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Many optimization problems for heating, ventilation, and air conditioning (HVAC) control systems usually refer to multiple timescales. This paper studies a two-timescale decision problem for indoor temperature regulation by HVAC with the objective to improve user’s comfort under limited energy consumption. A slow timescale is divided into several fast timescales, so the two timescales have inherent association. Using states of fast timescale to represent the state of its slow timescale properly is challenging, thereby the weighted mean type is proposed in this paper. We find that the realizability and consistency in two-timescale cannot be guaranteed in existing empirical models, which are the bases for physical application. Therefore, this paper proposes a method that building the fast timescale model first and then inducing the slow timescale model from the fast timescale model. In addition, such a problem in the high-order system is more complex, whose solution is also discussed in this paper. The results of case studies show that the induced model can guarantee the consistency and realizability and meet the user desired temperature for comfort. Note to Practitioners—This paper was motivated by the multi-timescale problem that making a decision of controlling the indoor temperature for the user’s comfort with energy constraint. Existing approaches to build a two-timescale model by experience would cause the inconsistent deviation. If the HVAC works in a closed environment system like a space station, besides crew comfort, the temperature for experiments in the space station should be accurate. Therefore, the deviation from the actual temperature and the desired temperature will cause adverse effects. In this paper, we mathematically derive the thermal state transfer equations and analyze some problems. Then, this paper suggests a new approach to build the two-timescale model for various conditions, in which the models of two timescales are consistent with each other. Preliminary experiments suggest that this approach is feasible and effective. In future research, we will jointly make optimization and decision of multiple appliances in home energy management (HEM) system. [ABSTRACT FROM AUTHOR]

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak convergence to a centered Normal distribution. The notion of noncentral moderate deviations is used when the weak convergence is towards a non-Gaussian distribution. In this paper, noncentral moderate deviation results are presented for two fractional Skellam processes known in the literature (see [20]). It is established that, for the fractional Skellam process of type 2 (for which one can refer to the recent results for compound fractional Poisson processes in [3]), the convergences to zero are usually faster because one can prove suitable inequalities between rate functions. [ABSTRACT FROM AUTHOR]

Triangular distributions are widely used in many applications with limited sample data, business simulations, and project management. As with other distributions, a standard way to measure deviations is to compute the standard deviation. However, the standard deviation is sensitive to outliers. In this paper, we consider and compare other deviation metrics, namely the mean absolute deviation from the mean, the median, and the quantile-based deviation. We show the simple geometric interpretations for these deviation measures and how to construct them using a compass and a straightedge. The explicit formula of mean absolute deviation from the median for triangular distribution is derived in this paper for the first time. It has a simple geometric interpretation. It is the least volatile and is always better than the standard or mean absolute deviation from the mean. Although greater than the quantile deviation, it is easier to compute with limited sample data. We present a new procedure to estimate the parameters of this distribution in terms of this deviation. This procedure is computationally simple and may be superior to other methods when dealing with limited sample data, as is often the case with triangle distributions. [ABSTRACT FROM AUTHOR]

The article focuses on the paper "Variabilità eMutabilità" published by C. Ginni in 1912 that discusses different conclusions leads by the use of different variability indices. It presents various applications related to indices including simple mean deviation, probable deviation, and mean difference.

Purpose: This study aims to analyse the level of awareness and knowledge of Islamic accounting among accounting students in the Nigerian universities. Furthermore, the study also compares the students' understanding of Islamic and conventional accounting. Design/methodology/approach: The study used survey research design through the administration of questionnaire on a sample of university undergraduate and post-graduate accounting students across the north-west region in Nigeria. The data generated for the study was analysed using Cronbach's alpha, mean, standard deviation and inferential statistics. Findings: The study found that the accounting students have an adequate awareness and basic knowledge of Islamic accounting as they were able to contrast Islamic accounting from conventional accounting. Also, in their aspiration towards learning Islamic accounting, they agreed that Islamic accounting should be made a compulsory course in accounting curriculum. Research limitations/implications: This study focusses on north-west region of Nigeria. Hence, data and more in-depth analysis can be further improved by considering a whole country as diverse as Nigeria. Also, only a questionnaire was used by the study. Hence, further studies can use face-to-face interviews to fully extract the awareness and knowledge of the target respondents. Lastly, majority of the respondents are Muslims given the area where the study was conducted, hence, non-Muslims are not properly represented. Practical implications: Despite its limitations, this study is still of importance in providing insights on both undergraduate and post-graduate students' level of awareness and knowledge of Islamic accounting. This course is unique as it is different in orientation compared with other existing courses on offer. This paper also provides an invaluable insight, therefore, National University Commission of Nigeria, Islamic institutions and professional bodies like Institute of Chartered Accountants of Nigeria and Association of National Accountants of Nigeria should make continues effort towards promoting the awareness and knowledge of Islamic accounting by properly integrating same into academic and professional curricula and other training and sensitisation programs. In doing so, Islamic accounting subjects could be introduced as independent courses for selection by the student. Courses like Islamic Accounting and Finance, Accounting for Islamic Financial Institutions (IFIs), Accounting for Waqf, Accounting for Zakat, Shariah auditing, Corporate Shariah Governance, Education and Ethics could be introduced across levels to enable students learn more of Islamic accounting. Social implications: Proper integration of Islamic accounting into academic and professional courses would greatly contribute to the production of experts most importantly ethical and God-fearing accountants for the growth and development of IFIs in Nigeria. Originality/value: This paper examines Nigerian university undergraduate and post-graduate students' level of awareness and knowledge of Islamic accounting in the north-west region of Nigeria. [ABSTRACT FROM AUTHOR]

