Search

There are several classical characterisations of the valuative dimension of a commutative ring. Constructive versions of this dimension have been given and proven to be equivalent to the classical notion within classical mathematics, and they can be used for the usual examples of commutative rings. To the contrary of the classical versions, the constructive versions have a clear computational content. This paper investigates the computational relationship between three possible constructive definitions of the valuative dimension of a commutative ring. In doing so, it proves these constructive versions to be equivalent within constructive mathematics. [ABSTRACT FROM AUTHOR]

In this paper, a conservative numerical method for the Vlasov–Darwin system is proposed. The Darwin model was assumed to be valid only in the Coulomb gauge, but recently this model has also been extended to the Lorenz gauge [1]. The Darwin model, based on the Lorenz gauge, exhibits a good symmetry between scalar and vector potentials, making the proofs of physical constraints relatively easy. In addition, the total energy was believed to be one of the conservative quantities of the Vlasov–Darwin system. However, the improved theory suggests that the Hamiltonian is the conservative quantity rather than the total energy. The structure-preserving scheme proposed in this paper exactly maintains the Lorenz gauge and the conservation laws of charge, canonical momentum, and Hamiltonian in discrete form. • The first Vlasov-Darwin scheme which exactly conserves the charge, canonical momentum, and Hamiltonian. • The proposed scheme is based on a modified Darwin model that was derived in the previous study. • The Lorenz gauge revealed that the Hamiltonian is the conservative quantity of this system rather than the total energy. [ABSTRACT FROM AUTHOR]

Currently, the majority of retrieval-based question-answering systems depend on supervised training using question pairs. However, there is still a significant need for further exploration of how to employ unsupervised methods to improve the accuracy of retrieval-based question-answering systems. From the perspective of question topic keywords, this paper presents TFCSG, an unsupervised question-retrieval approach based on topic keyword filtering and multi-task learning. Firstly, we design the topic keyword filtering algorithm, which, unlike the topic model, can sequentially filter out the keywords of the question and can provide a training corpus for subsequent unsupervised learning. Then, three tasks are designed in this paper to complete the training of the question-retrieval model. The first task is a question contrastive learning task based on topic keywords repetition strategy, the second is questions and its corresponding sequential topic keywords similarity distribution task, and the third is a sequential topic keywords generation task using questions. These three tasks are trained in parallel in order to obtain quality question representations and thus improve the accuracy of question-retrieval task. Finally, our experimental results on the four publicly available datasets demonstrate the effectiveness of the TFCSG, with an average improvement of 7.1%, 4.4%, and 3.5% in the P@1, MAP, and MRR metrics when using the BERT model compared to the baseline model. The corresponding metrics improved by 5.7%, 3.5% and 3.0% on average when using the RoBERTa model. The accuracy of unsupervised similar question-retrieval task is effectively improved. In particular, the values of P@1, P@5, and P@10 are close, the retrieved similar questions are ranked more advance. [ABSTRACT FROM AUTHOR]

• A novel positivity-preserving algorithm for implicit NS solver. • A residual correction to compute the correction factor. • A flux correction to enforce the positivity of the solution conservatively. • Positivity-preserving combined with implicit iterations. • Numerical experiments to verify the positivity-preserving capability. This paper presents a general positivity-preserving algorithm for implicit high-order finite volume schemes that solve compressible Euler and Navier-Stokes equations to ensure the positivity of density and internal energy (or pressure). Previous positivity-preserving algorithms are mainly based on the slope limiting or flux limiting technique, which rely on the existence of low-order positivity-preserving schemes. This dependency poses serious restrictions on extending these algorithms to temporally implicit schemes since it is difficult to know if a low-order implicit scheme is positivity-preserving. In the present paper, a new positivity-preserving algorithm is proposed in terms of the flux correction technique. And the factors of the flux correction are determined by a residual correction procedure. For a finite volume scheme that is capable of achieving a converged solution, we show that the correction factors are in the order of unity with additional high-order terms corresponding to the spatial and temporal rates of convergence. Therefore, the proposed positivity-preserving algorithm is accuracy-reserving and asymptotically consistent. The notable advantage of this method is that it does not rely on the existence of low-order positivity-preserving baseline schemes. Therefore, it can be applied to the implicit schemes solving Euler and especially Navier-Stokes equations. In the present paper, the proposed technique is applied to an implicit dual time-stepping finite volume scheme with temporal second-order and spatial high-order accuracy. The present positivity-preserving algorithm is implemented in an iterative manner to ensure that the dual time-stepping iteration will converge to the positivity-preserving solution. Another similar correction technique is also proposed to ensure that the solution remains positivity-preserving at each sub-iteration. Numerical results demonstrate that the proposed algorithm preserves positive density and internal energy in all test cases and significantly improves the robustness of the numerical schemes. [ABSTRACT FROM AUTHOR]

