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In this paper, by using the notions of equality algebras, filters, prime filters, maximal filters and other properties of equality algebras, some different representations of equality algebras are investigated. First of all, by maximal and prime filters, we proved Chang's subdirect representation theorem. Then by using the notion of ℓ -groups, we defined two binary operations on it and showed that they made an equality algebra and investigated that under what condition the converse holds. In addition, ordinal sum of two equality algebras are introduced and by using the notion of simple and subdirectly irreducible equality algebras we proved that a special kind of equality algebra can be ordinal sum of two special subalgebras of it. [ABSTRACT FROM AUTHOR]

The concept of entropy and information gain of BE-algebras in scientific disciplines such as information theory, data science, supply chain and machine learning assists us to calculate the uncertanity of the scientific processes of phenomena. In this respect the notion of filter entropy for a transitive BE-algebra is introduced and its properties are investigated. The notion of a dynamical system on a transitive BE-algebra is introduced. The concept of the entropy for a transitive BE-algebra dynamical system is developed and, its characteristics are considered. The notion of equivalent transitive BE-algebra dynamical systems is defined, and it is proved the fact that two equivalent BE-algebra dynamical systems have the same entropy. Theorems to help calculate the entropy are given. Specifically, a new version of Kolmogorov– Sinai Theorem has been proved. The study introduces the concept of information gain of a transitive BE-algebra with respect to its filters and investigates its properties. This study proposes the use of filter entropy to approximate the level of risk introduced by a BE-algebra dynamical system. This aim is reached by defining the information gain with respect to the filters of a BE-algebra. This methodology is well developed for use in engineering, especially in industrial networks. This paper proposes a novel approach to assess the quantity of uncertainty, and the impact of information gain of a BE-algebra dynamical system. [ABSTRACT FROM AUTHOR]

Let £ be a bounded distributive lattice and S a join closed subset of £. Following the concept of S-2-absorbing submodules, we define S-2- absorbing filters of £. Let p be a filter of £ disjoint with S. We say that p is an S-2-absorbing filter of £ if there is a fixed s ∈ S such that for all x, y, z ∈ £ if x ∨ y ∨ z ∈ p, then s ∨ x ∨ y ∈ p or s ∨ y ∨ z ∈ p or s ∨ x ∨ z ∈ p. We will make an intensive investigation of the basic properties and possible structures of these filters. [ABSTRACT FROM AUTHOR]

We answer the long-standing question whether it is consistent to have simple P-points of two different characters. For a filter F over w Guzmán and Kalajdzievski introduced a parametrised version of Miller forcing called PT(F). By combining iterands of the type PT(F)with others we establish: It is consistent relative to ZFC that there is a simple P%1 -point and a simple P%2 -point. A main technical point is the use of properness and descriptive complexity in the limit steps of uncountable cofinality [ABSTRACT FROM AUTHOR]

Nonlinear (NL) and multilinear (ML) systems play a fundamental role in engineering and science. Over the last two decades, active research has been carried out on exploiting the intrinsically multilinear structure of input–output signals and/or models in order to develop more efficient identification algorithms. This has been achieved using the notion of tensors, which are the central objects in multilinear algebra, giving rise to tensor-based approaches. The aim of this paper is to review such approaches for modeling and identifying NL and ML systems using input–output data, with a reminder of the tensor operations and decompositions needed to render the presentation as self-contained as possible. In the case of NL systems, two families of models are considered: the Volterra models and block-oriented ones. Volterra models, frequently used in numerous fields of application, have the drawback to be characterized by a huge number of coefficients contained in the so-called Volterra kernels, making their identification difficult. In order to reduce this parametric complexity, we show how Volterra systems can be represented by expanding high-order kernels using the parallel factor (PARAFAC) decomposition or generalized orthogonal basis (GOB) functions, which leads to the so-called Volterra–PARAFAC, and Volterra–GOB models, respectively. The extended Kalman filter (EKF) is presented to estimate the parameters of a Volterra–PARAFAC model. Another approach to reduce the parametric complexity consists in using block-oriented models such as those of Wiener, Hammerstein and Wiener–Hammerstein. With the purpose of estimating the parameters of such models, we show how the Volterra kernels associated with these models can be written under the form of structured tensor decompositions. In the last part of the paper, the notion of tensor systems is introduced using the Einstein product of tensors. Discrete-time memoryless tensor-input tensor-output (TITO) systems are defined by means of a relation between an Nth-order tensor of input signals and a Pth-order tensor of output signals via a (P + N) th-order transfer tensor. Such systems generalize the standard memoryless multi-input multi-output (MIMO) system to the case where input and output data define tensors of order higher than two. The case of a TISO system is then considered assuming the system transfer is a rank-one Nth-order tensor viewed as a global multilinear impulse response (IR) whose parameters are estimated using the weighted least-squares (WLS) method. A closed-form solution is proposed for estimating each individual IR associated with each mode-n subsystem. [ABSTRACT FROM AUTHOR]

