On the Efetov-Wegner terms by diagonalizing a Hermitian supermatrix

The diagonalization of Hermitian supermatrices is studied. Such a change of coordinates is inevitable to find certain structures in random matrix theory. However it still poses serious problems since up to now the calculation of all Rothstein contributions known as Efetov-Wegner terms in physics was quite cumbersome. We derive the supermatrix Bessel function with all Efetov-Wegner terms for an arbitrary rotation invariant probability density function. As applications we consider representations of generating functions for Hermitian random matrices with and without an external field as integrals over eigenvalues of Hermitian supermatrices. All results are obtained with all Efetov-Wegner terms which were unknown before in such an explicit and compact representation.Comment: 23 pages, PACS: 02.30.Cj, 02.30.Fn, 02.30.Px, 05.30.Ch, 05.30.-d, 05.45.M

Introductory clifford analysis

In this chapter an introduction is given to Clifford analysis and the underlying Clifford algebras. The functions under consideration are defined on Euclidean space and take values in the universal real or complex Clifford algebra, the structure and properties of which are also recalled in detail. The function theory is centered around the notion of a monogenic function, which is a null solution of a generalized Cauchy–Riemann operator, which is rotation invariant and factorizes the Laplace operator. In this way, Clifford analysis may be considered as both a generalization to higher dimension of the theory of holomorphic functions in the complex plane and a refinement of classical harmonic analysis. A notion of monogenicity may also be associated with the vectorial part of the Cauchy–Riemann operator, which is called the Dirac operator; some attention is paid to the intimate relation between both notions. Since a product of monogenic functions is, in general, no longer monogenic, it is crucial to possess some tools for generating monogenic functions: such tools are provided by Fueter’s theorem on one hand and the Cauchy–Kovalevskaya extension theorem on the other hand. A corner stone in this function theory is the Cauchy integral formula for representation of a monogenic function in the interior of its domain of monogenicity. Starting from this representation formula and related integral formulae, it is possible to consider integral transforms such as Cauchy, Hilbert, and Radon transforms, which are important both within the theoretical framework and in view of possible applications

Hilbert space for quantum mechanics on superspace

In superspace a realization of sl2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl2-representation is proven. Finally the Heisenberg uncertainty principle for the super Fourier transform is constructed

q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials

We define a q-deformation of the Dirac operator, inspired by the one dimensional q-derivative. This implies a q-deformation of the partial derivatives. By taking the square of this Dirac operator we find a q-deformation of the Laplace operator. This allows to construct q-deformed Schroedinger equations in higher dimensions. The equivalence of these Schroedinger equations with those defined on q-Euclidean space in quantum variables is shown. We also define the m-dimensional q-Clifford-Hermite polynomials and show their connection with the q-Laguerre polynomials. These polynomials are orthogonal with respect to an m-dimensional q-integration, which is related to integration on q-Euclidean space. The q-Laguerre polynomials are the eigenvectors of an su_q(1|1)-representation

MARIS: Scalable Online Scenario Development Tool for Rangeland Conservancy Managers Using High Spatial-Temporal Resolution Carrying Capacity Maps and Livestock Market Data

Although the management of livestock numbers within the bounds of carrying capacity of African rangelands is a way to manage risks, both scientists and practitioners, caution against a momentary and local use of carrying capacity as a management indicator. Carrying capacity should be seen in wider spatial and temporal/seasonal context as well as in a social and economic context. Given the large numbers of conservancies across Kenya, and its Maasai Mara region in particular, with many more landowner members, it is difficult for conservancies’ managers to contextualize phenomena such as carrying capacity and market price over space and time. We report the results of an investigation in the Maasai Mara rangelands, into functional characteristics a tool for spatial-temporal carrying capacity assessment and livestock markets prices monitoring should have to provide relevant management information to conservancy managers and conservancy members. A scalable web-application called the Mara Rangeland Information System, or MARIS, was developed, which assesses, at 23 meter resolution and 10 day historic or 1-day near-future intervals, both grassland dry matter production, and consumption by 19 wildlife and livestock species, as well as rangeland carrying capacity. MARIS facilitates managers to develop scenarios by varying input variables of either grass production or consumption, or by drawing different management blocks on a carrying capacity map assessing different management practices under scenarios of rainfall. Managers can relate the carrying capacity scenarios to offtake prices at different markets that MARIS monitors over time. After testing MARIS in 6 workshop iterations across the whole development process, Maasai Mara rangeland managers concluded that the prototype is ready for pilot use in management plan development

