Related papers: The Power of Self-Reducibility: Selectivity, Infor…
Computational reductions are an important and powerful concept in computer science. However, they are difficult for many students to grasp. In this paper, we outline a concept for how the learning of reductions can be supported by…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
We consider the class of counting problems,i.e. functions in $\#$P, which are self reducible, and have easy decision version, i.e. for every input it is easy to decide if the value of the function $f(x)$ is zero. For example,…
Reproducibility is one of the core dimensions that concur to deliver Trustworthy Artificial Intelligence. Broadly speaking, reproducibility can be defined as the possibility to reproduce the same or a similar experiment or method, thereby…
This is the first part of a small-scale explorative study in an effort to start assessing reproducibility issues specific to scientometrics research. This effort is motivated by the desire to generate empirical data to inform debates about…
In recent years, Deep Learning has gained popularity for its ability to solve complex classification tasks, increasingly delivering better results thanks to the development of more accurate models, the availability of huge volumes of data…
One challenge (or opportunity!) that many instructors face is how varied the backgrounds, abilities, and interests of students are. In order to simultaneously instill confidence in those with weaker preparations and still challenge those…
We introduce the notion of a reproducible algorithm in the context of learning. A reproducible learning algorithm is resilient to variations in its samples -- with high probability, it returns the exact same output when run on two samples…
Reproducibility is a confused terminology. In this paper, I take a fundamental view on reproducibility rooted in the scientific method. The scientific method is analysed and characterised in order to develop the terminology required to…
"Systems that Explain Themselves" appears a provocative wording, in particular in the context of mathematics education -- it is as provocative as the idea of building educational software upon technology from computer theorem proving. In…
Re-finding electronic documents from a personal computer is a frequent demand to users. In a simple re-finding task, people can use many methods to retrieve a document, such as navigating directly to the document's folder, searching with a…
Readability assessment is the task of evaluating the reading difficulty of a given piece of text. Although research on computational approaches to readability assessment is now two decades old, there is not much work on synthesizing this…
Resource limitations make it hard to provide all students with one of the most effective educational interventions: personalized instruction. Reinforcement learning could be a key tool to reduce the development cost and improve the…
A significant amount of research has considered mathematical proofs, the students who learn them, and the instructors that teach them, from a variety of perspectives. This paper considers this topic from four main perspectives: students'…
One finding of cognitive research is that people do not automatically acquire usable knowledge by spending lots of time on task. Because students' knowledge hierarchy is more fragmented, "knowledge chunks" are smaller than those of experts.…
The problem of Information Retrieval is, given a set of documents D and a query q, providing an algorithm for retrieving all documents in D relevant to q. However, retrieval should depend and be updated whenever the user is able to provide…
This work discusses an approach to teach to mathematicians the importance and effectiveness of the application of Interactive Theorem Proving tools in their specific fields of interest. The approach aims to motivate the use of such tools…
This is the second part of a small-scale explorative study in an effort to assess reproducibility issues specific to scientometrics research. This effort is motivated by the desire to generate empirical data to inform debates about…
The design of recommendations strategies in the adaptive learning system focuses on utilizing currently available information to provide individual-specific learning instructions for learners. As a critical motivate for human behaviors,…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…