On the dynamics of a class of multi-group models for vector-borne diseases

The resurgence of vector-borne diseases is an increasing public health concern, and there is a need for a better understanding of their dynamics. For a number of diseases, e.g. dengue and chikungunya, this resurgence occurs mostly in urban environments, which are naturally very heterogeneous, particularly due to population circulation. In this scenario, there is an increasing interest in both multi-patch and multi-group models for such diseases. In this work, we study the dynamics of a vector borne disease within a class of multi-group models that extends the classical Bailey-Dietz model. This class includes many of the proposed models in the literature, and it can accommodate various functional forms of the infection force. For such models, the vector-host/host-vector contact network topology gives rise to a bipartite graph which has different properties from the ones usually found in directly transmitted diseases. Under the assumption that the contact network is strongly connected, we can define the basic reproductive number $\mathcal{R}_0$ and show that this system has only two equilibria: the so called disease free equilibrium (DFE); and a unique interior equilibrium---usually termed the endemic equilibrium (EE)---that exists if, and only if, $\mathcal{R}_0>1$. We also show that, if $\mathcal{R}_0\leq1$, then the DFE equilibrium is globally asymptotically stable, while when $\mathcal{R}_0>1$, we have that the EE is globally asymptotically stable

THRESHOLD MODELS IN THEORY AND PRACTICE

Threshold models have gained much recent attention in applied economics for modeling nonlinear behavior. The appeal for these models is due in part to the observable pattern that many economic variables follow, such as asymmetric adjustment towards equilibrium. This paper reviews the literature and provides links to software programs.Research Methods/ Statistical Methods,

_Limusaurus_ and bird digit identity

_Limusaurus_ is a remarkable herbivorous ceratosaur unique among theropods in having digits II, III and IV, with only a small metacarpal vestige of digit I. This raises interesting questions regarding the controversial identity of avian wing digits. The early tetanuran ancestors of birds had tridactyl hands with digital morphologies corresponding to digits I, II & III of other dinosaurs. In bird embryos, however, the pattern of cartilage formation indicates that their digits develop from positions that become digits II, III, & IV in other amniotes. _Limusaurus_ has been argued to provide evidence that the digits of tetanurans, currently considered to be I, II and III, may actually be digits II, III, & IV, thus explaining the embryological position of bird wing digits. However, morphology and gene expression of the anterior bird wing digit specifically resemble digit I, not II, of other amniotes. We argue that digit I loss in _Limusaurus_ is derived and thus irrelevant to understanding the development of the bird wing

Photon correlations in positron annihilation

The two-photon positron annihilation density matrix is found to separate into a diagonal center of energy factor implying maximally entangled momenta, and a relative factor describing decay. For unknown positron injection time, the distribution of the difference in photon arrival times is a double exponential at the para-Ps decay rate, consistent with experiment (V. D. Irby, Meas. Sci. Technol. 15, 1799 (2004)).Comment: Accepted for publication in Phys. Rev.

Ultra-high-frequency piecewise-linear chaos using delayed feedback loops

We report on an ultra-high-frequency (> 1 GHz), piecewise-linear chaotic system designed from low-cost, commercially available electronic components. The system is composed of two electronic time-delayed feedback loops: A primary analog loop with a variable gain that produces multi-mode oscillations centered around 2 GHz and a secondary loop that switches the variable gain between two different values by means of a digital-like signal. We demonstrate experimentally and numerically that such an approach allows for the simultaneous generation of analog and digital chaos, where the digital chaos can be used to partition the system's attractor, forming the foundation for a symbolic dynamics with potential applications in noise-resilient communications and radar

Supersymmetric free-damped oscillators: Adaptive observer estimation of the Riccati parameter

A supersymmetric class of free damped oscillators with three parameters has been obtained in 1998 by Rosu and Reyes through the factorization of the Newton equation. The supplementary parameter is the integration constant of the general Riccati solution. The estimation of the latter parameter is performed here by employing the recent adaptive observer scheme of Besancon et al., but applied in a nonstandard form in which a time-varying quantity containing the unknown Riccati parameter is estimated first. Results of computer simulations are presented to illustrate the good feasibility of this approach for a case in which the estimation is not easily accomplished by other meansComment: 8 pages, 6 figure

Self-trapped bidirectional waveguides in a saturable photorefractive medium

We introduce a time-dependent model for the generation of joint solitary waveguides by counter-propagating light beams in a photorefractive crystal. Depending on initial conditions, beams form stable steady-state structures or display periodic and irregular temporal dynamics. The steady-state solutions are non-uniform in the direction of propagation and represent a general class of self-trapped waveguides, including counterpropagating spatial vector solitons as a particular case.Comment: 4 pages, 5 figure

Palbociclib plus letrozole as first-line therapy in estrogen receptor-positive/human epidermal growth factor receptor 2-negative advanced breast cancer with extended follow-up.

PurposeIn the initial PALOMA-2 (NCT01740427) analysis with median follow-up of 23 months, palbociclib plus letrozole significantly prolonged progression-free survival (PFS) in women with estrogen receptor-positive (ER+)/human epidermal growth factor receptor 2-negative (HER2-) advanced breast cancer (ABC) [hazard ratio (HR) 0.58; P < 0.001]. Herein, we report results overall and by subgroups with extended follow-up.MethodsIn this double-blind, phase 3 study, post-menopausal women with ER+/HER2- ABC who had not received prior systemic therapy for their advanced disease were randomized 2:1 to palbociclib-letrozole or placebo-letrozole. Endpoints include investigator-assessed PFS (primary), safety, and patient-reported outcomes (PROs).ResultsAfter a median follow-up of approximately 38 months, median PFS was 27.6 months for palbociclib-letrozole (n = 444) and 14.5 months for placebo-letrozole (n = 222) (HR 0.563; 1-sided P < 0.0001). All subgroups benefited from palbociclib treatment. The improvement of PFS with palbociclib-letrozole was maintained in the next 2 subsequent lines of therapy and delayed the use of chemotherapy (40.4 vs. 29.9 months for palbociclib-letrozole vs. placebo-letrozole). Safety data were consistent with the known profile. Patients' quality of life was maintained.ConclusionsWith approximately 15 months of additional follow-up, palbociclib plus letrozole continued to demonstrate improved PFS compared with placebo plus letrozole in the overall population and across all patient subgroups, while the safety profile remained favorable and quality of life was maintained. These data confirm that palbociclib-letrozole should be considered the standard of care for first-line therapy in patients with ER+/HER2- ABC, including those with low disease burden or long disease-free interval. Sponsored by Pfizer; ClinicalTrials.gov: NCT01740427

Ultra-Slow Light and Enhanced Nonlinear Optical Effects in a Coherently Driven Hot Atomic Gas

We report the observation of small group velocities of order 90 meters per second, and large group delays of greater than 0.26 ms, in an optically dense hot rubidium gas (~360 K). Media of this kind yield strong nonlinear interactions between very weak optical fields, and very sharp spectral features. The result is in agreement with previous studies on nonlinear spectroscopy of dense coherent media