In this paper, the transformed sine Dagum distribution is proposed using the Dagum distribution as a baseline distribution in the transformed sin-G family of distributions. The purpose of this paper is to propose and explore a modified version of the Dagum distribution, based on the transformed sin-G family of distributions. The density of the transformed sine Dagum distribution shows that it can adequately model datasets that are positively skewed, approximately symmetric and decreasing. The hazard rate plot shows that the proposed distribution can adequately model both monotonic and non-monotonic hazard rate datasets. Statistical properties such quantile function, moments, inverse moments, moments generating functions, mean and median deviation and order statistics are derived. The plots of the skewness and kurtosis show that the skewness is always positive and the kurtosis is increasing. Maximum likelihood estimation is used to estimate the parameters of the transformed sine Dagum distribution. Monte Carlo simulations are performed to ascertain the behavior of the estimators. The results show that the estimators are consistent. The proposed distribution is applied to two real life datasets. The results show that the proposed distribution provide a reasonable parametric fit to the datasets compared with the other competing distribution. [ABSTRACT FROM AUTHOR]

Accurate modeling and parameter identification of photovoltaic (PV) cells is a difficult task due to the nonlinear characteristics of PV cells. The goal of this paper is to propose a multi strategy sine–cosine algorithm (SCA), named enhanced sine–cosine algorithm (ESCA), to evaluate nondirectly measurable parameters of PV cells. The ESCA introduces the concept of population average position to increase the population exploration ability, and at the same time introduces the personal destination agent mutation mechanism and competitive selection mechanism into SCA to provide more search directions for ESCA while ensuring the search accuracy and diversity maintenance. To prove that the proposed ESCA is the best choice for extracting nondirectly measurable parameters of PV cells, ESCA is evaluated by the single‐diode model, the double‐diode model, the three‐diode model, and the photovoltaic module model (PVM), and compared with eight existing popular methods. Experimental results show that ESCA outperforms similar methods in terms of diversity maintenance, high efficiency, and stability. In particular, the proposed ESCA method is less than the SCA by 0.081, 0.144, and 0.578 in the standard deviation statistics metrics of the three PVM models (PV‐PWP201, STM6‐40/36, and STP6‐120/36), respectively. Therefore, the proposed ESCA is an accurate and reliable method for parameter identification of PV cells. [ABSTRACT FROM AUTHOR]

Additive Manufacturing (AM) has emerged as an innovative technology that gives designers several advantages, such as geometric freedom of design and less waste. However, the quality of the parts produced is affected by different design and manufacturing parameters, such as the part orientation, the nozzle temperature and speed, the support material, and the layer thickness. In this context, the layer thickness is considered an important AM parameter affecting the part quality and accuracy. Thus, in this paper, a new adaptative slicing method based on the cusp vector and the surface deviation is proposed with the aim of minimizing the dimensional defects of FFF printed parts and investigate the impact on the dimensional part tolerancing. An algorithm is developed to automatically extract data from the STL file, select the build orientation, and detect intersection points between the initial slicing and the STL mesh. The innovation of this algorithm is exhibited via adapting the slicing according to the surface curvature based on two factors: the cusp vector and the surface deviation. The suggested slicing technique guarantees dimensional accuracy, especially for complex feature shapes that are challenging to achieve using a uniform slicing approach. Finally, a preview of the slicing is displayed, and the G-code is generated to be used by the FFF machine. The case study consists of the dimensional tolerance inspection of prototypes manufactured using the conventional and adaptive slicing processes. The proposed method's effectiveness is investigated using RE and CMM processes. The method demonstrates its reliability through the observed potential for accuracy improvements exceeding 0.6% and cost savings of up to 4.3% in specific scenarios. This reliability is substantiated by comparing the resulting dimensional tolerances and manufacturing costs. [ABSTRACT FROM AUTHOR]

Permeability is one of the most important petrophysical parameters to describe the reservoir potential of sedimentary rocks, contributing to problems in hydrology, geothermics, or hydrocarbon reservoir analysis. Outcrop analog studies, well core measuremeasurements, 5 or individual sample analysis take advantage of a variety of commercially available devices for permeability measurements. Very often, permeability data derived from different devices need to be merged within one study, e.g. outcrop mini-permeametry and lab-based core plug measurements. To enhance accuracy of different gas-driven permeability measurements, device-specific aberrations need to be taken into account The application of simple one-to-one correlations may draw a wrong picture of permeability trends. For this purpose, transform equations need to be established. This study presents a detailed comparison of permeability data derived from a selection of commonly used Hassler cells and probe permeameters. As a result of individual cross-plots, typical aberrations and transform equations are elaborated which enable corrections for the specific permeameters. Permeability measurements of the commercially available ErgoTech Gas Permeameter and the TinyPerm II probe-permeameter are well-comparable over the entire range of permeability, with R2 = 0.967. Major aberrations are identified among the TinyPerm II and the mini-permeameter/Hassler-cell combination at Darmstadt University, which need to be corrected and standardized within one study. However, transforms are critical to their use, as aberrations are frequently limited to certain permeability intervals. In the presented examples, deviations typically tend to occur in the lower permeability range < 10 mD. Applying standardizations which consider these aberration intervals strongly improve the comparability of permeability datasets and facilitate the combination of measurement principles. There-fore, the utilization of such correlation tests is highly recommended for all kinds of reservoir studies using integrated permeability databases. [ABSTRACT FROM AUTHOR]

Abstract: In recent years, many results on oscillation criteria of second-order nonlinear neutral delay differential equations with distributed deviating argument have been obtained, but some of these criteria are incorrect due to a mistake in a crucial auxiliary result. We give two counterexamples. [Copyright &y& Elsevier]

