Hermite and Gegenbauer polynomials in superspace using Clifford analysis

The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an integration theory in superspace. Furthermore a lot of basic properties, such as orthogonality relations, differential equations and recursion formulae are proven. Finally, an interesting physical application of the super Clifford-Hermite polynomials is discussed, thus giving an interpretation to the super-dimension.Comment: 18 pages, accepted for publication in J. Phys.

Mapping Wheat Growing Areas of Turkey by Integrating Multi-Temporal NDVI Data and Official Crop Statistics

Wheat is the most widely cultivated crop in the world providing critical food source of most countries. It exceeds most of the grain crops in acreage and production because of its ability to grow in wide range of climatic and geographic conditions. Timely and reliable information on wheat acreages is essential for government services in order to formulate their policies for planning of agricultural production and monitoring their food supply. Traditionally, agricultural statistics is considered as the main source of such information. Unfortunately, existing statistical data of wheat acreages of Turkey, mostly dependent on farmers’ declarations, does not provide spatial information of where this crop specifically is grown. Satellite remote sensing technology can enable the acquisition of such information indirectly with the use of ancillary data of crop statistics. This study aims to determine wheat cultivation areas of Turkey as percentage per unit area in a crop map by integrating time series satellite NDVI imagery with the official crop statistics through regression analysis. The regression results indicated that satellite data explained 95.8% of the variability in official wheat crop statistics and actual wheat cropping areas were significantly related to NDVI-based wheat classes. Validation of the produced wheat map showed that there was good agreement between actual wheat fractions and estimated NDVI-based wheat fractions explaining approximately 69% (Adj. R2) of the total variability between them. This study suggests use of the methodology employed here to governing bodies that need to identify and to map current wheat cropping areas

Spherical harmonics and integration in superspace

In this paper the classical theory of spherical harmonics in R^m is extended to superspace using techniques from Clifford analysis. After defining a super-Laplace operator and studying some basic properties of polynomial null-solutions of this operator, a new type of integration over the supersphere is introduced by exploiting the formal equivalence with an old result of Pizzetti. This integral is then used to prove orthogonality of spherical harmonics of different degree, Green-like theorems and also an extension of the important Funk-Hecke theorem to superspace. Finally, this integration over the supersphere is used to define an integral over the whole superspace and it is proven that this is equivalent with the Berezin integral, thus providing a more sound definition of the Berezin integral.Comment: 22 pages, accepted for publication in J. Phys.

CSNE: Conditional Signed Network Embedding

Signed networks are mathematical structures that encode positive and negative relations between entities such as friend/foe or trust/distrust. Recently, several papers studied the construction of useful low-dimensional representations (embeddings) of these networks for the prediction of missing relations or signs. Existing embedding methods for sign prediction generally enforce different notions of status or balance theories in their optimization function. These theories, however, are often inaccurate or incomplete, which negatively impacts method performance. In this context, we introduce conditional signed network embedding (CSNE). Our probabilistic approach models structural information about the signs in the network separately from fine-grained detail. Structural information is represented in the form of a prior, while the embedding itself is used for capturing fine-grained information. These components are then integrated in a rigorous manner. CSNE's accuracy depends on the existence of sufficiently powerful structural priors for modelling signed networks, currently unavailable in the literature. Thus, as a second main contribution, which we find to be highly valuable in its own right, we also introduce a novel approach to construct priors based on the Maximum Entropy (MaxEnt) principle. These priors can model the \emph{polarity} of nodes (degree to which their links are positive) as well as signed \emph{triangle counts} (a measure of the degree structural balance holds to in a network). Experiments on a variety of real-world networks confirm that CSNE outperforms the state-of-the-art on the task of sign prediction. Moreover, the MaxEnt priors on their own, while less accurate than full CSNE, achieve accuracies competitive with the state-of-the-art at very limited computational cost, thus providing an excellent runtime-accuracy trade-off in resource-constrained situations

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

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/

The effect of taping versus semi-rigid bracing on patient outcome and satisfaction in ankle sprains: A prospective, randomized controlled trial