Accurate transport algorithms are crucial for computational fluid dynamics and more accurate and efficient schemes are always in development. One dimensional limiting is commonly employed to suppress nonphysical oscillations. However, the application of such limiters can reduce accuracy. It is important to identify the weakest set of sufficient conditions required on the limiter as to allow the development of successful numerical algorithms. The main goal of this paper is to identify new less restrictive sufficient conditions for flux form in-compressible advection to remain monotonic. We identify additional necessary conditions for incompressible flux form advection to be monotonic, demonstrating that the Spekreijse limiter region is not sufficient for incompressible flux form advection to remain monotonic. Then a convex combination argument is used to derive new sufficient conditions that are less restrictive than the Sweby region for a discrete maximum principle. This allows the introduction of two new more general limiter regions suitable for flux form incompressible advection. • The introduction of two limiter regions sufficient for flux form incompressible advection to retain a maximum principle. • Some necessary conditions for flux form incompressible advection to remain positive are shown to be incompatible with Spekreijse's limiter region. • Sufficient conditions for maintaining a discrete maximum principle for flux form incompressible advection are shown to be more general than the Sweby region. [ABSTRACT FROM AUTHOR]

In this paper, a multi-harmonic mixing demodulation scheme based on Levenberg-Marquardt (LM) algorithm, called PGC-LM-Arctan, is proposed to eliminate the influence of phase modulation depth on demodulation results. The relation between the C value and ratio of Bessel function is fitted by LM algorithm, and then the ratio of fourth harmonic and second harmonic is substituted into the above relation. The C value is calculated to eliminate the influence of coefficients on the demodulation results in Arctan algorithm. The experimental results show that when the modulation depth is from 1.5 rad to 4.8 rad, the harmonic distortion of the improved algorithm is lower than 0.7 %, which keeps the best level of the traditional PGC algorithm. The signal-to-noise-and-distortion-ratio is 41.69 dB, which is 17.58 dB higher than the traditional PGC-Arctan algorithm. [ABSTRACT FROM AUTHOR]

In 2015, Abatzoglou, Silverberg, Sutherland, and Wong presented a framework for primality proving algorithms for special sequences of integers using an elliptic curve with complex multiplication. They applied their framework to obtain algorithms for elliptic curves with complex multiplication by imaginary quadratic field of class numbers one and two, but, they were not able to obtain primality proving algorithms in cases of higher class number. In this paper, we present a method to apply their framework to imaginary quadratic fields of class number three. In particular, our method provides a more efficient primality proving algorithm for special sequences of integers than the existing algorithms by using an imaginary quadratic field of class number three in which 2 splits. As an application, we give two special sequences of integers derived from Q (− 23) and Q (− 31) , which are all the imaginary quadratic fields of class number three in which 2 splits. Finally, we give a computational result for the primality of these sequences. [ABSTRACT FROM AUTHOR]

Let q be a power of a prime such that q ≡ 1 (mod r). Let c be an r -th power residue over F q. In this paper, we present a new r -th root formula which generalizes G.H. Cho et al.'s cube root algorithm, and which provides a refinement of Williams' Cipolla-Lehmer based procedure. Our algorithm which is based on the recurrence relations arising from irreducible polynomial h (x) = x r + (− 1) r + 1 (b + (− 1) r r) (x − 1) with b = c + (− 1) r + 1 r requires only O (r 2 log ⁡ q + r 4) multiplications for r > 1. The multiplications for computation of the main exponentiation of our algorithm are half of that of the Williams' Cipolla-Lehmer type algorithms. [ABSTRACT FROM AUTHOR]

How to automatically recognize compound fault of mechanical equipment based on data-driven algorithms, has always been a research focus in modern intelligent manufacturing. Nonetheless, owing to the intricate nature of intelligent models in comprehending unknown knowledge, existing methods for compound fault recognition necessitate a training dataset comprising enough known compound fault samples. In order to address this issue, this paper first proposes an autonomous recognition framework based on reinforced adversarial open set (RAOS) algorithm, which can accurately recognize compound faults by utilizing the label information from single fault samples. Firstly, single fault and compound fault are represented as the known class and unknown class, respectively. Subsequently, a feature sub-network and a policy sub-network with adversarial learning are devised to classify and align the features of samples of two classes. Additionally, a deep reinforcement learning (DRL) model is formulated following a question-and-answer paradigm. Ultimately, the DRL model undertakes a sequence decision-making task to optimize the feature sub-network and the policy sub-network. Through a laboratory experiment and an engineering application, the results robustly validate the effectiveness of the proposed ROSA framework in accurately recognizing compound fault samples, even when only single fault samples are known in the training dataset. [ABSTRACT FROM AUTHOR]

