Lower Bound Research Articles

VFLGAN: Vertical Federated Learning-based Generative Adversarial Network for Vertically Partitioned Data Publication

In the current artificial intelligence (AI) era, the scale and quality of the dataset play a crucial role in training a high-quality AI model. However, good data is not a free lunch and is always hard to access due to privacy regulations like the General Data Protection Regulation (GDPR). A potential solution is to release a synthetic dataset with a similar distribution to that of the private dataset. Nevertheless, in some scenarios, it has been found that the attributes needed to train an AI model belong to different parties, and they cannot share the raw data for synthetic data publication due to privacy regulations. In PETS 2023, Xue et al. [29] proposed the first generative adversary network-based model, VertiGAN, for vertically partitioned data publication. However, after thoroughly investigating, we found that VertiGAN is less effective in preserving the correlation among the attributes of different parties. This article proposes a Vertical Federated Learning-based Generative Adversarial Network, VFLGAN, for vertically partitioned data publication to address the above issues. Our experimental results show that compared with VertiGAN, VFLGAN significantly improves the quality of synthetic data. Taking the MNIST dataset as an example, the quality of the synthetic dataset generated by VFLGAN is 3.2 times better than that generated by VertiGAN w.r.t. the Frechet Distance. We also designed a more efficient and effective Gaussian mechanism for the proposed VFLGAN to provide the synthetic dataset with a differential privacy guarantee. On the other hand, differential privacy only gives the upper bound of the worst-case privacy guarantee. This article also proposes a practical auditing scheme that applies membership inference attacks to estimate privacy leakage through the synthetic dataset.

GNSS positioning uncertainty prediction over a planned path considering signal attenuation for urban autonomous driving

Autonomous driving requires path planning to choose an optimal path to destination. Most works on path planning focus on the shortest travelling time, but neglect positioning condition of a path while positioning accuracy is significant for autonomous driving. In this work, we predict GNSS protection level (PL), which is positioning uncertainty upper bound, over planned paths to help choose the optimal path. We propose an improved stochastic model that considers the signal attenuation caused by trees and buildings using laser scanning point cloud. An adaptive strategy is proposed to linearly correlate the improved model and the carrier-to-noise-density ratio to make our stochastic model more practical. Finally, pseudorange-based RTD PL is calculated by advanced receiver autonomous integrity monitoring (ARAIM) using the planned path information and GNSS ephemeris. The experiments demonstrate that our method reduces the misleading rate by over 90% both in horizontal and vertical directions compared to the original stochastic model, with the lowest false alarm rates.

A Switching Memory-Based Event-Trigger Scheme for Synchronization of Lur'e Systems With Actuator Saturation: A Hybrid Lyapunov Method.

This article is concerned with the event-triggered synchronization of Lur'e systems subject to actuator saturation. Aiming at reducing control costs, a switching-memory-based event-trigger (SMBET) scheme, which allows a switching between the sleeping interval and the memory-based event-trigger (MBET) interval, is first presented. In consideration of the characteristics of SMBET, a piecewise-defined but continuous looped-functional is newly constructed, under which the requirement of positive definiteness and symmetry on some Lyapunov matrices is dropped within the sleeping interval. Then, a hybrid Lyapunov method (HLM), which bridges the gap between the continuous-time Lyapunov theory (CTLT) and the discrete-time Lyapunov theory (DTLT), is used to make the local stability analysis of the closed-loop system. Meanwhile, using a combination of inequality estimation techniques and the generalized sector condition, two sufficient local synchronization criteria and a codesign algorithm for the controller gain and triggering matrix are developed. Furthermore, two optimization strategies are, respectively, put forward to enlarge the estimated domain of attraction (DoA) and the allowable upper bound of sleeping intervals on the premise of ensuring local synchronization. Finally, a three-neuron neural network and the classical Chua's circuit are used to carry out some comparison analyses and to display the advantages of the designed SMBET strategy and the constructed HLM, respectively. Also, an application to image encryption is provided to substantiate the feasibility of the obtained local synchronization results.

