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We introduce and study the spatial replicator equation with higher order interactions and both infinite (spatially homogeneous) populations and finite (spatially inhomogeneous) populations. We show that in the special case of three strategies (rock–paper–scissors) higher order interaction terms allow travelling waves to emerge in non-declining finite populations. We show that these travelling waves arise from diffusion stabilisation of an unstable interior equilibrium point that is present in the aspatial dynamics. Based on these observations and prior results, we offer two conjectures whose proofs would fully generalise our results to all odd cyclic games, both with and without higher order interactions, assuming a spatial replicator dynamic. Intriguingly, these generalisations for N ⩾ 5 strategies seem to require declining populations, as we show in our discussion. [ABSTRACT FROM AUTHOR]

The study and modeling of water exchange in complex media using different applications of diffusion and relaxation magnetic resonance (MR) have been of interest in recent years. Most models attempt to describe this process using a first order kinetics expression, which is appropriate to describe chemical exchange; however, it may not be suitable to describe diffusion-driven exchange since it has no direct relationship to diffusion dynamics of water molecules. In this paper, these limitations are addressed through a more general exchange expression that does consider such important properties. This exchange fraction expression features a multi-exponential recovery at short times and a mono-exponential decay at long times, both of which are not captured by the first order kinetics expression. Furthermore, simplified exchange expressions containing partial information of the analyzed system's diffusion and relaxation processes and geometry are proposed, which can potentially be employed in already established estimation protocols. Finally, exchange fractions estimated from simulated MR data and derived here were compared, showing qualitative similarities but quantitative differences, suggesting that the features of the derived exchange fraction in this paper can be partially recovered by employing an existing estimation framework. [ABSTRACT FROM AUTHOR]

Biased and accelerated molecular simulations (BAMS) are widely used tools to observe relevant molecular phenomena occurring on time scales inaccessible to standard molecular dynamics, but evaluation of the physical time scales involved in the processes is not directly possible from them. For this reason, the problem of recovering dynamics from such kinds of simulations is the object of very active research due to the relevant theoretical and practical implications of dynamics on the properties of both natural and synthetic molecular systems. In a recent paper [A. Rapallo et al., J. Comput. Chem. 42, 586–599 (2021)], it has been shown how the coupling of BAMS (which destroys the dynamics but allows to calculate average properties) with Extended Diffusion Theory (EDT) (which requires input appropriate equilibrium averages calculated over the BAMS trajectories) allows to effectively use the Smoluchowski equation to calculate the orientational time correlation function of the head–tail unit vector defined over a peptide in water solution. Orientational relaxation of this vector is the result of the coupling of internal molecular motions with overall molecular rotation, and it was very well described by correlation functions expressed in terms of weighted sums of suitable time-exponentially decaying functions, in agreement with a Brownian diffusive regime. However, situations occur where exponentially decaying functions are no longer appropriate to capture the actual dynamical behavior, which exhibits persistent long time correlations, compatible with the so called subdiffusive regimes. In this paper, a generalization of EDT will be given, exploiting a fractional Smoluchowski equation (FEDT) to capture the non-exponential character observed in the relaxation of intramolecular distances and molecular radius of gyration, whose dynamics depend on internal molecular motions only. The calculation methods, proper to EDT, are adapted to implement the generalization of the theory, and the resulting algorithm confirms FEDT as a tool of practical value in recovering dynamics from BAMS, to be used in general situations, involving both regular and anomalous diffusion regimes. [ABSTRACT FROM AUTHOR]

This paper introduces a spin-free formulation of the supporting subspace factorization [C. Song and T. J. Martínez, J. Chem. Phys. 149, 044108 (2018)], enabling a reduction in the computational scaling of the extended multi-state complete active space second-order perturbation (XMS-CASPT2) method for arbitrary spins. Compared to the original formulation that is defined in the spin orbitals and is limited to singlet states, the spin-free formulation in this work treats different spin states equivalently, thus naturally generalizing the idea beyond singlet states. In addition, we will present a new way of deriving the supporting subspace factorization with the purpose of understanding its physical interpretation. In this new derivation, we separate the sources that make CASPT2 difficult into the "same-site interactions" and "inter-site interactions." We will first show how the Kronecker sum can be used to remove the same-site interactions in the absence of inter-site interactions, leading to MP2 energy in dressed orbitals. We will then show how the inter-site interactions can be exactly recovered using Löwdin partition, where the supporting subspace concept will naturally arise. The new spin-free formulation maintains the main advantage of the supporting subspace factorization, i.e., allowing XMS-CASPT2 energies to be computed using highly optimized MP2 energy codes and Fock build codes, thus reducing the scaling of XMS-CASPT2 to the same scaling as MP2. We will present and discuss results that benchmark the accuracy and performance of the new method. To demonstrate how the new method can be useful in studying real photochemical systems, the supporting subspace XMS-CASPT2 is applied to a photoreaction sensitive to magnetic field effects. The new spin-free formulation makes it possible to calculate the doublet and quartet states required in this particular photoreaction mechanism. [ABSTRACT FROM AUTHOR]

