Exact Estimation Research Articles

Moments and tails of hitting times of Bessel processes and convolutions of elementary mixtures of exponential distributions

We present explicit estimates of right and left tails and exact (up to universal, multiplicative constants) estimates of tails and moments of hitting times of Bessel processes. The latter estimates are obtained from more general estimates of moments and tails established for convolutions of elementary mixtures of exponential distributions.

Maximum Voltage Gain Tracking Algorithm for High-Efficiency of Two-Stage Induction Heating Systems Using Resonant Impedance Estimation

A boost power factor correction (PFC) circuit has replaced the diode rectifier to improve its poor power factor performance, low efficiency, and output power limitation for conventional induction heating (IH) applications. Accordingly, many studies have been conducted, but they considered only the efficiency of the boost PFC rather than the entire IH system, or their control and design were complicated. In this paper, an algorithm tracking the maximum voltage gain of the resonant network is proposed to improve the entire efficiency of the two-stage IH system based on an exact online resonant frequency estimation. It can make the resonant network operate at the maximum voltage gain point which can improve the efficiency of the series-resonant inverter (SRI) included in the IH system with low circulating current, the minimum switching frequency, and zero voltage switching (ZVS) capability. The proposed algorithm also induces the minimum output voltage of the boost PFC, which can reduce its switching losses and total harmonic distortion (THD). The validity of the proposed algorithm is experimentally verified using a 2.4-kW prototype IH system, including the boost PFC and the IH-SRI controlled by a digital signal processor (DSP).

Isomorphic shut form valuation for quantum field theory and biological population models

Abstract The fundamental objective of this work is focused to achieve a class of advanced and impressive exact estimations to the Zoomeron equation and the time-fraction biological population model through contrivance by a couple of important and magnificent techniques, namely, the modified extended tanh-function method which depend on the balance theory and the Ricatti–Bernoulli sub-ODE method which is independent of the balancing principle. The suggested model is one of the major concerns for studying population distribution dynamics as well as the quantum field theory which is an important discipline for the description of interactions between light and electrons. The two suggested reliable, effective techniques are considered famous among ths ansatz methods that have various visions to realize the exact solutions to the non linear partial differential equation that reduce the volume of calculations examined before and usually give good results. It is solicited for this contrivance finding new exact solutions for two models in terms of some variable. The models are significant in quantum field theory, description of interactions between light and electron, quantum electrodynamics, demographic model, important to bring it into line with the reasonable distribution of wealth, resources, income, etc. The achieved results predict many types of solutions as trigonometric functions, hyperbolic functions, perfect periodic soliton solutions, singular periodic soliton solutions, and other rational solitons solutions. The efficiency of the techniques is demonstrated by the satisfactory results obtained through the derivation of closed-form soliton solutions from the exact solution by assigning definite values to the variables present in it.

Beyond Correlations: Deep Learning for Seismic Interferometry.

Passive seismic interferometry is a vastly generalized blind deconvolution question, where different paths through the Earth correspond to different channels called Green's functions; the sources are completely incoherent and not shared by the channels, and the question is to estimate paths (channels) that are not present in the dataset. SI, turning noise to signal, has numerous applications, from monitoring industrial activities to crustal structure investigation. No standard method of signal processing will solve SI. Instead, domain scientists resort to a simple cross-correlation operation, a.k.a. correlogram, which can retrieve the Green's function directly, but only under restrictive assumptions of ergodicity (energy equipartitioning) of the random process generating the seismic source. However, in practice, correlograms are not equal to the empirical Green's function, because these assumptions are generally far from being satisfied in realistic situations. In the framework of supervised learning, we propose to train deep neural networks (NNs) to overcome two limitations of correlation-based SI: the temporal limitation of passive recordings and the spatial limitation of the random source distribution. Deep NNs are trained to implicitly find the relationship between the empirical Green's functions and the correlograms and then used to extract the correct Green's functions from ambient noise. The input of the network is correlograms (a virtual shot gather), and the desired output is the empirical Green's function (the active shot gather). The NN can often retrieve Green's functions from 5-min passive recordings with acceptable accuracy in our synthetic example. Although an exact estimation of the source locations may not be necessary, a prior knowledge of the source directionality (through a preliminary beamforming step) is helpful when training the NN to mitigate the challenges associated with inhomogeneous source distributions (directional wave fields). In this work, all the numerical examples are based on the retrieval of P-wave reflections in the exploration scale and are conducted on synthetic data. We use a modified ResNet in our numerical experiments.

