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Abstract: We show that the main results in the recent paper [4] by Sadiq Basha (2012) are not real generalizations but particular cases of existing fixed point theorems in the literature. [Copyright &y& Elsevier]

Abstract: The high fidelity generalized method of cells (HFGMC) has been originally developed by as a micromechanical method for periodic multi-phase composite media. A computational implementation of the HFGMC equations has been proposed by to enhance numerical efficiency, still with direct reference to the HFGMC formulation. Later, the same computational implementation is recast as a new method called “finite volume direct averaging micromechanics” (FVDAM), starting by . The current discussion paper has two aims. The first is to show that the FVDAM is not a new method and that it has the same assumptions and identical governing equations as those originally derived by the HFGMC. The only difference is in the solution procedure where intermediate dependent variables, in the form of average displacements at the interfaces, are used instead of directly solving for the unknown micro-variables; the coefficients of the displacement polynomials. Thus, renaming the HFGMC micromodel to FVDAM has not been justified. In fact, () have shown that the same reduction of variables can be achieved by a simple static condensation carried out at the global system of equations instead of introducing intermediate variables. The second aim of this paper is to address misrepresentations in a recent discussion paper by the FVDAM authors claiming, in part, that the HFGMC method using parametric geometry of the subcells should follow their formulation (termed parametric FVDAM). We show that the latter is limited to an incomplete quadratic expansion of the displacement and an approximation in the form of a priori constant Jacobian of the parametric mapping. However, the HFGMC with arbitrary cell geometry, (), has been formulated in a direct and general manner, i.e. retaining the full quadratic expansion of the displacement together with the complete Jacobian. Thus, the parametric FVDAM is a special case of the parametric HFGMC, i.e. when the Jacobian is sampled and evaluated only at one point, namely the origin of the parametric coordinate system. The intended new contribution of to refined micromechanics and progressive damage has been completely ignored by the FVDAM-discussion paper. Therefore, in order to maintain scientific clarity, it is strongly advocated to preserve the original name of the HFGMC method, regardless of the different computational implementations used for solving the governing equations for both orthogonal and parametric geometries of the subcells. [Copyright &y& Elsevier]

Abstract: Computer-based interventions are being used more in the classroom. Student responses to these interventions often contribute to decisions making regarding important outcomes. It is important to understand the effect of these interventions within the context of the intervention as well as across related context. The current study examined the generalization of math fact fluency gains resulting from a computer-based intervention to paper-and-pencil performance. A total of 31 second grade students completed fluency drills on the computer or with paper and pencil. Pretest–posttest performance on both computer and paper and pencil for all students was evaluated using a doubly multivariate repeated measure ANOVA. Results indicated that gains achieved on the computer did not generalize to paper-and-pencil performance. [Copyright &y& Elsevier]

Abstract: A generalization of two sharp inequalities in a recent paper by N. Ujević is established. Applications in numerical integration are also given and the results of N. Ujević are revised and improved. [Copyright &y& Elsevier]

Preferential Attachment (PA) models the scientific citation process. In the PA model, a new paper attaches itself to the citation network based only on the popularity of the currently existing papers. This invariably leads to a network whose degree distribution satisfies the Power Law. Yet, empirical results show that paper age should also play a role in the citation process. In other words, when references are chosen for a new paper, the age of an existing paper may also affect the choice for citing. In this paper, we derive a generalized PA model that includes the effect of aging, with analytical solution. Such a model can be used to analyze the competing influence of preferential attachment and aging effect quantitatively in citation process and explain differences in various research domains by the extent of aging. It may also serve as a general model of network formation. [ABSTRACT FROM AUTHOR]

Abstract: In a commentary about the paper ‛Asynchronous Little Ice Age glacial maximum extent in southeast Iceland’ (Geomorphology 114 (2010) 253-260), M. Dąbski questioned the validity of the generalized extreme value method and the Bayesian approach in lichenometric dating of the outermost LIA Fláajökull moraines in SE Iceland. This paper responds to these criticisms by explaining the relevance of the method applied and the relevance of the dates obtained. [Copyright &y& Elsevier]

In this paper, we examine almost (strictly) semimonotone matrices which are also either Z -matrices or matrices having Property (+ +) and show that both parts of Wendler's conjecture [22] (2019) hold for these matrices. Another important result of this paper is the characterization of copositive matrices beyond the matrices with non-positive off-diagonal elements. We discuss some interesting properties related to the structure of almost (strictly) semimonotone matrices and also present results pertaining to the existence and multiplicity of solutions to the linear complementarity problem associated with an almost strictly semimonotone matrix. [ABSTRACT FROM AUTHOR]

The vision enhancement of autonomous underwater vehicle (AUV) has received increasing attention and rapid development in recent years. However, existing methods based on prior knowledge struggle to adapt to all scenarios, while learning-based approaches lack paired datasets from real-world scenes, limiting their enhancement capabilities. Consequently, this severely hampers their generalization and application in AUVs. Besides, the existing deep learning-based methods largely overlook the advantages of prior knowledge-based approaches. To address the aforementioned issues, a novel architecture called CodeUNet is proposed in this paper. Instead of relying on physical scattering models, a real-world scene vision enhancement network based on a codebook prior is considered. First, the VQGAN is pretrained on underwater datasets to obtain a discrete codebook, encapsulating the underwater priors (UPs). The decoder is equipped with a novel feature alignment module that effectively leverages underwater features to generate clean results. Then, the distance between the features and the matches is recalibrated by controllable matching operations, enabling better matching. Extensive experiments demonstrate that CodeUNet outperforms state-of-the-art methods in terms of visual quality and quantitative metrics. The testing results of geometric rotation, SIFT salient point detection, and edge detection applications are shown in this paper, providing strong evidence for the feasibility of CodeUNet in the field of autonomous underwater vehicles. Specifically, on the full reference dataset, the proposed method outperforms most of the 14 state-of-the-art methods in four evaluation metrics, with an improvement of up to 3.7722 compared to MLLE. On the no-reference dataset, the proposed method achieves excellent results, with an improvement of up to 0.0362 compared to MLLE. Links to the dataset and code for this project can be found at: https://github.com/An-Shunmin/CodeUNet. [ABSTRACT FROM AUTHOR]

