Joint Markov Chain Research Articles

Broken blue-tilted inflationary gravitational waves: a joint analysis of NANOGrav 15-year and BICEP/Keck 2018 data

Recently, the pulsar timing array (PTA) collaborations havereported the evidence for a stochastic gravitational wavebackground (SGWB) at nano-Hertz band. The spectrum of inflationarygravitational wave (IGW) is unknown, which might exhibit differentpower law at different frequency-bands, thus if the PTA signal isprimordial, it will be significant to explore the underlyingimplications of current PTA and CMB data on IGW. In this Letter,we perform a joint Markov Chain Monte Carlo analysis for a brokenpower-law spectrum of IGW with the NANOGrav 15-year and BICEP/Keck2018 data. It is found that though the bestfit spectral tilt ofIGW at PTA band is n PTA T = 2.42+0.32 -0.91,at CMB band the bestfit is n CMB T = 0.55+0.37 -0.10 while a detectable amplitude of r with n CMB T ≃ 0 is still compatible. Theimplication of our results for inflation is also discussed.

Observational Constraints on Close Binary Star Evolution. I. Putative Contact Binaries with Long Periods and High Mass Ratios

Evolutionary and structural models for contact binary stars make quantitative predictions about the distribution of systems in the mass ratio (q)–orbital period (P) plane. Specifically, contact binaries containing primaries with convective envelopes are predicted to be absent at mass ratios larger than a critical threshold that is a function of orbital period and total mass. We test this prediction by characterizing candidate contact binaries that appear to have mass ratios in violation of this threshold. We obtained quadrature-phase echelle spectra (R ≈ 31,000) for 18 close binaries (0.65 day < P < 2.00 days) in the Kepler field, from which we extracted radial velocity profiles for each system. Use of a joint Markov Chain Monte Carlo fitting routine on the Kepler light curves and the radial velocity profiles allows us to retrieve all fundamental system and component parameters. Of the 18 systems, only one is a contact binary, and both components likely have radiative—not convective—envelopes. The 17 remaining systems are detached binaries (eight) or semidetached binaries (four) with ellipsoidal variations, rotating variables (four), or pulsating variables (one). Therefore, none of the systems are in violation of the theoretical mass ratio thresholds for low-mass contact binaries. The 12 noncontact binaries follow a T 2/T 1–q relation significantly weaker than expected for main-sequence components, suggesting radiative heating of the secondaries. Most of the secondaries have radii larger than main-sequence expectations, a possible consequence of heating. Four secondaries fill their Roche lobes, while none of the primaries do, possibly indicating prior mass-ratio reversal.

Adaptive neural network control for Markov jumping systems against deception attacks

This paper proposes an innovative approach for mitigating the effects of deception attacks in Markov jumping systems by developing an adaptive neural network control strategy. To address the challenge of dual-mode monitoring mechanisms, two independent Markov chains are used to describe the state changes of the system and the intermittent actuator. By employing a mapping technique, these individual chains are amalgamated into a unified joint Markov chain. Additionally, to effectively approximate the unbounded false signals injected by deception attacks, an adaptive neural network technique is skillfully built. A mode monitoring scheme is implemented to design an asynchronous control law that links the mode information between the joint Markov chain and controller with fewer modes. The paper derives sufficient criteria for the mean-square bounded stability of the resulting system based on Lyapunov theories. Finally, a numerical experiment is conducted to demonstrate the effectiveness of the proposed method.

A warm super-Neptune around the G-dwarf star TOI-1710 revealed with TESS, SOPHIE, and HARPS-N

We report the discovery and characterization of the transiting extrasolar planet TOI-1710 b. It was first identified as a promising candidate by the Transiting Exoplanet Survey Satellite. Its planetary nature was then established with SOPHIE and HARPS-N spectroscopic observations via the radial-velocity method. The stellar parameters for the host star are derived from the spectra and a joint Markov chain Monte-Carlo adjustment of the spectral energy distribution and evolutionary tracks of TOI-1710. A joint MCMC analysis of the TESS light curve and the radial-velocity evolution allows us to determine the planetary system properties. From our analysis, TOI-1710 b is found to be a massive warm super-Neptune (Mp = 28.3 ± 4.7 M⊕ and Rp = 5.34 ± 0.11 R⊕) orbiting a G5V dwarf star (Teff = 5665 ± 55 K) on a nearly circular 24.3-day orbit (e = 0.16 ± 0.08). The orbital period of this planet is close to the estimated rotation period of its host star Prot = 22.5 ± 2.0 days and it has a low Keplerian semi-amplitude K = 6.4 ± 1.0 m s−1; we thus performed additional analyses to show the robustness of the retrieved planetary parameters. With a low bulk density of 1.03 ± 0.23 g cm−3 and orbiting a bright host star (J = 8.3, V = 9.6), TOI-1710 b is one of the best targets in this mass-radius range (near the Neptunian desert) for atmospheric characterization via transmission spectroscopy, a key measurement in constraining planet formation and evolutionary models of sub-Jovian planets.

