arXiv subjects

Francois Dufour

Publications and source records attributed to Francois Dufour.

9 recordsLinked to original sources

arXiv2025

Absorbing Markov Decision Processes: Geometric Properties and Sufficiency of Finite Mixtures of Deterministic Policies

In this paper we investigate several geometric properties of the set of occupancy measures. In particular, we analyse the structure of the faces generated by a given occupancy measure, together with their relative algebraic interior. We also determine the affine hulls of these faces and describe the associated parallel linear subspaces. It is shown that these structures can be fully characterised in terms of the parameters that define the underlying Markov decision process (MDP). Moreover, we establish that the class of finite mixtures of deterministic stationary policies constitutes a sufficient class of policies for uniformly absorbing MDPs with a measurable state space and multiple criteria. We also provide a characterisation of the minimal order required for a finite mixture of deterministic stationary policies to represent the performance vector of an arbitrary policy.

math.OC↗

arXiv2025

On the Feinberg-Piunovskiy Theorem and its extension to chattering policies

The Feinberg-Piunovskiy Theorem established in [14, Theorem 3.8] asserts that for a discrete-time uniformly absorbing and atomless Markov Decision Process (MDP) with Borel state space and multiple criteria, the family of deterministic stationary policies is a sufficient class of policies. In this paper, we study some related problems and some extensions. In particular dropping the atomless hypothesis, we establish that the set of chattering stationary policies is a sufficient class of policies for uniformly absorbing MDPs with measurable state space and multiple criteria. We also prove the Feinberg-Piunovskiy Theorem in the context of a measurable state space in two different ways that differ from \cite{piunovskiy19}. In particular, we show that the sufficiency of chattering stationary policies directly yields the sufficiency of deterministics stationary policies for atomless models. Our approach is partially based on the analysis of extreme points of certain convex sets of occupation measures satisfying integral type constraints. We show that for a uniformly absorbing model an extreme point of such sets is necessarily given by occupation measures induced by chattering stationary policies of order $d+1$ where $d$ is the dimension of the vector of constraints. When in addition the model $\mathsf{M}$ is atomless, then the extreme points of this constrained set of occupation measures are precisely the occupation measures generated by deterministic stationary policies satisfying these constraints.

math.PR↗

arXiv2018

Power-of-$d$-Choices with Memory: Fluid Limit and Optimality

In multi-server distributed queueing systems, the access of stochastically arriving jobs to resources is often regulated by a dispatcher, also known as load balancer. A fundamental problem consists in designing a load balancing algorithm that minimizes the delays experienced by jobs. During the last two decades, the power-of-$d$-choice algorithm, based on the idea of dispatching each job to the least loaded server out of $d$ servers randomly sampled at the arrival of the job itself, has emerged as a breakthrough in the foundations of this area due to its versatility and appealing asymptotic properties. In this paper, we consider the power-of-$d$-choice algorithm with the addition of a local memory that keeps track of the latest observations collected over time on the sampled servers. Then, each job is sent to a server with the lowest observation. We show that this algorithm is asymptotically optimal in the sense that the load balancer can always assign each job to an idle server in the large-system limit. This holds true if and only if the system load $\lambda$ is less than $1-\frac{1}{d}$. If this condition is not satisfied, we show that queue lengths are tightly bounded by $\left\lceil - \frac{ \log (1-\lambda)}{\log (\lambda d +1)} \right\rceil$. This is in contrast with the classic version of the power-of-$d$-choice algorithm, where at the fluid scale a strictly positive proportion of servers containing $i$ jobs exists for all $i\ge 0$, in equilibrium. Our results quantify and highlight the importance of using memory as a means to enhance performance in randomized load balancing.

math.PR↗

arXiv2014

A broadband X-ray study of the Geminga pulsar with NuSTAR and XMM-Newton

We report on the first hard X-ray detection of the Geminga pulsar above 10 keV using a 150 ks observation with the NuSTAR observatory. The double-peaked pulse profile of non-thermal emission seen in the soft X-ray band persists at higher energies. Broadband phase-integrated spectra over the 0.2-20 keV band with NuSTAR and archival XMM-Newton data do not fit to a conventional two-component model of a blackbody plus power-law, but instead exhibit spectral hardening above ~5 keV. We find two spectral models fit the data well: (1) a blackbody (kT1 ~ 42 eV) with a broken power-law (Gamma1 ~ 2.0, Gamma2 ~ 1.4 and Ebreak ~ 3.4 keV), and (2) two blackbody components (kT1 ~ 44 eV and kT2 ~ 195 eV) with a power-law component (Gamma ~ 1.7). In both cases, the extrapolation of the Rayleigh-Jeans tail of the thermal component is consistent with the UV data, while the non-thermal component overpredicts the near-infrared data, requiring a spectral flattening at E ~ 0.01 - 1 keV. While strong phase variation of the power-law index is present below ~5 keV, our phase-resolved spectroscopy with NuSTAR indicates that another hard non-thermal component with Gamma ~ 1.3 emerges above ~5 keV. The spectral hardening in non-thermal X-ray emission as well as spectral flattening between the optical and X-ray bands argue against the conjecture that a single power-law may account for multi-wavelength non-thermal spectra of middle-aged pulsars.

astro-ph.HE↗

arXiv2014

NuSTAR results and future plans for magnetar and rotation-powered pulsar observations