Bivariate iterated Farlie–Gumbel–Morgenstern stress–strength reliability model for Rayleigh margins: Properties and estimation

In this paper, we propose bivariate iterated Farlie–Gumbel–Morgenstern (FGM) due to [Huang and Kotz (1984). Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions. Biometrika 71(3), 633–636. https://doi.org/10.2307/2336577] with Rayleigh marginals. The dependence stress–strength reliability function is derived with its important reliability characteristics. Estimates of dependence reliability parameters are obtained. We analyse the effects of dependence parameters on the reliability function. We found that the upper bound of the positive correlation coefficient is attaining to 0.41 under a single iteration with Rayleigh marginals. A comprehensive comparison between classical FGM with iterated FGM copulas is graphically examined to assess the over or under estimation of reliability with respect to α and β. We propose a two-phase estimation procedure for estimating the reliability parameters. A Monte-Carlo simulation study is conducted to assess the finite sample behaviour of the proposed reliability estimators. Finally, the proposed estimators are examined and validated with real data sets.

Maleimide-induced crosslinking of polyimide membranes for high gas separation performance and plasticization resistance

Trade-off effect and plasticization are the key issues confronted in the area of membrane separation when dealing with applications involving high-pressure, soluble gases like CO2. In this study, a novel diamine (TAPA-MAA) was synthesized derived from tris(4-aminophenyl)amine (TAPA) and maleic anhydride (MA). This diamine was copolymerized with DAM (2,4,6-trimethylbenzene-1,3-diamine) and 6FDA (4,4′-(hexafluoroisopropylidene)diphthalic anhydride) to form the polyimide (PI) membrane containing maleimide (MI) cross-linking sites via chemical imidization way. Then, under the action of heat treatment, the crosslinked PI (cPI) membrane was constructed since the MI crosslinking initiates a radical cycloaddition reaction to form a succinimide-linked structure, and named as cPSI membrane for short. Further, an increase in the ratio of TAPA-MAA gives rise to the resultant cPSI membrane with elevated cross-linking density. The obtained cPSI membranes showed significantly enhanced gas selectivities and superior anti-plasticization property compared to the un-crosslinked PI membranes due to the MI-induced crosslinking reaction in the PI main chain, resulting in a marked increment (24 %) in ultra-microporosity (<7 Å) and a reduction in the d-spacing value (6.10 Å vs 5.80 Å), generating a strong molecular sieving effect. Meanwhile, the highly interconnected covalent structure formed by the MI-induced crosslinking will suppress the plasticizing phenomenon induced by high-pressure soluble gases. The typical membrane (cPSI-3:7-350) possessed great CO2/CH4 separation performance, CO2 permeability of 334.4barrer and a CO2/CH4 selectivity of 61.9 that is exceeded the 2008Roberson upper bound, along withCO2 plasticization pressures above 44 bar. Besides, its mixed CO2/CH4 separation performance exceeded the 2018 upper gas mixture limit when the upstream pressure changed from 2-20 bar. This study provides valuable insights for the design of PIs containing MI cross-linking sites, which can enhance the performance of membrane-based gas separation.

Finite-Time Stability Analysis and Stabilization of Switched Affine Systems via an Event-Triggered Strategy.

This article investigates the finite-time control problem of the switched affine systems via an event-triggered strategy. It is well known that the existence of affine terms brings great difficulties in analysis of the finite-time property of such systems. Furthermore, the design of the globally feasible event-triggered mechanism (ETM) under a finite-time control framework is challenging. Thus, a two-step hybrid control scheme is proposed in this article. The first step focuses on the event-triggered finite-time control for practical stability, while the second step aims to achieve finite-time stabilization. Particularly, in step one, by constructing the intersection between the affine term's threshold and feasible state region of the established ETM, it is verified that the Zeno behavior can be excluded. Thereafter, an affine state-dependent switching law and sufficient conditions are provided for achieving practical stability. Meanwhile, an estimation for the practical settling time to enter the bounded set is provided. In step two, the criteria for finite-time stabilization of the considered systems are further presented, and an overall settling-time upper bound is derived. Finally, a numerical example is illustrated to demonstrate the effectiveness of our proposed method.

Ultimate Regime of Rayleigh-Bénard Turbulence: Subregimes and Their Scaling Relations for the Nusselt vs Rayleigh and Prandtl Numbers.

