On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics

This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.

Modification of the biological intercept model to account for ontogenetic effects in laboratory-reared delta smelt (Hypomesus transpacificus)*

We investigated age, growth, and ontogenetic effects on the proportionality of otolith size to fish size in laboratory-reared delta smelt (Hypomesus transpacificus) from the San Francisco Bay estuary. Delta smelt larvae were reared from hatching in laboratory mesocosms for 100 days. Otolith increments from known-age fish were enumerated to validate that growth increments were deposited daily and to validate the age of fish at first ring formation. Delta smelt were found to lay down daily ring increments; however, the first increment did not form until six days after hatching. The relationship between otolith size and fish size was not biased by age or growth-rate effects but did exhibit an interruption in linear growth owing to an ontogenetic shift at the postflexon stage. To back-calculate the size-at-age of individual fish, we modified the biological intercept (BI) model to account for ontogenetic changes in the otolith-size−fish-size relationship and compared the results to the time-varying growth model, as well as the modified Fry model. We found the modified BI model estimated more accurately the size-at-age from hatching to 100 days after hatching. Before back-calculating size-at-age with existing models, we recommend a critical evaluation of the effects that age, growth, and ontogeny can have on the otolith-size−fish-size relations

Probabilistic Fréchet means for time varying persistence diagrams

© 2015, Institute of Mathematical Statistics. All rights reserved.In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [23], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (Dp, Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a finite set of diagrams always exists, but is not necessarily unique. The means of a continuously-varying set of diagrams do not themselves (necessarily) vary continuously, which presents obvious problems when trying to extend the Fréchet mean definition to the realm of time-varying persistence diagrams, better known as vineyards. We fix this problem by altering the original definition of Fréchet mean so that it now becomes a probability measure on the set of persistence diagrams; in a nutshell, the mean of a set of diagrams will be a weighted sum of atomic measures, where each atom is itself a persistence diagram determined using a perturbation of the input diagrams. This definition gives for each N a map (Dp)^N→ℙ(Dp). We show that this map is Hölder continuous on finite diagrams and thus can be used to build a useful statistic on vineyards.

Telescoping is not time compression: a model of the dating of autobiographical events.

A model of telescoping is proposed that assumes no systematic errors in dating. Rather, the overestimation of recent occurrences of events is based on the combination of three factors: (1) Retention is greater for recent events; (2) errors in dating, though unbiased, increase linearly with the time since the dated event; and (3) intrusions often occur from events outside the period being asked about, but such intrusions do not come from events that have not yet occurred. In Experiment 1, we found that recall for colloquia fell markedly over a 2-year interval, the magnitude of errors in psychologists' dating of the colloquia increased at a rate of .4 days per day of delay, and the direction of the dating error was toward the middle of the interval. In Experiment 2, the model used the retention function and dating errors from the first study to predict the distribution of the actual dates of colloquia recalled as being within a 5-month period. In Experiment 3, the findings of the first study were replicated with colloquia given by, instead of for, the subjects.