This paper explores the generalization ability of defogging algorithms on RICE (A Remote Sensing Image Dataset for Cloud Removal) remotely sensed images. RICE is a dataset of remotely sensed images used for removing clouds, allowing the researcher to better evaluate the performance of defogging algorithms for cloud removal from remotely sensed images. In this paper, four classical defogging algorithms, including AOD-Net, FFA-Net, dark channel prior, and DehazeFormer, are selected and applied to the task of de-cloud in RICE remote sensing images. The performance of these algorithms on the RICE dataset is analyzed by comparing the experimental results, and their differences, advantages, and disadvantages in dealing with de-clouded remote sensing images are explored. The experimental results show that the four defogging algorithms are capable of performing well on uniform thin cloud images, but there is a color distortion and the performance is weak when it comes to inhomogeneous clouds as well as thick clouds. So, the generalization ability of the algorithms is weak when the defogging algorithms are applied to the problem of cloud removal. Finally, this paper proposes improvement ideas for the de-cloud problem of RICE remote sensing images and looks forward to possible future research directions. [ABSTRACT FROM AUTHOR]

Sketch maps are valuable tools used across various disciplines including spatial cognition, environmental psychology, and spatial reasoning. A common approach to evaluate sketch maps in research is to align and compare them with metric maps. However, sketch maps are highly abstract and contain generalized information causing difficulty in their alignment. Current approaches to study sketch maps cannot handle generalized information. They require a one-on-one correspondence between features in the metric map and features in the sketch map. But memory is often generalized. This paper makes two contributions to the research on sketch maps: (i) we present an algorithmic approach to detect generalization in sketch maps (ii) we present an online tool that creates a generalized metric map corresponding to features in sketch maps. Previously, we identified nine types of generalization in sketch maps. In this paper, we develop formal operators to detect these generalizations and implement them as an online tool. We evaluated our algorithm with a set of 11 sketch maps containing 84 instances of generalization. The results indicated that our algorithm consistently detects instances of generalization in sketch maps. [ABSTRACT FROM AUTHOR]

The Friendship Paradox is a simple and powerful statement about node degrees in a graph. However, it only applies to undirected graphs with no edge weights, and the only node characteristic it concerns is degree. Since many social networks are more complex than that, it is useful to generalize this phenomenon, if possible, and a number of papers have proposed different generalizations. Here, we unify these generalizations in a common framework, retaining the focus on undirected graphs and allowing for weighted edges and for numeric node attributes other than degree to be considered, since this extension allows for a clean characterization and links to the original concepts most naturally. While the original Friendship Paradox and the Weighted Friendship Paradox hold for all graphs, considering non-degree attributes actually makes the extensions fail around 50% of the time, given random attribute assignment. We provide simple correlation-based rules to see whether an attribute-based version of the paradox holds. In addition to theory, our simulation and data results show how all the concepts can be applied to synthetic and real networks. Where applicable, we draw connections to prior work to make this an accessible and comprehensive paper that lets one understand the math behind the Friendship Paradox and its basic extensions. [ABSTRACT FROM AUTHOR]

