Global Assumption Research Articles

A censored quantile transformation model for Alzheimer’s Disease data with multiple functional covariates

Abstract Alzheimer’s disease (AD) is a progressive disease that starts from mild cognitive impairment and may eventually lead to irreversible memory loss. It is imperative to explore the risk factors associated with the conversion time to AD that is usually right-censored. Classical statistical models like mean regression and Cox models fail to quantify the impact of risk factors across different quantiles of a response distribution, and previous research has primarily focused on modelling a single functional covariate, possibly overlooking the interdependence among multiple functional covariates and other crucial features of the distribution. To address these issues, this paper proposes a multivariate functional censored quantile regression model based on dynamic power transformations, which relaxes the global linear assumption and provides more robustness and flexibility. Uniform consistency and weak convergence of the quantile process are established. Simulation studies suggest that the proposed method outperforms the existing approaches. Real data analysis shows the importance of both left and right hippocampal radial distance curves for predicting the conversion time to AD at different quantile levels.

Asymmetric distributed trust

Quorum systems are a key abstraction in distributed fault-tolerant computing for capturing trust assumptions. They can be found at the core of many algorithms for implementing reliable broadcasts, shared memory, consensus and other problems. This paper introduces asymmetric Byzantine quorum systems that model subjective trust. Every process is free to choose which combinations of other processes it trusts and which ones it considers faulty. Asymmetric quorum systems strictly generalize standard Byzantine quorum systems, which have only one global trust assumption for all processes. This work also presents protocols that implement abstractions of shared memory, broadcast primitives, and a consensus protocol among processes prone to Byzantine faults and asymmetric trust. The model and protocols pave the way for realizing more elaborate algorithms with asymmetric trust.

Theoretical prediction model for the compressive behavior of the hybrid tube considering compression angle

AbstractThe oblique collision happening in vehicle accidents poses a huge threat to passive safety, which causes great difficulties in the design of energy absorption (EA) structures and the prediction of EA capacity due to its highly nonlinear deformation characteristics. This study aims to establish a theoretical prediction model for the compression performance of Carbon Fiber Reinforced Polymer (CFRP)/Al hybrid tube considering the loading angle. First, a high‐precision FE model was established to obtain the influence laws of tube diameter, Al thickness, and CFRP thickness on the crashworthiness of CFRP/Al hybrid tubes, laying the foundation for subsequent theoretical model validation. Second, by summarizing the deformation modes of hybrid tubes generated by various parameter combinations, a modified global origami deformation assumption was proposed under multi‐angle compression conditions, and the key terms in energy composition are extracted based on the initial and final states of folding elements. Third, a theoretical model for predicting the mean crushing forces (MCFs) of hybrid tubes was established by revealing the correlation mechanism between energy composition terms and loading angle. Finally, the theoretical prediction model was validated by experiment and simulation results and the application premise was given. Results showed that the theoretical prediction model was proved to be of high accuracy, as the average absolute prediction errors of MCF under axial, 10°, 20°, and 30° compression conditions were 6.54%, 4.63%, 3.72%, and 3.93%, respectively. This study provides valuable guidance for the forward design and development of multi‐material hybrid structures facing complex crushing conditions.Highlights An analytical model of the hybrid circular tubes considering compression angle is newly proposed. Deformation mode and axial crushing response are analyzed by experiments. The major energy dissipation mechanism for hybrid circular tubes is explicitly derived. The Al thickness has the most significant impact on energy absorption. The recommendations for the design and development of hybrid tube are provided.

Difference-of-Convex Algorithm with Extrapolation for Nonconvex, Nonsmooth Optimization Problems

In this paper, we focus on the problem of minimizing the sum of a nonconvex differentiable function and a difference of convex (DC) function, where the differentiable function is not restricted to the global Lipschitz gradient continuity assumption. This problem covers a broad range of applications in machine learning and statistics, such as compressed sensing, signal recovery, sparse dictionary learning, matrix factorization, etc. We first take inspiration from the Nesterov acceleration technique and the DC algorithm to develop a novel algorithm for the considered problem. We then study the subsequential convergence of our algorithm to a critical point. Furthermore, we justify the global convergence of the whole sequence generated by our algorithm to a critical point and establish its convergence rate under the Kurdyka–Łojasiewicz condition. Numerical experiments on the nonnegative matrix completion problem are performed to demonstrate the efficiency of our algorithm and its superiority over well-known methods.