In recent years, queuing systems with batch service are emerging as powerful and flexible mathematical models in different frameworks. In this paper, we consider a single server queuing system with Poissonian arrivals, infinite buffers, and a constant batch size b. This paper addresses a little-studied optimization problem, namely the existence of an optimal arrival rate that minimizes the average sojourn time. Unlike the classical M / M / 1 queue, for any batch size b, the problem admits a non-trivial solution that can be found by solving a polynomial equation of degree b + 1 . Since, in general, only numerical solutions are available, a simple first-order approximation is also derived and the corresponding deviations (in terms of input rate and sojourn time) are calculated. In more detail, it is shown that the approximation improves as the batch size increases and, in any case, the relative error for the average sojourn time is less than 0.34%. Finally, the paper provides new theoretical results about the asymptotic service rate in the equivalent birth–death process, highlighting how it depends on all queue parameters. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic behavior of the Helmholtz free energy of mixtures at small compressibility. We start from a general representation for the local free energy that is valid in stable subregions of the phase diagram. On the basis of this representation we classify the admissible data to construct a thermodynamically consistent constitutive model. We then analyze the incompressible limit, where the molar volume becomes independent of pressure. Here we are confronted with two problems: (i)Our study shows that the physical system at hand cannot remain incompressible for arbitrary large deviations from a reference pressure unless its volume is linear in the composition.(ii)As a consequence of the 2nd$^\textrm {nd}$ law of thermodynamics, the incompressible limit implies that the molar volume becomes independent of temperature as well. Most applications, however, reveal the non‐appropriateness of this property.According to our mathematical treatment, the free energy as a function of temperature and partial masses tends to a limit in the sense of epi– or Gamma–convergence. In the context of the first problem, we study the mixing of two fluids to compare the linearity with experimental observations. The second problem will be treated by considering the asymptotic behavior of both a general inequality relating thermal expansion and compressibility and a PDE‐system relying on the equations of balance for partial masses, momentum and the internal energy. This paper investigates the asymptotic behavior of the Helmholtz free energy of mixtures at small compressibility. We start from a general representation for the local free energy that is valid in stable subregions of the phase diagram. On the basis of this representation we classify the admissible data to construct a thermodynamically consistent constitutive model. We then analyze the incompressible limit, where the molar volume becomes independent of pressure.... [ABSTRACT FROM AUTHOR]

Purpose: Limited geometric accuracy is one of the major challenges that hinder the wider application of additive manufacturing (AM). This paper aims to predict in-plane shape deviation for online inspection and compensation to prevent error accumulation and improve shape fidelity in AM. Design/methodology/approach: A sequence-to-sequence model with an attention mechanism (Seq2Seq+Attention) is proposed and implemented to predict subsequent layers or the occluded toolpath deviations after the multiresolution alignment. A shape compensation plan can be performed for the large deviation predicted. Findings: The proposed Seq2Seq+Attention model is able to provide consistent prediction accuracy. The compensation plan proposed based on the predicted deviation can significantly improve the printing fidelity for those layers detected with large deviations. Practical implications: Based on the experiments conducted on the knee joint samples, the proposed method outperforms the other three machine learning methods for both subsequent layer and occluded toolpath deviation prediction. Originality/value: This work fills a research gap for predicting in-plane deviation not only for subsequent layers but also for occluded paths due to the missing scanning measurements. It is also combined with the multiresolution alignment and change point detection to determine the necessity of a compensation plan with updated G-code. [ABSTRACT FROM AUTHOR]

When dealing with engineering design problems, designers often encounter nonlinear and nonconvex features, multiple objectives, coupled decision making, and various levels of fidelity of sub-systems. To realize the design with limited computational resources, problems with the features above need to be linearized and then solved using solution algorithms for linear programming. The adaptive linear programming (ALP) algorithm is an extension of the Sequential Linear Programming algorithm where a nonlinear compromise decision support problem (cDSP) is iteratively linearized, and the resulting linear programming problem is solved with satisficing solutions returned. The reduced move coefficient (RMC) is used to define how far away from the boundary the next linearization is to be performed, and currently, it is determined based on a heuristic. The choice of RMC significantly affects the efficacy of the linearization process and, hence, the rapidity of finding the solution. In this paper, we propose a rule-based parameter-learning procedure to vary the RMC at each iteration, thereby significantly increasing the speed of determining the ultimate solution. To demonstrate the efficacy of the ALP algorithm with parameter learning (ALPPL), we use an industry-inspired problem, namely, the integrated design of a hot-rolling process chain for the production of a steel rod. Using the proposed ALPPL, we can incorporate domain expertise to identify the most relevant criteria to evaluate the performance of the linearization algorithm, quantify the criteria as evaluation indices, and tune the RMC to return the solutions that fall into the most desired range of each evaluation index. Compared with the old ALP algorithm using the golden section search to update the RMC, the ALPPL improves the algorithm by identifying the RMC values with better linearization performance without adding computational complexity. The insensitive region of the RMC is better explored using the ALPPL—the ALP only explores the insensitive region twice, whereas the ALPPL explores four times throughout the iterations. With ALPPL, we have a more comprehensive definition of linearization performance—given multiple design scenarios, using evaluation indices (EIs) including the statistics of deviations, the numbers of binding (active) constraints and bounds, the numbers of accumulated linear constraints, and the number of iterations. The desired range of evaluation indices (DEI) is also learned during the iterations. The RMC value that brings the most EIs into the DEI is returned as the best RMC, which ensures a balance between the accuracy of the linearization and the robustness of the solutions. For our test problem, the hot-rolling process chain, the ALP returns the best RMC in twelve iterations considering only the deviation as the linearization performance index, whereas the ALPPL returns the best RMC in fourteen iterations considering multiple EIs. The complexity of both the ALP and the ALPPL is O(n2). The parameter-learning steps can be customized to improve the parameter determination of other algorithms. [ABSTRACT FROM AUTHOR]

The escalating demand for heat dissipation has prompted considerable interest in the manifold micro-pin–fin heat sink (MMPFHS) as a promising solution for high heat flux cooling applications. The two-dimensional topology of this multi-layered heat sink plays a pivotal role in organizing the three-dimensional spatial flow, consequently influencing both hydraulic and thermal performance. This study proposes and comparatively analyzes the only three rhombus-based tiling topologies applicable to MMPFHS, specifically the rhombus topology (RT), triangle hexies topology (THT), and firecracker topology (FT), all of which adhere to the principles of gapless, non-overlapping, and spatially expandable tiling topology. The relations of topological geometry and the hydraulic and thermal performances are explored and compared. And figure of merit (FOM) is also introduced to assess their overall performance. The results indicate that the overall performance of THT is predominant. When DPF = 100 μm, a = 200 μm, Din = 50, Re = 64.87, the temperature non-uniformity on the heating surface of THT is only 0.022 K, the thermal resistance is 9.4 × 10–6 km2 W−1, and the FOM of THT is about 1.14 times of that of RT. RT and FT have a similar performance, and the maximum deviation of FOM for both of them within the conditions studied in this paper is only 0.04. The paper provides a reference for selecting topologies in MMPFHS design. [ABSTRACT FROM AUTHOR]