The class of generalized S D D 1 (G S D D 1 ) matrices is a new subclass of H -matrices. In this paper, we focus on the subdirect sum of G S D D 1 matrices, and some sufficient conditions to ensure that the subdirect sum of G S D D 1 matrices with strictly diagonally dominant (S D D) matrices is in the class of G S D D 1 matrices are given. Moreover, corresponding examples are given to illustrate our results. The class of generalized matrices is a new subclass of -matrices. In this paper, we focus on the subdirect sum of matrices, and some sufficient conditions to ensure that the subdirect sum of matrices with strictly diagonally dominant matrices is in the class of matrices are given. Moreover, corresponding examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper presents an extension of Bhargava's theory of factorials associated to any nonempty subset S of Z. Bhargava's factorials k ! S are invariants, constructed using the notion of p -orderings of S where p is a prime. This paper defines b -orderings of any nonempty subset S of Z for all integers b ≥ 2 , as well as "extreme" cases b = 1 and b = 0. It defines generalized factorials k ! S , T and generalized binomial coefficients ( k + ℓ k ) S , T as nonnegative integers, for all nonempty S and allowing only b in T ⊆ N. It computes b -ordering invariants when S is Z and when S is the set of all primes. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite Systems (GNSS) offer comprehensive position, navigation, and timing (PNT) estimates worldwide. Given the growing demand for reliable location awareness in both indoor and outdoor contexts, the advent of fifth-generation mobile communication technology (5G) has enabled expansive coverage and precise positioning services. However, the power received by the signal of interest (SOI) at terminals is notably low. This can lead to significant jamming, whether intentional or unintentional, which can adversely affect positioning receivers. The diagnosis of jamming types, such as classification, assists receivers in spectrum sensing and choosing effective mitigation strategies. Traditional jamming diagnosis methodologies predominantly depend on the expertise of classification experts, often demonstrating a lack of adaptability for diverse tasks. Recently, researchers have begun utilizing convolutional neural networks to re-conceptualize a jamming diagnosis as an image classification issue, thereby augmenting recognition performance. However, in real-world scenarios, the assumptions of independent and homogeneous distributions are frequently violated. This discrepancy between the source and target distributions frequently leads to subpar model performance on the test set or an inability to procure usable evaluation samples during training. In this paper, we introduce LJCD-Net, a deep adversarial migration-based cross-domain jamming generalization diagnostic network. LJCD-Net capitalizes on a fully labeled source domain and multiple unlabeled auxiliary domains to generate shared feature representations with generalization capabilities. Initially, our paper proposes an uncertainty-guided auxiliary domain labeling weighting strategy, which estimates the multi-domain sample uncertainty to re-weight the classification loss and specify the gradient optimization direction. Subsequently, from a probabilistic distribution standpoint, the spatial constraint imposed on the cross-domain global jamming time-frequency feature distribution facilitates the optimization of collaborative objectives. These objectives include minimizing both the source domain classification loss and auxiliary domain classification loss, as well as optimizing the inter-domain marginal probability and conditional probability distribution. Experimental results demonstrate that LJCD-Net enhances the recognition accuracy and confidence compared to five other diagnostic methods. [ABSTRACT FROM AUTHOR]

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]

We provide generalizations of a class of stochastic Gronwall inequalities that has been studied by von Renesse and Scheutzow (2010), Scheutzow (2013), Xie and Zhang (2020) and Mehri and Scheutzow (2021). This class of stochastic Gronwall inequalities is a useful tool for SDEs. Our focus are convex generalizations of the Bihari-LaSalle type. The constants we obtain are sharp. In particular, we provide new sharp constants for the stochastic Gronwall inequalities. The proofs are connected to a domination inequality by Lenglart (1977), an inequality by Pratelli (1976) and a characterization of Lenglart's concept of domination via the Snell envelope. The inequalities we study appear for example in connection with exponential moments of solutions to path-dependent SDEs: For non-path-dependent SDEs, criteria for the finiteness of exponential moments are known. To be able to extend these proofs to the path-dependent case, a convex generalization of a stochastic Gronwall inequality seems necessary. Using the results of this paper, we obtain a criterion for the finiteness of exponential moments which is similar to that known for non-path-dependent SDEs. Stochastic Gronwall inequalities can also be applied to study other types of SDEs than path-dependent SDEs: An estimate of this paper is applied by Agresti and Veraar (2023) to prove global well-posedness for reaction-diffusion systems with transport noise. [ABSTRACT FROM AUTHOR]

In this paper, we propose a unified concept encompassing generalizations of two types of families defined based on Levine's notions of generalized closed sets and Maki's  Λ  sets. The methods used in this investigation are described in my previous work, where a unified concept of general closedness is presented. From a methodology point of view, the present concept is symmetric to the previous. In generalizing open subsets, one can use the two methods. According to the first one, the family of Levine's generalization is used as some base to build the family of closed subsets of the new topology. In the second method, the family of open subsets is extended, in the same way, as the family of closed subsets in the classic Levine's method. The results obtained in this general conception easily extend and imply well-known theorems of this area of investigation. In the literature on this issue, many versions of generalizations of  Λ -sets have been investigated. The tools used in this paper enabled us to prove that there exist at most 10 generalizations of these types, and we show the relationships between them in the graph. As a result, it turns out that some generalizations investigated in the literature are trivial. [ABSTRACT FROM AUTHOR]

