Test Problems Research Articles

Fuzzy-stochastic distributional robust approach for microalgae-based bio-plastic supply chain with new sustainability aspects

The current study offers a sustainable supply chain model that can be used to identify opportunities and constraints for the future of the microalgae-based bio-diesel and bio-plastic industry. The network’s carbon emissions are restricted by an uncertain constraint that allows for flexibility in controlling emissions as needed. The social constraints of the model provides a transparent depiction of labour needs in dynamic business landscape and foster women’s empowerment through a preference coefficient. The proposed model introduces a new upside risk measures under fuzzy-stochastic setting to quantify the upward financial risk. To characterize and manage the model uncertainty, a fuzzy-stochastic distributional robust model is presented. Credibility distribution is utilized to handle fuzzy uncertainty, while box and polyhedral uncertainty sets are included to handle stochastic uncertainty. After that, tractable deterministic formulations of the uncertain model for two ambiguity sets are presented to solve the model. Finally, a number of insights are obtained by means of five test problems that are implemented in Python and resolved by one exact and five meta-heuristic algorithms. Experiments indicate that, when faced with uncertainty, two robust models have produced more stable solutions (16.23% and 19.67% higher stability, respectively) than nominal stochastic model. Further, a 4.68% decline in total cost and 3.27% increment in bio-diesel production can be achieved by increasing bio-diesel conversion rate to 10%. In addition, a 9.09% downturn in total cost and 10.44% rise in bio-plastic production can be obtained by 10% increment in bio-plastic conversion rate. Moreover, 45.38% more woman labours can be recruited by increasing the preference coefficient from −0.2 to +0.2.

Two modified conjugate gradient methods for unconstrained optimization

Conjugate gradient (CG) methods are a popular class of iterative methods for solving linear systems of equations and nonlinear optimization problems. Motivated by the construction of some modern CG methods, we propose two modified CG methods, named DHS* and DPRP*. Under the strong Wolfe line search (SWLS), the two presented methods are proven to be sufficient descent and globally convergent. Preliminary numerical results show that the DHS* and DPRP* methods are effective for the given test problems.

Global Inference and Test for Eigensystems of Imaging Data Over Complicated Domains

A nonparametric approach for analyzing eigensystems of image data over a complex domain is novelly developed. The proposed estimators, which are based on bivariate splines, have both oracle efficiency of O p ( n − 1 / 2 ) , meaning they are asymptotically indistinguishable from estimators computed with true trajectories, and computational efficiency with more convenient spectrum decomposition forms. Under mild conditions, we derive consistency and weak convergence of our proposed estimators, which can be used to construct confidence intervals and simultaneous confidence corridors for any individual eigenvalue and eigenfunction, as well as design uniform inference procedures for eigensystems with a diverging number of components. In addition, we extend our method to two-sample test problems. Extensive simulation results provide strong support for the asymptotic theory, and the procedures are applied to two potential seawater temperature data sets to demonstrate its validity.

Beyond Neyman–Pearson: E-values enable hypothesis testing with a data-driven alpha

A standard practice in statistical hypothesis testing is to mention the P-value alongside the accept/reject decision. We show the advantages of mentioning an e-value instead. With P-values, it is not clear how to use an extreme observation (e.g. [Formula: see text]) for getting better frequentist decisions. With e-values it is straightforward, since they provide Type-I risk control in a generalized Neyman-Pearson setting with the decision task (a general loss function) determined post hoc, after observation of the data-thereby providing a handle on "roving [Formula: see text]'s." When Type-II risks are taken into consideration, the only admissible decision rules in the post hoc setting turn out to be e-value-based. Similarly, if the loss incurred when specifying a faulty confidence interval is not fixed in advance, standard confidence intervals and distributions may fail, whereas e-confidence sets and e-posteriors still provide valid risk guarantees. Sufficiently powerful e-values have by now been developed for a range of classical testing problems. We discuss the main challenges for wider development and deployment.

