Optimal Estimation Research Articles

Optimal new physics estimation in the presence of standard model backgrounds

In this work, we develop a numerical technique for the optimal estimation of the new physics (NP) couplings applicable to any collider process without any simplifying assumptions. This approach also provides a way to measure the quality of the NP estimates derived using standard χ2 analysis, and can be used to gauge the advantages of various modalities of collider design. We illustrate the techniques and arguments by considering the pair production of heavy charged fermions at an e+e− collider. Published by the American Physical Society 2025

Determining Spatial Correlation Structure Using a Flexible Method

ABSTRACTModelling spatial data using geostatistical methods relies on parametric variograms and covariances. Ordinary, weighted and generalized least square, maximum and restricted maximum likelihood are some methods to estimate spatial processes' variogram (covariogram) parameters. Nevertheless, these methods necessarily do not result in the best prediction values for each desired loss function. This paper introduced a new method to estimate and optimize parameters of the spatial variogram and covariance functions based on a desired loss function to achieve cross‐validated prediction results. The proposed method can be used for different kriging techniques to perform the best prediction values and some desired loss functions such as mean, mean square and mean absolute error and complicated loss function like Linex conveniently. The variogram parameters were estimated under optional desired criteria to control how much they overestimate or underestimate observations. This feature can apply a wide range of controlled conditions to the model. The results indicated the interesting advantages of the suggested workflow versus previous variogram estimation methods. This method provides the best directional variogram, which enhances cross‐validation results when used with generalized least squares as an optimal estimation method for statistical efficiency.

Design of On-Site Calibration Device for Electricity Meter Based on Pulse Detection

At present, the error calibration of electricity meters in operation generally adopts an off-site method; that is, the electricity meter is taken out of operation and then calibrated in the laboratory. Off-site calibration, while beneficial, may not fully capture the operational error of the electricity meter due to potential differences in environmental conditions. An on-site calibration device for electricity meters based on pulse detection is designed, which obtains the error of the electricity meter under calibration by comparing the energy pulses of the standard electricity meter with those of the electricity meter under calibration. High-precision voltage and current sampling channels are designed, with a voltage measurement error of less than 0.02% and a current measurement error of less than 0.03%. In response to the non-synchronous sampling problem caused by frequency fluctuations in the on-site verification environment, a fast optimal frequency estimation algorithm is applied to accurately calculate the signal frequency within two cycles. The sampling time interval is adjusted to achieve lock-frequency synchronous sampling, and ensure the accurate calculation of electrical parameters. In order to reduce the complexity of the device circuit structure and equipment cost, a standard electric energy pulses generation method based on digital integration-to-frequency is proposed, which uses software to generate electric energy pulses, with a maximum output frequency of up to 10 kHz. Tests conducted in the laboratory on the developed on-site calibration device for electricity meters show that its accuracy is better than the 0.05 accuracy class, meeting the application requirements for on-site verification of electricity energy meters.

Preoperative Carcinoembryonic Antigen as a Predictor of 5-Year Survival in Rectal Cancer: Proposing a New Prognostic Cutoff.

Carcinoembryonic antigen (CEA) is an important prognostic factor for rectal cancer. This study aims to introduce a novel cutoff point for CEA within the normal range to improve prognosis prediction and enhance patient stratification in rectal cancer patients. A total of 316 patients with stages I to III rectal cancer who underwent surgical tumor resection were enrolled. The Cox proportional hazards regression model was used to evaluate the impact of preoperative CEA level and other co-variates on overall survival (OS). The Youden Index method was used for CEA optimal cutoff estimation. The mean follow-up period was 46.47months. In risk-adjusted Cox proportional analysis, higher preoperative CEA levels (HR 1.17, CI 1.131.21; P < 0.001), and T-stage were associated with poor OS. The mean preoperative CEA level was significantly higher in patients with positive lymphovascular invasion (LVI) and perineural invasion (PNI) (CI: 1.06-2.45 and 0.75-2.33, respectively, P < 0.001, t test). Pathologic complete response (pCR) occurred in 71 (22.4%) cases. Patients with pCR had lower levels of preoperative CEA than non-pCR group (P = 0.002, CEApCR-CEAnonpCR = - 1.3; t test). Using Youden Index, the estimated optimal CEA cutoff value for predicting OS was 2.8ng/mL (sensitivity 90%; specificity 78.5%). Lower preoperative CEA levels predict higher pCR rates, aiding patient stratification and planning. Preoperative CEA may play a role in the prediction of pCR in rectal cancer. Considering the CEA level of 2.8ng/ml, as a newly defined cutoff point, patients with a worse prognosis can be identified prior to operation. PNI, along with LVI as independent predictors, may be contemplated as prognostic indicators to improve treatment strategies.

