First passage time processes and subordinated SLE

We study the first passage time processes of anomalous diffusion on self similar curves in two dimensions. The scaling properties of the mean square displacement and mean first passage time of the ballistic motion, fractional Brownian motion and subordinated walk on different fractal curves (loop erased random walk, harmonic explorer and percolation front) are derived. We also define natural parametrized subordinated Schramm Loewner evolution (NS-SLE) as a mathematical tool that can model diffusion on fractal curves. The scaling properties of the mean square displacement and mean first passage time for NS-SLE are obtained by numerical means.Comment: 8 pages, 3 figure

Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network

Based on an analysis of the short range chemical environment of each atom in a system, standard machine learning based approaches to the construction of interatomic potentials aim at determining directly the central quantity which is the total energy. This prevents for instance an accurate description of the energetics of systems where long range charge transfer is important as well as of ionized systems. We propose therefore not to target directly with machine learning methods the total energy but an intermediate physical quantity namely the charge density, which then in turn allows to determine the total energy. By allowing the electronic charge to distribute itself in an optimal way over the system, we can describe not only neutral but also ionized systems with unprecedented accuracy. We demonstrate the power of our approach for both neutral and ionized NaCl clusters where charge redistribution plays a decisive role for the energetics. We are able to obtain chemical accuracy, i.e. errors of less than a milli Hartree per atom compared to the reference density functional results. The introduction of physically motivated quantities which are determined by the short range atomic environment via a neural network leads also to an increased stability of the machine learning process and transferability of the potential.Comment: 4 figure

Moment problem for symmetric algebras of locally convex spaces

It is explained how a locally convex (lc) topology $\tau$ on a real vector space $V$ extends to a locally multiplicatively convex (lmc) topology $\overline{\tau}$ on the symmetric algebra $S(V)$. This allows the application of the results on lmc topological algebras obtained by Ghasemi, Kuhlmann and Marshall to obtain representations of $\overline{\tau}$-continuous linear functionals $L: S(V)\rightarrow \mathbb{R}$ satisfying $L(\sum S(V)^{2d}) \subseteq [0,\infty)$ (more generally, $L(M) \subseteq [0,\infty)$ for some $2d$-power module $M$ of $S(V)$) as integrals with respect to uniquely determined Radon measures $\mu$ supported by special sorts of closed balls in the dual space of $V$. The result is simultaneously more general and less general than the corresponding result of Berezansky, Kondratiev and \v Sifrin. It is more general because $V$ can be any lc topological space (not just a separable nuclear space), the result holds for arbitrary $2d$-powers (not just squares), and no assumptions of quasi-analyticity are required. It is less general because it is necessary to assume that $L : S(V) \rightarrow \mathbb{R}$ is $\overline{\tau}$-continuous (not just continuous on each homogeneous part of $S(V)$).Comment: 19 pages, revised according to referee's comments, updated references, to appear in Integral Equations and Operator Theor

The Influence of Anton Chekhov on Samuel Beckett: Inaction and Investment of Hope Into Godot-like Figures in Three Sisters and Waiting for Godot

Anton Chekhov has been very much influential on modern drama, especially on the Theatre of the Absurd; however, not much work has been done on his influence on the absurdist playwrights. Considering Harold Bloom's definition of ‘influence'—writing “much like” someone in the past—the seminal influence of Chekhov on Beckett is studied in this article. Chekhov in his plays, especially his major plays, very much like Beckett's waiting for Godot, portrays people who are passively waiting and investing their entire hope into Godot-like figures without taking any action. Thus, the sense of ennui, desperation and consequently disappointment of these characters originates from their unreasonable inaction, stagnancy and their passivity while waiting, rather than ‘waiting for Godot figures'. This article tries to show the influence of Chekhov on Samuel Beckett, investigating the similarities in form, atmosphere and theme between Waiting for Godot, the paradigm of the Theatre of the Absurd, and Three Sisters, one of Chekhov's major play

Importance of analyzing the genomic instability in stem cell-based therapies

Stem cells are the main component in cell-based therapies and regenerative medicine to replace damaged tissues and cure various diseases. In regenerative medicine, in vitro stem cells’ culture is required for proliferation and differentiation. Although the risk of using these cells has not been established; but in addition to the possibility of spontaneous differentiation of undifferentiated cells after transplantation and teratoma formation, genome of these cells in culture media is instable and can be changed. Genomic instability can affect the transplantation safety of these cells or tissues derived from them. Genomic instability is one of the common features in stem cells and cancer. Hence, there is concern that the genomic instability during the manipulation of stem cells can be tumorigenic. Genomic instabilities are included in different sizes from point mutation to aneuploidy and mosaicism. Types of stem cells, culture conditions and some manipulation of cells such a long time are effective in creation and the rate of these instabilities. Therefore, in addition to optimizing the time and culture conditions, it is recommended to examine and follow the genomic abnormalities before therapeutic uses with appropriate methods

The effects of orientation of an inclined enclosure on laminar natural convection

Natural convective laminar flow is numerically investigated in a two-dimensional and square enclosure at various angles of inclination respect to horizontal. Two adjacent walls of the enclosure are insulated and the other two are kept at different temperatures. The influence of Rayleigh number representing the effects due to the differential heating of the enclosure walls as well as the effect of inclination angle on natural convection flow are studied. The flow field and isothermal lines show different patterns at high Rayleigh numbers. The average Nusselt number, maximum stream function and average temperature appear to be a little affected by the inclination angle at low Rayleigh numbers. However, as the Rayleigh numbers rises, these parameters behave differently at various inclination angles. In this study, the effects of inclination on the temperature along the centerline of the enclosure and the local Nusselt number along the cold wall are also examined. The results show negligible effects of inclination angle at low Rayleigh numbers and considerable effects at high Rayleigh numbers