相关论文: Necklaces and bracelets in R
"mdendro" is an R package that provides a comprehensive collection of linkage methods for agglomerative hierarchical clustering on a matrix of proximity data (distances or similarities), returning a multifurcated dendrogram or…
The dirichletprocess package provides software for creating flexible Dirichlet process objects. Users can perform nonparametric Bayesian analysis using Dirichlet processes without the need to program their own inference algorithms. Instead,…
Recurrent Neural Networks are powerful machine learning frameworks that allow for data to be saved and referenced in a temporal sequence. This opens many new possibilities in fields such as handwriting analysis and speech recognition. This…
Network science established itself as a prominent tool for modeling time series and complex systems. This modeling process consists of transforming a set or a single time series into a network. Nodes may represent complete time series,…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…
In this short paper, we study some trace inequalities of the products of the matrices and the power of matrices by the use of elementary calculations.
Routinely collected data in electronic healthcare records are often underpinned by clinical concept dictionaries. Increasingly data sets from these sources are being made available and used for research purposes, but without additional…
A $k$-ary charm bracelet is an equivalence class of length $n$ strings with the action on the indices by the additive group of the ring of integers modulo $n$ extended by the group of units. By applying an $O(n^3)$ amortized time algorithm…
We study the problem of indexing irreducible polynomials over finite fields, and give the first efficient algorithm for this problem. Specifically, we show the existence of poly(n, log q)-size circuits that compute a bijection between {1,…
Writing functions in R is an important skill for anyone using R. S3 methods allow for functions to be generalised across different classes and are easy to implement. Whilst many R users are be adept at creating their own functions, it seems…
Simple formulas for the number of different cyclic and dihedral necklaces containing $n_j$ beads of the $j$-th color, $j\leq m$ and $\sum_{j=1}^mn_j=N$, are derived.
Background: Current nomogram can only be created for regression algorithm. Providing nomogram for any machine learning (ML) algorithms may accelerate model deployment in clinical settings or improve model availability. We developed an R…
The family of stable distributions received extensive applications in many fields of studies since it incorporates both the skewness and heavy tails. In this paper, we introduce a package written in the R language called alphastable. The…
This paper focuses on the modeling of musical melodies as networks. Notes of a melody can be treated as nodes of a network. Connections are created whenever notes are played in sequence. We analyze some main tracks coming from different…
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
We define the notion of circular words, then consider on such words a constraint derived from the Fibonacci condition. We give several results on the structure of these circular words, then mention possible applications to various…
Randomness is a crucial resource for a broad range of important applications, such as Monte Carlo simulation and computation, generative artificial intelligence and cryptography. But what is randomness? A widely accepted definition has…
This study investigates the capabilities of Cyclic Redundancy Checks(CRCs) to detect burst and random errors. Researchers have favored these error detection codes throughout the evolution of computing and have implemented them in…
Every binary De~Bruijn sequence of order n satisfies a recursion 0=x_n+x_0+g(x_{n-1}, ..., x_1). Given a function f on (n-1) bits, let N(f; r) be the number of functions generating a De Bruijn sequence of order n which are obtained by…
Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by non-principal ideals yields simple…