BEYONDPLANCK

We present posterior sample-based cosmic microwave background (CMB) constraints fromPlanckLFI and WMAP observations as derived through global end-to-end Bayesian processing within the BEYONDPLANCKframework. We first used these samples to study correlations between CMB, foreground, and instrumental parameters. We identified a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales (400 ≲ ℓ ≲ 600), mitigated through model reduction, masking, and resampling. We compared our posterior-based CMB results with previousPlanckproducts and found a generally good agreement, however, with notably higher noise due to our exclusion ofPlanckHFI data. We found a best-fit CMB dipole amplitude of 3362.7 ± 1.4 μK, which is in excellent agreement with previousPlanckresults. The quoted dipole uncertainty is derived directly from the sampled posterior distribution and does not involve any ad hoc contributions forPlanckinstrumental systematic effects. Similarly, we find a temperature quadrupole amplitude of $ \sigma^{TT}_2=229\pm97\,\muup{\rm K}^2 $ , which is in good agreement with previous results in terms of the amplitude, but the uncertainty is one order of magnitude greater than the naive diagonal Fisher uncertainty. Concurrently, we find less evidence of a possible alignment between the quadrupole and octopole than previously reported, due to a much larger scatter in the individual quadrupole coefficients that is caused both by marginalizing over a more complete set of systematic effects – as well as by requiring a more conservative analysis mask to mitigate the free-free degeneracy. For higher multipoles, we find that the angular temperature power spectrum is generally in good agreement with bothPlanckand WMAP. At the same time, we note that this is the first time that the sample-based, asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up toℓ ≤ 600. It now accounts for the majority of the cosmologically important information. Overall, this analysis demonstrates the unique capabilities of the Bayesian approach with respect to end-to-end systematic uncertainty propagation and we believe it can and should play an important role in the analysis of future CMB experiments. Cosmological parameter constraints are presented in a companion paper.

Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions

Exact order estimates for some characteristics of linear and nonlinear approximation of the isotropic Nikol'skii-Besov classes $\mathbf{B}^r_{p,\theta}$ of periodic multivariate functions in the spaces $B_{q,1}$, $1\leq q \leq \infty$, are obtained. Among them are the best orthogonal trigonometric approximations, best $m$-term trigonometric approximations, Kolmogorov, linear and trigonometric widths.
 For all considered characteristics, their estimates coincide in order with the corresponding estimates in the spaces $L_{q}$. Moreover, the obtained exact in order estimates (except the case $1<p<2\leq q < \frac{p}{p-1}$) are realized by the approximation of functions from the classes ${\mathbf{B}}^r_{p,\theta}$ by trigonometric polynomials with the spectrum in cubic regions. In any case, they do not depend on the smoothness parameter $\theta$.

Electric vehicle battery state-of-charge estimation based on optimized deep learning strategy with varying temperature at different C Rate

The estimation of the state-of-charge (SOC) in battery technology is a vital task for the battery management system (BMS). In this study, a modeling framework is presented for SOC estimation that makes use of methodologies that involve machine learning (ML). Aside from providing the user with real-time feedback on the battery's remaining capacity, precise knowledge of SOC imposes further control over the charging/discharging process, hence elongating the battery's useful lifespan. This decreases the possibility of over-voltage. As a result, the proposed work creates a foundation for the development of realistic training data at different temperature and different C rate. This analysis demonstrates how the discharge voltage curves change at various temperatures and various C Rate. Change in voltage, internal resistance and SOC is analyzed at various temperature and various C Rate. This paves the way for a more exact SOC estimation that is driven by data-driven methods. According to the findings of this study, the energy storage capacity is greater when the C rate of charging is lower, and it is possible to deliver more energy when the C rate of discharging is lower. According to the findings of this study, the discharge of the battery is linear for the SoC values that are less than 90%. The error in the SoC estimation is brought down to 0.835% by using this approach.