Peak-to-peak fuzzy filtering of nonlinear discrete-time systems with markov communication protocol

This study deals with the peak-to-peak fuzzy filtering problem for a class of nonlinear discrete-time systems with analog fading channels and communication protocol, in which the nonlinear system is modeled by the Takagi-Sugeno fuzzy model. In analog fading channels, a homogeneous Markov chain is forwarded to model the random time-varying amplitude attenuation. Aiming at alleviating the utilization of energy consumption and preventing data collision/congestion in constraint networks, a Markov communication protocol is exploited to orchestrate the data transmission, in which only one sensor can get permission to release the measurement during each time interval. In virtue of the merging strategy, a new joint Markov chain is presented to incorporate the fading channels and the communication protocol. Differently, in order to eliminate the obstacle of design conservatism, a novel peak-to-peak filter design methodology is developed, whose asynchronization is described by a nonhomogeneous hidden Markov model. Under the aforementioned framework, the resulting system is stochastically stable with a desired peak-to-peak performance index. To this end, a practical example is addressed to indicate the validity and applicability of the presented peak-to-peak filter design strategy.

Revisiting Proxima with ESPRESSO

Context.The discovery of Proxima b marked one of the most important milestones in exoplanetary science in recent years. Yet the limited precision of the available radial velocity data and the difficulty in modelling the stellar activity calls for a confirmation of the Earth-mass planet.Aims.We aim to confirm the presence of Proxima b using independent measurements obtained with the new ESPRESSO spectrograph, and refine the planetary parameters taking advantage of its improved precision.Methods.We analysed 63 spectroscopic ESPRESSO observations of Proxima (Gl 551) taken during 2019. We obtained radial velocity measurements with a typical radial velocity photon noise of 26 cm s−1. We combined these data with archival spectroscopic observations and newly obtained photometric measurements to model the stellar activity signals and disentangle them from planetary signals in the radial velocity (RV) data. We ran a joint Markov chain Monte Carlo analysis on the time series of the RV and full width half maximum of the cross-correlation function to model the planetary and stellar signals present in the data, applying Gaussian process regression to deal with the stellar activity signals.Results.We confirm the presence of Proxima b independently in the ESPRESSO data and in the combined ESPRESSO+ HARPS+UVES dataset. The ESPRESSO data on its own shows Proxima b at a period of 11.218 ± 0.029 days, with a minimum mass of 1.29 ± 0.13M⊕. In the combined dataset we measure a period of 11.18427 ± 0.00070 days with a minimum mass of 1.173 ± 0.086M⊕. We get a clear measurement of the stellar rotation period (87 ± 12 d) and its induced RV signal, but no evidence of stellar activity as a potential cause for the 11.2 days signal. We find some evidence for the presence of a second short-period signal, at 5.15 days with a semi-amplitude of only 40 cm s−1. If caused by a planetary companion, it would correspond to a minimum mass of 0.29 ± 0.08M⊕. We find that forthe case of Proxima, the full width half maximum of the cross-correlation function can be used as a proxy for the brightness changes and that its gradient with time can be used to successfully detrend the RV data from part of the influence of stellar activity. The activity-induced RV signal in the ESPRESSO data shows a trend in amplitude towards redder wavelengths. Velocities measured using the red end of the spectrograph are less affected by activity, suggesting that the stellar activity is spot dominated. This could be used to create differential RVs that are activity dominated and can be used to disentangle activity-induced and planetary-induced signals. The data collected excludes the presence of extra companions with masses above 0.6M⊕at periods shorter than 50 days.

Finite-Length Analyses for Source and Channel Coding on Markov Chains.

We derive finite-length bounds for two problems with Markov chains: source coding with side-information where the source and side-information are a joint Markov chain and channel coding for channels with Markovian conditional additive noise. For this purpose, we point out two important aspects of finite-length analysis that must be argued when finite-length bounds are proposed. The first is the asymptotic tightness, and the other is the efficient computability of the bound. Then, we derive finite-length upper and lower bounds for the coding length in both settings such that their computational complexity is low. We argue the first of the above-mentioned aspects by deriving the large deviation bounds, the moderate deviation bounds, and second-order bounds for these two topics and show that these finite-length bounds achieve the asymptotic optimality in these senses. Several kinds of information measures for transition matrices are introduced for the purpose of this discussion.

