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In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
To cluster data that are not linearly separable in the original feature space, $k$-means clustering was extended to the kernel version. However, the performance of kernel $k$-means clustering largely depends on the choice of kernel…
Transforming an input sequence into its constituent k-mers is a fundamental operation in computational genomics. To reduce storage costs associated with k-mer datasets, we introduce and formally analyze MCTR, a novel two-stage algorithm for…
Large language models (LLMs) face significant inference latency due to inefficiencies in GEMM operations, weight access, and KV cache access, especially in real-time scenarios. This highlights the need for a versatile compute-memory…
In bioinformatics, minimizers have become an inescapable method for handling $k$-mers (words of fixed size $k$) extracted from DNA or RNA sequencing, whether for sampling, storage, querying or partitioning. According to some fixed order on…
Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of…
Microplastics (MPs) are ubiquitous in all ecosystems, affecting wildlife and, ultimately, human health. The complexity of natural samples plus the unspecificity of their treatments to isolate polymers renders the characterization of…
Sequence classification has numerous applications in various fields. Despite extensive studies in the last decades, many challenges still exist, particularly in pattern-based methods. Existing pattern-based methods measure the…
Longest Common Subsequence ($LCS$) deals with the problem of measuring similarity of two strings. While this problem has been analyzed for decades, the recent interest stems from a practical observation that considering single characters is…
Recently, due to the genomic sequence analysis in several types of cancer, the genomic data based on {\em copy number profiles} ({\em CNP} for short) are getting more and more popular. A CNP is a vector where each component is a…
Deep sequencing has enabled the investigation of a wide range of environmental microbial ecosystems, but the high memory requirements for {\em de novo} assembly of short-read shotgun sequencing data from these complex populations are an…
Compressed sensing magnetic resonance imaging (CS-MRI) is a theoretical framework that can accurately reconstruct images from undersampled k-space data with a much lower sampling rate than the one set by the classical Nyquist-Shannon…
Due to the progressive growth of the amount of data available in a wide variety of scientific fields, it has become more difficult to ma- nipulate and analyze such information. Even though datasets have grown in size, the K-means algorithm…
In the era of big data, k-means clustering has been widely adopted as a basic processing tool in various contexts. However, its computational cost could be prohibitively high as the data size and the cluster number are large. It is well…
The Shortest Superstring Problem (SSP) consists, for a set of strings S = {s_1,...,s_n}, to find a minimum length string that contains all s_i, 1 <= i <= k, as substrings. This problem is proved to be NP-Complete and APX-hard. Guaranteed…
In a distributed storage systems (DSS) with $k$ systematic nodes, robustness against node failure is commonly provided by storing redundancy in a number of other nodes and performing repair mechanism to reproduce the content of the failed…
Minimum sum-of-squares clustering (MSSC) is a widely used clustering model, of which the popular K-means algorithm constitutes a local minimizer. It is well known that the solutions of K-means can be arbitrarily distant from the true MSSC…
Low-field magnetic resonance imaging (MRI) offers a cost-effective alternative for medical imaging in resource-limited settings. However, its widespread adoption is hindered by two key challenges: prolonged scan times and reduced image…
Image reconstruction from undersampled k-space data plays an important role in accelerating the acquisition of MR data, and a lot of deep learning-based methods have been exploited recently. Despite the achieved inspiring results, the…
CRYSTAL-Kyber (Kyber) is one of the post-quantum cryptography (PQC) key-encapsulation mechanism (KEM) schemes selected during the standardization process. This paper addresses optimization for Kyber architecture with respect to latency and…