Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.

Limiting conditional distributions for birth-death processes

In a recent paper [16], one of us identified all of the quasi-stationary distributions for a non-explosive, evanescent birth-death process for which absorption is certain, and established conditions for the existence of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of directions. We shall consider separately two cases depending on whether or not the process is evanescent. In the former case we shall relax the condition that absorption is certain. Furthermore, we shall allow for the possibility that the minimal process might be explosive, so that the transition rates alone will not necessarily determine the birth-death process uniquely. Although we shall be concerned mainly with the minimal process, our most general results hold for any birth-death process whose transition probabilities satisfy both the backward and the forward Kolmogorov differential equations.

Aspects of adaptive management of coastal wetlands: Case studies of processes, conservation, restoration, impacts and assessment

Coastal wetlands are dynamic and include the freshwater-intertidal interface. In many parts of the world such wetlands are under pressure from increasing human populations and from predicted sea-level rise. Their complexity and the limited knowledge of processes operating in these systems combine to make them a management challenge.Adaptive management is advocated for complex ecosystem management (Hackney 2000; Meretsky et al. 2000; Thom 2000;National Research Council 2003).Adaptive management identifies management aims,makes an inventory/environmental assessment,plans management actions, implements these, assesses outcomes, and provides feedback to iterate the process (Holling 1978;Walters and Holling 1990). This allows for a dynamic management system that is responsive to change. In the area of wetland management recent adaptive approaches are exemplified by Natuhara et al. (2004) for wild bird management, Bunch and Dudycha (2004) for a river system, Thom (2000) for restoration, and Quinn and Hanna (2003) for seasonal wetlands in California. There are many wetland habitats for which we currently have only rudimentary knowledge (Hackney 2000), emphasizing the need for good information as a prerequisite for effective management. The management framework must also provide a way to incorporate the best available science into management decisions and to use management outcomes as opportunities to improve scientific understanding and provide feedback to the decision system. Figure 9.1 shows a model developed by Anorov (2004) based on the process-response model of Maltby et al. (1994) that forms a framework for the science that underlies an adaptive management system in the wetland context.

Similar Markov chains

enin et al. (2000) recently introduced the idea of similarity in the context of birth-death processes. This paper examines the extent to which their results can be extended to arbitrary Markov chains. It is proved that, under a variety of conditions, similar chains are strongly similar in a sense which is described, and it is shown that minimal chains are strongly similar if and only if the corresponding transition-rate matrices are strongly similar. A general framework is given for constructing families of strongly similar chains; it permits the construction of all such chains in the irreducible case.

Lexical decision in Parkinson's disease: A reply to Brown, McDonald, and Spicer (1999)

Recent semantic priming investigations in Parkinsons disease (PD) employed variants of Neelys (1977) lexical decision paradigm to dissociate the automatic and attentional aspects of semantic activation (McDonald, Brown, Gorell, 1996; Spicer, Brown, Gorell, 1994). In our earlier review, we claimed that the results of Spicer, McDonald and colleagues normal control participants violated the two-process model of information processing (Posner Snyder, 1975) upon which their experimental paradigm had been based (Arnott Chenery, 1999). We argued that, even at the shortest SOA employed, key design modifications to Neelys original experiments biased the tasks employed by Spicer et al. and McDonald et al. towards being assessments of attention-dependent processes. Accordingly, we contended that experimental procedures did not speak to issues of automaticity and, therefore, Spicer, McDonald and colleagues claims of robust automatic semantic activation in PD must be treated with caution.

Semantic priming in Alzheimer's dementia: Evidence for dissociation of automatic and attentional processes

The nature of the semantic memory deficit in dementia of the Alzheimer's type (DAT) was investigated in a semantic priming task which was designed to assess both automatic and attention-induced priming effects. Ten DAT patients and 10 age-matched control subjects completed a word naming semantic priming task in which both relatedness proportion (RP) and stimulus-onset asynchrony (SOA) were varied. A clear dissociation between automatic and attentional priming effects in both groups was demonstrated; however, the DAT subjects pattern of priming deviated significantly from that of the normal controls. The DAT patients failed to produce any priming under conditions which encouraged automatic semantic processing and produced facilitation only when the RP was high. In addition, the DAT group produced hyperpriming, with significantly larger facilitation effects than the control group. These results suggest an impairment of automatic spreading activation in DAT and have implications for theories of semantic memory impairment in DAT as well as models of normal priming. (C) 2001 Academic Press.