3D Road Lane Classification with Improved Texture Patterns and Optimized Deep Classifier.

The understanding of roads and lanes incorporates identifying the level of the road, the position and count of lanes, and ending, splitting, and merging roads and lanes in highway, rural, and urban scenarios. Even though a large amount of progress has been made recently, this kind of understanding is ahead of the accomplishments of the present perceptual methods. Nowadays, 3D lane detection has become the trending research in autonomous vehicles, which shows an exact estimation of the 3D position of the drivable lanes. This work mainly aims at proposing a new technique with Phase I (road or non-road classification) and Phase II (lane or non-lane classification) with 3D images. Phase I: Initially, the features, such as the proposed local texton XOR pattern (LTXOR), local Gabor binary pattern histogram sequence (LGBPHS), and median ternary pattern (MTP), are derived. These features are subjected to the bidirectional gated recurrent unit (BI-GRU) that detects whether the object is road or non-road. Phase II: Similar features in Phase I are further classified using the optimized BI-GRU, where the weights are chosen optimally via self-improved honey badger optimization (SI-HBO). As a result, the system can be identified, and whether it is lane-related or not. Particularly, the proposed BI-GRU + SI-HBO obtained a higher precision of 0.946 for db 1. Furthermore, the best-case accuracy for the BI-GRU + SI-HBO was 0.928, which was better compared with honey badger optimization. Finally, the development of SI-HBO was proven to be better than the others.

Molecular degradation mechanism of segmented polyurethane and life prediction through accelerated aging test

Polyurethane (PU) has numerous applications in daily life, such as coating, cushions, and insulation materials. It is also used as an encapsulation material for sensors. In the case of PU used as an encapsulant, PU elastomer containing an ether-based polyol is generally used and has a long lifespan in a general environment. However, it is challenging to predict its lifespan when used as an encapsulation material for sonar sensors because PU is exposed to the filling liquid. It is required to accurately predict the encapsulation material's lifespan to ensure the sensor's safety. For the exact estimation of PU lifespan, an accelerated aging experiment was conducted on PU elastomer in a filling solution at various temperatures. Fourier transform infrared spectroscopy was used to track the chemical changes in the PU elastomer, and it was observed that both urethane and urea bonds were degraded. Modulated differential scanning calorimetry and thermogravimetric analysis were also used to study changes in the structure of PU elastomer by heat aging. The tensile strength, elongation, and hardness of the heat-aged elastomer at various temperatures were obtained, and the Arrhenius plots were constructed. Finally, the lifespan was considered when the tensile strength was 70% of the initial state by using the ASTM D2000 standard. Thus, the lifespan of PU at 25 °C was calculated to be 12.2 years.

Factors associated with challenges in skin wound length and depth prediction of physicians in forensic cases

Aim: We aimed to display factors associated with error rates in identifying skin lesions with subjective methods and determine potential effectiveness of objective and metric measurements on judicial processes which may result in unwanted social and legal outcomes and raise the awareness of physicians.
 Material and Method: We made an incision on a piece of sponge with a lencet in order to model a skin lesion. The length and depth of the lesion was measured by compass device. Then, a face to face interview was planned with the physicians working in the hospital and they were asked to estimate the length and depth of the lesion. Estimations of the physicians were recorded.
 Results: Total of 146 physicians were involved into the study. Of these, 41.8% (n=61) were female and 58.2% (n=85) were male. Mean age of the physicians was 33.46±7.94 (24-61) years. Of the physicians, 7.5% (n=11) were a member of basic medical sciences, 26% (n=38) were a member of surgical medical sciences and 21.9% (n=32) were practitioner physician. When titles of the physicians were investigated, it was found that 21.9% (n=32) were practitioners, 34.9% (n=51) were residents, 34.9% (n=51) were specialists, 8.2% (n=12) were lecturers. The rate of the participants who estimated the incision more than 8 cm was higher than those who estimated less than 8 cm. Standart deviation of the depth estimation was 1.35 cm. Thirty-nine (26.7%) participants made an exact estimation of the depth of the incision.
 Conclusion: The measurement accuracy without a device is not associated with experience and errors of both inexperienced physicians and experienced physicians of any grade do similar mistakes during judicial report preparation process. These high error levels reveal that use of devices may avoid errors of physicians at any grade and protect physicians from possible judicial challenges.

