Random-time processes governed by differential equations of fractional distributed order

We analyze here different types of fractional differential equations, under the assumption that their fractional order $\nu \in (0,1]$ is random\ with probability density $n(\nu).$ We start by considering the fractional extension of the recursive equation governing the homogeneous Poisson process $N(t),t>0.$\ We prove that, for a particular (discrete) choice of $n(\nu)$, it leads to a process with random time, defined as $N(\widetilde{\mathcal{T}}_{\nu_{1,}\nu_{2}}(t)),t>0.$ The distribution of the random time argument $\widetilde{\mathcal{T}}_{\nu_{1,}\nu_{2}}(t)$ can be expressed, for any fixed $t$, in terms of convolutions of stable-laws. The new process $N(\widetilde{\mathcal{T}}_{\nu_{1,}\nu_{2}})$ is itself a renewal and can be shown to be a Cox process. Moreover we prove that the survival probability of $N(\widetilde{\mathcal{T}}_{\nu_{1,}\nu_{2}})$, as well as its probability generating function, are solution to the so-called fractional relaxation equation of distributed order (see \cite{Vib}%). In view of the previous results it is natural to consider diffusion-type fractional equations of distributed order. We present here an approach to their solutions in terms of composition of the Brownian motion $B(t),t>0$ with the random time $\widetilde{\mathcal{T}}_{\nu_{1,}\nu_{2}}$. We thus provide an alternative to the constructions presented in Mainardi and Pagnini \cite{mapagn} and in Chechkin et al. \cite{che1}, at least in the double-order case.Comment: 26 page

Rank-based multi-scale entropy analysis of heart rate variability

The method of MultiScale Entropy (MSE) is an invaluable tool to quantify and compare the complexity of physiological time series at different time scales. Although MSE traditionally employs sample entropy to measure the unpredictability of each coarse-grained series, the same framework can be applied to other metrics. Here we investigate the use of a rank-based entropy measure within the MSE framework. Like in the traditional method, the series are studied in an embedding space of dimension m. The novel entropy assesses the unpredictability of the series quantifying the "amount of shuffling" that the ranks of the mutual distances between pairs of m-long vectors undergo when considering the next observation. The algorithm was tested on recordings from the Fantasia database in a time-varying fashion using non-overlapping 300-samples windows. The method was able to find statistically significant differences between young and healthy elderly subjects at 7 scales/time-windows after accounting for multiple comparisons using the Holm-Bonferroni correction. These promising results suggest the possibility of using this measure to perform a time-varying assessment of complexity with increased accuracy and temporal resolution

Spatially fractional-order viscoelasticity, non-locality and a new kind of anisotropy

Spatial non-locality of space-fractional viscoelastic equations of motion is studied. Relaxation effects are accounted for by replacing second-order time derivatives by lower-order fractional derivatives and their generalizations. It is shown that space-fractional equations of motion of an order strictly less than 2 allow for a new kind anisotropy, associated with angular dependence of non-local interactions between stress and strain at different material points. Constitutive equations of such viscoelastic media are determined. Explicit fundamental solutions of the Cauchy problem are constructed for some cases isotropic and anisotropic non-locality

The periodic repolarization dynamics index identifies changes in ventricular repolarization oscillations associated with music-induced emotions

The effect of music on cardiovascular dynamics may be useful in a variety of clinical settings. The aim of this study was to assess whether listening to music characterized by different emotional valence affected ventricular periodic repolarization dynamics (PRD), a recently-proposed non-invasive index of sympathetic ventricular modulation. The 12 lead ECG was recorded in 71 healthy volunteers exposed to six 90 s excerpts of pleasant music and unpleasant acoustic stimuli as well as six 90 s intervals of silence. A 20 s interval was allowed between excerpts during which the participants were asked to evaluate the previous excerpt. A simulation study was carried out to assess the capability of the algorithm of tracking fast small changes in PRD. The simulation study shows that the algorithm implemented in this study has a time-frequency resolution sufficient to capture the fast dynamics observed in this study. PRD were higher during listening to both pleasant and unpleasant music than during silence. There was a (weak) trend for the PRD to be higher during listening to pleasant than unpleasant music that may indicate the existence of a (weak) interaction between the valence of music-induced emotions and sympathetic ventricular response. The PRD significantly increased during the 20 s interval in between conditions, possibly reflecting a sympathetic response to the evaluation task and/or to the expectation of the following excerpt

