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We study the fundamental problem of \emph{moduli selection} in the Robust Chinese Remainder Theorem (RCRT), where each residue may be perturbed by a bounded error. Consider $L$ moduli of the form $m_i = \Gamma_i m$ ($1 \le i \le L$), where…
The number of classes of gamma-ray bursts (GRBs), besides the well-established short and long ones, remains a debatable issue. It was already shown, however, that when invoking skewed distributions, the $\log T_{90}$ and $\log T_{90} - \log…
Purpose: In the field of vulnerability repair, previous research has leveraged pretrained models and LLM-based prompt engineering, among which LLM-based approaches show better generalizability and achieve the best performance. However, the…
Despite the impressive performance of Retrieval-augmented Generation (RAG) systems across various NLP benchmarks, their robustness in handling real-world user-LLM interaction queries remains largely underexplored. This presents a critical…
We study part sizes of supercritical locally restricted sequential structures. This extends previous results about locally restricted integer compositions and part sizes in smooth supercritical compositional structures. Applications are…
In this work, we construct the first locally-correctable codes (LCCs), and locally-testable codes (LTCs) with constant rate, constant relative distance, and sub-polynomial query complexity. Specifically, we show that there exist binary LCCs…
A code over a finite field is called locally recoverable code (LRC) if every coordinate symbol can be determined by a small number (at most r, this parameter is called locality) of other coordinate symbols. For a linear code with length n,…
As an important coding scheme in modern distributed storage systems, locally repairable codes (LRCs) have attracted a lot of attentions from perspectives of both practical applications and theoretical research. As a major topic in the…
This work focuses on sequential locally recoverable codes (SLRCs), a special family of locally repairable codes, capable of correcting multiple code symbol erasures, which are commonly used for distributed storage systems. First, we…
We present results of an intensive spectroscopic variability campaign of the very broad-line Seyfert 1 galaxy Mrk 926. Our aim is to investigate the broad-line region (BLR) by studying the intensity and line profile variations of this…
Automatic and robust segmentation of the left ventricle (LV) in magnetic resonance images (MRI) has remained challenging for many decades. With the great success of deep learning in object detection and classification, the research focus of…
Using the archives of the American Association of Variable Stars Observers and our own data, we analyse the long-term variability of several well-studied Luminous Blue Variables (LBVs) aiming on a general picture of stochastic variability…
This paper describes a fast speaker search system to retrieve segments of the same voice identity in the large-scale data. A recent study shows that Locality Sensitive Hashing (LSH) enables quick retrieval of a relevant voice in the…
Accurate segmentation of heart structures imaged by cardiac MR is key for the quantitative analysis of pathology. High-resolution 3D MR sequences enable whole-heart structural imaging but are time-consuming, expensive to acquire and they…
PKS 1155+251 is a radio-loud quasar source at z=0.203. Observations using very long baseline interferometry (VLBI) at ~2, 5, 8 and 15 GHz show that the structure of the radio source is quite complicated on parsec scales and that the outer…
Semidefinite programming (SDP) problems are challenging to solve because of their high dimensionality. However, solving sparse SDP problems with small tree-width are known to be relatively easier because: (1) they can be decomposed into…
We present a study of the radio variability of bright, $S_{1.4}\geq100$ mJy, high-redshift quasars at $z\geq3$ on timescales up to 30-40 years. The study involved simultaneous RATAN-600 measurements at frequencies of 2.3, 4.7, 8.2, 11.2,…
We re-examine the ten Reverberation Mapping (RM) sources with public data based on the two-component model of the Broad Line Region (BLR). In fitting their broad H-beta lines, six of them only need one Gaussian component, one of them has a…
The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Local Reconstruction Codes (LRCs) have emerged as the codes of choice for these…
DNA read mapping is a ubiquitous task in bioinformatics, and many tools have been developed to solve the read mapping problem. However, there are two trends that are changing the landscape of readmapping: First, new sequencing technologies…