(f(x), m)-interleaved sequences over Fq have been proposed and studied. Roughly speaking, an (f(x), m)-interleaved sequence is a sequence which is made of (or say, interleaved by) m component sequences with a common c...
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(f(x), m)-interleaved sequences over Fq have been proposed and studied. Roughly speaking, an (f(x), m)-interleaved sequence is a sequence which is made of (or say, interleaved by) m component sequences with a common characteristic polynomial (f(x)(∈Fq [x]). in this note, (7(x), m)-interleaved sequences are studied further. As a result, it is made clear how their minimal characteristic polynomials, linear spans and periods are determined by their component sequences. And also, their period distribution and the number of (f(x), m)-interleaved sequences with maximal linear spans are derived. Furthermore, a large number of interleaved sequences with the lowest correlation among ali the (f(x), m)-interleaved sequences are constructed.
The multiplication of points on elliptic curves is the most important operation in the implementation of elliptic curve cryptosystems. Based on Frobenius map, a fast multiplication on the curves defined by y2 + xy = x...
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The multiplication of points on elliptic curves is the most important operation in the implementation of elliptic curve cryptosystems. Based on Frobenius map, a fast multiplication on the curves defined by y2 + xy = x3 + x2 + 1 over finite fields of characteristic 2 is given, and its optimality in the sense of using minimal numbers of additions of points is proved.
In this paper, the theory of continued fractions of algebraic functions will be used to give a general theorem on lower bounds for class numbers of real quadratic function fields K=k(D). The bounds are given more expl...
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In this paper, the theory of continued fractions of algebraic functions will be used to give a general theorem on lower bounds for class numbers of real quadratic function fields K=k(D). The bounds are given more explicitly for six types of real quadratic function fields. As a consequence, six classes of real quadratic function fields with ideal class number greater than one are given.[
LetR be a finite commutative ring with identity and τ be a nonnegative integer. In studying linear finite automata, one of the basic problems is how to characterize the class of rings which have the property that eve...
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LetR be a finite commutative ring with identity and τ be a nonnegative integer. In studying linear finite automata, one of the basic problems is how to characterize the class of rings which have the property that every (weakly) invertible linear finite automaton ? with delay τ over R has a linear finite automaton ?′ over R which is a (weak) inverse with delay τ of ?. The rings and linear finite automata are studied by means of modules and it is proved that *-rings are equivalent to self-injective rings, and the unsolved problem (for τ=0) is solved. Moreover, a further problem of how to characterize the class of rings which have the property that every invertible with delay τ linear finite automaton ? overR has a linear finite automaton ?′ over R which is an inverse with delay τ′ for some τ′?τ is studied and solved.
Knowledge graphs have proven highly effective for learning representations of entities and relations, with hyper-relational knowledge graphs (HKGs) gaining increased attention due to their enhanced representation capa...
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Knowledge graphs have proven highly effective for learning representations of entities and relations, with hyper-relational knowledge graphs (HKGs) gaining increased attention due to their enhanced representation capabilities. Each fact in an HKG consists of a main triple supplemented by attribute-value qualifiers that provide additional contextual information. Due to the complexity of hyper-relations, HKGs typically contain complex geometric structures, such as hierarchical, ring, and chain structures, often mixed together. However, previous work mainly embeds HKGs into Euclidean space, limiting their ability to capture these complex geometric structures simultaneously. To address this challenge, we propose a novel model called Geometry Aware Hyper-relational Embedding (GAHE). Specifically, GAHE adopts a multi-curvature geometry-aware approach by modeling HKGs in Euclidean space (zero curvature), hyperbolic space (negative curvature), and hyperspherical space (positive curvature) in a unified framework. In this way, it can integrate space-invariant and space-specific features to accurately capture the diverse structures in HKGs. In addition, GAHE introduces a module termed hyper-relational subspace learning, which allocates multiple sub-relations for each hyper-relation. It enables the exploitation of abundant latent semantic interactions and facilitates the exploration of fine-grained semantics between attribute-value pairs and hyper-relations across multiple subspaces. Furthermore, we provide theoretical guarantees that GAHE is fully expressive and capable of modeling a wide range of semantic patterns for hyper-relations. Empirical evaluations demonstrate that GAHE achieves state-of-the-art results on both hyper-relational and binary-relational benchmarks.
Explainable Fake News Detection (EFND) is a new challenge that aims to verify news authenticity and provide clear explanations for its decisions. Traditional EFND methods often treat the tasks of classification and ex...
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Explainable Fake News Detection (EFND) is a new challenge that aims to verify news authenticity and provide clear explanations for its decisions. Traditional EFND methods often treat the tasks of classification and explanation as separate, ignoring the fact that explanation content can assist in enhancing fake news detection. To overcome this gap, we present a new solution: the End-to-end Explainable Fake News Detection Network (\(EExpFND\)). Our model includes an evidence-claim variational causal inference component, which not only utilizes explanation content to improve fake news detection but also employs a variational approach to address the distributional bias between the ground truth explanation in the training set and the prediction explanation in the test set. Additionally, we incorporate a masked attention network to detail the nuanced relationships between evidence and claims. Our comprehensive tests across two public datasets show that \(EExpFND\) sets a new benchmark in performance. The code is available at https://***/r/EExpFND-F5C6.
This book aims to provide a comprehensive understanding of tensor computation and its applications in seismic data analysis, exclusively catering to seasoned researchers, graduate students, and industrial engineers al...
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ISBN:
(数字)9783031789007
ISBN:
(纸本)9783031788994;9783031789021
This book aims to provide a comprehensive understanding of tensor computation and its applications in seismic data analysis, exclusively catering to seasoned researchers, graduate students, and industrial engineers alike. Tensor emerges as a natural representation of multi-dimensional modern seismic data, and tensor computation can help prevent possible harm to the multi-dimensional geological structure of the subsurface that occurred in classical seismic data analysis.
It delivers a wealth of theoretical, computational, technical, and experimental details, presenting an engineer's perspective on tensor computation and an extensive investigation of tensor-based seismic data analysis techniques. Embark on a transformative exploration of seismic data processing—unlock the potential of tensor computation and reshape your approach to high-dimensional geological structures.
The discussion begins with foundational chapters, providing a solid background in both seismic data processing and tensor computation. The heart of the book lies in its seven chapters on tensor-based seismic data analysis methods. From structured low-tubal-rank tensor completion to cutting-edge techniques like tensor deep learning and tensor convolutional neural networks, each method is meticulously detailed. The superiority of tensor-based data analysis methods over traditional matrix-based data analysis approaches is substantiated through synthetic and real field examples, showcasing their prowess in handling high-dimensional modern seismic data. Notable chapters delve into seismic noise suppression, seismic data interpolation, and seismic data super-resolution using advanced tensor models. The final chapter provides a cohesive summary of the conclusion and future research directions, ensuring readers facilitate a thorough understanding of tensor computation applications in seismic data processing. The appendix includes a hatful of information on existing tensor computation software, enhancing the b
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