Drift Control of High-Dimensional Reflected Brownian Motion: A Computational Method Based on Neural Networks

Motivated by applications in queueing theory, we consider a stochastic control problem whose state space is the d-dimensional positive orthant. The controlled process Z evolves as a reflected Brownian motion whose covariance matrix is exogenously specified, as are its directions of reflection from the orthant’s boundary surfaces. A system manager chooses a drift vector [Formula: see text] at each time t based on the history of Z, and the cost rate at time t depends on both [Formula: see text] and [Formula: see text]. In our initial problem formulation, the objective is to minimize expected discounted cost over an infinite planning horizon, after which we treat the corresponding ergodic control problem. Extending the earlier work by Han et al. [Han J, Jentzen A, Weinan E (2018) Solving high-dimensional partial differential equations using deep learning. Proc. Natl. Acad. Sci. USA 115(34):8505–8510], we develop and illustrate a simulation-based computational method that relies heavily on deep neural network technology. For the test problems studied thus far, our method is accurate to within a fraction of 1% and is computationally feasible in dimensions up to at least [Formula: see text].

Universally consistent K-sample tests via dependence measures

The K-sample testing problem involves determining whether K groups of data points are each drawn from the same distribution. Analysis of variance is arguably the most classical method to test mean differences, along with several recent methods to test distributional differences. In this paper, we demonstrate the existence of a transformation that allows K-sample testing to be carried out using any dependence measure. Consequently, universally consistent K-sample testing can be achieved using a universally consistent dependence measure, such as distance correlation and the Hilbert–Schmidt independence criterion. This enables a wide range of dependence measures to be easily applied to K-sample testing.

Rank-transformed subsampling: inference for multiple data splitting and exchangeable p-values

Abstract Many testing problems are readily amenable to randomized tests, such as those employing data splitting. However, despite their usefulness in principle, randomized tests have obvious drawbacks. Firstly, two analyses of the same dataset may lead to different results. Secondly, the test typically loses power because it does not fully utilize the entire sample. As a remedy to these drawbacks, we study how to combine the test statistics or p-values resulting from multiple random realizations, such as through random data splits. We develop rank-transformed subsampling as a general method for delivering large-sample inference about the combined statistic or p-value under mild assumptions. We apply our methodology to a wide range of problems, including testing unimodality in high-dimensional data, testing goodness-of-fit of parametric quantile regression models, testing no direct effect in a sequentially randomized trial and calibrating cross-fit double machine learning confidence intervals. In contrast to existing p-value aggregation schemes that can be highly conservative, our method enjoys Type I error control that asymptotically approaches the nominal level. Moreover, compared to using the ordinary subsampling, we show that our rank transform can remove the first-order bias in approximating the null under alternatives and greatly improve power.

Local powers of least‐squares‐based test for panel fractional Ornstein–Uhlenbeck process

In recent years, significant advancements have been made in the field of identifying financial asset price bubbles, particularly through the development of time‐series unit‐root tests featuring fractionally integrated errors and panel unit‐root tests. This study introduces an innovative approach for assessing the sign of the persistence parameter () within a panel fractional Ornstein‐Uhlenbeck process, based on the least squares estimator of . This method incorporates three distinct test statistics based on the Hurst parameter (), which can take values in the range of , be equal to , or fall within the interval of . The null hypothesis corresponds to . Based on a panel of continuous records of observations, the null asymptotic distributions are obtained when the time span () is fixed and the number of cross sections () goes to infinity. The power function of the tests is obtained under the local alternative where is close to zero in the order of . This alternative covers the departure from the unit root hypothesis from the explosive side, enabling the calculation of lower power in bubble tests. The hypothesis testing problem and the local power function are also considered when a panel of discrete‐sampled observations is available under a sequential limit, that is, the sampling interval shrinks to zero followed by the goes to infinity.

Natural Frequencies Improve Public Understanding of Medical Test Results: An Experimental Study on Various Bayesian Inference Tasks with Multiple Scoring Methods and Non-Bayesian Reasoning Strategies.