Global solutions to a haptotaxis system with a potentially degenerate diffusion tensor in two and three dimensions

We consider the potentially degenerate haptotaxis system ut=∇⋅(D∇u+u∇⋅D)−χ∇⋅(uD∇w)+μu(1−ur−1),wt=−uw in a smooth bounded domain , , with a no-flux boundary condition, positive initial data u 0, w 0 and parameters χ > 0, µ > 0, and , positive semidefinite on . Our main result regarding the above system is the construction of weak solutions under fairly mild assumptions on as well as the initial data, encompassing scenarios of degenerate diffusion in the first equation. As a step in this construction as well as a result of potential independent interest, we further construct classical solutions for the same system under a global positivity assumption for , which ensures the full regularising influence of its associated diffusion operator. In both constructions, we naturally rely on the regularising properties of a sufficiently strong logistic source term in the first equation.

Second-Order Guarantees of Stochastic Gradient Descent in Nonconvex Optimization

Recent years have seen increased interest in performance guarantees of gradient descent algorithms for nonconvex optimization. A number of works have uncovered that gradient noise plays a critical role in the ability of gradient descent recursions to efficiently escape saddle-points and reach second-order stationary points. Most available works limit the gradient noise component to be bounded with probability one or sub-Gaussian and leverage concentration inequalities to arrive at high-probability results. We present an alternate approach, relying primarily on mean-square arguments and show that a more relaxed relative bound on the gradient noise variance is sufficient to ensure efficient escape from saddle points without the need to inject additional noise, employ alternating step sizes, or rely on a global dispersive noise assumption, as long as a gradient noise component is present in a descent direction for every saddle point.

Low-light image enhancement and denoising via dual-constrained Retinex model

For low-light image enhancement, Retinex-based models have been acknowledged as a representative technique, yet they frequently amplify noise hidden in dark image. There have been some attempts to noise reduction. Because they assume a uniform level of noise, the background seems blurry. In this paper, a dual constraint is developed to perform Retinex decomposition and de-noising. First, a patch-aware low-rank model (PALR) is proposed to reject noise. In contrast to the global noise intensity assumption, PALR can measure noise intensity for each image patch, and flexibly control the regularization extent to achieve a trade-off between noise removal and details preservation. Second, noise looks like image background texture instead of image structure. Relative total variation (RTV) is used to simulate the visual difference and works well in enlarging image gradients for highlighting details. By imposing PALR constraint on clean scene image, enforcing visual difference constraint on the illumination and reflectance, a dual-constrained Retinex decomposition model (DCRD) is proposed, which can remove noise during decomposition. DCRD can be solved by an alternating optimization algorithm. Experiments on commonly tested low-light image datasets demonstrate the competing performance of our proposed model in comparison with the state-of-the-art methods.

Investigation of macro-kinetics of coal-oxygen reactions under varying oxygen concentrations: Towards the understanding of combustion characteristics in underground coal fires

The typical combustion mode of underground coal fires (UCFs) is smoldering during which the reaction zone is not exposed to a constant oxygen concentration. Understanding the macro-kinetics of coal-oxygen reactions under varying oxygen concentrations, especially the extremely oxygen-depleted condition, is of both theoretical importance and practical relevance to the control and extinguishment of UCFs. Considering the actual conditions of UCFs, thermal analysis tests under four oxygen concentrations (from 21% to 3%) and three heating rates (1, 2 and 5 °C /min) were carried out. Thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) results were obtained for a bituminous coal sample from Inner Mongolia, China. With the global reaction assumption, the macro-kinetics parameters (the apparent activation energy, the pre-exponential factor and the kinetics model function) were determined. On the profiles of the apparent activation energy (Ea), three peak values were observed, physically interpreted as the depletion of volatiles, the formation of plastic mass and the depletion of char, respectively. This interpretation was verified by characteristic temperatures extracted from the experimental data. With the decrease of the oxygen concentration from 21% to 9%, two peak values diminish gradually. The case with 3% oxygen concentration gives a nearly monotonically declining Ea, indicating that under that particular condition, oxygen diffusion stands as the only limiting factor across all stages of coal-oxygen reactions. The best-fit kinetics model functions suggest that the char oxidation stage falls into the kinetics-controlled regime when the oxygen concentration is as low as 9%. For the volatiles burning stage, the universal ignition index (Fz) is found to be effectively related to the reaction regime for a variety of coal ranks. The quantitative results obtained can be integrated into any CFD multi-physics models as a sub-model for chemical kinetics.

