Related papers: Python for education: permutations
Binary classification is a fundamental task in machine learning, with applications spanning various scientific domains. Whether scientists are conducting fundamental research or refining practical applications, they typically assess and…
stream-learn is a Python package compatible with scikit-learn and developed for the drifting and imbalanced data stream analysis. Its main component is a stream generator, which allows to produce a synthetic data stream that may incorporate…
We describe some "unrestricted" algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by…
We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group of minimal degree m and on the number of its elements of any given support.…
In this paper, we study the staircase encoding of permutations, which maps a permutation to a staircase grid with cells filled with permutations. We consider many cases, where restricted to a permutation class, the staircase encoding…
Instruction tuning significantly enhances the performance of large language models (LLMs) across various tasks. However, the procedure to optimizing the mixing of instruction datasets for LLM fine-tuning is still poorly understood. This…
Can a machine learn Machine Learning? This work trains a machine learning model to solve machine learning problems from a University undergraduate level course. We generate a new training set of questions and answers consisting of course…
Meta-learning (a.k.a. learning to learn) has recently emerged as a promising paradigm for a variety of applications. There are now many meta-learning methods, each focusing on different modeling aspects of base and meta learners, but all…
This paper describes a design that can be used for Explainable AI. The lower level is a nested ensemble of patterns created by self-organisation. The upper level is a hierarchical tree, where nodes are linked through individual concepts, so…
We consider uniform random permutations in proper substitution-closed classes and study their limiting behavior in the sense of permutons. The limit depends on the generating series of the simple permutations in the class. Under a mild…
The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group…
Permutation tests are a distribution free way of performing hypothesis tests. These tests rely on the condition that the observed data are exchangeable among the groups being tested under the null hypothesis. This assumption is easily…
We present a bijective algorithm with which an arbitrary permutation decomposes canonically into elementary blocks which we call families, which are sets with a specified number of ascents and descents. We show that families, arranged in an…
Structural Equation Modeling (SEM) is an umbrella term that includes numerous multivariate statistical techniques that are employed throughout a plethora of research areas, ranging from social to natural sciences. Until recently, SEM…
The use of Python is noticeably growing among the scientific community, and Astronomy is not an exception. The power of Python consists of being an extremely versatile high-level language, easy to program that combines both traditional…
Organizations have realized the importance of data analysis and its benefits. This in combination with Machine Learning algorithms has allowed to solve problems more easily, making these processes less time-consuming. Neural networks are…
We introduce the notion of a weighted inversion statistic on the symmetric group, and examine its distribution on each conjugacy class. Our work generalizes the study of several common permutation statistics, including the number of…
Analogies help learners understand unfamiliar concepts by relating them to known concepts. Despite recent advances, large language models (LLMs) continue to struggle to generate analogies of comparable quality to those produced by humans.…
We determine the permutation groups that arise as the automorphism groups of cyclic combinatorial objects. As special cases we classify the automorphism groups of cyclic codes. We also give the permutations by which two cyclic combinatorial…
An algorithm is presented for unranking permutations in transposition order: Given a seed s\in N, the algorithm produces a permutation P(s) that differs from the permutation P(s+1) by the transposition of two elements.