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While multiple testing procedures have been the focus of much statistical research, an important facet of the problem is how to deal with possible confounding. Procedures have been developed by authors in genetics and statistics. In this…
The lifetime measurement of molecular excited state has been the subject of many papers and experiments. Very often the experimental data are fitted by single or bi exponential decays which in many case is the best fit that can be done…
Based on the principle of causality, I advance a new principle of variation and try to use it as the most general principle for research into laws of nature.
Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction…
Classical statistical learning theory predicts a U-shaped relationship between test loss and model capacity, driven by the bias-variance trade-off. Recent advances in modern machine learning have revealed a more complex pattern,…
Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…
The key findings of classical population genetics are derived using a framework based on information theory using the entropies of the allele frequency distribution as a basis. The common results for drift, mutation, selection, and gene…
This paper uses decision-theoretic principles to obtain new insights into the assessment and updating of probabilities. First, a new foundation of Bayesianism is given. It does not require infinite atomless uncertainties as did Savage s…
We prove a multivariate version of Bernstein's inequality about the probability that degenerate $U$-statistics take a value larger than some number $u$. This is an improvement of former estimates for the same problem which yields an…
We consider a group synchronization problem with multiple frequencies which involves observing pairwise relative measurements of group elements on multiple frequency channels, corrupted by Gaussian noise. We study the computational phase…
We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions…
Conditional mutual information is important in the selection and interpretation of graphical models. Its empirical version is well known as a generalised likelihood ratio test and that it may be represented as a difference in entropy. We…
Mounting evidence shows that oscillatory activity is widespread in cell signaling. Here we review some of this recent evidence, focusing on both the molecular mechanisms that potentially underlie such dynamical behavior, and the potential…
We show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems. Information about the behavior of the relevant quantities, such as the signal-to-noise ratio, upon variations of the noise…
The capacity to adapt can greatly influence the success of systems that need to compensate for damaged parts, learn how to achieve robust performance in new environments, or exploit novel opportunities that originate from new technological…
Numeracy is the ability to understand and work with numbers. It is a necessary skill for composing and understanding documents in clinical, scientific, and other technical domains. In this paper, we explore different strategies for…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
A noise source model, consisting of a pulse sequence at random times with memory, is presented. By varying the memory we can obtain variable randomness of the stochastic process. The delay time between pulses, i. e. the noise memory,…
Identifying the causal structure of systems with multiple dynamic elements is critical to several scientific disciplines. The conventional approach is to conduct statistical tests of causality, for example with Granger Causality, between…
This note provides a theorem showing, under suitable technical assumptions, that if a system S adapts to a class of external signals U, in the sense of egulation against disturbances or tracking signals in U, then S must ecessarily contain…