It is well established that the natural frequencies (NF) format is cognitively more beneficial for Bayesian inference than the conditional probabilities (CP) format. However, empirical studies have suggested that the NF facilitation effect might be limited to specific groups of individuals. Unlike previous studies that focused on a limited number of Bayesian inference problems evaluated by a single scoring method, it was essential to examine multiple Bayesian problems using various scoring metrics. This study also explored the impact of numeracy on Bayesian inference and assessed non-Bayesian cognitive strategies using the numerical information in problem solving. In a Web-based experimental survey, 175 South Korean adults were randomly assigned to 1 of 2 format groups (NF v. CP). After completing numeracy scales, participants were asked to estimate 4 Bayesian inference problems and document the numerical information used in their problem-solving process. Four scoring methods-strict rounding, loose rounding, absolute deviation, and 50-Split-were used to evaluate participants' estimations. The NF format generally outperformed the CP format across all problems, except in a chorionic villus sampling test problem when evaluated using the 50-Split method. In addition, numeracy levels significantly influenced Bayesian inference; participants with higher numeracy demonstrated better performance. In addition, participants used various non-Bayesian strategies influenced by the format and the nature of the problems. The NF facilitation effect was consistently observed across multiple Bayesian problems and scoring methods. Individuals with higher numeracy levels benefited more from the NF format. The use of various non-Bayesian strategies varied with the formats and nature of specific tasks. The natural frequencies (NF) format is known to foster understanding of medical test results compared with the conditional probabilities (CP) format, but some studies have reported that this benefit is either nonexistent or limited to specific groups.This study aims to replicate previous empirical studies using various Bayesian problems using multiple scoring methods.The NF format fosters understanding of medical test results across all Bayesian problems by all scoring methods, except in the CVS problem when using a 50-Split scoring method.Participants with high numeracy perform better Bayesian inference than those with lower numeracy. Particularly, higher numerates benefit more in the NF format than lower numerates do. In addition, the public tend to use various non-Bayesian reasoning strategies depending on the format and the nature of the tasks.

Determining the factors influencing the reproducibility of measurements in the asymmetric cycle «coercive return—magnetization»

The induction of coercive return and induction of coercive force inversion can be used for magnetic structure analysis. On the example of the problem of heat treatment testing of 20H2M steel, the influence of the remagnetization rate and the resolving power of the current source on the magnitude and character of the obtained dependences is shown. It is established that a high rate of remagnetization and a large step of current setting are interfering factors complicating the reproduction of measurement results and obtaining reliable dependences.

Research on FPC coils with limited turns in planar electromagnetic tomography

Electromagnetic tomography (EMT) is a non-destructive testing method that reconstructs electrical parameter distribution based on boundary electromagnetic measurement data along electromagnetic rotation projection. The coil is a critical component of the EMT system, used to excite and detect changing magnetic fields. The performance of excitation-detection with specific coils directly affects the quality of the reconstructed image. The traditional EMT coils are wound coils. The excitation-detection performance of the coils is enhanced by increasing the number of turns to obtain better imaging quality. A larger coil volume has better sensitivity, but it cannot meet the space constraints of many applications. To solve this problem, this paper proposes a method using extremely thin FPC coil arrays as EMT sensors. To verify the feasibility of FPC coil imaging with a limited number of turns, firstly, this article analyses the excitation-detection capabilities of FPC coil with 1 to 12 turns through a combination of simulation and experiment. Secondly, the impact of excitation-detection capability on the EMT sensitivity matrix was studied. Finally, a 4×4 8-Turns FPC coil sensor was designed for image reconstruction experiments. The experimental results show that FPC coils with limited turns can be used for image reconstruction and to solve the problem of planar nondestructive testing in a small space.

Design, development and multi-scenario application of portable multifunctional test master based on μM-PMU: The case study of Lingang new City Grid, Shanghai

With the large-scale access of new energy generation and electric vehicle charging piles to the grids, power generation and loads are characterized by random fluctuations and intermittency, which affect the stable operation of the distribution network. μM-PMU is capable of realizing the dynamic process monitoring of the grids. In order to solve the function and performance testing problems of multiple application scenarios of μM-PMU, this thesis develops a portable master station based on synchronous phasor measurement system to realize zero drift, voltage amplitude measurement accuracy, voltage phase angle accuracy, current amplitude measurement accuracy, current phase angle measurement accuracy, frequency measurement accuracy, voltage amplitude change with frequency accuracy, and voltage phase angle change with frequency accuracy, Accuracy of current amplitude with frequency change, accuracy of current phase angle with frequency change, active power accuracy, reactive power accuracy, amplitude step response, phase angle step response, frequency step response, a total of 15 test items. It can automatically calculate test results and generate test reports according to different equipment models, reducing the mistakes and calculation errors that may be caused by manually recording test data and improving the accuracy of test results and calculation precision.

