S5 0716+714 : GeV variability study

The GeV observations by Fermi-LAT give us the opportunity to characterize the high-energy emission (100 MeV - 300 GeV) variability properties of the BL Lac object S5 0716+714. In this study, we performed flux and spectral analysis of more than 3 year long (August 2008 to April 2012) Fermi-LAT data of the source. During this period, the source exhibits two different modes of flux variability with characteristic timescales of ~75 and ~140 days, respectively. We also notice that the flux variations are characterized by a weak spectral hardening. The GeV spectrum of the source shows a clear deviation from a simple power law, and is better explained by a broken power law. Similar to other bright Fermi blazars, the break energy does not vary with the source flux during the different activity states. We discuss several possible scenarios to explain the observed spectral break.Comment: 21 pages, 10 figures, Accepted for publication in Advances in Space Research journa

On Minimum Violations Ranking in Paired Comparisons

Ranking a set of objects from the most dominant one to the least, based on the results of paired comparisons, proves to be useful in many contexts. Using the rankings of teams or individuals players in sports to seed tournaments is an example. The quality of a ranking is often evaluated by the number of violations, cases in which an object is ranked lower than another that it has dominated in a comparison, that it contains. A minimum violations ranking (MVR) method, as its name suggests, searches specifically for rankings that have the minimum possible number of violations which may or may not be zero. In this paper, we present a method based on statistical physics that overcomes conceptual and practical difficulties faced by earlier studies of the problem.Comment: 10 pages, 10 figures; typos corrected (v2

Upper bounds on the first eigenvalue for a diffusion operator via Bakry-\'{E}mery Ricci curvature II

Let $L=\Delta-\nabla\varphi\cdot\nabla$ be a symmetric diffusion operator with an invariant measure $d\mu=e^{-\varphi}dx$ on a complete Riemannian manifold. In this paper we prove Li-Yau gradient estimates for weighted elliptic equations on the complete manifold with $|\nabla \varphi|\leq\theta$ and $\infty$-dimensional Bakry-\'{E}mery Ricci curvature bounded below by some negative constant. Based on this, we give an upper bound on the first eigenvalue of the diffusion operator $L$ on this kind manifold, and thereby generalize a Cheng's result on the Laplacian case (Math. Z., 143 (1975) 289-297).Comment: Final version. The original proof of Theorem 2.1 using Li-Yau gradient estimate method has been moved to the appendix. The new proof is simple and direc

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces (X,d,m). Our main results are: - A general study of the relations between the Hopf-Lax semigroup and Hamilton-Jacobi equation in metric spaces (X,d). - The equivalence of the heat flow in L^2(X,m) generated by a suitable Dirichlet energy and the Wasserstein gradient flow of the relative entropy functional in the space of probability measures P(X). - The proof of density in energy of Lipschitz functions in the Sobolev space W^{1,2}(X,d,m). - A fine and very general analysis of the differentiability properties of a large class of Kantorovich potentials, in connection with the optimal transport problem. Our results apply in particular to spaces satisfying Ricci curvature bounds in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop. 4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6 simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients, still equivalent to all other ones, has been propose

Fermi Large Area Telescope Fourth Source Catalog Data Release 4 (4FGL-DR4)

We present an incremental version (4FGL-DR4, for Data Release 4) of the fourth Fermi-LAT catalog of gamma-ray sources. Based on the first 14 years of science data in the energy range from 50 MeV to 1 TeV, it uses the same analysis methods as the 4FGL-DR3 catalog did for 12 years of data, with only a few improvements. The spectral parameters, spectral energy distributions, light curves and associations are updated for all sources. We add four new extended sources and modify two existing ones. Among the 6658 4FGL-DR3 sources, we delete 14 and change the localization of 10, while 26 are newly associated and two associations were changed. We add 546 point sources, among which 8 are considered identified and 228 have a plausible counterpart at other wavelengths. Most are just above the detection threshold, and 14 are transient sources below the detection threshold that can affect the light curves of nearby sources.Comment: Data files at https://fermi.gsfc.nasa.gov/ssc/data/access/lat/14yr_catalog/. Refereed paper is DOI 10.3847/1538-4365/ac675

Generic metrics and the mass endomorphism on spin three-manifolds

Let $(M,g)$ be a closed Riemannian spin manifold. The constant term in the expansion of the Green function for the Dirac operator at a fixed point $p\in M$ is called the mass endomorphism in $p$ associated to the metric $g$ due to an analogy to the mass in the Yamabe problem. We show that the mass endomorphism of a generic metric on a three-dimensional spin manifold is nonzero. This implies a strict inequality which can be used to avoid bubbling-off phenomena in conformal spin geometry.Comment: 8 page

Folding and unfolding phylogenetic trees and networks

Phylogenetic networks are rooted, labelled directed acyclic graphs which are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any phylogenetic network $N$ can be "unfolded" to obtain a MUL-tree $U(N)$ and, conversely, a MUL-tree $T$ can in certain circumstances be "folded" to obtain a phylogenetic network $F(T)$ that exhibits $T$. In this paper, we study properties of the operations $U$ and $F$ in more detail. In particular, we introduce the class of stable networks, phylogenetic networks $N$ for which $F(U(N))$ is isomorphic to $N$, characterise such networks, and show that they are related to the well-known class of tree-sibling networks.We also explore how the concept of displaying a tree in a network $N$ can be related to displaying the tree in the MUL-tree $U(N)$. To do this, we develop a phylogenetic analogue of graph fibrations. This allows us to view $U(N)$ as the analogue of the universal cover of a digraph, and to establish a close connection between displaying trees in $U(N)$ and reconcilingphylogenetic trees with networks

Ricci Solitons and Einstein-Scalar Field Theory

B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to associate to each static Ricci flat spacetime a local Ricci soliton in one higher dimension. As well, solutions of Euclidean-signature Einstein gravity coupled to a free massless scalar field with nonzero cosmological constant are associated to shrinking or expanding Ricci solitons. We exhibit examples, including an explicit family of complete expanding solitons which can be thought of as a Ricci flow for a complete Lorentzian metric. The possible generalization to Ricci-flat stationary metrics leads us to consider an alternative to Ricci flow.Comment: 17 pages, 1 figure; Revised version (organizational changes, other minor revisions and corrections, citations corrected and added), to appear in CQ

Ricci Flow Gravity

A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gravity. In particular there is no adjustable coupling constant. For the solar system the effects of Ricci flow gravity cannot be distinguished from Einstein gravity and therefore it passes all classical tests. However for cosmology significant deviations from standard Einstein cosmology will appear.Comment: 15 pages. V2: improved presentation, in particular Jordan vs. Brans-Dicke and on viability. Added section on physical interpretation. V3: more references. Reworked to agree with published versio