In this work we propose a generalization of the family of Time-Accurate and highly-Stable Explicit (TASE) operators recently introduced by Calvo, Montijano and Rández (2021). In this family the TASE operator of order p depends on p free real parameters. Here we consider operators that can also be defined by complex parameters occurring in conjugate pairs. Despite this choice the calculations continue to be done only in real arithmetic, thus not burdening the computational cost of the previous version of the family. Conversely, this generalization leads to improve both the accuracy and stability properties of explicit Runge-Kutta schemes supplemented with TASE operators. Numerical experiments showing the competitiveness of the methods proposed in this paper with respect to classical integrators for stiff problems are also presented. [ABSTRACT FROM AUTHOR]

In PROPELLER MRI, obtaining sufficient high-quality blade data remains a challenge, so the efficiency and generalization of deep learning-based reconstruction models are deteriorated. Due to narrow rotated and translated blades acquired in PROPELLER, the technique of data augmentation that is used for deep learning-based Cartesian MRI reconstruction cannot be directly applied. To address the issue, this paper introduces a novel approach for the generation of synthetic PROPELLER blades, and it is subsequently employed in data augmentation for undersampled blades reconstruction. The principal aim of this study is to address the challenges of reconstructing undersampled blades to enhance both image quality and computational efficiency. Evaluation metrics including PSNR, NMSE, and SSIM indicate superior performance of the model trained with augmented data compared to non-augmented counterparts. The synthetic blade augmentation significantly enhances the model's generalization capability and enables robust performance across varying imaging conditions. Furthermore, the study demonstrates the feasibility of utilizing synthetic blades exclusively in the training phase, suggesting a reduced dependency on real PROPELLER blades. This innovation in synthetic blade generation and data augmentation technique contributes to enhanced image quality and improved generalization capability of the associated deep learning model for PROPELLER MRI reconstruction. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a generalization of Schrödinger operator, known as Hamiltonian with finite range. We prove the related Gordon's lemma with quantitative conditions which means the absence of point spectrum. [ABSTRACT FROM AUTHOR]

Deepfake videos present a significant challenge in the current media landscape. While current deepfake detection methods demonstrate satisfactory performance, there is still room for improvement in their ability to generalize and detect unseen scenarios, particularly those involving imperceptible cues. This paper introduces a novel multi-modal deepfake detection model named SpectraVisionFusion Transformer (SVFT), which incorporates spatial and frequency domain statistical artifacts to improve generalization performance. The SVFT framework uses two different backbone encoder models to take advantage of both spatial and frequency domain cues in video sequences, along with a decoder and classifier, for common cross-attention and classification, respectively. The spatial domain branch uses a convolutional transformer-based encoder to analyze facial visual features. In contrast, the frequency domain branch employs a language transformer encoder. Additionally, we introduce a weighted feature embedding fusion mechanism that integrates spectral-based statistical feature embeddings and visual cues to achieve a more comprehensive and balanced spatial-frequency feature representation. By coordinately analyzing these modalities, our model exhibits improved detection and generalization capabilities in unseen scenarios. Our proposed SVFT model achieved 92.57% and 80.63% accuracy in extensive cross-manipulation and dataset evaluation, respectively, while surpassing the performance of traditional and single-domain-based approaches. [ABSTRACT FROM AUTHOR]

Guaranteeing the monotonicity of a learned model is crucial to address concerns such as fairness, interpretability, and generalization. This paper develops a new monotonic neural network named Deep Isotonic Embedding Network (DIEN), which uses different modules to deal with monotonic and non-monotonic features respectively, and then combine outputs of these modules linearly to obtain the prediction result. A new embedding tool called Isotonic Embedding Unit is developed to process monotonic features and turn each one into an isotonic embedding vector. By converting non-monotonic features into a series of non-negative weight vectors and then combining them with isotonic embedding vectors that have special properties, we enable DIEN to guarantee monotonicity. Besides, we also introduce a module named Monotonic Feature Learning Network to capture complex dependencies between monotonic features. This module is a monotonic feedforward neural network with non-negative weights and can handle scenarios where there are few non-monotonic features or only monotonic features. In comparison to existing methods, DIEN does not require intricate structures like lattices or the use of additional verification techniques to ensure monotonicity. Additionally, the relationship between DIEN's inputs and outputs is obvious and intuitive. Results from experiments on both synthetic and real-world datasets demonstrate DIEN's superiority over existing methodologies. • A monotonic neural network named Deep Isotonic Embedding Network (DIEN) is proposed. • DIEN employs different modules to deal with monotonic and non-monotonic features. • Outputs of all modules are combined linearly to obtain the prediction result. • A module that captures complex dependencies among monotonic features is introduced. [ABSTRACT FROM AUTHOR]

In a previous paper [4] we tried to build the basic theory of unbounded Tomita's observable algebras called T †-algebras which are related to unbounded operator algebras, especially unbounded Tomita-Takesaki theory, operator algebras on Krein spaces, studies of positive linear functionals on *-algebras and so on. And we defined the notions of regularity, semisimplicity and singularity of T †-algebras and characterized them. In this paper we shall proceed further with our studies of T †-algebras and investigate whether a T †-algebra is decomposable into a regular part and a singular part. [ABSTRACT FROM AUTHOR]

• This paper proposes a novel Multi-scale self-attention mixup approach for graph classification. • This paper innovatively introduces multi-scale graph representation for Mixup. • A novel self-attention strategy is proposed to capture the internal dependencies between different scales within a graph. • Extensive experiments are conducted to demonstrate the effectiveness of the proposed MSSA-Mixup. [Display omitted] Data augmentation can effectively improve the generalization performance of neural networks. However, data augmentation for the graph domain is challenging due to the fact of irregular nature of the special non-Euclidean structure. In this paper, we propose a novel graph data augmentation solution, Multi-Scale Self-Attention Mixup (MSSA-Mixup), which extends the training distribution by interpolating multi-scale graph representation with self-attention. The MSSA-Mixup improves the generalization ability of graph neural networks (GNNs) effectively. Extensive experiments illustrate that the proposed method yields consistent and robust performance boost across graph classification tasks on the frequently-used benchmark datasets. [ABSTRACT FROM AUTHOR]