Encoding innate ability through a genomic bottleneck

Animals are born with extensive innate behavioral capabilities, which arise from neural circuits encoded in the genome. However, the information capacity of the genome is orders of magnitude smaller than that needed to specify the connectivity of an arbitrary brain circuit, indicating that the rules encoding circuit formation must fit through a "genomic bottleneck" as they pass from one generation to the next. Here, we formulate the problem of innate behavioral capacity in the context of artificial neural networks in terms of lossy compression of the weight matrix. We find that several standard network architectures can be compressed by several orders of magnitude, yielding pretraining performance that can approach that of the fully trained network. Interestingly, for complex but not for simple test problems, the genomic bottleneck algorithm also captures essential features of the circuit, leading to enhanced transfer learning to novel tasks and datasets. Our results suggest that compressing a neural circuit through the genomic bottleneck serves as a regularizer, enabling evolution to select simple circuits that can be readily adapted to important real-world tasks. The genomic bottleneck also suggests how innate priors can complement conventional approaches to learning in designing algorithms for AI.

Turret-index optimisation with mathematical programming and metaheuristic approaches

This paper addresses the turret-index optimisation problem by proposing two mathematical programming approaches based on quadratic programming (QP) and constraint programming (CP). In addition, a metaheuristic algorithm based on weighted superposition attraction (WSA) is developed due to the combinatorial complexity of the problem. Despite attempting to linearise the QP formulation for problem resolution, both the QP and Linearized QP models prove ineffective for medium and larger-sized instances, providing solutions only for small-sized problems. In the second mathematical programming approach, a novel CP model is introduced in the literature. While CP can rapidly offer optimal solutions for small-sized problems, it only provides satisfactory solutions for medium and larger-sized problems within the predetermined computational time limits and does not guarantee optimal results. On the other hand, through computational analysis and relevant statistical tests, the proposed WSA algorithm provides the best solutions for all test problems within a reasonable computational time.

On the Dai–Liao conjugate gradient method for vector optimization

Several conjugate gradient (CG) parameters have led to promising methods for optimization problems. However, some parameters, such as the Dai-Liao (DL+) and modified Polak-Ribière-Polyak (EPRP) methods, have not yet been explored in the vector optimization setting. This paper addresses this gap by proposing the DL+ and EPRP+ methods to vector optimization. We start by developing a self-adjusting DL+ algorithm to find critical points of vector-valued functions within a closed, convex, pointed cone with a nonempty interior. The algorithm is designed to satisfy the sufficient descent condition (SDC) with a Wolfe line search; if this condition is not satisfied, the algorithm adjusts by redefining the DL+ to meet the SDC. We establish the global convergence of this algorithm under the assumption of SDC without requiring regular restarts or convexity assumption on the objective functions. Similarly, we developed the EPRP+ algorithm using the same approach as the DL+ algorithm. Furthermore, under exact line search, the DL+ and EPRP+ methods reduce to Hestenes-Stiefel (HS) and Polak-Ribière-Polyak (PRP) methods, respectively. We present numerical experiments on some selected test problems sourced from the multiobjective optimization literature that demonstrate the effectiveness and practical implementation of the proposed algorithms, highlighting their promising potential.

Bounding the family-wise error rate in local causal discovery using Rademacher averages

Many algorithms have been proposed to learn local graphical structures around target variables of interest from observational data, focusing on two sets of variables. The first one, called Parent–Children (PC) set, contains all the variables that are direct causes or consequences of the target while the second one, known as Markov boundary (MB), is the minimal set of variables with optimal prediction performances of the target. In this paper we introduce two novel algorithms for the PC and MB discovery tasks with rigorous guarantees on the Family-Wise Error Rate (FWER), that is, the probability of reporting any false positive in output. Our algorithms use Rademacher averages, a key concept from statistical learning theory, to properly account for the multiple-hypothesis testing problem arising in such tasks. Our evaluation on simulated data shows that our algorithms properly control for the FWER, while widely used algorithms do not provide guarantees on false discoveries even when correcting for multiple-hypothesis testing. Our experiments also show that our algorithms identify meaningful relations in real-world data.

