Tiler : Software for Human-Guided Data Exploration

Peer reviewe

Integration in superspace using distribution theory

In this paper, a new class of Cauchy integral formulae in superspace is obtained, using formal expansions of distributions. This allows to solve five open problems in the study of harmonic and Clifford analysis in superspace

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

Operator identities in q-deformed Clifford analysis

In this paper, we define a q-deformation of the Dirac operator as a generalization of the one dimensional q-derivative. This is done in the abstract setting of radial algebra. This leads to a q-Dirac operator in Clifford analysis. The q-integration on R(m), for which the q-Dirac operator satisfies Stokes' formula, is defined. The orthogonal q-Clifford-Hermite polynomials for this integration are briefly studied

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

Orthosymplectically invariant functions in superspace

The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically symmetric functions can be used to solve orthosymplectically invariant Schroedinger equations in superspace, such as the (an)harmonic oscillator or the Kepler problem. Finally the obtained machinery is used to prove the Funk-Hecke theorem and Bochner's relations in superspace.Comment: J. Math. Phy

The gait and balance of patients with diabetes can be improved: a randomised controlled trial

Aims/hypothesis: Gait characteristics and balance are altered in diabetic patients. Little is known about possible treatment strategies. This study evaluates the effect of a specific training programme on gait and balance of diabetic patients. Methods: This was a randomised controlled trial (n = 71) with an intervention (n = 35) and control group (n = 36). The intervention consisted of physiotherapeutic group training including gait and balance exercises with function-orientated strengthening (twice weekly over 12weeks). Controls received no treatment. Individuals were allocated to the groups in a central office. Gait, balance, fear of falls, muscle strength and joint mobility were measured at baseline, after intervention and at 6-month follow-up. Results: The trial is closed to recruitment and follow-up. After training, the intervention group increased habitual walking speed by 0.149m/s (p < 0.001) compared with the control group. Patients in the intervention group also significantly improved their balance (time to walk over a beam, balance index recorded on Biodex balance system), their performance-oriented mobility, their degree of concern about falling, their hip and ankle plantar flexor strength, and their hip flexion mobility compared with the control group. After 6months, all these variables remained significant except for the Biodex sway index and ankle plantar flexor strength. Two patients developed pain in their Achilles tendon: the progression for two related exercises was slowed down. Conclusions/interpretation: Specific training can improve gait speed, balance, muscle strength and joint mobility in diabetic patients. Further studies are needed to explore the influence of these improvements on the number of reported falls, patients' physical activity levels and quality of life. Trial registration:: ClinicalTrials.gov NCT00637546 Funding:: This work was supported by the Swiss National Foundation (SNF): PBSKP-123446/

Automating Data Science: Prospects and Challenges

Given the complexity of typical data science projects and the associated demand for human expertise, automation has the potential to transform the data science process. Key insights: * Automation in data science aims to facilitate and transform the work of data scientists, not to replace them. * Important parts of data science are already being automated, especially in the modeling stages, where techniques such as automated machine learning (AutoML) are gaining traction. * Other aspects are harder to automate, not only because of technological challenges, but because open-ended and context-dependent tasks require human interaction.Comment: 19 pages, 3 figures. v1 accepted for publication (April 2021) in Communications of the AC

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