This paper presents some generalizations of a Thébault conjecture, provides an analog of the Thébault conjecture for the -simplex, and also solves a conjecture in a 2022 paper by the authors by using linear algebra. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a complete and simplified solution procedure for the inventory model under trapezoidal type demand, Weibull-distributed deterioration, and partial backlogging. A published paper already provide a solution approach for this kind of inventory models. However, we will show that his approach is too complicated that depending on the partition the domain of a trapezoidal type demand to result in three sub-optimal problems. However, this paper will show that the already exist approach is correct but tedious. Moreover, a generalization of this kind of inventory systems from a trapezoidal type demand to any positive demand under a condition of generalized backlogged rate is also developed by this paper. [ABSTRACT FROM AUTHOR]

Long Short-Term Memory (LSTM) is an effective method for stock price prediction. However, due to the nonlinear and highly random nature of stock price fluctuations over time, LSTM exhibits poor stability and is prone to overfitting, resulting in low prediction accuracy. To address this issue, this paper proposes a novel variant of LSTM that couples the forget gate and input gate in the LSTM structure, and adds a "simple" forget gate to the long-term cell state. In order to enhance the generalization ability and robustness of the variant LSTM, the paper introduces an attention mechanism and combines it with the variant LSTM, presenting the Attention Mechanism Variant LSTM (AMV-LSTM) model along with the corresponding backpropagation algorithm. The parameters in AMV-LSTM are updated using the Adam gradient descent method. Experimental results demonstrate that the variant LSTM alleviates the instability and overfitting issues of LSTM, effectively improving prediction accuracy. AMV-LSTM further enhances accuracy compared to the variant LSTM, and compared to AM-LSTM, it exhibits superior generalization ability, accuracy, and convergence capability. [ABSTRACT FROM AUTHOR]

Gothic preverb compounds illustrate several interesting characteristics, including multiple preverb stacking, idiomatisation, tmesis (i.e., separation by clitics), and P-copying (i.e., multiple pronunciation of the preverb). This paper is a close examination of the morphosyntax of these compounds, highlighting novel empirical generalisations about the Gothic language with key theoretical implications for our understanding of Germanic complex verbs and the alternations they participate in. In particular, this paper proposes a structural distinction between preverb compounds which are obligatorily semantically transparent and those which are optionally idiomatic. In arguing that transparent compounds involve the mechanism of preposition incorporation and m-merger, paralleling recent accounts of clitic doubling, while idiomatic compounds involve a thematic high applicative projection, this paper captures nuanced differences in these compounds' case assignment and argument licensing behaviour. These structural differences will be shown to derive these two compound types' constrained interaction with the aforementioned phenomena of stacking, tmesis, and copying. In addition, this paper compares Gothic complex verbs to their cross-linguistic correlates within and beyond Germanic, whilst also providing a diachronic pathway for the development of (multiple) preverb compounds. [ABSTRACT FROM AUTHOR]

This paper reviews several theoretical works on the computation of the Rate of Occurrence of Failure (ROCOF) for general multi-state random systems, focusing on recent generalizations. The discussion begins by defining the ROCOF for a Markov process and discussing the main results achieved in the literature, then moves towards the richer framework represented by semi-Markov systems. The paper discusses complications that arise when extending the ROCOF to higher orders so that a measure of the association of failures in time can be obtained. The work then analyzes possible modifications in terms of a conditional version of the ROCOF, which is of special interest in applications. The findings are illustrated by a numerical example from reliability, and the broad applicability is demonstrated by a discussion of different applications in other domains. [ABSTRACT FROM AUTHOR]

In this article, 3-parameter generalized quaternionic Leonardo p-sequence which is a quaternion generalization of the Leonardo p-sequence is presented. Several properties are examined by means of their homogeneous and non-homogeneous recursive relations. According to the special cases of 3-parameter, λ iє {1,2,3} and p all the results given in paper are reducible to all quaternions mentioned in this paper. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to advance the concept of region reaching control for a single robot to the study of region reaching consistency for uncertain fully‐actuated multi‐robot systems formulated by Lagrange dynamics. By introducing a directed network communication topology and utilizing the pinning‐like control methods, a distributed region reaching consensus control strategy is proposed. The desired region shape can be specified by selecting an appropriate potential objective function. A feature of the developed region reaching consensus algorithm is fully distributed, which is also an important generalization of pinning‐like set point tracking scheme based on the typical proportion‐integration‐differentiation control scheme. More importantly, the scope of consistency in this paper can be explicitly defined, which is different from traditional consistency control algorithms. Subsequently, numerical examples are presented to illustrate the performance of the designed controllers. [ABSTRACT FROM AUTHOR]

