Static and Dynamical, Fractional Uncertainty Principles

We study the process of dispersion of low-regularity solutions to the Schrödinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get a lower bound for the concentration of mass. We consider also the evolution when the initial datum is the Dirac comb in $\mathbb{R}$. In this case we find fluctuations that concentrate at rational times and that resemble a realization of a Lévy process. Furthermore, the evolution exhibits multifractality

The Frisch–Parisi formalism for fluctuations of the Schrödinger equation

We consider the solution of the Schrödinger equation $u$ in $\mathbb{R}$ when the initial datum tends to the Dirac comb. Let $h_{\text{p}, \delta}(t)$ be the fluctuations in time of $\int\lvert x \rvert^{2\delta}\lvert u(x,t) \rvert^2\,dx$, for $0 < \delta < 1$, after removing a smooth background. We prove that the Frisch--Parisi formalism holds for $H_\delta(t) = \int_{[0,t]}h_{\text{p}, \delta}(2s)\,ds$, which is morally a simplification of the Riemann's non-differentiable curve $R$. Our motivation is to understand the evolution of the vortex filament equation of polygonal filaments, which are related to $R$.BERC 2022-2025, FJC2019-039804-I, RYC2018-025477-I, Ikerbasque, PGC2018-094522-B-I0

Nutrition is Perceived as an Ecosystem Service of the Mangrove by Rural People in Ecuador

The mangrove ecosystem is considered as the source of livelihood, particularly for coastal areas. This study explores the perception of the inhabitants of Puerto El Morro and the island of Costa Rica (Ecuador) against the ecosystem services of the mangrove. Seven quantitative variables were used on the Likert scale by performing exploratory factor analysis. The results were based on a sample of 94 participants finding 2 factors, tourism (29.07% of variance) and nutritious food production (25.45% of variance remaining). The reliability of the questionnaire was acceptable according to Cronbach’s Alpha 0.654. A confirmatory factor analysis is necessary to revalidate the items of the factors. Keywords: coastal communities, eating, mangroves, livelihoods, nutrition. Resumen El ecosistema de manglar se considera fuente de medios de vida, en particular para zonas costeras. Este estudio explora la percepción de los habitantes de Puerto El Morro y la isla Costa Rica (Ecuador) frente a los servicios ecosistémicos del manglar. Se utilizaron 7 variables cuantitativas en escala de Likert realizando análisis factorial exploratorio. Los resultados parten de una muestra de 94 participantes, hallando 2 factores: turismo (29,07% de varianza) y producción alimentos nutritivos (25,45% de varianza restante). La confiabilidad del cuestionario fue aceptable según el Alfa de Cronbach 0.654. Es necesario un análisis factorial confirmatorio para revalidar los ítems de los factores. Palabras Clave: comunidades costeras; alimentación; manglares; medios de vida; nutrición

Claim Reserving via Inverse Probability Weighting: A Micro-Level Chain-Ladder Method

Claim reserving is primarily accomplished using macro-level models, with the Chain-Ladder method being the most widely adopted method. These methods are usually constructed heuristically and rely on oversimplified data assumptions, neglecting the heterogeneity of policyholders, and frequently leading to modest reserve predictions. In contrast, micro-level reserving leverages on stochastic modeling with granular information for improved predictions, but usually comes at the cost of more complex models that are unattractive to practitioners. In this paper, we introduce a simple macro-level type approach that can incorporate granular information from the individual level. To do so, we imply a novel framework in which we view the claim reserving problem as a population sampling problem and propose a reserve estimator based on inverse probability weighting techniques, with weights driven by policyholders' attributes. The framework provides a statistically sound method for aggregate claim reserving in a frequency and severity distribution-free fashion, while also incorporating the capability to utilize granular information via a regression-type framework. The resulting reserve estimator has the attractiveness of resembling the Chain-Ladder claim development principle, but applied at the individual claim level, so it is easy to interpret and more appealing to practitioners

Finite element models for brush-debris interaction in road sweeping

In this paper, 2-D and 3-D finite element (FE) models for particle removal mechanisms are constructed to study the interaction between brush tines and debris in road sweeping processes. A 2-D contact FE analysis is first performed to analyse the contact behaviour between a flicking brush tine and an object to sweep. Using this model, the removal mechanisms are studied and analysed. Furthermore, the effect of brush penetration on debris removal is investigated. The 2-D sweeping model is extended to an accurate 3-D contact model, which overcomes some geometric errors in the 2-D model. From the results, it is suggested that the major removal mechanisms are a horizontal dragging force and a rolling moment generated by the external forces. It is also found that penetration has a positive contribution when it is relatively small in a non-sticky environment. Furthermore, in this environment, it is found that sweeping loads have a small effect on the removal process as either flicking tines or cutting tines can produce adequate removal loads

Synthesis of novel sulfide-based cyclic peptidomimetic analogues to solonamides

Eight new sulfide-based cyclic peptidomimetic analogues of solonamides A and B have been synthesized via solid-phase peptide synthesis and SN2’ reaction on a Morita–Baylis–Hillman (MBH) residue introduced at the N-terminal of a tetrapeptide. This last step takes advantage of the electrophilic feature of the MBH residue and represents a new cyclization strategy occurring. The analogues were prepared in moderate overall yields and did not show toxic effects on Staphylococcus aureus growth and were not toxic to human fibroblasts. Two of them inhibited the hemolytic activity of S. aureus, suggesting an interfering action in the bacterial quorum sensing similar to the one already reported for solonamides.This work has been supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) - Finance Code 001, Conselho Nacional de Desen-volvimento Científico e Tecnológico – Brasil (CNPq) – J. B-V graduate fellow and L. A. M. undergraduate fellow, Fundação de Apoio à Pesquisa do Distrito Federal – Brasil 0193.001.560/ 2017, Decanato de Pesquisa e Pós-graduação (DPG-UnB). We also acknowledge Prof. Dr. Guilherme D. Brand (IQ-UnB), Prof. Dr. Carlos K. Z. Andrade (IQ-UnB), Prof. Dr. Peter Bakuzis (IQ-UnB), Departamento de Polícia Federal (SEPLAB-INC-DPF) and CAIQ-UnB