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TechRxiv 2020年

作者： Ren, Wei School of Computer Science China University of Geosciences Wuhan China Key Laboratory of Network Assessment Technology CAS Institute of Information Engineering Chinese Academy of Sciences Beijing100093 China Guizhou Provincial Key Laboratory of Public Big Data Guizhou University Guizhou China

We propose Reduced Collatz Conjecture that is equivalent to Collatz Conjecture but is easier to explore, because reduced dynamics is more primitive than original dynamics and presents better structures (e.g., period and ratio). Reduced dynamics (that are occurred computation sequence from a starting integer to the first integer less than the starting integer) is the component of original dynamics (from a starting integer to 1). Reduced dynamics of x is represented by a sequence of computation that is either (3*x+1)/2 or x/2, because 3*x+1 is always even and followed by x/2. We prove that reduced dynamics is periodical and its period equals 2 to the power of the count of x/2. More specifically, if there exists reduced dynamics of x, then there exists reduced dynamics of x+P, where P equals 2L and L is the total count of x/2 computations in reduced dynamics of x (equivalently, L is the length of the sequence). © 2020, CC BY.

关键词： Dynamics

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A reduced collatz dynamics maps to a residue class, and its count of x/2 over count of 3*x+1 is larger than ln3/ln2

TechRxiv

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TechRxiv 2020年

作者： Ren, Wei School of Computer Science China University of Geosciences Wuhan China Key Laboratory of Network Assessment Technology CAS [Institute of Information Engineering Chinese Academy of Sciences Beijing100093 China Guizhou Provincial Key Laboratory Public Big Data Guizhou University Guizhou China

We propose Reduced Collatz conjecture and prove that it is equivalent to Collatz conjecture but more primitive due to reduced dynamics. We study reduced dynamics (that consists of occurred computations from any starting integer to the first integer less than it), because it is the component of original dynamics (from any starting integer to 1). Reduced dynamics is denoted as a sequence of "I" that represents (3*x+1)/2 and "O" that represents x/2. Here 3*x+1 and x/2 are combined together because 3*x+1 is always even and thus followed by x/2. We discover and prove two key properties on reduced dynamics: (1) Reduced dynamics is invertible. That is, given a reduced dynamics, a residue class that presents such reduced dynamics, can be computed directly by our derived formula. (2) Reduced dynamics can be constructed algorithmically, instead of by computing concrete 3*x+1 and x/2 step by step. We discover the sufficient and necessary condition that guarantees a sequence consisting of "I" and "O" to be a reduced dynamics. Counting from the beginning of a sequence, if and only if the count of x/2 over the count of 3*x+1 is larger than ln3/ln2, reduced dynamics will be obtained (i.e., current integer will be less than starting integer). © 2020, CC BY.

关键词： Dynamics

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Collatz dynamics is partitioned by residue class regularly

TechRxiv

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TechRxiv 2020年

We propose Reduced Collatz Conjecture that is equivalent to Collatz Conjecture, which states that every positive integer can return to an integer less than it, instead of 1. Reduced Collatz Conjecture should be easier because some properties are presented in reduced dynamics, rather than in original dynamics (e.g., ratio and period). Reduced dynamics is a computation sequence from starting integer to the first integer less than it, and original dynamics is a computation sequence from starting integer to 1. Reduced dynamics is a component of original dynamics. We denote dynamics of x as a sequence of either computations in terms of "I" that represents (3*x+1)/2 and "O" that represents x/2. Here 3*x+1 and x/2 are combined together, because 3*x+1 is always even and followed by x/2. We formally prove that all positive integers are partitioned into two halves and either presents "I" or "O" in next ongoing computation. More specifically, (1) if any positive integer x that is i module 2t (i is an odd integer) is given, then the first t computations (each one is either "I" or "O" corresponding to whether current integer is odd or even) will be identical with that of i. (2) If current integer after t computations (in terms of "I" or "O") is less than x, then reduced dynamics of x is available. Otherwise, the residue class of x (namely, i module 2t) can be partitioned into two halves (namely, i module 2t+1 and i+2t module 2t+1), and either half presents "I" or "O" in intermediately forthcoming (t+1)-th computation. © 2020, CC BY.

