Point Problems Research Articles

Backward induction and expected value calculations in an anonymous XVth century Italian manuscript

Blaise Pascal famously calculated the expected value of a risky lottery in the 1654 correspondence with Pierre de Fermat in the context of the so-called points problem. Pascal solved this problem by backward induction, whereas Fermat—by counting combinations. This paper analyzes a more complex version of the points problem from an anonymous XVth century Italian manuscript stored in the Vatican Apostolic Library. In this manuscript, the problem of points is solved by backward induction in a similar way to Pascal’s train of thought. In this light, Pascal’s pioneering contribution may be not as novel as it is traditionally believed.

Rationality Now!

Rationality Now!

Silence as Message (Gender-related aspects of communicative competence)

The 1920s saw the emergence of interest in gender-related issues of communication in the scholarly literature. Descriptive analyses of various cultural and linguistic patterns highlighted that there are speech communities within which women undergo linguistic discrimination in two ways: how they are taught to use language and how they actually use it. The present paper provides an analysis of the latter instance. Within the methodological framework of the Ethnography of Communication, and on the in/occurrence of components of the SPEAKING model, the paper aims at discussing speech events in which silence is a gender-specific fact. Illustrative data have been drawn from ethnographic records and travelogues. Such an analysis of the problem in point enables to discuss key issues of communicative competence and infer that, alongside acquiring vocabulary and grammar rules of a language, it is significant to be aware of who and when is expected to avoid verbal communication in a given speech community.

Double-layer geodesic and gradient-index lenses

A double-layer lens consists of a first gradient-index/geodesic profile in an upper waveguide, partially surrounded by a mirror that reflects the wave into a lower guide where there is a second profile. Here, we derive a new family of rotational-symmetric inhomogeneous index profiles and equivalent geodesic lens shapes by solving an inverse problem of pre-specified focal points. We find an equivalence where single-layer lenses have a different functionality as double-layer lenses with the same profiles. As an example, we propose, manufacture, and experimentally validate a practical implementation of a geodesic double-layer lens that is engineered for a low-profile antenna with a compact footprint in the millimeter wave band. Its unique double-layer configuration allows for two-dimensional beam scanning using the same footprint as an extension of the presented design. These lenses may find applications in future wireless communication systems and sensing instruments in microwave, sub-terahertz, and optical domains.

Research on Intelligent Estimation Method of Human Moving Target Pose Based on Adaptive Attention Mechanism

In daily physical education, posture performance is an important basis for making excellent results. This paper explores an intelligent method to estimate the target pose based on adaptive attention mechanism. First, the regional attention is iteratively generated from a global level to a local level based on the attention mechanism. Human decision-making patterns are imitated to evaluate the effectiveness of regional attention in real time. The level of attention mechanism is adaptively adjusted and focused layer by layer to achieve precise target detection and tracking. Second, with the target frame obtained from each frame, the pose estimation algorithm finds the key points of human body, enabling the human body pose optimization strategy to solve the crossover problem of the key points. Results of experiments on sports video images show that the proposed method has a higher accuracy in pose estimation than other algorithms and can help sportsmen adjust their training methods scientifically.

Comparison of parallel infill sampling criteria based on Kriging surrogate model

One of the key issues that affect the optimization effect of the efficient global optimization (EGO) algorithm is to determine the infill sampling criterion. Therefore, this paper compares the common efficient parallel infill sampling criterion. In addition, the pseudo-expected improvement (EI) criterion is introduced to minimizing the predicted (MP) criterion and the probability of improvement (PI) criterion, which helps to improve the problem of MP criterion that is easy to fall into local optimum. An adaptive distance function is proposed, which is used to avoid the concentration problem of update points and also improves the global search ability of the infill sampling criterion. Seven test problems were used to evaluate these criteria to verify the effectiveness of these methods. The results show that the pseudo method is also applicable to PI and MP criteria. The DMP and PEI criteria are the most efficient and robust. The actual engineering optimization problems can more directly show the effects of these methods. So these criteria are applied to the inverse design of RAE2822 airfoil. The results show the criterion including the MP has higher optimization efficiency.