Nearly optimal quasienergy estimation and eigenstate preparation of time-periodic Hamiltonians by Sambe space formalism

Nearly optimal quasienergy estimation and eigenstate preparation of time-periodic Hamiltonians by Sambe space formalism

Research on a Hybrid Correction Method for SINS/DVL Kalman Filter Integrated Navigation Based on Convergence Factor Judgment

Abstract The strapdown inertial navigation system (SINS)/doppler velocity log (DVL) integrated navigation is one of the primary methods for underwater navigation, providing autonomous underwater vehicles with precise information on position, velocity, and attitude. The core idea of the SINS/DVL integrated navigation using the Kalman filter is to establish the state and observation equations to estimate the SINS navigation error using DVL velocity. The optimal state estimation and correction strategies are critical to the accuracy of integrated navigation. To address this, this paper proposes a hybrid correction method for SINS/DVL Kalman filter integrated navigation based on a convergence factor judgment (HCKF-CFJ). First, the convergence factor for the Kalman filter is constructed using the diagonal elements of the estimated error covariance matrix corresponding to the velocity error state. Then, the filter's stability is assessed based on this convergence factor. When stability is confirmed, direct feedback correction is applied to the SINS velocity, and indirect feedback correction is applied to the SINS position. SINS velocity and position undergo feedforward correction if the stability condition is not met. Finally, ship experiments validate the effectiveness of the proposed method.

On the Convergence Rate of MCTS for the Optimal Value Estimation in Markov Decision Processes

On the Convergence Rate of MCTS for the Optimal Value Estimation in Markov Decision Processes

Transformer-based short-term traffic forecasting model considering traffic spatiotemporal correlation.

Traffic forecasting is crucial for a variety of applications, including route optimization, signal management, and travel time estimation. However, many existing prediction models struggle to accurately capture the spatiotemporal patterns in traffic data due to its inherent nonlinearity, high dimensionality, and complex dependencies. To address these challenges, a short-term traffic forecasting model, Trafficformer, is proposed based on the Transformer framework. The model first uses a multilayer perceptron to extract features from historical traffic data, then enhances spatial interactions through Transformer-based encoding. By incorporating road network topology, a spatial mask filters out noise and irrelevant interactions, improving prediction accuracy. Finally, traffic speed is predicted using another multilayer perceptron. In the experiments, Trafficformer is evaluated on the Seattle Loop Detector dataset. It is compared with six baseline methods, with Mean Absolute Error, Mean Absolute Percentage Error, and Root Mean Square Error used as metrics. The results show that Trafficformer not only has higher prediction accuracy, but also can effectively identify key sections, and has great potential in intelligent traffic control optimization and refined traffic resource allocation.

Visible-driven industrial wastewater remediation using black titania: optimization, energy consumption, treatment, and material preparation costs estimation

Visible-driven industrial wastewater remediation using black titania: optimization, energy consumption, treatment, and material preparation costs estimation

Quantum metrology using quantum combs and tensor network formalism

Abstract We develop an efficient algorithm for determining optimal adaptive quantum estimation protocols with arbitrary quantum control operations between subsequent uses of a probed channel. We introduce a tensor network representation of an estimation strategy, which drastically reduces the time and memory consumption of the algorithm, and allows us to analyze metrological protocols involving up to N=50 qubit channel uses, whereas the state-of-the-art approaches are limited to N&lt;5. The method is applied to study the performance of the optimal adaptive metrological protocols in presence of various noise types, including correlated noise.