关键词： Dynamics

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The minority matters: a diversity-promoting collaborative metric learning algorithm 22

The minority matters: a diversity-promoting collaborative me...

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Proceedings of the 36th International Conference on Neural Information Processing Systems

作者： Shilong Bao Qianqian Xu Zhiyong Yang Yuan He Xiaochun Cao Qingming Huang State Key Laboratory of Information Security Institute of Information Engineering CAS and School of Cyber Security University of Chinese Academy of Sciences Key Lab. of Intelligent Information Processing Institute of Computing Technology CAS School of Computer Science and Tech. University of Chinese Academy of Sciences Alibaba Group School of Cyber Science and Technology Shenzhen Campus Sun Yat-sen University Key Lab. of Intelligent Information Processing Institute of Computing Technology CAS and School of Computer Science and Tech. University of Chinese Academy of Sciences and Key Laboratory of Big Data Mining and Knowledge Management CAS and Peng Cheng Laboratory

ISBN: (纸本)9781713871088

Collaborative Metric Learning (CML) has recently emerged as a popular method in recommendation systems (RS), closing the gap between metric learning and Collaborative Filtering. Following the convention of RS, existing methods exploit unique user representation in their model design. This paper focuses on a challenging scenario where a user has multiple categories of interests. Under this setting, we argue that the unique user representation might induce preference bias, especially when the item category distribution is imbalanced. To address this issue, we propose a novel method called Diversity-Promoting Collaborative Metric Learning (DPCML), with the hope of considering the commonly ignored minority interest of the user. The key idea behind DPCML is to include a multiple set of representations for each user in the system. Based on this embedding paradigm, user preference toward an item is aggregated from different embeddings by taking the minimum item-user distance among the user embedding set. Furthermore, we observe that the diversity of the embeddings for the same user also plays an essential role in the model. To this end, we propose a Diversity Control Regularization Scheme (DCRS) to accommodate the multi-vector representation strategy better. Theoretically, we show that DPCML could generalize well to unseen test data by tackling the challenge of the annoying operation that comes from the minimum value. Experiments over a range of benchmark datasets speak to the efficacy of DPCML.

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Proof-of-Principle Demonstration of Passive Decoy-State Quantum Digital Signatures Over 200 km

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Physical Review Applied 2018年第3期10卷 034033-034033页

作者： Chun-Hui Zhang Xing-Yu Zhou Hua-Jian Ding Chun-Mei Zhang Guang-Can Guo Qin Wang Institute of Quantum Information and Technology Nanjing University of Posts and Telecommunications Nanjing 210003 China Broadband Wireless Communication and Senser Network Technology Key Lab of Ministry of Education NUPT Nanjing 210003 China Telecommunication and Networks National Engineering Research Center NUPT Nanjing 210003 China Key Laboratory of Quantum Information CAS University of Science and Technology of China Hefei Anhui 230026 China

Quantum digital signatures (QDSs) offer the information-theoretic security verified by quantum mechanics to send a message that is robust against forging and repudiation. We report a proof-of-principle demonstration of a passive decoy-state QDS system that can avoid leaking the modulation information of decoy states. To realize this, four local detection events are generated from the idler light of a parametric down-conversion process, and are then used as decoy states to estimate channel parameters more accurately. As a result, we successfully sign a more-than-one-bit message within 7 s at 100 km. Besides, we achieve a transmission distance of 200 km, which represents a further step toward the practical application of QDSs.

