Related papers: New mathematical methods for psychophysical filter…
Processes of mass communications in complicated social or sociobiological systems such as marketing, economics, politics, animal populations, etc. as a subject for the special scientific discipline - "mediaphysics" - are considered in its…
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
Although there is growing interest in measuring integrated information in computational and cognitive systems, current methods for doing so in practice are computationally unfeasible. Existing and novel integration measures are investigated…
We present a generic way to hybridize physical and data-driven methods for predicting physicochemical properties. The approach `distills' the physical method's predictions into a prior model and combines it with sparse experimental data…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
These notes provide a systematic mathematical treatment of the subject of data assimilation.
This opening editorial aims to interest researchers and encourage novel research in the closely related fields of sociophysics and computational social science. We briefly discuss challenges and possible research directions in the study of…
The Iterative Filtering method is a technique developed recently for the decomposition and analysis of non-stationary and non-linear signals. In this work we propose two alternative formulations of the original algorithm which allows to…
Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…
Filter selection techniques are known for their simplicity and efficiency. However this kind of methods doesn't take into consideration the features inter-redundancy. Consequently the un-removed redundant features remain in the final…
This review examined the current advancements in data-driven methods for analyzing flow and transport in porous media, which has various applications in energy, chemical engineering, environmental science, and beyond. Although there has…
Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational…
Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call "mathematical data science". In this paradigm, one studies mathematical objects collectively rather than…
We review methods of data analysis for biophysical data with a special emphasis on single molecule applications. Our review is intended for anyone, from student to established researcher. For someone just getting started, we focus on…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
This is a short review of Monte Carlo methods for approximating filter distributions in state space models. The basic algorithm and different strategies to reduce imbalance of the weights are discussed. Finally, methods for more difficult…
The use of cross-diffusion systems as mathematical models of different image processes is investigated. The present paper is concerned with linear filtering. First, those systems satisfying the most important scale-space properties are…
Non-parametric methods avoid the problem of having to specify a particular data generating mechanism, but can be computationally intensive, reducing their accessibility for large data problems. Empirical likelihood, a non-parametric…
By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…