Stability of densities for perturbed Diffusions and Markov Chains

We are interested in studying the sensitivity of diffusion processes or their approximations by Markov Chains with respect to a perturbation of the coefficients.Comment: 26 page

PROSPECTS OF NANOTECHNOOGIES IN AEROENGINE CONTRUCTION

Here are considered the main aspects of the nanotechnology application in the production of aircraft gas turbine engines. Here are presented possibilities of synthesis technology of the thermal barrier coating on cooled turbine blades of next generation GTE, technology of nanostructured multilayer coatings for metal cutting tools. Here is made actual the issue of industrial production of leucosapphire single crystals. In conclusion, here are presented competence-based personnel training educational programs for nanoindustry companies

Role of Repressors in Fine Regulation of Development: Sxl and Its New Repressors Hey and Myc

In Drosophila, XX embryos express Sxl from the early promoter, SxlPe, and become females. At the same time, XY embryos with only one X chromosome become males. I investigated the role of repression in the establishment of the strict regulation of SxlPe. I found that the co-repressor Groucho, is responsible for amplification of the two-fold difference in X-encoded activator genes into an all-or-nothing difference in Sxl expression. Three new basic helix-loop-helix repressors of Sxl were identified: Hey, Cwo and the prooncogene Myc, all of which are maternally supplied. I have shown that Myc specific repression is important as early as cycle 10, which is 2 cycles earlier than the onset of normal Sxl expression

Maladaptive reactions of internship doctors during the period of adaptation to professional activities

Vyun Valeriy V., Kozhina Anna M. Maladaptive reactions of internship doctors during the period of adaptation to professional activities. Journal of Education, Health and Sport. 2017;7(2):612-617. eISSN 2391-8306. DOI http://dx.doi.org/10.5281/zenodo.825200 http://ojs.ukw.edu.pl/index.php/johs/article/view/4606 The journal has had 7 points in Ministry of Science and Higher Education parametric evaluation. Part B item 1223 (26.01.2017). 1223 Journal of Education, Health and Sport eISSN 2391-8306 7 © The Author (s) 2017; This article is published with open access at Licensee Open Journal Systems of Kazimierz Wielki University in Bydgoszcz, Poland Open Access. This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. This is an open access article licensed under the terms of the Creative Commons Attribution Non Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted, non commercial use, distribution and reproduction in any medium, provided the work is properly cited. This is an open access article licensed under the terms of the Creative Commons Attribution Non Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted, non commercial use, distribution and reproduction in any medium, provided the work is properly cited. The authors declare that there is no conflict of interests regarding the publication of this paper. Received: 02.02.2017. Revised 24.02.2017. Accepted: 27.02.2017. MALADAPTIVE REACTIONS OF INTERNSHIP DOCTORS DURING THE PERIOD OF ADAPTATION TO PROFESSIONAL ACTIVITIES Valeriy V. Vyun, Anna M. Kozhina Kharkiv National Medical University, Ukraine e-mail: [email protected] Abstract During the work on the basis of a systematic approach to the study of mechanisms of psychological adaptation of the internship doctors to the profession has developed a system of medical and psychological support during the specialist professional training. It was found that in the period of adaptation to professional activity by internship doctors marked asthenic, hypersthenic, apathetic, depressed, addictive and psychosomatic options of maladaptive reactions. Developed and tested system of medical and psychological support to the doctor in the period of adaptation to professional activity, which includes: a program of psychological and psychosocial training, system of psychological counseling for internship doctors. The results of the 3-year follow-up monitoring indicate a high efficiency of the proposed system of medical and psychological support to the doctor in the period of adaptation to the professional activity. Key words: internship doctor, professional activity, psychological adaptation, medical-and-psychological support

Role of Repressors in Fine Regulation of Development: Sxl and Its New Repressors Hey and Myc

In Drosophila, XX embryos express Sxl from the early promoter, SxlPe, and become females. At the same time, XY embryos with only one X chromosome become males. I investigated the role of repression in the establishment of the strict regulation of SxlPe. I found that the co-repressor Groucho, is responsible for amplification of the two-fold difference in X-encoded activator genes into an all-or-nothing difference in Sxl expression. Three new basic helix-loop-helix repressors of Sxl were identified: Hey, Cwo and the prooncogene Myc, all of which are maternally supplied. I have shown that Myc specific repression is important as early as cycle 10, which is 2 cycles earlier than the onset of normal Sxl expression