We offer a new model for the heat transfer and the turbulence intensity in strongly driven Rayleigh-Bénard turbulence (the so-called ultimate regime), which in contrast to hitherto models is consistent with the new mathematically exact heat transfer upper bound of Choffrut etal. [Upper bounds on Nusselt number at finite Prandtl number, J. Differ. Equations 260, 3860 (2016).JDEQAK0022-039610.1016/j.jde.2015.10.051] and thus enables extrapolations of the heat transfer to geo- and astrophysical flows. The model distinguishes between four subregimes of the ultimate regime and well describes the measured heat transfer in various large-Rayleigh experiments. In this new representation, which properly accounts for the Prandtl number dependence, the onset to the ultimate regime is seen in all available large-Rayleigh datasets, though at different Rayleigh numbers, as to be expected for a non-normal-nonlinear instability.

Efficient Approximation Algorithms for Minimum Cost Seed Selection with Probabilistic Coverage Guarantee

Given a social network G , a cost associated with each user, and an influence threshold η, the minimum cost seed selection problem (MCSS) aims to find a set of seeds that minimizes the total cost to reach η users. Existing works are mainly devoted to providing an &lt;u&gt;e&lt;/u&gt;xpected &lt;u&gt;c&lt;/u&gt;overage &lt;u&gt;g&lt;/u&gt;uarantee on reaching η, classified as MCSS-ECG, where their solutions either rely on an impractical influence oracle or cannot attain the expected influence threshold. More importantly, due to the expected coverage guarantee, the actual influence in a campaign may drift from the threshold evidently. Thus, the advertisers would like to request for a probability guarantee of reaching η. This motivates us to further solve the MCSS problem with a &lt;u&gt;p&lt;/u&gt;robabilistic &lt;u&gt;c&lt;/u&gt;overage &lt;u&gt;g&lt;/u&gt;uarantee, termed MCSS-PCG. In this paper, we first propose our algorithm CLEAR to solve MCSS-ECG, which reaches the expected influence threshold without any influence oracle or influence shortfall but a practical approximation ratio. However, the ratio involves an unknown term (i.e., the optimal cost). Thus, we further devise the STAR method to derive a lower bound of the optimal cost and then obtain the first explicit approximation ratio for MCSS-ECG. In MCSS-PCG, it is necessary to estimate the probability that the current seeds reach η, to decide when to stop seed selection. To achieve this, we design a new technique named MRR, which provides efficient probability estimation with a theoretical guarantee. With MRR in hand, we propose our algorithm SCORE for MCSS-PCG, whose performance guarantee is derived by measuring the gap between MCSS-ECG and MCSS-PCG, and applying the theoretical results in MCSS-ECG. Finally, extensive experiments demonstrate that our algorithms achieve up to two orders of magnitude speed-up compared to alternatives while meeting the requirement of MCSS-PCG with the smallest cost.

A discrete mean value of the Riemann zeta function

AbstractIn this work, we estimate the sum over the nontrivial zeros of the Riemann zeta function where is a complex number with and and are Dirichlet polynomials. Moreover, we estimate the discrete mean value above for higher derivatives where is replaced by for all . The formulae we obtain generalize a number of previous results in the literature. As an application, assuming the Riemann hypothesis, we obtain the lower bound which was previously known under the generalized Riemann hypothesis, only in the case .

Operator-pencil treatment of multi-interval Sturm-Liouville equation with boundary-transmission conditions

This paper is devoted to a new type of boundary-value problems for Sturm-Liouville equations defined on three disjoint intervals (−π,−π+d),(−π+d,π−d) and (π−d,π) together with eigenparameter dependent boundary conditions and with additional transmission conditions specified at the common end points −π+d and π−d, where 0&lt;d&lt;π. The considered problem cannot be treated by known techniques within the usual framework of classical Sturm-Liouville theory. To establish some important spectral characteristics we introduced the polynomial-operator formulation of the problem. Moreover, we develop a new modification of the Rayleigh method to obtain lower bound of eigenvalues.

The Asymptotic Behavior and Blow-Up Rate of a Solution with a Lower Bound on the Highest Existence Duration for Semi-Linear Pseudo-Parabolic Equations

This note addresses the initial-boundary value problem for a class of semi-linear pseudo-parabolic equations defined on a smooth bounded domain, with an emphasis on determining the asymptotic behavior and blow-up rate of the solution. Our analysis considers both low-initial energy and critical-initial energy cases, with a specific focus on establishing a lower bound on the maximal existence time of the solutions to this problem.