Exponential/extended Runge–Kutta–Nyström (ERKN) methods have been validated by numerous theoretical and numerical results to be more efficient and suitable than classical Runge–Kutta–Nyström (RKN) methods in dealing with highly oscillatory Hamiltonian systems. Once numerical solutions are required to achieve a prescribed local error tolerance for practical problems, the embedded ERKN pairs with adaptive stepsize are needed. Given the higher efficiency of high-order methods than low-order methods, this paper focuses on high-order embedded ERKN pairs. Using the particular mapping from RKN methods into ERKN methods, we establish an approach to constructing high-order embedded ERKN pairs. By diagonalizing the frequency matrix, an implementation algorithm with less calculation amount than the direct calculation procedure is proposed for high-dimensional problems. In addition, the dispersion and dissipation of the ERKN pairs ERKN4(3) and ERKN8(6) are analyzed. Furthermore, the application of ERKN pairs to an important highly oscillatory problem, i.e., the wave equation prescribed with different boundary conditions is discussed. For the periodic boundary condition, a special implementation algorithm incorporated with FFT techniques is presented, which decreases the calculation amount in one time step from O (N 2) to O (N log ⁡ N). Finally, numerical results with the FPU problem, the Klein–Gordon equation in the nonrelativistic limit regime, and a two-dimensional wave equation demonstrate the superiority of ERKN pairs over classical RKN pairs. • An effective approach is presented to establish high-order embedded ERKN pairs. • A special implementation algorithm by diagonalizing the frequency matrix is proposed to reduce the calculation amount. • The application of the embedded ERKN pairs to wave equations prescribed with different boundary conditions is discussed. [ABSTRACT FROM AUTHOR]

Based on the recently proposed multi-sub-step implicit β 1 / β 2 -Bathe method and a novel mapping strategy on the error equation, this paper presents two families of dual-explicit model-based integration algorithms for solving linear and nonlinear dynamic problems. Firstly, the dual-explicit formulations of the well-known Chen and Ricles (CR) algorithm are adopted for the new algorithms. By matching the error equations of the new algorithms and the implicit β 1 / β 2 -Bathe method, the model-based integration parameters of the new algorithms are then derived. After analyzing the numerical properties of the two algorithms, it can be found that they are unconditionally stable for linear and nonlinear softening dynamic problems when the governing integration parameters are within specific ranges. Besides the two algorithms' numerical dispersion and energy dissipation are identical to the parent algorithm, i.e., the β 1 / β 2 -Bathe method. The overshooting issue of the proposed algorithms is less prominent than in some representative model-based algorithms. Finally, two numerical examples are used to investigate the computational efficiency and accuracy of the new algorithms compared to the parent algorithm and some existing model-based algorithms, including those with controllable damping, i.e., the KR- α and MKR- α methods. The results show that the two families of new algorithms are less computationally expensive than the parent algorithm as they adopt dual-explicit and single-step formulation. In addition, it is also observed that the developed algorithms have a better performance of damping out the spurious effect at high modes than the KR- α and MKR- α methods. [ABSTRACT FROM AUTHOR]

A contra-rotating propfan consists of inner and outer propellers, having a dual inter-shaft bearing structure. The operating conditions are characterized by Slight Rotating Speed Differences (SRSDs) between the inner and outer rotors. These speed differences generate complex vibration transmission paths and harmonic cross-coupling between the dual rotors. Consequently, it becomes challenging to identify unbalanced vibration, leading to decreased low dynamic balance efficiency. Focusing on the prominent issues of low identification accuracy and poor stability in existing algorithms, mainly Least Square Method (LSM), Non-whole Beat Correlation Method (NWBCM), and Whole Beat Correlation Method (WBCM), when dealing with SRSDs under harmonic and noise interference, this paper introduces the Kalman Filter-Based Least Squares Identification Method for Filtering Harmonic Coupling (HLSM-KF). This method achieves precise, stable, and fast identification of unbalanced responses in contra-rotating rotors with SRSDs ranging from 1 to 30 rpm. Comparing the errors of the HLSM-KF algorithm to the other existing algorithms through simulations and experiments, the findings demonstrated that the identification accuracy and stability of the HLSM-KF algorithm are significantly dominant. Specifically, the Root Mean Square Error (RMSE) of the HLSM-KF algorithm is 47 % lower than that of the LSM algorithm. Therefore, a balancing experiment is conducted on the contra-rotating dual-rotor test rig, using the HLSM-KF algorithm. Consequently, the unbalanced vibrations of the inner and outer rotors are reduced by 86 % and 91 %, respectively, and the Root Mean Square (RMS) value of the whole system vibration is reduced by 87 %. [ABSTRACT FROM AUTHOR]

• Suppressing the spatial dispersion of FD modeling by the improved pix2pix algorithm. • Introducing the Sobel operator for robust neural network training. • Numerical tests demonstrating the significant advantages of the proposed method. Seismic finite-difference (FD) modeling inevitably suffers from the spatial dispersion artifacts. In this paper, we propose a new method to suppress the spatial dispersion of seismic FD modeling using the improved pix2pix algorithm by introducing the Sobel operator. The new method involves the following steps. First, a training data set which consists of a small number of wavefield data is generated. The training data set is composed of the high-accuracy wavefield data modeled by the high-order FD method and the low-accuracy wavefield data modeled by the low-order FD method. Second, the entire set of the wavefield data polluted by the spatial dispersion is computed using the low-order FD method. Third, the improved pix2pix neural network is trained and applied to the entire wavefield data set to suppress the spatial dispersion. Numerical tests on different modeling examples demonstrate the effectiveness of the proposed method, which includes the great accuracy in suppressing the spatial dispersion and the high efficiency for the large scale FD modeling. [ABSTRACT FROM AUTHOR]

