Related papers: A visualization tool to explore alphabet orderings…
A degenerate or indeterminate string on an alphabet $\Sigma$ is a sequence of non-empty subsets of $\Sigma$. Given a degenerate string $t$ of length $n$, we present a new method based on the Burrows--Wheeler transform for searching for a…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…
The goal of text ranking is to generate an ordered list of texts retrieved from a corpus in response to a query. Although the most common formulation of text ranking is search, instances of the task can also be found in many natural…
Large-alphabet strings are common in scenarios such as information retrieval and natural-language processing. The efficient storage and processing of such strings usually introduces several challenges that are not witnessed in…
Wavelet transforms are widely used in various fields of science and engineering as a mathematical tool with features that reveal information ignored by the Fourier transform. Unlike the Fourier transform, which is unique, a wavelet…
Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…
We propose a new technique for computational language representation called elementwise embedding, in which a material (semantic unit) is abstracted into a horizontal concatenation of lower-dimensional element (character) embeddings. While…
The Invertible Bloom Lookup Table (IBLT) is a probabilistic concise data structure for set representation that supports a listing operation as the recovery of the elements in the represented set. Its applications can be found in network…
The merging of succinct data structures is a well established technique for the space efficient construction of large succinct indexes. In the first part of the paper we propose a new algorithm for merging succinct representations of de…
Recently, Cenzato et al.\ proposed a new text index, called the \emph{suffixient array}, which is a subset of the suffix array and supports locating a single pattern occurrence or finding its maximal exact matches (MEMs), assuming random…
Transformer-based models, exemplified by GPT-3, ChatGPT, and GPT-4, have recently garnered considerable attention in both academia and industry due to their promising performance in general language tasks. Nevertheless, these models…
The continuous wavelet transform (CWT) is very useful for processing signals with intricate and irregular structures in astrophysics and cosmology. It is crucial to propose precise and fast algorithms for the CWT. In this work, we review…
Objective: Transformers, born to remedy the inadequate receptive fields of CNNs, have drawn explosive attention recently. However, the daunting computational complexity of global representation learning, together with rigid window…
One of the most common ways to represent and share visual designs is with vector graphics. Designers working with vector graphics often explore layout alternatives and generate them by moving and resizing elements. The motivation for this…
In recent years several compressed indexes based on variants of the Burrows-Wheeler transformation have been introduced. Some of these index structures far more complex than a single string, as was originally done with the FM-index…
In this paper we present an algorithm to compute the Lyndon array of a string $T$ of length $n$ as a byproduct of the inversion of the Burrows-Wheeler transform of $T$. Our algorithm runs in linear time using only a stack in addition to the…
Dictionary learning is an effective tool for pattern recognition and classification of time series data. Among various dictionary learning techniques, the dynamic time warping (DTW) is commonly used for dealing with temporal delays,…
The Invertible Bloom Lookup Table (IBLT) is a probabilistic data structure for set representation, with applications in network and traffic monitoring. It is known for its ability to list its elements, an operation that succeeds with high…
Quantum walks (QWs) are of interest as examples of uniquely quantum behavior and are applicable in a variety of quantum search and simulation models. Implementing QWs on quantum devices is useful from both points of view. We describe a…
The Transformer has quickly become the dominant architecture for various pattern recognition tasks due to its capacity for long-range representation. However, transformers are data-hungry models and need large datasets for training. In…