Related papers: The art of algorithmic guessing in $\texttt{gfun}$
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Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
This piece of work presents a meaningful example for the advantages of using bitwise operations for creating effective algorithms in programming. A task connected with mathematical modeling in weaving industry is examined and computed.
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…
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Discrete mixture models provide a well-known basis for effective clustering algorithms, although technical challenges have limited their scope. In the context of gene-expression data analysis, a model is presented that mixes over a finite…
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Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly possess some reasoning processes. The paper gives evidence that they also have metacognitive knowledge,…
Many algorithms and applications involve repeatedly solving variations of the same inference problem; for example we may want to introduce new evidence to the model or perform updates to conditional dependencies. The goal of adaptive…
This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be…
Probabilistic programming makes it easy to represent a probabilistic model as a program. Building an individual model, however, is only one step of probabilistic modeling. The broader challenge of probabilistic modeling is in understanding…
The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods for diffusion models. We recall these properties and develop some new generic tools associated with the gradient…
We describe various errors in the mathematical literature, and consider how some of them might have been avoided, or at least detected at an earlier stage, using tools such as Maple or Sage. Our examples are drawn from three broad…
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An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the…
Analogy is one of the core capacities of human cognition; when faced with new situations, we often transfer prior experience from other domains. Most work on computational analogy relies heavily on complex, manually crafted input. In this…
The Hastings algorithm is a key tool in computational science. While mathematically justified by detailed balance, it can be conceptually difficult to grasp. Here, we present two complementary and intuitive ways to derive and understand the…
In the spirit of "multi-culturalism", we use four kinds of computations: simulation, numeric, symbolic, and "conceptual" to explore some "games of pure chance" inspired by children board games like "Snakes and Ladders" (aka as "Chutes and…