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The Kibble-Zurek mechanism (KZM) predicts that the average number of topological defects generated upon crossing a continuous or quantum phase transition obeys a universal scaling law with the quench time. Fluctuations in the defect number…

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…

We present a general dynamic finite-size scaling theory for the quantum dynamics after an abrupt quench, at both continuous and first-order quantum transitions. For continuous transitions, the scaling laws are naturally ruled by the…

Causal inference permits us to discover covert relationships of various variables in time series. However, in most existing works, the variables mentioned above are the dimensions. The causality between dimensions could be cursory, which…

Many solitonic configurations in field theory have localized bound states in their spectrum of linear perturbations. This opens up the possibility of having long lived excitations of these solitons that could affect their dynamics. We start…

In this article, we present explicit estimates of the size of the domain on which the Implicit Function Theorem and the Inverse Function Theorem are valid. For maps that are twice continuously differentiable, these estimates depend upon the…

A brief overview of some open questions in general relativity with important consequences for causality theory is presented, aiming to a better understanding of the causal structure of the spacetime. Special attention is accorded to the…

Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad…

Stationary solution of one-dimensional Sine-Gordon system is embedded in a multidimensional theory with explicitly finite domain in the added spatial dimensions. Semiclassical corrections to energy are calculated for static kink solution…

We study the formation of domain walls in a phase transition in which an S_5\times Z_2 symmetry is spontaneously broken to S_3\times S_2. In one compact spatial dimension we observe the formation of a stable domain wall lattice. In two…

Identifying the causal structures between two statistically correlated events has been widely investigated in many fields of science. While some of the well-studied classical methods are carefully generalized to quantum version of causal…

We present new experimental results on the quenching dynamics of an extended thermo-convective system (a network array of approximately 100 convective oscillators) going through a secondary subcritical bifurcation. We characterize a…

This paper presents a framework for Quantum causal modeling based on the interpretation of causality as a relation between an observer's probability assignments to hypothetical or counterfactual experiments. The framework is based on the…

Knowledge of the underlying causal relations is essential for inferring the effect of interventions in complex systems. In a widely studied approach, structural causal models postulate noisy functional relations among interacting variables,…

Groups of cells, including clusters of cancerous cells, multicellular organisms, and developing organs, may both grow and break apart. What physical factors control these fractures? In these processes, what sets the eventual size of…

Planning is one of the most studied problems in computer science. In this paper, we consider the timeline-based approach, where the domain is modeled by a set of independent, but interacting, components, identified by a set of state…

Causal inequalities are bounds on correlations obtained when operations take place in a causal sequence, i.e. in which the background time or definite causal structure pre-exists such that every operation is either in the future, in the…

We consider the problem of estimating a causal effect in a multi-domain setting. The causal effect of interest is confounded by an unobserved confounder and can change between the different domains. We assume that we have access to a proxy…

Only recently the essential role of the percolation critical point has been considered on the dynamical properties of connected regions of aligned spins (domains) after a sudden temperature quench. In equilibrium, it is possible to resolve…

Medical imaging models frequently fail when deployed across hospitals, scanners, populations, or imaging protocols due to domain shift, limiting their clinical reliability. While transfer learning and domain adaptation address such shifts…