42 research outputs found

    Equations over free inverse monoids with idempotent variables

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    We introduce the notion of idempotent variables for studying equations in inverse monoids. It is proved that it is decidable in singly exponential time (DEXPTIME) whether a system of equations in idempotent variables over a free inverse monoid has a solution. The result is proved by a direct reduction to solve language equations with one-sided concatenation and a known complexity result by Baader and Narendran: Unification of concept terms in description logics, 2001. We also show that the problem becomes DEXPTIME hard , as soon as the quotient group of the free inverse monoid has rank at least two. Decidability for systems of typed equations over a free inverse monoid with one irreducible variable and at least one unbalanced equation is proved with the same complexity for the upper bound. Our results improve known complexity bounds by Deis, Meakin, and Senizergues: Equations in free inverse monoids, 2007. Our results also apply to larger families of equations where no decidability has been previously known.Comment: 28 pages. The conference version of this paper appeared in the proceedings of 10th International Computer Science Symposium in Russia, CSR 2015, Listvyanka, Russia, July 13-17, 2015. Springer LNCS 9139, pp. 173-188 (2015

    Evaluating multilevel resilience of Russian urban economies 2010–2019

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    In this paper we examine the coevolution of individual cities and the city networks to which they belong, during an economic shock. We take an individual city and its city network to be the meso and macro levels, respectively, of a social-economic system. Focusing on the economic shocks felt by Russian cities in 2014 following the Ukrainian conflict, we demonstrate that the same shock had different effects at the meso level (a city’s employment structure) and macro level (a city’s interfirm linkages to other cities, both national and international). To explain our findings, we draw on panarchy theory to propose a multilevel perspective of resilience through the coevolution of adaptive cycles at the meso and macro levels of urban economies. To evaluate resilience at each level, we first operationalize the panarchy concept of connectedness using a previously developed metric called “tightness,” which quantifies the interdependencies among economic activities. We next operationalize the panarchy concept of potential by measuring a city’s degree of economic specialization. At the meso level, we find that larger cities suffered less employment loss than smaller cities during the shock and that by 2019 the structure of the meso level had largely returned to its 2010 structure. On the other hand, at the macro level, we found that the 2019 macro level structure changed considerably from 2010. Thus, we show that the meso level was disturbed but returned to a previous state (engineering resilience) while the macro level transitioned to a new state (ecological resilience). Results suggest that policy makers would benefit from distinguishing between the meso and macro levels, enabling the development of multilevel urban policies to address future shocks

    Comparison of the effectiveness of a tailored cognitive behavioural therapy with a supportive listening intervention for depression in those newly diagnosed with multiple sclerosis (the ACTION-MS trial): protocol of an assessor-blinded, active comparator, randomised controlled trial

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    BACKGROUND: Multiple sclerosis (MS) is an unpredictable, chronic neurological disease accompanied with high rates of depression and anxiety, particularly in the early stages of diagnosis. There is evidence to suggest that cognitive behavioural therapy (CBT) is effective for the treatment of depression amongst individuals with MS; however, there is a paucity of tailored CBT interventions designed to be offered in the newly diagnosed period. This trial is the first to assess the effectiveness and cost-effectiveness of a tailored CBT intervention compared to a supportive listening (SL) intervention amongst individuals with MS who are depressed. METHODS: ACTION-MS is a two-arm parallel group, assessor-blinded, active comparator, randomised controlled trial which will test whether a tailored CBT-based intervention compared to an SL intervention can reduce depression and related factors such as anxiety, fatigue, pain and sleep problems in those newly diagnosed with MS. Sixty participants who are within 5 years of having received a diagnosis of MS and scored within the mild to moderate range of depression on the Beck Depression Inventory (BDI-II) will be recruited from MS clinics located across three hospital sites in Melbourne, Australia. The primary outcome is depression severity using the BDI-II at post-assessment. Intervention satisfaction and acceptability will be assessed. A cost-effectiveness analysis will also be conducted. Data will be analysed on an intention-to-treat basis. DISCUSSION: There is a scarcity of psychological interventions for depression targeting the newly diagnosed period. However, interventions during this time point have the potential to have a major impact on the mental and physical wellbeing of those newly diagnosed with MS. The current trial will provide data on the effectiveness of a tailored CBT intervention for the treatment of depression in those newly diagnosed with MS. Findings will also provide effect size estimates that can be used to power a later-stage multi-centre trial of treatment efficacy, and will provide information on the mechanisms underlying any treatment effects and cost-effectiveness data for delivering this intervention in outpatient MS clinics. TRIAL REGISTRATION: ISRCTN trials registry, ISRCTN63987586. Current controlled trials. Retrospectively registered on 20 October 2017
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