The use of the efficient score statistic in sequential monitoring procedures is reviewed and analysed. Various models that arise in applications are considered. The efficient score vector has the same optimality property as the generalized likelihood ratio, but it has a simple-structure requiring fewer estimations, and this is especially important when the data have a complicated structure. Furthermore, with the efficient score vector it is possible to detect which component of the parameter vector is different from the hypothetical or the historical value. The problems we solve here were the subjects of separate publications, but with the new methodology they are easily calculated examples. [ABSTRACT FROM PUBLISHER]

In this short paper we show that the results obtained by [N. Hussain, V. Parvaneh, B. Samet and C. Vetro, Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory and Applications (2015) 2015:185] can be obtained without the continuity assumption for the self mapping. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behaviour of a Caginalp-type phase field system derived from a heat conduction law which is a generalization of the Maxwell–Cattanéo law and whose potential is singular. This type of law has the advantage of correcting the paradox of heat conduction that appears when the Fourier law is considered. The potential considered is typically logarithmic. Using such a potential makes the model much more relevant from a physical point of view. However, from a theoretical point of view, it is essential to obtain the strict separation property of the phase field in order to give sense of the equations. We first prove the existence and uniqueness of the solution thanks to the separation property. We also address the question of the dissipativity of the system. Finally, we obtain the existence of the global attractor. [ABSTRACT FROM AUTHOR]

ABSTRACT Unlike the simplification of individual lines, the generalization of contour clusters oriented to geographical features is a structured generalization behavior that extracts knowledge of geographical features form the perspective of spatial cognition. In decision level, terrain generalization is essentially a similarity transformation between the geomorphic structures corresponding to multi‐scale contour cluster. However, the multi‐scale structural similarity relations are not directly connected with the application of contour generalization. Therefore, this paper presents an automated method for terrain contour structured generalization considering multi‐scale structural similarity. Firstly, a drainage tree structure is constructed from contour lines to establish associations between valley branches and contour bends. Then, the quantitative relationships between multi‐scale structural similarity and map scale changes are explored using an indirect quantitative expression method. Finally, the contour structural generalization is fully automated through iterative optimization principle based on the multi‐scale structural similarity relations. The experiment results demonstrate the rationality and feasibility of fully automating the contour generalization process based on multi‐scale geomorphic structural similarity relations. And the proposed method not only overcomes the challenge of determining “how much to select” in map generalization, but also is valuable for enriching the content of spatial similarity relations and map generalization, thereby providing a theoretical method system and support for the construction of national basic vector databases. [ABSTRACT FROM AUTHOR]

Aiming to improve the robustness and adaptiveness of the recently investigated capped norm linear discriminant analysis (CLDA), this paper proposes a regularized linear discriminant analysis based on the generalized capped l 2 , q -norm (GCLDA). Compared to CLDA, there are two improvements in GCLDA. Firstly, GCLDA uses the capped l 2 , q -norm rather than the capped l 2 , 1 -norm to measure the within-class and between-class distances for arbitrary q > 0 . By selecting an appropriate q, GCLDA is adaptive to different data, and also removes extreme outliers and suppresses the effect of noise more effectively. Secondly, by taking into account a regularization term, GCLDA not only improves its generalization ability but also avoids singularity. GCLDA is solved through a series of generalized eigenvalue problems. Experiments on an artificial dataset, some real world datasets and a high-dimensional dataset demonstrate the effectiveness of GCLDA. [ABSTRACT FROM AUTHOR]

AbstractThis paper is concerned with generalizing the results for Lie CT-algebras to Leibniz algebras. In some cases our results give a generalization even for the case of a Lie algebra. Results on A-algebras are used to show every Leibniz CT-algebra over an algebraically closed field of characteristic different from 2,3 is solvable or is isomorphic to sl2(F). A characterization is then given for solvable Leibniz CT-algebras. It is also shown that the class of solvable Leibniz CT-algebras is factor closed. [ABSTRACT FROM AUTHOR]

The Gross–Pitaevskii (GP) equation is a model for the description of the dynamics of Bose–Einstein condensates. Here, we consider the GP equation in a two‐dimensional setting with an external periodic potential in the x$x$‐direction and a harmonic oscillator potential in the y$y$‐direction in the so‐called tight‐binding limit. We prove error estimates which show that in this limit the original system can be approximated by a discrete nonlinear Schrödinger equation. The paper is a first attempt to generalize the results from [19] obtained in the one‐dimensional setting to higher space dimensions and more general interaction potentials. Such a generalization is a non‐trivial task due to the oscillations in the external periodic potential which become singular in the tight‐binding limit and cause some irregularity of the solutions which are harder to handle in higher space dimensions. To overcome these difficulties, we work in anisotropic Sobolev spaces. Moreover, additional non‐resonance conditions have to be satisfied in the two‐dimensional case. [ABSTRACT FROM AUTHOR]