A comparative inference on reliability estimation for a multi-component stress-strength model under power Lomax distribution with applications

<abstract><p>In this article, reliability estimation for a system of multi-component stress-strength model is considered. Working under progressively censored samples is of great advantage over complete and usual censoring samples, therefore Type-II right progressive censored sample is selected. The lifetime of the components and the stress and strength components are following the power Lomax distribution. Consequently, the problem of point and interval estimation has been studied from different points of view. The maximum likelihood estimate and the maximum product spacing of reliability are evaluated. Also approximate confidence intervals are constructed using the Fisher information matrix. For the traditional methods, bootstrap confidence intervals are calculated. Bayesian estimation is obtained under the squared error and linear-exponential loss functions, where the numerical techniques such as Newton-Raphson and the Markov Chain Monte Carlo algorithm are implemented. For dependability, the largest posterior density credible intervals are generated. Simulations are used to compare the results of the proposed estimation methods, where it shows that the Bayesian estimation method of the reliability function is significantly better than the other methods. Finally, a real data of the water capacity of the Shasta reservoir is examined for illustration.</p></abstract>

Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications

In this article, we discuss the hierarchical fixed point and split monotone variational inclusion problems and propose a new iterative method with the inertial terms involving a step size to avoid the difficulty of calculating the operator norm in real Hilbert spaces. A strong convergence theorem of the proposed method is established under some suitable control conditions. Furthermore, the proposed method is modified and used to derive a scheme for solving the split problems. Finally, we compare and demonstrate the efficiency and applicability of our schemes for numerical experiments as well as an example in the field of image restoration.

Fixed Point, Data Dependence, and Well-Posed Problems for Multivalued Nonlinear Contractions

The aim of the paper is to discuss data dependence, existence of fixed points, strict fixed points, and well posedness of some multivalued generalized contractions in the setting of complete metric spaces. Using auxiliary functions, we introduce Wardowski type multivalued nonlinear operators that satisfy a novel class of contractive requirements. Furthermore, the existence and data dependence findings for these multivalued operators are obtained. A nontrivial example is also provided to support the results. The results generalize, improve, and extend existing results in the literature.

Reliability analysis of Weibull multicomponent system with stress‐dependent parameters from accelerated life data

AbstractIn this paper, reliability estimation of multicomponent system under a multilevel accelerated life testing. When the lifetime of components follows Weibull distribution, the problem of point and interval estimates are discussed from different perspectives. Under a general life‐stress assumption that there are multiple nonconstant and stress‐dependent scale and shape parameters, the maximum likelihood estimates of unknown parameters along with associated existence and uniqueness are established. Approximate confidence intervals are constructed correspondingly via expected Fisher information matrix. Furthermore, some pivotal quantities are constructed and alternative generalized point and interval estimates are also proposed for comparison. In addition, predictive intervals for the lifetime of the multicomponent system are discussed under classical and generalized pivotal approaches, respectively. The results show that the proposed generalized estimates are superior to the conventional likelihood approach in terms of the accuracy. A real data example is carried out to illustrate the implementations of the proposed methods.

Jacobian Conjecture as a Problem on Integral Points on Affine Curves

It is shown that the Jacobian conjecture over number fields may be considered as an existence problem of integral points on affine curves. More specially, if the Jacobian conjecture over $\mathbb {C}$ is false, then for some n ≫ 1 there exists a counterexample $F\in \mathbb {Z}[X]^{n}$ of the form $F_{i}(X)=X_{i}+ (a_{i1}X_{1}+\cdots +a_{in}X_{n})^{d_{i}}$ , $a_{ij}\in \mathbb {Z}$ , di = 2;3, $i,j=1,\dots ,n$ , such that the affine curve F1(X) = F2(X) = ⋯ = Fn(X) has no non-zero integer points.

Disturbance Detection of Optical Fiber Sensing Electronic System and Its Loss Prediction Using Big Data Technology

Optical fiber sensing technology performs quite well in large-scale positioning, real-time monitoring and other fields, while its stability and environmental adaptability of the system need to be improved in the application of engineering. There are two aspects that need to be improved. The first is that the optical fiber signal disturbance needs to be located. The second is that the loss of fiber fusion joint needs to be predicted to replace the fiber components in time. Based on this, first, the transmission matrix model is established for interference optical path transmission of optical fiber sensing electronic system in the case of signal disturbance. The abstract model of backscatter signal and disturbance signal location in the case of signal disturbance are proposed respectively; then, many correlative experiments are carried out for the loss problem of optical fiber fusion points, and big data technologies such as grey model (GM (1,1)), ARIMA model and Elman neural network are introduced to predict the loss of fusion joint. In the experiment, the time difference between the singular signal and the optical pulse, or the corresponding time difference between singular signal and the beginning of the sensing region, can be obtained from the backscattering trajectory. Then, the disturbance location can be obtained based on the disturbance location abstract model; deviation maintaining welding machine is used, its loss of fusion joint is low, and the corresponding high temperature resistance and humidity resistance are good. The loss prediction performance of different models is compared, and the combined prediction model has smaller prediction error and higher prediction accuracy.

