Asymptotic solutions for linear ODEs with not-necessarily meromorphic coefficients: a Levinson type theorem on complex domains, and applications

In this paper, we consider systems of linear ordinary differential equations, with analytic coefficients on big sectorial domains, which are asymptotically diagonal for large values of $|z|$. Inspired by N. Levinson's work [Lev48], we introduce two conditions on the dominant diagonal term (the $L$-$condition$) and on the perturbation term (the $good\,\,decay\,\,condition$) of the coefficients of the system, respectively. Under these conditions, we show the existence and uniqueness, on big sectorial domains, of an $asymptotic$ fundamental matrix solution, i.e. asymptotically equivalent (for large $|z|$) to a fundamental system of solutions of the unperturbed diagonal system. Moreover, a refinement (in the case of subdominant solutions) and a generalization (in the case of systems depending on parameters) of this result are given. As a first application, we address the study of a class of ODEs with not-necessarily meromorphic coefficients. We provide sufficient conditions on the coefficients ensuring the existence and uniqueness of an asymptotic fundamental system of solutions, and we give an explicit description of the maximal sectors of validity for such an asymptotics. Furthermore, we also focus on distinguished examples in this class of ODEs arising in the context of open conjectures in Mathematical Physics relating Integrable Quantum Field Theories and affine opers ($ODE/IM\,\,correspondence$). Our results fill two significant gaps in the mathematical literature pertaining to these conjectural relations. As a second application, we consider the classical case of ODEs with meromorphic coefficients. Under an $adequateness$ condition on the coefficients, we show that our results reproduce (with a shorter proof) the main asymptotic existence theorems of Y. Sibuya [Sib62, Sib68] and W. Wasow [Was65] in their optimal refinements.Comment: 43 pages, 7 figure

Results on the extension of isomonodromy deformations to the case of a resonant irregular singularity

We explain some results of [G. Cotti, B. A. Dubrovin and D. Guzzetti, Isomonodromy deformations at an irregular singularity with coalescing eigenvalues, preprint (2017); arXiv:1706.04808.], discussed in our talk [G. Cotti, Monodromy of semisimple Frobenius coalescent structures, in Int. Workshop Asymptotic and Computational Aspects of Com- plex Differential Equations, CRM, Pisa, February 13\u201317, (2017).] in Pisa, February 2017. Consider an n 7 n linear system of ODEs with an irregular singularity of Poincar \u301e rank 1 at z = 1e and Fuchsian singularity at z = 0, holomorphically depending on parameter t within a polydisk in Cn centered at t = 0. The eigenvalues of the leading matrix at 1e, which is diagonal, coalesce along a coalescence locus 06 contained in the polydisk. Under minimal vanishing conditions on the residue matrix at z = 0, we show in [G. Cotti, B. A. Dubrovin and D. Guzzetti, Isomonodromy deformations at an irregular singular- ity with coalescing eigenvalues, preprint (2017); arXiv:1706.04808.] that isomonodromic deformations can be extended to the whole polydisk, including 06, in such a way that the fundamental matrix solutions and the constant monodromy data are well defined in the whole polydisk. These data can be computed just by considering the system at point of 06, where it simplifies. Conversely, if the t-dependent system is isomonodromic in a small domain contained in the polydisk not intersecting 06, and if suitable entries of the Stokes matrices vanish, then 06 is not a branching locus for the fundamental matrix solutions. The results have applications to Frobenius manifolds and Painlev \u301e equations

Linked education: interlinking educational resources and the web of data

Research on interoperability of technology-enhanced learning (TEL) repositories throughout the last decade has led to a fragmented landscape of competing approaches, such as metadata schemas and interface mechanisms. However, so far Web-scale integration of resources is not facilitated, mainly due to the lack of take-up of shared principles, datasets and schemas. On the other hand, the Linked Data approach has emerged as the de-facto standard for sharing data on the Web and offers a large potential to solve interoperability issues in the field of TEL. In this paper, we describe a general approach to exploit the wealth of already existing TEL data on the Web by allowing its exposure as Linked Data and by taking into account automated enrichment and interlinking techniques to provide rich and well-interlinked data for the educational domain. This approach has been implemented in the context of the mEducator project where data from a number of open TEL data repositories has been integrated, exposed and enriched by following Linked Data principles