For sparse system identification, a memory-improved proportionate affine projection sign algorithm with a simplified, generalized correntropy induced metric (SGCI-M-IPAPSA) has good filtering performance. However, the SGCI-M-IPAPSA is based on a fixed step size and is not always the best choice. To overcome the limitation of a fixed step size in filtering precision and convergence speed under non-Gaussian impulsive interferences, in this paper, we apply the combined-step-size idea and a variable-step-size method based on the mean-square deviation to the SGCI-M-IPAPSA, respectively, and propose two new robust algorithms to enhance the filtering performance of the SGCI-M-IPAPSA. In addition, by combining the combined-step-size and proposed variable-step-size methods, we propose a fresh combined variable-step-size way and apply it to the SGCI-M-IPAPSA. The convergence of the proposed algorithms is also elaborated, and a conditional decision on the mean-square error is used to cope with abrupt changes. The better performances of the proposed algorithms than the conventional SGCI-M-IPAPSA in terms of the filtering accuracy and convergence rate are demonstrated with non-Gaussian impulsive interferences for sparse system identification, abrupt changes and colored inputs. [ABSTRACT FROM AUTHOR]

In the present paper, we calculate the Mandel parameter QM for an oscillator-like system generated by generalized Chebyshev polynomials. The sign of the Mandel parameter QM characterizes the deviation of the excitation statistics from the Poisson one. This paper is a continuation of our works (2005). [ABSTRACT FROM AUTHOR]

This paper is concerned with the large deviation principle of the non-local fractional stochastic reaction-diffusion equation with a polynomial drift of arbitrary degree driven by multiplicative noise defined on unbounded domains. We first prove the strong convergence of the solutions of a control equation with respect to the weak topology of controls, and then show the convergence in distribution of the solutions of the stochastic equation when the noise intensity approaches zero. We finally establish the large deviations of the stochastic equation by the weak convergence method. The main difficulty of the paper is caused by the non-compactness of Sobolev embeddings on unbounded domains, and the idea of uniform tail-ends estimates is employed to circumvent the obstacle in order to obtain the tightness of distribution laws of the stochastic equation and the precompactness of the control equation. [ABSTRACT FROM AUTHOR]

This paper considers the difficulties that arise in the implementation of solutions to the optimal control problem. When implemented in real systems, as a rule, the object is subject to some perturbations, and the control obtained as a function of time as a result of solving the optimal control problem does not take into account these factors, which leads to a significant change in the trajectory and deviation of the object from the terminal goal. This paper proposes to supplement the formulation of the optimal control problem. Additional requirements are introduced for the optimal trajectory. The fulfillment of these requirements ensures that the trajectory remains close to the optimal one under perturbations and reaches the vicinity of the terminal state. To solve the problem, it is proposed to use numerical methods of machine learning based on symbolic regression. A computational experiment is presented in which the solutions of the optimal control problem in the classical formulation and with the introduced additional requirement are compared. [ABSTRACT FROM AUTHOR]

The wear of brake discs and their deformation during operation, due to various causes (sudden cooling due to contact with water, overheating due to frequent operation of the braking mechanism in a short time, etc.) is a common problem in the automotive industry. The purpose of this paper is to find an optimal solution for checking the deviations from the flatness of the brake discs, in the most usual form, by devising a method of making a device that allows measuring, checking and processing data in real time. The design of this device, along with the execution drawings, were created using a 3D program. In the introductory part, a current state of the art for brake unbalance checking devices was made, highlighting existing methods on the market, carried out up to now. An optimal but also functional variant of the device was adopted and organological calculations were carried out together with the technological route of one part of the whole assembly, namely the cone shaft. The description of the aspects regarding the realization of the installation and mentions of maintenance and operation of the stand designed for good operation has been described in detail. Or made calculations regarding the economic aspects by analyzing the production costs of the raw material and that of the manpower. At the end of the paper, the main conclusions regarding the technical condition and efficiency of the device are presented following the requests that appear. [ABSTRACT FROM AUTHOR]

In the article Quenched large deviation principle for words in a letter sequence, Probab. Theory Relat. Fields 148, no. 3/4 (2010), 403–456 we derived a quenched large deviation principle for the empirical process of words obtained by cutting an i.i.d. sequence of letters according to an independent renewal process. We derived a representation of the associated rate function for stationary word processes in terms of certain specific relative entropies. Our proof of this representation is correct when the mean word length is finite, but is flawed when the mean word length is infinite. In this paper we fix the flaw in the proof. Along the way we derive new representations of the rate function that are interesting in their own right. A key ingredient in the proof is the observation that if the rate function in the annealed large deviation principle is finite at a stationary word process, then the letters in the tail of the long words in this process are typical. [ABSTRACT FROM AUTHOR]

The aim of this paper is to get asymptotic deviation bounds via a Large Deviation Principle (LDP) for cumulative processes also known as compound renewal processes or renewal-reward processes. These processes cumulate independent random variables occurring in time interval given by a renewal process. Our result extends the one obtained in Lefevere et al. (2011) in the sense that we impose no specific dependency between the cumulated random variables and the renewal process and the proof uses Mariani and Zambotti (2014). In the companion paper Cattiaux et al. (2022) we apply this principle to Hawkes processes with inhibition. Under some assumptions Hawkes processes are indeed cumulative processes, but they do not enter the framework of Lefevere et al. (2011). [ABSTRACT FROM AUTHOR]

In this paper, the concept of generalized relative entropy is firstly introduced as the random measure between two probability measures μ and μ, then a class of strong deviation theorem (small deviation theorem) for array of dependent random variables is established. Based on the strong deviation theorem and its corollaries, a kind of strong deviation theorems and strong law of large numbers for row-wise negatively dependent random variables are obtained finally. [ABSTRACT FROM AUTHOR]

