Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment

The large deviations at level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasi-stationary states in terms of their empirical time-averaged density and of their time-averaged empirical flows over a large time-window T. The standard spectral problem for the slowest relaxation mode can be recovered from the full optimization of the extinction rate over all these empirical observables and the equivalence can be understood via the Doob generator of the process conditioned to survive up to time T. The large deviation properties of any time-additive observable of the Markov trajectory before extinction can be derived from the level 2.5 via the decomposition of the time-additive observable in terms of the empirical density and the empirical flows. This general formalism is described for continuous-time Markov chains, with applications to population birth–death model in a stable or in a switching environment, and for diffusion processes in dimension d.

Inhomogeneous asymmetric exclusion processes between two reservoirs: large deviations for the local empirical observables in the mean-field approximation

For a given inhomogeneous exclusion processes on N sites between two reservoirs, the trajectories probabilities allow to identify the relevant local empirical observables and to obtain the corresponding rate function at level 2.5. In order to close the hierarchy of the empirical dynamics that appear in the stationarity constraints, we consider the simplest approximation, namely the mean-field approximation for the empirical density of two consecutive sites, in direct correspondence with the previously studied mean-field approximation for the steady state. For a given inhomogeneous totally asymmetric model, this mean-field approximation yields the large deviations for the joint distribution of the empirical density profile and of the empirical current around the mean-field steady state; the further explicit contraction over the current allows to obtain the large deviations of the empirical density profile alone. For a given inhomogeneous asymmetric model, the local empirical observables also involve the empirical activities of the links and of the reservoirs; the further explicit contraction over these activities yields the large deviations for the joint distribution of the empirical density profile and of the empirical current. The consequences for the large deviations properties of time-additive space-local observables are also discussed in both cases.

A mean-field approach to self-interacting networks, convergence and regularity

The propagation of chaos property for a system of interacting particles, describing the spatial evolution of a network of interacting filaments is studied. The creation of a network of mycelium is analyzed as representative case, and the generality of the modeling choices are discussed. Convergence of the empirical density for the particle system to its mean-field limit is proved, and a result of regularity for the solution is presented.

Density - Velocity Relationship and Prediction of Lithology Variation Using Physical Analysis in Kf-4 Well of The Kifl Oil Field, Yamama Formation, South of Iraq

The density-velocity relation is an important tool used to predict one of these two parameters from the other. A new empirical density –velocity equation was derived in Kf-4 well at Kifl Oil Field, south of Iraq. The density was derived from Gardner equation and the results obtained were compared with the density log (ROHB) in Kl-4 well. The petrophysical analysis was used to predict the variations in lithology of Yamama Formation depending on the well logs data, such as density, gamma, and neutron logs. The physical analysis of rocks depended on the density, Vp, and Vs values to estimate the elastic parameters, i.e. acoustic impedance (AI) and Vp/Vs ratio, to predict the lithology and hydrocarbon indicators. According to the results of physical properties, Yamama Formation is divided into five units in Kf-4 well at Kifl Oil Field. The lithology of Yamama Formation was found to consist of limestone, dolomite, shale, and anhydrite rocks.

Brief communication: Evaluation of multiple empirical, density-dependent snow conductivity relationships at East Antarctica

Nine density-dependent empirical thermal conductivity relationships for firn were compared against data from three Automatic Weather Stations at climatically-different East Antarctica sites (Dome A, Eagle and LGB69). The empirical relationships were validated using a vertical, one-dimensional thermal diffusion model and a phase-change based firn diffusivity estimation method. The best relationships for these East Antarctica sites were identified by comparing the modeled and observed firn temperature at the depth of 1 m and 3 m, and from the mean heat conductivities over two depth intervals (1–3 m and 3–10 m). Among the nine relationships, that proposed by Calonne et al. (2011) appears to have the best performance. This study provides useful reference for firn thermal conductivity parameterizations in land modeling or snow-air interaction studies on the Antarctica Ice Sheet.

The promise and limitations of improved-accuracy gravity field measurements for Uranus and Neptune

<p>Uranus and Neptune present unique challenges to planetary modelers. The<br>composition of the so-called ice giants is very uncertain, even more so than the<br>composition of the gas giants. For instance, it is far from clear that either<br>planet's composition is dominated by water. Instead, the composition of Uranus and<br>Neptune likely includes water and other refractory elements in large quantities as<br>well as a substantial H/He envelope. Furthermore, formation models also predict<br>that composition gradients are likely in the interiors of these planets, rather<br>than a neat differentiation into layers of homogeneous composition. (See Helled<br>and Fortney 2020 and references within.)</p><p>A key question that impacts the science case for a potential orbiting mission to<br>Uranus or Neptune is how will more precise measurements of the gravitational field<br>better constrain either planet's interior density profile and composition.<br>Surprisingly, there is yet no published answer to this question.  Here, we present<br>new work that explores this issue, using a Bayesian framework that allows<br>exploration of a wide range of interior density profiles.</p><p>Our approach, which builds off our previous work for Saturn (Movshovitz et al.,<br>2020) and that of others  (e.g. Marley et al., 1995, Helled et al., 2011) takes a<br>relatively unbiased view of the interior structure by employing so-called<br>empirical density profiles. A parameterization is applied to the density profiles<br>directly (via mathematical base functions) instead of to an assumed layered<br>composition (H/He, water, rocks). While some of these empirical density profiles<br>may imply unrealistic compositions, they can also probe solutions that would be<br>missed by the standard layered-composition approach.</p><p>Here we will present models of Uranus and Neptune constructed with this approach,<br>and ask two questions: 1) How large is the space of possible solutions today? 2)<br>How much will it be reduced should a future mission to Uranus and Neptune improve<br>the precision on their gravity field measurements by several orders of magnitude,<br>to the level now available for Jupiter and Saturn?</p>

Confidence Interval for Change Point in Hazard Rate With Staggered Entry

We consider the construction of a con?dence region (interval) for a change point in hazard rate of the patients survival distribution when the patients enter the trial at random times. We show that the local- likelihood ratio process converges weakly to a certain process and obtain the maximum distribution of the process which does not depend on the change point, and thus can be used to construct the confidence region for the change point. We also compare the limiting density function to the empirical density and discuss the empirical coverage probability of the confidence interval by simulation. Stanford Heart Transplant data are used for illustration.

Limiting spectral distribution of large dimensional random matrices of linear processes

The limiting spectral distribution (LSD) of large sample radom matrices is derived under dependence conditions. We consider the matrices \(X_{N}T_{N}X_{N}^{\prime}\) , where \(X_{N}\) is a matrix (\(N \times n(N)\)) where the column vectors are modeled as linear processes, and \(T_{N}\) is a real symmetric matrix whose LSD exists. Under some conditions we show that, the LSD of \(X_{N}T_{N}X_{N}^{\prime}\) exists almost surely, as \(N \rightarrow \infty\) and \(n(N)/N \rightarrow c > 0\). Numerical simulations are also provided with the intention to study the convergence of the empirical density estimator of the spectral density of \(X_{N}T_{N}X_{N}^{\prime}\).