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Uncertainty quantification (UQ) in eruption source parameters, like tephra volume, plume height, and umbrella cloud radius, is a challenge for volcano scientists because tephra deposits are often sparsely sampled due to burial, erosion, and related factors. We find that UQ is improved by coupling an advection‐diffusion model with two Bayesian inversion approaches: (a) a robust but computationally expensive Generalized Likelihood Uncertainty Estimation algorithm, and (b) a more approximate but inexpensive parameter estimation algorithm combined with first‐order, second‐moment uncertainty estimation. We apply the two inversion methods to one sparsely sampled tephra fall unit from the 2070 BP El Misti (Peru) eruption and obtain: Tephra mass 0.78–1.4 × 1011 kg; umbrella cloud radius 4.5–16.5 km, and plume height 8–35 km (95% confidence intervals). These broad ranges demonstrate the significance of UQ for eruption classification based on mapped deposits, which has implications for hazard management. Plain Language Summary: Volcanologists use ashfall deposits to estimate the magnitudes and intensities of past or unobserved eruptions. Different processes can affect the ash deposits during and after the eruption (e.g., burial, remobilisation, and erosion) resulting in sparse sampling of the deposit and uncertainty in the deposit thickness where it is sampled. Uncertain data results in uncertain estimates of erupted volume, plume height, and umbrella cloud dimensions, which are essential parameters used to estimate future volcanic hazards. Here we present two methods to quantify the uncertainty in these parameter estimates from deposit data. As a case study, we estimate eruption parameters for a sparsely sampled ashfall deposit from the 2070 BP eruption of El Misti, Peru. We find that for this sampled unit the mass of the erupted tephra was 0.78–1.4 × 1011 kg, umbrella cloud radius was 4.5–16.5 km, and plume height was 8–35 km. These ranges are 95% confidence intervals, giving a much better idea of the eruption magnitude and intensity than that is achieved from point estimates, such as reporting the erupted mass as a single value. Key Points: Characterising volcanic eruptions based on incompletely preserved and sampled tephra deposits leads to uncertainty in classificationWe couple a tephra forward model to two inversion techniques to quantify eruption parameter uncertaintyResults show uncertainty quantification is crucial for sparsely sampled deposits because range in eruption parameters can be substantial [ABSTRACT FROM AUTHOR]

This paper will study Eckhaus-Kundu equation from the perspective of Lie symmetry analysis. We will systematically construct similarity reductions in order to perform the explicit invariant solutions of this version of the nonlinear Schrödinger equation with nonlinear dispersion and cubic-quintic nonlinearities, describing the propagation of ultrashort pulses in optical fibers. Some new wave solutions with real and imaginary parts of trigonometric type or of a compound of trigonometric and hyperbolic types will be pointed out. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method for solving linear algebraic systems based on the KSOR method. The new approach introduces a new coefficient in the assumed updated section from the KSOR method. It obtains the same solution as KSOR for a given linear algebraic system, but in order to get this, we have to modify the diagonal of the coefficient matrix of the initial system. The new method reaches the solution in fewer steps than KSOR on certain examples, but we have an additional step for the modification mentioned above with O(m) complexity, while a normal step of iteration has O (m 2) complexity, so overall our method has better performances than KSOR method. Furthermore, on certain examples, the spectral radius of the iteration matrix of the new method is strictly less than the one of KSOR and MKSOR methods. [ABSTRACT FROM AUTHOR]

Background and purpose Clinical symptoms and long-term outcome of autoimmune encephalitis are variable. Diagnosis requires multiple investigations, and treatment strategies must be individually tailored. Better biomarkers are needed for diagnosis, to monitor disease activity and to predict long-term outcome. The value of cerebrospinal fluid (CSF) markers of neuronal [neurofilament light chain protein (NFL), and total tau protein (T-tau)] and glial cell [glial fibrillary acidic protein (GFAP)] damage in patients with autoimmune encephalitis was investigated. Methods Demographic, clinical, magnetic resonance imaging, CSF and antibody-related data of 25 patients hospitalized for autoimmune encephalitis and followed for 1 year were retrospectively collected. Correlations between these data and consecutive CSF levels of NFL, T-tau and GFAP were investigated. Disability, assessed by the modified Rankin scale, was used for evaluation of disease activity and long-term outcome. Results The acute stage of autoimmune encephalitis was accompanied by high CSF levels of NFL and T-tau, whereas normal or significantly lower levels were observed after clinical improvement 1 year later. NFL and T-tau reacted in a similar way but at different speeds, with T-tau reacting faster. CSF levels of GFAP were initially moderately increased but did not change significantly later on. Final outcome (disability at 1 year) directly correlated with CSF-NFL and CSF-GFAP levels at all time-points and with CSF-T-tau at 3 ± 1 months. This correlation remained significant after age adjustment for CSF-NFL and T-tau but not for GFAP. Conclusion In autoimmune encephalitis, CSF levels of neuronal and glial cell damage markers appear to reflect disease activity and long-term disability. [ABSTRACT FROM AUTHOR]

