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A class of robust estimators which are obtained from dual representation of $\phi$-divergences, are studied empirically for the normal location model. Members of this class of estimators are compared, and it is found that they are efficient…

Robustness is widely regarded as a fundamental problem in the analysis of machine learning (ML) models. Most often robustness equates with deciding the non-existence of adversarial examples, where adversarial examples denote situations…

With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…

Increasingly sophisticated experiments, coupled with large-scale computational models, have the potential to systematically test biological hypotheses to drive our understanding of multicellular systems. In this short review, we explore key…

The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…

This thesis is about the study of complex systems through simple models. Our work evidences the relevance of this kind of modeling in science, which provides us with a better understanding of nature at minimum cost. The fundamentals tools…

Probabilistic model checking is an approach to the formal modelling and analysis of stochastic systems. Over the past twenty five years, the number of different formalisms and techniques developed in this field has grown considerably, as…

In computational materials science, mechanical properties are typically extracted from simulations by means of analysis routines that seek to mimic their experimental counterparts. However, simulated data often exhibit uncertainties that…

Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…

Different research communities have developed various approaches to assess the credibility of predictive models. Each approach usually works well for a specific type of model, and under some epistemic conditions that are normally satisfied…

Reproducibility is a cornerstone of science, as the replication of findings is the process through which they become knowledge. It is widely considered that many fields of science are undergoing a reproducibility crisis. This has led to the…

This position paper reflects on the state-of-the-art in decision-making under uncertainty. A classical assumption is that probabilities can sufficiently capture all uncertainty in a system. In this paper, the focus is on the uncertainty…

The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…

Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complex system with highly simplified or toy models. In introductory physics classes, we tend to use them…

Computational simulations are a popular method for testing hypotheses about the emergence of communication. This kind of research is performed in a variety of traditions including language evolution, developmental psychology, cognitive…

Modeling and topological analysis of networks in biological and other complex systems, must venture beyond the limited consideration of very few network metrics like degree, betweenness or assortativity. A proper identification of…

In the presence of model risk, it is well-established to replace classical expected values by worst-case expectations over all models within a fixed radius from a given reference model. This is the "robustness" approach. We show that…

Can one demonstrate quantitative effects of diversity within a system comprised of distinct individuals on the performance of the system as a whole? Assuming that individuals can be different, we develop a model to interpolate between…

We show that there may exist an inherent tension between the goal of adversarial robustness and that of standard generalization. Specifically, training robust models may not only be more resource-consuming, but also lead to a reduction of…

Many widely used models amount to an elaborate means of making up numbers--but once a number has been produced, it tends to be taken seriously and its source (the model) is rarely examined carefully. Many widely used models have little…