Related papers: Python for education: permutations
This is a review of group entropy and its application to permutation complexity. Specifically we revisit a new approach to the notion of complexity in time serie analysis, based on both permutation entropy and group entropy. As a result,…
The representation of units and dimensions in informatics systems is barely codified and often ignored. For instance, the major languages used in scientific computing (Fortran, C and Python), have no type for dimension or unit, and so…
The interval poset of a permutation catalogues the intervals that appear in its one-line notation, according to set inclusion. We study this poset, describing its structural, characterizing, and enumerative properties.
Understanding student difficulties in programming is a complex challenge due to the wide range of topics and the abundant varieties of misconceptions and errors. This paper presents the design and development of a fine-grained taxonomy that…
Process mining, i.e., a sub-field of data science focusing on the analysis of event data generated during the execution of (business) processes, has seen a tremendous change over the past two decades. Starting off in the early 2000's, with…
Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…
A personalized learning system needs a large pool of items for learners to solve. When working with a large pool of items, it is useful to measure the similarity of items. We outline a general approach to measuring the similarity of items…
The graphs with permutation-representation number (\textit{prn}) at most two are known. While a characterization for the class of graphs with the \textit{prn} at most three is an open problem, we summarize the graphs of this class that are…
Ordinary Differential Equations (ODE) are used throughout science where the capture of rates of change in states is sought. While both pieces of commercial and open software exist to study such systems, their efficient and accurate usage…
We introduce a family of sequence transformations, defined via partial Bell polynomials, that may be used for a systematic study of a wide variety of problems in enumerative combinatorics. This family includes some of the transformations…
Many learning algorithms have invariances: when their training data is transformed in certain ways, the function they learn transforms in a predictable manner. Here we formalize this notion using concepts from the mathematical field of…
We explain the notion of the {\em entropy} of a discrete random variable, and derive some of its basic properties. We then show through examples how entropy can be useful as a combinatorial enumeration tool. We end with a few open…
The statistical literature is known to be inconsistent in the use of the terms "permutation test" and "randomization test". Several authors succesfully argue that these terms should be used to refer to two distinct classes of tests and that…
In this paper, we describe TRIPs-Py, a new Python package of linear discrete inverse problems solvers and test problems. The goal of the package is two-fold: 1) to provide tools for solving small and large-scale inverse problems, and 2) to…
We describe a practical algorithm which computes the accepting automaton for the insertion encoding of a permutation class, whenever this insertion encoding is regular. This algorithm is implemented in the accompanying Maple package INSENC,…
We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation…
A learning algorithm based on primary school teaching and learning is presented. The methodology is to continuously evaluate a student and to give them training on the examples for which they repeatedly fail, until, they can correctly…
The classification problem's complexity assessment is an essential element of many topics in the supervised learning domain. It plays a significant role in meta-learning -- becoming the basis for determining meta-attributes or…
Python has become the de-facto language for training deep neural networks, coupling a large suite of scientific computing libraries with efficient libraries for tensor computation such as PyTorch or TensorFlow. However, when models are used…
The purpose of this paper is to show how existing scientific software can be parallelized using a separate thin layer of Python code where all parallel communication is implemented. We provide specific examples on such layers of code, and…