We discuss the Tzitzeica equation and the spectral properties associated with its Lax operator L. We prove that the continuous spectrum of L is rotated with respect to the contour of the Riemann-Hilbert problem with angle π/6. We also show that the poles of the dressing factors and their inverses are discrete eigenvalues of L. [ABSTRACT FROM AUTHOR]

Background Low levels of serum urate are associated with a higher risk of Parkinson's disease ( PD). Higher serum and cerebrospinal fluid ( CSF) urate levels are associated with slower rates of clinical decline in PD and in multiple system atrophy ( MSA). Aims To compare CSF and blood urate levels in healthy controls, patients with synucleinopathies and with tauopathies. Methods We investigated urate levels in serum and CSF from 18 healthy controls, 19 patients with synucleinopathies (six patients with PD and 13 with MSA), and 24 patients with tauopathies (18 with progressive supranuclear palsy and six with corticobasal degeneration). None of the patients were treated with dopaminergic medications. Results No significant differences were seen when comparing serum and CSF urate levels from controls across the parkinsonian diagnostic groups. However, in men, serum urate levels were significantly lower in the synucleinopathy group compared with the tauopathy group ( P = 0.046), although with a broad overlap. Conclusion Our study suggests that urate levels might provide new insights into the potential pathophysiological mechanisms underlying Parkinsonism and thereby contribute to the future management of these disorders. [ABSTRACT FROM AUTHOR]

Constantinescu R, Holmberg B, Rosengren L, Corneliusson O, Johnels B, Zetterberg H. Light subunit of neurofilament triplet protein in the cerebrospinal fluid after subthalamic nucleus stimulation for Parkinson's disease. Acta Neurol Scand: 2011: 124: 206-210. © 2010 John Wiley & Sons A/S. Objectives - Cerebrospinal fluid (CSF) levels of neurofilament triplet protein (NFL), a non-specific marker of neuronal damage, are normal in Parkinson's disease (PD) but increased after brain trauma and in several neurological disorders. Using longitudinal CSF-NFL measurements as an indicator of neuronal damage, this study investigated the impact of deep brain stimulation (DBS) of the subthalamic nucleus (STN) on the brain, directly following the surgical intervention and in chronically treated patients with PD. Materials and methods - CSF-NFL levels were measured consecutively in eight patients with PD before and after STN-DBS treatment. Results - CSF-NFL levels were normal prior to STN-DBS and increased sharply during the first 2 weeks post-operatively, but normalized after 12 months or more. Conclusion - The STN-DBS procedure leads to an acute but limited neuronal damage, as expected. However, normal CSF-NFL levels at 12 months post-operatively and beyond suggest the absence of any long-term neuronal damage caused by long-term STN-DBS stimulation. [ABSTRACT FROM AUTHOR]

Abstract: The paper is devoted to the Lie symmetries of  nonlinear dynamical systems described by second order partial differential equations. By imposing the invariance condition of the equations under the action of the Lie symmetry operator we obtained a determining system which could be solved in two directions: (i) to find the symmetries of a concrete equation; (ii) to obtain all the compatible equations with an imposed form of symmetry algebra. This paper will pay attention to the indirect problem (ii) and will use the algorithm for determining the most general equations which belong, following their symmetries, to the same class with two interesting and important physical models: the nonlinear heat equation and the transfer equation with power-law nonlinearities. [Copyright &y& Elsevier]

Background – Motor fluctuations in patients with advanced Parkinson’s disease may be successfully treated with subcutaneous apomorphine infusion or intraduodenal levodopa/carbidopa infusion. No comparative trials of these two alternatives were performed. Aims of the study – We present a subanalysis from a randomized crossover clinical trial where levodopa infusion as monotherapy was compared with any other combination of pharmacotherapy in fluctuating patients. Four patients used apomorphine infusion and oral levodopa in the comparator arm. The results of these four patients are presented in detail. Methods – The duration of the trial was 3 + 3 weeks. Patients were video-recorded half-hourly on two non-consecutive days of both treatment arms. Blinded video ratings were used. Patient self-assessments of motor function and quality-of-life (QoL) parameters were captured using an electronic diary. Results – Ratings in moderate to severe ‘off’ state ranged 0–44% on apomorphine infusion and 0–6% on levodopa infusion. Moderate to severe dyskinesias were not recorded in any of the treatments. QoL was reported to be improved in all patients on duodenal levodopa infusion. Conclusions – Monotherapy with duodenal infusion of levodopa was more efficacious and brought greater QoL than combination therapy with apomorphine infusion in these fluctuating patients. [ABSTRACT FROM AUTHOR]