Default Logics are a family of non-monotonic formalisms having so-called defaults and extensions as their common foundation. Traditionally, default logics have been defined and dealt with via syntactic notions of consequence in propositional or first-order logic. Here, we build default logics on modal logics. First, we present these default logics syntactically. Then, we elaborate on an algebraic counterpart. More precisely, we extend the notion of a modal algebra to accommodate for defaults and extensions. Our algebraic view of default logics concludes with an algebraic completeness result and a way of comparing default logics borrowing ideas from the concept of bisimulation in modal logic. To our knowledge, this take on default logics approach is novel. Interestingly, it also lays the groundwork for studying default logics from a dynamic logic perspective. [ABSTRACT FROM AUTHOR]

Let £ be a bounded distributive lattice. Following the concept of weakly 1-absorbing prime ideals, we define weakly 1-absorbing prime filters of £. A proper filter p of £ is called weakly 1-absorbing prime filter of £ if whenever non-zero elements a, b, c ∈ £ and 1 ̸= a ∨ b ∨ c ∈ p, then either a ∨ b ∈ p or c ∈ p. We will make an intensive investigation of the basic properties and possible structures of these filters. [ABSTRACT FROM AUTHOR]

In this paper, we defined the ε, δ - filters and (φ, ρ)- filters of Lattice Wajsberg algebras and related assets are discussed. We prove that every (ε, ε)- filters are (ε, ε V δ)- filters and provide the condition for (ε, ε V δ)- filters are (ε, ε)- filters. Further conditions for ε V δ -filters are discussed. [ABSTRACT FROM AUTHOR]

An expanded-sandwich system is a nonlinear extended block-oriented system in which memoryless elements in conventional block-oriented systems are displaced by memory submodels. Expanded-sandwich system identification has received extensive attention in recent years due to the powerful ability of these systems to describe actual industrial systems. This study proposes a novel recursive identification algorithm for an expanded-sandwich system, in which an estimator is developed on the basis of parameter identification error data rather than the traditional prediction error output information. In this scheme, a filter is introduced to extract the available system information based on miserly structure layout, and some intermediate variables are designed using filtered vectors. According to the developed intermediate variables, the parameter identification error data can be obtained. Thereafter, an adaptive estimator is established by integrating the identification error data compared with the classic adaptive estimator based on the prediction error output information. Thus, the design framework introduced in this research provides a new perspective for the design of identification algorithms. Under a general continuous excitation condition, the parameter estimation values can converge to the true values. Finally, experimental results and illustrative examples indicate the availability and usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to present a few characteristics of the neutrosophic filter of BL-algebras. Also, we introduce the notion of the neutrosophic fantastic filter of BL-algebras with an illustration and discuss a few of its properties. Moreover, we prove every neutrosophic fantastic filter is a neutrosophic filter in BL-algebras. Finally, we acquire an extension property and equivalent condition of the neurosophic fantastic filter of BL-algebras. [ABSTRACT FROM AUTHOR]

Variability is an intrinsic property of biological systems and is often at the heart of their complex behaviour. Examples range from cell-to-cell variability in cell signalling pathways to variability in the response to treatment across patients. A popular approach to model and understand this variability is nonlinear mixed effects (NLME) modelling. However, estimating the parameters of NLME models from measurements quickly becomes computationally expensive as the number of measured individuals grows, making NLME inference intractable for datasets with thousands of measured individuals. This shortcoming is particularly limiting for snapshot datasets, common e.g. in cell biology, where high-throughput measurement techniques provide large numbers of single cell measurements. We introduce a novel approach for the estimation of NLME model parameters from snapshot measurements, which we call filter inference. Filter inference uses measurements of simulated individuals to define an approximate likelihood for the model parameters, avoiding the computational limitations of traditional NLME inference approaches and making efficient inferences from snapshot measurements possible. Filter inference also scales well with the number of model parameters, using state-of-the-art gradient-based MCMC algorithms such as the No-U-Turn Sampler (NUTS). We demonstrate the properties of filter inference using examples from early cancer growth modelling and from epidermal growth factor signalling pathway modelling. Author summary: Nonlinear mixed effects (NLME) models are widely used to model differences between individuals in a population. In pharmacology, for example, they are used to model the treatment response variability across patients, and in cell biology they are used to model the cell-to-cell variability in cell signalling pathways. However, NLME models introduce parameters, which typically need to be estimated from data. This estimation becomes computationally intractable when the number of measured individuals—be they patients or cells—is too large. But, the more individuals are measured in a population, the better the variability can be understood. This is especially true when individuals are measured only once. Such snapshot measurements are particularly common in cell biology, where high-throughput measurement techniques provide large numbers of single cell measurements. In clinical pharmacology, datasets consisting of many snapshot measurements are less common but are easier and cheaper to obtain than detailed time series measurements across patients. Our approach can be used to estimate the parameters of NLME models from snapshot time series data with thousands of measured individuals. [ABSTRACT FROM AUTHOR]