A mixed dominating set of a graph G = (V , E) is a mixed set D of vertices and edges, such that for every edge or vertex, if it is not in D , then it is adjacent or incident to at least one vertex or edge in D. The mixed domination problem is to find a mixed dominating set with a minimum cardinality. It has applications in system control and some other scenarios and it is NP -hard to compute an optimal solution. This paper studies approximation algorithms and hardness of the weighted mixed dominating set problem. The weighted version is a generalization of the unweighted version, where all vertices are assigned the same nonnegative weight w v and all edges are assigned the same nonnegative weight w e , and the question is to find a mixed dominating set with a minimum total weight. Although the mixed dominating set problem has a simple 2-approximation algorithm, few approximation results for the weighted version are known. The main contributions of this paper include: 1. for w e ≥ w v , a 2-approximation algorithm; 2. for w e ≥ 2 w v , inapproximability within ratio 1.3606 unless P = N P and within ratio 2 under UGC; 3. for 2 w v > w e ≥ w v , inapproximability within ratio 1.1803 unless P = N P and within ratio 1.5 under UGC; 4. for w e < w v , inapproximability within ratio (1 − ϵ) ln ⁡ | V | unless P = N P for any ϵ > 0. [ABSTRACT FROM AUTHOR]

Canonical decompositions, such as the Gallai–Edmonds and Dulmage–Mendelsohn decompositions, are a series of structure theorems that form the foundation of matching theory. The classical Kotzig–Lovász decomposition is a canonical decomposition applicable to a special class of graphs with perfect matchings, called factor-connected graphs, and is famous for its contribution to the studies of perfect matching polytopes and lattices. Recently, this decomposition has been generalized for general graphs with perfect matchings; this generalized decomposition is called the general Kotzig–Lovász decomposition. In fact, this generalized decomposition can be presented as a component of a more composite canonical decomposition called the Basilica decomposition. As such, the general Kotzig–Lovász decomposition has contributed to the derivation of various new results in matching theory, such as an alternative proof of the tight cut lemma and a characterization of maximal barriers in general graphs. Joins in grafts, also known as T -joins in graphs, is a classical concept in combinatorics and is a generalization of perfect matchings in terms of parity. More precisely, minimum joins and grafts are generalizations of perfect matchings and graphs with perfect matchings, respectively. Under the analogy between matchings and joins, analogues of the canonical decompositions for grafts are expected to be strong and fundamental tools for studying joins. In this paper, we provide a generalization of the general Kotzig–Lovász decomposition for arbitrary grafts. Our result also contains Sebö's generalization of the classical Kotzig–Lovász decomposition for factor-connected grafts. From our results in this paper, a generalization of the Dulmage–Mendelsohn decomposition, which is originally a classical canonical decomposition for bipartite graphs, has been obtained for bipartite grafts. This paper is the first of a series of papers that establish a generalization of the Basilica decomposition for grafts. [ABSTRACT FROM AUTHOR]

From the perspective of input features, information can be divided into independent information and correlation information. Current neural networks mainly concentrate on the capturing of correlation information through connection weight parameters supplemented by bias parameters. This paper introduces feature-wise scaling and shifting (FwSS) into neural networks for capturing independent information of features, and proposes a new neural network FwSSNet. In the network, a pair of scale and shift parameters is added before each input of each network layer, and bias is removed. The parameters are initialized as 1 and 0, respectively, and trained at separate learning rates, to guarantee the fully capturing of independence and correlation information. The learning rates of FwSS parameters depend on input data and the training speed ratios of adjacent FwSS and connection sublayers, meanwhile those of weight parameters remain unchanged as plain networks. Further, FwSS unifies the scaling and shifting operations in batch normalization (BN), and FwSSNet with BN is established through introducing a preprocessing layer. FwSS parameters except those in the last layer of the network can be simply trained at the same learning rate as weight parameters. Experiments show that FwSS is generally helpful in improving the generalization capability of both fully connected neural networks and deep convolutional neural networks, and FWSSNets achieve higher accuracies on UCI repository and CIFAR-10. [ABSTRACT FROM AUTHOR]

Deep neural networks are highly vulnerable to adversarial samples. Most existing adversarial defense methods do not consider the distribution of adversarial samples. We argue that very few adversarial samples in the natural sample set prevent the deep neural networks from learning a complete and effective representation of the adversarial samples. This causes the spatial structures between the natural and the adversarial samples to be vastly different from that of the input space, thus making the models vulnerable to adversarial attacks. Based on this viewpoint, this paper proposes an effective deep-learning adversarial defense method, which incorporates information about the spatial structures of the natural and the adversarial samples in the embedding space during the training process. This proposed approach improves the deep learning model's generalization to new adversarial samples and achieves the purpose of defending against adversarial attacks. Four deep neural networks with different scales are used and experimentally verified on four typical publicly available image data. The experimental results show that our method effectively improves the defense ability of deep learning models against adversarial attacks. • Development of an effective adversarial training method using spatial structure constraints in embedding space. • Spatial structure information of the natural and adversarial samples can help improve the adversarial robustness of DNNs. • The spatial structure constrain can be extended to adversarial training of semi-supervised and unsupervised learning. [ABSTRACT FROM AUTHOR]

No, but the paper argues that Bohr understood his correspondence principle, or at least an aspect of that principle expressed by the notion of rational generalization, as grounded in Hankel's principle of permanence, adapted to new historical and theoretical contexts. This is shown to illuminate some otherwise obscure aspects of Bohr's approach to quantum theory, as well as a seemingly strange criticism against this approach, due to Feyerabend and Bohm. [ABSTRACT FROM AUTHOR]

A matching in a graph G is a collection of edges of G such that no two of them share a vertex. The number of all matchings in G is called its Hosoya index. In this paper, we compute Hosoya indices of several classes of unbranched polymers made of cycles of the same lengths arranged around a middle path and decorated by attaching to each vertex, a given number of pendent vertices or thorns. We establish linear recurrences satisfied by those numbers and obtain explicit formulas in terms of Fibonacci polynomials and their generalizations. Some possible directions of future research are also indicated. [ABSTRACT FROM AUTHOR]

We analyze generalization performance of over-parameterized learning methods for classification, under VC-theoretical framework. Recently, practitioners in Deep Learning discovered 'double descent' phenomenon, when large networks can fit perfectly available training data, and at the same time, achieve good generalization for future (test) data. The current consensus view is that VC-theoretical results cannot account for good generalization performance of Deep Learning networks. In contrast, this paper shows that double descent can be explained by VC-theoretical concepts, such as VC-dimension and Structural Risk Minimization. We also present empirical results showing that double descent generalization curves can be accurately modeled using classical VC-generalization bounds. Proposed VC-theoretical analysis enables better understanding of generalization curves for data sets with different statistical characteristics, such as low vs high-dimensional data and noisy data. In addition, we analyze generalization performance of transfer learning using pre-trained Deep Learning networks. • VC-theoretical modeling of double descent. • Different generalization mechanisms for high-dimensional vs. low-dimensional data. • VC approach to modeling generalization performance of transfer learning. [ABSTRACT FROM AUTHOR]

