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Understanding and creating mathematics using natural mathematical language - the mixture of symbolic and natural language used by humans - is a challenging and important problem for driving progress in machine learning. As a step in this…
We axiomatize the molecular-biology reasoning style, show compliance of the standard reference: Ptashne, A Genetic Switch, and present proof-theory-induced technologies to help infer phenotypes and to predict life cycles from genotypes. The…
Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed…
Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…
As computational work becomes more and more integral to many aspects of scientific research, computational reproducibility has become an issue of increasing importance to computer systems researchers and domain scientists alike. Though…
Over the past few years, deep learning methods have been applied for a wide range of Software Engineering (SE) tasks, including in particular for the important task of automatically predicting and localizing faults in software. With the…
Currently it is widely accepted that the language of science is mathematics. This book explores an alternative idea where the future of science is based on the language of algorithms and programs. How such a language can actually be…
Turing computability is the standard computability paradigm which captures the computational power of digital computers. To understand whether one can create physically realistic devices which have super-Turing power, one needs to…
This report describes the state of the art in verifiable computation. The problem being solved is the following: The Verifiable Computation Problem (Verifiable Computing Problem) Suppose we have two computing agents. The first agent is the…
Computational method for statistical measures of reliability, confidence, and assurance are available for infinite population size. If the population size is finite and small compared to the number of samples tested, these computational…
Increased reproducibility of machine learning research has been a driving force for dramatic improvements in learning performances. The scientific community further fosters this effort by including reproducibility ratings in reviewer forms…
Proof competence, i.e. the ability to write and check (mathematical) proofs, is an important skill in Computer Science, but for many students it represents a difficult challenge. The main issues are the correct use of formal language and…
It is an unfortunate convention of science that research should pretend to be reproducible; our top tips will help you mitigate this fussy conventionality, enabling you to enthusiastically showcase your irreproducible work.
A recent trend in mathematical modeling is to publish the computer code together with the research findings. Here we explore the formal question, whether and in which sense a computer implementation is distinct from the mathematical model.…
This paper introduces reproducible research, and explains its importance, benefits and challenges. Some important tools for conducting reproducible research in Transportation Research are also introduced. Moreover, the source code for…
The ability of a quantum computer to reproduce or replicate the results of a quantum circuit is a key concern for verifying and validating applications of quantum computing. Statistical variations in circuit outcomes that arise from…
Large language models are increasingly capable at closed-world mathematical reasoning, but research assistance also requires source-grounded use of the literature. When a proof reaches a non-trivial step, a useful assistant should determine…
What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical…
Study reproducibility is essential to corroborate, build on, and learn from the results of scientific research but is notoriously challenging in bioinformatics, which often involves large data sets and complex analytic workflows involving…
AI agents have the potential to aid users on a variety of consequential tasks, including conducting scientific research. To spur the development of useful agents, we need benchmarks that are challenging, but more crucially, directly…