Eigenvalues of Wigner matrices has been a major topic of investigation. A particularly important subclass of such random matrices, useful in many applications, are what are known as sparse or diluted random matrices, where each entry in a Wigner matrix is multiplied by an independent Bernoulli random variable with mean p$p$. Alternatively, such a matrix can be viewed as the adjacency matrix of an Erdős–Rényi graph Gn,p$\mathcal {G}_{n,p}$ equipped with independent and identically distributed (i.i.d.) edge‐weights. An observable of particular interest is the largest eigenvalue. In this paper, we study the large deviations behavior of the largest eigenvalue of such matrices, a topic that has received considerable attention over the years. While certain techniques have been devised for the case when p$p$ is fixed or perhaps going to zero not too fast with the matrix size, we focus on the case p=dn$p = \frac{d}{n}$, that is, constant average degree regime of sparsity, which is a central example due to its connections to many models in statistical mechanics and other applications. Most known techniques break down in this regime and even the typical behavior of the spectrum of such random matrices is not very well understood. So far, results were known only for the Erdős–Rényi graph Gn,dn$\mathcal {G}_{n,\frac{d}{n}}$without edge‐weights and with Gaussian edge‐weights. In the present article, we consider the effect of general weight distributions. More specifically, we consider entry distributions whose tail probabilities decay at rate e−tα$e^{-t^\alpha }$ with α>0$\alpha >0$, where the regimes 0<α<2$0<\alpha < 2$ and α>2$\alpha > 2$ correspond to tails heavier and lighter than the Gaussian tail, respectively. While in many natural settings the large deviations behavior is expected to depend crucially on the entry distribution, we establish a surprising and rare universal behavior showing that this is not the case when α>2$\alpha > 2$. In contrast, in the α<2$\alpha < 2$ case, the large deviation rate function is no longer universal and is given by the solution to a variational problem, the description of which involves a generalization of the Motzkin–Straus theorem, a classical result from spectral graph theory. As a byproduct of our large deviation results, we also establish the law of large numbers behavior for the largest eigenvalue, which also seems to be new and difficult to obtain using existing methods. In particular, we show that the typical value of the largest eigenvalue exhibits a phase transition at α=2$\alpha = 2$, that is, corresponding to the Gaussian distribution. [ABSTRACT FROM AUTHOR]

Stochastic variational inequalities (SVIs) have been used widely in modelling various optimization and equilibrium problems subject to data uncertainty. The sample average approximation (SAA) solution is an asymptotically consistent point estimator for the true solution to a stochastic variational inequality. Some central limit results and large deviation estimates for the SAA solution have been obtained. The purpose of this paper is to study the convergences in regimes of moderate deviations for the SAA solution. Using the delta method and the exponential approximation, we establish some results on moderate deviations. We apply the results to the hypotheses testing for the SVIs, and prove that the rejection region constructed by the central limit theorem has the probability of the type II error with exponential decay speed. We also give some simulations and numerical results for the tail probabilities. [ABSTRACT FROM AUTHOR]

In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity. In this paper, we develop a new approach to PCRs, with respect to strong norm distances on parameter spaces of functions. Critical to our approach is the combination of a local Lipschitz-continuity for the posterior distribution with a dynamic formulation of the Wasserstein distance, which allows to set forth an interesting connection between PCRs and some classical problems arising in mathematical analysis, probability and statistics, e.g., Laplace methods for approximating integrals, Sanov's large deviation principles in the Wasserstein distance, rates of convergence of mean Glivenko–Cantelli theorems, and estimates of weighted Poincaré–Wirtinger constants. We first present a theorem on PCRs for a model in the regular infinite-dimensional exponential family, which exploits sufficient statistics of the model, and then extend such a theorem to a general dominated model. These results rely on the development of novel techniques to evaluate Laplace integrals and weighted Poincaré–Wirtinger constants in infinite-dimension, which are of independent interest. The proposed approach is applied to the regular parametric model, the multinomial model, the finite-dimensional and the infinite-dimensional logistic-Gaussian model and the infinite-dimensional linear regression. In general, our approach leads to optimal PCRs in finite-dimensional models, whereas for infinite-dimensional models it is shown explicitly how the prior distribution affect PCRs. [ABSTRACT FROM AUTHOR]

With the development of speech synthesis technology, the existing synthetic speech detection (SSD) methods cannot generalize well for unknown synthesis algorithms. And thus, this kind of speech forensics task meets a great challenge and has attracted great enthusiasm. We observe that the process of speech synthesis always includes the resampling and pooling/smoothing operations, which will change the speech’s local autoregressive (AR) and statistic distribution. In this paper, based on AR modeling and standard deviation statistics, we propose novel front-end speech features, i.e., ARS in short form, as the input of an SSD classifier. In addition, a new back-end classifier is constructed based on the dense convolution and short connection, and we name it scDenseNet. Experimental results on the ASVspoof2019 logical access (LA) dataset demonstrate that the ARS has a strong representation and sensitivity to spoofing attacks, and achieves promising performance on SSD. The proposed scDenseNet outperforms the previous version DenseNet on both EER and t-DCF scores, and achieves the best performance when compared with other state-of-the-art classifiers studied in this paper. Furthermore, based on the proposed scDenseNet, incorporating ARS with popular features such as the linear frequency cepstral coefficients (LFCC) significantly enhances the fusion performance and yields an EER score of 0.98%. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the moderate deviation principle of sample quantiles and order statistics for stationary m -dependent random variables. The results obtained in this paper extend the corresponding ones for an independent and identically distributed sequence to a stationary m -dependent sequence. [ABSTRACT FROM AUTHOR]

The aim of this paper is threefold. Firstly, we prove the existence and uniqueness of a global strong (in both the probabilistic and the PDE senses) H¹2-valued solution to the 2D stochastic Navier--Stokes equations (SNSEs) driven by a multiplicative Lévy noise under the natural Lipschitz condition on balls and linear growth assumptions on the jump coefficient. Secondly, we prove a Girsanov-type theorem for Poisson random measures and apply this result to a study of the wellposedness of the corresponding stochastic controlled problem for these SNSEs. Thirdly, we apply these results to establish a Freidlin--Wentzell-type large deviation principle for the solutions of these SNSEs by employing the weak convergence method introduced by Budhiraja et al. (2011, 2013). [ABSTRACT FROM AUTHOR]

