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This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…

In the chirally-invariant context of the $U_{em}(1)$ gauge interaction and four-fermion interactions for ordinary and mirror fermions, the Schwinger-Dyson equation for the fermion self-energy function is studied on a lattice. We find that a…

It is shown that the theory of causal fermion systems gives rise to a novel mechanism of baryogenesis. This mechanism is worked out computationally in globally hyperbolic spacetimes in a way which enables the quantitative study in concrete…

We develop a principled framework for discovering causal structure in partial differential equations (PDEs) using physics-informed neural networks and counterfactual perturbations. Unlike classical residual minimization or sparse regression…

We consider geometric variational problems for a functional defined on a curve in three-dimensional space. The functional is assumed to be written in a form invariant under the group of Euclidean motions. We present the Euler-Lagrange…

Relationship between two popular modeling frameworks of causal inference from observational data, namely, causal graphical model and potential outcome causal model is discussed. How some popular causal effect estimators found in…

The analysis of the causality is important in many fields of research. I propose a causal theory to obtain the causal effects in a causal loglinear model. It calculates them using the odds ratio and Pearl's causal theory. The effects are…

Traditional models of climate change use complex systems of coupled equations to simulate physical processes across the Earth system. These simulations are highly computationally expensive, limiting our predictions of climate change and…

Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and in the…

We propose a method to infer causal structures containing both discrete and continuous variables. The idea is to select causal hypotheses for which the conditional density of every variable, given its causes, becomes smooth. We define a…

In studies of interfaces with dynamic chemical composition, bulk and interfacial quantities coupled via surface conservation laws of excess surface quantities. While this approach is for microscopically sharp interfaces, its applicability…

The interplay between off-shell and on-shell unfolded systems is analysed. The formulation of invariant constraints that put an off-shell system on shell is developed by adding new variables and derivation in the target space, that extends…

Causal representation learning (CRL) aims at recovering latent causal variables from high-dimensional observations to solve causal downstream tasks, such as predicting the effect of new interventions or more robust classification. A…

Much of our experiments are designed to uncover the cause(s) and effect(s) behind a data generating mechanism (i.e., phenomenon) we happen to be interested in. Uncovering such relationships allows us to identify the true working of a…

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be…

The causal action principle is analyzed for a system of relativistic fermions composed of massive Dirac particles and neutrinos. In the continuum limit, we obtain an effective interaction described by classical gravity as well as the strong…

Causal inference uses observations to infer the causal structure of the data generating system. We study a class of functional models that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual…

The surface partition of large fragments is derived analytically within a simple statistical model by the Laplace-Fourier transformation method. In the limit of small amplitude deformations, a suggested Hills and Dales Model reproduces the…

In the present work, we formulate a necessary condition for functionals with Lagrangians depending on fractional derivatives of differentiable functions to possess an extremum. The Euler-Lagrange equation we obtained generalizes previously…

We study causal inference in a multi-environment setting, in which the functional relations for producing the variables from their direct causes remain the same across environments, while the distribution of exogenous noises may vary. We…