AbstractLeibniz algebras are certain generalizations of Lie algebras. Motivated by the concept of subinvariance and ascendancy in group theory, Schenkman studied properties of subinvariant subalgebras of a Lie algebra. Kawamoto studied ascendency in Lie algebras. In this paper we define subinvariance and asendency in Leibniz algebras and study their properties. It is shown that the signature results on subinvariance and ascendency in Lie algebras have analogs for Leibniz algebras. [ABSTRACT FROM AUTHOR]

AbstractIntegral equations form an essential part of nonlinear analysis. In many situations, when seeking solutions to such equations, we utilize fixed-point theorems. Among the most well-known and useful in this regard are the theorems of Darbo and Sadovskii, which generalize the classical results of Schauder and Tikhonov. These theorems have seen many generalizations. The aim of the paper is to strengthen (by weakening the assumptions) several known Darbo- and Sadovskii-type fixed-point theorems in the so-called power version for Fréchet spaces, which are particularly useful for studying the solvability of equations defined on an unbounded interval. A theorem on the existence of solutions to a nonlinear integral equation, illustrating the application of our main result, is also provided. [ABSTRACT FROM AUTHOR]

Performing data augmentation in medical named entity recognition (NER) is crucial due to the unique challenges posed by this field. Medical data is characterized by high acquisition costs, specialized terminology, imbalanced distributions, and limited training resources. These factors make achieving high performance in medical NER particularly difficult. Data augmentation methods help to mitigate these issues by generating additional training samples, thus balancing data distribution, enriching the training dataset, and improving model generalization. This paper proposes two data augmentation methods—Contextual Random Replacement based on Word2Vec Augmentation (CRR) and Targeted Entity Random Replacement Augmentation (TER)—aimed at addressing the scarcity and imbalance of data in the medical domain. When combined with a deep learning-based Chinese NER model, these methods can significantly enhance performance and recognition accuracy under limited resources. Experimental results demonstrate that both augmentation methods effectively improve the recognition capability of medical named entities. Specifically, the BERT-BiLSTM-CRF model achieved the highest F1 score of 83.587%, representing a 1.49% increase over the baseline model. This validates the importance and effectiveness of data augmentation in medical NER. [ABSTRACT FROM AUTHOR]

AbstractRoad network selection plays a key role in map generalization for creating multi-scale road network maps. Existing methods usually determine road importance based on road geometric and topological features, few evaluate road importance from the perspective of road utilization based on human travel data, ignoring the functional values of roads, which leads to a mismatch between the generated results and people’s needs. This paper develops two functional semantic features (i.e. travel path selection probability and regional attractiveness) to measure the functional importance of roads and proposes an automatic road network selection method based on graph convolutional networks (GCN), which models road network selection as a binary classification. Firstly, we create a dual graph representing the source road network and extract road features including six graphical and two functional semantic features. Then, we develop an extended GCN model with connectivity loss for generating multi-scale road networks and propose a refinement strategy based on the road continuity principle to ensure road topology. Experiments demonstrate the proposed model with functional features improves the quality of selection results, particularly for large and medium scale maps. The proposed method outperforms state-of-the-art methods and provides a meaningful attempt for artificial intelligence models empowering cartography. [ABSTRACT FROM AUTHOR]

The precise formal account of the contextuality of the quantum measurement provided by the Kochen-Specker theorem allows for a unique insight into the nature of the contextuality of theological language. The conceptual analysis carried out in this paper has demonstrated that despite of the methodological difficulties in juxtaposing theoretical physics and theology, legitimate bridges can be established between them whereby quantum contextuality may serve as a model of contextuality in theology. A structural factor in the form of a richer logic proper to the Divine nature has been identified as the possible source of contextuality of theological discourse. [ABSTRACT FROM AUTHOR]

Feedforward multilayer perceptron models (MLPs) have been applied to power distribution system state estimation (DSSE) in the past. Existing methods usually employ an ad-hoc or trial and error approach to MLP hyperparameter selection, and thus a systematic way of selecting the optimal hyperparameters including the number of neurons per hidden layer, learning rate, number of training epochs and training batch size is desirable and needed. This paper presents an approach based on Bayesian Optimization with Gaussian Processes for selecting MLP model hyperparameters for state estimation purposes. Results of the optimized MLP models are presented alongside the unoptimized models to compare performance of training, testing, and validation in terms of root-mean-squared-error (RMSE). Additionally, machine learning pipelines were employed and total execution time (seconds) for each trial is presented. The study shows that the MLP models obtained through the proposed optimization method outperform unoptimized models in terms of generalization capability for unseen, new cases. [ABSTRACT FROM AUTHOR]