Pseudo-label-based semi-supervised learning (SSL) recently has achieved significant success in unlabeled data utilization. Recent success on pseudo-label-based SSL methods crucially hinges on thresholded pseudo-labeling and consistency regularization for the unlabeled data. However, most of the existing methods do not measure and incorporate the uncertainties due to the noisy pseudo-labels or out-of-distribution unlabeled samples. Therefore, the model's discernment becomes noisier in real-life applications that involve a substantial amount of out-of-distribution unannotated data. This leads to slow convergence in the training process and poor generalization performance. Inspired by the recent developments in SSL, our goal in this paper is to propose a novel unsupervised uncertainty-aware objective and threshold-mediated pseudo-labeling scheme that rely on uncertainty quantification from aleatoric and epistemic sources. By incorporating recent techniques in SSL, our proposed uncertainty-aware framework can mitigate the issue of confirmation bias and the impact of noisy pseudo-labels, resulting in improved training efficiency and enhanced generalization performance within the SSL domain. Despite its simplicity and computational efficiency, our approach demonstrates improved performance compared to state-of-the-art SSL methods on challenging datasets, such as CIFAR-100 and the real-world dataset Semi-iNat. • We introduce an uncertainty SSL loss using the aleatoric and epistemic uncertainty. • The goal is to align the uncertainty distributions of labeled and unlabeled data. • The proposed uncertainty-aware framework improves confidence thresholding in SSL. • Experiments verifies alleviation in noisy pseudo-labeling leading in robust learning. • Our method can be used with any pseudo-label-based SSL to mitigate confirmation bias. [ABSTRACT FROM AUTHOR]

A trigraph is a graph where each pair of vertices is labelled either 0 (a non-arc), 1 (an arc) or ⋆ (both an arc and a non-arc). In a series of papers, Hell and co-authors (see for instance [P. Hell, 2014 [21] ]) proposed to study the complexity of homomorphisms from graphs to trigraphs, called Matrix Partition Problems , where arcs and non-arcs can be both mapped to ⋆-arcs, while a non-arc cannot be mapped to an arc, and vice-versa. Even though Matrix Partition Problems are generalisations of Constraint Satisfaction Problems (CSPs) , they share with them the property of being "intrinsically" combinatorial. So, the question of a possible P-time vs NP-complete dichotomy is a very natural one and was raised in Hell et al.'s papers. We propose a generalisation of Matrix Partition Problems to relational structures and study them with respect to the question of a dichotomy. We first show that trigraph homomorphisms and Matrix Partition Problems are P-time equivalent, and then prove that one can also restrict (with respect to having a dichotomy) to relational structures with a single relation. Failing in proving that Matrix Partition Problems on directed graphs are not P-time equivalent to Matrix Partitions on relational structures, we give some evidence that it might be unlikely by formalising the reductions used in the case of CSPs and by showing that such reductions cannot work for the case of Matrix Partition Problems. We then turn our attention to Matrix Partition problems that can be described by finite sets of (induced-subgraph) obstructions. We show, in particular, that any such problem has finitely many minimal obstructions if and only if it has finite duality. We conclude by showing that on trees (seen as trigraphs) it is NP-complete to decide whether a given tree has a homomorphism to another input trigraph. The latter shows a notable difference on tractability between CSP and Matrix Partition Problems as it is well-known that CSP is tractable on the class of trees. [ABSTRACT FROM AUTHOR]

Accurate sea surface temperature (SST) prediction is of great significance for fishery farming, marine ecological protection, and planning of maritime activities. In this paper, the stacked generalization ensemble is demonstrated for SST prediction to improve every single deep-learning model. Long-term high-resolution satellite-derived SST is used with the sub-regions of the Taiwan Strait and East China Sea taken as the study area. We select the Multilayer Perceptron, Long short-term memory (LSTM), Convolutional Neural Networks (CNN), CNN-LSTM as individual learners, and Convolutional LSTM as the meta-learner. The individual learners are trained and validated on the retained data subset I, while the meta-learner is trained and validated by constructing the samples with the predictions of validated individual learners on the retained data subset II. The two types of models are evaluated on the same test dataset with root-mean-square error and coefficient of efficiency as the scoring criteria. We find that the meta-model outperforms any individual model and other baselines for the one-day-/three-day-ahead forecasts in the Taiwan Strait and one-day-/three-day-/five-day-ahead predictions in the East China Sea. Furthermore, when the lead time is 1 day and 3 days, the meta-model has a better spatial distribution of prediction metrics across all grid points in the Taiwan Strait sub-area. For the East China Sea sub-region, the meta-model advantage is extended to the lead time of 5 days. Probably due to the higher quality of offshore satellite data, the prediction ability enhancement of the stacked ensemble applied in the East China Sea is better than that in the Taiwan Strait. The better-performing meta-model prediction suggests that the stacked generalization ensemble is encouraging and promising for improving the short-term prediction of the daily SST field. • The stacked ensemble of multiple models is conducted for SST prediction. • The stacked ensemble enhancement effects are investigated for different oceans. • Results indicate that stacking can effectively enhance short-term performance. • The improvement effect of the open sea area is better than the near-shore one. [ABSTRACT FROM AUTHOR]

A k -limited packing partition (k LP partition) of a graph G is a partition of V (G) into k -limited packing sets. We consider the k LP partitions with minimum cardinality (with emphasis on k = 2). The minimum cardinality is called k LP partition number of G and denoted by χ × k (G). This problem is the dual problem of k -tuple domatic partitioning as well as a generalization of the well-studied 2-distance coloring problem in graphs. We give the exact value of χ × 2 for trees and bound it for general graphs. A section of this paper is devoted to the dual of this problem, where we give a solution to an open problem posed in 1998. We also revisit the total limited packing number in this paper and prove that the problem of computing this parameter is NP-hard even for some special families of graphs. We give some inequalities concerning this parameter and discuss the difference between 2TLP number and 2LP number with emphasis on trees. [ABSTRACT FROM AUTHOR]

