相关论文: On Solving a Generalized Chinese Remainder Theorem…
Protocol sequences are used for channel access in the collision channel without feedback. Each user accesses the channel according to a deterministic zero-one pattern, called the protocol sequence. In order to minimize fluctuation of…
In near-term quantum computations that do not employ error correction, noise can proliferate rapidly, corrupting the quantum state and making results unreliable. These errors originate from both decoherence and control imprecision. The…
The problem of corrupted data, missing features, or missing modalities continues to plague the modern machine learning landscape. To address this issue, a class of regularization methods that enforce consistency between imputed and fully…
In this paper we propose several strategies for the exact computation of the determinant of a rational matrix. First, we use the Chinese Remaindering Theorem and the rational reconstruction to recover the rational determinant from its…
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. A traditional approach is to look for codes which simultaneously maximize error tolerance and minimize storage space consumption. However, this…
Recent results on constant overhead LDPC code-based fault-tolerance against i.i.d. errors naturally lead to the question of fault-tolerance against errors with long-range correlations. Ideally, any correlation can be captured by a joint…
Orthogonal frequency division multiplexing (OFDM) is a widely adopted wireless communication technique but is sensitive to the carrier frequency offset (CFO). For high-mobility environments, severe Doppler shifts cause the CFO to extend…
This work continues the study of linear error correcting codes against adversarial insertion deletion errors (insdel errors). Previously, the work of Cheng, Guruswami, Haeupler, and Li \cite{CGHL21} showed the existence of asymptotically…
In this paper, we consider the mismatched rate-distortion problem, in which the encoding is done using a codebook, and the encoder chooses the minimum-distortion codeword according to a mismatched distortion function that differs from the…
Contention resolution schemes (or CR schemes), introduced by Chekuri, Vondrak and Zenklusen, are a class of randomized rounding algorithms for converting a fractional solution to a relaxation for a down-closed constraint family into an…
A general error correction method is presented which is capable of correcting coherent errors originating from static residual inter-qubit couplings in a quantum computer. It is based on a randomization of static imperfections in a…
In this paper, with respect to multichannel synthetic aperture radars (SAR), we first formulate the problems of Doppler ambiguities on the radial velocity (RV) estimation of a ground moving target in range-compressed domain, range-Doppler…
This paper introduces two new notions of graded linear resolution and graded linear quotients, which generalize the concepts of linear resolution property and linear quotient for modules over the polynomial ring $A=k[x_1, \dots ,x_n]$.…
Modified Rayleigh conjecture (MRC) in scattering theory was proposed and justified by the author (J.Phys A, 35 (2002), L357-L361). MRC allows one to develop efficient numerical algorithms for solving boundary-value problems. It gives an…
Augmenting the balanced residue number system moduli-set $\{m_1=2^n,m_2=2^n-1,m_3=2^n+1\}$, with the co-prime modulo $m_4=2^{2n}+1$, increases the dynamic range (DR) by around 70%. The Mersenne form of product $m_2 m_3 m_4=2^{4n}-1$, in the…
In recent years, pre-trained models have been extensively studied, and several downstream tasks have benefited from their utilization. In this study, we verify the effectiveness of two methods that incorporate a BERT-based pre-trained model…
Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault tolerant schemes. Recently, error mitigation has been…
The primary objective of Chinese grammatical error correction (CGEC) is to detect and correct errors in Chinese sentences. Recent research shows that large language models (LLMs) have been applied to CGEC with significant results. For LLMs,…
The compensated quotient-difference (Compqd) algorithm is proposed along with some applications. The main motivation is based on the fact that the standard quotient-difference (qd) algorithm can be numerically unstable. The Compqd algorithm…
In this paper, we present a new iterative rounding framework for many clustering problems. Using this, we obtain an $(\alpha_1 + \epsilon \leq 7.081 + \epsilon)$-approximation algorithm for $k$-median with outliers, greatly improving upon…