Parameter identification of fractional‐order Wiener system based on FF‐ESG and GI algorithms

AbstractFractional‐order calculus has broad application scenarios in engineering and physics. Unlike integer‐order calculus, fractional‐order calculus has the ability to analyze nonclassical phenomena in science and engineering. For industrial processes with strong nonlinear characteristics, nonlinear models such as the Wiener model have become research hotspots. This paper studies the parameter identification of the fractional‐order Wiener system. In this paper, the forgetting factor extended stochastic gradient (FF‐ESG) algorithm and the gradient iterative (GI) algorithm are proposed to identify the parameters of the fractional‐order Wiener system. Then, the convergence of the FF‐ESG algorithm for the fractional‐order Wiener system is analyzed. Both proposed algorithms can obtain exact parameter estimates, which are verified by a numerical example and a case study of a fluid control valve.

The person-time ratio distribution for the exact monitoring of adverse events: Historical vs surveillance Poisson data.

In the postmarket drug and vaccine safety surveillance, when the number of adverse events follows a Poisson distribution, the ratio between the exposed and the unexposed person-time information is the random variable that governs the decision rule about the safety of the drug or vaccine. The probability distribution function of such a ratio is derived in this paper. Exact point and interval estimators for the relative risk are discussed as well as statistical hypothesis testing. To the best of our knowledge, this is the first paper that provides an unbiased estimator for the relative risk based on the person-time ratio. The applicability of this new distribution is illustrated through a real data analysis aimed to detect increased risk of occurrence of Myocarditis/Pericarditis following mRNA COVID-19 vaccination in Manitoba, Canada.

Prevalence and global trends of polypharmacy in patients with chronic liver disease: A systematic review and meta-analysis.

Despite its central role in drug metabolism, the exact prevalence estimates and factors affecting global trends of polypharmacy in patients with chronic liver disease (CLD) have remained unexamined. The aim of this systematic review and meta-analysis is to estimate the prevalence of polypharmacy in patients with CLD and to comprehensively synthesize the socio-demographic factors that drive this. We conducted a comprehensive search of relevant databases (PubMed, EMBASE, Science citation index, Cochrane Database of Systematic Reviews, and database of abstracts of reviews of effectiveness) for studies published from inception to May 30, 2022 that reported on prevalence estimates of polypharmacy in patients with CLD. The risk of bias was conducted utilizing Loney criteria. The primary outcome was the pooled prevalence of polypharmacy in patients with CLD. We subsequently performed a systematic review and weighted meta-analysis to ascertain the exact pooled prevalence of polypharmacy among patients with CLD. We identified approximately 50 studies from the initial literature search, of which 7 (enrolling N = 521,435 patients) with CLD met the inclusion criteria; of these, 58.7% were male, with a mean age of 53.9 (SD ± 12.2) years. The overall pooled prevalence of polypharmacy among patients with CLD was 31% (95% confidence interval [CI]: 4%-66%, I2 = 100%, τ2 ≤ 0.001, P ≤ .0001). We found higher pooled prevalence estimates among patients aged 50 years and older compared to their younger cohorts (42%, [CI 10-77]; I2 = 100%, P = <.001 vs 21%, [CI 0-70]; I2 = 100%, P = <.001). In an examination of multiple community- and hospital-based databases of patients with CLD, we found a pooled prevalence estimate of polypharmacy of approximately 31%. This represents a case burden within the range reported in the general population and will likely respond to mitigation strategies employed thus far for patients in that population.

Impact of a digitized workflow for knee endoprothesis implantations on hospital-specific ratios.

