Improving the utility of locally differentially private protocols for longitudinal and multidimensional frequency estimates

This paper investigates the problem of collecting multidimensional data throughout time(i.e.,longitudinal studies)for the fundamental task of frequency estimation under Local Differential Privacy(LDP)guarantees.Contrary to frequency estimation of a single attribute,the multidimensional aspect demands particular attention to the privacy budget.Besides,when collecting user statistics longitudinally,privacy progressively degrades.Indeed,the“multiple”settings in combination(i.e.,many attributes and several collections throughout time)impose several challenges,for which this paper proposes the first solution for frequency estimates under LDP.To tackle these issues,we extend the analysis of three state-of-the-art LDP protocols(Generalized Randomized Response–GRR,Optimized Unary Encoding–OUE,and Symmetric Unary Encoding–SUE)for both longitudinal and multidimensional data collections.While the known literature uses OUE and SUE for two rounds of sanitization(a.k.a.memoization),i.e.,L-OUE and L-SUE,respectively,we analytically and experimentally show that starting with OUE and then with SUE provides higher data utility(i.e.,L-OSUE).Also,for attributes with small domain sizes,we propose Longitudinal GRR(L-GRR),which provides higher utility than the other protocols based on unary encoding.Last,we also propose a new solution named Adaptive LDP for LOngitudinal and Multidimensional FREquency Estimates(ALLOMFREE),which randomly samples a single attribute to be sent with the whole privacy budget and adaptively selects the optimal protocol,i.e.,either L-GRR or L-OSUE.As shown in the results,ALLOMFREE consistently and considerably outperforms the state-of-the-art L-SUE and L-OUE protocols in the quality of the frequency estimates.

Genetic and Agronomic Parameter Estimates of Growth, Yield and Related Traits of Maize (Zea mays L.) under Different Rates of Nitrogen Fertilization

This study evaluated the genetic and agronomic parameter estimates of maize under different nitrogen rates. The trial was established at the Njala Agricultural Research Centre experimental site during 2021 and 2022 in a split block design with three maize varieties (IWCD2, 2009EVDT, and DMR-ESR-Yellow) and seven nitrogen (0, 30, 60, 90, 120, 150 and 180 kg∙N∙ha−1) rates. Findings showed that cob diameter and anthesis silking time (ASI) had intermediate heritability, ASI had high genetic advance, ASI and grain yield had high genotypic coefficient of variation (GCV), while traits with high phenotypic coefficient of variation (PCV) were plant height, ASI, grain yield, number of kernel per cob, number of kernel rows, ear length, and ear height. The PCV values were higher than GCV, indicating the influence of the environment in the studied traits. Nitrogen rates and variety significantly (p < 0.05) influenced grain yield production. Mean grain yields and economic parameter estimates increased with increasing nitrogen rates, with the 30 and 180 kg∙N∙ha−1 plots exhibiting the lowest and highest grain yields of 1238 kg∙ha−1 and 2098 kg∙ha−1, respectively. Variety and nitrogen effects on partial factor productivity (PFPN), agronomic efficiency (AEN), net returns (NR), value cost ratio (VCR) and marginal return (MR) indicated that these parameters were significantly affected (p < 0.05) by these factors. The highest PFPN (41.3 kg grain kg−1∙N) and AEN (29.4 kg grain kg−1∙N) were obtained in the 30 kg∙N∙ha−1 plots, while the highest VCR (2.8) and MR (SLL 1.8 SLL−1 spent on N) were obtained in the 180 kg∙N∙ha−1. The significant influence of variety and nitrogen on traits suggests that increasing yields and maximizing profits require use of appropriate nitrogen fertilization and improved farming practices that could be exploited for increased productivity of maize.

