Generic Modal Cut Elimination Applied to Conditional Logics

We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies also to a wide variety of logics outside the realm of normal modal logic. We give extensive example instantiations of our framework to various conditional logics. For these, we obtain fully internalised calculi which are substantially simpler than those known in the literature, along with leaner proofs of cut elimination and complexity. In one case, conditional logic with modus ponens and conditional excluded middle, cut elimination and complexity were explicitly stated as open in the literature

On the Complexity of Query Result Diversification

Query result diversification is a bi-criteria optimization problem for ranking query results. Given a database D, a query Q and a positive integer k, it is to find a set of k tuples from Q(D) such that the tuples are as relevant as possible to the query, and at the same time, as diverse as possible to each other. Subsets of Q(D) are ranked by an objective function defined in terms of relevance and diversity. Query result diversification has found a variety of applications in databases, information retrieval and operations research. This paper studies the complexity of result diversification for relational queries. We identify three problems in connection with query result diversification, to determine whether there exists a set of k tuples that is ranked above a bound with respect to relevance and diversity, to assess the rank of a given k-element set, and to count how many k-element sets are ranked above a given bound. We study these problems for a variety of query languages and for three objective functions. We establish the upper and lower bounds of these problems, all matching, for both combined complexity and data complexity. We also investigate several special settings of these problems, identifying tractable cases. 1

Intuitionistic implication makes model checking hard

We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal propositional logic FPL, and Jankov's logic KC. We show that the model checking problem is P-complete for the implicational fragments of all these intuitionistic logics. For BPL and FPL we reach P-hardness even on the implicational fragment with only one variable. The same hardness results are obtained for the strictly implicational fragments of their modal companions. Moreover, we investigate whether formulas with less variables and additional connectives make model checking easier. Whereas for variable free formulas outside of the implicational fragment, FPL model checking is shown to be in LOGCFL, the problem remains P-complete for BPL.Comment: 29 pages, 10 figure

The Computational Complexity of Generating Random Fractals

In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several widely used algorithms for equilibrating the Ising model are shown to be highly sequential; it is unlikely they can be simulated efficiently in parallel. This is in contrast to Mandelbrot percolation that can be simulated in constant parallel time. Our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have been recently studied using complexity theory. In addition, the results may serve as a guide to simulation physics.Comment: 28 pages, LATEX, 8 Postscript figures available from [email protected]

Flow Phase Diagram for the Helium Superfluids

The flow phase diagram for He II and $^3$He-B is established and discussed based on available experimental data and the theory of Volovik [JETP Letters {\bf{78}} (2003) 553]. The effective temperature - dependent but scale - independent Reynolds number $Re_{eff}=1/q=(1+\alpha')/\alpha$, where $\alpha$ and $\alpha'$ are the mutual friction parameters and the superfluid Reynolds number characterizing the circulation of the superfluid component in units of the circulation quantum are used as the dynamic parameters. In particular, the flow diagram allows identification of experimentally observed turbulent states I and II in counterflowing He II with the turbulent regimes suggested by Volovik.Comment: 2 figure

Value of systolic pulmonary arterial pressure as a prognostic factor of death in the systemic sclerosis EUSTAR population.

The aim of this study was to assess the prognostic value of systolic pulmonary artery pressure (sPAP) estimated by echocardiography in the multinational European League Against Rheumatism Scleroderma Trial and Research (EUSTAR) cohort.Data for patients with echocardiography documented between 1 January 2005 and 31 December 2011 were extracted from the EUSTAR database. Stepwise forward multivariable statistical Cox pulmonary hypertension analysis was used to examine the independent effect on survival of selected variables.Based on our selection criteria, 1476 patients were included in the analysis; 87\% of patients were female, with a mean age of 56.3 years (s.d. 13.5) and 31\% had diffuse SSc. The mean duration of follow-up was 2.0 years (s.d. 1.2, median 1.9). Taking index sPAP of 50 mmHg. In a multivariable Cox model, sPAP and the diffusing capacity for carbon monoxide (DLCO) were independently associated with the risk of death [HR 1.833 (95\% CI 1.035, 3.247) and HR 0.973 (95\% CI 0.955, 0.991), respectively]. sPAP was an independent risk factor for death with a HR of 3.02 (95\% CI 1.91, 4.78) for sPAP ≥36 mmHg.An estimated sPAP >36 mmHg at baseline echocardiography was significantly and independently associated with reduced survival, regardless of the presence of pulmonary hypertension based on right heart catheterization