Overlooked gall-inducing moths revisited, with the description of Andescecidium parrai gen. et sp. n. and Oliera saizi sp. n. from Chile (Lepidoptera, Cecidosidae)

There are still many gall systems associated with larvae of Lepidoptera in which the true gall-inducers have not been identified to species. Reports on misidentification of gall inducers have been recurrent for these galls, particularly in complex gall-systems that may include inquilines, kleptoparasites, and cecidophages, among other feeding guilds such as predators and parasitoid wasps. Here we describe and illustrate the adults, larvae, pupae and galls, based on light and scanning microscopy, of Andescecidium parrai gen. et sp. n. and Oliera saizi sp. n., two sympatric cecidosid moths that are associated with Schinus polygamus (Cav.) Cabrera (Anacardiaceae) in central Chile. Adults, immatures, and galls of the former did not conform to any known cecidosid genus. Galls of A. parrai are external, spherical, and conspicuous, being known for more than one century. However, their induction has been mistakenly associated with either unidentified Coleoptera (original description) or Oliera argentinana Br糨es (recently), a distinct cecidosid species with distribution restricted to the eastern Andes. Galls of O. saizi had been undetected, as they are inconspicuous. They occur under the bark within swollen stems, and may occur on the same plant, adjacent to those of A. parrai. We also propose a time-calibrated phylogeny using sequences from mitochondrial and nuclear loci, including specimens of the new proposed taxa. Thus in addition to clarifying the taxonomy of the Chilean cecidosid species we also tested their monophyly in comparison to congeneric species and putative specimens of all genera of Neotropical and African cecidosids.Fil: Silva, Gabriela T.. Universidade Federal do Rio Grande do Sul; BrasilFil: Moreira, Gilson R. P.. Universidade Federal do Rio Grande do Sul; BrasilFil: Vargas, Héctor A.. Universidad de Tarapacá de Arica; ChileFil: Gonçalves, Gislene L.. Universidade Federal do Rio Grande do Sul; Brasil. Universidad de Tarapacá de Arica; ChileFil: Mainardi, Marina D.. Universidade Federal do Rio Grande do Sul; BrasilFil: San Blas, Diego German. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Pampa; ArgentinaFil: Davis, Donald. National Museum of Natural History; Estados Unido

Differences in daptomycin and vancomycin ex vivo behaviour can lead to false interpretation of negative blood cultures

AbstractIn clinical studies on bacteraemia, the negativity of blood cultures is an important endpoint for comparing the efficacy of different therapeutic regimens. In FAN° anaerobic blood culture medium (BacT/ALERT system), daptomycin displayed increased MIC against Staphylococcus aureus and improved abolishment of its carryover effect in charcoal when compared with vancomycin. Differences between these two drugs can lead to a false interpretation of negative blood cultures. To compare different antibiotic regimens for the treatment of bacteraemia, preliminary studies are mandatory to ensure that ex vivo antibiotic behaviour is similar in the blood-culture system used

Diffusion in multiscale spacetimes

We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are partly based on the literature in probability and percolation theory but their physical interpretation here is different since they apply to quantum spacetime itself. The case of multiscale (in particular, multifractal) spacetimes is then considered through a number of examples and the most general spectral-dimension profile of multifractional spaces is constructed.Comment: 23 pages, 5 figures. v2: discussion improved, typos corrected, references adde