Related papers: A mathematical approach to resilience

This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We…

A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…

In the present paper, our goal is to establish a framework for the mathematical modelling and the analysis of the spread of an epidemic in a large population commuting regularly, typically along a time-periodic pattern, as is roughly…

Modelling, analysing and inferring triggering mechanisms in population reproduction is fundamental in many biological applications. It is also an active and growing research domain in mathematical biology. In this chapter, we review the…

This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…

Models with many signals, high-dimensional models, often impose structures on the signal strengths. The common assumption is that only a few signals are strong and most of the signals are zero or close (collectively) to zero. However, such…

Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…

Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…

In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding…

Within the biological, physical, and social sciences, there are two broad quantitative traditions: statistical and mathematical modeling. Both traditions have the common pursuit of advancing our scientific knowledge, but these traditions…

Resilience is the ability to positively respond to adversity. It has been studied in psychology for several decades, with focus on how individuals overcome traumata or cope with setbacks and obstacles in their professional career. Research…

Building resilience into today's complex infrastructures is critical to the daily functioning of society and its ability to withstand and recover from natural disasters, epidemics, and cyber-threats. This study proposes quantitative…

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…

This paper derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a…

In this paper we investigate the flexibility of matrix distributions for the modeling of mortality. Starting from a simple Gompertz law, we show how the introduction of matrix-valued parameters via inhomogeneous phase-type distributions can…

The significance of mortality modeling extends across multiple research areas, ranging from life insurance valuation to optimal lifetime decision-making. Existing approaches, such as mortality laws and factor-based models, often fall short…

Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…

Focusing on a specific crowd dynamics situation, including real life experiments and measurements, our paper targets a twofold aim: (1) we present a Bayesian probabilistic method to estimate the value and the uncertainty (in the form of a…

By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…

Comparable to the traditional notion of stability in system dynamics, resilience is typically measured in a way that assesses the quality of a system's response, for example the speed of its recovery. We present a broadly applicable…