Upper Bounds of the Third Hankel Determinant for Bi-Univalent Functions in Crescent-Shaped Domains

This paper investigates the third Hankel determinant, denoted H3(1), for functions within the subclass RS∑*(λ) of bi-univalent functions associated with crescent-shaped regions φ⦅z=z+1+z2. The primary aim of this study is to establish upper bounds for H3(1). By analyzing functions within this specific geometric context, we derive precise constraints on the determinant, thereby enhancing our understanding of its behavior. Our results and examples provide valuable insights into the properties of bi-univalent functions in crescent-shaped domains and contribute to the broader theory of analytic functions.

Rayleigh Quotient and Surjectivity of Nonlinear Operators in Hilbert space

We consider continuous operators acting in a real Hilbert space and indicate conditions ensuring their continuous invertibility and/or surjectivity. In the case of bounded linear operators, these facts are well-known from basic Functional Analysis. The objective of this work is to indicate how similar properties can be proved also when the operators are not necessarily linear, using as a main tool their Rayleigh quotient and especially its lower and upper bound. In particular, we focus our attention on gradient operators and show a quantitative criterion that ensures their surjectivity through the positivity of an additional constant related to the measure of noncompactness.

A novel cross-entropy-based importance sampling method for cumulative time-dependent failure probability function

Cumulative time-dependent failure probability function (C-T-FPF) can reflect the effects of distribution parameters of random inputs and the upper bound of service time interval, which vary in their design domains, on time-dependent failure probability. However, solving C-T-FPF involves a time-consuming triple-layer framework. Thus, we propose an efficient method by combining cross-entropy-based importance sampling (IS) with adaptive Kriging model (CE-IS-AK). The innovations of CE-IS-AK include two aspects. Firstly, we construct a space augmented by both distribution parameters and the upper bound of service time interval, on which the triple-layer framework is decoupled to a single-layer one. And in the augmented space, an optimal IS density is proposed to reduce the required candidate sample size for estimating C-T-FPF. Secondly, we employ Gaussian mixture model (GMM) to approximate the optimal IS density, and the parameters in GMM are determined by minimizing the cross entropy of GMM and the optimal IS density. Moreover, to reduce the model evaluations in the proposed method, Kriging model is adaptively embedded to replace the actual model, and a first failure instant based learning function is proposed to train Kriging model adaptively. Due to the proposed single-layer framework and IS strategy assisted by the Kriging model, the efficiency is greatly improved for estimating C-T-FPF, which is validated by several examples.

Active Brownian information engine: Self-propulsion induced colossal performance.

The information engine is a feedback mechanism that extorts work from a single heat bath using the mutual information earned during the measurement. We consider an overdamped active Ornstein-Uhlenbeck particle trapped in a 1D harmonic oscillator. The particle experiences fluctuations from an inherent thermal bath with a diffusion coefficient (D) and an active reservoir, with characteristic correlation time (τa) and strength (Da). We design a feedback-driven active Brownian information engine (ABIE) and analyze its best performance criteria. The optimal functioning criteria, the information gained during measurement, and the excess output work are reliant on the dispersion of the steady-state distribution of the particle's position. The extent of enhanced performance of such ABIE depends on the relative values of two underlying time scales of the process, namely, thermal relaxation time (τr) and the characteristic correlation time (τa). In the limit of τa/τr → 0, one can achieve the upper bound on colossal work extraction as ∼0.202γ(D+Da) (γ is the friction coefficient). The excess amount of extracted work reduces and converges to its passive counterpart (∼0.202γD) in the limit of τa/τr → high. Interestingly, when τa/τr = 1, half the upper bound of excess work is achieved irrespective of the strength of either reservoirs, thermal or active. Finally, we look into the average displacement of active Brownian particles in each feedback cycle, which surpasses its thermal analog due to the broader marginal probability distribution.