Detection of Earth’s free oscillation and analysis of the non-synchronous oscillation phenomenon of normal modes

Earth’s free oscillation can provide essential constraints for refining Earth models, inverting seismic source mechanisms, and studying the deep internal structure of the Earth. Large earthquakes can simultaneously excite numerous normal modes. Due to the Earth’s ellipticity, rotation, and internal heterogeneities, these normal modes undergo splitting, with the frequencies of singlets of normal modes becoming very close (only a few µHz apart). This imposes greater demands on the detection of normal modes. This paper introduces a novel method for normal mode detection based on the normal time–frequency transform (NTFT). Compared to classical FT spectrum methods and recent optimal sequence estimation (OSE), the proposed method not only detects more weak normal modes but also reveals the spatial distribution of the phase of each normal mode. Taking the detection of 0S2 as an example, the phase measurements of each singlet are spatially inconsistent. This phenomenon can provide prior information for other methods, such as product spectrum analysis (PSA), spherical harmonic stacking (SHS), multistation experiments (MSE), and OSE. Additionally, understanding the phase distribution patterns contributes to further study of geological structures, offering crucial foundational data and observational support.

Optimal Speed and Range Estimation Using Dual Linear Frequency Modulated Signals

Optimal Speed and Range Estimation Using Dual Linear Frequency Modulated Signals

A new analysis of optimal estimation and prediction under linear mixed models

A new analysis of optimal estimation and prediction under linear mixed models

Уточнение коэффициента сжатия для внешней оценки предельного множества 0-управляемости линейной дискретной системы с ограниченным управлением

&lt;p&gt;The problem of constructing an optimal external estimate of the limit controllable set for a linear discrete-time system with convex control constraints is considered. The estimation is based on the principle of contraction mappings. The optimal estimation parameters are determined based on the analysis of the results of numerical modeling. Examples are given.&lt;/p&gt;

Optimal estimation of cloud properties from thermal infrared observations with a combination of deep learning and radiative transfer simulation

Abstract. While traditional thermal infrared retrieval algorithms based on radiative transfer models (RTMs) could not effectively retrieve the cloud optical thickness of thick clouds, machine-learning-based algorithms were found to be able to provide reasonable estimations for both daytime and nighttime. Nevertheless, stand-alone machine learning algorithms are occasionally criticized for the lack of explicit physical processes. In this study, RTM simulations and a machine learning algorithm are synergistically utilized using the optimal estimation (OE) method to retrieve cloud properties from thermal infrared radiometry measured by the Moderate Resolution Imaging Spectroradiometer (MODIS). In the new algorithm, retrievals from a machine learning algorithm are used to provide a priori states for the iterative process of the OE method, and an RTM is used to create radiance lookup tables that are used in the iteration processes. Compared with stand-alone OE, the cloud properties retrieved by the new algorithm show an overall better performance by using statistical a priori information obtained by the machine learning algorithm. Compared with the stand-alone machine-learning-based algorithm, the radiances simulated based on retrievals from the new method align more closely with observations, and physical radiative processes are handled explicitly in the new algorithm. Therefore, the new method combines the advantages of RTM-based cloud retrieval methods and machine learning models. These findings highlight the potential for machine-learning-based algorithms to enhance the efficacy of conventional remote sensing techniques.

Optimal Joint Scheduling and Congestion Window Estimation for Congestion Avoidance in Mobile Opportunistic Networks

Optimal Joint Scheduling and Congestion Window Estimation for Congestion Avoidance in Mobile Opportunistic Networks

Optimal estimation of high-dimensional sparse covariance matrices with missing data

Missing data have emerged in broad disciplines such as biology, geophysics, economics, public health, and social science. This article explores the optimal estimation of high-dimensional covariance matrix with missing data over a general sparse space ℋ ε (c n, p ). First, the upper bounds of adaptive entrywise thresholding estimator are proposed. Then the minimax lower bound is established by a simple and effective approach. Finally, numerical simulations and real data analysis demonstrate the advantages of our estimator Σ ̂ τ over the estimator Σ ̂ a t of Cai and Zhang (2016).