Separation Logic with One Quantified Variable

International audienceWe investigate first-order separation logic with one record field restricted to a unique quantified variable (1SL1). Undecidability is known when the number of quantified variables is unbounded and the satisfiability problem is PSPACE-complete for the propositional fragment. We show that the satisfiability problem for 1SL1 is PSPACE-complete and we characterize its expressive power by showing that every formula is equivalent to a Boolean combination of atomic properties. This contributes to our understanding of fragments of first-order separation logic that can specify properties about the memory heap of programs with singly-linked lists. When the number of program variables is fixed, the complexity drops to polynomial time. All the fragments we consider contain the magic wand operator and first-order quantification over a single variable

Social and Financial Outcomes of Living Liver Donation: A Prospective Investigation Within the Adult‐to‐Adult Living Donor Liver Transplantation Cohort Study 2 (A2ALL‐2)

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136356/1/ajt14055_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136356/2/ajt14055.pd

The Complexity of Computing Minimal Unidirectional Covering Sets

Given a binary dominance relation on a set of alternatives, a common thread in the social sciences is to identify subsets of alternatives that satisfy certain notions of stability. Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory. Brandt and Fischer [BF08] proved that it is NP-hard to decide whether an alternative is contained in some inclusion-minimal upward or downward covering set. For both problems, we raise this lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and provide a Sigma_{2}^{p} upper bound. Relatedly, we show that a variety of other natural problems regarding minimal or minimum-size covering sets are hard or complete for either of NP, coNP, and Theta_{2}^{p}. An important consequence of our results is that neither minimal upward nor minimal downward covering sets (even when guaranteed to exist) can be computed in polynomial time unless P=NP. This sharply contrasts with Brandt and Fischer's result that minimal bidirectional covering sets (i.e., sets that are both minimal upward and minimal downward covering sets) are polynomial-time computable.Comment: 27 pages, 7 figure

Development and validation of a patient-reported outcome measure for systemic sclerosis: the EULAR Systemic Sclerosis Impact of Disease (ScleroID) questionnaire

OBJECTIVES: Patient-reported outcome measures (PROMs) are important for clinical practice and research. Given the high unmet need, our aim was to develop a comprehensive PROM for systemic sclerosis (SSc), jointly with patient experts. METHODS: This European Alliance of Associations for Rheumatology (EULAR)-endorsed project involved 11 European SSc centres. Relevant health dimensions were chosen and prioritised by patients. The resulting Systemic Sclerosis Impact of Disease (ScleroID) questionnaire was subsequently weighted and validated by Outcome Measures in Rheumatology criteria in an observational cohort study, cross-sectionally and longitudinally. As comparators, SSc-Health Assessment Questionnaire (HAQ), EuroQol Five Dimensional (EQ-5D), Short Form-36 (SF-36) were included. RESULTS: Initially, 17 health dimensions were selected and prioritised. The top 10 health dimensions were selected for the ScleroID questionnaire. Importantly, Raynaud's phenomenon, impaired hand function, pain and fatigue had the highest patient-reported disease impact. The validation cohort study included 472 patients with a baseline visit, from which 109 had a test-retest reliability visit and 113 had a follow-up visit (85% female, 38% diffuse SSc, mean age 58 years, mean disease duration 9 years). The total ScleroID score showed strong Pearson correlation coefficients with comparators (SSc-HAQ, 0.73; Patient's global assessment, Visual Analogue Scale 0.77; HAQ-Disability Index, 0.62; SF-36 physical score, -0.62; each p<0.001). The internal consistency was strong: Cronbach's alpha was 0.87, similar to SSc-HAQ (0.88) and higher than EQ-5D (0.77). The ScleroID had excellent reliability and good sensitivity to change, superior to all comparators (intraclass correlation coefficient 0.84; standardised response mean 0.57). CONCLUSIONS: We have developed and validated the EULAR ScleroID, which is a novel, brief, disease-specific, patient-derived, disease impact PROM, suitable for research and clinical use in SSc