With the rapid development of society, ideological and political education courses have occupied a very important position in various courses in major universities, playing a series of important functions and roles in student quality education, excellent quality cultivation, and other aspects. In the new era, the evaluation and assessment of ideological and political education quality is not only the primary factor to improve the teaching quality of ideological and political education courses in universities, but also an important means to promote the deepening reform of ideological and political education. However, there are many problems in the process of evaluating the quality of ideological and political education in colleges and universities at present, such as the deviation in understanding the importance of evaluation, the relatively single evaluation method, and the low quality of application of evaluation results. The teaching quality evaluation of ideological and political courses in universities is a classical multiple attribute group decision making (MAGDM). Spherical fuzzy sets (SFSs) provide more free space for decision makers (DMs) to express preference information during the teaching quality evaluation of ideological and political courses in universities. Therefore, this paper we first extend partitioned Maclaurin symmetric mean (PMSM) operator and IOWA operator to SFSs and develop induced spherical fuzzy weighted PMSM (I-SFWPMSM) operator. Subsequently, a new MAGDM method is established based on I-SFWPMSM operator and SFNWG operator under SFSs. Finally, a numerical example for teaching quality evaluation of ideological and political courses in universities is used to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

Let (λ1,...,λn) be β-Laguerre ensembles with parameters β,p,n and with for 1 ≤ i ≤ n. In this paper, as β varies and satisfies , we offer a modified Marchenko–Pastur law or semicircle law as the weak limits for the sequence μn when or , respectively. This recovers some well-known results. Moreover, we give a full large deviation principle of μn with speed βn2 and good rate function Iγ under the same condition to characterize the speed of the convergence. The minimizer of Iγ is a modified Marchenko–Pastur law for β ∈ (0,1] and the semicircle law for γ = 0. [ABSTRACT FROM AUTHOR]

This paper presents a novel coupling discretization method for modelling multiphase heat exchangers. In the method, the moving boundary method is adopted as the solver to solve each of the finite volume control volume divided by the method of finite volume method. When all finite volume control volume are solved, the finite volume control volume boundary values are updated based on the relationships of finite volume control volume. The solving procedure is initiated when the starting values of hot source fluid and cold source fluid outlet of the heat exchanger are given by the user and terminated when these values no longer change anymore. The experimental results of a plate heat exchanger with R245fa and Therminol 66 as cold source fluid and hot source fluid are adopted to validate the proposed model. Simulation results of 11 operating conditions show that the maximum deviation is within ±4% compared to the measured values. The model presented in this paper is appropriate for heat exchangers under operating conditions either with or without fluid phase change, such as the evaporator and condenser in the ORC system. [ABSTRACT FROM AUTHOR]

Under the new geometric product specification (GPS), a two-dimensional chain cannot completely guarantee quality of the product. To optimize the allocation of three-dimensional tolerances in the conceptual design stage, the geometric variations of the tolerance zone to the deviation domain will be mapped in this paper. The deviation-processing cost, deviation-quality loss cost, and deviation-sensitivity cost function relationships combined with the tolerance zone described by the small displacement torsor theory are discussed. Then, synchronous constraint of the function structure and tolerance is realized. Finally, an improved bat algorithm is used to solve the established three-dimensional tolerance mathematical model. A case study in the optimization of three-part tolerance design is used to illustrate the proposed model and algorithms. The performance and advantage of the proposed method are discussed in the end. [ABSTRACT FROM AUTHOR]

The fundamental objective of structural damage detection is to ascertain the presence of damage in the structure under monitoring. Environmental variations (especially temperature) may also cause the aberration of dynamic properties. This could result in false alarms and pose a threat to the reliability of vibration-based damage detection. In this paper, a new approach toward damage detection under varying environmental conditions is investigated based on the deviation patterns of natural frequencies. The idea is derived from the fact that most damage occurs in a local area of a structure while environmental variations affect the whole structure. Natural frequencies deviate from their previous state in different patterns based on the causation of the deviation. The method uses simple mathematics to distinguish the two patterns using the first 10 natural frequencies of a structure. The proposed method was applied in two case studies including a numerical model with severe temperature variations simulated in ABAQUS and 1-year health monitoring data of a cable-stayed bridge in China as a real case study. By implementing the proposed method, the effects of environmental variations were eliminated in both case studies and damage was accurately detected before it was evident to the visual inspections of the bridge. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the geometric invariant properties of a normal curve on a smooth immersed surface under conformal transformation. We obtain an invariant-sufficient condition for the conformal image of a normal curve. We also find the deviations of normal and tangential components of the normal curve under the same motion. [ABSTRACT FROM AUTHOR]

Since the angular deviation produced when shooting a QR code image by a camera would cause geometric distortion of the QR code image, the traditional algorithm of QR code image correction would produce distortion. Therefore this paper puts forward the algorithm which combines corner detection with convex hull algorithm. Firstly, binaryzation of the collected QR code image with uneven light is obtained by the methods of local threshold and mathematical morphology. Next, the outline of the QR code and the dots on it are found and the distorted image is recovered by perspective collineation, according to the algorithm raised by this paper. Finally, experimental verification is made that the algorithm raised by this paper can correctly find the four apexes of QR code and achieves good effects of geometric correction. It will also significantly increase the recognition rate of seriously distorted QR code images. [ABSTRACT FROM AUTHOR]

