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We collected the optical light curve data of 227 gamma-ray bursts (GRBs) observed with the TAROT, COATLI, and RATIR telescopes. These consist of 133 detections and 94 upper limits. We constructed average light curves in the observer and rest frames in both X-rays (from {\itshape Swift}/XRT) and in the optical. Our analysis focused on investigating the observational and intrinsic properties of GRBs. Specifically, we examined observational properties, such as the optical brightness function of the GRBs at $T=1000$ seconds after the trigger, as well as the temporal slope of the afterglow. We also estimated the redshift distribution for the GRBs within our sample. Of the 227 GRBs analysed, we found that 116 had a measured redshift. Based on these data, we calculated a local rate of $\rho_0=0.2$ Gpc$^{-3}$ yr$^{-1}$ for these events with $z<1$. To explore the intrinsic properties of GRBs, we examined the average X-ray and optical light curves in the rest frame. We use the {\scshape afterglowpy} library to generate synthetic curves to constrain the parameters typical of the bright GRB jet, such as energy (${\langle} {E_{0}}{\rangle}\sim 10^{53.6}$~erg), opening angle (${\langle}\theta_\mathrm{core}{\rangle}\sim 0.2$~rad), and density (${\langle}n_\mathrm{0}{\rangle}\sim10^{-2.1}$ cm$^{-3}$). Furthermore, we analyse microphysical parameters, including the fraction of thermal energy in accelerated electrons (${\langle}\epsilon_e{\rangle}\sim 10^{-1.37}$) and in the magnetic field (${\langle}\epsilon_B{\rangle}\sim10^{-2.26}$), and the power-law index of the population of non-thermal electrons (${\langle}p{\rangle}\sim 2.2$)., Comment: Accepted for publication in MNRAS, 13 pages and 9 figures

GRB~210704A is a burst of intermediate duration ($T_{90} \sim 1-4$~s) followed by a fading afterglow and an optical excess that peaked about 7 days after the explosion. Its properties, and in particular those of the excess, do not easily fit into the well established classification scheme of GRBs as being long or short, leaving the nature of its progenitor uncertain. We present multi-wavelength observations of the GRB and its counterpart, observed up to 160 days after the burst. In order to decipher the nature of the progenitor system, we present a detailed analysis of the GRB high-energy properties (duration, spectral lag, and Amati correlation), its environment, and late-time optical excess. We discuss three possible scenarios: a neutron star merger, a collapsing massive star, and an atypical explosion possibly hosted in a cluster of galaxies. We find that traditional kilonova and supernova models do not match well the properties of the optical excess, leaving us with the intriguing suggestion that this event was an exotic high-energy merger., Comment: Revised version submitted to MNRAS after minor comments, 14 pages, 9 figures

We present optical and near-infrared photometric observations of GRB 191016 with the COATLI, DDOTI and RATIR ground-based telescopes over the first three nights. We present the temporal evolution of the optical afterglow and describe 5 different stages that were not completely characterized in previous works, mainly due to scarcity of data points to accurately fit the different components of the optical emission. After the end of the prompt gamma-ray emission, we observed the afterglow rise slowly in the optical and near-infrared (NIR) wavelengths and peak at around T+1450s in all filters. This was followed by an early decay, a clear plateau from T+5000s to T+11000s, and then a regular late decay. We also present evidence of the jet break at later times, with a temporal index in good agreement with the temporal slope obtained from X-ray observations. Although many of the features observed in the optical light curves of GRBs are usually well explained by a reverse shock (RS) or forward shock(FS), the shallowness of the optical rise and enhanced peak emission in the GRB191016A afterglow is not well-fitted by only a FS or a RS. We propose a theoretical model which considers both of these components and combines an evolving FS with a later embedded RS and a subsequent late energy injection from the central engine activity. We use this model to successfully explain the temporal evolution of the light curves and discuss its implications on the fireball properties., Comment: 15 pages, 5 figures, 7 Tables, Submitted to MNRAS

