Laplacians with point interactions -- expected and unexpected spectral properties

We study the one-dimensional Laplace operator with point interactions on the real line identified with two copies of the half-line $[0,\infty)$. All possible boundary conditions that define generators of $C_0$-semigroups on $L^2\big([0,\infty)\big)\oplus L^2\big([0,\infty)\big)$ are characterized. Here, the Cayley transform of the boundary conditions plays an important role and using an explicit representation of the Green's functions, it allows us to study invariance properties of semigroups

Well-Posedness and Symmetries of Strongly Coupled Network Equations

We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered interactions take place at the boundary, i. e., in the nodes of the network. We discuss well-posedness of the associated initial value problem as well as contractivity and positivity properties of its solutions. Finally, we discuss qualitative properties that can be formulated in terms of invariance of linear subspaces of the state space, i. e., of symmetries of the associated physical system. Applications to a neurobiological model as well as to a system of linear Schroedinger equations on a quantum graph are discussed.Comment: 25 pages. Corrected typos and minor change

A family of diameter-based eigenvalue bounds for quantum graphs

We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph. This extends a result of, and resolves an open problem from, [J. B. Kennedy, P. Kurasov, G. Malenov\'a and D. Mugnolo, Ann. Henri Poincar\'e 17 (2016), 2439--2473, Section 7.2], and also complements an analogous lower bound for the corresponding eigenvalue of the combinatorial Laplacian on a discrete graph. We also give a family of corresponding lower bounds for the higher eigenvalues under the assumption that the total length of the graph is sufficiently large compared with its diameter. These inequalities are sharp in the case of trees.Comment: Substantial revision of v1. The main result, originally for the first eigenvalue, has been generalised to the higher ones. The title has been changed and the proofs substantially reorganised to reflect the new result, and a section containing concluding remarks has been adde

Dilute acid-hydrolized cotton cellulose : An electron diffraction study

A comparative morphological investigation by electron diffraction analysis was carried out on samples of cotton cellulose from different stages of dilute-acid-catalysed hydrolytic degradation reactions. Within the range from $\overline {DP_n }$ 13000 (native material) to 500 only a gentle decrease of the relative crystallinity was observed. For $\overline {DP_n }$ below 500 the crystallinity decreases much faster, together with a simultaneous marked increase in paracrystalline lattice distortion and the show up of crystallographic evidence for a new cellulose phase which became better defined as degradation proceeded. A clearly defined parallel can be established between the different kinetic stages of the degradation reaction and the degree-of-polymerization dependence of the morphological features. The resulting evidence is at odds with the traditionally held views about the effects of acid hydrolysis of cellulose on its morphological fine structure.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

A variational approach to strongly damped wave equations

We discuss a Hilbert space method that allows to prove analytical well-posedness of a class of linear strongly damped wave equations. The main technical tool is a perturbation lemma for sesquilinear forms, which seems to be new. In most common linear cases we can furthermore apply a recent result due to Crouzeix--Haase, thus extending several known results and obtaining optimal analyticity angle.Comment: This is an extended version of an article appeared in \emph{Functional Analysis and Evolution Equations -- The G\"unter Lumer Volume}, edited by H. Amann et al., Birkh\"auser, Basel, 2008. In the latest submission to arXiv only some typos have been fixe

COVID-19-Related Social Isolation Predispose to Problematic Internet and Online Video Gaming Use in Italy

COVID-19 pandemic and its related containment measures have been associated with increased levels of stress, anxiety and depression in the general population. While the use of digital media has been greatly promoted by national governments and international authorities to maintain social contacts and healthy lifestyle behaviors, its increased access may also bear the risk of inappropriate or excessive use of internet-related resources. The present study, part of the COVID Mental hEalth Trial (COMET) study, aims at investigating the possible relationship between social isolation, the use of digital resources and the development of their problematic use. A cross sectional survey was carried out to explore the prevalence of internet addiction, excessive use of social media, problematic video gaming and binge watching, during Italian phase II (May-June 2020) and III (June-September 2020) of the pandemic in 1385 individuals (62.5% female, mean age 32.5 ± 12.9) mainly living in Central Italy (52.4%). Data were stratified according to phase II/III and three groups of Italian regions (northern, central and southern). Compared to the larger COMET study, most participants exhibited significant higher levels of severe-to-extremely-severe depressive symptoms (46.3% vs. 12.4%; p < 0.01) and extremely severe anxiety symptoms (77.8% vs. 7.5%; p < 0.01). We also observed a rise in problematic internet use and excessive gaming over time. Mediation analyses revealed that COVID-19-related general psychopathology, stress, anxiety, depression and social isolation play a significant role in the emergence of problematic internet use, social media addiction and problematic video gaming. Professional gamers and younger subjects emerged as sub-populations particularly at risk of developing digital addictions. If confirmed in larger and more homogenous samples, our findings may help in shedding light on possible preventive and treatment strategies for digital addictions