Parametrix Method and its Applications in Probability Theory

The present thesis investigates applications and developments of the parametrix technique. The parametrix technique comes from the theory of ODEs. Now it reformulates as a continuity technique that provides a formal representation for the density of the SDE's solutions in terms of infinite series involving the density of another, simpler, Markov process. Although the method itself has been known for many years there are still many open problems. The project is divided into three parts. Firstly, we are going to introduce the parametrix method for diffusions and Markov chains in general settings. After presenting main concepts and objects we emphasize that the technique can be fruitfully used also in case of non-smooth coeffcients. Secondly, we study the sensitivity of densities of non-degenerate diffusion processes and related Markov Chains with respect to a perturbation of the coeffcients. Natural applications of these results appear, for example, in models with misspecifed coeffcients or for the investigation of the weak error of the Euler scheme with irregular coeffcients. The stability controls have been derived under Hölder continuity assumptions on coeffcients regularity only. Continuing the research, V. Konakov and S. Menozzi applied the results mentioned above to study the weak error of the Euler scheme approximations in their paper[V. Konakov, S. Menozzi, 2017, Weak Error for the Euler Scheme Approximation of Diffusions with non-smooth coeffcients]. Motivated by these extensions, we continue with the most challenging and diffcult part - the weak and global error controls for the case of rough coefficients to Kolmogorov's degenerate SDEs in the last part of the thesis. Such equations were first introduced in 1933 by Kolmogorov. Adapting the techniques, introduced in the paper written by V. Konakov, S Menozzi and S. Molchanov in 2010 (where authors considered Lipschitz coefficients), it is now possible to investigate the Holder settings for degenerate Kolmogorov diffusions. To specify the notation of the weak and global error in our framework, we also introduce the specific version of the Euler scheme for the degenerate Kolmogorov equation, which can be also seen as an Ito process. The sensitivity analysis which we need to prove controls for the weak end global errors naturally extends from the non-degenerate case to the degenerate framework. However, some structural difficulties appear due to the different time scales for the first and the second space variable of the transition density. These aspects can be also found in the published article [A. Kozhina, 2016, Stability of densities for perturbed degenerate diffusions]. One of the key results in the last part provides the weak error controls for degenerate diffusions with non-smooth coefficients. To derive that we have proved the heat kernel derivatives bounds with respect to a non-degenerate first component of the transition density. Up to the best of our knowledge, these are the first pointwise bounds obtained on the derivatives w.r.t. the non-degenerate variables under the sole Hölder continuity assumption on the coefficients. They extend the well-known controls derived by Il'in et al. in 1962 to Kolmogorov diffusions. Investigating the quantitative behaviour of the derivatives w.r.t. the degenerate variable under minimal smoothness assumptions remains a very interesting and open problem. Finally, we studied the controls for the direct difference of transition densities of the diffusion and the Markov chain. Unfortunately, when handling directly the difference of the densities we cannot avoid to control sensitivities of the kernels w.r.t. to the degenerate variable. Such sensitivities lead to higher time singularities and make the unbounded transport term appear. The higher time-singularities yield the stated restriction on the Hölder exponent in our assumptions on the coefficients

Maternal Groucho and bHLH repressors amplify the dose-sensitive X chromosome signal in Drosophila sex determination

AbstractIn Drosophila, XX embryos are fated to develop as females, and XY embryos as males, because the diplo-X dose of four X-linked signal element genes, XSEs, activates the Sex-lethal establishment promoter, SxlPe, whereas the haplo-X XSE dose leaves SxlPe off. The threshold response of SxlPe to XSE concentrations depends in part on the bHLH repressor, Deadpan, present in equal amounts in XX and XY embryos. We identified canonical and non-canonical DNA-binding sites for Dpn at SxlPe and found that cis-acting mutations in the Dpn-binding sites caused stronger and earlier Sxl expression than did deletion of dpn implicating other bHLH repressors in Sxl regulation. Maternal Hey encodes one such bHLH regulator but the E(spl) locus does not. Elimination of the maternal corepressor Groucho also caused strong ectopic Sxl expression in XY, and premature Sxl activation in XX embryos, but Sxl was still expressed differently in the sexes. Our findings suggest that Groucho and associated maternal and zygotic bHLH repressors define the threshold XSE concentrations needed to activate SxlPe and that they participate directly in sex signal amplification. We present a model in which the XSE signal is amplified by a feedback mechanism that interferes with Gro-mediated repression in XX, but not XY embryos