Randomized Delayed-Start Trial of Levodopa in Parkinson's Disease

BACKGROUND Levodopa is the main treatment for symptoms of Parkinson's disease. Determining whether levodopa also has a disease-modifying effect could provide guidance as to when in the course of the disease the treatment with this drug should be initiated. METHODS In a multicenter, double-blind, placebo-controlled, delayed-start trial, we randomly assigned patients with early Parkinson's disease to receive levodopa (100 mg three times per day) in combination with carbidopa (25 mg three times per day) for 80 weeks (early-start group) or placebo for 40 weeks followed by levodopa in combination with carbidopa for 40 weeks (delayed-start group). The primary outcome was the between-group difference in the mean change from baseline to week 80 in the total score on the Unified Parkinson's Disease Rating Scale (UPDRS; scores range from 0 to 176, with higher scores signifying more severe disease). Secondary analyses included the progression of symptoms, as measured by the UPDRS score, between weeks 4 and 40 and the noninferiority of early initiation of treatment to delayed initiation between weeks 44 and 80, with a noninferiority margin of 0.055 points per week. RESULTS A total of 445 patients were randomly assigned: 222 to the early-start group and 223 to the delayed-start group. The mean (+/- SD) UPDRS score at baseline was 28.1 +/- 11.4 points in the early-start group and 29.3 +/- 12.1 points in the delayed-start group. The change in UPDRS score from baseline to week 80 was -1.0 +/- 13.1 points and -2.0 +/- 13.0 points, respectively (difference, 1.0 point; 95% confidence interval [CI], -1.5 to 3.5; P = 0.44); this finding of no significant between-group difference at week 80 implies that levodopa had no disease-modifying effect. Between weeks 4 and 40, the rate of progression of symptoms, as measured in UPDRS points per week, was 0.04 +/- 0.23 in the early-start group and 0.06 +/- 0.34 in the delayed-start group (difference, -0.02; 95% CI, -0.07 to 0.03). The corresponding rates between weeks 44 and 80 were 0.10 +/- 0.25 and 0.03 +/- 0.28 (difference, 0.07; two-sided 90% CI, 0.03 to 0.10); the difference in the rate of progression between weeks 44 and 80 did not meet the criterion for noninferiority of early receipt of levodopa to delayed receipt. The rates of dyskinesia and levodopa-related fluctuations in motor response did not differ significantly between the two groups. CONCLUSIONS Among patients with early Parkinson's disease who were evaluated over the course of 80 weeks, treatment with levodopa in combination with carbidopa had no disease-modifying effect

Preparing children with a mock scanner training protocol results in high quality structural and functional MRI scans

We evaluated the use of a mock scanner training protocol as an alternative for sedation and for preparing young children for (functional) magnetic resonance imaging (MRI). Children with severe mental retardation or developmental disorders were excluded. A group of 90 children (median age 6.5 years, range 3.65–14.5 years) participated in this study. Children were referred to the actual MRI investigation only when they passed the training. We assessed the pass rate of the mock scanner training sessions. In addition, the quality of both structural and functional MRI (fMRI) scans was rated on a semi-quantitative scale. The overall pass rate of the mock scanner training sessions was 85/90. Structural scans of diagnostic quality were obtained in 81/90 children, and fMRI scans with sufficient quality for further analysis were obtained in 30/43 of the children. Even in children under 7 years of age, who are generally sedated, the success rate of structural scans with diagnostic quality was 53/60. FMRI scans with sufficient quality were obtained in 23/36 of the children in this younger age group. The association between age and proportion of children with fMRI scans of sufficient quality was not statistically significant. We conclude that a mock MRI scanner training protocol can be useful to prepare children for a diagnostic MRI scan. It may reduce the need for sedation in young children undergoing MRI. Our protocol is also effective in preparing young children to participate in fMRI investigations

Action research and democracy

This contribution explores the relationship between research and learning democracy. Action research is seen as being compatible with the orientation of educational and social work research towards social justice and democracy. Nevertheless, the history of action research is characterized by a tension between democracy and social engineering. In the social-engineering approach, action research is conceptualized as a process of innovation aimed at a specific Bildungsideal. In a democratic approach action research is seen as research based on cooperation between research and practice. However, the notion of democratic action research as opposed to social engineering action research needs to be theorized. So called democratic action research involving the implementation by the researcher of democracy as a model and as a preset goal, reduces cooperation and participation into instruments to reach this goal, and becomes a type of social engineering in itself. We argue that the relationship between action research and democracy is in the acknowledgment of the political dimension of participation: ‘a democratic relationship in which both sides exercise power and shared control over decision-making as well as interpretation’. This implies an open research design and methodology able to understand democracy as a learning process and an ongoing experiment