The Norton–Simon hypothesis and the onset of non-genetic resistance to chemotherapy induced by stochastic fluctuations

By studying a simple but realistic biophysical model of tumor growth in the presence of a constant continuous chemotherapy, we show that if an extended Norton–Simon hypothesis holds, the system may have multiple equilibria. Thus, the stochastic bounded fluctuations that affect both the tumor carrying capacity and/or the drug pharmacodynamics (and/or the drug pharmacokinetics) may cause the transition from a small equilibrium to a far larger one, not compatible with the life of the host. In particular, we mainly investigated the effects of fluctuations that involve parameters nonlinearly affecting the deterministic model. We propose to frame the above phenomena as a new and non-genetic kind of resistance to chemotherapy.     

Optimal rejection curves for exact false discovery rate control

Finner et al. (2012) provided multiple hypothesis testing procedures based on a nonlinear rejection curve for exact false discovery rate control. This paper constructs classes of such procedures and compares the most powerful procedure in each class to competing procedures.     

Blind separation of vibration signals and source change detection – Application to machine monitoring

The paper presents a new approach for machine vibration analysis and health monitoring combining blind source separation (BSS) and change detection in source signals. So, the problem is transferred from the original space of the measurements to the space of independent sources, where the reduced number of components is going to simplify the monitoring problem while the change detection methods are going to be applied for scalar signals. The assessment of the approach on a real machine is presented in this paper.     

On effective linearly ordered sets of comparison functions

Both the existence and the nonexistence of a linearly ordered (by certain natural order relations) effective set of comparison functions (=dense comparison class) are compatible with the ZFC axioms of set theory. Translated fromMaternaticheskie Zametki, Vol. 67, No. 4, pp. 629–637, April, 2000.     

Aspects of the Mach–Einstein Doctrine and Geophysical Application (A Historical Review)

The present authors have given a mathematical model of Mach's principle and of the Mach–Einstein doctrine about the complete induction of the inertial masses by the gravitation of the universe. The analytical formulation of the Mach–Einstein doctrine is based on Riemann's generalization of the Lagrangian analytical mechanics (with a generalization of the Galilean transformation) on Mach's definition of the inertial mass and on Einstein's principle of equivalence. All local and cosmological effects—which are postulated as consequences of Mach's principle by C. Neumann, Mach, Friedl?nder and Einstein—result from the Riemannian dynamics with the Mach–Einstein doctrine. In celestial mechanics it follows, in addition, Einstein's formula for the perihelion motion. In cosmology, the Riemannian mechanics yields two models of an evolutionary universe with the expansion lows R ~ t or R ~ t². In this paper, secular consequences of the Mach–Einstein doctrine are examined concerning palaeogeophysics and celestial mechanics. The research predicted secular decrease of the Earth's flattening and secular acceleration of the motion of the Moon and of the planets. The numerical values of this secular effect agree very well with the empirical facts. In all cases, the secular variation of the parameter α is the order of magnitude , where H₀ is the instantaneous value of the Hubble constant: . The relation of the secular consequences of the Mach–Einstein doctrine to those of Dirac's hypothesis on the expanding Earth, and to Darwin's theory of tidal friction are also discussed.     

General framework for testing Poisson‐Voronoi assumption for real microstructures

Modeling microstructures is an interesting problem not just in materials science, but also in mathematics and statistics. The most basic model for steel microstructure is the Poisson‐Voronoi diagram. It has mathematically attractive properties and it has been used in the approximation of single‐phase steel microstructures. The aim of this article is to develop methods that can be used to test whether a real steel microstructure can be approximated by such a model. Therefore, a general framework for testing the Poisson‐Voronoi assumption based on images of two‐dimension sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, three different model tests are proposed. The first two are based on the coefficient of variation and the cumulative distribution function of the cells area. The third exploits tools from to topological data analysis, such as persistence landscapes.     

由Lévy过程驱动的双重反射型倒向随机微分方程(英文)

证明了由Lévy过程驱动的双重反射型倒向随机微分方程解的存在唯一性.主要方法是Snell包络和不动点定理.     

The strong predictable representation property in initially enlarged filtrations under the density hypothesis

We study the strong predictable representation property in filtrations initially enlarged with a random variable $L$. We prove that the strong predictable representation property can always be transferred to the enlarged filtration as long as the classical density hypothesis of Jacod (1985) holds. This generalizes the existing martingale representation results and does not rely on the equivalence between the conditional and the unconditional laws of $L$. Depending on the behavior of the density process at zero, different forms of martingale representation are established. The results are illustrated in the context of hedging contingent claims under insider information.     

Club isomorphisms on higher Aronszajn trees

We prove the consistency, assuming an ineffable cardinal, of the statement that CH holds and any two normal countably closed ${\omega }_2$-Aronszajn trees are club isomorphic. This work generalizes to higher cardinals the property of Abraham–Shelah [1] that any two normal ${\omega }_1$-Aronszajn trees are club isomorphic, which follows from PFA. The statement that any two normal countably closed ${\omega }_2$-Aronszajn trees are club isomorphic implies that there are no ${\omega }_2$-Suslin trees, so our proof also expands on the method of Laver–Shelah [5] for obtaining the ${\omega }_2$-Suslin hypothesis.