iMARS Phase 2

The file attached is the Published/publisher’s pdf version of the articl

De parásitos ubicuos: el caso de Blastocystis

Blastocystis es uno de los parásitos intestinales zoonóticos de mayor prevalencia y de distribución mundial. Es un organismo unicelular, anaerobio, cuya taxonomía ha sido motivo de estudios, controversias y revisiones. Se caracteriza por una gran variabilidad genética, con la existencia de al menos 10 genotipos o subtipos, lo que hace dificultoso su estudio y que ha llevado también a controversias en cuanto a características morfológicas, ciclo vital y su rol como patógeno tanto en una amplia variedad de animales como en humanos. El subtipo 3 es el genotipo más frecuentemente hallado en el hombre. Su potencialidad patogénica estaría asociada a un determinado subtipo que aún no se ha definido completamente por estudios moleculares. En nuestro grupo hemos efectuado relevamientos epidemiológicos a fin de detectar la presencia del parásito en diversas fuentes. En estudios sobre poblaciones infantiles en zonas periféricas de La Plata hemos hallado que sobre 408 muestras, el 45 % de ellas estaban parasitadas y el 56 % por Blastocystis.Facultad de Ciencias Veterinaria

De parásitos ubicuos: el caso de Blastocystis

Blastocystis es uno de los parásitos intestinales zoonóticos de mayor prevalencia y de distribución mundial. Es un organismo unicelular, anaerobio, cuya taxonomía ha sido motivo de estudios, controversias y revisiones. Se caracteriza por una gran variabilidad genética, con la existencia de al menos 10 genotipos o subtipos, lo que hace dificultoso su estudio y que ha llevado también a controversias en cuanto a características morfológicas, ciclo vital y su rol como patógeno tanto en una amplia variedad de animales como en humanos. El subtipo 3 es el genotipo más frecuentemente hallado en el hombre. Su potencialidad patogénica estaría asociada a un determinado subtipo que aún no se ha definido completamente por estudios moleculares. En nuestro grupo hemos efectuado relevamientos epidemiológicos a fin de detectar la presencia del parásito en diversas fuentes. En estudios sobre poblaciones infantiles en zonas periféricas de La Plata hemos hallado que sobre 408 muestras, el 45 % de ellas estaban parasitadas y el 56 % por Blastocystis.Facultad de Ciencias Veterinaria

De parásitos ubicuos: el caso de <i>Blastocystis</i>

Blastocystis es uno de los parásitos intestinales zoonóticos de mayor prevalencia y de distribución mundial. Es un organismo unicelular, anaerobio, cuya taxonomía ha sido motivo de estudios, controversias y revisiones. Se caracteriza por una gran variabilidad genética, con la existencia de al menos 10 genotipos o subtipos, lo que hace dificultoso su estudio y que ha llevado también a controversias en cuanto a características morfológicas, ciclo vital y su rol como patógeno tanto en una amplia variedad de animales como en humanos. El subtipo 3 es el genotipo más frecuentemente hallado en el hombre. Su potencialidad patogénica estaría asociada a un determinado subtipo que aún no se ha definido completamente por estudios moleculares. En nuestro grupo hemos efectuado relevamientos epidemiológicos a fin de detectar la presencia del parásito en diversas fuentes. En estudios sobre poblaciones infantiles en zonas periféricas de La Plata hemos hallado que sobre 408 muestras, el 45 % de ellas estaban parasitadas y el 56 % por Blastocystis.Facultad de Ciencias Veterinaria