We introduced Neutrosophic implicative filters and Neutrosophic positive implicative filters in Lattice implication algebra. We proved some properties and equivalent conditions of both the filters. Finally we proved that "Every Neutrosophic positive implicative filter is a Neutrosophic implicative filter" and "Every Neutrosophic positive implicative filter is a Neutrosophic filter". [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of neutrosophic hesitant fuzzy UP (BCC)-filters of UP (BCC)-algebras. The characteristic neutrosophic hesitant fuzzy UP (BCC)-filters have also been studied. The relationship between neutrosophic hesitant fuzzy UP (BCC)-filters and their level subsets is provided. The Cartesian product of neutrosophic hesitant fuzzy UP (BCC)-filters is also supplied. Finally, we also find the property of the homomorphic pre-image of neutrosophic hesitant fuzzy UP (BCC)-filters. [ABSTRACT FROM AUTHOR]

In this paper, we provide a new and more general filtration to the family of noncommutative rings known as skew PBW extensions. We introduce the notion of σ -filtered skew PBW extension and study some homological properties of these algebras. We show that the homogenization of a σ -filtered skew PBW extension A over a ring R is a graded skew PBW extension over the homogenization of R. Using this fact, we prove that if the homogenization of R is Auslander-regular, then the homogenization of A is a domain Noetherian, Artin–Schelter regular, and A is Noetherian, Zariski and (ungraded) skew Calabi–Yau. [ABSTRACT FROM AUTHOR]

Infinite game is a power tool in studying various objects and finding descriptions of some properties of filters in mathematics. Game-theoretic characterizations for meager filters, Q-filters and Ramsey filters were obtained by Tomek Bartoszynski, Claude Laflamme and Marion Scheepers. In this paper, the authors obtain two game-theoretic characterizations for rapid filters on ω. [ABSTRACT FROM AUTHOR]

Modeling the nonlinearity of a system is of primary importance both for optimizing its design and for controlling the behavior of physical systems operating with a wide dynamic range of input values, for which the linearity hypothesis may not be sufficient. To become of practical use, the identification of nonlinear models must be accurate and computationally efficient. For these reasons, in recent years, among the numerous models of nonlinear systems that have been proposed in the technical literature, the Hammerstein model has been widely applied as a consequence of the proposal of a new pattern identification technique based on pulse compression, which makes the identification of the model very accurate in numerous applications for which it has been adopted. Hammerstein model identification of a nonlinear system requires characterization of the linear filters present on the different branches of the model. These linear filters, which constitute the parameters of the model to be identified, must be considered with respect to their trends over time or, equivalently, in their frequency trends, as amplitude and phase responses. The identification can be considered accurate if the trends obtained for each filter adequately characterize it for the entire frequency range to which that specific filter is subjected in the normal operation of the system to be identified. This work focuses on this aspect, i.e., on the adequacy of the frequency range for which the filter is identified and on how to obtain correct identification in the entire frequency range of interest. The identification procedure based on exponential swept-sine signals defines these filters in the time domain by making use of intermediate functions that are related to the impulse responses of the model filters through a linear transformation. In this paper, we analyze, in detail, the roles of the bandwidths of both the excitation signal and the matched filter, which are the basis of the procedure, we verify the assumptions made about the amplitudes of their frequency bands, and we propose criteria for defining the bandwidths in order to maximize accuracy in model identification. The experiment performed makes it possible to verify that the proposed procedure avoids possible limitations and significantly improves the quality of the identification results, both if the description is made in the time domain and in the frequency domain. [ABSTRACT FROM AUTHOR]

