in terms of memory abilities and pre-play evaluation of strategies, the less heterogeneous they are in their actions. At the limit case of full rationality, the outcome converges to the standard result of uniform individual behavior.

Complexity and Bounded Rationality in Individual Decision Problemsing.

I develop a model of endogenous bounded rationality due to search costs, arising implicitly from the problems complexity. The decision maker is not required to know the entire structure of the problem when making choices but can think ahead, through costly search, to reveal more of it. However, the costs of search are not assumed exogenously; they are inferred from revealed preferences through her choices. Thus, bounded rationality and its extent emerge endogenously: as problems become simpler or as the benefits of deeper search become larger relative to its costs, the choices more closely resemble those of a rational agent. For a fixed decision problem, the costs of search will vary across agents. For a given decision maker, they will vary across problems. The model explains, therefore, why the disparity, between observed choices and those prescribed under rationality, varies across agents and problems. It also suggests, under reasonable assumptions, an identifying prediction: a relation between the benefits of deeper search and the depth of the search. As long as calibration of the search costs is possible, this can be tested on any agent-problem pair. My approach provides a common framework for depicting the underlying limitations that force departures from rationality in different and unrelated decision-making situations. Specifically, I show that it is consistent with violations of timing independence in temporal framing problems, dynamic inconsistency and diversification bias in sequential versus simultaneous choice problems, and with plausible but contrasting risk attitudes across small- and large-stakes gambles.

Dynamics of experimental populations of native and introduced blowflies (Diptera: Calliphoridae): mathematical modelling and the transition from asymptotic equilibrium to bounded oscillations

The equilibrium dynamics of native and introduced blowflies is modelled using a density-dependent model of population growth that takes into account important features of the life-history in these flies. A theoretical analysis indicates that the product of maximum fecundity and survival is the primary determinant of the dynamics. Cochliomyia macellaria, a blowfly native to the Americas and the introduced Chrysomya megacephala and Chrysomya putoria, differ in their dynamics in that the first species shows a damping oscillatory behavior leading to a one-point equilibrium, whereas in the last two species population numbers show a two-point limit cycle. Simulations showed that variation in fecundity has a marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations and aperiodic behavior. Variation in survival has much less influence on the dynamics.

Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Spatio-temporal dynamics and transition from asymptotic equilibrium to bounded oscillations in Chrysomya albiceps (Diptera, Calliphoridae)

The sensitivity of parameters that govern the stability of population size in Chrysomya albiceps and describe its spatial dynamics was evaluated in this study. The dynamics was modeled using a density-dependent model of population growth. Our simulations show that variation in fecundity and mainly in survival has marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations. C. albiceps exhibits a two-point limit cycle, but the introduction of diffusive dispersal induces an evident qualitative shift from two-point limit cycle to a one fixed-point dynamics. Population dynamics of C. albiceps is here compared to dynamics of Cochliomyia macellaria, C. megacephala and C. putoria.