Resurgence of refined topological strings and dual partition functions

We study the resurgent structure of the refined topological string partition function on a non-compact Calabi-Yau threefold, at large orders in the string coupling constant $g_s$ and fixed refinement parameter $b$. For $b\neq 1$, the Borel transform admits two families of simple poles, corresponding to integral periods rescaled by $b$ and $1/b$. We show that the corresponding Stokes automorphism is expressed in terms of a generalization of the non-compact quantum dilogarithm, and we conjecture that the Stokes constants are determined by the refined DT invariants counting spin-$j$ BPS states. This jump in the refined topological string partition function is a special case (unit five-brane charge) of a more general transformation property of wave functions on quantum twisted tori introduced in earlier work by two of the authors. We show that this property follows from the transformation of a suitable refined dual partition function across BPS rays, defined by extending the Moyal star product to the realm of contact geometry.Comment: 33 pages, 1 figur

Конкурсы в Иркутске

The article presents the open architectural competitions for the projects of the Concert Hall on Tsesovskaya Embankment in Irkutsk and their results. The competitions are focused on preservation and development of the unique historical environment of the city, as well as on raising the rating of Irkutsk as a cultural center. The article describes the siting requirements for the Concert Hall and the characteristics of town-planning solutions for both projects.Рассматриваются организация и результаты открытых архитектурных конкурсов на проекты концертного зала и Цесовской набережной, прошедших в Иркутске. Подчеркивается, что их целью является сохранение и развитие уникальной исторической среды города, повышение рейтинга Иркутска как культурного центра. Описываются требования к размещению концертного зала и характер градостроительных решений обоих проектов

Nanosized vertical nanosheets made of molybdenum disulphide: Electrical and optoelectronic properties

In the paper, the results of the studies in the electrical and optoelectronic properties of vertical sheets made of MoS2 have been presented for the first time. These objects are characterized by a high surface area, exposed edges, reasonable carrier mobility values and high light absorptance. Samples with an average size of about 150 nm were grown by the one-stage metal-organic chemical vapor deposition (MOCVD) technique. Vertically oriented MoS2 sheets were investigated using the scanning electron and X-ray photoelectron microscopy, the X-ray diffraction and Raman spectroscopy. I-V characteristics of the samples were obtained as well. Optoelectronic properties of the samles were studied using an argon laser (operates at a wavelength of 513 nm) with a mechanical light modulator. An analysis of the obtained results allows us to state that the studied V-MoS2 sheets should be considered as a very promising material for optoelectronics needs

KP integrability through the x−yx-y swap relation

We discuss a universal relation that we call the $x-y$ swap relation, which plays a prominent role in the theory of topological recursion, Hurwitz theory, and free probability theory. We describe in a very precise and detailed way the interaction of the $x-y$ swap relation and KP integrability. As an application, we prove a recent conjecture that relates some particular instances of topological recursion to the Mironov-Morozov-Semenoff matrix integrals.Comment: 27 pages; minor correction

Log topological recursion through the prism of x−yx-y swap

We introduce a new concept of logarithmic topological recursion that provides a patch to topological recursion in the presence of logarithmic singularities and prove that this new definition satisfies the universal $x-y$ swap relation. This result provides a vast generalization and a proof of a very recent conjecture of Hock. It also uniformly explains (and conceptually rectifies) an approach to the formulas for the $n$-point functions proposed by Hock.Comment: 30 pages; minor corrections and modifications; Section 3.11 on the new Family III of generalized double Hurwitz numbers adde

Molecular dynamics simulations of oxide memristors: crystal field effects

We present molecular-dynamic simulations of memory resistors (memristors) including the crystal field effects on mobile ionic species such as oxygen vacancies appearing during operation of the device. Vacancy distributions show different patterns depending on the ratio of a spatial period of the crystal field to a characteristic radius of the vacancy-vacancy interaction. There are signatures of the orientational order and of spatial voids in the vacancy distributions for some crystal field potentials. The crystal field stabilizes the patterns after they are formed, resulting in a non-volatile switching of the simulated devices

Nanosensitive optical coherence tomography to assess wound healing within the cornea

Optical Coherence Tomography (OCT) is a non-invasive depth resolved optical imaging modality, that enables high resolution, cross-sectional imaging in biological tissues and materials at clinically relevant depths. Though OCT offers high resolution imaging, the best ultra-high-resolution OCT systems are limited to imaging structural changes with a resolution of one micron on a single B-scan within very limited depth. Nanosensitive OCT (nsOCT) is a recently developed technique that is capable of providing enhanced sensitivity of OCT to structural changes. Improving the sensitivity of OCT to detect structural changes at the nanoscale level, to a depth typical for conventional OCT, could potentially improve the diagnostic capability of OCT in medical applications. In this paper, we demonstrate the capability of nsOCT to detect structural changes deep in the rat cornea following superficial corneal injury.Comment: 21 pages, 8 figure