An improved algorithm for pile damage localization based on complex continuous wavelet transform

Since the complex continuous wavelet transform (CCWT) based pile damage detection method is empirical and subjective, an improved algorithm for pile damage localization based on CCWT is proposed by introducing K-means clustering and fast Fourier transform (FFT). In this method, the K-means clustering algorithm is used to accurately calculate the time coordinates of two energy concentrating points caused by the incident and reflected waves, respectively. Meanwhile, FFT is employed to estimate the concerned frequency band of the response signal. Therefore, a specific region in the time frequency plane is defined objectively and it can be used to search the phase angle turning points and localize pile damage. The proposed method is verified by numerical examples of piles with single and multiple damage positions. A parameter analysis is also conducted to investigate how damage depth and damage degree in piles affect the accuracy and effectiveness of the proposed method. The results demonstrate that the proposed method is able to localize a pile with a damage at least 2.5 m away from the pile head when the damage degree is as less as 5%. After that, dynamic tests of an actual square reinforced concrete pile and an actual circular reinforced concrete pile are investigated to verify the application of the proposed method on practical engineering. Although the proposed method is capable of localizing actual piles more accurately than the CCWT method, the problem of interference points needs to be addressed by mutual verification with other pile damage localization methods.

Strongly essential set of vector Ky Fan's points problem and its applications

In this paper, several existence results of strongly essential set of the solution set for Ky Fan's section problems and vector Ky Fan's point problems are obtained. Firstly, two kinds of strongly essential sets of Ky Fan's section problems are defined, and some further results on existence of the strongly essential component of solutions set of Ky Fan's section problems are proved, which generalize the conclusion in ^{[<span class="xref"><a href="#b22" ref-type="bibr">22</a></span>]}, and further generalize the conclusions in ^{[<span class="xref"><a href="#b21" ref-type="bibr">21</a></span>,<span class="xref"><a href="#b28" ref-type="bibr">28</a></span>]}. Secondly, based on the above results, two classes of stronger perturbations of vector-valued inequality functions are proposed respectively, and several existence results of the strongly essential component of set of vector Ky Fan's points are obtained. By comparing several metrics, we give some strong and weak relationships among the various metrics involved in the text. The main results of this paper actually generalize the relevant conclusions in the current literature. Finally, as an application, we obtain an existence result of the strongly essential component of weakly Pareto-Nash equilibrium for multiobjective games.

An Intestinal Centerline Extraction Algorithm Based on Federated Framework

The intestine is an important organ of the human body, and its internal structure always needs to be observed in clinical applications so as to provide a basis for accurate diagnosis. However, due to the limited intestinal data obtained by a single institution, deep learning cannot effectively train the intestines, and the effect is not satisfied. For this reason, we propose a distributed training method to carry out federated learning to alleviate the situation of patient sample data shortage, not shared and uneven data distribution. And the blockchain is introduced to enhance the interaction between networks, to solve the problem of a single point of failure of the federated learning server. Fully excavate the multiscale features of samples, to construct a fusion enhancement model and intestinal segmentation module for accurate positioning. At the local end, the centerline extraction algorithm is optimized, with the edge as the main and the source as the auxiliary to realize centerline extraction.

Refinement of estimates of the success probability of a double-spend attack on the Blockchain System, Based on the Independent Players Model

Blockchain technology is being studied in many innovative applications, such as: cryptocurrencies, smart contracts, communication systems, healthcare, Internet of Things, financial systems, software development, electronic voting and many others. Using a transparent and fully distributed peer-to-peer blockchain architecture, applications benefit from a data-only model, in which “transactions” are accepted into the blockchain ledger and, if the system is functioning properly, cannot be modified or deleted. The transparency of blockchain systems makes it possible to store publicly available and irrefutable records. A peer-to-peer blockchain system provides verifiable ledger maintenance without centralized management, which solves the problems of a single point of failure and a single point of trust. The article deals with the issue of the security of application of accounting systems built on decentralized principles using blockchain technology. Particular attention is paid to the problem of the possibility of double spending in such accounting systems. The article exemplifies the reorganization of records in blockchain ledgers, performed by successfully carrying out a 51% attack on consensus algorithms based on proof of work. Given refinement of analytical expressions of 51% attack probability obtained in the works of S. Nakamoto and M. Rosenfeld using a more general model, namely, the model of independent players, where the probability of block formation by attackers and an honest network are independent events. The results of comparing of the success probability of a double-spending attack on the blockchain systems calculated according to different models are presented.