A Novel Resource-Aware Distributed Cooperative Decision-Making Mechanism for Connected Automated Vehicles

<div>This article proposes a new model for a cooperative and distributed decision-making mechanism for an ad hoc network of automated vehicles (AVs). The goal of the model is to ensure safety and reduce energy consumption. The use of centralized computation resource is not suitable for scalable cooperative applications, so the proposed solution takes advantage of the onboard computing resources of the vehicle in an intelligent transportation system (ITS). This leads to the introduction of a distributed decision-making mechanism for connected AVs. The proposed mechanism utilizes a novel implementation of the resource-aware and distributed–vector evaluated genetic algorithm (RAD-VEGA) in the vehicular ad hoc network of connected AVs as a solver to collaborative decision-making problems. In the first step, a collaborative decision-making problem is formulated for connected AVs as a multi-objective optimization problem (MOOP), with a focus on energy consumption and collision risk reduction as example objectives. RAD-VEGA then cooperatively solves this MOOP, taking into account the availability of AV’s onboard resources and the application layer characteristics of today’s ITS communication tools. The performance of the proposed mechanism is evaluated by solving the ZDT1 test problem and studying pareto-frontier solutions to the true front over time. The scalability of the proposed solution is estimated to be 305 CAVs, considering a communication bandwidth of 6 MB/s. Additionally, cooperative AV planning scenario examples are simulated, and the effectiveness of the proposed mechanism is demonstrated by comparing final and initial solutions after solving the MOOP using RAD-VEGA.</div>

An unconditionally stable numerical scheme for solving nonlinear Fisher equation

Abstract In this study, novel numerical methods are presented for solving nonlinear Fisher equations. These equations have a wide range of applications in various scientific and engineering fields, particularly in the biomedical sciences for determining the size of brain tumors. The challenges posed by the nonlinearity of the equations are effectively addressed through the development of numerical techniques. The nonlinearity is tackled using a combination of the method of lines and backward differentiation formulas of varied orders. This method is unconditionally stable, and its accuracy is evaluated using error norms. The methods are successfully validated against test problems with known solutions, demonstrating their superiority through comparative analyses with existing methodologies in the literature.

EFFECTS IN DISCRETE AND CONTINUOUS STRENGTHENING OF MACHINES ELEMENTS

The work describes approaches to problem solving of operational and effective improvement of the technical and tactical characteristics of military and civilian machines: tanks, armored vehicles, diesel locomotives, turbo-expander power plants, autonomous power plants of strategic objects, etc. For this purpose, fundamentally new methods of strengthening of contacting machines elements are being developed. These methods combine the advantages of discrete and continuous strengthening methods, which have largely exhausted their capabilities by now. Qualitative features and advantages of proposed discrete-continuous strengthening methods require effective implementation. We are talking about the justification of progressive technical solutions based on the criteria of strength and durability. For this purpose, the methodology of multi-criteria synthesis in the expanded space of design and technological parameters will be improved. In addition, as a basis for substantiating advanced technological solutions, a set of related problems of analysis of the stress-strain state, friction and wear is formed. Therefore, based on the improved system approach, a much higher level of strength and durability of the reinforced structural parts is achieved than with traditional methods. The results of test problems solving are illustrated. In the result, micro-macromodels are generalized to determine the joint influence of structural and technological factors, microstructure, physical and mechanical properties of materials of reinforced layers on the contact interaction and stress-strain state of representative fragments of the system of discrete-continuous reinforced bodies. The results of analysis of combined influence of structural and technological factors, microstructure, physical and mechanical properties of materials reinforced layers have been established on the contact interaction and stress-strain state of test representative fragments of the system of discrete-continuously reinforced bodies. At the same time, a significant influence of reinforced layers properties was established on strength of contacting bodies.

Vector synthesis of fault testing map for logic

Vector synthesis of fault testing (simulation) map for logic is proposed, which without simulation allows to determine of all faults detected on test sets, as well as determining test sets to detect specified faults. For synthesis, a superposition of smart data structures is used, containing: a deductive matrix D, as a derivative of the logical vector L, test truth table T, and fault truth table F. The deductive matrix is seen as the gene of functionality and base of fault simulation mechanism to solve all the problems of testing and verification. In the matrix synthesis, an axiom is used: all the mentioned tables are identical in shape to each other and always interact with each other convolutionally T⊕L⊕F=0. A universal deductive reversing converter “test-faults” and “faults-test” for logical functionalities of any dimension is proposed. Converter functions: fault simulation on test sets T→F and synthesis of test sets F→T to detect the specified faults. The converter can be used as a test generation and fault simulation service for IP-core system-on-chip (SoC) under the IEEE 1500 SECT standard. Based on the deductive matrix, a fault testing map for logic is built, where each test set is matched with the logic-detected faults of the input lines.