We report the results of our follow-up campaign for the neutron star - black hole (NSBH) merger GW200115 detected during the O3 run of the Advanced LIGO and Advanced Virgo detectors. We obtained wide-field observations with the Deca-Degree Optical Transient Imager (DDOTI) covering ~20% of the total probability area down to a limiting magnitude of $w$=20.5 AB at ~23 h after the merger. Our search for counterparts returns a single candidate (AT2020aeo), likely not associate to the merger. In total, only 25 sources of interest were identified by the community and later discarded as unrelated to the GW event. We compare our upper limits with the emission predicted by state-of-the-art kilonova simulations and disfavor high mass ejecta (>0.1$M_{\odot}$), indicating that the spin of the system is not particularly high. By combining our optical limits with gamma-ray constraints from $Swift$ and $Fermi$, we disfavor the presence of a standard short duration burst for viewing angles $\lesssim$15 deg from the jet axis. Our conclusions are however limited by the large localization region of this GW event, and accurate prompt positions remain crucial to improving the efficiency of follow-up efforts., Comment: 6 pages, 4 figures, accepted for publication ApJ

We present optical follow-up observations with the DDOTI telescope of gravitational-wave events detected during the Advanced LIGO and Advanced Virgo O3 observing run. DDOTI is capable of responding to an alert in a few minutes, has an instantaneous field of about 69 deg$^{2}$, and obtains $10\sigma$ upper limits of $w_{\rm lim}=18.5$ to 20.5 AB mag in 1000~s of exposure, depending on the conditions. We observed 54\% (26 out of 48) of the unretracted gravitational-wave alerts and did not find any electromagnetic counterparts. We compare our upper limits to various possible counterparts: the kilonova AT~2017gfo, models of radioactive- and magnetar-powered kilonovae, short gamma-ray burst afterglows, and AGN flares. Although the large positional uncertainties of GW sources do not allow us to place strong constraints during O3, DDOTI observations of well-localized GW events in O4 and beyond could meaningfully constrain models of compact binary mergers. We show that DDOTI is able to detect kilonovae similar to AT~2017gfo up to about 200~Mpc and magnetar-powered kilonovae up to 1~Gpc. We calculate that nearby ($\lesssim$200 Mpc) afterglows have a high chance ($\approx$70\%) to be detected by rapid ($\lesssim$3 hours) DDOTI observations if observed on-axis, whereas off-axis afterglows are unlikely to be seen. Finally, we suggest that long-term monitoring of massive BBH events with DDOTI could confirm or rule out late AGN flares associated with these events., Comment: 26 pages, 5 figures. Accepted for publication in MNRAS

We report on our observing campaign of the compact binary merger GW190814, detected by the Advanced LIGO and Advanced Virgo detectors on August 14th, 2019. This signal has the best localisation of any observed gravitational wave (GW) source, with a 90% probability area of 18.5 deg$^2$, and an estimated distance of ~ 240 Mpc. We obtained wide-field observations with the Deca-Degree Optical Transient Imager (DDOTI) covering 88% of the probability area down to a limiting magnitude of $w$ = 19.9 AB. Nearby galaxies within the high probability region were targeted with the Lowell Discovery Telescope (LDT), whereas promising candidate counterparts were characterized through multi-colour photometry with the Reionization and Transients InfraRed (RATIR) and spectroscopy with the Gran Telescopio de Canarias (GTC). We use our optical and near-infrared limits in conjunction with the upper limits obtained by the community to constrain the possible electromagnetic counterparts associated with the merger. A gamma-ray burst seen along its jet's axis is disfavoured by the multi-wavelength dataset, whereas the presence of a burst seen at larger viewing angles is not well constrained. Although our observations are not sensitive to a kilonova similar to AT2017gfo, we can rule out high-mass (> 0.1 M$_{\odot}$) fast-moving (mean velocity >= 0.3c) wind ejecta for a possible kilonova associated with this merger., Comment: 17 pages, 11 figures, 5 tables; updated acknowledgement section. Accepted for publication in MNRAS (10 September 2020)

An algorithm for robot formation path planning is presented in this paper. Given a map of the working environment, the algorithm finds a path for a formation taking into account possible split of the formation and its consecutive merge. The key part of the solution works on a graph and sequentially employs an extended version of Dijkstra's graph-based algorithm for multiple robots. It is thus deterministic, complete, computationally inexpensive, and finds a solution for a fixed source node to another node in the graph. Moreover, the presented solution is general enough to be incorporated into high-level tasks like cooperative surveillance and it can benefit from state-of-the-art formation motion planning approaches, which can be used for evaluation of edges of an input graph. The performed experimental results demonstrate the behavior of the method in complex environments for formations consisting of tens of robots., Comment: 2017 IEEE Latin American Conference on Computational Intelligence (LA-CCI). arXiv admin note: substantial text overlap with arXiv:1901.07408