• We employ the triangular mesh subdivision (TMS) algorithm to subdivide the 3D mesh model and expand the number of embedded vertices. • We employ the Multi-Layer Embedding Strategy (MLES) to achieve high-capacity reversible data hiding. • Experiments demonstrate that the proposed algorithm achieves a higher embedding rate compared to existing algorithms. Reversible data hiding in encrypted domain (RDH-ED) is widely used in sensitive fields such as privacy protection and copyright authentication. However, the embedding capacity of existing methods is generally low due to the insufficient use of model topology. In order to improve the embedding capacity, this paper proposes a high-capacity multi-MSB predictive reversible data hiding in encrypted domain (MMPRDH-ED). Firstly, the 3D model is subdivided by triangular mesh subdivision (TMS) algorithm, and its vertices are divided into reference set and embedded set. Then, in order to make full use of the redundant space of embedded vertices, Multi-MSB prediction (MMP) and Multi-layer Embedding Strategy (MLES) are used to improve the capacity. Finally, stream encryption technology is used to encrypt the model and data to ensure data security. The experimental results show that compared with the existing methods, the embedding capacity of MMPRDH-ED is increased by 53 %, which has higher advantages. [ABSTRACT FROM AUTHOR]

Copy-move forgery detection is a common image tampering detection technology. In this paper, a novel copy-move forgery detection scheme is proposed. The proposed scheme is based on Regional Density Center (RDC) clustering and Refined Length Homogeneity Filtering (RLHF) policy. First, to obtain an adequate number of keypoints in smooth or small areas of the image, the proposed scheme employs scale normalization and adjustment of the contrast threshold of the input image. Subsequently, to speed up the feature matching process, a matching algorithm based on gray value grouping is used to match the keypoints. RLHF policy is applied to filter the mismatched pairs. To guarantee a good estimation of the affine transformation, the RDC clustering algorithm is proposed to group the matched pairs. Finally, the correlation coefficients are computed to precisely locate the tampered regions. The proposed copy-move forgery detection scheme based on RDC and RLHF can effectively identify duplicated regions of digital images. It demonstrates the effectiveness and robustness of the proposed scheme over many state-of-the-art schemes on public datasets. [ABSTRACT FROM AUTHOR]

Arrowed Gelfand–Tsetlin patterns have recently been introduced to study alternating sign matrices. In this paper, we show that a (− 1) -enumeration of arrowed Gelfand–Tsetlin patterns can be expressed by a simple product formula. The numbers are up to 2 n a one-parameter generalization of the numbers 2 n (n − 1) / 2 ∏ j = 0 n − 1 (4 j + 2) ! (n + 2 j + 1) ! that appear in recent work of Di Francesco. A second result concerns the (− 1) -enumeration of arrowed Gelfand–Tsetlin patterns when excluding double-arrows as decoration in which case we also obtain a simple product formula. We are also able to provide signless interpretations of our results. The proofs of the enumeration formulas are based on a recent Littlewood-type identity, which allows us to reduce the problem to the evaluations of two determinants. The evaluations are accomplished by means of the LU-decompositions of the underlying matrices, and an extension of Sister Celine's algorithm as well as creative telescoping to evaluate certain triple sums. In particular, we use implementations of such algorithms by Koutschan, and by Wegschaider and Riese. [ABSTRACT FROM AUTHOR]

In this paper, we firstly give the notion of relative ϵ -approximate bisimulations between two fuzzy two-dimensional on-line tessellation automata (F2OTAs) and elaborate that the relative error between two F2OTAs, accompanying with a relative ϵ -approximate bisimulation between them, is less than or equal to ϵ where ϵ ∈ [ 0 , 1 ]. Moreover, if relative ϵ -approximate bisimulations between two F2OTAs are restricted to be surjective functional, then some properties are drawn and by which relative ϵ -approximate bisimulations on a F2OTA are defined. We construct the factor F2OTA of a F2OTA with respect to a relative ϵ -approximate bisimulation on it and describe the relationship between this factor automaton and the original F2OTA. Whereafter, we novelly design two algorithms to compute all maximal relative ϵ -approximate bisimulations on a given F2OTA. Finally, we discuss some interesting properties of bisimulations on F2OTAs. [ABSTRACT FROM AUTHOR]

