Related papers: Bit catastrophes for the Burrows-Wheeler Transform
This article shows that any type of binary data can be defined as a collection from codewords of variable length. This feature helps us to define an Injective and surjective function from the suggested codewords to the required codewords.…
In this article we extend the elegant in-place Burrows-Wheeler transform (BWT) algorithm proposed by Crochemore et al. (Crochemore et al., 2015). Our extension is twofold: we first show how to compute simultaneously the longest common…
We review lessons from the AdS/CFT correspondence that indicate that the emergence of locality in quantum gravity is contingent on considering observables with a small number of insertions. Correlation functions where the number of…
The following critical phenomenon was recently discovered. When a memoryless source is compressed using a variable-length fixed-distortion code, the fastest convergence rate of the (pointwise) compression ratio to the optimal $R(D)$…
Transformer architecture has become the fundamental element of the widespread natural language processing~(NLP) models. With the trends of large NLP models, the increasing memory and computation costs hinder their efficient deployment on…
We identify string corrections to the EM memory effect. Though largely negligible in the low-energy limit, the effect become relevant in high-energy collisions and in extreme events. We illustrate our findings in a simple unoriented bosonic…
We classify all possible singularities in the electronic dispersion of two-dimensional systems that occur when the Fermi surface changes topology, using catastrophe theory. For systems with up to seven control parameters (i.e., pressure,…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
In this paper, we show that the LZ77 factorization of a text T {\in\Sigma^n} can be computed in O(R log n) bits of working space and O(n log R) time, R being the number of runs in the Burrows-Wheeler transform of T reversed. For extremely…
In the fillable array problem one must maintain an array A[1..n] of $w$-bit entries subject to random access reads and writes, and also a $\texttt{fill}(\Delta)$ operation which sets every entry of to some $\Delta\in\{0,\ldots,2^w-1\}$. We…
The dynamics of phase transitions (PT) in quantum field theories at finite temperature is most accurately described within the framework of dimensional reduction. In this framework, thermodynamic quantities are computed within the…
A parameterized string (p-string) is a string over an alphabet $(\Sigma_{s} \cup \Sigma_{p})$, where $\Sigma_{s}$ and $\Sigma_{p}$ are disjoint alphabets for static symbols (s-symbols) and for parameter symbols (p-symbols), respectively.…
Ductility quantifies a material's capacity for plastic deformation, and it is a key property for preventing fracture driven failure in engineering parts. While some brittle materials exhibit improved ductility at small scales, the processes…
Size-Change Termination (SCT) is a method of proving program termination based on the impossibility of infinite descent. To this end we may use a program abstraction in which transitions are described by monotonicity constraints over…
Converting a compressed format of a string into another compressed format without an explicit decompression is one of the central research topics in string processing. We discuss the problem of converting the run-length Burrows-Wheeler…
We consider massless string scattering amplitudes in a limit where the number of external particles becomes very large, while the energy of each particle remains small. Using the growth of the volume of the relevant moduli space, and by…
A convolutional encoder is said to be catastrophic if it maps an information sequence of infinite weight into a code sequence of finite weight. As a consequence of this mapping, a finite number of channel errors may cause an infinite number…
The FM-index is a well-known compressed full-text index, based on the Burrows-Wheeler transform (BWT). During a pattern search, the BWT sequence is accessed at "random" locations, which is cache-unfriendly. In this paper, we are interested…
We consider the problem of constructing binary codes for correcting deletions that are localized within certain parts of the codeword that are unknown a priori. The model that we study is when $\delta \leq w$ deletions are localized in a…
A reconstruction problem of words from scattered factors asks for the minimal information, like multisets of scattered factors of a given length or the number of occurrences of scattered factors from a given set, necessary to uniquely…