177,627 research outputs found
Deficiency and the geometric invariants of a group (with an appendix by Pascal Schweitzer)
No full textAbstractIt is known that the geometric invariants of a group G (which contain information on finiteness properties of certain submonoids and normal subgroups of G) have a description in terms of the vanishing of group homology of G with Novikov-ring-coefficients [see J.-C. Sikorav, Homologie de Novikov associée à une classe de cohomologie réelle de degré un, Thèse Orsay, 1987; R. Bieri, The geometric invariants of a group, in: G.A. Niblo, M.A. Roller (Eds.), Geometric Group Theory, in: London Math. Soc. Lecture Notes Series, vol. 181, Cambridge University Press, Cambridge, 1993; R. Bieri, R. Strebel, Geometric invariants for discrete groups, manuscript-preprint of a monograph (in preparation)], and [R. Bieri, R. Geoghegan, Kernels of actions on non-positively curved spaces, in: P.H. Kropholler, G. Niblo, R. Stöhr (Eds.), Geometry and Cohomology in Group Theory, in: London Math. Soc. Lecture Notes Series, vol. 252, Cambridge University Press, Cambridge, 1998, pp. 24–38]. In a recent paper Kochloukova [D. Kochloukova, Some Novikov rings that are von Neumann finite and knot-like groups (submitted for publication)] uses this to prove a conjecture of E. Rapaport-Strasser on knot-like groups. We extend her approach to establish a rather general relationship between deficiency and the geometric invariants of a group
Analytic Transcendental Arguments
No full textBennett J. Analytische transzendentale Argumente. Stoecker R, tran.; In: Bieri P, ed. Analytische Philosophie der Erkenntnis. Philosophie. Vol 13. Frankfurt am Main: Athenäum-Verlag; 1987: 367-389
Is justified True Belief Knowledge?
No full textGettier EL. Ist gerechtfertigte, wahre Meinung Wissen? Stoecker R, tran.; In: Bieri P, ed. Analytische Philosophie der Erkenntnis . Philosophie. Vol 13. Frankfurt am Main: Athenäum; 1987: 91-93
Transcendental arguments, analytic and synthetic
No full textBittner R. Transcendental arguments, analytic and synthetic. In: Bieri P, Horstmann RP, Krüger L, eds. Transcendental arguments and science. Synthese library, 133. Dordrecht [u.a.]: Reidel; 1979: 27-35
The Bieri-Neumann-Strebel invariant for graph products of groups
No full textAbstractGiven a simplicial graph Δ with vertex set V and a function F that assigns to each vertex ν ϵ V a group Gν, the graph product G(Δ,F)is the quotient of the free product ∐gνϵV Gν modulo the normal subgroup generated by all commutators [Gν, Gw] with adjacent vertices ν, w ϵ V. Using K.S. Brown's approach to the Bieri-Neumann-Strebel invariant ∑1(−) via R-tree actions we give an explicit formula for ∑1(G(Δ, F))
Rapid magnetic resonance tissue relaxometry in the steady state
No full textLongitudinal (T1) and transverse (T2) relaxation are the most fundamental physical processes governing the signal intensity and the soft tissue contrast in magnetic resonance imaging (MRI). The T1 and T2 relaxation times are characteristic properties of living tissues and they were observed to be altered in the context of several diseases. Commonly, the MR images acquired in the clinical routine for medical assessment provide qualitative rather than quantitative information about the T1 and T2 relaxation times of the tissues of interest. The signal intensity generated by conventional qualitative MR imaging may be predominantly T1- or T2-weighted but is generally dependent on other tissue-specific parameters such as the proton density, the acquisition protocol, and the used MR hardware.
It is beneficial to directly measure the T1 and T2 relaxation times by acquiring typically two or more MR images of the same anatomical region but of different contrasts and to represent the results in quantitative maps. While these maps have the same structural appearance as the acquired base images, the individual pixel values have a physical meaning (i.e. the values of T1 and T2 in milliseconds) instead of displaying the signal intensity in arbitrary units. Quantitative maps of tissue-specific MR parameters are superior to conventional MR images since they are ideally independent of the MR protocol and hardware, and thus offer the possibility to directly compare the results from studies across multiple subjects, time-points, and imaging sites. Relaxation time measurements (also referred to as relaxometry) have demonstrated increased specificity and sensitivity to detect pathological tissue changes compared to conventional T1- and T2-weighted MR imaging.
In practice, T1 and T2 quantification techniques which are based on the acquisition of purely T1- and T2-weighted images without residual sensitivity on T2 and T1, respectively, require prohibitively long scan times making them not suited for the clinical practice. As a consequence, fast MR imaging using steady-state free precession (SSFP) sequences has come into the research focus of quantitative MRI. The images obtained from SSFP acquisitions show generally a mixed T1 and T2 contrast. Contemporary SSFP-based techniques for relaxation time measurements are impaired by a T2-related bias in the T1 quantification and by a T1-related bias in the T2 quantification. In addition, their speed comes at the expense of increased sensitivity to extrinsic instrumental factors (e.g. static or transmit field inhomogeneities).
In this thesis, new robust SSFP-based relaxometry methods are developed which offer clinically acceptable scan times and considerably reduce or even eliminate the T2- and T1-bias in the T1 and T2 calculation, respectively, of targets such as the human brain and the musculoskeletal system
Appropriate Similarity Measures for Author Cocitation Analysis
No full textWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
On subsets of S^n whose (n + 1)-point subsets are contained in open hemispheres
No full textWe investigate the nature of subsets of spheres which satisfy a tameness condition associated with the Bieri–Groves FPm-conjecture. We find that there is a natural polyhedrality in the case of n-tame subsets of an (n − 1)-sphere. In the case n = 3 we establish a strong polyhedrality condition for certain maximal open 3-tame sets. Many examples are included
"Closing the R&D Gap, Evaluating the Sources of R&D Spending"
No full textBoth spending and tax policies have been implemented in the United States with the goal of stimulating private sector research and development (R&D). Karier questions whether current R&D policy, especially the research and experimentation tax credit, can contribute to closing the gap between nondefense expenditures on R&D in the United States and such expenditures in other countries, such as Japan and Germany. He also explores possible changes to our current R&D policy to make it more effective.
Bieri-Eckmann criteria for profinite groups
No full textIn this paper we derive necessary and sufficient homological and cohomological conditions for profinite groups and modules to be of type FP n over a profinite ring R, analogous to the Bieri–Eckmann criteria for abstract groups. We use these to prove that the class of groups of type FP n is closed under extensions, quotients by subgroups of type FP n , proper amalgamated free products and proper HNN-extensions, for each n. We show, as a consequence of this, that elementary amenable profinite groups of finite rank are of type FP? over all profinite R. For any class C of finite groups closed under subgroups, quotients and extensions, we also construct pro-C groups of type FP n but not of type FP n+1 over Z ? for each n. Finally, we show that the natural analogue of the usual condition measuring when pro-p groups are of type FP n fails for general profinite groups, answering in the negative the profinite analogue of a question of Kropholler
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