In multi-core processor systems, the Network-on-Chip (NoC) serves as a vital communication infrastructure. To ensure chip reliability during potential failures, this paper proposes a two-level topology reconfiguration algorithm with core-level redundancy technology. Initially, a heuristic topology reconfiguration method utilizing a greedy strategy is proposed to perform local replacement of faulty processing elements (PEs) and generate an initial logical topology with shorter interconnection paths between PEs. Then, an intelligent optimization method based on memetic algorithm is introduced to optimize the generated initial topology for better communication performance. The experimental results demonstrate that compared to the current state-of-the-art algorithm, the proposed algorithm achieves an average improvement of 13.92% and 30.83% on various size topologies in terms of distance factor (DF) and congestion factor (CF), which represent communication delay and traffic balance respectively. The proposed algorithm significantly enhances the communication performance of the target topology, mitigating communication latency and potential congestion problems. • The candidate set aids greedy selection for optimal fault-free PE replacements. • Local greedy strategy reduces communication delay, eases congestion issues. • Memetic algorithm further optimizes the target topology in the reconfiguration. • The proposed algorithms show strong stability, adaptability in large-scale arrays. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical study on the implementation of a self-tuning vibration absorber for tonal vibration control. The study considers a tuneable vibration absorber, composed by a spring-mass-damper system with variable stiffness and damping components, which is attached to a single degree of freedom mechanical system subjected to a harmonic excitation. The online tuning of the absorber stiffness and damping parameters is performed using an extremum seeking algorithm set to minimise the vibration kinetic energy of the hosting system. The paper proposes a two-paths tuning approach, which, starting from initial estimates of the stiffness and damping parameters of the absorber, searches for their optimal values along constant-damping and constant-stiffness paths respectively. The study presents a comprehensive analysis on the implementation of the algorithm at off-resonance and at resonance frequencies of the hosting system. Also, it investigates how the intrinsic parameters of the algorithm influence the convergence to the optimal stiffness and damping values. The proposed tuning methodology does not require a reference signal for the tonal excitation and, thus, can be suitably implemented both for fixed and time-varying tonal disturbances. [ABSTRACT FROM AUTHOR]

In this paper we analyze the computational costs of various operations and algorithms in algebraic number fields using exact arithmetic. Let K be an algebraic number field. In the first half of the paper, we calculate the running time and the size of the output of many operations in K in terms of the size of the input and the parameters of K. We include some earlier results about these, but we go further than them, e.g. we also analyze some R -specific operations in K like less-than comparison. In the second half of the paper, we analyze two algorithms: the Bareiss algorithm, which is an integer-preserving version of the Gaussian elimination, and the LLL algorithm, which is for lattice basis reduction. In both cases, we extend the algorithm from Z n to K n , and give a polynomial upper bound on the running time when the computations in K are performed exactly (as opposed to floating-point approximations). [ABSTRACT FROM AUTHOR]

• An adaptive HEVC video steganography algorithm is designed, which can effectively resist the PU shift-based steganalysis. • The introduction of multivariate STC allows for smaller modifications with the same embedding capacity. • The superiority of this algorithm over the state-of-the-art video steganography algorithm is verified through extensive experiments. Calibration-based steganalysis methods are a fatal threat to current HEVC steganography algorithms. The current steganography algorithms based on prediction unit (PU) still lack resistance to this type of steganalysis. The reason is that the improvements in HEVC codec provide more potential steganographic space as well as introduce more detectable distortion. Therefore, a HEVC video steganography method that has resistance to PU shift-based steganalysis is proposed in this paper. First, the PU shift phenomenon that exists in PU-based steganography is introduced. Then the existing calibration-based steganalysis method is enhanced. According to the encoding rules of HEVC, the distortion cost function according to the difference of rate distortion cost (RD cost) during recompression is designed, which aims to obtain better resistance to calibration-based steganalysis. Experimental results demonstrate that the steganography algorithm designed in this paper provides excellent resistance ability for calibration-based steganalysis. [ABSTRACT FROM AUTHOR]

Protein–protein interactions (PPIs) are crucial for various biological processes, and predicting PPIs is a major challenge. To solve this issue, the most common method is link prediction. Currently, the link prediction methods based on network Paths of Length Three (L3) have been proven to be highly effective. In this paper, we propose a novel link prediction algorithm, named SMS, which is based on L3 and protein similarities. We first design a mixed similarity that combines the topological structure and attribute features of nodes. Then, we compute the predicted value by summing the product of all similarities along the L3. Furthermore, we propose the Max Similarity Multiplied Similarity (maxSMS) algorithm from the perspective of maximum impact. Our computational prediction results show that on six datasets, including S. cerevisiae, H. sapiens, and others, the maxSMS algorithm improves the precision of the top 500, area under the precision–recall curve, and normalized discounted cumulative gain by an average of 26.99%, 53.67%, and 6.7%, respectively, compared to other optimal methods. [Display omitted] • A mixed similarity combining sequence and topological structure is introduced. • A link prediction algorithm based on complementarity and similarity is proposed. • The proposed method performs better than existing L3, Sim and other methods. [ABSTRACT FROM AUTHOR]

