Related papers: Covariant Growth Dynamics
We introduce and explore the notion of "spaces of input histories", a broad family of combinatorial objects which can be used to model input-dependent, dynamical causal order. We motivate our definition with reference to traditional partial…
Macroevolutionary dynamics often display sudden, explosive surges, where systems remain relatively stable for extended periods before experiencing dramatic acceleration that frequently exceeds traditional exponential growth. This pattern is…
General Relativity traces the evolution of our Universe back to a Big Bang singularity. To probe physics before the singularity -- if indeed there is a ``before'' -- we must turn to quantum gravity. The Causal Set approach to quantum…
Covariate adjustment is one method of causal effect identification in non-experimental settings. Prior research provides routes for finding appropriate adjustments sets, but much of this research assumes knowledge of the underlying causal…
We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…
Theoretical developments in sequential Bayesian analysis of multivariate dynamic models underlie new methodology for causal prediction. This extends the utility of existing models with computationally efficient methodology, enabling routine…
In many scientific contexts, different investigators experiment with or observe different variables with data from a domain in which the distinct variable sets might well be related. This sort of fragmentation sometimes occurs in molecular…
Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…
This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of…
Causal set quantum gravity is a Lorentzian approach to quantum gravity, based on the causal structure of spacetime. It models each spacetime configuration as a discrete causal network of spacetime points. As such, key questions of the…
Dynamics of coarsening of a statistically homogeneous fractal cluster, created by a morphological instability of diffusion-controlled growth, is investigated theoretically. An exact mathematical setting of the problem is presented that…
The ghost-free theory of massive gravity with two dynamical metrics has been shown to produce viable cosmological expansion, where the late-time acceleration of the Universe is due to the finite range of the gravitational interaction rather…
The notion of causal effect is fundamental across many scientific disciplines. Traditionally, quantitative researchers have studied causal effects at the level of variables; for example, how a certain drug dose (W) causally affects a…
In this paper, we consider the problem of causal order discovery within the framework of monotonic Structural Causal Models (SCMs), which have gained attention for their potential to enable causal inference and causal discovery from…
For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the…
We develop two statistical models for space-time abundance data based on a stochastic underlying continuous individual movement. In contrast to current models for abundance in statistical ecology, our models exploit the explicit connection…
A probabilistic expert system emulates the decision-making ability of a human expert through a directional graphical model. The first step in building such systems is to understand data generation mechanism. To this end, one may try to…
Detecting and localizing change points in sequential data is of interest in many areas of application. Various notions of change points have been proposed, such as changes in mean, variance, or the linear regression coefficient. In this…
We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the…
The initial conditions of our universe appear to us in the form of a classical probability distribution that we probe with cosmological observations. In the current leading paradigm, this probability distribution arises from a quantum…