Verifying nondeterministic probabilistic channel systems against ω\omega-regular linear-time properties

Lossy channel systems (LCSs) are systems of finite state automata that communicate via unreliable unbounded fifo channels. In order to circumvent the undecidability of model checking for nondeterministic LCSs, probabilistic models have been introduced, where it can be decided whether a linear-time property holds almost surely. However, such fully probabilistic systems are not a faithful model of nondeterministic protocols. We study a hybrid model for LCSs where losses of messages are seen as faults occurring with some given probability, and where the internal behavior of the system remains nondeterministic. Thus the semantics is in terms of infinite-state Markov decision processes. The purpose of this article is to discuss the decidability of linear-time properties formalized by formulas of linear temporal logic (LTL). Our focus is on the qualitative setting where one asks, e.g., whether a LTL-formula holds almost surely or with zero probability (in case the formula describes the bad behaviors). Surprisingly, it turns out that -- in contrast to finite-state Markov decision processes -- the satisfaction relation for LTL formulas depends on the chosen type of schedulers that resolve the nondeterminism. While all variants of the qualitative LTL model checking problem for the full class of history-dependent schedulers are undecidable, the same questions for finite-memory scheduler can be solved algorithmically. However, the restriction to reachability properties and special kinds of recurrent reachability properties yields decidable verification problems for the full class of schedulers, which -- for this restricted class of properties -- are as powerful as finite-memory schedulers, or even a subclass of them.Comment: 39 page

Exploring compassion: a meta-analysis of the association between self-compassion and psychopathology

Compassion has emerged as an important construct in studies of mental health and psychological therapy. Although an increasing number of studies have explored relationships between compassion and different facets of psychopathology there has as yet been no systematic review or synthesis of the empirical literature. We conducted a systematic search of the literature on compassion and mental health. We identified 20 samples from 14 eligible studies. All studies used the Neff Self Compassion Scale (Neff 2003, a). We employed meta-analysis to explore associations between self-compassion and psychopathology using random effects analyses of Fisher's Z correcting for attenuation arising from scale reliability. We found a large effect size for the relationship between compassion and psychopathology of r= -0.54 (95%CI = -0.57 to -0.51; Z=-34.02; p<.0001). Heterogeneity was significant in the analysis. There was no evidence of significant publication bias. Compassion is an important explanatory variable in understanding mental health and resilience. Future work is needed to develop the evidence base for compassion in psychopathology, and explore correlates of compassion and psychopathology

A robust and efficient implementation of LOBPCG

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely used to compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from numerical instability if it is not implemented with care. This is especially problematic when the number of eigenpairs to be computed is relatively large. In this paper we propose an improved basis selection strategy based on earlier work by Hetmaniuk and Lehoucq as well as a robust convergence criterion which is backward stable to enhance the robustness. We also suggest several algorithmic optimizations that improve performance of practical LOBPCG implementations. Numerical examples confirm that our approach consistently and significantly outperforms previous competing approaches in both stability and speed