Nonuniform Estimates Research Articles

Estimation of nonuniformity in characteristics of strong rock masses for radioactive waste disposal

Estimation of nonuniformity in characteristics of strong rock masses for radioactive waste disposal

Single image dehazing using extended local dark channel prior

Image dehazing is an important technique aimed at eliminating the haze in the atmosphere to enhance the image's visual quality. There are many applications where it has been used as a prepossessing step, such as in event detection. In recent years, the dark channel prior methodology has been recognised as an effective approach for eliminating haze from hazy images. However, the main drawback of the existing dark channel prior methodology is that it only considers a single colour channel of the RGB image with pixels having minimum intensity values. This non-uniform selection of the dark channel from a single channel eradicates the effect of the transmission across the different channels of the hazy image. Hence, the haze cannot be removed to a great extent using the existing method. Thus, to address the problem of non-uniform estimation of the dark channel by the existing dark channel prior method, we propose an approach where the dark channel will be computed from all three channels of an image by selecting the minimum intensity. The main advantage of using the proposed prior-based methodology for image dehazing over deep neural network-based models such as CNN or GANs is that training deep models requires a large amount of training data, thus resulting in a longer training time. Experimental outcomes exhibit that the proposed technique outperforms state-of-the-art methods on synthetic datasets as well as real-world hazy images. The findings demonstrate that the proposed technique obtains better accuracy as compared to the state-of-the-art methods and recent deep learning-based models over the D-HAZY, I-HAZE, O-HAZE and Middlebury databases.

Navier–Stokes–Fourier system with phase transitions

We consider the Navier–Stokes–Fourier (mathcal NSF) system for a class of compressible fluids that exhibit a gas-liquid phase transition at low temperatures. For the initial-boundary value problem corresponding to thermally insulated end-points that are held at a constant pressure, we establish the existence and uniqueness of temporally global classical solutions. A novel feature of the analysis presented here is the derivation of uniform point-wise apriori estimates on the specific volume, which refines the non-uniform estimates framework developed in Watson (Arch Ration Mech Anal 153:1–37, 2000).

A Refinement of Non-Uniform Estimates of the Rate of Convergence in the Central Limit Theorem Under the Existence of Moments of Orders No Higher Than Two

Non-uniform estimates of the rate of convergence in the central limit theorem for sums of independent identically distributed summands are refined under the condition that the summands possess moments of orders no higher than two.

Non-uniform Gradient Estimates for SDEs with Local Monotonicity Conditions

By using the coupling method and the localization technique, we establish non-uniform gradient estimates for Markov semigroups of diffusions or stochastic differential equations driven by pure jump Levy noises, where the coefficients only satisfy local monotonicity conditions.

Approximations for sums of three-valued 1-dependent symmetric random variables

The sum of symmetric three-point 1-dependent nonidentically distributed random variables is approximated by a compound Poisson distribution. The accuracy of approximation is estimated in the local and total variation norms. For distributions uniformly bounded from zero,the accuracy of approximation is of the order O(n–1). In the general case of triangular arrays of identically distributed summands, the accuracy is at least of the order O(n–1/2). Nonuniform estimates are obtained for distribution functions and probabilities. The characteristic functionmethod is used.

Rate of convergence in the transfer theorem for min-scheme

In this paper non-uniform estimate of convergence rate in the min-scheme is obtained. Presented results make the estimates, given in [1] and [2], more precise.

Lower Bounds for the Constants in Non-Uniform Estimates of the Rate of Convergence in the CLT

We conduct a comparative analysis of the constants in the Nagaev–Bikelis and Bikelis–Petrov inequalities that establish non-uniform estimates of the rate of convergence in the central limit theorem for sums of independent random variables possessing finite absolute moments of order 2 + δ with δ ∈ [0, 1]. We provide lower bounds for the above constants and also for the constants in the structural improvements of Nagaev–Bikelis’ inequality. The lower bounds in Nagaev–Bikelis’ inequality and its structural improvements are given as a function of δ and a structural parameter s as well as uniform with respect to both δ and s. Lower bounds for the constants in Nagaev–Bikelis’ with δ < 1 and Bikelis–Petrov’s inequalities are presented for the first time.

Mathematical Simulation of Processes in Air ICP/RF Plasma Torch for High-Power Applications

This article presents the results of the mathematical simulation of processes in air ICP/RF plasma torch for high-power applications. This investigation is a part of a wide research focused on estimation and reduction of nonuniformity of plasma temperature and velocity fields. The results showed the effect of dissipated power and gas flow rate on the plasma temperature and axial velocity distributions.

Non-Uniform Bounds in the Poisson Approximation With Applications to Informational Distances I

We explore asymptotically optimal bounds for deviations of Bernoulli convolutions from the Poisson limit in terms of the Shannon relative entropy and the Pearson $\chi^2$-distance. The results are based on proper non-uniform estimates for densities. They deal with models of non-homogeneous, non-degenerate Bernoulli distributions.

Asymptotics for the sum of three state Markov dependent random variables

The insurance model when the amount of claims depends on the state of the insured person (healthy, ill, or dead) and claims are connected in a Markov chain is investigated. The signed compound Poisson approximation is applied to the aggregate claims distribution after $n\in \mathbb {N}$ periods. The accuracy of order $O(n^{-1})$ and $O(n^{-1/2})$ is obtained for the local and uniform norms, respectively. In a particular case, the accuracy of estimates in total variation and non-uniform estimates are shown to be at least of order $O(n^{-1})$. The characteristic function method is used. The results can be applied to estimate the probable loss of an insurer to optimize an insurance premium.