Vector Fitting (VF) is a successful methodology for both time and frequency domain estimation of dynamic systems. These algorithms have gained popularity as a system identification tool due to their ability to provide a practical procedure for accurately approximating the measured frequency response behavior of complex and highly resonant dynamic systems using rational models. Instrumental Variable (IV) techniques can also be added to the VF algorithm to enhance the optimality of the solutions in the presence of measurement noise. In this context, this paper presents a multiple-input multiple-output (MIMO) generalization of instrumental variable (IV-)VF. The proposed algorithm can be applied to accurately estimating models formed by either continuous- or discrete-time rational basis functions (RBFs). We show that such a generalization preserves the main implementation features observed in Standard VF, but with improved optimality property for its solutions. Additionally, in order to alleviate convergence problems that may arise from the fixed high-frequency normalization, we also present in this paper how to incorporate in the proposed IV-VF method the relaxed formulation found in standard VF for both the continuous and discrete-time cases. The resulting MIMO IV-VF algorithm can be easily understood by VF users, and its applicability is discussed by using an estimation case study with two power system pieces of equipment (an 88 kV Transformer and a 550 kV Instrument Transformer) for which actual frequency domain measurements were collected in the field. It is shown that the proposed algorithm significantly improves the modeling accuracy when compared to standard VF algorithms. • Advances in optimal rational approximation of systems using frequency response data. • A MIMO generalization of the Instrumental Variables Vector Fitting method is proposed. • Such a generalization can be used for further refining parameter estimates. • Convergence problems are mitigated by relaxing the proposed method. • Practical validation is performed by fitting actual admittance data of HV transformers. [ABSTRACT FROM AUTHOR]

Modern machine learning algorithms aim to extract fine-grained information from data to provide accurate predictions, which often conflicts with the goal of privacy protection. This paper addresses the practical and theoretical importance of developing privacy-preserving machine learning algorithms that ensure good performance while preserving privacy. In this paper, we focus on the privacy and utility (measured by excess risk bounds) performances of differentially private stochastic gradient descent (SGD) algorithms in the setting of stochastic convex optimization. Specifically, we examine the pointwise problem in the low-noise setting for which we derive sharper excess risk bounds for the differentially private SGD algorithm. In the pairwise learning setting, we propose a simple differentially private SGD algorithm based on gradient perturbation. Furthermore, we develop novel utility bounds for the proposed algorithm, proving that it achieves optimal excess risk rates even for non-smooth losses. Notably, we establish fast learning rates for privacy-preserving pairwise learning under the low-noise condition, which is the first of its kind. [ABSTRACT FROM AUTHOR]

Over the past few decades, Piaget's forms of abstraction have proved productive for developing explanatory models of student and teacher knowledge, yet the broader applicability of his abstraction forms to mathematics education remains an open question. In this paper, we adopt the Piagetian forms of abstraction to accomplish two interrelated goals. Firstly, we analyze instructional tasks to develop hypothetical accounts of the abstractions that might occur during students' engagement with them. Secondly, we draw on middle- and secondary-grades classroom data to discuss the abstractions that occurred during the implementation of those instructional tasks. Because this paper represents an initial attempt at extending the applicability of Piagetian forms of abstraction, we close with potential implications of such use and possible avenues for future research. Most notably, we highlight the complexities involved in supporting abstraction through curriculum and instruction. • We examine task materials and implementation. • We differentiate between forms of abstraction. • We identify abstraction's viability for such analysis. • We differentiate between student learning outcomes. • We suggest avenues for future research. [ABSTRACT FROM AUTHOR]

Post-hoc explaining approaches for deep learning (DL) models has attracted much attention in safety–critical applications such as rotating machinery intelligent fault diagnosis (IFD). However, with the help of the explanation techniques, the models are still fragile to domain shifts caused by varying speeds and loads without help for improving their cross-domain performance. Since humans in the decision-making loop are essential for a reliable diagnostic system to determine the reliability of diagnosis, this paper proposes a causal explaining guided domain generalization (CXDG) method to realize trust worthy IFD with human in the decision loop. Specifically, an explaining model is trained with the conditional mutual information, which is a causal strength metric, and utilized to tell the causal features in the input data as the attributions of the diagnostic model. A translation process of the attributions is proposed to make the explaining process understandable. Furthermore, the aim of this paper is not only explaining but also beyond that the diagnostic model is guided to focus on the causal features to improve its generalization ability in unseen domains. The effectiveness of the method is validated on two experiment datasets. The results show that the proposed method can both explain the attributions of the diagnosis model and be beneficial to the generalization ability. [ABSTRACT FROM AUTHOR]

In data sets some attributes may have higher or lower importance. One of the tools used for data analysis of such datasets are subspace neuro-fuzzy systems. They elaborate fuzzy rules to describe data sets. In subspace neuro-fuzzy systems fuzzy rules exist in subspaces defined with subsets of attributes. In the paper we propose a novel fuzzy biclustering algorithm that groups both objects and attributes in fuzzy clusters. In that way we create a subspace fuzzy rule base for a subspace fuzzy system. The paper is accompanied with numerical examples that show this approach can lead to better generalisation (and thus lower data prediction errors) with preserved interpretation of fuzzy models. [ABSTRACT FROM AUTHOR]

Let G be a group and F an infinite field. Assume that A is a finite dimensional F -algebra with an elementary G -grading. In this paper, we study the graded identities satisfied by the tensor product grading on the F -algebra A ⊗ C , where C is an H -graded colour β -commutative algebra. More precisely, under a technical condition, we provide a basis for the T G -ideal of graded polynomial identities of A ⊗ C , up to graded monomial identities. Furthermore, the F -algebra of upper block-triangular matrices U T (d 1 , ... , d n) , as well as the matrix algebra M n (F) , with an elementary grading such that the neutral component corresponds to its diagonal, are studied. As a consequence of our results, a basis for the graded identities, up to graded monomial identities of degrees ≤ 2 d − 1 , for M d (E) and M q (F) ⊗ U T (d 1 , ... , d n) , with a tensor product grading, is exhibited. In this latter case, d = d 1 + ... + d n. Here E denotes the infinite dimensional Grassmann algebra with its natural Z 2 -grading, and the grading on M q (F) is Pauli grading. The results presented in this paper generalize results from [14] and from other papers which were obtained for fields of characteristic zero. [ABSTRACT FROM AUTHOR]

