Worst-case bounds on the quality of max-product fixed-points

We study worst-case bounds on the quality of any fixed point assignment of the max-product algorithm for Markov Random Fields (MRF). We start proving a bound independent of the MRF structure and parameters. Afterwards, we show how this bound can be improved for MRFs with particular structures such as bipartite graphs or grids. Our results provide interesting insight into the behavior of max-product. For example, we prove that max-product provides very good results (at least 90% of the optimal) on MRFs with large variable-disjoint cycles (MRFs in which all cycles are variable-disjoint, namely that they do not share any edge and in which each cycle contains at least 20 variables)

Chirping compact stars: gravitational radiation and detection degeneracy with binary systems A conceptual pathfinder for space-based gravitational-wave observatories

Compressible, Riemann S-type ellipsoids can emit gravitational waves (GWs) with a chirp-like behavior (hereafter chirping ellipsoids, CELs). We show that the GW frequency-amplitude evolution of CELs (mass $\sim 1$~M$_\odot$, radius $\sim10^3$~km, polytropic equation of state with index $n\approx 3$) is indistinguishable from that emitted by double white dwarfs (DWDs) and by extreme mass-ratio inspirals (EMRIs) composed of an intermediate-mass (e.g.~$10^3~M_\odot$) black hole and a planet-like (e.g.~$10^{-4}~M_\odot$) companion, in a specific frequency interval within the detector sensitivity band in which the GWs of all these systems are quasi-monochromatic. We estimate that for reasonable astrophysical assumptions, the rates in the local Universe of CELs, DWDs and EMRIs in the mass range considered here, are very similar, posing a detection-degeneracy challenge for space-based GW detectors. The astrophysical implications of this CEL-binary detection degeneracy by space-based GW-detection facilities, are outlined.Comment: Submitted to Phys. Rev.

The dynamical equation of the effective gluon mass

In this article we derive the integral equation that controls the momentum dependence of the effective gluon mass in the Landau gauge. This is accomplished by means of a well-defined separation of the corresponding "one-loop dressed" Schwinger-Dyson equation into two distinct contributions, one associated with the mass and one with the standard kinetic part of the gluon. The entire construction relies on the existence of a longitudinally coupled vertex of nonperturbative origin, which enforces gauge invariance in the presence of a dynamical mass. The specific structure of the resulting mass equation, supplemented by the additional requirement of a positive-definite gluon mass, imposes a rather stringent constraint on the derivative of the gluonic dressing function, which is comfortably satisfied by the large-volume lattice data for the gluon propagator, both for SU(2) and SU(3). The numerical treatment of the mass equation, under some simplifying assumptions, is presented for the aforementioned gauge groups, giving rise to a gluon mass that is a non-monotonic function of the momentum. Various theoretical improvements and possible future directions are briefly discussed.Comment: 38 pages, 17 figure

Gluon mass through ghost synergy

In this work we compute, at the 'one-loop-dressed' level, the nonperturbative contribution of the ghost loops to the self-energy of the gluon propagator, in the Landau gauge. This is accomplished within the PT-BFM formalism, which guarantees the gauge-invariance of the emerging answer. In particular, the contribution of the ghost-loops is automatically transverse, by virtue of the QED-like Ward identities satisfied in this framework. Using as nonperturbative input the available lattice data for the ghost dressing function, we show that the ghost contributions have a rather sizable effect on the overall shape of the gluon propagator, both for d=3,4. Then, by exploiting a recently introduced dynamical equation for the effective gluon mass, whose solutions depend crucially on the characteristics of the gluon propagator at intermediate energies, we show that if the ghost loops are removed from the gluon propagator then the gluon mass vanishes. These findings strongly suggest that, at least at the level of the Schwinger-Dyson equations, the effects of gluons and ghosts are inextricably connected, and must be combined suitably in order to reproduce the results obtained in the recent lattice simulations

Kinetic study of nordihydroguaiaretic acid recovery from Larrea tridentata by microwave-assisted extraction

Nordihydroguaiaretic acid (NDGA) is a powerful antioxidant that can be found in plants like Larrea tridentata (Zygophyllaceae), also known as creosote bush, which grows in semidesert areas of Southwestern United States and Northern Mexico [1]. Several studies have demonstrated that NDGA has important biological activities with great interest in the health area, such as antiviral, cancer chemopreventive, and antitumorgenic activities [2]. Extraction of bioactive compounds from plants is conventionally performed using a heat‐reflux extraction method. However, different techniques have been developed in order to decrease extraction time and solvent consumption, as well as to increase the extraction yield and enhance the extracts quality [3]. The objective of this study was to develop a microwave‐assisted extraction (MAE) method for NDGA recovery from Larrea tridentata leaves, and compare the obtained results with those found by using the conventional heat‐reflux extraction (HRE)

Massless bound-state excitations and the Schwinger mechanism in QCD

The gauge invariant generation of an effective gluon mass proceeds through the well-known Schwinger mechanism, whose key dynamical ingredient is the nonperturbative formation of longitudinally coupled massless bound-state excitations. These excitations introduce poles in the vertices of the theory, in such a way as to maintain the Slavnov-Taylor identities intact in the presence of massive gluon propagators. In the present work we first focus on the modifications induced to the nonperturbative three-gluon vertex by the inclusion of massless two-gluon bound-states into the kernels appearing in its skeleton-expansion. Certain general relations between the basic building blocks of these bound-states and the gluon mass are then obtained from the Slavnov-Taylor identities and the Schwinger-Dyson equation governing the gluon propagator. The homogeneous Bethe-Salpeter equation determining the wave-function of the aforementioned bound state is then derived, under certain simplifying assumptions. It is then shown, through a detailed analytical and numerical study, that this equation admits non-trivial solutions, indicating that the QCD dynamics support indeed the formation of such massless bound states. These solutions are subsequently used, in conjunction with the aforementioned relations, to determine the momentum-dependence of the dynamical gluon mass. Finally, further possibilities and open questions are briefly discussed.Comment: 37 pages, 20 figure

Nonperturbative study of the four gluon vertex

In this paper we study the nonperturbative structure of the SU(3) four-gluon vertex in the Landau gauge, concentrating on contributions quadratic in the metric. We employ an approximation scheme where 'one-loop' diagrams are computed using fully dressed gluon and ghost propagators, and tree-level vertices. When a suitable kinematical configuration depending on a single momentum scale p is chosen, only two structures emerge: the tree-level four-gluon vertex, and a tensor orthogonal to it. A detailed numerical analysis reveals that the form factor associated with this latter tensor displays a change of sign (zero-crossing) in the deep infrared, and finally diverges logarithmically. The origin of this characteristic behavior is proven to be entirely due to the masslessness of the ghost propagators forming the corresponding ghost-loop diagram, in close analogy to a similar effect established for the three-gluon vertex. However, in the case at hand, and under the approximations employed, this particular divergence does not affect the form factor proportional to the tree-level tensor, which remains finite in the entire range of momenta, and deviates moderately from its naive tree-level value. It turns out that the kinematic configuration chosen is ideal for carrying out lattice simulations, because it eliminates from the connected Green's function all one-particle reducible contributions, projecting out the genuine one-particle irreducible vertex. Motivated by this possibility, we discuss in detail how a hypothetical lattice measurement of this quantity would compare to the results presented here, and the potential interference from an additional tensorial structure, allowed by Bose symmetry, but not encountered within our scheme