A Formulation of the Porous Medium Equation with Time-Dependent Porosity: A Priori Estimates and Regularity Results

We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to depend very little of) the time variable t. In this work, we want to study the case where it does depend on t(and xas well). For this purpose, we make a change of unknown function V=ϕSin order to obtain a saturation-like (advection-diffusion) equation. A priori estimates and regularity results are established for the new equation based in part on what is known from the saturation equation, when ϕis independent of the time t. These results are then extended to the full saturation equation with time-dependent porosity ϕ=ϕ(x,t). In this analysis, we make explicitly the dependence of the various constants in the estimates on the porosity ϕby the introduced transport vector w, through the change of unknown function. Also we do not assume zero-flux boundary, but we carry the analysis for the case Q≡0.

A time-space network-based model for transportation service optimization of China Railway Express

This paper describes the development and optimization plans for the China Railway Express(CR Express).As a new type of international land transport organization,CR Express has emerged with the continuous expansion of China toward European investment and trade,and in particular,has expanded with the continuous progress of the One Belt and One Road(OBOR)initiative.In addition to improving the service quality of CR Express,the operating costs must be reduced for developing“smart railways”that serve“smart cities”.We propose a dualobjective-based function mathematical optimization model;the satisfaction of the cargo owner is considered,and the timeliness,transportation capacity,and goods category constraints of CR Express transportation are designed.Moreover,we present the normalized equivalent method of the two-objective function of the model.Finally,a case study is conducted against the background of certain trains in the western corridor of CR Express to validate the effectiveness of the model and research methods proposed in this study.

Method for rapid warning and activity concentration estimates in online waterγ-spectrometry systems

Onlineγ-spectrometry systems for inland waters,most of which extract samples in situ and in real time,are able to produce reliable activity concentration measurements for waterborne radionuclides only when they are distributed relatively uniformly and enter into a steady-state diffusion regime in the measurement chamber.To protect residents’health and ensure the safety of the living environment,better timeliness is required for this measurement method.To address this issue,this study established a mathematical model of the online waterγ-spectrometry system so that rapid warning and activity estimates can be obtained for water under non-steady-state(NSS)conditions.In addition,the detection efficiency of the detector for radionuclides during the NSS diffusion process was determined by applying the computational fluid dynamics technique in conjunction with Monte Carlo simulations.On this basis,a method was developed that allowed the online waterγ-spectrometry system to provide rapid warning and activity concentration estimates for radionuclides in water.Subsequent analysis of the NSS-mode measurements of^(40)K radioactive solutions with different activity concentrations determined the optimum warning threshold and measurement time for producing accurate activity concentration estimates for radionuclides.The experimental results show that the proposed NSS measurement method is able to give warning and yield accurate activity concentration estimates for radionuclides 55.42 and 69.42 min after the entry of a 10 Bq/L^(40)K radioactive solution into the measurement chamber,respectively.These times are much shorter than the 90 min required by the conventional measurement method.Furthermore,the NSS measurement method allows the measurement system to give rapid(within approximately 15 min)warning when the activity concentrations of some radionuclides reach their respective limits stipulated in the Guidelines for Drinking-water Quality of the WHO,suggesting that this method considerably enhances the warning capacity of in situ online waterγ-spectrometry systems.

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

Improving the accuracy of precipitation estimates in a typical inland arid area of China using a dynamic Bayesian model averaging approach