The continuous decrease of healthcare resources requires hospitals to improve efficiency while striving to improve quality standards that deliver better patient outcomes. The objective of this study was to analyze whether the implementation of digital support systems during orthopedic surgery positively affected clinical processes and quality ratios. A retrospective case-control study of 297 knee joint replacement procedures was conducted between 2015 and 2020. Thirty-five patients were allocated to the treatment and control groups after they were identified with exact matching and estimation of the propensity score. Both groups were balanced regarding the selected covariates. The effect of the surgical procedure manager (SPM) on the incidence of acute haemorrhagic anaemia between the two groups was evaluated with a t-test, and the odds ratio was calculated. SPM-supported surgery has no significant influence on the incidence of acute haemorrhagic anaemia but leads to significantly shorter hospital stay (1.93 days), changeover (4.14 minutes) and recovery room time (20.20 minutes). In addition, it reduces the standard deviation of operation room times. The study concludes that SPM enhances surgical efficiency and maintains quality outcomes. To overcome their increasing financial pressure hospital management should commercially evaluate the implementation of digital support systems.

Hyperspectral Estimation of Nitrogen Content in Wheat Based on Fractional Difference and Continuous Wavelet Transform

Nitrogen content is a crucial index for crop growth diagnosis and the exact estimation of nitrogen content is of great significance for grasping crop growth status in real-time. This paper takes winter wheat as the study object and the precision agriculture demonstration area of the Jiaozuo Academy of Agricultural and Forestry Sciences in Henan Province as the research area. The hyperspectral reflectance data of the wheat canopy in different growth periods are obtained with the ASD ground object hyperspectral instrument, and the original canopy spectral data are preprocessed by fractional differential and continuous wavelet transform; then, the vegetation indices are established, correlation analysis with nitrogen content is conducted, and the fractional differential spectra are selected; finally, based on the wavelet energy coefficient and the vegetation indices with strong correlations, the methods of support vector machine (SVM), ridge regression, stepwise regression, Gaussian process regression (GPR), and the BP neural network are used to construct the estimation model for nitrogen content in wheat at different growth stages. By adopting the R2 and root mean square error (RMSE) indices, the best nitrogen content estimation model at every growth stage is selected. The overall analysis of the nitrogen content estimation effect indicated that for the four growth periods, the maximum modeling and validation R2 of the nitrogen content estimation models of the SVM, ridge regression, stepwise regression, GPR, and BP neural network models reached 0.95 and 0.93, the average reached 0.76 and 0.71, and the overall estimation effect was good. The average values of the modeling and validation R2 of the nitrogen content estimation model at the flag picking stage were 0.85 and 0.81, respectively, which were 37.10% and 44.64%, 1.19% and 3.85%, and 14.86% and 17.39% higher than those at the jointing stage, flowering stage, and filling stage, respectively. Therefore, the model of the flag picking stage has higher estimation accuracy and a better estimation effect on the nitrogen content. For the different growth stages, the optimal estimation models of nitrogen content were different. Among them, continuous wavelet transform combined with the BP neural network model can be the most effective method for estimating the N content in wheat at the flagging stage. The paper provides an effective method for estimating the nitrogen content in wheat and a new idea for crop growth monitoring.

Sharp estimates for W-invariant Dunkl and heat kernels in the An case

In this article, we prove exact estimates for the W-invariant Dunkl kernel and heat kernel, for the root system of type A with arbitrary positive multiplicities. We apply the estimates of the W-invariant Dunkl heat kernel to compute sharp estimates for the Newton kernel and for the s-stable semigroups generated by a fractional power of the W-invariant Dunkl Laplacian.

Evaluating serological tests for foot-and-mouth disease while accounting for different serotypes and uncertain vaccination status

