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Quantum catalysts enable transformations that otherwise would be forbidden, offering a pathway to surpass conventional limits in quantum information processing. Among them, embezzling catalysts stand out for achieving near-perfect…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
We study the problem of entropy calibration, which asks whether a language model's entropy over generations matches its log loss on human text. Past work found that models are miscalibrated, with entropy per step increasing as generations…
Mutation is introduced into autocatalytic reaction networks. Examples of low dimensional dynamical systems --- n = 2, 3 and 4 --- are discussed and complete qualitative analysis is presented. Error thresholds known from simple…
Biological systems are driven by intricate interactions among the complex array of molecules that comprise the cell. Many methods have been developed to reconstruct network models of those interactions. These methods often draw on large…
A deep learning system typically suffers from a lack of reproducibility that is partially rooted in hardware or software implementation details. The irreproducibility leads to skepticism in deep learning technologies and it can hinder them…
Being a dual purpose enzyme, the DNA polymerase is responsible for elongation of the newly formed DNA strand as well as cleaving the erroneous growth in case of a misincorporation. The efficiency of replication depends on the coordination…
Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore it is reasonable to expect mutation rates will evolve downwards. However, we find this…
We determine conditions under which a random biochemical system is likely to contain a subsystem that is both autocatalytic and able to survive on some ambient `food' source. Such systems have previously been investigated for their…
We simulate the evolution of model protein sequences subject to mutations. A mutation is considered neutral if it conserves 1) the structure of the ground state, 2) its thermodynamic stability and 3) its kinetic accessibility. All other…
Point processes are finding growing applications in numerous fields, such as neuroscience, high frequency finance and social media. So classic problems of classification and clustering are of increasing interest. However, analytic study of…
DNA is emerging as an increasingly attractive medium for data storage due to a number of important and unique advantages it offers, most notably the unprecedented durability and density. While the technology is evolving rapidly, the…
The prevalence and low cost of LLMs have led to a rise of synthetic content. From review sites to court documents, "natural" content has been contaminated by data points that appear similar to natural data, but are in fact LLM-generated. In…
Though the problem of sequence-reversed protein folding is largely unexplored, one might speculate that reversed native protein sequences should be significantly more foldable than purely random heteropolymer sequences. In this article, we…
Enzyme mining is rapidly evolving as a data-driven strategy to identify biocatalysts with tailored functions from the vast landscape of uncharacterized proteins. The integration of machine learning into these workflows enables…
We precisely quantify the impact of statistical error in the quality of a numerical approximation to a random matrix eigendecomposition, and under mild conditions, we use this to introduce an optimal numerical tolerance for residual error…
We put forward an adaptive alpha (Type I Error) that decreases as the information grows, for hypothesis tests in which nested linear models are compared. A less elaborate adaptation was already presented in \citet{PP2014} for comparing…
Reconstruction error-based neural architectures constitute a classical deep learning approach to anomaly detection which has shown great performances. It consists in training an Autoencoder to reconstruct a set of examples deemed to…
Reconstruction error is a prevalent score used to identify anomalous samples when data are modeled by generative models, such as (variational) auto-encoders or generative adversarial networks. This score relies on the assumption that normal…
The asymptotic behavior of estimates and information criteria in linear models are studied in the context of hierarchically correlated sampling units. The work is motivated by biological data collected on species where autocorrelation is…