Related papers: Phase transitions in Paradigm models
Predicting counterfactual outcomes in longitudinal data, where sequential treatment decisions heavily depend on evolving patient states, is critical yet notoriously challenging due to complex time-dependent confounding and inadequate…
Using the renormalization group approach, we consider the $O(N)\otimes O(M)$ model in four and more dimensions. We find that independently on $N$ and $M$, for $N\geq M\geq 2$, a transition can be of both the first and second order. In…
The sequential dependence model (SDM) is a popular retrieval model which is based on the theory of probabilistic graphical models. While it was originally introduced by Metzler and Croft as a Markov Random Field (aka discriminative…
In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the…
Branching processes are a class of continuous-time Markov chains (CTMCs) prevalent for modeling stochastic population dynamics in ecology, biology, epidemiology, and many other fields. The transient or finite-time behavior of these systems…
In the real world, planning is often challenged by distribution shifts. As such, a model of the environment obtained under one set of conditions may no longer remain valid as the distribution of states or the environment dynamics change,…
Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter $\alpha$, called the pathway parameter, one can connect generalized type-1 beta family…
Mathematical and simulation models are often used to predict the spread of a disease and estimate the impact of public health interventions, and many such models have been developed and used during the COVID-19 pandemic. This paper…
The temperature phase transition in the $N$-component scalar field theory with spontaneous symmetry breaking is investigated using the method combining the second Legendre transform and with the consideration of gap equations in the extrema…
We report a dynamical phase transition in the information spreading within a classical 2D deterministic interacting many-body system. Specifically, the transition is observed in a recently introduced momentum-conserving parity check…
Obtaining accurate forecasts for the evolution of epidemic outbreaks from deterministic compartmental models represents a major theoretical challenge. Recently, it has been shown that these models typically exhibit trajectories' degeneracy,…
Diffusion models (DMs) have recently emerged as SoTA tools for generative modeling in various domains. Standard DMs can be viewed as an instantiation of hierarchical variational autoencoders (VAEs) where the latent variables are inferred…
Performative distribution shift captures the setting where the choice of which ML model is deployed changes the data distribution. For example, a bank which uses the number of open credit lines to determine a customer's risk of default on a…
Since the scale factor and the crossover rate significantly influence the performance of differential evolution (DE), parameter adaptation methods (PAMs) for the two parameters have been well studied in the DE community. Although PAMs can…
The potential of applying diffusion models (DMs) for multiple antenna communications is discussed. A unified framework of applying DM for multiple antenna tasks is first proposed. Then, the tasks are innovatively divided into two…
We provide a mean-field description for a leader-follower dynamics with mass transfer among the two populations. This model allows the transition from followers to leaders and vice versa, with scalar-valued transition rates depending…
We propose a simple stochastic model of market behavior. Dividing market participants into two groups: trend-followers and fundamentalists, we derive the general form of a stochastic equation of market dynamics. The model has two…
State space models (SSMs) have shown remarkable empirical performance on many long sequence modeling tasks, but a theoretical understanding of these models is still lacking. In this work, we study the learning dynamics of linear SSMs to…
Game theory formalizes certain interactions between physical particles or between living beings in biology, sociology, and economics, and quantifies the outcomes by payoffs. The prisoner's dilemma (PD) describes situations in which it is…
In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response.…