This article is concerned with the fault detection and isolation (FDI) problem for a class of nonlinear systems described by the T–S fuzzy models. Based on the concept of minimum unobservability subspace and geometric property of factor space, a set of FDI filters where each residual is only affected by one fault and completely decoupled from other faults is designed. Furthermore, in the decoupling space, the $H_{\infty }/H_{-}$ performance indexes are provided to enhance the sensitivity of residual to faults and robustness to disturbances. In particular, to solve the nonconvex filter design problem caused by introducing the $H_{-}$ index, the Gerschgorin theorem is first used to linearize the corresponding filter design conditions in the outer region of a ball. Then, the FDI filter design problem is converted into a convex optimization one, which is solved via the linear matrix inequality (LMI) control Toolbox, and the advantages and effectiveness of the proposed FDI method are verified through two simulation examples. [ABSTRACT FROM AUTHOR]

Previously, several notions of T0 and T1 objects have been studied and examined in various topological categories. In this paper, we characterize each of T0 and T1 objects in the categories of several types of bounded uniform filter spaces and examine their mutual relations, and compare that with the usual ones. Moreover, it is shown that under T0 (resp. T1) condition, the category of preuniform (resp. semiuniform) convergence spaces and the category of bornological (resp. symmetric) bounded uniform filter spaces are isomorphic. Finally, it is proved that the category of each of T0 (resp. T1) bounded uniform filter space are quotient reflective subcategories of the category of bounded uniform filter spaces. [ABSTRACT FROM AUTHOR]

Lattice recursive least-squares (LRLS) adaptive filters are well known for their fast convergence to achieve the minimum least-squares error. This accelerated decaying error property, however, comes with a high cost filter structure. Using a variable tap-length technique known as the fractional tap-length (FT) algorithm, this article provides an adaptive method to search for the optimum length of LRLS filters. To validate the performance of the proposed algorithm, simulations are conducted under low noise and high noise conditions. All the simulation results show the advantages of the proposed algorithm compared with fixed length LRLS filters as well as with the fractional tap-length lattice based least-mean-squares (FT-LLMS) algorithm. With a fast convergence rate and a small steady-state error of the tap-length, the proposed algorithm can efficiently track any change in the impulse response and estimate the filter's optimum structure. [ABSTRACT FROM AUTHOR]

High-frequency and correlated noise filtering is one of the important preprocessing steps for GRACE level-2 products before calculating mass anomaly. Decorrelation and denoising kernel (DDK) filters are usually considered as such optimal filters to solve this problem. In this work, a sparse DDK filter is proposed. This is achieved by replacing Tikhonov regularization in traditional DDK filters with weighted L1 norm regularization. The proposed sparse DDK filter adopts a time-varying error covariance matrix, while the equivalent signal covariance matrix is adaptively determined by the Gravity Recovery and Climate Experiment (GRACE) monthly solution. The covariance matrix of the sparse DDK filtered solution is also developed from the Bayesian and error-propagation perspectives, respectively. Furthermore, we also compare and discuss the properties of different filters. The proposed sparse DDK has all the advantages of traditional filters, such as time-varying, location inhomogeneity, and anisotropy, etc. In addition, the filtered solution is sparse; that is, some high-degree and high-order terms are strictly zeros. This sparsity is beneficial in the following sense: high-degree and high-order sparsity mean that the dominating noise in high-degree and high-order terms is completely suppressed, at a slight cost that the tiny signals of these terms are also discarded. The Center for Space Research (CSR) GRACE monthly solutions and their error covariance matrices, from January 2004 to December 2010, are used to test the performance of the proposed sparse DDK filter. The results show that the sparse DDK can effectively decorrelate and denoise these data. [ABSTRACT FROM AUTHOR]

The aim of the study is to introduce an obstinate SBE-filter, a tile, a branch and a chain of Sheffer stroke BE-algebras (brie y, SBE-algebras). An obstinate SBE-filter is defined and some properties are investigated. Also, we determine a tile of a SBE-algebra and state the case which a SBE-subalgebra of a SBE-algebra is its SBE-filter. It is shown that the set of all tiles of a SBE-algebra is a SBE-subalgebra of this algebra but it is not a SBE-filter of this algebra. Finally, we describe a branch of a SBE-algebra by means of a tile of the algebraic structure and branchwise commutative and branchwise self-distibutive branches of SBE-algebras. [ABSTRACT FROM AUTHOR]

