Discriminating groups: a comprehensive overview

Discriminating groups were introduced by G.Baumslag, A.Myasnikov and V.Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. However they have taken on a life of their own and have been an object of a considerable amount of study. In this paper we survey the large array results concerning the class of discriminating groups that have been developed over the past decade.

The equation xpyq=zr and groups that act freely on Λ-trees

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Immunogold Detection of L-glutamate and D-serine in Small Synaptic-Like Microvesicles in Adult Hippocampal Astrocytes.

Glutamate and the N-methyl-D-aspartate receptor ligand D-serine are putative gliotransmitters. Here, we show by immunogold cytochemistry of the adult hippocampus that glutamate and D-serine accumulate in synaptic-like microvesicles (SLMVs) in the perisynaptic processes of astrocytes. The estimated concentration of fixed glutamate in the astrocytic SLMVs is comparable to that in synaptic vesicles of excitatory nerve terminals (∼45 and ∼55 mM, respectively), whereas the D-serine level is about 6 mM. The vesicles are organized in small spaced clusters located near the astrocytic plasma membrane. Endoplasmic reticulum is regularly found in close vicinity to SLMVs, suggesting that astrocytes contain functional nanodomains, where a local Ca(2+) increase can trigger release of glutamate and/or D-serine.

Renal transplantation following aorto-iliac reconstruction is a safe a strategy

Introduction: Renal transplantation is considered the treatment of choice for end-stage renal disease. However, the association of occlusive aorto-iliac disease and chronic renal failure is frequent and aorto-iliac reconstruction may be necessary prior to renal transplantation. This retrospective study reviews the results of this operative strategy.Material and Methods: Between January 2001 and June 2010, 309 patients underwent renal transplantation at our institution and 8 patients had prior aorto-iliac reconstruction using prosthetic material. There were 6 men and 2 women with a median age of 62 years (range 51-70). Five aorto-bifemoral and 2 aorto-bi-iliac bypasses were performed for stage II (n=5), stage IV (n=1) and aortic aneurysm (n=1). In one patient, iliac kissing stents and an ilio-femoral bypass were implanted. 4 cadaveric and 4 living donor renal transplantations were performed with an interval of 2 months to 10 years after revascularization.The results were analysed with respect of graft and patients survival. Differences between groups were tested by the log rank method.Results: No complications and no death occurred in the post-operative period. All bypasses remained patent during follow-up. The median time of post transplantation follow-up was 46 months for all patients and 27 months for patients with prior revascularization. In the revascularized group and control group, the graft and patient survival at 1 year were respectively 100%/96%, 100%/99% and at 5 years 86%/86%, 86%/94%, without significant differences between both groups.Discussion: Our results suggest that renal transplantation following prior aorto-iliac revascularisation with prosthetic material is safe and effective. Patients with end-stage renal disease and concomitant aorto-iliac disease should therefore be considered for renal transplantation. However, caution in the interpretation of the results is indicated due to the small sample size of our study.

Subgroups of small index in Aut(Fn) and Kazhdan's property (T)

We give a series of interesting subgroups of finite index in Aut(Fn). One of them has index 42 in Aut(F3) and infinite abelianization. This implies that Aut(F3) does not have Kazhdan’s property (T) (see [3] and [6] for another proofs). We proved also that every subgroup of finite index in Aut(Fn), n &= 3, which contains the subgroup of IA-automorphisms, has a finite abelianization.

Orbit decidability and the conjugacy problem for some extensions of groups

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Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Metric properties of the braided Thompson's groups

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Model structures on the category of small double categories

In this paper we obtain several model structures on DblCat, the category of small double categories. Our model structures have three sources. We first transfer across a categorification-nerve adjunction. Secondly, we view double categories as internal categories in Cat and take as our weak equivalences various internal equivalences defined via Grothendieck topologies. Thirdly, DblCat inherits a model structure as a category of algebras over a 2-monad. Some of these model structures coincide and the different points of view give us further results about cofibrant replacements and cofi brant objects. As part of this program we give explicit descriptions and discuss properties of free double categories, quotient double categories, colimits of double categories, and several nerves and categorifications.

On the intersection of free subgroups in free products of groups

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A classification, up to hyperbolicity, of groups given by 2 generators and one relator of length 8

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Volvulus de l'intestin grêle comme cause primaire d'abdomen aigu [Volvulus of the small intestine as a cause of primary acute abdomen].

As a cause of small intestine occlusion, volvulus is often a consequence of a band or adhesions. Except in infants, it is rarely the primary cause of symptomatology. Between January 1976 and December 1992, 13 patients (7 women and 6 men, mean age of 56.8 years) were admitted in our department for an acute abdomen due to a spontaneous primary volvulus of the small bowel. Clinical examination and laboratory tests did not help in preoperative diagnosis. All patients underwent an explorative laparotomy. Six patients had had prior abdominal surgery but none of them presented adhesion or band. In 8 patients (62%), detorsion was sufficient. Resection of a segment of small bowel was necessary in 4 patients. Gangrenous of the entire bowel was observed in one patient who rapidly died. Two patients presented minor complications. One patient with Down syndrome died of bronchoaspiration. One patient has been reoperated on one year later for recurrence of the volvulus, and underwent a Noble procedure. We conclude that volvulus of the small bowel is a rare cause of acute abdomen that must be remembered. Early surgery is mandatory to reduce the risk of gangrene, which is known to double the mortality. Laparoscopy will be helpful in early diagnosis and therapy.

Social polarization: introducing distances between and within groups

The measurement of social polarization has received little attention from the literature. The only social polarization index that has been used to measure religious or ethnic polarization (the RQ index) has several shortcomings that are critically discussed in the paper. In particular, that index is not taking into account the existing distance between and within different groups. A couple of axiomatically characterized social polarization indices that overcome these limitations are presented. In the empirical section we show that the rankings of countries according to the levels of polarization change to a great extent when we replace the RQ index by the indices presented in this paper.