Limit Synchronization in Markov Decision Processes

Markov decision processes (MDP) are finite-state systems with both strategic and probabilistic choices. After fixing a strategy, an MDP produces a sequence of probability distributions over states. The sequence is eventually synchronizing if the probability mass accumulates in a single state, possibly in the limit. Precisely, for 0 <= p <= 1 the sequence is p-synchronizing if a probability distribution in the sequence assigns probability at least p to some state, and we distinguish three synchronization modes: (i) sure winning if there exists a strategy that produces a 1-synchronizing sequence; (ii) almost-sure winning if there exists a strategy that produces a sequence that is, for all epsilon > 0, a (1-epsilon)-synchronizing sequence; (iii) limit-sure winning if for all epsilon > 0, there exists a strategy that produces a (1-epsilon)-synchronizing sequence. We consider the problem of deciding whether an MDP is sure, almost-sure, limit-sure winning, and we establish the decidability and optimal complexity for all modes, as well as the memory requirements for winning strategies. Our main contributions are as follows: (a) for each winning modes we present characterizations that give a PSPACE complexity for the decision problems, and we establish matching PSPACE lower bounds; (b) we show that for sure winning strategies, exponential memory is sufficient and may be necessary, and that in general infinite memory is necessary for almost-sure winning, and unbounded memory is necessary for limit-sure winning; (c) along with our results, we establish new complexity results for alternating finite automata over a one-letter alphabet

An Axiomatic Approach to Liveness for Differential Equations

This paper presents an approach for deductive liveness verification for ordinary differential equations (ODEs) with differential dynamic logic. Numerous subtleties complicate the generalization of well-known discrete liveness verification techniques, such as loop variants, to the continuous setting. For example, ODE solutions may blow up in finite time or their progress towards the goal may converge to zero. Our approach handles these subtleties by successively refining ODE liveness properties using ODE invariance properties which have a well-understood deductive proof theory. This approach is widely applicable: we survey several liveness arguments in the literature and derive them all as special instances of our axiomatic refinement approach. We also correct several soundness errors in the surveyed arguments, which further highlights the subtlety of ODE liveness reasoning and the utility of our deductive approach. The library of common refinement steps identified through our approach enables both the sound development and justification of new ODE liveness proof rules from our axioms.Comment: FM 2019: 23rd International Symposium on Formal Methods, Porto, Portugal, October 9-11, 201

Emergence of four dimensional quantum mechanics from a deterministic theory in 11 dimensions

We develop a deterministic theory which accounts for the coupling of a high dimensional continuum of environmental excitations (called gravonons) to massive particle in a very localized and very weak fashion. For the model presented Schrodinger's equation can be solved practically exactly in 11 spacetime dimensions and the result demonstrates that as a function of time an incoming matter wave incident on a screen extinguishes, except at a single interaction center on the detection screen. This transition is reminiscent of the wave - particle duality arising from the "collapse" (also called "process one") postulated in the Copenhagen-von Neumann interpretation. In our theory it is replaced by a sticking process of the particle from the vacuum to the surface of the detection screen. This situation was verified in experiments by using massive molecules. In our theory this "wave-particle transition" is connected to the different dimensionalities of the space for particle motion and the gravonon dynamics, the latter propagating in the hidden dimensions of 11 dimensional spacetime. The fact that the particle is detected at apparently statistically determined points on the screen is traced back to the weakness and locality of the interaction with the gravonons which allows coupling on the energy shell alone. Although the theory exhibits a completely deterministic "chooser" mechanism for single site sticking, an apparent statistical character results, as it is found in the experiments, due to small heterogeneities in the atomic and gravonon structures

Divergence in Dialogue

Copyright: 2014 Healey et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.This work was supported by the Economic and Social Research Council (ESRC; http://www.esrc.ac.uk/) through the DynDial project (Dynamics of Conversational Dialogue, RES-062-23-0962) and the Engineering and Physical Sciences Research Council (EPSRC; http://www.epsrc.ac.uk/) through the RISER project (Robust Incremental Semantic Resources for Dialogue, EP/J010383/1). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Probabilistic Bisimulation: Naturally on Distributions

In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a long-standing open problem concerning the representation of memoryless continuous time by memory-full continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems

Predictors of linkage to care following community-based HIV counseling and testing in rural Kenya