A two-stage subsynchronous oscillation assessment method for DFIG-based wind farm grid-connected system

In the power system, the wind farm based on Doubly-Fed Induction Generator (DFIG) may lead to Subsynchronous Oscillation (SSO), which poses a challenge to the stability of the power grid. In order to accurately evaluate SSO, this paper proposes a new evaluation method. It is divided into two main stages: firstly, the interference level of Phasor Measurement Unit (PMU) data is identified by using the classification model based on Upper Confidence Bound (UCB) and Double Deep Q Network (DDQN). Then, an SSO parameter estimation model based on Local Feature Fusion Transformer (LFF-Transformer) network is designed for data with different interference levels. Experimental results show that the errors of eRMSE-f and EMAPE-F are 0.001 and 0.003 respectively, and the errors of eRMSE-δ and EMAPE-δ are 0.009 and 0.015 respectively. In terms of training and testing time, this method is 90 s and 18 s respectively, which is significantly better than Multi-SVR and Multi-CNN. After application, the frequency deviation decreased from 0.05 to 0.02 Hz, the voltage deviation decreased from 3.5 to 1.5%, the power fluctuation decreased from 10 to 5 MW, the SSO frequency decreased from 1.5 Hz to less than 0.5 Hz, and the SSO damping ratio increased from 0.08 to 0.15. This shows that the proposed method effectively increases the stability of the power grid.

On uniform confidence intervals for the tail index and the extreme quantile

This paper presents two results concerning uniform confidence intervals for the tail index and the extreme quantile. First, we show that there exists a lower bound of the length for confidence intervals that satisfy the correct uniform coverage over a nonparametric family of tail distributions. Second, in light of the impossibility result, we construct honest confidence intervals that are uniformly valid by incorporating the worst-case bias in the nonparametric family. The proposed method is applied to simulated data and real data of financial time series.

Upper Bound for the Conjunction Probability of Smooth Stationary Two-dimensional Gaussian Fields

Upper Bound for the Conjunction Probability of Smooth Stationary Two-dimensional Gaussian Fields

Self-improved multi-view interactive knowledge transfer

Multi-view learning (MVL) is a promising data fusion technique based on the principles of consensus and complementarity. Despite significant advancements in this field, several challenges persist. First, scalability remains an issue, as many existing approaches are limited to two-view scenarios, making them difficult to extend to more complex multi-view settings. Second, implementing consensus principles in current techniques often requires adding extra terms to the model’s objective function or constraints, leading to increased complexity. Additionally, when applying complementarity principles, most studies focus on pairwise interactions between views, overlooking the benefits of deeper and broader multi-view interactions. To address these challenges, this paper proposes the multi-view interactive knowledge transfer (MVIKT) model, which enhances scalability by effectively managing interactions across multiple views, thereby overcoming the limitations of traditional two-view models. More importantly, MVIKT introduces a novel interactive knowledge transfer strategy that simplifies the application of the consensus principle by eliminating the need for additional terms. By treating margin distances as transferable knowledge and facilitating multiple rounds of interaction, MVIKT uncovers deeper complementary information, thereby improving the overall effectiveness of MVL. Theoretical analysis further supports the MVIKT model, demonstrating that transferring knowledge through margin distance is capable of lowering the upper bound of the generalization error. Extensive experiments across diverse datasets validate MVIKT’s superiority, showing statistically significant improvements over benchmark methods.

Evaluating Effects of Continuous Occlusion on Visual Letter Identification

Visual letter identification refers to humans’ use of a visual system to recognize the 26 letters in the English alphabet. Letters may be partially occluded by nonadjacent small occlusion blocks (called discrete occlusion) or a single occlusion block (called continuous occlusion) in the real world, thereby affecting visual letter identification. The effects caused by discrete occlusion have been investigated in existing research. The results indicate that humans possess the ability to identify partially occluded letters and a large occlusion ratio results in low identification accuracy. However, few studies have explored the effects caused by continuous occlusion and revealed precise reflections on occlusion effects. This study presents an evaluation to explore the effects of continuous occlusion on visual letter identification. A controlled experiment is designed to achieve two research goals: identifying the maximum extent of occlusion ratio (named upper bound) that does not affect visual letter identification and investigating the change patterns of the accuracy of occluded letter identification with the gradual increase in occlusion ratio. The experimental results are analyzed in detail, and three main findings are obtained. First, moderately occluded letters can be accurately identified in a continuous occlusion scene. Second, the precise upper bounds are obtained for each of the 26 letters. Lastly, the change patterns for the 26 letters present three nonlinear decline patterns. The findings could inspire technical advancements in the fields of visualization, computer vision, and healthcare.