Online learning is an efficient approach in machine learning and statistics, which iteratively updates models upon the observation of a sequence of training examples. A representative online learning algorithm is the online gradient descent, which has found wide applications due to its low complexity and scalability to large datasets. Kernel-based learning methods have been proven to be quite successful in dealing with nonlinearity in the data and multivariate optimization. In this paper we present a class of kernel-based online gradient descent algorithm for addressing regression problems, which generates sparse estimators in an iterative way to reduce the algorithmic complexity for training streaming datasets and model selection in large-scale learning scenarios. In the setting of support vector regression (SVR), we design the sparse online learning algorithm by introducing a sequence of insensitive distance-based loss functions. We prove consistency and error bounds quantifying the generalization performance of such algorithms under mild conditions. The theoretical results demonstrate the interplay between statistical accuracy and sparsity property during learning processes. We show that the insensitive parameter plays a crucial role in providing sparsity as well as fast convergence rates. The numerical experiments also support our theoretical results. [ABSTRACT FROM AUTHOR]

In recent years there has been increased use of machine learning (ML) techniques within mathematics, including symbolic computation where it may be applied safely to optimise or select algorithms. This paper explores whether using explainable AI (XAI) techniques on such ML models can offer new insight for symbolic computation, inspiring new implementations within computer algebra systems that do not directly call upon AI tools. We present a case study on the use of ML to select the variable ordering for cylindrical algebraic decomposition. It has already been demonstrated that ML can make the choice well, but here we show how the SHAP tool for explainability can be used to inform new heuristics of a size and complexity similar to those human-designed heuristics currently commonly used in symbolic computation. [ABSTRACT FROM AUTHOR]

The selective delayless subband structure stands out as a promising algorithmic choice for the multi-channel active control of vehicle interior noise, particularly in the context of road noise. This type of algorithm reduces the eigenvalue spread of the autocorrelation matrix of the signal by decomposing the signal into subbands, and the desired subbands are activated selectively, thus achieving a significant performance improvement while consuming less computational resources compared with the traditional fullband algorithms. Nevertheless, the effectiveness of the subband algorithm appears to be closely tied to the configuration of the primary disturbance signal. In cases where the primary disturbance signal encompasses both broadband and tonal components, the performance advantage of the subband algorithm becomes constrained. In this paper, we conduct a thorough comparative analysis of two extensively employed subband algorithms, namely the Morgan and the Milani methods, through simulations employing data obtained from a multi-channel active noise control (ANC) headrest system. The results indicate that the Morgan method outperforms the Milani method when configured optimally. Subsequently, we propose an enhanced version of the subband algorithm based on the Morgan method. The enhanced algorithm incorporates an additional sinusoidal noise canceller (SNC) subsystem and a narrowband active noise control (NANC) subsystem based on local secondary path modeling to address tonal components, while the selective subband structure is employed for controlling broadband components. In addition, the computational complexity of the algorithm is analyzed. The effectiveness of the proposed algorithm is validated through numerous simulations and the ANC tests conducted on an actual vehicle utilizing the multi-channel ANC headrest system. The performance of the proposed algorithm surpasses that of traditional selective subband and fullband algorithms, and balanced binaural noise reduction is achieved. [ABSTRACT FROM AUTHOR]

DNA 4 mC plays a crucial role in the genetic expression process of organisms. However, existing deep learning algorithms have shortcomings in the ability to represent DNA sequence features. In this paper, we propose a 4 mC site identification algorithm, DNABert-4mC, based on a fusion of the pruned pre-training DNABert-Pruning model and artificial feature encoding to identify 4 mC sites. The algorithm prunes and compresses the DNABert model, resulting in the pruned pre-training model DNABert-Pruning. This model reduces the number of parameters and removes redundancy from output features, yielding more precise feature representations while upholding accuracy.Simultaneously, the algorithm constructs an artificial feature encoding module to assist the DNABert-Pruning model in feature representation, effectively supplementing the information that is missing from the pre-trained features. The algorithm also introduces the AFF-4mC fusion strategy, which combines artificial feature encoding with the DNABert-Pruning model, to improve the feature representation capability of DNA sequences in multi-semantic spaces and better extract 4 mC sites and the distribution of nucleotide importance within the sequence. In experiments on six independent test sets, the DNABert-4mC algorithm achieved an average AUC value of 93.81%, outperforming seven other advanced algorithms with improvements of 2.05%, 5.02%, 11.32%, 5.90%, 12.02%, 2.42% and 2.34%, respectively. [Display omitted] • Train a new pruning pretraining model on DNA sequences to extract feature information. • The introduction of manually assisted features has expanded the search space for sequence feature. • Attention fusion strategy better promotes the fusion output of features from different dimensions. • The complementary nature of machine features and manual features better fits the target features. [ABSTRACT FROM AUTHOR]