Controlling foot-and-mouth disease (FMD) by vaccination requires adequate population coverage and high vaccine efficacy under field conditions. To assure veterinary services that animals have acquired sufficient immunity, strategic post-vaccination surveys can be conducted to monitor the coverage and performance of the vaccine. Correct interpretation of these serological data and an ability to derive exact prevalence estimates of antibody responses requires an awareness of the performance of serological tests. Here, we used Bayesian latent class analysis to evaluate the diagnostic sensitivity and specificity of four tests. A non-structural protein (NSP) ELISA determines vaccine independent antibodies from environmental exposure to FMD virus (FMDV), and three assays measuring total antibodies derived from vaccine antigen or environmental exposure to two serotypes (A, O): the virus neutralisation test (VNT), a solid phase competitive ELISA (SPCE), and a liquid phase blocking ELISA (LPBE). Sera (n=461) were collected by a strategic post-vaccination monitoring survey in two provinces of Southern Lao People's Democratic Republic (PDR) after a vaccination campaign in early 2017. Not all samples were tested by every assay and each serotype: VNT tested for serotype A and O, whereas SPCE and LPBE tested for serotype O, and only NSP-negative samples were tested by VNT, with 90 of them not tested (missing by study design). These data challenges required informed priors (based on expert opinion) for mitigating possible lack of model identifiability. The vaccination status of each animal, its environmental exposure to FMDV, and the indicator of successful vaccination were treated as latent (unobserved) variables. Posterior median for sensitivity and specificity of all tests were in the range of 92-99 %, except for the sensitivity of NSP (∼66%) and the specificity of LPBE (∼71 %). There was strong evidence that SPCE outperformed LPBE. In addition, the proportion of animals recorded as having been vaccinated that showed a serological immune response was estimated to be in the range of 67-86 %. The Bayesian latent class modelling framework can easily and appropriately impute missing data. It is important to use field study data as diagnostic tests are likely to perform differently on field survey samples compared to samples obtained under controlled conditions.

Robust Near-Optimal Coordination in Uncertain Multiagent Networks With Motion Constraints.

This article addresses the robust coordination problem for nonlinear uncertain second-order multiagent networks with motion constraints, including velocity saturation and collision avoidance. A single-critic neural network-based approximate dynamic programming approach and exact estimation of unknown dynamics are employed to learn online the optimal value function and controller. By incorporating avoidance penalties into tracking variable, constructing a novel value function, and designing of suitable learning algorithms, multiagent coordination and collision avoidance are achieved simultaneously. We show that the developed feedback-based coordination strategy guarantees uniformly ultimately bounded convergence of the closed-loop dynamical stability and all underlying motion constraints are always strictly obeyed. The effectiveness of the proposed collision-free coordination law is finally illustrated using numerical simulations.

A theoretical framework for nonlinear dynamics in finance systems: Implications for stability, control and synchronization

It has been widely observed that most deterministic dynamical systems go into chaos for some values of their parameters. One of the most popular and widely used criteria is the conditional Lyapunov exponents, which constitute average measurements of expansion or shrinkage of small displacements along the synchronized trajectory. The Lyapunov characteristic exponents play a crucial role in the description of the behaviour of dynamical systems as they can be used to analyse the stability limit sets and to check sensitive dependence on initial conditions, that is, the presence of chaotic attractors. In this paper, Lyapunov stability theory and linear matrix inequalities (LMI) are employed to design control functions for the respective, control, and synchronization of the chaotic and hyperchaotic finance systems. The designed linear matrix inequalities (LMI) nonlinear controllers are capable of stabilizing the chaotic and hyperchaotic finance systems at any position as well as controlling it to track any trajectory that is a smooth function of time. The respective chaotic attractors were found to have a moderate value of the largest Lyapunov exponents (0.874959 s^(-1) and 0.650847 s^(-1)) with associated (Lyapunov) dimensions of 1.00 and 2.00 for the chaotic and hyperchaotic finance systems respectively. Based on Lyapunov stability theory and linear matrix inequalities (LMI), some necessary and sufficient criteria for stable synchronous behaviour are obtained and an exact analytic estimate of the threshold coupling, k_th, for complete chaos synchronization is derived. Finally, numerical simulation results are presented to validate the feasibility of the theoretical analysis.

Spatial Autoregressive Modeling on Linear Mixed Models for Dependency Between Regions

This study develops a linear mixed model (LMM) that includes spatial effects between regions with a spatial autoregressive model (SAR model). Between observations (regions) on that LMM are usually assumed to be independent. However, these assumptions are not always fulfilled due to dependency between regions. There are two important parts in spatial modeling: spatial dependence and spatial heterogeneity. In this study, we are concerned with the spatial lag or SAR models because dependency between variables of interest is easier to predict. On the other hand, all observations are real and can be directly seen from the data patterns. In addition, as a challenge for researchers to find all estimators while the values of the spatial dependence, sampling variance, and component variance are all unknown. This study aims to find all parameter estimators using a numerical approach and exact solutions. All exact estimators obtained are consistent estimators.