Search

We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a transform order. Notably, this method exhibits broad applicability, particularly since several well-known nonparametric distribution families can be defined using relevant transform orders, including the convex and the star transform orders. In the context of convex-ordered families, we demonstrate that applying Jensen's inequality enables the derivation of bounds for the probability that a random variable exceeds the expected value of its corresponding order statistic.

Floods are one of the deadliest natural hazards and are fueled by excessive urbanization. Urban development decreases infiltration by reducing pervious areas and increases the accumulation of pollutants during dry weather. During wet weather events, there is an increase in the levels of pollution concentrations and stormwater runoff that eventually reach creeks and rivers. Polluted stormwater runoff may be sources of water supply. Modeling the quantity and quality dynamics of stormwater runoff requires a coupled hydrodynamic module capable of estimating the transport and fate of pollutants. In this paper, we evaluate the applicability of a distributed hydrodynamic model coupled with a water quality model (HydroPol2D). First, the model is compared to GSSHA and WCA2D in the V-Tilted catchment, and the limitation of the critical velocity of WCA2D is investigated. We also applied the model in a laboratory wooden board catchment, focusing on the validation of the numerical approach to simulate water quality dynamics. Then, we apply HydroPol2D in the Tijuco Preto catchment, in Sao Carlos - Brazil, and compare the modeling results with the full momentum solver of the Hydrologic Engineering Center - River System Analysis (HEC-RAS). The model implementation, the governing equations, and the estimation of input data are discussed, indicating the challenges and opportunities of the application of distributed models in poorly-gauged catchments. For a 1-yr return period of rainfall and antecedent dry days and assuming an uncertainty of $40\%$ in the water quality parameters, the results indicate that the maximum concentration of total suspended solids (TSS), the maximum load and the mass of the pollutant washed in $30\%$ of the volume are, $456~\pm~260~\mathrm{mg.L^{-1}.km^{-2}}$, $\mathrm{2.56 \pm 0.4~kg.s^{-1}.km^{-2}}$, and $\mathrm{89\%~\pm~10\%}$, respectively., Comment: Preprint submitted to Journal of Hydrology

This paper proposes an integrated architecture for Thrust Vector Control (TVC) and state estimation for low-cost small-scale launchers, naturally unstable, and propelled by a solid motor. The architecture is based on a non-linear, six-degrees-of-freedom model for the generic thrust-vector-controlled launcher dynamics and kinematics, deduced and implemented in a realistic simulation environment. For estimation and control design purposes, a linearized version of the model is proposed. Single-nozzle TVC actuation is adopted, allowing for pitch and yaw control, with the control law being derived from the Linear Quadratic Regulator (LQR) with additional integral action (LQI). The control system is implemented through gain scheduling. Full state estimation is performed resorting to complementary kinematic filters, closely related to linear Kalman fitering theory. The architecture, composed by the navigation and control systems, is tested in simulation environment, demonstrating satisfactory attitude tracking performance and robustness to both external disturbances and model uncertainties., Comment: 15 pages, 20 figures, preprint submitted to Aerospace Science and Technology (AESCTE)

The modified Rodrigues parameters (MRP) consist of two numerically different triplets that, by switching between them, yield a minimal globally non-singular attitude description with advantageous properties. The MRP space results from the Alexandroff compactification of the three-dimensional Euclidean space and is a double cover of $\mathrm{SO(3)}$. By capitalizing on instrumental properties of the covering map, this paper proposes a novel hybrid dynamic path-lifting mechanism to unambiguously and robustly extract the MRP from the attitude space. This hybrid solution allows applying an MRP-based feedback controller to the attitude dynamics in the base space while preserving its asymptotic and exponential stability properties. Furthermore, by profiting from the distinct characteristics of the MRP, the resulting interconnection is impervious to the unwinding phenomenon. The design and validation of an MRP-based controller exemplify the application of the proposed algorithm alongside the novel results for equivalence of stability between spaces. The solution renders the attitude space tracking dynamics robustly globally exponentially stable, demonstrating the potential of this novel methodology.

To improve nonparametric estimates of lifetime distributions, we propose using the increasing odds rate (IOR) model as an alternative to other popular, but more restrictive, ``adverse ageing'' models, such as the increasing hazard rate one. This extends the scope of applicability of some methods for statistical inference under order restrictions, since the IOR model is compatible with heavy-tailed and bathtub distributions. We study a strongly uniformly consistent estimator of the cumulative distribution function of interest under the IOR constraint. Numerical evidence shows that this estimator often outperforms the classic empirical distribution function when the underlying model does belong to the IOR family. We also study two different tests, aimed at detecting deviations from the IOR property, and we establish their consistency. The performance of these tests is also evaluated through simulations.

After a sudden quench from the disordered high-temperature $T_0\to\infty$ phase to a final temperature below the critical point $T_F \ll T_c$, the non-conserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a square lattice (2dIM) initially approaches the critical percolation state before entering the coarsening regime. This approach involves two timescales associated with the first appearance (at time $t_{{\rm p}_1}>0$) and stabilization (at time $t_{\rm p}>t_{{\rm p}_1}$) of a giant percolation cluster, as previously reported. However, the microscopic mechanisms that control such timescales are not yet fully understood. In this paper, in order to study their role on each time regime after the quench ($T_F=0$), we distinguish between spin flips that decrease the total energy of the system from those that keep it constant, the latter being parametrized by the probability $p$. We show that the cluster size heterogeneity $H(t,p)$ and the typical domain size $\ell (t,p)$ have no dependence on $p$ in the first time regime up to $t_{{\rm p}_1}$. On the other hand, the time for stabilizing a percolating cluster is controlled by the acceptance probability of constant-energy flips: $t_{\rm p}(p) \sim p^{-1}$ for $p\ll 1$ (at $p=0$, the dynamics gets stuck in a metastable state). These flips are also the relevant ones in the later coarsening regime where dynamical scaling takes place. Because the phenomenology on the approach to the percolation point seems to be shared by many 2d systems with a non-conserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and effective way to set, through the dynamics itself, $t_{{\rm p}_1}$ and $t_{\rm p}$ in such systems., Comment: 7 pages, 4 figures; supplemental material: 1 video

The size and shape of the region affected by an outbreak is relevant to understand the dynamics of a disease and help to organize future actions to mitigate similar events. A simple extension of the SIR model is considered, where agents diffuse on a regular lattice and the disease may be transmitted when an infected and a susceptible agents are nearest neighbors. We study the geometric properties of both the connected cluster of sites visited by infected agents (outbreak cluster) and the set of clusters with sites that have not been visited. By changing the density of agents, our results show that there is a mixed-order (hybrid) transition where the region affected by the disease is finite in one phase but percolates through the system beyond the threshold. Moreover, the outbreak cluster seems to have the same exponents of the backbone of the critical cluster of the ordinary percolation while the clusters with unvisited sites have a size distribution with a Fisher exponent $\tau<2$., Comment: 7 pages, 7 figures

In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of statistical functionals, aside from their large sample properties. We study such behavior in terms of the usual stochastic order. For this purpose, we introduce a generalized family of stochastic orders, which is referred to as transform orders, showing that it provides a flexible framework for deriving stochastic monotonicity results. Given that our general definition makes it possible to obtain some well-known ordering relations as particular cases, we can easily apply our method to different families of functionals. These include some prominent inequality measures, such as the generalized entropy, the Gini index, and its generalizations. We also illustrate the applicability of our approach by determining the least favorable distribution, and the behavior of some bootstrap statistics, in some goodness-of-fit testing procedures.