Recently, the fixed-point theorem for fuzzy contractive mappings has been investigated within the framework of intuitionistic fuzzy metric-like spaces. This interesting topic was explored through the utilization of G-Cauchy sequences as defined by Grabiec. The aim of this study is to enhance the aforementioned results in a few aspects. Initially, the proof of the fixed-point theorem is simplified and condensed, allowing for potential generalization to papers focusing on similar fixed-point analyses. Furthermore, instead of G-Cauchy sequences, the classical Cauchy sequences proposed by George and Veeramani are examined, incorporating an additional condition on the fuzzy metric. Within this context, a solution to an old unresolved question posed by Gregory and Sapena is provided. The findings are reinforced by relevant examples. Finally, the introduced fuzzy metrics are applied to the field of image processing. [ABSTRACT FROM AUTHOR]

In this paper, by introducing multiple parameters, we establish a discrete version of the Hardy–Littlewood–Polya inequality in the whole plane. For the obtained inequality, we give the equivalent statements of the best possible constant factor linked to the parameters and deal with the equivalent inequalities. Our main result provided a new generalization of Hardy–Littlewood–Polya inequality, and as a consequence, we show that some new inequalities of the Hardy–Littlewood–Polya type can be derived from the current results by taking the special values of parameters. [ABSTRACT FROM AUTHOR]

This paper addressed the finite-time multistability of a Caputo fractional order multidirectional associative memory neural network (FMAMNN) with multiple orders, where the fractional orders are not limited to 0 to 1. There are three main findings. Firstly, by using Brouwer fixed point theorem, the existence conditions of multiple equilibria of FMAMNN with Gaussian-wavelet-type activation functions were obtained, and the number of equilibria is (2 + s 2) l , where the exponent l is determined by the number of neurons, and s is the number of segments in the middle of Gaussian-wavelet-type activation function. Another important contribution of this article is the generalization of the Gronwall inequality. By utilizing the multivariable Mittag-Leffler function, a more general form of the Gronwall inequality was obtained, which can be applied to systems with many different fractional derivatives. Lastly, based on the generalized Gronwall inequality, and using the Laplace transform, inverse Laplace transform, some conditions of finite-time multistability of FMAMNN were found, which depend on all fractional orders. Numerical calculations show that compared to the existing finite-time stability conditions of neural networks, the conditions based on the generalized Gronwall inequality have less conservatism. An example was given to show the validity of theoretical results. [ABSTRACT FROM AUTHOR]

The transient stability assessment based on machine learning faces challenges such as sample data imbalance and poor generalization. To address these problems, this paper proposes an intelligent enhancement method for real-time adaptive assessment of transient stability. In the offline phase, a convolutional neural network (CNN) is used as the base classifier. A model training method based on contrastive learning is introduced, aiming to increase the spatial distance between positive and negative samples in the mapping space. This approach effectively improves the accuracy of the model in recognizing unbalanced samples. In the online phase, when real data with different distribution characteristics from the offline data are encountered, an active transfer strategy is employed to update the model. New system samples are obtained through instance transfer from the original system, and an active sampling strategy considering uncertainty is designed to continuously select high-value samples from the new system for labeling. The model parameters are then updated by fine-tuning. This approach drastically reduces the cost of updating while improving the model's adaptability. Experiments on the IEEE39-node system verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Nowadays, autonomous driving technology has become widely prevalent. The intelligent vehicles have been equipped with various sensors (e.g., vision sensors, LiDAR, depth cameras etc.). Among them, the vision systems with tailored semantic segmentation and perception algorithms play critical roles in scene understanding. However, the traditional supervised semantic segmentation needs a large number of pixel-level manual annotations to complete model training. Although few-shot methods reduce the annotation work to some extent, they are still labor intensive. In this paper, a self-supervised few-shot semantic segmentation method based on Multi-task Learning and Dense Attention Computation (dubbed MLDAC) is proposed. The salient part of an image is split into two parts; one of them serves as the support mask for few-shot segmentation, while cross-entropy losses are calculated between the other part and the entire region with the predicted results separately as multi-task learning so as to improve the model's generalization ability. Swin Transformer is used as our backbone to extract feature maps at different scales. These feature maps are then input to multiple levels of dense attention computation blocks to enhance pixel-level correspondence. The final prediction results are obtained through inter-scale mixing and feature skip connection. The experimental results indicate that MLDAC obtains 55.1% and 26.8% one-shot mIoU self-supervised few-shot segmentation on the PASCAL- 5 i and COCO- 20 i datasets, respectively. In addition, it achieves 78.1% on the FSS-1000 few-shot dataset, proving its efficacy. [ABSTRACT FROM AUTHOR]

