Related papers: Recombination and bitsets
In this note we consider the question how the set of inversions of a permutation $\pi \in S_n$ can be partitioned into two subset, such that those are itself inversion sets of permutations. This is archived by exploiting a connection to a…
In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…
It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with…
The set of prime numbers has been analyzed, based on their algebraic and arithmetical structure. Here by obtaining a sort of linear formula for the set of prime numbers, they are redefined and identified; under a systematic procedure it has…
We introduce a binary latent space autoencoder architecture to rehearse training samples for the continual learning of neural networks. The ability to extend the knowledge of a model with new data without forgetting previously learned…
Dataset Condensation is a newly emerging technique aiming at learning a tiny dataset that captures the rich information encoded in the original dataset. As the size of datasets contemporary machine learning models rely on becomes…
We present an involution on set partitions that interchanges two statistics related to relative size of block entries and use it to establish an equidistribution on objects counted by the Bessel numbers.
We introduce Bayesian Bits, a practical method for joint mixed precision quantization and pruning through gradient based optimization. Bayesian Bits employs a novel decomposition of the quantization operation, which sequentially considers…
The circular descent of a permutation $\sigma$ is a set $\{\sigma(i)\mid \sigma(i)>\sigma(i+1)\}$. In this paper, we focus on the enumerations of permutations by the circular descent set. Let $cdes_n(S)$ be the number of permutations of…
We introduce ballot matrices, a signed combinatorial structure whose definition naturally follows from the generating function for labeled interval orders. A sign reversing involution on ballot matrices is defined. We show that matrices…
The subject of pattern avoiding permutations has its roots in computer science, namely in the problem of sorting a permutation through a stack. A formula for the number of permutations of length n that can be sorted by passing it twice…
A superpermutation is a sequence that contains every permutation of $n$ distinct symbols as a contiguous substring. For instance, a valid example for three symbols is a sequence that contains all six permutations. This paper introduces a…
This article introduces byteSteady -- a fast model for classification using byte-level n-gram embeddings. byteSteady assumes that each input comes as a sequence of bytes. A representation vector is produced using the averaged embedding…
Residue Number System (RNS), which originates from the Chinese Remainder Theorem, offers a promising future in VLSI because of its carry-free operations in addition, subtraction and multiplication. This property of RNS is very helpful to…
Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been…
Theorems relating permutations with objects in other fields of mathematics are often stated in terms of avoided patterns. Examples include various classes of Schubert varieties from algebraic geometry (Billey and Abe 2013), commuting…
Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher…
An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a…
Bit-depth is the number of bits for each color channel of a pixel in an image. Although many modern displays support unprecedented higher bit-depth to show more realistic and natural colors with a high dynamic range, most media sources are…
In many real-world binary classification tasks (e.g. detection of certain objects from images), an available dataset is imbalanced, i.e., it has much less representatives of a one class (a minor class), than of another. Generally, accurate…