The concept of quasi-ordered residuated systems was introduced in 2018 by S. Bonzio and I. Chajda. This author designed the concepts of ideals and filters in such systems as implicative, associated, comparative, weak implicative, shift and normal filters. The introduction of the concept of strong quasi-ordered residuated systems has made it possible to create the concept of irreducible filters and concepts of three types of prime filters in them. This article provides an overview of the results obtained about the created ideals, filters and their interrelationships in quasi-ordered residuated systems and in strong quasi-ordered residuated systems. [ABSTRACT FROM AUTHOR]

We present a detailed analysis of a setup capable of arbitrary amplitude, phase, and polarization shaping of broadband visible femtosecond pulses at 1?kHz via a pair of actively phase stabilized acousto-optic programmable dispersive filters arranged in a Mach-Zehnder interferometer geometry. The setup features phase stability values around λ/225 at 580?nm as well as degrees of polarization of at least 0.9 for any polarization state. Both numbers are important metrics to evaluate a setup's potential for applications based on polarization-shaped femtosecond pulses, such as fully coherent multi-dimensional electronic spectroscopy. [ABSTRACT FROM AUTHOR]

Fingerprint authentication systems have become ubiquitous with the event of smart devices and cheap sensors. Because of its use in a wide range of devices, it is important that the biometric authentication systems are computationally cheap, and at the same time robust to distortions and noises. Most of the existing fingerprint authentication systems are based on conventional mathematics or complex filter and consequently features extracted are computationally expensive or gross approximate with a large margin of errors leading to drops in the accuracy of the system. In this paper, we propose a fingerprint template based on translation and rotation invariant features of the delaunay triangulation of minutiae. However existing methods of comparison of delaunay triangles features do not always result in an optimum match because of the distortion in the different prints of the same finger. In the proposed method, features extracted from the delaunay triangulation are augmented with the information of local ridges based on discrete curvature and digital straightness. Experimentation with FVC2000 shows that the proposed method has better performances compared to the latest techniques. [ABSTRACT FROM AUTHOR]

In the paper, an overview of the methods and algorithms of synthesis, realization and implementation used by the author to obtain orthogonal 3-D filters with a structure made of Givens rotations has been presented. The main advantage of orthogonal filters, which may have a lower sensitivity to quantization of the coefficients, was indicated. The author proposed a number of possible changes and modifications of individual stages, which may result in obtaining filters with even better parameters. The work will be the basis for the direction of further research. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a new family of low‐profile resonators and filters that achieve high performance and low insertion loss without the need for post‐production tuning. The new resonator is termed ceramic‐element based distributed resonator and consists of a matrix of subwavelength‐length ceramic posts connected in the inter‐digital fashion to the top and bottom ground planes. Such a disposition of elements is beneficial for two main reasons. First, the frequency of operation of such a resonator becomes a function of its height, unlike in the case of standard ceramic resonators. Second, the ceramic element matrix performs inherent dimensional averaging, resulting in a filter that requires no post‐production tuning. As a demonstrator of the proposed technology, a two‐pole filter using a ceramic with a dielectric permittivity of 37 and a loss tangent of 0.0033 and operating at a centre frequency of 3.5 GHz was designed, fabricated and tested. The measured and predicted results are in excellent agreement and are extensively discussed. [ABSTRACT FROM AUTHOR]

The fuzzy Kalman filter (FKF), introduced some years ago, is revisited. In the initial version, trapezoidal possibility distributions functions instead of gaussian probability distributions were proposed, and trapezius were modeled by four representative points. Nevertheless, and although the algorithm works properly, an implementation problem occurs when propagating uncertainty through a non-linear function in multi-variable systems, something that was solved by linearization. In this work we propose an alternative method to represent uncertainty, still using trapezoidal distributions, which avoids the previous inconvenience and eases the Kalman filter steps computation. We reformulate the FKF algorithm, presenting a new theoretical approach as well as validation tests in both simulation and a real mobile robot. [ABSTRACT FROM AUTHOR]

