Related papers: How acausal equations emerge from causal dynamics

Structural Causal Models are widely used in causal modelling, but how they relate to other modelling tools is poorly understood. In this paper we provide a novel perspective on the relationship between Ordinary Differential Equations and…

From ancient philosophers to modern economists, biologists, and other researchers, there has been a continuous effort to unveil causal relations. The most formidable challenge lies in deducing the nature of the causal relationship: whether…

We derive causal relativistic fluid dynamical equations from the relaxation model of kinetic theory as in a procedure previously applied in the case of non-relativistic rarefied gases. By treating space and time on an equal footing and…

It is commonplace to encounter nonstationary data, of which the underlying generating process may change over time or across domains. The nonstationarity presents both challenges and opportunities for causal discovery. In this paper we…

Causal discovery from data affected by unobserved variables is an important but difficult problem to solve. The effects that unobserved variables have on the relationships between observed variables are more complex in nonlinear cases than…

Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…

Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called…

A one-dimensional continuum-mechanical model of axonal elongation due to assembly of tubulin dimers in the growth cone is presented. The conservation of mass leads to a coupled system of three differential equations. A partial differential…

We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretation in terms of continuum and microscopic physics. It is also…

A particle system with a single locally-conserved field (density) in a bounded interval with different densities maintained at the two endpoints of the interval is under study here. The particles interact in the bulk through a long range…

We introduce a new formulation of structural causal models for extremes, called the extremal structural causal model (eSCM). Unlike conventional structural causal models, where randomness is governed by a probability distribution, eSCMs use…

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…

Causal discovery from observational data is a challenging task that can only be solved up to a set of equivalent solutions, called an equivalence class. Such classes, which are often large in size, encode uncertainties about the orientation…

Causal representation learning aims to recover the latent causal variables and their causal relations, typically represented by directed acyclic graphs (DAGs), from low-level observations such as image pixels. A prevailing line of research…

Causal emergence is the theory that macroscales can reduce the noise in causal relationships, leading to stronger causes at the macroscale. First identified using the effective information and later the integrated information in model…

Systems with conserved currents driven by reservoirs at the boundaries offer an opportunity for a general analytic study that is unparalleled in more general out of equilibrium systems. The evolution of coarse-grained variables is governed…

Much of the causal discovery literature prioritises guaranteeing the identifiability of causal direction in statistical models. For structures within a Markov equivalence class, this requires strong assumptions which may not hold in…

In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide…

Directed acyclic graphical (DAG) models are a powerful tool for representing causal relationships among jointly distributed random variables, especially concerning data from across different experimental settings. However, it is not always…

We consider causal models with two observed variables and one latent variables, each variable being discrete, with the goal of characterizing the possible distributions on outcomes that can result from controlling one of the observed…