Profiling the Bladder Microbiota in Patients With Bladder Cancer.

Evidence suggests that microbiota may contribute to the pathogenesis of several diseases, including cancer. In the case of bladder cancer, preliminary studies have found alterations in the urinary microbiota of patients with urothelial carcinoma compared with healthy individuals. Conversely, the urinary microbiota differ between men and women, and it has been hypothesized that these differences are associated with the lower incidence of bladder cancers in women. The objective of this study was to characterize the bladder microbiota in paired samples of tumor and non-tumor mucosa of patients with malignant bladder neoplasia using next-generation sequencing. In addition, we aimed to study potential differences in microbial composition in tumor samples according to clinical and pathological variables, and to determine possible microbial profiles. We found significant differences in microbial richness at the genus level, with a higher richness observed in the non-tumor compared with the tumor mucosa. It was also shown that Actinobacteria were significantly more enriched in the non-tumor compared with the tumor mucosa (P = 0.014). In the multivariate analysis, we found significant differences in microbial composition according to tumor grade (P = 0.03 and 0.04 at the phylum and genus levels, respectively). Moreover, we detected a higher microbial richness in non-tumor vs. tumor tissues which agrees with the global assumption that microbial richness is an indicator of health. The greater abundance of members of the Actinobacteria phylum in the non-neoplastic bladder mucosa samples supports the hypothesis that a higher abundance of Actinomycetes is associated with a lower rate of bladder cancer in women and suggests a protective role for these microbiota. We detected a microbial profile that was enriched for Enterococcus in low-grade tumors. Finally, we identified the presence of two clusters in the microbial composition of the tumor mucosa samples, significantly enriched for the genera Barnesiella, Parabacteroides, Prevotella, Alistipes, and Lachnospiracea_incertae_sedis (Cluster 1), or Staphylococcus (Cluster 2). Further longitudinal studies are needed to assess the role of the bladder microbiota in carcinogenesis.

An automatic clustering algorithm based on the density-peak framework and Chameleon method

• The proposed method only needs a single discrete input parameter. • The proposed method has a robust performance in the different density scenario. • The proposed method can automatically detect the number of clusters. • We adapt the cluster stability for our method and find a new way to calculate it. The density-peak clustering (DPC) method (Rodriguez and Laio, 2014) clusters the data efficiently by fast searching density peaks. Recently, an improved DPC algorithm named 3DC method (Liang and Chen, 2016) was proposed for automatically detecting the correct structure of the clusters. However, it is difficult to select correct parameters for the DPC and 3DC methods and the local property of data set can’t be revealed due to their global density assumption in some scenarios. To overcome this drawback, the K-nearest neighbor (KNN) framework is adapted for defining the density of the DPC method. Nevertheless, such KNN-based methods can’t automatically detect the number of the clusters compared with the 3DC method. In this paper, an automatic clustering method is proposed, which needs only a discrete input parameter. Meanwhile, by utilizing the cluster stability for the Chameleon framework, the proposed method can automatically detect the correct structure of the clusters. The experimental results on the synthetic and real world data demonstrate that the proposed method has a more robust performance. Besides, the proposed method is robust to the choices of the input parameter.

Optimal futures hedging strategies based on an improved kernel density estimation method.

In this paper, we study the hedging effectiveness of crude oil futures on the basis of the lower partial moments (LPMs). An improved kernel density estimation method is proposed to estimate the optimal hedge ratio. We investigate crude oil price hedging by contributing to the literature in the following twofold: First, unlike the existing studies which focus on univariate kernel density method, we use bivariate kernel density to calculate the estimated LPMs, wherein the two bandwidths of the bivariate kernel density are not limited to the same, which is our main innovation point. According to the criterion of minimizing the mean integrated square error, we derive the conditions that the optimal bandwidths satisfy. In the process of derivation, we make a distribution assumption locally in order to simplify calculation, but this type of local distribution assumption is far better than global distribution assumption used in parameter method theoretically and empirically. Second, in order to meet the requirement of bivariate kernel density for independent random variables, we adopt ARCH models to obtain the independent noises with related to the returns of crude oil spot and futures. Genetic algorithm is used to tune the parameters that maximize quasi-likelihood. Empirical results reveal that, at first, the hedging strategy based on the improved kernel density estimation method is of highly efficiency, and then it achieves better performance than the hedging strategy based on the traditional parametric method. We also compare the risk control effectiveness of static hedge ratio vs. time-varying hedge ratio and find that static hedging has a better performance than time-varying hedging.