Learning-Based Resource Partitioning in Heterogeneous Networks With Multiple Network Operators

In heterogeneous network, it is important to mitigate cross-tier interference. Resource partitioning is the one of solution to reduce interference. However, most of studies on partitioning assumed that there was only one network operator to cooperate with. In this letter, we study the network selection problem of small access points in heterogeneous networks, which are provided by multiple network operators. We model the multiple network operators scenario as a congestion game. To solve the equilibrium point of suggested game, we analyze some features of proposed model such as potential game property, smoothed best response dynamics and logit equilibrium. Then, we propose a reinforcement learning algorithm that can reach logit equilibrium in distributed way. Moreover, we also suggest the adjustment of learning parameters to enhance adaptability. By means of simulations, it is shown that proposed algorithm has near-optimal performance in view of throughput, fairness and adaptability.

Globally Asymptotically Stable Equilibrium Points in Kukles Systems

The problem of determining the basin of attraction of equilibrium points is of great importance for applications of stability theory. In this article, we address the global asymptotic stability problem of an equilibrium point of an ordinary differential equation on the plane. More precisely, we study equilibrium points of Kukles systems from the global asymptotic stability point of view. First of all, we classify the Kukles systems satisfying the assumptions: the origin is the unique equilibrium point which is locally asymptotically stable, and the divergence is negative except possibly at the origin. Then, for each of such Kukles system, we prove that the origin is globally asymptotically stable. Poincare compactification is used to study the systems on the complements of compact sets.

Multi-objective optimal formation reconfiguration with scalarization and stochastic boundaries

Abstract A new method is proposed for multi-objective optimal control of satellite formation reconfiguration. First, necessary optimality conditions of single-objective fuel-optimal reconfiguration are studied. Problem of initial guess of the costate and control discontinuity are addressed by using a new developed stochastic based method. Terminal conditions of Two Point Boundary Value Problem (TPBVP) of the optimal control equations are relaxed using augmented Gaussian. Variances or bandwidths of the terminal conditions are set to decision variables to be optimized. Responses of varied initial costate are modeled and propagated using Riccati equation. Using quadratic convolution of relaxed terminal conditions, objective function of the fuel-optimal problem is reformulated into a quadratic equation, and a gradient based optimizer is used to search the optimal initial guess. In the second part of the paper, optimal control of format flying reconfiguration with two competitive objectives:fuel and time of flight (ToF) is studied. With Pascoletti-Serafini scalarization, the Multi-objective Optimal Control Problem (MOCP) is scalarized into a set of weighted Single-objective Optimal Control Problems (SOCP). Hamiltonian and switch function for the weighted SOCP are developed and constructed. New developed stochastic based approach is then used to search the optimal Pareto solutions. Verification and performances of proposed algorithms are demonstrated through numerical simulations of single-objective and multi-objective optimal control of low-thrust elliptical orbit formation reconfiguration. Potential applications of the algorithms to some other preliminary space mission designs are also discussed.

Robust monocular pose tracking of less-distinct objects using contour part model

<p indent=0mm>Less-distinct objects are those that are similar to the background in terms of color or texture. The presence of interference, e.g., noise, dynamic light, and cluttered background, further reduce their distinctiveness. Owing to the lack of distinctiveness with the background, robust monocular 6 DOF pose tracking of less-distinct objects remains an unresolved issue. We propose a novel contour part model based on a robust monocular pose tracking method for less-distinct objects. This work uses the traditional contour feature for monocular pose tracking in a new strategy called a contour part model. First, the contour part model is built segmenting the projected contour rendered from the 3-D model into contour segments of a certain length adaptively, according to the Shi-Tomasi cornerness scores. Further, for each contour part, the correspondence is detected in the input image by the proposed gradient orientation-based template matching. Finally, robust pose tracking is achieved solving the Perspective-<italic>n</italic>-Point problem. Results of the experiments carried out using a publicly available dataset and semi-synthetic images indicate that the proposed method performs better than the current methods when pose tracking less-distinct objects, showing great robustness toward interference. The superior performance of the proposed method is validated by the experiments.