关键词： Photon pairs & parametric down-conversion Quantum communication Quantum cryptography

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A symmetric uniform formula and sole index method for sieving (twin) primes

TechRxiv

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TechRxiv 2020年

作者： Ren, Wei School of Computer Science China University of Geosciences Wuhan430074 China Key Laboratory of Network Assessment Technology CAS Institute of Information Engineering Chinese Academy of Sciences Beijing100093 China Guizhou Provincial Key Laboratory of Public Big Data GuiZhou University Guizhou China

All primes can be indexed by k, as primes must be in the form of 6k+1 or 6k-1. In this paper, we explore for the set of k such that either 6k+1 or 6k-1 is not a prime. Our method provides a uniform formula for k that can sieve primes and twin primes as well. The uniform presents symmetry in terms of k that works as single index in sieving. We also propose a new conjecture that is equivalent to Twin Prime Conjecture but possibly be easier to approach by merely exploring of sole index in term of k. The uniform formula for prime sieving are as follows: k ∈ Sl ⇒ 6k−1 6∈ , where Sl = [−I]6I+1 = [I]6I−1\min([I]6I−1), I ∈ . k ∈ Sr ⇒ 6k + 1 6∈ , where Sr = [−I]6I−1 ∪ ([I]6I+1\min([I]6I+1)), I ∈ . © 2020, CC BY.

关键词： Number theory

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iSplit LBI: Individualized partial ranking with ties via split LBI

arXiv

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arXiv 2019年

作者： Xu, Qianqian Sun, Xinwei Yang, Zhiyong Cao, Xiaochun Huang, Qingming Yao, Yuan Key Lab. of Intelligent Information Processing Institute of Computing Technology CAS Microsoft Research Asia State Key Laboratory of Information Security Institute of Information Engineering CAS School of Cyber Security University of Chinese Academy of Sciences School of Computer Science and Tech. University of Chinese Academy of Sciences Key Laboratory of Big Data Mining and Knowledge Management CAS Peng Cheng Laboratory Department of Mathematics Hong Kong University of Science and Technology Hong Kong

Due to the inherent uncertainty of data, the problem of predicting partial ranking from pairwise comparison data with ties has attracted increasing interest in recent years. However, in real-world scenarios, different individuals often hold distinct preferences. It might be misleading to merely look at a global partial ranking while ignoring personal diversity. In this paper, instead of learning a global ranking which is agreed with the consensus, we pursue the tie-aware partial ranking from an individualized perspective. Particularly, we formulate a unified framework which not only can be used for individualized partial ranking prediction, but also be helpful for abnormal user selection. This is realized by a variable splitting-based algorithm called iSplitLBI. Specifically, our algorithm generates a sequence of estimations with a regularization path, where both the hyperparameters and model parameters are updated. At each step of the path, the parameters can be decomposed into three orthogonal parts, namely, abnormal signals, personalized signals and random noise. The abnormal signals can serve the purpose of abnormal user selection, while the abnormal signals and personalized signals together are mainly responsible for individual partial ranking prediction. Extensive experiments on simulated and real-world datasets demonstrate that our new approach significantly outperforms state-of-the-art alternatives. The code is now availiable at https://***/qianqianxu010/ NeurIPS2019-iSplitLBI. Copyright © 2019, The Authors. All rights reserved.

关键词： Forecasting

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Local and global structure-aware entropy regularized mean teacher model for 3d left atrium segmentation 23rd

Local and global structure-aware entropy regularized mean te...

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23rd International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2020

作者： Hang, Wenlong Feng, Wei Liang, Shuang Yu, Lequan Wang, Qiong Choi, Kup-Sze Qin, Jing School of Computer Science and Technology Nanjing Tech University Nanjing China State Key Laboratory for Novel Software Technology Nanjing University Nanjing China Smart Health Big Data Analysis and Location Services Engineering Lab of Jiangsu Province Nanjing University of Posts and Telecommunications Nanjing China Department of Radiation Oncology Stanford University StanfordCA94305 United States CAS Key Laboratory of Human-Machine Intelligence-Synergy Systems Shenzhen Institutes of Advanced Technology Shenzhen China School of Nursing Hong Kong Polytechnic University Hong Kong