Adaptive backstepping quantized control for a class of unknown nonlinear systems

In this paper, the stability problem for a class of nonlinear systems in the form of strict-feedback with applying input quantization has been addressed. By considering a sector-bounded hysteresis quantizer, signal quantization has been achieved. The employed quantizer can reduce the potential chattering which can occur in some approaches. By using a common Lyapunov function (CLF) and the backstepping method, a control scheme has been introduced to stabilize the uncertain nonlinear system. Compared with the recent papers, in order to handle the quantization error, one of the sector-bounding features has been utilized straightly instead of decomposing the quantized input into linear and nonlinear parts, in this case, the possible disturbance-like term has been ignored. The designed control scheme does not need the global Lipschitz assumption over the system mismatched nonlinearities. Besides, the asymptotic stability of system trajectories to the origin is guaranteed and the imposed restrictions over quantization design parameters such as quantization density have been eliminated. Finally, in the simulation results, the accuracy and efficiency of the this control scheme are shown.

Existence and multiplicity results for the fractional magnetic Schrödinger equations with critical growth

In this paper, we study the following critical fractional Schrödinger equations with the magnetic field: ε2s(−Δ)A/εsu+V(x)u=λf(|u|)u+|u|2s*−2uinRN, where ɛ and λ are positive parameters and V:RN→R and A:RN→RN are continuous electric and magnetic potentials, respectively. Under a global assumption on the potential V, by applying the method of Nehari manifold, Ekeland’s variational principle, and Ljusternick–Schnirelmann theory, we show the existence of ground state solution and multiplicity of non-negative solutions for the above equation for all sufficiently large λ and small ɛ. In this problem, f is only continuous, which allows us to study larger classes of nonlinearities.

Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods

In this paper, we consider the equivalence of the pth moment exponential stability for stochastic differential equations (SDEs), stochastic differential equations with piecewise continuous arguments (SDEPCAs) and the corresponding Euler-Maruyama methods EMSDEs and EMSDEPCAs. We show that if one of the SDEPCAs, SDEs, EMSDEs and EMSDEPCAs is pth moment exponentially stable, then any of them is pth moment exponentially stable for a sufficiently small step size h and τ under the global Lipschitz assumption on the drift and diffusion coefficients.

Sampled-output observer design in the presence of nonlinear heat PDE sensor

The problem of observer design is addressed for linear plants that are observed with heat PDE sensors, leading to a global system with ODE-PDE cascade structure. One novelty of the study is that the PDE sensor includes globally Lipschitz nonlinear dynamics. The other novelty is that the proposed observer relies on sampled measurements at the sensor boundary. The observer provides online estimates of both the plant (finite-dimensional) state vector and the sensor PDE distributed state. Exponential stability of the observation error system is analysed using backstepping-like transformation, Lyapunov-Krasovski type functional, Wirtinger’s and Halanay’s inequalities. Additional observer features are highlighted by simulation results, including its robustness to global Lipschitz assumption, and its applicability to output feedback stabilisation.

Deep Reinforcement Learning-Based Resource Allocation and Power Control in Small Cells With Limited Information Exchange

In multi-user downlink small cell networks, cooperative resource allocation (RA) within a small cell cluster is a key technique to enhance network capacity. However, capacity-maximizing RA in frequency-selective fading channels requires global channel state information (CSI) of users within a small cell cluster, which makes it infeasible in practical networks with limited direct link capacity. To circumvent this global CSI assumption, most of the existing studies on RA have been based on several CSI assumptions such as local CSI and local CSI at the transmitters (CSIT). Nevertheless, cost functions with local CSI or local CSIT in the literature rely on heuristic formulations, because the sum-rate cannot be computed if without global CSI. In this paper, we propose a deep reinforcement learning-based RA algorithm to maximize the sum-rate for any given limited information on instantaneous CSI or sum-rate at the previous period. The proposed scheme is not restricted to certain CSI assumptions, but attempts to find the best RA for any given information such as quantized local CSI and quantized local CSIT; thus, it is applicable to any given direct link capacity. The proposed algorithm is self-adaptive in time-varying channels, since it is not divided into training and test phases. We modify the target neural network (TNN) scheme to enhance the sum-rate and the convergence speed. Numerical simulations confirm that: i) the proposed algorithm outperforms the conventional algorithms even under the same CSI assumption such as local CSI and local CSIT; ii) a flexible trade-off between the amount of CSI and the sum-rate is realizable in practical systems.