We provide an atomic decomposition of the product Hardy spaces $H^p(\widetilde{X})$ which were recently developed by Han, Li, and Ward in the setting of product spaces of homogeneous type $\widetilde{X} = X_1 \times X_2$. Here each factor $(X_i,d_i,\mu_i)$, for $i = 1$, $2$, is a space of homogeneous type in the sense of Coifman and Weiss. These Hardy spaces make use of the orthogonal wavelet bases of Auscher and Hyt\"onen and their underlying reference dyadic grids. However, no additional assumptions on the quasi-metric or on the doubling measure for each factor space are made. To carry out this program, we introduce product $(p,q)$-atoms on $\widetilde{X}$ and product atomic Hardy spaces $H^{p,q}_{{\rm at}}(\widetilde{X})$. As consequences of the atomic decomposition of $H^p(\widetilde{X})$, we show that for all $q > 1$ the product atomic Hardy spaces coincide with the product Hardy spaces, and we show that the product Hardy spaces are independent of the particular choices of both the wavelet bases and the reference dyadic grids. Likewise, the product Carleson measure spaces ${\rm CMO}^p(\widetilde{X})$, the bounded mean oscillation space ${\rm BMO}(\widetilde{X})$, and the vanishing mean oscillation space ${\rm VMO}(\widetilde{X})$, as defined by Han, Li, and Ward, are also independent of the particular choices of both wavelets and reference dyadic grids., Comment: Minor typos corrected, reference added. Submitted

We give an explicit construction of Haar functions associated to a system of dyadic cubes in a geometrically doubling quasi-metric space equipped with a positive Borel measure, and show that these Haar functions form a basis for $L^p$. Next we focus on spaces $X$ of homogeneous type in the sense of Coifman and Weiss, where we use these Haar functions to define a discrete square function, and hence to define dyadic versions of the function spaces $H^1(X)$ and ${\rm BMO}(X)$. In the setting of product spaces $\widetilde{X} = X_1 \times \cdots \times X_n$ of homogeneous type, we show that the space ${\rm BMO}(\widetilde{X})$ of functions of bounded mean oscillation on $\widetilde{X}$ can be written as the intersection of finitely many dyadic ${\rm BMO}$ spaces on $\widetilde{X}$, and similarly for $A_p(\widetilde{X})$, reverse-H\"older weights on $\widetilde{X}$, and doubling weights on $\widetilde{X}$. We also establish that the Hardy space $H^1(\widetilde{X})$ is a sum of finitely many dyadic Hardy spaces on $\widetilde{X}$, and that the strong maximal function on $\widetilde{X}$ is pointwise comparable to the sum of finitely many dyadic strong maximal functions. These dyadic structure theorems generalize, to product spaces of homogeneous type, the earlier Euclidean analogues for ${\rm BMO}$ and $H^1$ due to Mei and to Li, Pipher and Ward., Comment: 37 pages, submitted

We study the line widths in the [\ion{O}{3}]$\lambda$5007 and H$\alpha$ lines for two groups of planetary nebulae in the Milky Way bulge based upon spectroscopy obtained at the Observatorio Astron\'omico Nacional in the Sierra San Pedro M\'artir (OAN-SPM) using the Manchester Echelle Spectrograph. The first sample includes objects early in their evolution, having high H$\beta$ luminosities, but [\ion{O}{3}]$\lambda 5007/\mathrm H\beta < 3$. The second sample comprises objects late in their evolution, with \ion{He}{2} $\lambda 4686/\mathrm H\beta > 0.5$. These planetary nebulae represent evolutionary phases preceeding and following those of the objects studied by Richer et al. (2008). Our sample of planetary nebulae with weak [\ion{O}{3}]$\lambda$5007 has a line width distribution similar to that of the expansion velocities of the envelopes of AGB stars, and shifted to systematically lower values as compared to the less evolved objects studied by Richer et al. (2008). The sample with strong \ion{He}{2} $\lambda 4686$ has a line width distribution indistinguishable from that of the more evolved objects from Richer et al. (2008), but a distribution in angular size that is systematically larger and so they are clearly more evolved. These data and those of Richer et al. (2008) form a homogeneous sample from a single Galactic population of planetary nebulae, from the earliest evolutionary stages until the cessation of nuclear burning in the central star. They confirm the long-standing predictions of hydrodynamical models of planetary nebulae, where the kinematics of the nebular shell are driven by the evolution of the central star., Comment: accepted for publication in the Astrophysical Journal