Distribution function estimates by Wasserstein metric and Bernstein approximation for C-1 functions

The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learningBased on the classical Bernstein approximation, a scheme is presented.To get the error estimates of the scheme, the problem turns to estimating the L1 norm of the Bernstein approximation for monotone C-1functions, which was rarely discussed in the classical approximation theoryFinally, we get a probability estimate by the statistical distance.     

Symplectic invariants for curves and integrable systems in similarity symplectic geometry

In this paper, similarity symplectic geometry for curves is proposed and studied. Explicit expressions of the symplectic invariants, Frenet frame and Frenet formulae for curves in similarity symplectic geometry are obtained by using the equivariant moving frame method. The relationships between the Euclidean symplectic invariants, Frenet frame, Frenet formulae and the similarity symplectic invariants, Frenet frame, Frenet formulae for curves are established. Invariant curve flows in four-dimensional similarity symplectic geometry are also studied. It is shown that certain intrinsic invariant curve flows in four-dimensional similarity symplectic geometry are related to the integrable Burgers and matrix Burgers equations.     

Barrier method in nonsmooth convex optimization without convex representation

In this article we want to demonstrate that under mild conditions the barrier method is an effective solution approach for convex optimization problems whose objective is nonsmooth and whose feasible set is described by smooth inequality constraints in which all the constraint functions need not be convex.     

Quantitative stability of full random two-stage stochastic programs with recourse

In this paper, we consider quantitative stability analysis for two-stage stochastic linear programs when recourse costs, the technology matrix, the recourse matrix and the right-hand side vector are all random. For this purpose, we first investigate continuity properties of parametric linear programs. After deriving an explicit expression for the upper bound of its feasible solutions, we establish locally Lipschitz continuity of the feasible solution sets of parametric linear programs. These results are then applied to prove continuity of the generalized objective function derived from the full random second-stage recourse problem, from which we derive new forms of quantitative stability results of the optimal value function and the optimal solution set with respect to the Fortet–Mourier probability metric. The obtained results are finally applied to establish asymptotic behavior of an empirical approximation algorithm for full random two-stage stochastic programs.     

On a convex set with nondifferentiable metric projection

A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with \(C^{1,1}\) boundary which possesses the same property.     

Ragnar Frisch and interior-point methods

The distinguished econometrician Ragnar Frisch (1895–1973) also played an important role in optimization theory. In fact, he was a pioneer of interior-point methods. This note reconsiders his contribution, relating it to history and modern developments.     

Random Copolymers of 1,5-Dioxepan-2-one

ABSTRACT

Copolymers of 1,5-dioxepan-2-one (DXO) and e-caprolactone (?-CL), δ-valerolactone (δ-VL) or L-lactide (LLA) have been synthesized and characterized. High molecular weight copolymers were obtained using stannous-2-ethyl hexanoate as catalyst in bulk. Reactivity ratios for the copolymerization of DXO and δ-VL were determined at 110°C as r_VL=0.5 and r_DXO=2.3. At high conversion, depolymerization of δ-VL occurred, resulting in lower molecular weight and variations in the copolymer composition.

Physical properties, such as crystallinity and melting temperature of the DXO-copolymers proved to be strongly dependent on the choice of comonomer and on the molar composition of the copolymers. DXO appears to be incorporated into the poly-?-caprolactone (PCL) crystals and to some extent into the poly-δ-valerolactone (PVL) crystals, resulting in a more gradual decrease in crystallinity with increasing amount of DXO.     

U6 is unsuitable for normalization of serum miRNA levels in patients with sepsis or liver fibrosis

MicroRNA (miRNA) levels in serum have recently emerged as potential novel biomarkers for various diseases. miRNAs are routinely measured by standard quantitative real-time PCR (qPCR); however, the high sensitivity of qPCR demands appropriate normalization to correct for nonbiological variation. Presently, RNU6B (U6) is used for data normalization of circulating miRNAs in many studies. However, it was suggested that serum levels of U6 themselves might differ between individuals. Therefore, no consensus has been reached on the best normalization strategy in ‘circulating miRNA''. We analyzed U6 levels as well as levels of spiked-in SV40-RNA in sera of 44 healthy volunteers, 203 intensive care unit patients and 64 patients with liver fibrosis. Levels of U6 demonstrated a high variability in sera of healthy donors, patients with critical illness and liver fibrosis. This high variability could also be confirmed in sera of mice after the cecal ligation and puncture procedure. Most importantly, levels of circulating U6 were significantly upregulated in sera of patients with critical illness and sepsis compared with controls and correlated with established markers of inflammation. In patients with liver fibrosis, U6 levels were significantly downregulated. In contrast, levels of spiked-in SV40 displayed a significantly higher stability both in human cohorts (healthy, critical illness, liver fibrosis) and in mice. Thus, we conclude that U6 levels in the serum are dysregulated in a disease-specific manner. Therefore, U6 should not be used for data normalization of circulating miRNAs in inflammatory diseases and previous studies using this approach should be interpreted with caution. Further studies are warranted to identify specific regulatory processes of U6 levels in sepsis and liver fibrosis.     

Application of thermovision for estimation of the optimal and safe parameters of the whole body cryotherapy

Exposure to the extreme low temperatures, ranging between ?60 and ?140 °C, has many beneficial effects on the human body what is exploited for example in sport medicine, for treatment of locomotory system diseases or even some psychiatric disorders. To insure the safe treatment in a cryochamber, careful planning of the procedure and proper qualification of patients, is required. Cardiovascular system, especially skin vasculature plays the major role of the body response to the extreme cold. The changes in skin blood flow are reflected in changes of the temperature distribution. Therefore, the thermal imaging, which allows to analyze the temperature distribution on the human body, may be successfully exploited to examine the influence of extremely low temperatures on the skin vascular system. The aim of this work was to examine the temperature, blood pressure, and heart rate changes after the whole body cryotherapy in healthy subjects to determine the safety conditions of the treatment. 480 healthy students of the Wroc?aw University School of Physical Education were divided into two groups (each 240 persons). All subjects were exposed for 1–3 min to the extremely low temperatures: ?60, ?100, ?120, and ?140 °C. In one group, the thermograms were recorded before and 5 and 30 min after the cryotherapy by means of ThermoVision A20 M thermal camera. In the other one, heart rate and blood pressure were measured before and 5 min after the cryotherapy. It was demonstrated that 3-min exposure in the cryochamber and the temperature ?120 °C are the optimal and safe cryotherapy parameters.     

Synthesis, characterization, thermal and optical properties of styrene derivatives having pendant p-substituted benzylic ether groups

The derivatives of styrene monomer, 4-chlorophenyl-4-vinylbenzyl ether (M1), 4-methoxyphenyl-4-vinylbenzyl ether (M2), 4-ethylphenyl-4-vinylbenzyl ether (M3) and 1-naphtylphenyl-4-vinylbenzyl ether (M4) were synthesized. The normal free radical polymerization of monomers in 1,4-dioxane were performed by using 2,2′-azobisisobutyronitrile as an initiator at 65 °C. The monomers and their homopolymers were characterized by FT-IR, NMR and elemental analyses measurements. The thermal stability of polymers was investigated by thermogravimetric and differential scanning calorimetric analysis. Thermal degradation activation energies of the polymers were calculated by the Ozawa and Kissinger methods. In addition, photo-stability tests of the polymers under near-UV irradiation were performed.