Optimal fidelity estimation for density matrix

Fidelity estimation is a necessary tool for evaluating noise in quantum measurement and quantum computation. The traditional fidelity estimation is to calculate the distance between two density matrices by employing direct fidelity estimation, which consumes too much copies of state. To reduce the number of copies of the state, we develop optimal fidelity estimation by proposing an optimal model. It calculates the minimum number of copies of state given a fixed value for the fidelity deviation. The result shows it saves a large number of copies of state compared with traditional approach (Direct Fidelity estimation) that is developed several years ago.The number of copies of the state employed increases slower than linear increase with increase of the dimension of density matrix when pauli measurement basis is applied. In addition, it consumes roughly a constant number of copies of the state with the increase of dimension of density matrix when the measurement bases are freely chosen.

Synergistic Impact of Active Case Detection and Early Hospitalization for Controlling the Spread of Yellow Fever Outbreak in Nigeria: An Epidemiological Modeling and Optimal Control Analysis

Capturing the factors influencing yellow fever (YF) outbreaks is essential for effective public health interventions, especially in regions like Nigeria, where the disease poses significant health risks. This study explores the synergistic effects of active case detection (ACD) and early hospitalization on controlling YF transmission dynamics. We develop a dynamic model that integrates vaccination, active case detection, and hospitalization to enhance our understanding of disease spread and inform prevention strategies. Our methodology encompasses mechanistic dynamic modeling, optimal control analysis, parameter estimation, model fitting, and sensitivity analyses to study YF transmission dynamics, ensuring the robustness of control measures. We employ advanced mathematical techniques, including next-generation matrix methods, to accurately compute the reproduction number and assess outbreak transmissibility. Rigorous qualitative analysis of the model reveals two equilibria: disease-free and endemic, demonstrating global asymptotic stability and its impact on overall YF transmission dynamics, significantly affecting control and prevention mechanisms. Furthermore, through sensitivity analysis, we identify crucial parameters of the model that require urgent attention for more effective YF control. Moreover, our results highlight the critical roles of ACD and early hospitalization in reducing YF transmission. These insights provide a foundation for informed decision making and resource allocation in epidemic control efforts, ultimately contributing to the enhancement of public health strategies aimed at mitigating the impact of YF outbreaks.

Enhancing Leaf Area Index Estimation in Southern Xinjiang Fruit Trees: A Competitive Adaptive Reweighted Sampling-Successive Projections Algorithm and Three-Band Index Approach with Fractional-Order Differentiation

The Leaf Area Index (LAI) is a key indicator for assessing fruit tree growth and productivity, and accurate estimation using hyperspectral technology is essential for monitoring plant health. This study aimed to improve LAI estimation accuracy in apricot, jujube, and walnut trees in Xinjiang, China. Canopy hyperspectral data were processed using fractional-order differentiation (FOD) from 0 to 2.0 orders to extract spectral features. Three feature selection methods—Competitive Adaptive Reweighted Sampling (CARS), Successive Projections Algorithm (SPA), and their combination (CARS-SPA)—were applied to identify sensitive spectral bands. Various band combinations were used to construct three-band indices (TBIs) for optimal LAI estimation. Random forest (RF) models were developed and validated for LAI prediction. The results showed that (1) the reflectance spectra of jujube and walnut trees were similar, while apricot spectra differed. (2) The correlation between fractional-order differential spectra and LAI was highest at orders 1.4 and 1.7, outperforming integer-order spectra. (3) The CARS-SPA selected a smaller set of feature bands in the 1100~2500 nm, reducing collinearity and improving spectral index construction. (4) The RF model using TBI4 demonstrated high R², low RMSE, and an RPD value &gt; 2, indicating optimal prediction accuracy. This approach holds promise for hyperspectral LAI monitoring in fruit trees.