UP-algebra was introduced by Iampan 2017 as a generalization of KU-algebra. In such logical-algebraic structures, many types of UP-filters have been introduced and analyzed in 2019, such as implicative, comparative, allied and shift UP-filters by Iampan and Jun. Also, the concept of weak implicative UP-filters was introduced in 2020 by Romano and Jun. Further, normal UP-filters were analyzed by Romano. The concept of near UP-filters, as a generation of UP-filters, was designed in 2021 by A. Iampan and he showed that this notion lies between the notion of UP-subalgebras and the notion of UP-filters. Moreover, the concept of meet-commutative UP-algebras was introduced by Sawika et al. Furthermore, in such special UP-algebras, the notions of prime and irreducible UP-filters in UP-algebras are discussed by Muhiuddin et al. As a follow up, Romano introduced the concepts of prime UP-filters of the second and third kinds and he analyzed interrelationships of these three types of prime UP-filters. In addition, Romano introduced in 2021 the concept of weakly irreducible UP-filters in meet-commutative UP-algebras. Finally, the concept of semi-prime UP-filters in such algebras is discussed by Iampan and Romano. This paper gives a brief overview of the mentioned UP-filters and describes their established interconnections. [ABSTRACT FROM AUTHOR]

The environment of this article is the Bishop's constructive math- ematics - a mathematics based on the Intuitionisic logic. In this paper, in lean- ing on published article: A. Iampan. A new branch the logical algebra: UP- Algebras. J. Algebra Rel. Topics, 5(1)(2017), 35-54, we introduce the concept of a new algebraic structure, called an 'UP-algebra with apartness' and con- cepts of UP-ideals, UP-coideals, UP-filters and UP-cofilters, co-congruences and strongly extensional UP- homomorphisms in UP-algebras with apartness. In addition, we investigated some related properties of them. [ABSTRACT FROM AUTHOR]

Summary: In this article, considering one type of fuzzy discrete‐time networked control systems (NCSs) under stochastic communication protocol (SCP), a fuzzy‐based nonfragile H∞ filter is developed to detect the subsistent fault signal. The Takagi‐Sugeno (T‐S) mathematical model is employed to approximate the nonlinearities in the concerned fuzzy NCSs. The SCP is adopted to decide which sensor gets the access to the communication network at certain time instant, and the scheduling model of which is constructed as a Markov chain. Taking into account that the filter gain parameters in real practice may suffer fluctuations during the implementation, a modified nonfragile fuzzy filter is designed to detect the fault occurred in the signal transmission. By using the strong centralized stochastic analysis technique and the matrix calculation method, a Lyapunov function is adopted to derive sufficient conditions under which the filtering error dynamics is stochastically stable and the H∞ performance is satisfied. Then, the desired nonfragile fuzzy fault detection filter is realized by solving a certain linear matrix inequality. Finally, the effectiveness of the develop fault detection scheme is verified in the simulation example. [ABSTRACT FROM AUTHOR]

Comparing fuzzy sets by computing their similarity is common, with a large set of measures of similarity available. However, while commonplace in the computational intelligence community, the application and results of similarity measures are less common in the wider scientific context, where statistical approaches are the standard for comparing distributions. This is challenging, as it means that developments around similarity measures arising from the fuzzy community are inaccessible to the wider scientific community and that the fuzzy community fails to take advantage of a strong statistical understanding, which may be applicable to comparing (fuzzy membership) functions. In this paper, we commence a body of work on systematically relating the outputs of similarity measures to the notion of statistically significant difference; that is, how (dis)similar do two fuzzy sets need to be for them to be statistically different? We explain that in this context, it is useful to initially focus on dis-similarity, rather than similarity, as the former aligns directly with the widely used concept of statistical difference. We propose two methods of applying statistical tests to the outputs of fuzzy dissimilarity measures to determine significant difference. We show how the proposed work provides deeper insight into the behavior and possible interpretation of degrees of dis-similarity and, consequently, similarity, and how the interpretation differs with respect to context (e.g., the complexity of the fuzzy sets). [ABSTRACT FROM AUTHOR]

The notion of -filters is introduced on the lines of a dual annihilator of commutative BE-algebras. An equivalent condition is given for a proper ω-filter of a commutative BE-algebra to become a prime filter. A characterization theorem of ω-filters is established which in turn establishes some of equivalent conditions for a prime filter of a commutative BE-algebra to become an ω-filter. It is proved that every ω-filter is an intersection of all minimal prime filters. [ABSTRACT FROM AUTHOR]

The overall architectural complexity of autonomous underwater vehicles continuous to increase, enlarging the probability of fault occurrence in subsystems. Estimating the thrust loss by particle filter provided a useful method to detect the fault in propeller subsystem. In order to detect the fault in propellers as early as possible, the particle filter direct prediction method could amplify the fault trend and detect the fault earlier, but at the same time increase the possibility of false diagnosis. Therefore, a more accurate fault diagnosis method was required to discover the fault early and decrease the occurrence of false diagnosis. In this paper, an improved particle filter prediction method was proposed, combining the advantage of grey prediction to forecast the motion state, reducing the uncertainty in particle filter direct prediction process. Besides, the Gaussian kernel function was applied to judge the credibility of the prediction result, decreasing the possibility of the false diagnosis. In the experiments with simulated working conditions data and a section of actual sea trial data with propeller fault, the proposed method detected the fault earlier compared with the original particle filter method, and reduced the false diagnosis rate compared with the particle filter direct prediction method. The results show that the proposed method is effective in detecting the fault early with low false diagnosis. [ABSTRACT FROM AUTHOR]

