The complexity of detecting taut angle structures on triangulations

There are many fundamental algorithmic problems on triangulated 3-manifolds whose complexities are unknown. Here we study the problem of finding a taut angle structure on a 3-manifold triangulation, whose existence has implications for both the geometry and combinatorics of the triangulation. We prove that detecting taut angle structures is NP-complete, but also fixed-parameter tractable in the treewidth of the face pairing graph of the triangulation. These results have deeper implications: the core techniques can serve as a launching point for approaching decision problems such as unknot recognition and prime decomposition of 3-manifolds.Comment: 22 pages, 10 figures, 3 tables; v2: minor updates. To appear in SODA 2013: Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithm

Separation index of graphs and stacked 2-spheres

In 1987, Kalai proved that stacked spheres of dimension $d\geq 3$ are characterised by the fact that they attain equality in Barnette's celebrated Lower Bound Theorem. This result does not extend to dimension $d=2$. In this article, we give a characterisation of stacked $2$-spheres using what we call the {\em separation index}. Namely, we show that the separation index of a triangulated $2$-sphere is maximal if and only if it is stacked. In addition, we prove that, amongst all $n$-vertex triangulated $2$-spheres, the separation index is {\em minimised} by some $n$-vertex flag sphere for $n\geq 6$. Furthermore, we apply this characterisation of stacked $2$-spheres to settle the outstanding $3$-dimensional case of the Lutz-Sulanke-Swartz conjecture that "tight-neighbourly triangulated manifolds are tight". For dimension $d\geq 4$, the conjecture has already been proved by Effenberger following a result of Novik and Swartz.Comment: Some typos corrected, to appear in "Journal of Combinatorial Theory A

Functional MRI in Patients with Band Heterotopia

Functional activation associated with a motor task (fist movements) was studied in three patients with band heterotopias by fMRI. In two patients, additional visual fMRI studies were performed using a flickering checkerboard stimulus. In all patients activation of the outer cortex and of the inner neuronal band could be found during performance of the motor task. Visual stimulation elicited a normal activation pattern without activation of the ectopic neuronal layer in one patient; in another patient activation extended toward the ventricular wall, i.e., along the route of embryonic neuronal migration. The potential participation of ectopic neuronal tissue in physiologic cerebral functions is of clinical impact in patients with neuronal heterotopias suffering from medically intractable seizures prior to epilepsy surgery

Combinatorial 3-manifolds with transitive cyclic symmetry

In this article we give combinatorial criteria to decide whether a transitive cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes, together with an explicit construction in the case that such a family exists. In addition, we substantially extend the classification of combinatorial 3-manifolds with transitive cyclic symmetry up to 22 vertices. Finally, a combination of these results is used to describe new infinite families of transitive cyclic combinatorial manifolds and in particular a family of neighborly combinatorial lens spaces of infinitely many distinct topological types.Comment: 24 pages, 5 figures. Journal-ref: Discrete and Computational Geometry, 51(2):394-426, 201

Cerebrospinal fluid findings in adults with acute Lyme neuroborreliosis

Presence of BB-specific antibodies in the cerebrospinal fluid (CSF) with evidence of their intrathecal production in conjunction with the white cell count in the CSF and typical clinical symptoms is the traditional diagnostic gold standard of Lyme neuroborreliosis (LNB). Few data are available on the CSF lactate concentration in European adults with the diagnosis of acute LNB. The objective of the study was to investigate the CSF changes during acute LNB. Routine CSF parameters [leukocyte count, protein, lactate and albumin concentrations, CSF/serum quotients of albumin (QAlb), IgG, IgA and IgM, and oligoclonal IgG bands] and the Borrelia burgdorferi (BB)-specific antibody index were retrospectively studied in relation to the clinical presentation in patients diagnosed with acute LNB. A total of 118 patients with LNB were categorized into the following groups according to their symptoms at presentation; group 1: polyradiculoneuritis (Bannwarth’s syndrome), group 2: isolated facial palsy and group 3: predominantly meningitic course of the disease. In addition to the CSF of patients with acute LNB, CSF of 19 patients with viral meningitis (VM) and 3 with neurolues (NL) were analyzed. There were 97 patients classified with definite LNB, and 21 as probable LNB. Neck stiffness and fever were reported by 15.3% of patients. Most of these patients were younger than 50 years. Polyradiculoneuritis was frequently found in patients older than 50 years. Lymphopleocytosis was found in all patients. Only 5 patients had a CSF lactate ≥3.5 mmol/l, and the mean CSF lactate level was not elevated (2.1 ± 0.6 mmol/l). The patients with definite LNB had significantly higher lactate levels than patients with probable LNB. Elevated lactate levels were accompanied by fever and headache. In the Reiber nomograms, intrathecal immunoglobulin synthesis was found for IgM in 70.2% followed by IgG in 19.5%. Isoelectric focussing detected an intrathecal IgG synthesis in 83 patients (70.3%). Elevated BB AIs in the CSF were found in 97 patients (82.2%). Patients with VM showed lower CSF protein concentration and CSF/serum quotients of albumin than LNB patients. In acute LNB, all patients had elevated cerebrospinal fluid (CSF) leukocyte counts. In contrast to infections by other bacteria, CSF lactate was lower than 3.5 mmol/l in all but 5 patients. The CSF findings did not differ between polyradiculoneuritis, facial palsy, and meningitis. The CSF in LNB patients strongly differed from CSF in VM patients with respect to protein concentration and the CSF/serum albumin quotient

The role of pneumolysin in mediating lung damage in a lethal pneumococcal pneumonia murine model

BACKGROUND: Intranasal inoculation of Streptococcus pneumoniae D39 serotype 2 causes fatal pneumonia in mice. The cytotoxic and inflammatory properties of pneumolysin (PLY) have been implicated in the pathogenesis of pneumococcal pneumonia. METHODS: To examine the role of PLY in this experimental model we performed ELISA assays for PLY quantification. The distribution patterns of PLY and apoptosis were established by immunohistochemical detection of PLY, caspase-9 activity and TUNEL assay on tissue sections from mice lungs at various times, and the results were quantified with image analysis. Inflammatory and apoptotic cells were also quantified on lung tissue sections from antibody treated mice. RESULTS: In bronchoalveolar lavages (BAL), total PLY was found at sublytic concentrations which were located in alveolar macrophages and leukocytes. The bronchoalveolar epithelium was PLY-positive, while the vascular endothelium was not PLY reactive. The pattern and extension of cellular apoptosis was similar. Anti-PLY antibody treatment decreased the lung damage and the number of apoptotic and inflammatory cells in lung tissues. CONCLUSION: The data strongly suggest that in vivo lung injury could be due to the pro-apoptotic and pro-inflammatory activity of PLY, rather than its cytotoxic activity. PLY at sublytic concentrations induces lethal inflammation in lung tissues and is involved in host cell apoptosis, whose effects are important to pathogen survival