Related papers: Modelling comonotonic group-life under dependent d…
In some randomized clinical trials, patients may die before the measurements of their outcomes. Even though randomization generates comparable treatment and control groups, the remaining survivors often differ significantly in background…
We examine interacting cognitive modules of human biology which, in the asymptotic limit of long sequences of responses, define the output of an appropriate 'dual' information source. Applying a 'necessary condition' communication theory…
The decay process of the schematic one-dimensional three-body system is considered. A time-dependent approach is used in combination with a one-dimensional three-body model, which is composed of a heavier core nucleus and two nucleons, with…
Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study the instabilities of a mixture…
We discuss a simple model of co-evolution. In order to emphasise the effect of interaction between individuals the entire population is subjected to the same physical environment. Species are emergent structures and extinction, origination…
Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting…
When a large number of similar entities interact among each other and with their environment at a low scale, unexpected outcomes at higher spatio-temporal scales might spontaneously arise. This nontrivial phenomenon, known as emergence,…
A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…
Recent work shows issues of consistency with explanations, with methods generating local explanations that seem reasonable instance-wise, but that are inconsistent across instances. This suggests not only that instance-wise explanations can…
In these lectures I discuss peculiarities of the critical behaviour of ``non-ideal'' systems as it is explained by the renormalization group approach. Examples considered here include account of the single-ion anisotropy, structural…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
Using 2-loop renormalisation group calculations, we study a system of $N$ two-dimensional Potts models with random bonds coupled together by their local energy density. This model can be seen as a generalization of the random Ashkin-Teller…
Handling highly dependent data is crucial in clinical trials, particularly in fields related to ophthalmology. Incorrectly specifying the dependency structure can lead to biased inferences. Traditionally, models rely on three fixed…
Using 1-loop renormalisation group equations, we analyze the effect of randomness on multi-critical unitary minimal conformal models. We study the case of two randomly coupled $M_p$ models and found that they flow in two decoupled $M_{p-1}$…
The Basener-Ross system is a known model in Population Dynamics for the interaction of consumers and resources in an isolated habitat. For an extended version with time-dependent coefficients as a model of possible variations of the…
We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the…
When longitudinal outcomes are evaluated in mortal populations, their non-existence after death complicates the analysis and its causal interpretation. Where popular methods often merge longitudinal outcome and survival into one scale or…
Extreme events are often multivariate in nature. A compound extreme occurs when a combination of variables jointly produces a significant impact, even if individual components are not necessarily marginally extreme. Compound extremes have…
We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case-control studies. Graphical models represent assumptions about the…
Multi-dimensional data frequently occur in many different fields, including risk management, insurance, biology, environmental sciences, and many more. In analyzing multivariate data, it is imperative that the underlying modelling…