Distributed robust Nash equilibrium seeking for aggregative games under persistent attacks: A hybrid systems approach

An aggregative game involving double-integrator agents is investigated. In this game, the dynamics of all players are subjected to unknown time-varying disturbances and unmodeled terms, and are also influenced by networked attacks on the communication topology. To seek a Nash equilibrium for such games, a novel distributed robust Nash equilibrium seeking algorithm is proposed and the complete closed-loop system is modeled as a hybrid system using an average dwell-time automaton and a time-ratio monitor to constrain attacks. Then, to analyze stability for the proposed algorithm, a Lyapunov function is constructed and uniform asymptotic stability is obtained under a local Lipschitz assumption on the gradients of the payoff functions. In addition, global uniform asymptotic stability is obtained under a global Lipschitz assumption on the gradients. Finally, an example is used to illustrate the results.

Strongly convergent error analysis for a spatially semidiscrete approximation of stochastic partial differential equations with non-globally Lipschitz continuous coefficients

We study a spatially semidiscrete approximation of nonlinear stochastic partial differential equations (SPDEs) driven by multiplicative noise under weak assumptions on the coefficients avoiding the standard global Lipschitz assumption in the literature. The discretization in space is done by a piecewise linear finite element method. Under some suitable regularity assumption for the exact solution, we present here a rigorous convergence error analysis for the proposed semidiscrete scheme—showing that the numerical scheme admits a convergent rate depending on the regularity of the exact solution.

RGBD Scene Flow Estimation with Global Nonrigid and Local Rigid Assumption

RGBD scene flow has attracted increasing attention in the computer vision with the popularity of depth sensor. To estimate the 3D motion of object accurately, a RGBD scene flow estimation method with global nonrigid and local rigid motion assumption is proposed in this paper. Firstly, the preprocessing is implemented, which includes the colour-depth registration and depth image inpainting, to processing holes and noises in the depth image; secondly, the depth image is segmented to obtain different motion regions with different depth values; thirdly, scene flow is estimated based on the global nonrigid and local rigid assumption and spatial-temporal correlation of RGBD information. In the global nonrigid and local rigid assumption, each segmented region is divided into several blocks, and each block has a rigid motion. With this assumption, the interaction of motion from different parts in the same segmented region is avoided, especially the nonrigid object, e.g., a human body. Experiments are implemented on RGBD tracking dataset and deformable 3D reconstruction dataset. The visual comparison shows that the proposed method can distinguish the motion parts from the static parts in the same region better, and the quantitative comparisons proved more accurate scene flow can be obtained.

The Inhomogeneous Dirichlet problem for natural operators on manifolds

We shall discuss the inhomogeneous Dirichlet problem for: $f(x,u, Du, D^2u) = \psi(x)$ where $f$ is a differential operator, with a restricted domain $F$, on a manifold $X$. By we mean operators that arise intrinsically from a given geometry on $X$. An important point is that the equation need not be convex and can be highly degenerate. Furthermore, the inhomogeneous term can take values at the boundary of the restricted domain $F$ of the operator $f$. A simple example is the real Monge-Ampere operator ${\rm det}({\rm Hess}\,u) = \psi(x)$ on a riemannian manifold $X$, where ${\rm Hess}$ is the riemannian Hessian, the restricted domain is $F = \{{\rm Hess} \geq 0\}$, and $\psi$ is continuous with $\psi\geq0$. A main new tool is the idea of local jet-equivalence, which gives rise to local weak comparison, and then to comparison under a natural and necessary global assumption. The main theorem applies to pairs $(F,f)$, which are locally jet-equivalent to a given constant coefficient pair $({\bf F}, {\bf f})$. This covers a large family of geometric equations on manifolds: orthogonally invariant operators on a riemannian manifold, G-invariant operators on manifolds with G-structure, operators on almost complex manifolds, and operators, such as the Lagrangian Monge-Ampere operator, on symplectic manifolds. It also applies to all branches of these operators. Complete existence and uniqueness results are established with existence requiring the same boundary assumptions as in the homogeneous case [10]. We also have results where the inhomogeneous term $\psi$ is a delta function.