Path integrals for continuous-time Markov chains

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

A Feedback Learning and Mental Models Perspective on Strategic Decision Making

This study aims to be a contribution to a theoretical model that explains the effectiveness of the learning and decision-making processes by means of a feedback and mental models perspective. With appropriate mental models, managers should be able to improve their capacity to deal with dynamically complex contexts, in order to achieve long-term success. We present a set of hypotheses about the influence of feedback information and systems thinking facilitation on mental models and management performance. We explore, under controlled conditions, the role of mental models in terms of structure and behaviour. A test based on a simulation experiment with a system dynamics model was performed. Three out of the four hypotheses were confirmed. Causal diagramming positively influences mental model structure similarity, mental model structure similarity positively influences mental model behaviour similarity, and mental model behaviour similarity positively influences the quality of the decision.

A Feedback Learning and Mental Models Perspective on Strategic Decision Making

This study aims to be a contribution to a theoretical model that explains the effectiveness of the learning and decision-making processes by means of a feedback and mental models perspective. With appropriate mental models, managers should be able to improve their capacity to deal with dynamically complex contexts, in order to achieve long-term success. We present a set of hypotheses about the influence of feedback information and systems thinking facilitation on mental models and management performance. We explore, under controlled conditions, the role of mental models in terms of structure and behaviour. A test based on a simulation experiment with a system dynamics model was performed. Three out of the four hypotheses were confirmed. Causal diagramming positively influences mental model structure similarity, mental model structure similarity positively influences mental model behaviour similarity, and mental model behaviour similarity positively influences the quality of the decision

VirtualECare: group decision supported by idea generation and argumentation

In the last years there has been a considerable increase in the number of people in need of intensive care, especially among the elderly, a phenomenon that is related to population ageing (Brown 2003). However, this is not exclusive of the elderly, as diseases as obesity, diabetes, and blood pressure have been increasing among young adults (Ford and Capewell 2007). As a new fact, it has to be dealt with by the healthcare sector, and particularly by the public one. Thus, the importance of finding new and cost effective ways for healthcare delivery are of particular importance, especially when the patients are not to be detached from their environments (WHO 2004). Following this line of thinking, a VirtualECare Multiagent System is presented in section 2, being our efforts centered on its Group Decision modules (Costa, Neves et al. 2007) (Camarinha-Matos and Afsarmanesh 2001).On the other hand, there has been a growing interest in combining the technological advances in the information society - computing, telecommunications and knowledge – in order to create new methodologies for problem solving, namely those that convey on Group Decision Support Systems (GDSS), based on agent perception. Indeed, the new economy, along with increased competition in today’s complex business environments, takes the companies to seek complementarities, in order to increase competitiveness and reduce risks. Under these scenarios, planning takes a major role in a company life cycle. However, effective planning depends on the generation and analysis of ideas (innovative or not) and, as a result, the idea generation and management processes are crucial. Our objective is to apply the GDSS referred to above to a new area. We believe that the use of GDSS in the healthcare arena will allow professionals to achieve better results in the analysis of one’s Electronically Clinical Profile (ECP). This attainment is vital, regarding the incoming to the market of new drugs and medical practices, which compete in the use of limited resources.

Context-aware emotion-based model for group decision making

Involving groups in important management processes such as decision making has several advantages. By discussing and combining ideas, counter ideas, critical opinions, identified constraints, and alternatives, a group of individuals can test potentially better solutions, sometimes in the form of new products, services, and plans. In the past few decades, operations research, AI, and computer science have had tremendous success creating software systems that can achieve optimal solutions, even for complex problems. The only drawback is that people don’t always agree with these solutions. Sometimes this dissatisfaction is due to an incorrect parameterization of the problem. Nevertheless, the reasons people don’t like a solution might not be quantifiable, because those reasons are often based on aspects such as emotion, mood, and personality. At the same time, monolithic individual decisionsupport systems centered on optimizing solutions are being replaced by collaborative systems and group decision-support systems (GDSSs) that focus more on establishing connections between people in organizations. These systems follow a kind of social paradigm. Combining both optimization- and socialcentered approaches is a topic of current research. However, even if such a hybrid approach can be developed, it will still miss an essential point: the emotional nature of group participants in decision-making tasks. We’ve developed a context-aware emotion based model to design intelligent agents for group decision-making processes. To evaluate this model, we’ve incorporated it in an agent-based simulator called ABS4GD (Agent-Based Simulation for Group Decision), which we developed. This multiagent simulator considers emotion- and argument based factors while supporting group decision-making processes. Experiments show that agents endowed with emotional awareness achieve agreements more quickly than those without such awareness. Hence, participant agents that integrate emotional factors in their judgments can be more successful because, in exchanging arguments with other agents, they consider the emotional nature of group decision making.