The acoustic stealth shape design of the underwater vehicle has become a topic of considerable current interest to the experts engaging underwater acoustic countermeasure technology in recent years. During tracking the target, the echo strength of head shape is easily exposed and detected for the underwater vehicle, which directly affects its acoustic stealth performance. This paper proposes an optimal design method for the acoustic stealth shape of the underwater vehicle head with relatively lower target strength (TS), based on the Nelder–Mead optimization algorithm and finite element method. In this method, Bernstein polynomials are used to describe the underwater vehicle head shape deviation, and the optimization objective function is given as the weighting function of the TS of underwater vehicles head with different angles and frequencies. Then, the two optimized results with different situations are given, which are evaluated using the angle detecting rate. Finally, the 2D axisymmetric calculation method of the underwater acoustic scattering field is used to verify the TS calculation in this paper. The optimization design method may provide guidance for the lower TS shape design of the underwater vehicle, which may realize the automatic design of the lower TS shape with incident plane waves at given angles and given frequency bands. [ABSTRACT FROM AUTHOR]

The purpose of this study was to try to clarify relative relationships among deviations on each tooth of gears by using the graph theory. Our previous study proposed a method to derive correlation coefficients among the tooth helix deviations and applied it to a ground helical gear. In addition, the coefficients were used as edges, and a network image of the relative helix deviations was generated. In this paper, this method was applied to the analysis of super-finished helical gears, and the phase relationship among the helix deviations was derived. Furthermore, this paper proposed a method, which enables us to derive the magnitude of helix deviation as a norm of signal, which disappeared from the phase network. Then, the derived magnitude was added to the network as the intensity of the vertices. As a result of the application of the proposed method to an analysis of the ground and super-finished helical gears, it was found that the newly created network images were able to show the different characteristics between the gear-finishing processes. [ABSTRACT FROM AUTHOR]

Compared with frequency-domain algorithms, time-domain algorithms (TDAs) can achieve image focusing under the conditions of arbitrary trajectories and large integration angles. However, the interpolations in both range and bearing angle directions are required in the coordinate transformation of fast TDAs, which inevitably increases the computational load and introduces interpolation errors. In this paper, a fast time-domain imaging and corresponding autofocus method based on the hybrid coordinate (HC) system is proposed. First, the interpolation operation is optimized in the process of fast TDAs. It transforms the 2-D interpolation into 1-D interpolation only in the bearing angle direction, which improves the execution efficiency and reduces the interpolation error. Next, a 3-D trajectory deviation estimation method based on Gauss–Newton iteration is investigated for the motion compensation in the HC system. By iterative optimization, the 3-D motion errors during the flight are estimated accurately, and the space-variant phase error is compensated precisely. This method has good robustness and universality. Simulation results and real data processing demonstrate the effectiveness and the practicability of the method presented in this paper. [ABSTRACT FROM AUTHOR]

Mining aeroengine operational data and developing fault diagnosis models for aeroengines are to avoid running aeroengines under undesired conditions. Because of the complexity of working environment and faults of aeroengines, it is unavoidable that the monitored parameters vary widely and possess larger noise levels. This paper reports the extrapolation of a diagnosis model for 20 gas path faults of a double-spool turbofan civil aeroengine. By applying support vector machine (SVM) algorithm together with genetic algorithm (GA), the fault diagnosis model is obtained from the training set that was based on the deviations of the monitored parameters superimposed with the noise level of 10%. The SVM model (C = 24.7034; γ = 179.835) was extrapolated for the samples whose noise levels were larger than 10%. The accuracies of extrapolation for samples with the noise levels of 20% and 30% are 97% and 94%, respectively. Compared with the models reported on the same faults, the extrapolation results of the GASVM model are accurate. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of adding redundancy to a collection of physical objects so that the overall system is more robust to failures. In contrast to its information counterpart, which can exploit parity to protect multiple information symbols from a single erasure, physical redundancy can only be realized through duplication and substitution of objects. We propose a bipartite graph model for designing defect-tolerant systems, in which the defective objects are replaced by the judiciously connected redundant objects. The fundamental limits of this model are characterized under various asymptotic settings and both asymptotic and finite-size systems that approach these limits are constructed. Among other results, we show that the simple modular redundancy is in general suboptimal. As we develop, this combinatorial problem of defect tolerant system design has a natural interpretation as one of graph coloring, and the analysis is significantly different from that traditionally used in information redundancy for error-control codes. [ABSTRACT FROM AUTHOR]

We consider a random walk with zero mean and finite variance whose steps are arithmetic. The arcsine law for the time the walk reaches its maximum is well known. In this paper, we consider the distribution of the moment of reaching the maximum under the assumption that the maximum value itself is fixed. We show that, in the case of a moderate deviation of the maximum, the distribution of the moment of the maximum with appropriate normalization converges to the chi-square distribution with one degree of freedom. Similar results are obtained in the nonlattice case. [ABSTRACT FROM AUTHOR]

The large deviations of linear control system trajectories from the equilibrium position during the stabilization process, known as peak-effect, represent a serious obstacle to the design of cascade control systems and to guidance stabilization. Evaluation of such deviations is an important problem not only for control theory but also for other branches of mathematics where similar phenomenon appears as, for example, in numerical analysis, in the study of hydrodynamic stability and transition to turbulence, in the dynamics of vehicular platoons, and many others. The aim of this paper is to improve one of the main results concerning upper bounds for the peak-effect in linear control systems in the work by B.T. Polyak and myself in 2016. As the lower bound for overshoot proved by R.N. Izmailov in 1987 shows, the asymptotic estimate for the upper bound obtained here cannot be improved. [ABSTRACT FROM AUTHOR]

Gear rolling is a cold-forming process by using a cylindrical blank to produce gear teeth with high strength, good surface finish, and high material utilization rate. Gear tooth profile deviation is one of the most important factors in evaluating the gear accuracy. In order to understand the forming process of gear tooth, this paper is dedicated to studying the rolling process from geometry relation based on gear mesh theory. Then, the way of material flow to form the gear tooth in the rolling process is investigated by finite element method. The comparison results show that tooth profile rolled by standard rigid body tool still has a certain tooth profile deviation and tooth thickness deviation during the process of one-way rolling. The left side of the rolled gears has a longer effective length and a worse profile deviation than the right side. The increase in material plasticity and a slower increase in reduction are conducive to improving the accuracy of the precision of the formed workpiece the height of the effective tooth profile. This research will be helpful for process parameter selection and subsequent research for defect compensation. [ABSTRACT FROM AUTHOR]

