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This chapter presents an overview of a specific form of limited dependent variable models, namely discrete choice models, where the dependent (response or outcome) variable takes values which are discrete, inherently ordered, and…
In this paper, the main purpose is to explore an SIRS epidemic model with a general nonlinear incidence rate $f(I)S=\beta I(1+\upsilon I^{k-1})S$ ($k>0$). We analyzed the existence and stability of equilibria of the epidemic model. Local…
The proximal causal inference framework enables the identification and estimation of causal effects in the presence of unmeasured confounding by leveraging two disjoint sets of observed strong proxies: negative control treatments and…
The time-dependent reproduction number Rt can be used to track pathogen transmission and to assess the efficacy of interventions. This quantity can be estimated by fitting renewal equation models to time series of infectious disease case…
Inspired by an example of Grebogi et al [1], we study a class of model systems which exhibit the full two-step scenario for the nonautonomous Hopf bifurcation, as proposed by Arnold [2]. The specific structure of these models allows a…
Large language and music models are increasingly used for constrained generation: rhyming lines, fixed meter, inpainting or infilling, positional endings, and other global form requirements. These systems often perform strikingly well, but…
In this paper we study the simultaneous reconstruction of two coefficients in a reaction-subdiffusion equation, namely a nonlinearity and a space dependent factor. The fact that these are coupled in a multiplicative matter makes the…
We consider the dynamics of the disordered trap model, which is known to be completely out-of-equilibrium and to present strong localization effects in its aging phase. We are interested into the influence of an external force, when it is…
We consider a system of two linear and linearly coupled oscillators with ideal impact constraints. Primary resonant energy exchange is investigated by analysis of the slow-flow using the action-angle (AA) formalism. Exact inversion of the…
Autoregressive models are widely used for the analysis of time-series data, but they remain underutilized when estimating effects of interventions. This is in part due to endogeneity of the lagged outcome with any intervention of interest,…
We revisit the sequential variants of linear regression with the squared loss, classification problems with hinge loss, and logistic regression, all characterized by unbounded losses in the setup where no assumptions are made on the…
In contrast to problems of interference in (exogenous) treatments, models of interference in unit-specific (endogenous) outcomes do not usually produce a reduced-form representation where outcomes depend on other units' treatment status…
We analyze the renormalization of systems whose effective degrees of freedom are described in terms of fluctuations which are ``environment'' dependent. Relevant environmental parameters considered are: temperature, system size, boundary…
In this manuscript, we study a Leslie-Gower predator-prey model with a hyperbolic functional response and weak Allee effect. The results reveal that the model supports coexistence and oscillation of both predator and prey populations. We…
We study the codimension-two bifurcations exhibited by a recently-developed SIR-type mathematical model for the spread of COVID-19, as its two main parameters -- the susceptible individuals' cautiousness level and the hospitals'…
Causal inference, estimating causal effects from observational data, is a fundamental tool in many disciplines. Of particular importance across a variety of domains is the continuous treatment setting, where the variable of intervention has…
In recent years, advanced model-based and data-driven control methods are unlocking the potential of complex robotics systems, and we can expect this trend to continue at an exponential rate in the near future. However, ensuring safety with…
Much traditional statistical modelling assumes that the outcome variables of interest are independent of each other when conditioned on the explanatory variables. This assumption is strongly violated in the case of infectious diseases,…
We show that a certain model for the spread of an infection has a phase transition in the recuperation rate. The model is as follows: There are particles or individuals of type A and type B, interpreted as healthy and infected,…
In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as…