Student''s t mixture models for stock indices. A comparative study

We perform a comparative study for multiple equity indices of different countries using different models to determine the best fit using the Kolmogorov–Smirnov statistic, the Anderson–Darling statistic, the Akaike information criterion and the Bayesian information criteria as goodness-of-fit measures. We fit models both to daily and to hourly log-returns. The main result is the excellent performance of a mixture of three Student''s t distributions with the numbers of degrees of freedom fixed a priori (3St). In addition, we find that the different components of the 3St mixture with small/moderate/high degree of freedom parameter describe the extreme/moderate/small log-returns of the studied equity indices. © 2021 Elsevier B.V

Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains

This article is concerned with the discretisation of the Stokes equations on time- dependent domains in an Eulerian coordinate framework. Our work can be seen as an extension of a recent paper by Lehrenfeld and Olshanskii (ESAIM: M2AN 53(2):585–614, 2019), where BDF-type time-stepping schemes are studied for a parabolic equation on moving domains. For space discretisation, a geometrically unfit- ted finite element discretisation is applied in combination with Nitsche’s method to impose boundary conditions. Physically undefined values of the solution at previous time-steps are extended implicitly by means of so-called ghost penalty stabilisations. We derive a complete a priori error analysis of the discretisation error in space and time, including optimal L2(L2)-norm error bounds for the velocities. Finally, the theoretical results are substantiated with numerical examples

A note on the stability parameter in Nitsche's method for unfitted boundary value problems

Nitsche's method is a popular approach to implement Dirichlet-type boundary conditions in situations where a strong imposition is either inconvenient or simply not feasible. The method is widely applied in the context of unfitted finite element methods. Of the classical (symmetric) Nitsche's method it is well-known that the stabilization parameter in the method has to be chosen sufficiently large to obtain unique solvability of discrete systems. In this short note we discuss an often used strategy to set the stabilization parameter and describe a possible problem that can arise from this. We show that in specific situations error bounds can deteriorate and give examples of computations where Nitsche's method yields large and even diverging discretization errors. <br/

A stable cut finite element method for partial differential equations on surfaces: The Helmholtz–Beltrami operator

We consider solving the surface Helmholtz equation on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We consider a Galerkin method based on using the restrictions of continuous piecewise linears defined on the tetrahedra to the surface as trial and test functions. Using a stabilized method combining Galerkin least squares stabilization and a penalty on the gradient jumps we obtain stability of the discrete formulation under the condition hk<C, where h denotes the mesh size, k the wave number and C a constant depending mainly on the surface curvature κ, but not on the surface/mesh intersection. Optimal error estimates in the H1 and L2-norms follow

Health effects of dietary phospholipids

Beneficial effects of dietary phospholipids (PLs) have been mentioned since the early 1900's in relation to different illnesses and symptoms, e.g. coronary heart disease, inflammation or cancer. This article gives a summary of the most common therapeutic uses of dietary PLs to provide an overview of their approved and proposed benefits; and to identify further investigational needs

Micromorphic theory as a model for blood in the microcirculation: correction and analysis

This paper analyzes the applicability of Eringen’s Generalized Continuum Theories as a model for human blood in the microcirculation. The applied theory considers a fluid with a fully deformable substructure, namely a micromorphic fluid. This analysis is motivated by the fact that blood itself can be considered a suspension of deformable particles, i.e., red blood cells (RBCs), suspended in a Newtonian fluid, i.e., blood plasma. As a consequence, non-Newtonian phenomena such as shear-thinning are observed in blood. To test the micromorphic fluid as a model for blood, the solution for the velocity and the motion of substructure is determined for a cylindrical pipe flow and compared to experimental results of blood flow through narrow glass capillaries representing idealized blood vessels. A similar analysis was also conducted by Kang and Eringen in 1976, but it contains some misprints and minor errors regarding the mathematical expressions and subsequent discussion which are corrected in this paper. For certain material parameters, the micromorphic fluid models capture high-shear blood flow in narrow glass capillaries very well. This concerns both the velocity profiles and the shear-thinning behavior. Furthermore, a parameter study reveals that the flexibility of substructure governs the micromorphic shear-thinning. In this regard, parallels can be drawn to the shear-thinning of human blood, which is also induced by the deformability of RBCs. This makes the micromorphic fluid a complex but accurate model for human blood, at least for the considered experiments

A Stabilized Cut Streamline Diffusion Finite Element Method for Convection-Diffusion Problems on Surfaces

We develop a stabilized cut finite element method for the stationary convection diffusion problem on a surface embedded in R d . The cut finite element method is based on using an embedding of the surface into a three dimensional mesh consisting of tetrahedra and then using the restriction of the standard piecewise linear continuous elements to a piecewise linear approximation of the surface. The stabilization consists of a standard streamline diffusion stabilization term on the discrete surface and a so called normal gradient stabilization term on the full tetrahedral elements in the active mesh. We prove optimal order a priori error estimates in the standard norm associated with the streamline diffusion method and bounds for the condition number of the resulting stiffness matrix. The condition number is of optimal order for a specific choice of method parameters. Numerical examples supporting our theoretical results are also included

Plasma lyso-phosphatidylcholine concentration is decreased in cancer patients with weight loss and activated inflammatory status

<p>Abstract</p> <p>Background</p> <p>It has been observed that ras-transformed cell lines in culture have a higher phosphatidylcholine (PC) biosynthesis rate as well as higher PC-degradation rate (increased PC-turnover) than normal cells. In correspondence to these findings, the concentrations of the PC-degradation product lyso-phosphatidylcholine (LPC) in cancer patients were found to be decreased. Our objective was the systematic investigation of the relationship between LPC and inflammatory and nutritional parameters in cancer patients. Therefore, plasma LPC concentrations were assessed in 59 cancer patients and related to nutritional and inflammatory parameters. To determine LPC in blood plasma we developed and validated a HPTLC method.</p> <p>Results</p> <p>Average plasma LPC concentration was 207 ± 59 μM which corresponds to the lower limit of the reported range in healthy subjects. No correlation between LPC and age, performance status, body mass index (BMI) or fat mass could be seen. However, LPC correlated inversely with plasma C-reactive protein (CRP) and whole blood hydrogen peroxides (HPO). Further, a negative correlation could be observed between LPC and whole body extra cellular fluid volume (ECF) as well as with relative change in body weight since cancer diagnosis.</p> <p>Conclusion</p> <p>In conclusion, LPC concentrations were decreased in cancer patients. LPC plasma concentrations correlated with weight loss and inflammatory parameters and, therefore, might be a general indicator of severity of malignant disease.</p