Related papers: Chinese Remainder Theorem Approach to Montgomery-T…
The practical application of a new class of coprime arrays based on the Chinese remainder theorem (CRT) over quadratic fields is presented in this paper. The proposed CRT arrays are constructed by ideal lattices embedded from coprime…
We prove the equidistribution of subsets of $(\Rr/\Zz)^n$ defined by fractional parts of subsets of~$(\Zz/q\Zz)^n$ that are constructed using the Chinese Remainder Theorem.
Chinese text recognition is more challenging than Latin text due to the large amount of fine-grained Chinese characters and the great imbalance over classes, which causes a serious overfitting problem. We propose to apply Maximum Entropy…
In his celebrated book "Mathematical Treatise in Nine Sections" of 1247, Qin, Jiushao described the Chinese remainder theorem with great detail and generality. He also gave a method for computing modular inverse under the name of "DaYan…
Recent deep learning based approaches have achieved great success on handwriting recognition. Chinese characters are among the most widely adopted writing systems in the world. Previous research has mainly focused on recognizing handwritten…
We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier…
We take the generation of Chinese classical poem lines as a sequence-to-sequence learning problem, and build a novel system based on the RNN Encoder-Decoder structure to generate quatrains (Jueju in Chinese), with a topic word as input. Our…
A fundamental challenge in deep metric learning is the generalization capability of the feature embedding network model since the embedding network learned on training classes need to be evaluated on new test classes. To address this…
The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…
This paper presents a new refutation procedure for multimodular systems of integer constraints that commonly arise when verifying cryptographic protocols. These systems, involving polynomial equalities and disequalities modulo different…
Residue Number System (RNS), which originates from the Chinese Remainder Theorem, offers a promising future in VLSI because of its carry-free operations in addition, subtraction and multiplication. This property of RNS is very helpful to…
Recently, the Transformer model that is based solely on attention mechanisms, has advanced the state-of-the-art on various machine translation tasks. However, recent studies reveal that the lack of recurrence hinders its further improvement…
We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…
Variations on a theorem of Cand\`es, Romberg and Tao The CRT theorem reconstructs a signal from a sparse set of frequencies, a paradigm of Compressed sensing. The signal is assumed to be carried by a small number of points, s, in a large…
A recent work of Harn and Fuyou presents the first multilevel (disjunctive) threshold secret sharing scheme based on the Chinese Remainder Theorem. In this work, we first show that the proposed method is not secure and also fails to work…
The prevalent approaches of Chinese word segmentation task almost rely on the Bi-LSTM neural network. However, the methods based the Bi-LSTM have some inherent drawbacks: hard to parallel computing, little efficient in applying the Dropout…
Neural machine translation (NMT) models generally adopt an encoder-decoder architecture for modeling the entire translation process. The encoder summarizes the representation of input sentence from scratch, which is potentially a problem if…
We consider the problem of intruder deduction in security protocol analysis: that is, deciding whether a given message $M$ can be deduced from a set of messages $\Gamma$ under the theory of blind signatures and arbitrary convergent…
Recovering a low rank matrix from a subset of its entries, some of which may be corrupted, is known as the robust matrix completion (RMC) problem. Existing RMC methods have several limitations: they require a relatively large number of…
This is a pedagogical article cited in the foregoing research note, quant-ph/9911050