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We introduce a new method, combination of random testing and abstract interpretation, for the analysis of programs featuring both probabilistic and non-probabilistic nondeterminism. After introducing "ordinary" testing, we show how to…
Recent research reveals that machine learning (ML) models are highly sensitive to minor changes in their training procedure, such as the inclusion or exclusion of a single data point, leading to conflicting predictions on individual data…
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…
We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense…
Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
Most of the data produced in software projects is of textual nature: source code, specifications, or documentations. The advances in quantitative analysis methods drove a lot of data analytics in software engineering. This has overshadowed…
This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
The astrophysics community uses different tools for computational tasks such as complex systems simulations, radiative transfer calculations or big data. Programming languages like Fortran, C or C++ are commonly present in these tools and,…
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers. The random access machine with unit or logarithmic cost is not adequate for measuring the complexity…
Randomized libraries are increasingly popular in protein engineering and other biomedical research fields. Statistics of the libraries are useful to guide and evaluate randomized library construction. Previous works only give the mean of…
Reproducibility is increasingly important to statistical research, but many details are often omitted from the published version of complex statistical analyses. A reader's comprehension is limited to what the author concludes, without…
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…