Xinjiang Uygur Autonomous Region is a typical inland arid area in China with a sparse and uneven distribution of meteorological stations,limited access to precipitation data,and significant water scarcity.Evaluating and integrating precipitation datasets from different sources to accurately characterize precipitation patterns has become a challenge to provide more accurate and alternative precipitation information for the region,which can even improve the performance of hydrological modelling.This study evaluated the applicability of widely used five satellite-based precipitation products(Climate Hazards Group InfraRed Precipitation with Station(CHIRPS),China Meteorological Forcing Dataset(CMFD),Climate Prediction Center morphing method(CMORPH),Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks-Climate Data Record(PERSIANN-CDR),and Tropical Rainfall Measuring Mission Multi-satellite Precipitation Analysis(TMPA))and a reanalysis precipitation dataset(ECMWF Reanalysis v5-Land Dataset(ERA5-Land))in Xinjiang using ground-based observational precipitation data from a limited number of meteorological stations.Based on this assessment,we proposed a framework that integrated different precipitation datasets with varying spatial resolutions using a dynamic Bayesian model averaging(DBMA)approach,the expectation-maximization method,and the ordinary Kriging interpolation method.The daily precipitation data merged using the DBMA approach exhibited distinct spatiotemporal variability,with an outstanding performance,as indicated by low root mean square error(RMSE=1.40 mm/d)and high Person's correlation coefficient(CC=0.67).Compared with the traditional simple model averaging(SMA)and individual product data,although the DBMA-fused precipitation data were slightly lower than the best precipitation product(CMFD),the overall performance of DBMA was more robust.The error analysis between DBMA-fused precipitation dataset and the more advanced Integrated Multi-satellite Retrievals for Global Precipitation Measurement Final(IMERG-F)precipitation product,as well as hydrological simulations in the Ebinur Lake Basin,further demonstrated the superior performance of DBMA-fused precipitation dataset in the entire Xinjiang region.The proposed framework for solving the fusion problem of multi-source precipitation data with different spatial resolutions is feasible for application in inland arid areas,and aids in obtaining more accurate regional hydrological information and improving regional water resources management capabilities and meteorological research in these regions.

Heat Kernel Estimates on Simple Random Walks and On-Diagonal Upper Bounds

We primarily provide several estimates for the heat kernel defined on the 2-dimensional simple random walk. Additionally, we offer an estimate for the heat kernel on high-dimensional random walks, demonstrating that the heat kernel in higher dimensions converges rapidly. We also compute the constants involved in the estimate for the 1-dimensional heat kernel. Furthermore, we discuss the general case of on-diagonal estimates for the heat kernel.

A REFINEMENT OF THE SCHWARZ-PICK ESTIMATES AND THE CARATHéODORY METRIC IN SEVERAL COMPLEX VARIABLES

In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of X.We next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of X.The results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.

Finite Difference Schemes for Time-Space Fractional Diffusion Equations in One-and Two-Dimensions

In this paper,finite difference schemes for solving time-space fractional diffusion equations in one dimension and two dimensions are proposed.The temporal derivative is in the Caputo-Hadamard sense for both cases.The spatial derivative for the one-dimensional equation is of Riesz definition and the two-dimensional spatial derivative is given by the fractional Laplacian.The schemes are proved to be unconditionally stable and convergent.The numerical results are in line with the theoretical analysis.

Deep learning for joint channel estimation and feedback in massive MIMO systems

The great potentials of massive Multiple-Input Multiple-Output(MIMO)in Frequency Division Duplex(FDD)mode can be fully exploited when the downlink Channel State Information(CSI)is available at base stations.However,the accurate CsI is difficult to obtain due to the large amount of feedback overhead caused by massive antennas.In this paper,we propose a deep learning based joint channel estimation and feedback framework,which comprehensively realizes the estimation,compression,and reconstruction of downlink channels in FDD massive MIMO systems.Two networks are constructed to perform estimation and feedback explicitly and implicitly.The explicit network adopts a multi-Signal-to-Noise-Ratios(SNRs)technique to obtain a single trained channel estimation subnet that works well with different SNRs and employs a deep residual network to reconstruct the channels,while the implicit network directly compresses pilots and sends them back to reduce network parameters.Quantization module is also designed to generate data-bearing bitstreams.Simulation results show that the two proposed networks exhibit excellent performance of reconstruction and are robust to different environments and quantization errors.

