Suppl. 1 -S16 with greater mortality after acute ischemic stroke (p=0.0002). Nonetheless, abnormal BPC was not associated with degree of impairment (p=0.3734), degree of disability (p=0.684), or length of stay (LOS) in the acute stroke care center (p=0.9541) after adjustment for major potential confounders. Conclusions: In patients with acute ischemic stroke, thrombocytopenia and thrombocytosis on the initial admission is associated with higher mortality after stroke. Abnormal BPC does not adversely affect the degree of impairment and disability, or LOS in the acute care center after acute ischemic stroke.
Background and Purpose Arteriopathy is the leading cause of childhood arterial ischemic stroke (AIS). Mechanisms are poorly understood but may include inherent abnormalities of arterial structure. Extracranial dissection is associated with connective tissue disorders in adult stroke. Focal cerebral arteriopathy (FCA) is a common syndrome where pathophysiology is unknown but may include intracranial dissection or transient cerebral arteriopathy (TCA). We aimed to quantify cerebral arterial tortuosity in childhood AIS, hypothesizing increased tortuosity in dissection. Methods Children (1month-18 years) with AIS were recruited within the Vascular Effects of Infection in Pediatric Stroke (VIPS) study with controls from the Calgary Pediatric Stroke Program. Objective, multi-investigator review defined diagnostic categories. A validated imaging software method calculated mean arterial tortuosity of the major cerebral arteries using 3D time-of-flight MR angiography source images. Tortuosity of unaffected vessels was compared between children with dissection, TCA, meningitis, moyamoya, cardioembolic strokes and controls (ANOVA, post-hoc Tukey). Trauma-related versus spontaneous dissection was compared (Student's t-test). Results One hundred fifteen children were studied (median 6.8 years, 43% female). Age and sex were similar across groups. Tortuosity means and variances were consistent with validation studies. Tortuosity in controls (1.346±0.074,n=15) was comparable to moyamoya (1.324±0.038, n=15, p=0.998), meningitis (1.348±0.052, n=11, p=0.989) and cardioembolic (1.379±0.056, n=27, p=0.190) cases. Tortuosity was higher in both extracranial dissection (1.404±0.084, n=22, p=0.021) and TCA (1.390±0.040, n=27, p=0.001) children. Tortuosity was not different between traumatic versus spontaneous dissection (p=0.70). Conclusion In children with dissection and TCA cerebral arteries demonstrate increased tortuosity. Quantified arterial tortuosity may represent a clinically relevant imaging biomarker of vascular biology in pediatric stroke.
Abstract. We show that the model checking problem for intuitionistic propositional logic with one variable is complete for logspace-uniform AC 1 . The basic tool we use is the connection between intuitionistic logic and Heyting algebras, investigating its complexity theoretical aspects. For superintuitionistic logics with one variable, we obtain NC 1 -completeness for the model checking problem.Key words. complexity, intuitionistic logic, model checking, AC 1 , Heyting algebra AMS subject classifications. 03B20, 06D20, 68Q171. Introduction. Intuitionistic logic (see e.g. [10,28]) is a part of classical logic that can be proven using constructive proofs-e.g. by proofs that do not use reductio ad absurdum. For example, the law of the excluded middle a ∨ ¬a and the weak law of the excluded middle ¬a ∨ ¬¬a do not have constructive proofs and are not valid in intuitionistic logic. Not surprisingly, constructivism has its costs. Whereas the validity problem is coNP-complete for classical propositional logic [6], for intuitionistic propositional logic it is PSPACE-complete [24,25]. The computational hardness of intuitionistic logic is already reached with the fragment that has only formulas with two variables: the validity problem for this fragment is already PSPACE-complete [22]. Recall that every fragment of classical propositional logic with a fixed number of variables has an NC 1 -complete validity problem (follows from [2]).The most common semantics for intuitionistic logic are Heyting semantics [11] and Kripke semantics [14, 13]-see also [23, Chap. 2]. The Heyting semantics bases on Heyting algebras, and Kripke semantics bases on directed graphs that can straightforwardly be adapted to model state-transition systems. Therefore it is used as the standard semantics for modal and hybrid logics. Model checking as we do with Kripke models is not suited for Heyting algebras. Therefore we also use Kripke semantics for intuitionistic logic. All our and all mentioned complexity results below refer to Kripke semantics.In this paper, we consider the complexity of intuitionistic propositional logic IPC with one variable. The model checking problem-i.e. the problem to determine whether a given formula is satisfied by a given intuitionistic Kripke model-for IPC is P-complete [17], even for the fragment with two variables only [18]. More surprisingly, for the fragment with one variable IPC 1 we show the model checking problem to be AC 1 -complete. To our knowledge, this is the first "natural" AC 1 -complete problem, whereas formerly known AC 1 -complete problems (see e.g. [1]) have some explicit logarithmic bound in the problem definition. A basic ingredient for the AC 1 -completeness lies in normal forms for models and formulas as found by Nishimura [20], that we
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