Neural networks suffer performance degradation when the source and target data lie in a different distribution hampering direct deployment of the model to diverse target domains. To this end, domain generalization (DG) aims to generalize the model well to an unknown target domain by utilizing multiple source domains. This paper proposes two simple swapping mechanisms, texture and channel swapping (TCX), for DG. Texture swapping augments the source dataset by replacing textures of an image with other textures in source dataset to alleviate the texture bias problem in convolution neural networks (CNNs). Furthermore, channel swapping switches channels of input feature vectors of the classifier along with its labels to encourage the model to utilize more channels when classifying an image. Together, we expect the model to learn less domain-specific features but more generalized class-specific features resulting in better domain generalization performance. We demonstrate the effectiveness of our approach with state-of-the-art results on three domain generalization benchmarks. [ABSTRACT FROM AUTHOR]

For a Rirodan array, its vertical half and horizontal half are studied separately before. In this paper, we propose the (m 1 , s 1 , r , m 2 , s 2 , l) -halves of a 3-dimensional Riordan array, which are natural generalizations of the skew halves of a usual Riordan array in [21]. Let G = [ g i , j , k ] i , j , k ≥ 0 be a 3-dimensional Riordan array, its (m 1 , s 1 , r , m 2 , s 2 , l) -halves H = [ h i , j , k ] i , j , k ≥ 0 are defined by h i , j , k = g (m 1 + 1) i + (s 1 − 2) j + r , m 1 i + (s 1 − 1) j + r , m 2 i + (s 2 − 1) j + l k. We obtain that the (m 1 , s 1 , r , m 2 , s 2 , l) -halves of a 3-dimensional Riordan array are all 3-dimensional Riordan arrays. We also consider the (m 1 , s 1 , r , m 2 , s 2 , l) -antecedents of a 3-dimensional Riordan array. [ABSTRACT FROM AUTHOR]

Let G be a connected graph with vertex set V , where the distance between two vertices is the length of a shortest path between them. A set S ⊆ V is [ 1 , 2 ] -resolving if each vertex of G is at most distance-two away from a vertex in S and, given a pair of distinct vertices not in S , either there is a vertex in S adjacent to exactly one member of the given pair, or there are two vertices in S each of which is distance-two from exactly one member of the given pair. The [ 1 , 2 ] -dimension of G is the minimum cardinality of a [ 1 , 2 ] -resolving set of G. In this paper, we study the [ 1 , 2 ] -dimension of graphs by proving that the [ 1 , 2 ] -dimension problem is an NP-complete problem, and determine the [ 1 , 2 ] -dimension of some classes of graphs, such as paths, cycles, and full k -ary trees. We also introduce a generalization of metric dimension of which the (original) metric dimension and the [ 1 , 2 ] -dimension, as well as other metric dimension variants in the literature, are special instances. [ABSTRACT FROM AUTHOR]

Neural architecture search (NAS) is a framework for automating the design process of a neural network structure. While the recent one-shot approaches have reduced the search cost, there still exists an inherent trade-off between cost and performance. It is important to appropriately stop the search and further reduce the high cost of NAS. Meanwhile, the differentiable architecture search (DARTS), a typical one-shot approach, is known to suffer from overfitting. Heuristic early-stopping strategies have been proposed to overcome such performance degradation. In this paper, we propose a more versatile and principled early-stopping criterion on the basis of the evaluation of a gap between expectation values of generalisation errors of the previous and current search steps with respect to the architecture parameters. The stopping threshold is automatically determined at each search epoch without cost. In numerical experiments, we demonstrate the effectiveness of the proposed method. We stop the one-shot NAS algorithms and evaluate the acquired architectures on the benchmark datasets: NAS-Bench-201 and NATS-Bench. Our algorithm is shown to reduce the cost of the search process while maintaining a high performance. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a weaker notion of separability for set-systems and demonstrate that the class of maximal weakly separated systems precisely corresponds to the class of peak-pit maximal Condorcet domains. Additionally, we present a generalisation of arrangements of pseudolines and establish that the sets of chamber sets from them coincide with maximal weakly separated systems, enabling the construction of all peak-pit maximal Condorcet domains. Furthermore, we reveal that peak-pit maximal Condorcet domains coincide with connected maximal Condorcet domains. • Peak-pit maximal Condorcet domains are characterised by weakly separated ideals. • Weakly separated ideals are characterised by generalised arrangements of pseudolines. • Peak-pit maximal Condorcet domains coincide with connected maximal Condorcet domains. • Peak-pit maximal Condorcet domains are copious and ample. • The size of the ideal of any peak-pit maximal Condorcet domain on [n] is n + 1 2 + 1. [ABSTRACT FROM AUTHOR]

In this paper, we introduce weighted bootstrap algorithms for both non-degenerate and degenerate two-sample U -statistics with arbitrary degrees. For the non-degenerate case, weighted bootstrap with dependent weights is introduced as a generalization of Efron's conventional bootstrap. In addition, two weighted bootstrap procedures with independent productive weights and independent additive weights are proposed under non-degeneracy. More importantly, we extend the weighted bootstrap method to two-sample U -statistics under the degeneracy of order 2 with a novel construction of random weights. Theoretical supports of the proposed weighted bootstrap procedures under non-degeneracy and degeneracy of order 2 are established. Numerical studies illustrate that the proposed approaches are feasible and effective for statistical inferences. • Weighted bootstrap for non-degenerate and degenerate two-sample U -statistics. • Weighted bootstrap with independent productive/additive weights under nondegeneracy. • Weighted bootstrap involves a novel construction of random weights under degeneracy. • Proposed weighted bootstrap methods are supported by theoretically and numerically. [ABSTRACT FROM AUTHOR]

Convergence in the presence of multiple equilibrium points is one of the most fundamental dynamical properties of a neural network (NN). Goal of the paper is to investigate convergence for the classic Brain-State-in-a-Box (BSB) NN model and some of its relevant generalizations named Brain-State-in-a-Convex-Body (BSCB). In particular, BSCB is a class of discrete-time NNs obtained by projecting a linear system onto a convex body of R n. The main result in the paper is that the BSCB is convergent when the matrix of the linear system is symmetric and positive semidefinite or, otherwise, it is symmetric and the step size does not exceed a given bound depending only on the minimum eigenvalue of the matrix. This result generalizes previous results in the literature for BSB and BSCB and it gives a solid foundation for the use of BSCB as a content addressable memory (CAM). The result is proved via Lyapunov method and LaSalle's Invariance Principle for discrete-time systems and by using some fundamental inequalities enjoyed by the projection operator onto convex sets as Bourbaki–Cheney–Goldstein inequality. [ABSTRACT FROM AUTHOR]