A comparative study of data-driven battery capacity estimation based on partial charging curves

With its generality and practicality, the combination of partial charging curves and machine learning(ML) for battery capacity estimation has attracted widespread attention. However, a clear classification,fair comparison, and performance rationalization of these methods are lacking, due to the scattered existing studies. To address these issues, we develop 20 capacity estimation methods from three perspectives:charging sequence construction, input forms, and ML models. 22,582 charging curves are generated from 44 cells with different battery chemistry and operating conditions to validate the performance. Through comprehensive and unbiased comparison, the long short-term memory(LSTM) based neural network exhibits the best accuracy and robustness. Across all 6503 tested samples, the mean absolute percentage error(MAPE) for capacity estimation using LSTM is 0.61%, with a maximum error of only 3.94%. Even with the addition of 3 m V voltage noise or the extension of sampling intervals to 60 s, the average MAPE remains below 2%. Furthermore, the charging sequences are provided with physical explanations related to battery degradation to enhance confidence in their application. Recommendations for using other competitive methods are also presented. This work provides valuable insights and guidance for estimating battery capacity based on partial charging curves.

Efficient Unsupervised Image Stitching Using Attention Mechanism with Deep Homography Estimation

Traditional feature-based image stitching techniques often encounter obstacles when dealing with images lackingunique attributes or suffering from quality degradation. The scarcity of annotated datasets in real-life scenesseverely undermines the reliability of supervised learning methods in image stitching. Furthermore, existing deeplearning architectures designed for image stitching are often too bulky to be deployed on mobile and peripheralcomputing devices. To address these challenges, this study proposes a novel unsupervised image stitching methodbased on the YOLOv8 (You Only Look Once version 8) framework that introduces deep homography networksand attentionmechanisms. Themethodology is partitioned into three distinct stages. The initial stage combines theattention mechanism with a pooling pyramid model to enhance the detection and recognition of compact objectsin images, the task of the deep homography networks module is to estimate the global homography of the inputimages consideringmultiple viewpoints. The second stage involves preliminary stitching of the masks generated inthe initial stage and further enhancement through weighted computation to eliminate common stitching artifacts.The final stage is characterized by adaptive reconstruction and careful refinement of the initial stitching results.Comprehensive experiments acrossmultiple datasets are executed tometiculously assess the proposed model. Ourmethod’s Peak Signal-to-Noise Ratio (PSNR) and Structure Similarity Index Measure (SSIM) improved by 10.6%and 6%. These experimental results confirm the efficacy and utility of the presented model in this paper.

Cascaded ELM-Based Joint Frame Synchronization and Channel Estimation over Rician Fading Channel with Hardware Imperfections

Due to the interdependency of frame synchronization(FS)and channel estimation(CE),joint FS and CE(JFSCE)schemes are proposed to enhance their functionalities and therefore boost the overall performance of wireless communication systems.Although traditional JFSCE schemes alleviate the influence between FS and CE,they show deficiencies in dealing with hardware imperfection(HI)and deterministic line-of-sight(LOS)path.To tackle this challenge,we proposed a cascaded ELM-based JFSCE to alleviate the influence of HI in the scenario of the Rician fading channel.Specifically,the conventional JFSCE method is first employed to extract the initial features,and thus forms the non-Neural Network(NN)solutions for FS and CE,respectively.Then,the ELMbased networks,named FS-NET and CE-NET,are cascaded to capture the NN solutions of FS and CE.Simulation and analysis results show that,compared with the conventional JFSCE methods,the proposed cascaded ELM-based JFSCE significantly reduces the error probability of FS and the normalized mean square error(NMSE)of CE,even against the impacts of parameter variations.

SUFFICIENT AND NECESSARY CONDITIONS ON THE EXISTENCE AND ESTIMATES OF BOUNDARY BLOW-UP SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATIONS

Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.

High-Precision Doppler Frequency Estimation Based Positioning Using OTFS Modulations by Red and Blue Frequency Shift Discriminator

Orthogonal Time Frequency and Space(OTFS) modulation is expected to provide high-speed and ultra-reliable communications for emerging mobile applications, including low-orbit satellite communications. Using the Doppler frequency for positioning is a promising research direction on communication and navigation integration. To tackle the high Doppler frequency and low signal-to-noise ratio(SNR) in satellite communication, this paper proposes a Red and Blue Frequency Shift Discriminator(RBFSD) based on the pseudo-noise(PN) sequence.The paper derives that the cross-correlation function on the Doppler domain exhibits the characteristic of a Sinc function. Therefore, it applies modulation onto the Delay-Doppler domain using PN sequence and adjusts Doppler frequency estimation by red-shifting or blue-shifting. Simulation results show that the performance of Doppler frequency estimation is close to the Cramér-Rao Lower Bound when the SNR is greater than -15dB. The proposed algorithm is about 1/D times less complex than the existing PN pilot sequence algorithm, where D is the resolution of the fractional Doppler.

