The Collatz conjecture is a famous conjecture aiming to estimate the behaviors of positive integers after a series of iterations of the Collatz function f(n), where f(n) = {3n+1/2 if n is odd, n/2 if n is even. Collat...
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The Collatz conjecture is a famous conjecture aiming to estimate the behaviors of positive integers after a series of iterations of the Collatz function f(n), where f(n) = {3n+1/2 if n is odd, n/2 if n is even. Collatz conjecture has attracted a great deal of attention since it was put forward in 1930s due to the surprising nature. However, after strenuous efforts, many mathematicians think the current knowledge seems insufficient to solve Collatz conjecture, although it appears in a very simple form. As a replacement, a "periodic" (weaker) version of Collatz conjecture (called Collatz periodic conjecture) was proposed and discussed. In this paper, we would like to explore what properties Collatz (periodic) conjecture could imply. Maybe it is another possible direction to confirm or disprove Collatz (periodic) conjecture.
The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer ***,it adds difficulty to solving the coupled conduc...
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The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer ***,it adds difficulty to solving the coupled conduction,convection,and radiation problem,leading to suboptimal efficiency that fails to meet real-time control *** overcome this difficulty,comparable gray radiative properties of non-gray media are proposed and estimated by solving an inverse ***,the required iteration numbers by using a least-squares method are too many and resulted in a very low inverse *** is necessary to present an efficient method for the *** Levenberg-Marquardt algorithm is utilized to solve the inverse problem of coupled heat transfer,and the gray-equivalent radiative characteristics are successfully *** is our intention that the issue of low inverse efficiency,which has been observed when the least-squares method is employed,will be *** enhance the performance of the Levenberg-Marquardt algorithm,a modification is implemented for determining the damping *** investigations are also conducted to evaluate its accuracy,stability of convergence,efficiency,and robustness of the ***,a comparison is made between the results achieved using each method.
Autism Spectrum Disorder (ASD) is a neurodevelopmental disorder characterized by complex physiological processes. Previous research has predominantly focused on static cerebral interactions, often neglecting the brain...
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Autism Spectrum Disorder (ASD) is a neurodevelopmental disorder characterized by complex physiological processes. Previous research has predominantly focused on static cerebral interactions, often neglecting the brain's dynamic nature and the challenges posed by network noise. To address these gaps, we introduce the Masked Connection-based Dynamic Graph Learning Network (MCDGLN). Our approach first segments BOLD signals using sliding temporal windows to capture dynamic brain characteristics. We then employ a specialized weighted edge aggregation (WEA) module, which uses the cross convolution with channel-wise element-wise convolutional kernel, to integrate dynamic functional connectivity and to isolate task-relevant connections. This is followed by topological feature extraction via a hierarchical graph convolutional network (HGCN), with key attributes highlighted by a self-attention module. Crucially, we refine static functional connections using a customized task-specific mask, reducing noise and pruning irrelevant links. The attention-based connection encoder (ACE) then enhances critical connections and compresses static features. The combined features are subsequently used for classification. Applied to the Autism Brain Imaging Data Exchange I (ABIDE I) dataset, our framework achieves a 73.3 % classification accuracy between ASD and Typical Control (TC) groups among 1035 subjects. The pivotal roles of WEA and ACE in refining connectivity and enhancing classification accuracy underscore their importance in capturing ASD-specific features, offering new insights into the disorder.
Learning-based approaches inspired by the scattering model for enhancing underwater imagery have gained prominence. Nevertheless, these methods often suffer from time-consuming attributable to their sizable model dime...
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Learning-based approaches inspired by the scattering model for enhancing underwater imagery have gained prominence. Nevertheless, these methods often suffer from time-consuming attributable to their sizable model dimensions. Moreover, they face challenges in adapting unknown scenes, primarily because the scattering model's original design was intended for atmospheric rather than marine condition. To address these obstacles, we begin by investigating the inherent differences in imaging characteristics between atmospheric and marine conditions based on statistical distributions. Building on these observations, we introduce an efficient and effective algorithm called Deep Scene Curve, abbreviated as DSC. This method comprises two essential steps: scene-irrelevant zero-mean adjustment and scene-oriented hyperparameter estimation. The first step transforms scene features into a unified zero-mean space, thereby reducing interference from scene-specific attributes. In the second step, we employ a lightweight neural network to estimate scene-oriented hyperparameters for a defined pixel-level curve based on underwater observations. This approach enables us to generate a deep curve that excels in both adaptability and efficiency, as substantiated by extensive experiments. Notably, our method achieves a significant 56% improvement in average inference time while reducing FLOPs by 92% compared to existing techniques. Furthermore, our extensive experiments in low-light image enhancement tasks highlight the potential advantages of DSC.
Complex evidence theory (CET), as a generalized D-S evidence theory, has the ability to express uncertainty in the complex field. CET has been applied in many information fields. One of the key issues in CET is uncert...
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Complex evidence theory (CET), as a generalized D-S evidence theory, has the ability to express uncertainty in the complex field. CET has been applied in many information fields. One of the key issues in CET is uncertainty measurement of the complex basic belief assignment (CBBA). Previous research on uncertainty measures usually focused on classical probability theories such as belief function assignments, sets , probability. However, in recent years, research on quantum information has provided a novel thinking direction for the measurement of uncertainty. In this paper, a novel quantum representation of CBBA is proposed based on the density matrix. In addition, a novel quantum belief entropy based on CBBA has been proposed to describe the discord part of uncertainty. In the quantum belief entropy, a concept of quantum interference is introduced to express the quantum effect of element interaction. Furthermore, some properties are analyzed , explained in the paper, and some numerical examples are given to help illustrate the novel measurement of uncertainty.
Many topics in pattern recognition and machine learning, such as subspace learning, image restoration, background modeling, can be viewed as the matrix decomposing problem. Double nuclear norm-based matrix decompositi...
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Over the past few years, Graph Convolutional Networks (GCN) have emerged as a promising tool in the field of recommendation. They have the ability to effectively learn user and item embeddings by leveraging collaborat...
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作者：
Chen, YanboLiu, WeiweiSchool of Computer Science
Wuhan University National Engineering Research Center for Multimedia Software Wuhan University Institute of Artificial Intelligence Wuhan University Hubei Key Laboratory of Multimedia and Network Communication Engineering Wuhan University
Transfer-based attacks [1] are a practical method of black-box adversarial attacks in which the attacker aims to craft adversarial examples from a source model that is transferable to the target model. Many empirical ...
Cross-modality person re-identification between visible and infrared images has become a research hotspot in the image retrieval field due to its potential application scenarios. Existing research usually designs loss...
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In the cloud content delivery networks, when an edge CDN node lacks the video requested by a user, it needs to send video requests to the origin server or other edge CDN nodes. To enhance user experience quality, the ...
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