ISBN: (纸本)9783030597092

Emerging self-ensembling methods have achieved promising semi-supervised segmentation performances on medical images through forcing consistent predictions of unannotated data under different perturbations. However, the consistency only penalizes on independent pixel-level predictions, making structure-level information of predictions not exploited in the learning procedure. In view of this, we propose a novel structure-aware entropy regularized mean teacher model to address the above limitation. Specifically, we firstly introduce the entropy minimization principle to the student network, thereby adjusting itself to produce high-confident predictions of unannotated images. Based on this, we design a local structural consistency loss to encourage the consistency of inter-voxel similarities within the same local region of predictions from teacher and student networks. To further capture local structural dependencies, we enforce the global structural consistency by matching the weighted self-information maps between two networks. In this way, our model can minimize the prediction uncertainty of unannotated images, and more importantly that it can capture local and global structural information and their complementarity. We evaluate the proposed method on a publicly available 3D left atrium MR image dataset. Experimental results demonstrate that our method achieves outstanding segmentation performances than the state-of-the-art approaches in scenes with limited annotated images. © Springer Nature Switzerland AG 2020.

关键词： Forecasting

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FRCNet: Frequency and Region Consistency for Semi-supervised Medical Image Segmentation

arXiv

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arXiv 2024年

作者： He, Along Li, Tao Wu, Yanlin Zou, Ke Fu, Huazhu Tianjin Key Laboratory of Network and Data Security Technology College of Computer Science Nankai University Tianjin China Haihe Lab of ITAI China National Key Laboratory of Fundamental Science on Synthetic Vision Sichuan University Sichuan Chengdu China Institute of High Performance Computing Agency for Science Technology and Research Singapore

Limited labeled data hinder the application of deep learning in medical domain. In clinical practice, there are sufficient unlabeled data that are not effectively used, and semi-supervised learning (SSL) is a promising way for leveraging these unlabeled data. However, existing SSL methods ignore frequency domain and region-level information and it is important for lesion regions located at low frequencies and with significant scale changes. In this paper, we introduce two consistency regularization strategies for semi-supervised medical image segmentation, including frequency domain consistency (FDC) to assist the feature learning in frequency domain and multi-granularity region similarity consistency (MRSC) to perform multi-scale region-level local context information feature learning. With the help of the proposed FDC and MRSC, we can leverage the powerful feature representation capability of them in an effective and efficient way. We perform comprehensive experiments on two datasets, and the results show that our method achieves large performance gains and exceeds other state-of-the-art methods. © 2024, CC BY.

关键词： Deep learning

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Quantum key distribution with the single-photon-added coherent source

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Physical Review A 2014年第6期90卷 062315-062315页

作者： Dong Wang Mo Li Feng Zhu Zhen-Qiang Yin Wei Chen Zheng-Fu Han Guang-Can Guo Qin Wang Key Laboratory of Quantum Information University of Science and Technology of China CAS Hefei Anhui 230026 China Synergetic Innovation Center of Quantum Information & Quantum Physics University of Science and Technology of China Hefei Anhui 230026 China Institute of Signal Processing Transmission Nanjing University of Posts and Telecommunications Nanjing 210003 China Key Lab of Broadband Wireless Communication and Sensor Network Technology Nanjing University of Posts and Telecommunications Ministry of Education Nanjing 210003 China

In this paper, we present schemes on implementing the single-photon-added coherent source in quantum key distributions. We apply this source in either the standard BB84 protocol or the recently proposed measurement-device-independent quantum key distribution, comparing their performance with the cases of using other existing sources, e.g., the weak coherent source or the heralded single-photon source, and giving out corresponding numerical simulations. Our simulation results show that in both protocols the single-photon-added coherent source can greatly exceed all other existing sources. Moreover, even when taking statistical fluctuation into account, a high key generation rate can still be achieved at long distance by applying this source.

关键词： SINGLE photon generation QUANTUM measurement COHERENT scattering QUANTUM communication (Optics) QUANTUM states

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