This paper proposes predefined-time convergent guidance schemes that can drive the pursuer on a collision course corresponding to the target interception from a pre-specified impact direction, irrespective of initial engagement geometries. The target interception at the desired impact angle is first transformed into a problem of controlling the line-of-sight angle and its rate. Then, guidance commands are derived using sliding mode control (SMC) to ensure the convergence of corresponding errors to zero within a predefined time. A nonlinear disturbance observer is used to estimate the target's maneuver, and the estimation error is treated as an uncertainty while rejecting its effect by virtue of SMC. Guidance commands are also derived for the case where the target maneuver is completely unknown except for its upper bound. It was shown that the gain could be selected based on the maximum bound on target maneuver to enforce sliding mode on the chosen surface, and thus guarantees target interception at a pre-specified impact angle, provided the closing speed of the engagement is positive. Owing to the use of a nonlinear framework while deriving pursuer guidance commands, the proposed guidance strategies remain valid even for engagements with large initial deviations where schemes based on linearized dynamics may fail or have degraded performance. The efficacy of the proposed guidance methods is validated through simulations for the pursuers having constant speed and time-varying speed, for various engagement geometries. The results of proposed strategies are compared with those of existing guidance and shown to be superior. [ABSTRACT FROM AUTHOR]

There are many criticisms for the association between the Six Sigma concept and the two statistical metrics associated to 6σ processes: 1.5σ shift for maximum deviation and 3.4 PPM non-conformities for the long-term performance. As a result, the paper aims to carry out an analysis of this problem, and the first result obtained is that a stable process can reach a maximum drift, but its value depends on the volume of the sample. It is also highlighted that, using only the criterion "values outside the control limits" for monitoring stability through the Xbar chart, a minimum value can be calculated for the long-term performance of a process depending on the sample size. The main conclusion resulting from the calculations is that, in the case of a 6σ process, the long-term performance is much better than the established value of 3400 PPB: For small volume samples of two pieces it is below 700 PPB, for three pieces it is below 200 PPB, and for samples with a volume greater than or equal to four pieces the performance already reaches values below 100 PPB! So, the long-term performance of 6σ processes is certainly even better than the known value of 3.4 PPM. [ABSTRACT FROM AUTHOR]

A defect diagnosis procedure is an important part of the yield improvement process. As defects become more complex, the output responses they produce differ to larger extents from the output responses of modeled faults, and they become more difficult to diagnose. Biases in the defect diagnosis procedure can also cause defects to be more difficult to diagnose. It is important to study and remove such biases in order to ensure that they do not affect the accuracy of the procedure. This paper undertakes a study of the biases of a defect diagnosis procedure and suggests a way to improve it. The study illustrates an approach by which biases in defect diagnosis procedures can be analyzed in general. [ABSTRACT FROM AUTHOR]

In this paper we provide quenched central limit theorems, large deviation principles and local central limit theorems for random U(1) extensions of expanding maps on the torus. The results are obtained as special cases of corresponding theorems that we establish for abstract random dynamical systems. We do so by extending a recent spectral approach developed for quenched limit theorems for expanding and hyperbolic maps to be applicable also to partially hyperbolic dynamics. [ABSTRACT FROM AUTHOR]

Let (a_k)_{k\in \mathbb N} be an increasing sequence of positive integers satisfying the Hadamard gap condition a_{k+1}/a_k> q >1 for all k\in \mathbb N, and let \begin{equation*} S_n(\omega) = \sum _{k=1}^n \cos (2\pi a_k \omega), \qquad n\in \mathbb N, \; \omega \in [0,1]. \end{equation*} Then S_n is called a lacunary trigonometric sum, and can be viewed as a random variable defined on the probability space \Omega = [0,1] endowed with Lebesgue measure. Lacunary sums are known to exhibit several properties that are typical for sums of independent random variables. For example, a central limit theorem for (S_n)_{n\in \mathbb {N}} has been obtained by Salem and Zygmund, while a law of the iterated logarithm is due to Erdős and Gál. In this paper we study large deviation principles for lacunary sums. Specifically, under the large gap condition a_{k+1}/a_k \to \infty, we prove that the sequence (S_n/n)_{n \in \mathbb {N}} does indeed satisfy a large deviation principle with speed n and the same rate function \widetilde {I} as for sums of independent random variables with the arcsine distribution. On the other hand, we show that the large deviation principle may fail to hold when we only assume the Hadamard gap condition. However, we show that in the special case when a_k= q^k for some q\in \{2,3,\ldots \}, (S_n/n)_{n \in \mathbb {N}} satisfies a large deviation principle (with speed n) and a rate function I_q that is different from \widetilde {I}, and describe an algorithm to compute an arbitrary number of terms in the Taylor expansion of I_q. In addition, we also prove that I_q converges pointwise to \widetilde I as q\to \infty. Furthermore, we construct a random perturbation (a_k)_{k \in \mathbb {N}} of the sequence (2^k)_{k \in \mathbb {N}} for which a_{k+1}/a_k \to 2 as k\to \infty, but for which at the same time (S_n/n)_{n \in \mathbb {N}} satisfies a large deviation principle with the same rate function \widetilde {I} as in the independent case, which is surprisingly different from the rate function I_2 one might naïvely expect. We relate this fact to the number of solutions of certain Diophantine equations. Together, these results show that large deviation principles for lacunary trigonometric sums are very sensitive to the arithmetic properties of the sequence (a_k)_{k\in \mathbb N}. This is particularly noteworthy since no such arithmetic effects are visible in the central limit theorem or in the law of the iterated logarithm for lacunary trigonometric sums. Our proofs use a combination of tools from probability theory, harmonic analysis, and dynamical systems. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the quasi-periodic Jacobi operators with large potentials on Td (d ≥ 1) and establish the positivity and continuity of the Lyapunov exponent by combining the large deviation theorem with the avalanche principle. Moreover, we show that Anderson localization takes place for almost all Diophantine frequencies when the coupling is sufficiently large. [ABSTRACT FROM AUTHOR]