Communication overhead, computation load, and convergence speed are three major challenges in the scalability of distributed stochastic optimization algorithms in training large neural networks. In this paper, we propose the approach of hybrid-order distributed stochastic gradient descent (HO-SGD) which strikes a better balance between these three than the previous methods, for a general class of non-convex stochastic optimization problems. In particular, we advocate that by properly interleaving zeroth-order and first-order gradient updates, it is possible to significantly reduce the communication and computation overheads while guaranteeing a fast convergence. The proposed method guarantees the same order of convergence rate as in the fastest distributed methods (i.e., fully synchronous SGD) while having significantly less computational complexity and communication overhead per iteration, and the same order of communication overhead as in the state-of-the-art communication-efficient methods, with order-wisely less computational complexity. Moreover, it order-wisely improves the convergence rate of zeroth-order SGD methods. Finally and remarkably, empirical studies demonstrate that the proposed hybrid-order approach provides significantly higher test accuracies and superior generalization than all the baselines, owing to its novel exploration mechanism. • This paper proposes the novel approach of hybrid-order optimization and learning , which strikes a better balance between communication overhead, computational complexity, and convergence rate for distributed optimization and learning than the previous methods. • The proposed method can solve a general class of non-convex stochastic optimization problems with guaranteed convergence to the stationary point. • The proposed method guarantees the same order of convergence rate (in terms of the numbers of iterations and worker nodes) as in the fastest distributed methods (i.e., fully synchronous SGD), while having significantly less computational complexity and communication overhead per iteration. • The proposed method guarantees the same order of communication overhead as in the state-of-the-art communication-efficient methods, with order-wisely less computational complexity. • The proposed method order-wisely improves the convergence rate of zeroth-order SGD methods. • Finally and remarkably, empirical studies demonstrate that the proposed hybrid-order approach provides significantly higher test accuracies and superior generalization than all the baselines, owing to its novel exploration mechanism. • The paper proposes a novel exploration mechanism resulting in better generalization. [ABSTRACT FROM AUTHOR]

Vision transformers have been successfully applied to image recognition tasks due to their ability to capture long-range dependencies within an image. However, they still suffer from weak local feature extraction, easy loss of channel interaction information in one-dimensional multi-head self-attention modeling, and large number of parameters. This paper proposes a lightweight image classification hybrid architecture named EPSViTs (Efficient Parameter Shared Transformer, EPSViTs). Firstly, a new local feature extraction module is designed to effectively enhance the expression of local features. Secondly, using the parameter sharing approach, a lightweight multi-head self-attention module based on information interaction is designed, which can globally model the image from both spatial and channel dimensions, and mine the potential correlation of the image in space and channel. Extensive experiments are conducted on three public datasets, a subset of ImageNet, Cifar100 and APTOS2019, a private dataset Mushroom66, and the results show that the hybrid architecture EPSViTs proposed in this paper based on parameter sharing for multi-head self-attentive image classification has obvious advantages, especially on a subset of ImageNet to reach 89.18%, which is a 3.8% improvement compared to Edgevits_xxs, verifying the effectiveness of the model. • This paper designs a fine-grained local feature extraction module LFE. • This paper designs a lightweight parameter sharing attention mechanism EPSA. • A new lightweight hybrid architecture EPSViTs is built based on the LFE and EPSA. • The reliability and generalization of our model were validated on four datasets. [ABSTRACT FROM AUTHOR]

This paper analyses the process of generalisation of an innovative government-led public practice in the healthcare sector. The scaling and embedding involved in this generalisation process are assumed to be dependent on the multiple implementation processes (consecutive or simultaneous) that lead to a routine use of the innovation in different adopters. This paper, therefore, proposes the use of a configurational theory approach to conceptualise each implementation of the innovation during the generalisation process and shed light on the generalisation's scaling and embedding efforts. It suggests a set of recommendations and practices for generalisation managers, most notably: i) they should regard generalisations as organic processes where their main role is to create space for experimentation, learning and negotiation, and ii) they should adopt different modes of governance to identify adequate mechanisms and strategies and guide their actions. This configurational perspective allows them to monitor and manage the evolution of implementations, informs the valuable learning processes that take place in a generalisation and has been found to be a useful tool to support the crucial collaboration among the actors involved in a generalisation. • Configurational model for innovation implementations in generalisations • Model useful for managing scaling and embedding of government-led public practices • Configurational perspective informs valuable learning processes in generalisations. • Tool useful to support managerial actions to promote generalisation • Framing adequate to leverage the use of flexibility within socio-technical systems [ABSTRACT FROM AUTHOR]

• We show that the Independant Dominating set with Obligations problem is NPC in various cases including paths. • We approach the IDO problem according to the topology of the graph and the properties of the obligations. • We characterize the PIDO problem where the solution does not have to dominate all the vertices of the graphs. • We show that determining if a solution can dominate a square root factor of the vertices for the PIDO problem is NPC. • We show cases where PIDO problem is polynomial and propose a polynomial algorithm to solve them. A subset D ⊆ V is an independent (or stable) dominating set of a graph G = (V , E) if D is an independent set (i.e., there are no edges between vertices of D) and dominates all the vertices of G (each vertex of V − D has a neighbour in D). In this paper, we study a generalisation of this classical notion. Namely, an instance of our problem is a graph G = (V , E) and a partition Π = (V 1 , ... , V k) of V. Each subset V i of Π is called an obligation. An Independent Dominating set with Obligations (IDO) D in an instance (G , Π) is an independent dominating set of G with the additional property that if a vertex u that belongs to the obligation V i is in D , then all the other vertices of V i must also be in D (we say that D respects the obligations). Note that when each obligation of Π is a singleton, an IDO is just an independent dominating set of G that can be constructed with a greedy algorithm. Among other things, we show that the problem of determining whether an instance (G = (V , E) , Π) has an IDO is NP -complete, even if G is a path, if all the obligations are independent sets of G , and if they all have the same constant size λ > 1. We also show that the problem is NP -complete, even if Π is composed of | V | independent obligations each of size | V | or if the diameter of G is three. Our results clearly show that this problem is very difficult, even for extremely restricted instances. Hence, in a second part of the paper, we relax the condition to dominate all the vertices of G. However, we show that determining whether (G = (V , E) , Π) contains an independent set D respecting the obligations and dominating at least 3 | V | − 2 vertices of G is NP -complete, even if G is a collection of disjoint paths and obligations are all independent sets of G. On the positive side, we propose a greedy algorithm constructing a solution dominating at least 2 | V | − 1 vertices in any instance (G = (V , E) , Π) if all obligations of Π are independent sets of G. [ABSTRACT FROM AUTHOR]

