Related papers: Recombination and bitsets
A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper…
A mutation cycle is a cycle in a graph whose vertices are labeled by the quivers in a given mutation class and whose edges correspond to single mutations. For any fixed $n\ge 4$, we describe arbitrarily long mutation cycles involving…
Byte-Pair Encoding (BPE) is an algorithm commonly used in Natural Language Processing to build a vocabulary of subwords, which has been recently applied to symbolic music. Given that symbolic music can differ significantly from text,…
We discuss distributed reframing control of bittide systems. In a bittide system, multiple processors synchronize by monitoring communication over the network. The processors remain in logical synchrony by controlling the timing of frame…
This paper introduces a binary encoding that supports arbitrarily large, small and precise decimals. It completely preserves information and order. It does not rely on any arbitrary use-case-based choice of calibration and is readily…
The one-bit quanta image sensor is a photon-counting device that produces binary measurements where each bit represents the presence or absence of a photon. In the presence of read noise, the sensor quantizes the analog voltage into the…
This paper describes a new method of data encoding which may be used in various modern digital, computer and telecommunication systems and devices. The method permits the compression of data for storage or transmission, allowing the exact…
Inversions, also sometimes called reversals, are a major contributor to variation among bacterial genomes, with studies suggesting that those involving small numbers of regions are more likely than larger inversions. Deletions may arise in…
When linear regression generates a relationship between a (dependent) scalar response and one or multiple independent variables, various datasets providing distinct graphical trends can develop resembling relationships based on the same…
We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension. At the core of this algorithm, we combine ideas from the…
We give an account on what is known on the subject of permutation matchings, which are bijections of a finite regular semigroup that map each element to one of its inverses. This includes partial solutions to some open questions, including…
Dynamic unary encoding takes unary encoding to the next level. Every n-bit binary string is an encoding of dynamic unary and every n-bit binary string is encodable by dynamic unary. By utilizing both forms of unary code and a single bit of…
The problem of reconstructing strings from their substring spectra has a long history and in its most simple incarnation asks for determining under which conditions the spectrum uniquely determines the string. We study the problem of coded…
Memoryless computation is a new technique to compute any function of a set of registers by updating one register at a time while using no memory. Its aim is to emulate how computations are performed in modern cores, since they typically…
Qubit readout is commonly performed by thresholding a collection of analog detector signals to obtain a sequence of single-shot bit values. The intrinsic irreversibility of the mapping from analog to digital signals discards soft…
This paper addresses the task of set prediction using deep feed-forward neural networks. A set is a collection of elements which is invariant under permutation and the size of a set is not fixed in advance. Many real-world problems, such as…
Given partial information about a set, we are interested in fully recovering the original set from what is given. If a set encodes itself robustly, any partial information about the set suffices to fully recover the information about the…
Extracting informative image features and learning effective approximate hashing functions are two crucial steps in image retrieval . Conventional methods often study these two steps separately, e.g., learning hash functions from a…
Compressed bitmap indexes are used to speed up simple aggregate queries in databases. Indeed, set operations like intersections, unions and complements can be represented as logical operations (AND,OR,NOT) that are ideally suited for…
Visontai conjectured in 2013 that the joint distribution of ascent and distinct nonzero value numbers on the set of subexcedant sequences is the same as that of descent and inverse descent numbers on the set of permutations. This conjecture…