An Excursion-Theoretic Approach to Stability ofDiscrete-Time Stochastic Hybrid Systems

We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of the system being different in each domain. We give conditions for L 1-boundedness of Lyapunov functions based on certain negative drift conditions outside the target set, together with some more minor assumptions. We then apply our results to a wide class of randomly switched systems (or iterated function systems), for which we give conditions for global asymptotic stability almost surely and in L 1. The systems need not be time-homogeneous, and our results apply to certain systems for which functional-analytic or martingale-based estimates are difficult or impossible to ge

Swift J1728.9-3613 is a black hole X-ray binary: spectral and timing study using NICER

We study different timing and spectral properties of the new Galactic X-ray transient Swift J1728.9-3613 using NICER and Swift, discovered by the Burst Alert Telescope (BAT) on the Neil Gehrels Swift Observatory. The source went through multiple transitions to different spectral states during the outburst, and the complete evolution created a q-shaped track in the hardness intensity diagram. A partial hysteresis is also observed in the RMS-intensity diagram, which is another well-defined phenomenon of black hole transients. In SIMS, power density spectra were dominated by broadband noise components, and two type B QPOs were detected. We have fitted 1-10 keV energy spectra obtained from NICER observations that were performed during the outburst, and the temporal evolution of spectral parameters were studied. On MJD 58584.69, a small-scale reflare happened, and we observed that the spectral index decreased to a much lower value associated with finite changes in other spectral parameters also, and the 1-10 keV averaged flux also increased. We observed that the innermost radius of the accretion disc was almost constant during the soft state, which corresponds to the Innermost Stable Circular Orbit (ISCO). We have measured the lower limit of mass of the compact object to be approximately 4.6 M, considering a non-spinning black hole binary system, by fitting 1-10 keV NICER spectra with the diskbb component. The soft-to-hard transition occurred when the bolometric luminosity was 0.01 times the Eddington luminosity. Based on our combined study of the evolution of the timing and spectral properties, we conclude that the new source Swift J1728.9-3613 is a black hole X-ray binary.Comment: 6 figures, 2 tables, submitted in MNRA

Rate enhancement of gated drift-diffusion process by optimal resetting

`Gating' is a widely observed phenomenon in biochemistry that describes the transition between the activated (or open) and deactivated (or closed) states of an ion-channel, which makes transport through that channel highly selective. In general, gating is a mechanism that imposes an additional restriction on a transport, as the process ends only when the `gate' is open and continues otherwise. When diffusion occurs in presence of a constant bias to a {\it gated} target, i.e., to a target that switches between an open and a closed state, the dynamics essentially slows down compared to {\it ungated} drift-diffusion, resulting in an increase in the mean completion time. In this work, we utilize stochastic resetting as an external protocol to counterbalance the delay due to gating. We consider a particle that undergoes drift-diffusion in the presence of a stochastically gated target and is moreover subjected to a rate-limiting resetting dynamics. Calculating the minimal mean completion time rendered by an optimal resetting for this exactly-solvable system, we construct a phase diagram that owns three distinct phases: (i) where resetting can make gated drift-diffusion faster even compared to the original ungated process, (ii) where resetting still expedites gated drift-diffusion, but not beyond the original ungated process, and (iii) where resetting fails to expedite gated drift-diffusion. Gated drift-diffusion aptly models various stochastic processes such as chemical reactions that exclusively take place for certain activated state of the reactants. Our work predicts the conditions where stochastic resetting can act as a useful strategy to enhance the rate of such processes without compromising on their selectivity.Comment: 12 Pages, 8 Figure