An Example of a Bounded Potential q(x) on the Half-Line, for Estimates of A(α) Amplitude

We show an example of a bounded potential on the half-line obtained as the image of an Inverse Transformation Operator of the Bessel singular potential of the Reduced Radial Schr&#246;dinger Equation, and show us the Estimates of the A(α) amplitude.

Model-driven full system dynamics estimation of PMSM-driven chain shell magazine

Based on the system dynamic model, a full system dynamics estimation method is proposed for a chain shell magazine driven by a permanent magnet synchronous motor(PMSM). An adaptive extended state observer(AESO) is proposed to estimate the unmeasured states and disturbance, in which the model parameters are adjusted in real time. Theoretical analysis shows that the estimation errors of the disturbances and unmeasured states converge exponentially to zero, and the parameter estimation error can be obtained from the extended state. Then, based on the extended state of the AESO, a novel parameter estimation law is designed. Due to the convergence of AESO, the novel parameter estimation law is insensitive to controllers and excitation signal. Under persistent excitation(PE) condition, the estimated parameters will converge to a compact set around the actual parameter value. Without PE signal, the estimated parameters will converge to zero for the extended state. Simulation and experimental results show that the proposed method can accurately estimate the unmeasured states and disturbance of the chain shell magazine, and the estimated parameters will converge to the actual value without strictly continuous PE signals.

Methodology for Obtaining Optimal Sleeve Friction and Friction Ratio Estimates from CPT Data

Cone penetration testing (CPT) is a cost effective and popular tool for geotechnical site characterization. CPT consists of pushing at a constant rate an electronic penetrometer into penetrable soils and recording cone bearing (qc), sleeve friction (fc) and dynamic pore pressure (u) with depth. The measured qc, fs and u values are utilized to estimate soil type and associated soil properties. A popular method to estimate soil type from CPT measurements is the Soil Behavior Type (SBT) chart. The SBT plots cone resistance vs friction ratio, Rf [where: Rf = (fs/qc)100%]. There are distortions in the CPT measurements which can result in erroneous SBT plots. Cone bearing measurements at a specific depth are blurred or averaged due to qc values being strongly influenced by soils within 10 to 30 cone diameters from the cone tip. The qcHMM algorithm was developed to address the qc blurring/averaging limitation. This paper describes the distortions which occur when obtaining sleeve friction measurements which can in association with qc blurring result in significant errors in the calculated Rf values. This paper outlines a novel and highly effective algorithm for obtaining accurate sleeve friction and friction ratio estimates. The fc optimal filter estimation technique is referred to as the OSFE-IFM algorithm. The mathematical details of the OSFE-IFM algorithm are outlined in this paper along with the results from a challenging test bed simulation. The test bed simulation demonstrates that the OSFE-IFM algorithm derives accurate estimates of sleeve friction from measured values. Optimal estimates of cone bearing and sleeve friction result in accurate Rf values and subsequent accurate estimates of soil behavior type.

Side Information-Based Stealthy False Data Injection Attacks Against Multi-Sensor Remote Estimation

Dear Editor,This letter investigates a novel stealthy false data injection(FDI)attack scheme based on side information to deteriorate the multi-sensor estimation performance of cyber-physical systems(CPSs).Compared with most existing works depending on the full system knowledge,this attack scheme is only related to attackers'sensor and physical process model.The design principle of the attack signal is derived to diverge the system estimation performance.Next,it is proven that the proposed attack scheme can successfully bypass the residual-based detector.Finally,all theoretical results are verified by numerical simulation.