This paper introduces a novel parameter related to bearing degradation, namely the Equivalent Damaged Volume (EDV). An algorithm capable of extracting EDV values from experimental data is detailed. To this end, the proposed technique relies on the comparison between experimental and numerical signals. The former are the result of an extensive campaign of run-to-failure tests performed on a dedicated test rig. On the other hand, the latter are obtained by means of a lumped parameter model that accounts for the angular extent and the depth of either localized or extended defects. The potential of this novel technique is demonstrated by exploiting the values obtained by the algorithm as inputs for a prognostic model. In particular, the developed model aims at predicting the time until a certain threshold on the equivalent damaged volume is crossed, regardless of the applied load and the shaft rotation speed. The advantages and downsides introduced by the proposed approach are thoroughly discussed by providing examples based on real degradation histories. [ABSTRACT FROM AUTHOR]

• A near-field weighted subspace fitting algorithm is proposed for ultrasonic guided wave multi-damage localization. • A near-field multi-dimensional solution search algorithm based on a niche particle swarm optimization is proposed, which effectively improves the efficiency of damage localization. • Algorithm performance comparison, finite element simulation, real point damage and slot damage experiments verify the effectiveness of the proposed method. The ultrasonic guided wave-based method for multi-damage localization has been widely proposed. However, the precision of this method is directly correlated with both the quantity of sensors employed and the intricacy of the implementation process. This relationship poses a challenge in striking a balance between the accuracy and efficiency. To improve the computational efficiency under the premise of ensuring the accuracy of multi-damage localization, this paper proposes a near-field weighted subspace fitting algorithm based on niche-particle swarm optimization. Firstly, the fitting relationship between the signal subspace of the diffraction wave and the array steering vector is established under the uniform linear array. Secondly, a multi-dimensional solution space search algorithm based on niche-particle swarm optimization is proposed to improve the search efficiency of damage. Finally, the algorithm is verified by performance comparison, finite element simulation and experiment. The results show that compared with the same type of method, the algorithm improves the computational efficiency by nearly threefold under the identifiable multi-damage conditions. Additionally, the angle error is 1 ∼ 6°, and the distance error is 1 ∼ 20 mm. [ABSTRACT FROM AUTHOR]

Algorithmic stability is a fundamental concept in statistical learning theory to understand the generalization behavior of optimization algorithms. Existing high-probability bounds are developed for the generalization gap as measured by function values and require the algorithm to be uniformly stable. In this paper, we introduce a novel stability measure called pointwise uniform stability by considering the sensitivity of the algorithm with respect to the perturbation of each training example. We show this weaker pointwise uniform stability guarantees almost optimal bounds, and gives the first high-probability bound for the generalization gap as measured by gradients. Sharper bounds are given for strongly convex and smooth problems. We further apply our general result to derive improved generalization bounds for stochastic gradient descent. As a byproduct, we develop concentration inequalities for a summation of weakly-dependent vector-valued random variables. [ABSTRACT FROM AUTHOR]

In this paper we study the Shor relaxation of quadratic programs by fixing a feasible set and considering the space of objective functions for which the Shor relaxation is exact. We first give conditions under which this region is invariant under the choice of generators defining the feasible set. We then describe this region when the feasible set is invariant under the action of a subgroup of the general linear group. We conclude by applying these results to quadratic binary programs. We give an explicit description of objective functions where the Shor relaxation is exact and use this knowledge to design an algorithm that produces candidate solutions for binary quadratic programs. [ABSTRACT FROM AUTHOR]

The Chow ring of the moduli space of stable marked curves is generated by Keel's divisor classes. The top graded part of this Chow ring is isomorphic to the integers, generated by the class of a single point. In this paper, we give an equivalent graphical characterization on the monomials in this Chow ring, as well as the characterization on the algebraic reduction on such monomials. Moreover, we provide an algorithm for computing the intersection degree of tuples of Keel's divisor classes — we call it the forest algorithm; the complexity of which is O (n 3) in the worst case, where n refers to the number of marks on the stable curves in the ambient moduli space. Last but not least, we introduce three identities on multinomial coefficients which naturally came into play, showing that they are all equivalent to the correctness of the base case of the forest algorithm. [ABSTRACT FROM AUTHOR]

It is increasingly realized that taking stochastic effects into account is important in order to study biological cells. However, the corresponding mathematical formulation, the chemical master equation (CME), suffers from the curse of dimensionality and thus solving it directly is not feasible for most realistic problems. In this paper we propose a dynamical low-rank algorithm for the CME that reduces the dimensionality of the problem by dividing the reaction network into partitions. Only reactions that cross partitions are subject to an approximation error (everything else is computed exactly). This approach, compared to the commonly used stochastic simulation algorithm (SSA, a Monte Carlo method), has the advantage that it is completely noise-free. This is particularly important if one is interested in resolving the tails of the probability distribution. We show that in some cases (e.g. for the lambda phage) the proposed method can drastically reduce memory consumption and run time and provide better accuracy than SSA. • We propose a low-rank algorithm that does not rely on single orbital basis functions. • The proposed approach is better suited for biological/chemical reaction networks. • We demonstrate better accuracy and improved efficiency compared to SSA for some problems. • The proposed complexity reduction algorithm is noise free (in contrast to SSA). • We demonstrate that our algorithm accurately resolves the tails of the distribution (in contrast to SSA). [ABSTRACT FROM AUTHOR]