In many applications, we need to study a linear regression model that consists of a response variable and a large number of potential explanatory variables, and determine which variables are truly associated with the response. In Foygel Barber & Candès (2015, Ann. Statist. , 43 , 2055–2085), the authors introduced a new variable selection procedure called the knockoff filter to control the false discovery rate (FDR) and proved that this method achieves exact FDR control. In this paper, we propose a prototype knockoff filter for group selection by extending the Reid–Tibshirani (2016, Biostatistics , 17 , 364–376) prototype method. Our prototype knockoff filter improves the computational efficiency and statistical power of the Reid–Tibshirani prototype method when it is applied for group selection. In some cases when the group features are spanned by one or a few hidden factors, we demonstrate that the Principal Component Analysis (PCA) prototype knockoff filter outperforms the Dai–Foygel Barber (2016, 33rd International Conference on Machine Learning (ICML 2016)) group knockoff filter. We present several numerical experiments to compare our prototype knockoff filter with the Reid–Tibshirani prototype method and the group knockoff filter. We have also conducted some analysis of the knockoff filter. Our analysis reveals that some knockoff path method statistics, including the Lasso path statistic, may lead to loss of power for certain design matrices and a specially designed response even if their signal strengths are still relatively strong. [ABSTRACT FROM AUTHOR]

An undesirable side effect of reversible color space transformation, which consists of lifting steps (LSs), is that while removing correlation it contaminates transformed components with noise from other components. Noise affects particularly adversely the compression ratios of lossless compression algorithms. To remove correlation without increasing noise, a reversible denoising and lifting step (RDLS) was proposed that integrates denoising filters into LS. Applying RDLS to color space transformation results in a new image component transformation that is perfectly reversible despite involving the inherently irreversible denoising; the first application of such a transformation is presented in this paper. For the JPEG-LS, JPEG 2000, and JPEG XR standard algorithms in lossless mode, the application of RDLS to the RDgDb color space transformation with simple denoising filters is especially effective for images in the native optical resolution of acquisition devices. It results in improving compression ratios of all those images in cases when unmodified color space transformation either improves or worsens ratios compared with the untransformed image. The average improvement is 5.0–6.0% for two out of the three sets of such images, whereas average ratios of images from standard test-sets are improved by up to 2.2%. For the efficient image-adaptive determination of filters for RDLS, a couple of fast entropy-based estimators of compression effects that may be used independently of the actual compression algorithm are investigated and an immediate filter selection method based on the detector precision characteristic model driven by image acquisition parameters is introduced. [ABSTRACT FROM AUTHOR]

We consider portfolio optimization in a regime‐switching market. The assets of the portfolio are modeled through a hidden Markov model (HMM) in discrete time, where drift and volatility of the single assets are allowed to switch between different states. We consider different parametrizations of the involved asset covariances: statewise uncorrelated assets (though linked through the common Markov chain), assets correlated in a state‐independent way, and assets where the correlation varies from state to state. As a benchmark, we also consider a model without regime switches. We utilize a filter‐based expectation‐maximization (EM) algorithm to obtain optimal parameter estimates within this multivariate HMM and present parameter estimators in all three HMM settings. We discuss the impact of these different models on the performance of several portfolio strategies. Our findings show that for simulated returns, our strategies in many settings outperform naïve investment strategies, like the equal weights strategy. Information criteria can be used to detect the best model for estimation as well as for portfolio optimization. A second study using real data confirms these findings. [ABSTRACT FROM AUTHOR]

Different methods to obtain individual scores from multiple item latent variable models exist, but their performance under realistic conditions is currently underresearched. We investigate the performance of the regression method, the Bartlett method, the Kalman filter, and the mean score under misspecification in autoregressive panel models. Results from three simulations show different patterns of findings for the mean absolute error, for the correlations between individual scores and the true scores (correlation criterion), and for the coverage in our settings: a) all individual score methods are generally quite robust against the chosen misspecification in the loadings, b) all methods are similarly sensitive to positively skewed as well as leptokurtic response distributions with regard to the correlation criterion, c) only the mean score is not robust against an integrated trend component, and d) coverage for the mean score is consistently below the nominal value. [ABSTRACT FROM AUTHOR]