The Nuclear Spectroscopic Telescope Array (NuSTAR) is the first focusing hard X-ray mission in orbit and operates in the 3-79 keV range. NuSTAR's sensitivity is roughly two orders of magnitude better than previous missions in this energy band thanks to its superb angular resolution. Since its launch in 2012 June, NuSTAR has performed excellently and observed many interesting sources including four magnetars, two rotation-powered pulsars and the cataclysmic variable AE Aquarii. NuSTAR also discovered 3.76-s pulsations from the transient source SGR J1745-29 recently found by Swift very close to the Galactic Center, clearly identifying the source as a transient magnetar. For magnetar 1E 1841-045, we show that the spectrum is well fit by an absorbed blackbody plus broken power-law model with a hard power-law photon index of ~1.3. This is consistent with previous results by INTEGRAL and RXTE. We also find an interesting double-peaked pulse profile in the 25-35 keV band. For AE Aquarii, we show that the spectrum can be described by a multi-temperature thermal model or a thermal plus non-thermal model; a multi-temperature thermal model without a non-thermal component cannot be ruled out. Furthermore, we do not see a spiky pulse profile in the hard X-ray band, as previously reported based on Suzaku observations. For other magnetars and rotation-powered pulsars observed with NuSTAR, data analysis results will be soon available.

astro-ph.HE↗

arXiv2013

NuSTAR observations of magnetar 1E 1841-045

We report new spectral and temporal observations of the magnetar 1E 1841-045 in the Kes 73 supernova remnant obtained with the Nuclear Spectroscopic Telescope Array (NuSTAR). Combined with new Swift and archival XMM-Newton and Chandra observations, the phase-averaged spectrum is well characterized by a blackbody plus double power-law model, in agreement with previous, multi-mission X-ray results. However, we are unable to reproduce the spectral results reported using Suzaku observations. The pulsed fraction of the source is found to increase with photon energy. The measured rms pulsed fraction is ~12% and ~17% at ~20 keV and ~50 keV, respectively. We detect a new feature in the 24--35 keV band pulse profile that is uniquely double-peaked. This feature may be associated with a possible absorption or emission feature in the phase-resolved spectrum. We fit the X-ray data using the recently developed electron-positron outflow model of Beloborodov (2013) for the hard X-ray emission from magnetars. This produces a satisfactory fit allowing a constraint on the angle between the rotation and magnetic axes of the neutron star of ~20 degrees and on the angle between the rotation axis and line-of-sight of ~50 degrees. In this model, the soft X-ray component is inconsistent with a single blackbody; adding a second blackbody or a power-law component fits the data. The two-blackbody interpretation suggests a hot spot of temperature kT~0.9 keV occupying ~1% of the stellar surface.

astro-ph.HE↗

arXiv2013

Swift observations of 1FGL J1018.6-5856

We report on X-ray properties of the gamma-ray binary 1FGL J1018.6-5856 using observations obtained with the Swift X-ray telescope. Using 54 observations made between MJD 55575 and 55984, we find that the X-ray flux is modulated at a period of 16.57 +/- 0.11 days, consistent with previous reports based on gamma-ray data. We find that the X-ray maximum at phase 0 previously reported may not be a persistent feature of the source: the dramatic increases at phase 0 were detected only for ~100 days and not thereafter. Rather, the persistent sinusoidal maximum seems to be at phase 0.3--0.4, and is misaligned with the gamma-ray (GeV) peak. We also find evidence that the source's X-ray flux is correlated with the spectral hardness in the 0.5--10 keV band. Such a correlation has also been reported in the gamma-ray binaries LS 5039 and LS I+61d303 and can help us to understand the X-ray emission mechanisms of the sources.

astro-ph.HE↗

arXiv2013

NuSTAR discovery of a 3.76-second transient magnetar near Sagittarius A*

We report the discovery of 3.76-s pulsations from a new burst source near Sgr A* observed by the NuSTAR Observatory. The strong signal from SGR J1745-29 presents a complex pulse profile modulated with pulsed fraction 27+/-3 % in the 3-10 keV band. Two observations spaced 9 days apart yield a spin-down rate of Pdot = (6.5+/-1.4)x10^{-12}. This implies a magnetic field B = 1.6x10^14 G, spin-down power Edot = 5x10^33 erg/s, and characteristic age P/2Pdot = 9x10^3 yr, for the rotating dipole model. However, the current Pdot may be erratic, especially during outburst. The flux and modulation remained steady during the observations and the 3-79 keV spectrum is well fitted by a combined blackbody plus power-law model with temperature kT_BB = 0.96+/-0.02 keV and photon index = 1.5+/-0.4, respectively. The neutral hydrogen column density (nH ~ 1.4x10^23 cm^{-2}) measured by NuSTAR and Swift suggests that SGR J1745-29 is located at or near the Galactic Center. The lack of an X-ray counterpart in the published Chandra survey catalog sets a quiescent 2-8 keV luminosity limit of Lx ~< 10^32 erg/s. The bursting, timing, and spectral properties indicate a transient magnetar undergoing an outburst with 2-79 keV luminosity up to 3.5x10^35 erg/s for a distance of 8 kpc. SGR J1745-29 joins a growing subclass of transient magnetars, indicating that many magnetars in quiescence remain undetected in the X-ray band or have been detected as high-B radio pulsars. The peculiar location of SGR J1745-29 has important implications for the formation and dynamics of neutron stars in the Galactic Center region.

astro-ph.HE↗

arXiv2008

Almost Sure Stabilization for Adaptive Controls of Regime-switching LQ Systems with A Hidden Markov Chain

This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a hidden Markov chain. Different from previous work on stabilization of adaptive controlled systems with a hidden Markov chain, where average criteria were considered, this work focuses on the almost sure stabilization or sample path stabilization of the underlying processes. Under simple conditions, it is shown that as long as the feedback controls have linear growth in the continuous component, the resulting process is regular. Moreover, by appropriate choice of the Lyapunov functions, it is shown that the adaptive system is stabilizable almost surely. As a by-product, it is also established that the controlled process is positive recurrent.

math.PR↗