Performance Analysis of License Assisted Access LTE with Asymmetric Hidden Terminals

License Assisted Access (LAA) LTE (LTE-LAA) is a new type of LTE that aggregates the licensed LTE bands with the unlicensed bands via carrier aggregation. To operate in unlicensed bands, LTE-LAA adopts the listen-before-talk policy and designs its channel access mechanism similar to WLAN's DCF. In this paper, we consider an LAA network consisting of an LTE-LAA eNB coexisting with a Wi-Fi STA, and capture the {\em asymmetric hidden terminal problem} where the eNB recognizes the STA while the opposite is not true, which is caused by the asymmetric CCA thresholds between them. We model the network as a joint Markov chain (MC) consisting of two individual MCs, and derive its steady-state probabilities, throughput, and channel access delay along with other key metrics like transmit, busy, collision, and doubling probabilities. Through extensive evaluation, we confirm that the proposed model well predicts the dynamics of the LAA network, and identify important design guidelines for fair coexistence between LTE-LAA and WLAN as follows. First, LTE-LAA should design its contention window (CW) doubling policy by considering Wi-Fi's packet duration and subframe-dependent collision probabilities. Second, there exists a tradeoff between throughput and channel access delay, according to which the CW doubling policy should be adapted.

COSMOLOGICAL PARAMETERS FROM CMB MAPS WITHOUT LIKELIHOOD APPROXIMATION

ABSTRACT We propose an efficient Bayesian Markov chain Monte Carlo (MCMC) algorithm for estimating cosmological parameters from cosmic microwave background (CMB) data without the use of likelihood approximations. It builds on a previously developed Gibbs sampling framework that allows for exploration of the joint CMB sky signal and power spectrum posterior, P ( s , C &ell; &mid; d ) ?> , and addresses a long-standing problem of efficient parameter estimation simultaneously in regimes of high and low signal-to-noise ratio. To achieve this, our new algorithm introduces a joint Markov chain move in which both the signal map and power spectrum are synchronously modified, by rescaling the map according to the proposed power spectrum before evaluating the Metropolis–Hastings accept probability. Such a move was already introduced by Jewell et al., who used it to explore low signal-to-noise posteriors. However, they also found that the same algorithm is inefficient in the high signal-to-noise regime, since a brute-force rescaling operation does not account for phase information. This problem is mitigated in the new algorithm by subtracting the Wiener filter mean field from the proposed map prior to rescaling, leaving high signal-to-noise information invariant in the joint step, and effectively only rescaling the low signal-to-noise component. To explore the full posterior, the new joint move is then interleaved with a standard conditional Gibbs move for the sky map. We apply our new algorithm to simplified simulations for which we can evaluate the exact posterior to study both its accuracy and its performance, and find good agreement with the exact posterior; marginal means agree to ≲0.006σ and standard deviations to better than ∼3%. The Markov chain correlation length is of the same order of magnitude as those obtained by other standard samplers in the field.

On the feasibility of synchronous, retransmission-based cognitive networks

This paper presents a new, joint Markov chain model for the primary and secondary traffic in a cognitive radio network to assess the feasibility of opportunistic spectrum access for different operational scenarios, validated by extensive realistic Monte-Carlo simulations. Enhancing on the current literature, the generalized model allows for the consideration of a retransmission-based traffic as well as the presence of transmission queues for the primary user. The generalized model also allows for the investigation of the system behavior in the presence of imperfect sensing at the secondary users. The presented model is applicable for all primary user traffic models that use discrete-time Markov chains. An infinitely backlogged secondary user network is considered to investigate the maximum possible network utilization. The paper concludes that a percentile channel occupation of the primary user on its own is not always a sufficient metric to assess whether secondary transmission is feasible. It is shown that the interplay between primary network traffic characteristics, as well as the sensing frequency and probabilities of missed detection and false alarm for the secondary network detector are of primal importance for such feasibility claims. The results reveal that the preferred sensing frequency for the secondary users is a function of the primary user traffic pattern and that the commonly used frequency of sensing every transmission slot is not always optimal. The results also show that when sensing frequency is low, secondary utilization decreases with more bursty primary traffic, whereas the impact on primary utilization becomes less.

Tracking-by-detection of multiple persons by a resample-move particle filter

Camera networks make an important component of modern complex perceptual systems with widespread applications spanning surveillance, human/machine interaction and healthcare. Smart cameras that can perform part of the perceptual data processing improve scalability in both processing power and network resources. Based on these insights, this paper presents a particle filter for multiple person tracking designed for an FPGA-based smart camera. We propose a new joint Markov Chain Monte Carlo-based particle filter (MCMC-PF) with short Markov chains, devoted to each individual particle, in order to sample the particle swarm in relevant regions of the high dimensional state-space with increased particle diversity. Finding an efficient sampling method has become another challenge when designing particle filters, especially for those devoted to more than two or three targets. A proposal distribution, combining diffusion dynamics, learned HOG + SVM person detections, and adaptive background mixture models, limits here the well-known burst in terms of particles and MCMC iterations. This informed proposal based on saliency maps has only been marginally used in the literature in a joint state space PF framework. The presented qualitative and quantitative results--for proprietary and public video datasets--clearly show that our tracker outperforms the well-known MCMC-PF in terms of (1) tracking performances, i.e. robustness and precision, and (2) parallelization capabilities as the MCMC-PF processes the particles sequentially.