Local Moduli of Semisimple Frobenius Coalescent Structures

We extend the analytic theory of Frobenius manifolds to semisimple points with coalescing eigenvalues of the operator of multiplication by the Euler vector field. We clarify which freedoms, ambiguities and mutual constraints are allowed in the definition of monodromy data, in view of their importance for conjectural relationships between Frobenius manifolds and derived categories. Detailed examples and applications are taken from singularity and quantum cohomology theories. We explicitly compute the monodromy data at points of the Maxwell Stratum of the $A_3$-Frobenius manifold, as well as at the small quantum cohomology of the Grassmannian $mathbb G_2ig(mathbb C^4ig)$. In the latter case, we analyse in details the action of the braid group on the monodromy data. This proves that these data can be expressed in terms of characteristic classes of mutations of Kapranov's exceptional 5-block collection, as conjectured by one of the authors

Experimental Evaluation of a LoRa Wildlife Monitoring Network in a Forest Vegetation Area

Smart agriculture and wildlife monitoring are one of the recent trends of Internet of Things (IoT) applications, which are evolving in providing sustainable solutions from producers. This article details the design, development and assessment of a wildlife monitoring application for IoT animal repelling devices that is able to cover large areas, thanks to the low power wide area networks (LPWAN), which bridge the gap between cellular technologies and short range wireless technologies. LoRa, the global de-facto LPWAN, continues to attract attention given its open specification and ready availability of off-the-shelf hardware, with claims of several kilometers of range in harsh challenging environments. At first, this article presents a survey of the LPWAN for smart agriculture applications. We proceed to evaluate the performance of LoRa transmission technology operating in the 433 MHz and 868 MHz bands, aimed at wildlife monitoring in a forest vegetation area. To characterize the communication link, we mainly use the signal-to-noise ratio (SNR), received signal strength indicator (RSSI) and packet delivery ratio (PDR). Findings from this study show that achievable performance can greatly vary between the 433 MHz and 868 MHz bands, and prompt caution is required when taking numbers at face value, as this can have implications for IoT applications. In addition, our results show that the link reaches up to 860 m in the highly dense forest vegetation environment, while in the not so dense forest vegetation environment, it reaches up to 2050 m

Building the Web of Things with WS-BPEL and Visual Tags. Web of Things using Service-oriented Architecture standards

The Web of things is an emerging scenario in which everyday objects are connected to the Internet and can answer to HTTP queries with structured data. This paper presents a system that allows users to build networks of everyday objects using visual tags as proximity technology. The system backend is based on Service-oriented Architecture languages and tools for the runtime composition of “things” establishing connections we call hyperpipes.357-36

A Machine Learning Framework for Scalable Routing and Wavelength Assignment in Large Optical Networks

We perform a machine-learning-based network pruning that significantly reduces the complexity of routing and wavelength assignment in large optical networks. A significant computational time reduction is achieved by accepting a minor deterioration of the obtained solution

What does critical temperature tell us about the resistance of polar lichens to freezing stress? Applicability of linear cooling method to ecophysiological studies.

Lichens from polar regions are well adapted to low temperature and considered cryoresistant. However, interspecific differences in their cryoresistance exist according to the degree of their adaptation and severity of the environment. In our study, we applied linear cooling technique in order to evaluate the interspecific differences in several lichen species. Thalli segments of Umbilicaria antarctica, Nephroma antarctica, Placopsis contortuplicata and Lasallia pustulata were exposed to the cooling from 20 to –35°C at a constant rate of 2°C min-1. Simultaneously with the cooling, chlorophyll fluorescence parameters evaluating potential (FV/FM) and effective yield of primary photochemical processes in PSII (FPSII) were measured in 30 s interval. Temperature response curves of FV/FM and FPSII formed typical S-curves that were species specific. Critical temperature (cooling point at which FPSII equals 0), was found in a narrow range of –25 to –28°C, suggesting that all experimental lichen species have a high resistance to sub-zero temperatures. The method of linear cooling used in this study has proven its applicability in ecophysiological studies since it is sensitive enough for the evaluation of species-specific differences in cryoresistance. This study describes different parameters that can be derived from the S-curves and discuss their proper use in ecophysiological and stress physiology studies