Background: Functional treatment is a widely used and generally accepted treatment for ankle sprain. A meta-analysis comparing the different functional treatment options could not make definitive conclusions regarding the effectiveness, and until now, little was known about patient satisfaction in relation to the outcome. Methods: Patients with acute ankle sprain received rest, ice, compression and elevation with an compressive bandage at the emergency department. After 5-7 days, 100 patients with grade II and III sprains were randomized into two groups: one group was treated with tape and the other with a semi-rigid ankle brace, both for 4 weeks. Post-injury physical and proprioceptive training was standardized. As primary outcome parameter patient satisfaction and skin complications were evaluated using a predefined questionnaire and numeric rating scale. As secondary outcome parameter the ankle joint function was assessed using the Karlsson scoring scale and range of motion. Results: Patient-reported comfort and satisfaction during treatment with a semi-rigid brace was significantly increased. The rate of skin complication in this group was significantly lower compared to the tape group (14.6% versus 59.1%, P < 0.0001). Functional outcome of the ankle joint was similar between the two treatment groups, as well as reported pain. Conclusion: Treatment of acute ankle sprain with semi-rigid brace leads to significantly higher patient comfort and satisfaction, both with similar good outcome

Automated PGP9.5 immunofluorescence staining: a valuable tool in the assessment of small fiber neuropathy?

BACKGROUND: In this study we explored the possibility of automating the PGP9.5 immunofluorescence staining assay for the diagnosis of small fiber neuropathy using skin punch biopsies. The laboratory developed test (LDT) was subjected to a validation strategy as required by good laboratory practice guidelines and compared to the well-established gold standard method approved by the European Federation of Neurological Societies (EFNS). To facilitate automation, the use of thinner sections. (16 µm) was evaluated. Biopsies from previously published studies were used. The aim was to evaluate the diagnostic performance of the LDT compared to the gold standard. We focused on technical aspects to reach high-quality standardization of the PGP9.5 assay and finally evaluate its potential for use in large scale batch testing. RESULTS: We first studied linear nerve fiber densities in skin of healthy volunteers to establish reference ranges, and compared our LDT using the modifications to the EFNS counting rule to the gold standard in visualizing and quantifying the epidermal nerve fiber network. As the LDT requires the use of 16 µm tissue sections, a higher incidence of intra-epidermal nerve fiber fragments and a lower incidence of secondary branches were detected. Nevertheless, the LDT showed excellent concordance with the gold standard method. Next, the diagnostic performance and yield of the LDT were explored and challenged to the gold standard using skin punch biopsies of capsaicin treated subjects, and patients with diabetic polyneuropathy. The LDT reached good agreement with the gold standard in identifying small fiber neuropathy. The reduction of section thickness from 50 to 16 µm resulted in a significantly lower visualization of the three-dimensional epidermal nerve fiber network, as expected. However, the diagnostic performance of the LDT was adequate as characterized by a sensitivity and specificity of 80 and 64 %, respectively. CONCLUSIONS: This study, designed as a proof of principle, indicated that the LDT is an accurate, robust and automated assay, which adequately and reliably identifies patients presenting with small fiber neuropathy, and therefore has potential for use in large scale clinical studies

Early surgical complications after congenital diaphragmatic hernia repair by thoracotomy vs. laparotomy: A bicentric comparison

Purpose: The surgical strategy for congenital diaphragmatic hernia (CDH) repair remains debated and mainly depends on the training and preference of the surgeon. Our aim was to evaluate the occurrence and nature of surgical reinterventions within the first year of life, following repair through thoracotomy as compared to laparotomy. / Methods: This is a retrospective bi-centric cohort study comparing postero-lateral thoracotomy (n = 55) versus subcostal laparotomy (n = 62) for CDH repair (IRB: MP001882). We included neonates with isolated, left-sided, Bochdalek-type CDH who were operated on between 2000 and 2017, and had a minimum follow-up of 1 year. Excluded were patients treated prenatally and/or had extra-corporeal membrane oxygenation. Outcomes were occurrence and nature of surgical reinterventions and mortality by 1 year of life. / Results: Both groups had comparable neonatal severity risk profiles. The overall surgical reintervention rate by 1 year of age was higher in the thoracotomy group (29.1% vs. 6.5%; p = 0.001), mainly because of a higher prevalence of acute bowel complications (18.1% vs. 3.2%; p = 0.012) requiring surgery, such as perforation, obstruction and volvulus. At 1 year of follow-up, groups were similar in terms of recurrence (5.5% vs. 1.6%; p = 0.341), surgical interventions related to severe gastroesophageal reflux disease (3.6% vs. 1.6%; p = 0.600) and mortality (5.5% vs. 6.6%; p = 1.000). / Conclusion: Postnatal CDH repair through thoracotomy was associated with a higher rate of surgical reinterventions within the first year of life, especially for severe acute gastro-intestinal complications. There seemed to be no difference in recurrence and mortality rate. / Type of Study: Retrospective Comparative Cohort Study. / Level of Evidence: Level III