Gravitationally bound hierarchies containing three or more components are very common in our Universe. In this paper we study periodic gravitational wave (GW) form, their polarizations, response function, its Fourier transform, and energy loss rate of a triple system through three different channels of radiation, the scalar, vector and tensor modes, in Einstein-aether theory of gravity. The theory violates locally the Lorentz symmetry, and yet satisfies all the theoretical and observational constraints by properly choosing its four coupling constants ci's. In particular, in the weak-field approximations and with the recently obtained constraints of the theory, we first analyze the energy loss rate of a binary system, and find that the dipole contributions from the scalar and vector modes could be of the order of O (c14) O (GN m/d) 2 , where c14 (≡ c1 + c4) is constrained to c14 O 10 −5 by current observations, and GN , m and d are, respectively, the Newtonian constant, mass and size of the source. On the other hand, the "strong-field" effects for a binary system of neutron stars are about six orders lower than that of GR. So, in this paper we ignore these "strong-field" effects and first develop the general formulas to the lowest post-Newtonian order, by taking the coupling of the aether field with matter into account. Within this approximation, we find that the scalar breather mode and the scalar longitudinal mode are all suppressed by a factor of O (c14) with respect to the transverse-traceless modes (h+ and h×), while the vectorial modes (hX and hY ) are suppressed by a factor of c13 O 10 −15 . Applying the general formulas to a triple system with periodic orbits, we find that the corresponding GW form, response function, and its Fourier transform depend sensitively on the configuration of the triple system, their orientation with respect to the detectors, and the binding energies of the three compact bodies.

We study gravitational waves emitted by a binary system of non-spinning bodies in a quasi-circular inspiral within the framework of Einstein-aether theory. In particular, we compute explicitly and analytically the expressions for the time-domain and frequency-domain waveforms, gravitational wave polarizations, and response functions for both ground-and space-based detectors in the post-Newtonian approximation. We find that, when going beyond leading-order in the post-Newtonian approximation, the non-Einsteinian polarization modes contain terms that depend on both the first and the second harmonics of the orbital phase. We also calculate analytically the corresponding parameterized post-Einsteinian parameters, generalizing the existing framework to allow for different propagation speeds among scalar, vector and tensor modes, without assumptions about the magnitude of its coupling parameters, and meanwhile allowing the binary system to have relative motions with respect to the aether field. Such results allow for the easy construction of Einstein-aether templates that could be used in Bayesian tests of General Relativity in the future. * Anzhong Wang@baylor.edu; Corresponding Author 1 Recently, various GWs have been detected after LIGO/Virgo resumed operations on April 1, 2019, possibly including the coalescence of a neutron-star (NS)/BH binary. The details of these detections have not yet been released [3].

BackgroundComplex co-regulatory networks in plants may elicit responses during pathogen infections. A number of genes are activated when these responses take place. Identification of these genes would shed new light on understanding the mechanisms of rice response to pathogen infections and the elucidation of crosstalk among diverse signaling networks in rice disease resistance/susceptibility.ResultsHere we report the identification of genes with pathogen-inducible cis-regulatory elements (PICEs) (AS-1, G-box, GCC-box, and H-box) in the promoter regions in rice. Our results showed that a set of 882 rice genes contained these four elements in their promoter regions. Of these genes, 190 encode disease resistance/susceptibility related proteins, and 70 encode transcription factors. Analyses of the available microarray data demonstrated that 357 transcripts were differentially expressed after pathogen infections. 48 out of 53 differentially expressed transcription factors are up-regulated or down-regulated by more than 1.1-fold in response to pathogen infections. Analyses of the public mRNA-Seq data showed that 327 transcripts were differently expressed after pathogen infections. A total of 100 up-regulated genes and 37 down-regulated genes were found in common between the microarray and mRNA-Seq data.ConclusionsWe report here a set of rice genes that contain the four PICEs, i.e., AS-1, G-box, GCC-box, and H-box, in their promoter regions, of which, 53.5% were up- or down-regulated when pathogens attack. The PICEs in the gene promoters are critical for rice response to pathogen infections. They are also useful markers for identification of rice genes involved in response to pathogen infections.Electronic supplementary materialThe online version of this article (10.1186/s12284-018-0243-0) contains supplementary material, which is available to authorized users.