Coarse distinguishability of graphs with symmetric growth

Let $X$ be a connected, locally finite graph with symmetric growth. We prove that there is a vertex coloring $\phi\colon X\to\{0,1\}$ and some $R\in\mathbb{N}$ such that every automorphism $f$ preserving $\phi$ is $R$-close to the identity map; this can be seen as a coarse geometric version of symmetry breaking. We also prove that the infinite motion conjecture is true for graphs where at least one vertex stabilizer $S_x$ satisfies the following condition: for every non-identity automorphism $f\in S_x$, there is a sequence $x_n$ such that $\lim d(x_n,f(x_n))=\infty$

Some examples of first exit times

The purpose of this article is to compute the expected first exit times of Brownian motion from a variety of domains in the Euclidean plane and in the hyperbolic plane

On turbulent relations

This paper extends the theory of turbulence of Hjorth to certain classes of equivalence relations that cannot be induced by Polish actions. It applies this theory to analyze the quasi-isometry relation and finite Gromov-Hausdorff distance relation in the space of isometry classes of pointed proper metric spaces, called the Gromov space.Ministerio de Ciencia e Innovación, Proyectos MTM2011-25656 and MTM2008-02640.S

The Witten deformation of the Dolbeault complex

We introduce a Witten-Novikov type perturbation $\bar\partial_{\bar\omega}$ of the Dolbeault complex of any complex K\"ahler manifold, defined by a form $\omega$ of type $(1,0)$ with $\partial\omega=0$. We give an explicit description of the associated index density which shows that it exhibits a nontrivial dependence on $\omega$. The heat invariants of lower order are shown to be zero.Projects MTM2016-75897-P and MTM2017-89686-P (AEI/FEDER, UE).S

Transversal Hard Lefschetz theorem on transversely symplectic foliations

This is a pre-copyedited, author-produced version of an article accepted for publication in The Quarterly Journal of Mathematics following peer review. The version of record Jesús A Álvarez López, Seoung Dal Jung, Transversal Hard Lefschetz Theorem on Transversely Symplectic Foliations, The Quarterly Journal of Mathematics, Volume 72, Issue 4, December 2021, Pages 1235–1251 is available online at: https://doi.org/10.1093/qmath/haaa071We study the transversal hard Lefschetz theorem on a transversely symplectic foliation. This article extends the results of transversally symplectic flows (H.K. Pak, “Transversal harmonic theory for transversally symplectic flows”, J. Aust. Math. Soc. 84 (2008), 233–245) to general transversely symplectic foliations.FEDER/Ministerio de Ciencia, Innovación y Universidades/AEI/MTM2017-89686-P, Xunta de Galicia/2015 GPC GI-1574 [A.L]; National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2018R1A2B2002046) [D.J.].S

A Perturbation of the Dunkl Harmonic Oscillator on the Line

Let Jσ be the Dunkl harmonic oscillator on R (σ>−1/2. For 00, it is proved that, if σ>u−1/2, then the operator U=Jσ+ξ|x|−2u, with appropriate domain, is essentially self-adjoint in L2(R,|x|2σdx), the Schwartz space S is a core of U¯¯¯¯1/2, and U¯¯¯¯ has a discrete spectrum, which is estimated in terms of the spectrum of Jσ¯¯¯¯¯. A generalization Jσ,τ of Jσ is also considered by taking different parameters σ and τ on even and odd functions. Then extensions of the above result are proved for Jσ,τ, where the perturbation has an additional term involving, either the factor x−1 on odd functions, or the factor x on even functions. Versions of these results on R+ are derivedThe first author was partially supported by MICINN, Grants MTM2011-25656 and MTM2014-56950-P, and by Xunta de Galicia, Grant Consolidación e estructuración 2015 GPC GI-1574. The third author has received financial support from the Xunta de Galicia and the European Union (European Social Fund - ESF)S

A new approach to the synthesis of 2-aminoimidazo[1,2-a]pyridine derivatives through microwave-assisted N-alkylation of 2-halopyridines

A microwave (focused waves) assisted N-alkylation of 2-halopyridines provides a convenient entry to 2-amino-imidazo[1,2-a]pyridine derivatives after reaction of the alkylated substrates with cyanamide under basic conditions.CDTI program (Plan concertado 96/0036)PROFARMA program (Ministerio de Industria y Ministerio de Sanidad

Short synthesis and anti-rhinoviral activity of imidazo[1,2-a]pyridines: the effect of acyl groups at 3-position

Various 2-amino-3-acyl-6-[(E)-1-phenyl-2-N-methylcarbamoylvinyl]-imidazo[1,2-a]pyridines, structurally related to Enviroxime were prepared to determine the effect of acyl groups on the antirhinoviral activity. A short and efficient means for the construction of the imidazo nucleus as well as biological evaluation of the final compounds are disclosed.This research was supported by a CDTI program (Plan concertado 96/0036) and the Spanish Farma III programme (Ministerio de Industria y Ministerio de Sanidad). We are also grateful to the Lilly Rhinovirus Action Group for their advice and interest in this work

Measuring data‑centre workfows complexity through process mining: the Google cluster case

Data centres have become the backbone of large Cloud services and applica-tions, providing virtually unlimited elastic and scalable computational and storage resources. The search for the efficiency and optimisation of resources is one of the current key aspects for large Cloud Service Providers and is becoming more and more challenging, since new computing paradigms such as Internet of Things, Cyber-Physical Systems and Edge Computing are spreading. One of the key aspects to achieve efficiency in data centres consists of the discovery and proper analysis of the data-centre behaviour. In this paper, we present a model to automatically retrieve execution workflows of existing data-centre logs by employing process mining tech-niques. The discovered processes are characterised and analysed according to the understandability and complexity in terms of execution efficiency of data-centre jobs. We finally validate and demonstrate the usability of the proposal by applying the model in a real scenario, that is, the Google Cluster tracesMinisterio de Ciencia y Tecnología RTI2018–094283-B-C33Ministerio de Ciencia y Tecnología RTI2018-098062-A-I00Universidad de Sevilla 2018/0000052