Despite innovations in HIV counseling and testing (HCT), important gaps remain in understanding linkage to care. We followed a cohort diagnosed with HIV through a community-based HCT campaign that trained persons living with HIV/AIDS (PLHA) as navigators. Individual, interpersonal, and institutional predictors of linkage were assessed using survival analysis of self-reported time to enrollment. Of 483 persons consenting to follow-up, 305 (63.2%) enrolled in HIV care within 3 months. Proportions linking to care were similar across sexes, barring a sub-sample of men aged 18–25 years who were highly unlikely to enroll. Men were more likely to enroll if they had disclosed to their spouse, and women if they had disclosed to family. Women who anticipated violence or relationship breakup were less likely to link to care. Enrolment rates were significantly higher among participants receiving a PLHA visit, suggesting that a navigator approach may improve linkage from community-based HCT campaigns.Vestergaard Frandse

Behavioral Priming: It's All in the Mind, but Whose Mind?

The perspective that behavior is often driven by unconscious determinants has become widespread in social psychology. Bargh, Chen, and Burrows' (1996) famous study, in which participants unwittingly exposed to the stereotype of age walked slower when exiting the laboratory, was instrumental in defining this perspective. Here, we present two experiments aimed at replicating the original study. Despite the use of automated timing methods and a larger sample, our first experiment failed to show priming. Our second experiment was aimed at manipulating the beliefs of the experimenters: Half were led to think that participants would walk slower when primed congruently, and the other half was led to expect the opposite. Strikingly, we obtained a walking speed effect, but only when experimenters believed participants would indeed walk slower. This suggests that both priming and experimenters' expectations are instrumental in explaining the walking speed effect. Further, debriefing was suggestive of awareness of the primes. We conclude that unconscious behavioral priming is real, while real, involves mechanisms different from those typically assumed to cause the effect

Visual Recognition of Age Class and Preference for Infantile Features: Implications for Species-Specific vs Universal Cognitive Traits in Primates

Despite not knowing the exact age of individuals, humans can estimate their rough age using age-related physical features. Nonhuman primates show some age-related physical features; however, the cognitive traits underlying their recognition of age class have not been revealed. Here, we tested the ability of two species of Old World monkey, Japanese macaques (JM) and Campbell's monkeys (CM), to spontaneously discriminate age classes using visual paired comparison (VPC) tasks based on the two distinct categories of infant and adult images. First, VPCs were conducted in JM subjects using conspecific JM stimuli. When analyzing the side of the first look, JM subjects significantly looked more often at novel images. Based on analyses of total looking durations, JM subjects looked at a novel infant image longer than they looked at a familiar adult image, suggesting the ability to spontaneously discriminate between the two age classes and a preference for infant over adult images. Next, VPCs were tested in CM subjects using heterospecific JM stimuli. CM subjects showed no difference in the side of their first look, but looked at infant JM images longer than they looked at adult images; the fact that CMs were totally naïve to JMs suggested that the attractiveness of infant images transcends species differences. This is the first report of visual age class recognition and a preference for infant over adult images in nonhuman primates. Our results suggest not only species-specific processing for age class recognition but also the evolutionary origins of the instinctive human perception of baby cuteness schema, proposed by the ethologist Konrad Lorenz

Site Fidelity in Space Use by Spider Monkeys (Ateles geoffroyi) in the Yucatan Peninsula, Mexico

Animal home ranges may vary little in their size and location in the short term but nevertheless show more variability in the long term. We evaluated the degree of site fidelity of two groups of spider monkeys (Ateles geoffroyi) over a 10- and 13-year period, respectively, in the northeastern Yucatan peninsula, Mexico. We used the Local Convex Hull method to estimate yearly home ranges and core areas (defined as the 60% probability contour) for the two groups. Home ranges varied from 7.7 to 49.6 ha and core areas varied from 3.1 to 9.2 ha. We evaluated the degree of site fidelity by quantifying the number of years in which different areas were used as either home ranges or core areas. Large tracts were used only as home ranges and only for a few years, whereas small areas were used as either core area or home range for the duration of the study. The sum of the yearly core areas coincided partially with the yearly home ranges, indicating that home ranges contain areas used intermittently. Home ranges, and especially core areas, contained a higher proportion of mature forest than the larger study site as a whole. Across years and only in one group, the size of core areas was positively correlated with the proportion of adult males in the group, while the size of home ranges was positively correlated with both the proportion of males and the number of tree species included in the diet. Our findings suggest that spider monkey home ranges are the result of a combination of long-term site fidelity and year-to-year use variation to enable exploration of new resources