Carsten Thomassen and I proved that in any graph G , the number of cycles containing a specified edge as well as all the vertices of odd degree is odd if and only if G is eulerian. Where all vertices have even degree this is a theorem of Shunichi Toida and where all vertices have odd degree it is Andrew Thomason's extension of Smith's Theorem. Our proof was not algorithmic. In this paper, I extend Thomason's algorithm to one which, in a non-eulerian graph, finds a second cycle containing a specified edge and all the odd-degree vertices. Kenneth Berman extended Thomason's Theorem to spanning trees: he proved that if T is a spanning tree such that the degree of every vertex in G − E (T) is odd, then there is an even number of spanning trees of G with the same degree as T at each vertex. In this paper, I give a common generalization of all of these theorems to a parity theorem about "good" trees in general graphs. My proof provides an algorithm for finding a second "good" tree. [ABSTRACT FROM AUTHOR]

Generative adversarial imitation learning (GAIL) regards imitation learning (IL) as a distribution matching problem between the state–action distributions of the expert policy and the learned policy. In this paper, we focus on the generalization and computational properties of policy classes. We prove that the generalization can be guaranteed in GAIL when the class of policies is well controlled. With the capability of policy generalization, we introduce distributional reinforcement learning (RL) into GAIL and propose the greedy distributional soft gradient (GDSG) algorithm to solve GAIL. The main advantages of GDSG can be summarized as: (1) Q-value overestimation, a crucial factor leading to the instability of GAIL with off-policy training, can be alleviated by distributional RL. (2) By considering the maximum entropy objective, the policy can be improved in terms of performance and sample efficiency through sufficient exploration. Moreover, GDSG attains a sublinear convergence rate to a stationary solution. Comprehensive experimental verification in MuJoCo environments shows that GDSG can mimic expert demonstrations better than previous GAIL variants. • Prove the generalization property for policy classes of GAIL. • Demonstrate the reasonableness of reproducing kernel functions in computation. • Introduce distributional RL into GAIL and propose GDSG. • Relieve training imbalance between policy and discriminator; enhance GAIL stability. • GDSG converges to a stationary solution with a sublinear rate. [ABSTRACT FROM AUTHOR]

Fault detection and diagnosis (FDD) is a promising technology for safe operation, quality control, and profitability improvement in chemical process systems. In practice, chemical process systems usually switch among operating conditions in response to market demands, fatigue, malfunctions of components and environments. However, FDD models often deteriorate when transferred from one operating condition to another. Current widely used FDD models are trained and tested in identical domains (or operating conditions) without emphasis on the capability of domain generalization. Furthermore, they ignore the causality that remains invariant among domains but excessively rely on statistical correlation that varies from domain to domain. This paper presents an FDD model named CausalViT. Causality and a gradient reversal operation are designed to enhance domain generalization. In CausalViT, a Causal Layer is constructed to discover the causal mechanism in features to purify superfluous domain-specific statistical correlation. Then, a domain classifier cooperating with gradient reversal layers is developed to further enhance the domain invariance. To evaluate the CausalViT, comparisons have been made between it and other advanced FDD models in six domains/modes in Tennessee Eastman Process. CausalViT shows superiority from the perspectives of both fault detection ratio and domain generalization, obtaining an average 16% improvement on domain generalization. Dimension reduction visualization shows the significance of domain generalization and gives a deeper insight into CausalViT. Furthermore, the convergence of the model and the effectiveness of components in the model have been analyzed and demonstrated. [ABSTRACT FROM AUTHOR]

A graph is k -degenerate if every subgraph H has a vertex v with d H (v) ≤ k. The class of degenerate graphs plays an important role in the graph coloring theory. Observed that every k -degenerate graph is (k + 1) -choosable and (k + 1) -DP-colorable. Bernshteyn and Lee defined a generalization of k -degenerate graphs, which is called weakly k -degenerate. The weak degeneracy plus one is an upper bound for many graph coloring parameters, such as choice number, DP-chromatic number and DP-paint number. In this paper, we give two sufficient conditions for a plane graph without 4- and 6-cycles to be weakly 2-degenerate, which implies that every such graph is 3-DP-colorable and near-bipartite, where a graph is near-bipartite if its vertex set can be partitioned into an independent set and an acyclic set. [ABSTRACT FROM AUTHOR]

Domain shift is the problem in which trained models fail to maintain their performance when they confront new test domains. Cross-scene classification, a technique developed to overcome this challenge, has attracted significant research interest in the field of remote sensing (RS). By exploring the correlation between the source domain and the target domain, relevant models can have better generalization ability regarding the target domain. Nevertheless, Domain Adaptation (DA), as the main technique for cross-scene classification, necessarily requires access to the target samples to assist the model training, a condition that is difficult to satisfy in real-world applications. Domain Generalization (DG) has attracted increasing research attention in recent years. Given one or several source domain(s), DG tends to learn models that can perform well when dealing with unseen (inaccessible) target domains. DG can better deal with out-of-distribution generalization with fewer restrictions, making it a good fit for cross-scene classification. Notably, little research has been conducted on domain generalization in the field of remote sensing. Thus, we refer to this type of method as cross-scene generalization. Recent studies have shown that convolutional neural networks have a strong bias towards recognizing textures rather than shapes. Accordingly, we proposed a Style and Content Separation Network (SCSN) for RS image cross-scene generalization in this paper, which can improve the generalizability and discriminative capability. The Style and Content Separation (SCS) module uses instance normalization to obtain the content information and thereby ensure better generalization ability. Moreover, the residual feature, which contains the style information, can supplement the feature representations after refinement. We further proposed a separation loss to constrain the style and content separation process. Experimental results and relevant analysis demonstrate the effectiveness of the proposed SCSN on cross-scene generalization tasks. Code is available at https://github.com/WHUzhusihan96/SCSN. [ABSTRACT FROM AUTHOR]