Target localization accuracy improvement via sensor mobility

ABSTRACTSensor deployment positions play an important factor in determining target location estimation error performance in sensor networks employing received signal strength indicator measurements. The problem we investigate is as follows: Given a deployment area that has possibly non-uniform estimation error requirements and some initial sensor positions, then how can these sensors be deployed such that requirements are met as best as possible? We propose three variants of a low-complexity distributed strategy that require little information exchange between neighboring sensors. Each sensor locally calculates both the direction and magnitude of movement necessary to reduce the difference between achieved and required estimation errors at points within it sensing radius. The direction of movement is calculated as a weighted combination of these points. The weights can incorporate the error difference, number of sensors covering a point, the distance to a sensor and sensor density. Depending on the parameters chosen, three different weighing methods (namely, the density weighted centroid, error weighted centroid (EWC) and modified EWC) are proposed in this paper. We also provide an analytic derivation of the necessary distance a sensor should move. The proposed strategy is compared against a the RELOCATE algorithm and centralized generic genetic algorithm (GA) relocation method. Simulation results demonstrate that using the distributed strategy can achieve a comparable performance (within 10%) of the GA’s performance and significantly outperform that of the RELOCATE.Sensor movement for different k.

On Convergence Rate in the Local Limit Theorem for Densities Under Various Moment Conditions

We refine certain estimates of convergence rate in the local central limit theorem for the densities of sums of independent identically distributed random variables possessing finite absolute moments up to the order 2 + δ, where δ is some number from the half-interval (0, 1]. Along with the uniform estimates we obtain non-uniform estimates of the first, second, and third order (for δ = 1), and the estimates in the L p metrics. The obtained estimates have the form of the sum of two terms, the first of which is the Lyapunov fraction of the corresponding order with the coefficient depending only on δ, and the second one exponentially decays with the growth of the number of summands. The values of the coefficient in the Lyapunov fraction are considerably smaller than the known ones.

Non-uniform Estimates in the Approximation by the Irwin Law

We consider an approximation of a cumulative distribution function F(x) by the cumulative distributionfunction G(x) of the Irwin law. In this case, a function F(x) can be cumulative distribution functions of sums (products) ofindependent (dependent) random variables. Remainder term of the approximation is estimated by the cumulant method.The cumulant method is used by introducing special cumulants, satisfying the V. Statulevičius type condition. The mainresult is a nonuniform bound for the difference |F(x)-G(x)| in terms of special cumulants of the symmetric cumulativedistribution function F(x).

On Convergence Rate in CLT for Smooth Distributions

There are obtained nonuniform estimates of the first and second order for the rate of convergence in the central limit theorem for sums of independent identically distributed random variables with bounded density and finite absolute moments of order 2+δ, where 0 < δ ≤ 1. The obtained estimates represent a sum of two terms, the first one being the Lyapunov fraction of order 2 + δ with a factor depending only on δ, and the second one decaying exponentially. The values of the factor of the Lyapunov fraction are considerably less than the known. This is an updated version of the original paper.

Discounted payments theorems for large deviations

&#x0D; Let Z(t) = Σ j=1N(t) Xj, t ≥ 0, be a stochastic process, where Xj are independent identically distributed random variables, and N(t) is non-negative integer-valued process with independent increments. Throughout, we assume that N(t) and Xj are independent. The paper considers normal approximation to the distribution of properly centered and normed random variable Zδ =∫0∞e- δt dZ(t), δ &gt; 0, taking into consideration large deviations both in the Cramér zone and the power Linnik zones. Also, we obtain a nonuniform estimate in the Berry–Essen inequality.

On Nonuniform Estimates of Approximation Exactness in the Central Limit Theorem

We obtain nonuniform and quasi-nonuniform estimates, where the “main” summand under wide assumptions is equivalent to the difference of distribution functions. The construction of these estimates is given with the help of asymptotic expansions.

Fusion Estimation for Sensor Networks With Nonuniform Estimation Rates

This paper investigates the multi-sensor fusion estimation problem for wireless sensor networks with nonuniform estimation rates. First, each sensor generates local estimates with two rates, namely, a fast rate and a slow rate according to its power situation, where the estimation rates among the sensors are allowed to be different from each other. Second, a fusion rule with matrix weights is designed for each sensor to fuse available local estimates generated at different time scales, and a set of recursive equations are presented to compute estimation error cross-covariances. The fusion algorithm is applicable to both cases where the measurement noises are mutually correlated and are uncorrelated, and is also applicable to the case where the sensors are not time-synchronized. Two types of estimators are designed according to different considerations of design complexity and computation costs, and convergence analysis for the type II estimators is also presented. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed estimators.

Estimation and Reduction of Macroscopic Nonuniformity in CNT Thin Film Resistors

Carbon nanotube (CNT) thin film-based devices are expected to have better uniformity and reproducibility compared with single-tube devices due to statistical averaging. In this work, thin film resistors (TFR) were prepared from CNT dispersions and their nonuniformity estimated by multipoint, two-terminal resistance (TTR) measurements. I-V measurements were done for determining the nature of metal-CNT contact. For estimation of contact resistance, transmission line measurements (TLM) were carried out. Reduction of CNT-TFR nonuniformity was achieved using di-methyl formamide (DMF). Scanning electron microscopy and electrical measurements imply that DMF improves debundling of single-walled nanotubes, reduces the resistance and improves homogeneity of subsequently prepared thin films.

On One Asymptotic Expansion in the Central Limit Theorem

We obtain an asymptotic expansion which implies nonuniform estimates for the central limit theorem and for one of the known asymptotic expansions.