Treatment of Parkinson’s Disease:Early, Late, and Combined

Medical therapy in de novo Parkinson’s disease typically starts with a dopamine agonist or levodopa in combination with a decarboxylase inhibitor or if symptoms are still very mild with a MAO-B inhibitor. When patients do not (or no longer) respond satisfactorily to these initial therapies, different drugs can be initiated or combined (i.e., “add-on” treatments). These add-on therapies not only comprise oral agents but also intra-jejunal and intra-cutaneous treatments and functional neurosurgical procedures. This chapter starts with the treatment of de novo Parkinson’s disease whereafter indications and expected effects of the different “add-on” therapies will be described. The “add-on” therapies will be described in a hierarchical way and treatment algorithms will be provided based on prevailing symptoms including non-motor symptoms. The symptoms that will be discussed are: (1) bradykinesia and “wearing-OFF, " (2) tremor at rest, (3) dyskinesia, (4) gait and postural symptoms including freezing of gait, and (5) important non-motor symptoms. Finally, a comprehensive add-on treatment algorithm will be provided that takes into account non-motor symptoms that may limit the efficacy and tolerability of the different add-on therapies.</p

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

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

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

Abdominal aortic calcification on a plain X-ray and the relation with significant coronary artery disease in asymptomatic chronic dialysis patients

BACKGROUND: Coronary artery disease (CAD) is common in asymptomatic chronic dialysis patients and plays an important role in their poor survival. Early identification of these high-risk patients could improve treatment and reduce mortality. Abdominal aortic calcification (AAC) has previously been associated with CAD in autopsy studies. Since the AAC can be quantified easily using a lateral lumbar X-ray we hypothesized that the extent of AAC as assessed on a lateral lumbar X-ray might be predictive of the presence of significant CAD in dialysis patients. METHODS: All patients currently enrolled in the ICD2 trial without a history of CABG or a PCI with stent implantation were included in this study. All patients underwent CT-angiography (CTA) and a lateral X-ray of the abdomen. AAC on X-ray was quantified using a previously validated scoring system whereupon the association between AAC and the presence of significant CAD was assessed. RESULTS: A total of 90 patients were included in this study (71% male, 67 ± 7 years old). Forty-six patients were found to have significant CAD. AAC-score was significantly higher in patients with CAD (10.1 ± 4.9 vs 6.3 ± 4.6 (p < 0.05). Multivariate regression analysis revealed that AAC score is an independent predictor for the presence of CAD with a 1,2 fold higher risk per point increase (p < 0.01). The AAC score has a sensitivity of 85% and a specificity of 57% for the presence of significant CAD. CONCLUSION: This study shows that abdominal aortic calcification as assessed on a lateral lumbar X-ray is predictive for the presence of significant coronary artery disease in asymptomatic dialysis patients. This simple, non-invasive and cheap screening method could contribute to early identification of patients eligible for further screening of CAD. TRIAL REGISTRATION: NTR948, registered 10-4-2007 ; ISRCTN20479861, registered 2-5-200

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

Rangelands Vegetation Mapping at Species Composition Level Using the \u3cb\u3eSPiCla\u3c/b\u3e Method: \u3cb\u3eS\u3c/b\u3eDM Based \u3cb\u3ePi\u3c/b\u3exel \u3cb\u3eCla\u3c/b\u3essification and Fuzzy Accuracy. A New Approach of Map Making

Vegetation maps have been made since centuries. The vegetation cover was represented as homogeneous mapping units (polygons), representing different vegetation types, where each type consists a combination of different plant species (floristic composition). More recent, with the use of satellite imagery, the polygons have been replaced by pixels with similar content as the polygon maps. In both approaches, field-observations were linked to the mapping units (polygons or pixels) often resulting in a complex of different vegetation types per mapping unit. In our new approach field data (sample points) on presence and abundance of individual grass species are spatially extrapolated based on a set of environmental layers, using the species distribution modelling approach (SDM). When combined, each pixel will contain its own set of information about the vegetation structure and its floristic composition. This new methodology (SPiCla) results in a very accurate and detailed vegetation map at pixel level, allowing extraction of very detailed, accurate and easy to update spatial information on e.g., forage production and quality (palatability) for rangelands management. As no exact boundaries exist, but only gradients, we introduced fuzzy accuracy. The resolution mainly depends on the resolution of (or one of) the environmental layers used, scale of interest and workability. The methodology is generic and applicable to any other region in the world

A study of two-qubit density matrices with fermionic purifications

We study 12 parameter families of two qubit density matrices, arising from a special class of two-fermion systems with four single particle states or alternatively from a four-qubit state with amplitudes arranged in an antisymmetric matrix. We calculate the Wooters concurrences and the negativities in a closed form and study their behavior. We use these results to show that the relevant entanglement measures satisfy the generalized Coffman-Kundu-Wootters formula of distributed entanglement. An explicit formula for the residual tangle is also given. The geometry of such density matrices is elaborated in some detail. In particular an explicit form for the Bures metric is given.Comment: 21 pages, 1 figur