Related papers: Genealogical tree of Russian schools on Nonlinear …
Neural networks (NNs) and decision trees (DTs) are both popular models of machine learning, yet coming with mutually exclusive advantages and limitations. To bring the best of the two worlds, a variety of approaches are proposed to…
Biological and social systems are structured at multiple scales, and the incentives of individuals who interact in a group may diverge from the collective incentive of the group as a whole. Mechanisms to resolve this tension are responsible…
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
Molecular phylogeny has focused mainly on improving models for the reconstruction of gene trees based on sequence alignments. Yet, most phylogeneticists seek to reveal the history of species. Although the histories of genes and species are…
Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more…
The dynamics of the modern information society changes the usual areas of human activity, generates various innovations based on the widespread use of Information and Communication Technologies (ICTs). Virtually, every activity today is…
Scientific inference involves obtaining the unknown properties or behavior of a system in the light of what is known, typically, without changing the system. Here we propose an alternative to this approach: a system can be modified in a…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
In this paper we investigate the use of staged tree models for discrete longitudinal data. Staged trees are a type of probabilistic graphical model for finite sample space processes. They are a natural fit for longitudinal data because a…
064<p type="texpara" tag="Body Text" et="abstract" bin="clone" >There are two schools, or lines of thought, that try to unify the apparently divergent laws of dynamics and thermodynamics and to explain the observed time-asymmetry of the…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
Hidden tree Markov models allow learning distributions for tree structured data while being interpretable as nondeterministic automata. We provide a concise summary of the main approaches in literature, focusing in particular on the…
An acyclic causal structure can be described with directed acyclic graph (DAG), where arrows indicate the possibility of direct causation. The task of learning this structure from data is known as "causal discovery." Diverse populations or…
Physics-based simulations typically operate with a combination of complex differentiable equations and many scientific and geometric inputs. Our work involves gathering data from those simulations and seeing how well tree-based machine…
The dynamic analysis of structural change in the organization of the sciences requires methodologically the integration of multivariate and time-series analysis. Structural change--e.g., interdisciplinary development--is often an objective…
We propose a method to identify nonlinear acyclic networks in continuous time when the dynamics are located on the edges and all the nodes are excited. We show that it is necessary and sufficient to measure all the sinks to identify any…
It is well-established that the process of learning and capability building is core to economic development and structural transformation. Since knowledge is `sticky', a key component of this process is learning-by-doing, which can be…
Scientific research is a major driving force in a knowledge based economy. Income, health and wellbeing depend on scientific progress. The better we understand the inner workings of the scientific enterprise, the better we can prompt,…