The categorical limit of a sequence of dynamical systems

Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns out to be subject to ambiguity. Depending on the interpretation of the sequence, i.e. depending on how the behaviors of the systems in the sequence are related, it may vary what the limit should be. Topologies, and in particular metrics, define limits uniquely, if they exist. Thus they select one interpretation implicitly and leave no room for other interpretations. In this paper, we define limits using category theory, and use the mentioned relations between system behaviors explicitly. This resolves the problem of ambiguity in a more controlled way. We introduce a category of prefix orders on executions and partial history preserving maps between them to describe both discrete and continuous branching time dynamics. We prove that in this category all projective limits exist, and illustrate how ambiguity in the definition of limits is resolved using an example. Moreover, we show how various problems with known topological approaches are now resolved, and how the construction of projective limits enables us to approximate continuous time dynamics as a sequence of discrete time systems.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690

Psychological treatment of depression: A meta-analytic database of randomized studies

Abstract Background A large number of randomized controlled studies have clearly demonstrated that psychological interventions are effective in the treatment of depression. The number of studies in this area is increasing rapidly. In this paper, we present a database of controlled and comparative outcome studies on psychological treatments of depression, based on a series of meta-analyses published by our group. The database can be accessed freely through the Internet. Description We conducted a comprehensive literature search of the major bibliographical databases (Pubmed; Psycinfo; Embase; Cochrane Central Register of Controlled Trials) and we examined the references of 22 earlier meta-analyses of psychological treatment of depression. We included randomized studies in which the effects of a psychological therapy on adults with depression were compared to a control condition, another psychological intervention, or a combined treatment (psychological plus pharmacological). We conducted nine meta-analyses of subgroups of studies taken from this dataset. The 149 studies included in these 9 meta-analyses are included in the current database. In the 149 included studies, a total of 11,369 patients participated. In the database, we present selected characteristics of each study, including characteristics of the patients (the study population, recruitment method, definition of depression); characteristics of the experimental conditions and interventions (the experimental conditions, N per condition, format, number of sessions); and study characteristics (measurement times, measures used, attrition, type of analysis and country). Conclusion The data on the 149 included studies are presented in order to give other researchers access to the studies we collected, and to give background information about the meta-analyses we have published using this dataset. The number of studies examining the effects of psychological treatments of depression has increased considerably in the past decades, and this will continue in the future. The database we have presented in this paper can help to integrate the results of these studies in future meta-analyses and systematic reviews on psychological treatments for depression

Internet-Based and other computerized psychological treatments for adults depression: A meta-analysis

Computerized and, more recently, Internet-based treatments for depression have been developed and tested in controlled trials. The aim of this meta-analysis was to summarize the effects of these treatments and investigate characteristics of studies that may be related to the effects. In particular, the authors were interested in the role of personal support when completing a computerized treatment. Following a literature search and coding, the authors included 12 studies, with a total of 2446 participants. Ten of the 12 studies were delivered via the Internet. The mean effect size of the 15 comparisons between Internet-based and other computerized psychological treatments vs. control groups at posttest was d = 0.41 (95% confidence interval [CI]: 0.29-0.54). However, this estimate was moderated by a significant difference between supported (d = 0.61; 95% CI: 0.45-0.77) and unsupported (d = 0.25; 95% CI: 0.14-0.35) treatments. The authors conclude that although more studies are needed, Internet and other computerized treatments hold promise as potentially evidence-based treatments of depression. Keywords: computerized treatment; depression; Internet-based; role of suppor

Psychological treatment of late-life depression:a meta-analysis of randomized controlled trials

SUMMARY Background Older meta-analyses of the effects of psychological treatments for depression in older adults have found that these treatments have large effects. However, these earlier meta-analyses also included non-randomized studies, and did not include newer high-quality randomized controlled trials. Methods We conducted a meta-analysis of randomized studies on psychological treatments for depression in older adults. Results Twenty-five studies were included, of which 17 compared a psychological intervention to a control condition (mainly waiting list and care-as-usual control groups). The quality of the included studies varied. Psychological treatments have moderate to large effects on depression in older adults (standardized mean effect size d¼0.72). Heterogeneity was very low. No differences were found between individual, group or bibliotherapy format, or between cognitive behavioral therapy and other types of psychological treatment. The effects were comparable in studies where depression was defined according to diagnostic criteria, and those in which depression was measured with self-rating questionnaires. Conclusion Although the quality of many studies was not optimal, the results of this meta-analysis support the results of earlier meta-analyses, which also included non-randomized studies. Psychological treatments are effective in the treatment of depression in older adults

Strong, Weak and Branching Bisimulation for Transition Systems and Markov Reward Chains: A Unifying Matrix Approach

We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic apparatus. Next we consider Markov reward chains which are standardly presented in real matrix theory. By interpreting the obtained matrix conditions for bisimulations in this setting, we automatically obtain the definitions of strong, weak, and branching bisimulation for Markov reward chains. The obtained strong and weak bisimulations are shown to coincide with some existing notions, while the obtained branching bisimulation is new, but its usefulness is questionable

Are individual and group treatments equally effective in the treatment of depression in adults?

0.01). At follow-up no significant differences were found. Conclusions: Although individual therapy seems to be somewhat more effective than group therapy at the short term, it is not clear whether this is relevant from a clinical point of view. Because of the small number of studies and the limited quality, more research is needed to examine whether the difference between individual and group treatment is clinically relevant