Background: The most common histological subtypes of esophageal cancer are squamous cell carcinoma (ESCC) and adenocarcinoma (EAC). It has been demonstrated that non-marginal differences in gene expression and somatic alternation exist between these two subtypes; consequently, biomarkers that have prognostic values for them are expected to be distinct. In contrast, laryngeal squamous cell cancer (LSCC) has a better prognosis than hypopharyngeal squamous cell carcinoma (HSCC). Likewise, subtype-specific prognostic signatures may exist for LSCC and HSCC. Long non-coding RNAs (lncRNAs) hold promise for identifying prognostic signatures for a variety of cancers including esophageal cancer and head and neck squamous cell carcinoma (HNSCC). Methods: In this study, we applied a novel feature selection method capable of identifying specific prognostic signatures uniquely for each subtype – the Cox-filter method – to The Cancer Genome Atlas esophageal cancer and HSNCC RNA-Seq data, with the objectives of constructing subtype-specific prognostic lncRNA expression signatures for esophageal cancer and HNSCC. Results: By incorporating biological relevancy information, the lncRNA lists identified by the Cox-filter method were further refined. The resulting signatures include genes that are highly related to cancer, such as H19 and NEAT1, which possess perfect prognostic values for esophageal cancer and HNSCC, respectively. Conclusions: The Cox-filter method is indeed a handy tool to identify subtype-specific prognostic lncRNA signatures. We anticipate the method will gain wider applications. [ABSTRACT FROM AUTHOR]

Purpose: In precision radiotherapy, the intrafractional motion causes substantial uncertainty. Traditionally, the target volume is expanded to cover the tumor in all positions. Alternative approaches are gating and adaptive tracking, which require a time delay as small as possible between the actual tumor motion and the reaction to effectively compensate the motion. Current treatment machines often exhibit large time delays. Prediction filters offer a promising means to mitigate these time delays by predicting the future respiratory motion. Methods: A total of 18 prediction filters were implemented and their hyperparameters optimized for various time delays and noise levels. A set of 93 traces were standardized to a sampling frequency of 25 Hz and smoothed using the Fourier transform with a 3 Hz cutoff frequency. The hyperparameter optimization was carried out with ten traces, and the optimal hyperparameters were evaluated on the remaining 83 traces. Results: For smooth traces, the wavelet least mean squares prediction filter and the linear filter reached normalized root mean square errors of below 0.05 for time delays of 160 and 480 ms, respectively. For noisy signals, the performance of the prediction filters deteriorated and led to similar results. Conclusions: Linear methods for prediction filters are sufficient for respiratory motion signals. Reducing the measurement noise generally improves the performance of the prediction filters investigated in this study, even during breathing irregularities. [ABSTRACT FROM AUTHOR]

The present paper studies fuzzy matroids in view of degree. First we generalize the notion of (L,M)-fuzzy independent structure by introducing the degree of M-fuzzy family of independent L-fuzzy sets with respect to a mapping from LX to M. Such kind of degrees is proved to satisfy some axioms similar to those satisfied by (L,M)-fuzzy independent structure. Then we define and study some special degrees (e.g. quotient degrees and isomorphism degrees) with respect to mappings between two (L,M)-fuzzy matroid-like spaces in details. Finally we give characterizations of these degrees and investigate relationships between them. [ABSTRACT FROM AUTHOR]

A statistical process control framework is proposed to monitor non-linear profiles. The proposed methodology aims at identifying mean shifts or 'shape changes' in a profile. Discrete wavelet transformation (DWT) is applied to separate variation or noise from profile contours. B-splines are adopted to generate critical points to define the shape of a profile. The proposed method is innovative in that users can divide a profile into multiple segments to be monitored simultaneously. The high dimensionality problem that hinders the implementation of multivariate control charts can be solved by this framework. The distance difference statistic for each segment provides diagnostic information when the process of interest is out of control. These proposed statistics form a vector to be fed into any multivariate control chart such as the Hotelling T 2 control chart. A decomposition method can also be applied on the T 2 statistics when an out-of-control profile is detected. A simulation study applied to a forging process is conducted to demonstrate the property of the proposed method. The proposed method is capable of detecting profile shifts and identifying the exact location of problematic segments. [ABSTRACT FROM AUTHOR]