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The long-term evolution of astrophysical systems is driven by a Hamiltonian that is independent of the fast angle. As this Hamiltonian may contain explicitly time-dependent parameters, the conservation of mechanical energy is not guaranteed in such systems. We derive how the semi-major axis evolves in these cases. We analyze two astrophysically interesting examples, those of the harmonic and quadrupole perturbations., Comment: 7 pages (without appendix and reference list), 5 figures

Here we present a continuation of the work that was based on video observations of the Tau Her 2022 outburst from the McDonald Observatory, Texas, US. On the night of the maximum in 2022 we detected 626 individual Tau Her meteors, for which we estimated photovisual magnitudes and analysed their distribution on the sky to determine the radiant position in an innovative way. The derived population index is $5.56 \pm 1.83$, while the radiant position for the mid-time of the observations is: $\mathrm{RA} = 209.71 ^\circ \pm 1.01 ^\circ$, $\mathrm{Dec} = 27.73 ^\circ \pm 0.07 ^\circ$. Both measurements are in good agreement with other results in the literature, although our population index seems to be higher than most of the published values. We speculate this might be due to the higher sensitivity of our equipment to fainter meteors.

As part of an intensive effort to observe the predicted 2022 Tau Herculids outburst, we recorded almost 800 individual meteor streaks on May 30th and 31st, 2022, using a high-sensitivity Sony~$\alpha$7 camera. The video recordings were obtained under perfect conditions at the McDonald Observatory, Texas, USA. The meteor sample is dominated by the predicted Tau Herculids shower, however, we also noted significant activity of sporadic meteors and other possible weak showers. We found that the time of the maximum activity matched very well the predictions, while we note the large fraction of faint meteors that were not detectable visually. We determined the radiant, and the time evolution of the activities and currently we are working on the determination of the brightness statistics.

We present statistical analysis of visual meteor data taken with networks of meteor cameras operating in Hungary between 2020 and 2023. We use three different camera systems: a set of traditional MetRec-based video cameras, a self-developed automated DSLR camera system and a network of newly installed AllSky7 camera stations. Similarities and differences between the data produced by the three systems, aimed at recording different types of meteor phenomena, are presented and discussed., Comment: accepted for publication in WGN, the Journal of the International Meteor Organization (IMO)

Here we present an efficient method for finding and using a nonlocal symmetry admitted by a rational second order ordinary differential equation (rational 2ODE) in order to find a Liouvillian first integral (belonging to a vast class of Liouvillian functions). In a first stage, we construct an algorithm (improving the methodde veloped in [1]) that computes a nonlocal symmetry of a rational 2ODE. In ase cond stage, based on the knowledge of this symmetry, it is possible to construct three polynomial vector fields (in R2), which "share" the Liouvillian first integral with the rational 2ODE. These "plane" polynomial vector fields can be used to construct a procedure (based on an idea developed in [2]) to determine an integrating factor for the rational 2ODE with a fast probabilistic algorithm. The main advantages of the proposed method are: the obtaining of the nonlocal symmetry is algorithmic and very efficient and, furthermore, its use to find an integrating factor is a sequence of linear or quasilinear processes.

We investigate the use of spinors to describe the secular evolution of quasi-Keplerian systems. Evaluating their Poisson brackets, we show that the components of a properly-chosen spinor are canonical variables. We illustrate this formalism with a satellite's motion around an oblate body., Comment: 12 pages, no figures

We investigate the hierarchical gravitational three-body problem, in which a binary is perturbed by a distant object that orbits on a Keplerian ellipse around the binary itself. This phenomenon, known as Kozai-Lidov mechanism in the literature, results in large-amplitude oscillations of the orbital elements, like eccentricity, which may significantly influence the evolution of many astrophysical systems: from minor bodies and planets to even supermassive black holes. The standard approach found in the literature describes this phenomenon in the framework of Hamiltonian mechanics. Here we derive the long term evolution of the triple with elementary tools, treating the binary as a dipole interacting with the gravitational field of the tertiary and describe the dynamics using forces and torques instead of the usual Hamiltonian formalism. This highlights another aspect of the problem and is likely an easier way to introduce the problem at the undergraduate level., Comment: A pedagogical paper about Kozai-Lidov mechanism

Generalized extreme value (GEV) regression is often more adapted when we investigate a relationship between a binary response variable $Y$ which represents a rare event and potentiel predictors $\mathbf{X}$. In particular, we use the quantile function of the GEV distribution as link function. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, test of hypothesis) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods. Bootstrapping estimates the properties of an estimator by measuring those properties when sampling from an approximating distribution. In this paper, we fitted the generalized extreme value regression model, then we performed parametric bootstrap method for testing hupthesis, estimating confidence interval of parameters for generalized extreme value regression model and a real data application.

Logistic regression model is widely used in many studies to investigate the relationship between a binary response variable $Y$ and a set of potential predictors $\mathbf X$. The binary response may represent, for example, the occurrence of some outcome of interest ($Y=1$ if the outcome occurred and $Y=0$ otherwise). When the dependent variable $Y$ represents a rare event, the logistic regression model shows relevant drawbacks. In order to overcome these drawbacks we propose the Generalized Extreme Value (GEV) regression model. In particular, we suggest the quantile function of the GEV distribution as link function, so our attention is focused on the tail of the response curve for values close to one. A sample of observations is said to contain a cure fraction when a proportion of the study subjects (the so-called cured individuals, as opposed to the susceptibles) cannot experience the outcome of interest. One problem arising then is that it is usually unknown who are the cured and the susceptible subjects, unless the outcome of interest has been observed. In these settings, a logistic regression analysis of the relationship between $\mathbf X$ and $Y$ among the susceptibles is no more straightforward. We develop a maximum likelihood estimation procedure for this problem, based on the joint modeling of the binary response of interest and the cure status. We investigate the identifiability of the resulting model. Then, we conduct a simulation study to investigate its finite-sample behavior, and application to real data.

