Some results on homoclinic and heteroclinic connections in planar systems

Consider a family of planar systems depending on two parameters $(n,b)$ and having at most one limit cycle. Assume that the limit cycle disappears at some homoclinic (or heteroclinic) connection when $\Phi(n,b)=0.$ We present a method that allows to obtain a sequence of explicit algebraic lower and upper bounds for the bifurcation set ${\Phi(n,b)=0}.$ The method is applied to two quadratic families, one of them is the well-known Bogdanov-Takens system. One of the results that we obtain for this system is the bifurcation curve for small values of $n$, given by $b=\frac5 7 n^{1/2}+{72/2401}n- {30024/45294865}n^{3/2}- {2352961656/11108339166925} n^2+O(n^{5/2})$. We obtain the new three terms from purely algebraic calculations, without evaluating Melnikov functions

Galactic Gamma-Ray Background Radiation from Supernova Remnants

The contribution of the Source Cosmic Rays (SCRs), confined in Supernova Remnants, to the diffuse high energy \gr emission above 1 GeV from the Galactic disk is studied. \grs produced by the SCRs have a much harder spectrum compared with those generated by the Galactic Cosmic Rays which occupy a much larger residence volume uniformly. SCRs contribute less than 10% at GeV energies and become dominant at \gr energies above 100 GeV. The contributions from $\pi^0$-decay and Inverse Compton \grs have comparable magnitude and spectral shape, whereas the Bremsstrahlung component is negligible. At TeV energies the contribution from SCRs increases the expected diffuse \gr flux almost by an order of magnitude. It is shown that for the inner Galaxy the discrepancy between the observed diffuse intensity and previous model predictions at energies above a few GeV can be attributed to the SCR contribution.Comment: 25 pages, 1 figures, to appear in Ap

Contextual Object Detection with a Few Relevant Neighbors

A natural way to improve the detection of objects is to consider the contextual constraints imposed by the detection of additional objects in a given scene. In this work, we exploit the spatial relations between objects in order to improve detection capacity, as well as analyze various properties of the contextual object detection problem. To precisely calculate context-based probabilities of objects, we developed a model that examines the interactions between objects in an exact probabilistic setting, in contrast to previous methods that typically utilize approximations based on pairwise interactions. Such a scheme is facilitated by the realistic assumption that the existence of an object in any given location is influenced by only few informative locations in space. Based on this assumption, we suggest a method for identifying these relevant locations and integrating them into a mostly exact calculation of probability based on their raw detector responses. This scheme is shown to improve detection results and provides unique insights about the process of contextual inference for object detection. We show that it is generally difficult to learn that a particular object reduces the probability of another, and that in cases when the context and detector strongly disagree this learning becomes virtually impossible for the purposes of improving the results of an object detector. Finally, we demonstrate improved detection results through use of our approach as applied to the PASCAL VOC and COCO datasets

Low-lying bifurcations in cavity quantum electrodynamics

The interplay of quantum fluctuations with nonlinear dynamics is a central topic in the study of open quantum systems, connected to fundamental issues (such as decoherence and the quantum-classical transition) and practical applications (such as coherent information processing and the development of mesoscopic sensors/amplifiers). With this context in mind, we here present a computational study of some elementary bifurcations that occur in a driven and damped cavity quantum electrodynamics (cavity QED) model at low intracavity photon number. In particular, we utilize the single-atom cavity QED Master Equation and associated Stochastic Schrodinger Equations to characterize the equilibrium distribution and dynamical behavior of the quantized intracavity optical field in parameter regimes near points in the semiclassical (mean-field, Maxwell-Bloch) bifurcation set. Our numerical results show that the semiclassical limit sets are qualitatively preserved in the quantum stationary states, although quantum fluctuations apparently induce phase diffusion within periodic orbits and stochastic transitions between attractors. We restrict our attention to an experimentally realistic parameter regime.Comment: 13 pages, 10 figures, submitted to PR

Morse index and causal continuity. A criterion for topology change in quantum gravity

Studies in 1+1 dimensions suggest that causally discontinuous topology changing spacetimes are suppressed in quantum gravity. Borde and Sorkin have conjectured that causal discontinuities are associated precisely with index 1 or n-1 Morse points in topology changing spacetimes built from Morse functions. We establish a weaker form of this conjecture. Namely, if a Morse function f on a compact cobordism has critical points of index 1 or n-1, then all the Morse geometries associated with f are causally discontinuous, while if f has no critical points of index 1 or n-1, then there exist associated Morse geometries which are causally continuous.Comment: Latex, 20 pages, 3 figure

Future geodesic completeness of some spatially homogeneous solutions of the vacuum Einstein equations in higher dimensions

It is known that all spatially homogeneous solutions of the vacuum Einstein equations in four dimensions which exist for an infinite proper time towards the future are future geodesically complete. This paper investigates whether the analogous statement holds in higher dimensions. A positive answer to this question is obtained for a large class of models which can be studied with the help of Kaluza-Klein reduction to solutions of the Einstein-scalar field equations in four dimensions. The proof of this result makes use of a criterion for geodesic completeness which is applicable to more general spatially homogeneous models.Comment: 18 page

Family Caregiver Identity: A Literature Review

Background: Despite the multitude of available resources, family caregivers of those with chronic disease continually underutilize support services to cope with the demands of caregiving. Several studies have linked self-identification as a caregiver to the increased likelihood of support service use. Purpose: The present study reviewed the literature related to the development of family caregiver identity. Methods: After a systematic process to locate literature was completed, content analysis was conducted to determine major themes related to the development of caregiving identity. Results: Findings suggest that there are multiple factors related to the development of family caregiver identity, including role engulfment and reversal, loss of shared identity, family obligation and gender norming, extension of the former role, and development of a master identity. Discussion: Considering the role of identity in human behavior, health professionals can address the underutilization of support services by family caregivers of those with chronic disease by understanding the influences on the development of caregiver identity. Translation to Health Education Practice: This literature review will assist health educators in addressing the underutilization of support services by family caregivers of those with chronic disease

On the number of limit cycles of the Lienard equation

In this paper, we study a Lienard system of the form dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This sequence seems to converge to the exact equation of each limit cycle. We obtain also a sequence of polynomials R_n(x) whose roots of odd multiplicity are related to the number and location of the limit cycles of the system.Comment: 10 pages, 5 figures. Submitted to Physical Review