K-UR, K-LUR and K-R are the generalizations of UR, LUR and R respectively, which are of great significance in Banach space theory. While in Orlicz–Lorentz function space Λ φ , ω ∘ [ 0 , γ) equipped with the Orlicz norm, the research methods of K-UR, K-LUR and K-R are much more complicated than those of UR, LUR and R. In this paper we obtain some criteria of K-UR, K-LUR and K-R of Λ φ , ω ∘ [ 0 , γ) by means of the norm of dual space and Hμ property of Λ φ , ω ∘ [ 0 , γ) . [ABSTRACT FROM AUTHOR]

AbstractA J-frame is a pointfree topology counterpart of the concept of a J-space. In this paper, we present a study of some frames satisfying conditions that are stronger (and some that are weaker) than those defining J-frames. Conditions under which these frames coincide with J-frames are established - pointing out similarities and differences among these frames in the process. Moreover, JC-frames are introduced by mimicking the defining conditions of a J-frame, modulo replacing “compact” with “connected.” We show that all connected frames are JC-frames, not conversely. Any frame that can be written as a join of two disjoint connected sublocales is a JC-frame. Upon recalling that a frame with no points is a J-frame if and only if it is connected, we infer that all non-spatial J-frames are JC-frames. [ABSTRACT FROM AUTHOR]

For gapped periodic systems (insulators), it has been established that the insulator is topologically trivial (i.e., its Chern number is equal to 0) if and only if its Fermi projector admits an orthogonal basis with finite second moment (i.e., all basis elements satisfy ∫ | x | 2 | w (x) | 2 d x < ∞ ). In this paper, we extend one direction of this result to non-periodic gapped systems. In particular, we show that the existence of an orthogonal basis with slightly more decay ( ∫ | x | 2 + ϵ | w (x) | 2 d x < ∞ for any ϵ > 0 ) is a sufficient condition to conclude that the Chern marker, the natural generalization of the Chern number, vanishes. [ABSTRACT FROM AUTHOR]

In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define a Hitchin map and give a spectral correspondence. We also state a Hitchin–Kobayashi correspondence for a generalization of Hitchin's equations to this situation. In a certain sense, this theory lies halfway between the theories of Higgs bundles on a curve and on a higher-dimensional variety. [ABSTRACT FROM AUTHOR]

Starting from any finite simple graph, one can build a reflexive polytope known as a symmetric edge polytope. The first goal of this paper is to show that symmetric edge polytopes are intrinsically matroidal objects: more precisely, we prove that two symmetric edge polytopes are unimodularly equivalent precisely when they share the same graphical matroid. The second goal is to show that one can construct a generalized symmetric edge polytope starting from every regular matroid. Just like in the usual case, we are able to find combinatorial ways to describe the facets and an explicit regular unimodular triangulation of any such polytope. Finally, we show that the Ehrhart theory of the polar of a given generalized symmetric edge polytope is tightly linked to the structure of the lattice of flows of the dual regular matroid. [ABSTRACT FROM AUTHOR]

Recently, motivated by the theory of real local Arthur packets, making use of the wavefront sets of representations over non-Archimedean local fields |$F$|⁠ , Ciubotaru, Mason-Brown, and Okada defined the weak local Arthur packets consisting of certain unipotent representations and conjectured that they are unions of local Arthur packets. In this paper, we prove this conjecture for |$\textrm{Sp}_{2n}(F)$| and split |$\textrm{SO}_{2n+1}(F)$| with the assumption of the residue field characteristic of |$F$| being large. In particular, this implies the unitarity of these unipotent representations. We also discuss the generalization of the weak local Arthur packets beyond unipotent representations, which reveals the close connection with a conjecture of Jiang on the structure of wavefront sets for representations in local Arthur packets. [ABSTRACT FROM AUTHOR]

Since the 1970s and 1980s, significant contributions have been made by Weiss, Butnariu, Heilpern, Chitra, Subrahmanyam, and others, extending fixed-point theorems to fuzzy mappings and topological spaces. This paper provides two generalizations of two important fixed-point theorems, one provided by Butnariu and the other provided by Chitra. The first generalization ensures that, under certain conditions, an acyclic fuzzy mapping has a fixed point. The second result ensures the existence of a point in the intersection of two or more fuzzy mappings considering contractible finite dimensional ANR spaces, which is a generalization of the statement provided by Chitra. [ABSTRACT FROM AUTHOR]