In this paper, we propose an Adaptive Realized Hyperbolic GARCH (A-Realized HYGARCH) process to model the long memory of high-frequency time series with possible structural breaks. The structural change is modeled by allowing the intercept to follow the smooth and flexible function form introduced by Gallant (1984). In addition, stability conditions of the process are investigated. A Monte Carlo study is investigated in order to illustrate the performance of the A-Realized HYGARCH process compared to the Realized HYGARCH with or without structural change.

In this paper, we propose the realized Hyperbolic GARCH model for the joint-dynamics of lowfrequency returns and realized measures that generalizes the realized GARCH model of Hansen et al.(2012) as well as the FLoGARCH model introduced by Vander Elst (2015). This model is sufficiently flexible to capture both long memory and asymmetries related to leverage effects. In addition, we will study the strictly and weak stationarity conditions of the model. To evaluate its performance, experimental simulations, using the Monte Carlo method, are made to forecast the Value at Risk (VaR) and the Expected Shortfall (ES). These simulation studies show that for ES and VaR forecasting, the realized Hyperbolic GARCH (RHYGARCH-GG) model with Gaussian-Gaussian errors provide more adequate estimates than the realized Hyperbolic GARCH model with student- Gaussian errors.

We study dynamical systems which admit action-angle variables at leading order which are subject to nearly resonant perturbations. If the frequencies characterizing the unperturbed system are not in resonance, the long-term dynamical evolution may be integrated by orbit-averaging over the high-frequency angles, thereby evolving the orbit-averaged effect of the perturbations. It is well known that such integrators may be constructed via a canonical transformation, which eliminates the high frequency variables from the orbit-averaged quantities. An example of this algorithm in celestial mechanics is the von Zeipel transformation. However if the perturbations are inside or close to a resonance, i.e. the frequencies of the unperturbed system are commensurate, these canonical transformations are subject to divergences. We introduce a canonical transformation which eliminates the high frequency phase variables in the Hamiltonian without encountering divergences. This leads to a well-behaved symplectic integrator. We demonstrate the algorithm through two examples: a resonantly perturbed harmonic oscillator and the gravitational three-body problem in mean motion resonance., Comment: Some minor errors have been corrected. Published in AJ

A third object in the vicinity of a binary system causes variations in the eccentricity and the inclination of the binary through the Kozai-Lidov effect. We examine if such variations leave a detectable imprint on the gravitational waves of a binary consisting of intermediate mass black holes and stellar mass objects. As a proof of concept, we present an example where LISA may detect the Kozai-Lidov modulated gravitational wave signals of such sources from at least a distance of 1Mpc if the perturbation is caused by a supermassive black hole tertiary. Although the quick pericenter precession induced by general relativity significantly reduces the appropriate parameter space for this effect by quenching the Kozai-Lidov oscillations, we still find reasonable parameters where the Kozai-Lidov effect may be detected with high signal-to-noise ratios., Comment: 10 pages; resubmitted after minor revision; typo is corrected in Eq. (2)

Overlapping coefficient is a direct measure of similarity between two distributions which is recently becoming very useful. This paper investigates estimation for some well-known measures of overlap, namely Matusita's measure $\rho$, Weitzman's measure $\Delta$ and $\Lambda$ based on Kullback-Leibler. Two estimation methods considered in this study are point estimation and Bayesian approach. Two Inverse Lomax populations with different shape parameters are considered. The bias and mean square error properties of the estimators are studied through a simulation study and a real data example.

In this paper, we propose an estimator of Foster, Greer and Thorbecke class of measures $\displaystyle P(z,\alpha) = \int_0^{z}\Big(\frac{z-x}{z}\Big)^{\alpha}f(x)\, dx$, where $z>0$ is the poverty line, $f$ is the probabily density function of the income distribution and $\alpha$ is the so-called poverty aversion. The estimator is constructed with a bias reduced kernel estimator. Uniform almost sure consistency and uniform mean square consistenty are established. A simulation study indicates that our new estimator performs well.

Although their existence is not yet confirmed observationally, intermediate mass black holes (IMBHs) may play a key role in the dynamics of galactic nuclei. In this paper, we neglect the effect of the nuclear star cluster itself and investigate only how a small reservoir of IMBHs influences the secular dynamics of stellar-mass black hole binaries, using N-body simulations. We show that our simplifications are valid and that the IMBHs significantly enhance binary evaporation by pushing the binaries into the Hill-unstable region of parameter space, where they are separated by the SMBH's tidal field. For binaries in the S-cluster region of the Milky Way, IMBHs drive the binaries to merge in up to 1-6% of cases, assuming five IMBHs within 5 pc of mass 10,000 solar masses each. Observations of binaries in the Galactic center may strongly constrain the population of IMBHs therein., Comment: Accepted for publication in ApJ. 14 pages, 11 figures