Monitoring Phase II Comparative Clinical Trials with Two Endpoints and Penalty for Adverse Events

Adverse events in Phase II comparative clinical trials have received limited attention in the literature. Bersimis et al. (Stat Med 34:197–214, 2014) in proposed a class of comparative sequential designs with bivariate endpoints, where as a special case, the termination of the clinical trial due to the occurrence of a severe adverse event is treated. In this paper, using the Markov chain embedding technique, we extend this class of designs proposing two new designs, which treat cases where the development of an adverse event does not immediately stop the clinical trial, but penalizes appropriately the treatment that caused it. In both designs the penalty can be chosen either by assessing the severity of the adverse event or by optimizing the power. The numerical results show an excellent performance, achieving small expected sample sizes in conjunction with large values for power, satisfying in this way the ethical requirement for small sample sizes and fast decisions in clinical practice. The formulation of the procedure as a stochastic process is elegantly accomplished while it offers the necessary mathematical framework for further generalizing the designs covering more cases such as group sequential designs, etc.     

A didactical situation for the enhancement of meta-analogical awareness

The aim of this study was to propose a didactical situation for the confrontation of the epistemological obstacle of linearity (routine proportionality) and consequently for the enhancement of meta-analogical awareness. Errors caused by students’ spontaneous tendency to apply linear functions in various situations are strong, persistent and do not disappear with traditional instruction. The effects of a didactical situation on the way students perceive and handle proportional and non-proportional relations were examined. The situation consisted of four parts which referred to the situations of action, formulation, validation and institutionalisation and was presented as a game to four twelve-year students of different abilities. The results showed the potential of the application of a didactical situation towards enhancing students’ meta-analogical awareness and therefore their ability to discern and handle linear and non-proportional relations.     

Recent Advances in the Use of Black TiO2 for Production of Hydrogen and Other Solar Fuels

Black TiO₂ has emerged as one of the most promising photocatalysts recently discovered. The reason behind its catalytic activity is considered to be due to the presence of defects and Ti³⁺ species at the surface of black TiO₂ nanostructures, which are crucial for its diverse applications. Moreover, disordered/crystalline surface layers and bulk regions have been identified and appear to influence the intrinsic properties of the material. Here, we present the latest studies on the use of black TiO₂ for metal free hydrogen production, as well as for CO₂ photoreduction and N₂ photofixation. After highlighting the structure/property relations, we conclude with some critical questions and suggest further topics of research in order to better understand the underlying mechanisms of light absorption in black TiO₂, especially towards solar fuels production.     

A study concerning splitting and jointly continuous topologies on C(Y,Z)

Let Y and Z be two fixed topological spaces and C(Y, Z) the set of all continuous maps from Y into Z. We construct and study topologies on C(Y, Z) that w^{e call F}n(τn)-family-open topologies. Furthermore, we find necessary and su?cient conditions such that these topologies to be splitting and jointly continuous. Finally, we present questions concerning a further study on this area.     

Hydrodynamic limits for kinetic equations and the diffusive approximation of radiative transport for acoustic waves

We consider a class of kinetic equations, equipped with a single conservation law, which generate -contractions. We discuss the hydrodynamic limit to a scalar conservation law and the diffusive limit to a (possibly) degenerate parabolic equation. The limits are obtained in the ``dissipative' sense, equivalent to the notion of entropy solutions for conservation laws, which permits the use of the perturbed test function method and allows for simple proofs. A general compactness framework is obtained for the diffusive scaling in . The radiative transport equations, satisfied by the Wigner function for random acoustic waves, present such a kinetic model that is endowed with conservation of energy. The general theory is used to validate the diffusive approximation of the radiative transport equation.

     

An extension of labeling techniques for finding shortest path trees

Label setting techniques are all based on Dijkstra’s condition of always scanning the node with the minimum label, which guarantees that each node will be scanned exactly once; while this condition is sufficient it is not necessary. In this paper, we discuss less restrictive conditions that allow the scanning of a node that does not have the minimum label, yet still maintaining sufficiency in scanning each node exactly once; various potential shortest path schemes are discussed, based on these conditions. Two approaches, a label setting and a flexible hybrid one are designed and implemented. The performance of the algorithms is assessed both theoretically and computationally. For comparative analysis purposes, three additional shortest path algorithms – the commonly cited in the literature – are coded and tested. The results indicate that the approaches that rely on the less restrictive optimality conditions perform substantially better for a wide range of network topologies.     

Nondestructive technique for the characterization of the pore size distribution of soft porous constructs for tissue engineering

Polymer scaffolds tailored for tissue engineering applications possessing the desired pore structure require reproducible fabrication techniques. Nondestructive, quantitative methods for pore characterization are required to determine the pore size and its distribution. In this study, a promising alternative to traditional pore size characterization techniques is presented. We introduce a quantitative, nondestructive and inexpensive method to determine the pore size distribution of large soft porous solids based on the on the displacement of a liquid, that spreads without limits though a porous medium, by nitrogen. The capillary pressure is measured and related to the pore sizes as well as the pore size distribution of the narrowest bottlenecks of the largest interconnected pores in a porous medium. The measured pore diameters correspond to the narrowest bottleneck of the largest pores connecting the bottom with the top surface of a given porous solid. The applicability and reproducibility of the breakthrough technique is demonstrated on two polyurethane foams, manufactured using the thermally induced phase separation (TIPS) process, with almost identical overall porosity (60-70%) but very different pore morphology. By selecting different quenching temperatures to induce polymer phase separation, the pore structure could be regulated while maintaining the overall porosity. Depending on the quenching temperature, the foams exhibited either longitudinally oriented tubular macropores interconnected with micropores or independent macropores connected to adjacent pores via openings in the pore walls. The pore size and its distribution obtained by the breakthrough test were in excellent agreement to conventional characterization techniques, such as scanning electron microscopy combined with image analysis, BET technique, and mercury intrusion porosimetry. This technique is suitable for the characterization of the micro- and macropore structure of soft porous solids intended for tissue engineering applications. The method is sensitive for the smallest bottlenecks of the largest continuous pores throughout the scaffold that contributes to fluid flow.     

Hinged and supported plates with corners

We consider the Kirchhoff–Love model for the supported plate, that is, the fourth-order differential equation Δ² u?=?f with appropriate boundary conditions. Due to the expectation that a downwardly directed force f will imply that the plate, which is supported at its boundary, touches that support everywhere, one commonly identifies those boundary conditions with the ones for the so-called hinged plate: u?=?0?=?Δu ? (1 ? σ ) κ u _n . Structural engineers however are usually aware that rectangular roofs tend to bend upwards near the corners, and this would mean that u?=?0 is not appropriate. We will confirm this behavior and show the difference of the supported and the hinged plates in case of domains with corners.     

Samarium Based High Surface Area Perovskite Type Oxides SmFe1-XAlXO3 (X=0.00, 0.50, 0.95). Part II, Catalytic Combustion of CH4

The catalytic combustion of methane with stoichiometric amounts of oxygen to CO₂ and H₂O has been studied over samarium based high surface area perovskite type oxides SmFe_1-xAl_xO₃ (x=0.00, 0.50 0.95) prepared via a new sol-gel method. A comparison to other lanthanum perovskites prepared by the ceramic method shows higher catalytic activity for SmFeO₃ and SmFe_0.5Al_0.5O₃ samples.