It has been shown that any nonblocking algorithm for work-stealing in the standard asynchronous shared memory model of computation must use expensive Read-After-Write synchronization patterns or atomic Read-Modify-Write instructions. Algorithms for relaxations of work-stealing have been proposed, which only partially avoid this impossibility result. In restricted models of computation, work-stealing algorithms have been designed that avoid Read-After-Write patterns and atomic Read-Modify-Write instructions. This paper considers work-stealing with multiplicity , a relaxation in which every task is taken by at least one process, and any process can take any task at most once. We study two variants of the relaxation, for each variant designing a Read / Write wait-free algorithm in the standard asynchronous shared memory model. The two algorithms are devoid of Read-After-Write synchronization patterns in all their operations, and additionally, the algorithm for the second variant has constant step complexity and is fence-free. Namely, no specific ordering among the algorithm's instructions is required beyond what is implied by data dependence. To our knowledge, these are the first algorithms for relaxations of work-stealing possessing all these properties. The algorithms are also solutions to relaxed versions of single-enqueuer multi-dequeuer queues. The theoretical results are complemented with an experimental evaluation showing that the benefits of relaxed work-stealing vary depending on the application, concretely on the complexity of the work associated with each task. • We present two asynchronous work-stealing algorithms with relaxation, work-stealing with multiplicity and weak-multiplicity. • In the first one, tasks are taken by at least one operation and if taken by several operations, they must be pairwise concurrent. • In the second one, Take/Steal operations extracting the same task may not be concurrent, however, each process extracts tasks at most once. • The algorithms are wait-free, read/write, and devoid of read-after-write synchronization patterns. • The proposed algorithms outperform standard work-stealing algorithms and exhibit similar or better performance than known relaxed algorithms in some practical settings. [ABSTRACT FROM AUTHOR]

Operators from various industries have been pushing the adoption of wireless sensing nodes for industrial monitoring, and such efforts have produced sizeable condition monitoring datasets that can be used to build diagnosis algorithms capable of warning maintenance engineers of impending failure or identifying current system health conditions. However, single operators may not have sufficiently large fleets of systems or component units to collect sufficient data to develop data-driven algorithms. One potential solution to overcome the challenge of having limited representative datasets is to merge datasets from multiple operators with the same type of assets. However, directly sharing data across the company's borders yields privacy concerns. Federated learning (FL) has emerged as a promising solution to leverage datasets from multiple operators to train a decentralized asset fault diagnosis model while maintaining data confidentiality. However, the performance of traditional FL algorithms degrades when local clients' datasets are heterogeneous. The dataset heterogeneity is particularly prevalent in fault diagnosis applications due to the high diversity of operating conditions and system configurations. To address this challenge, this paper proposes a novel clustering-based FL algorithm where clients are clustered based on their dataset similarity. Estimating dataset similarity between clients without explicitly sharing data is achieved by training probabilistic deep learning models and having each client examine the predictive uncertainty of the other clients' models on its local dataset. Clients are then clustered for FL based on relative prediction accuracy and uncertainty. Experiments on three bearing fault datasets, two publicly available and one newly collected for this work, show that our algorithm significantly outperforms FedAvg and a cosine similarity-based algorithm by 5.1% and 30.7% on average over the three datasets. Further, using a probabilistic classification model has the additional advantage of accurately quantifying its predictive uncertainty, which we show it does exceptionally well. [ABSTRACT FROM AUTHOR]

Steepest descent methods combining complex contour deformation with numerical quadrature provide an efficient and accurate approach for the evaluation of highly oscillatory integrals. However, unless the phase function governing the oscillation is particularly simple, their application requires a significant amount of a priori analysis and expert user input, to determine the appropriate contour deformation, and to deal with the non-uniformity in the accuracy of standard quadrature techniques associated with the coalescence of stationary points (saddle points) with each other, or with the endpoints of the original integration contour. In this paper we present a novel algorithm for the numerical evaluation of oscillatory integrals with general polynomial phase functions, which automates the contour deformation process and avoids the difficulties typically encountered with coalescing stationary points and endpoints. The inputs to the algorithm are simply the phase and amplitude functions, the endpoints and orientation of the original integration contour, and a small number of numerical parameters. By a series of numerical experiments we demonstrate that the algorithm is accurate and efficient over a large range of frequencies, even for examples with a large number of coalescing stationary points and with endpoints at infinity. As a particular application, we use our algorithm to evaluate cuspoid canonical integrals from scattering theory. A Matlab implementation of the algorithm is made available and is called PathFinder. • An algorithm for the evaluation of oscillatory integrals with polynomial phase. • The algorithm automates the numerical steepest descent method. • Our implementation is robust and efficient across all frequencies. [ABSTRACT FROM AUTHOR]