相关论文: Which causality? Differences between the trajector…

This investigation presents evidence of the relation between the dynamics of intense events in small-scale turbulence and the energy cascade. We use the generalised (H\"older) means to track the temporal evolution of intense events of the…

The reflection time, during which a particle is in the classically forbidden region, is described by the trajectory representation for reflection by a semi-infinite rectangular barrier. The Schr\"odinger wave function has microstates for…

Can the direction of time and the causal structure of space-time be inferred from operational principles? Causal models and tensor networks offer complementary perspectives: the former encodes cause-effect relations via directed graphs,…

Density fluctuations of fluids with negative pressure exhibit decreasing time behaviour in the long wavelength limit, but are strongly unstable in the small wavelength limit when a hydrodynamical approach is used. On the other hand, the…

Unstable periodic orbits scar wave functions in chaotic systems. This also influences the associated spectra, that follow the otherwise universal Porter--Thomas intensity distribution. We show here how this deviation extend to other longer…

We define a new measure of causation from a fluctuation-response theorem for Kullback-Leibler divergences, based on the information-theoretic cost of perturbations. This information response has both the invariance properties required for…

We analyze the linear causality and stability of third-order fluid dynamics considering perturbations around a global equilibrium state. We investigate the formulation derived from kinetic theory, using the Chapman-Enskog expansion, in PRC…

The concepts of information transfer and causal effect have received much recent attention, yet often the two are not appropriately distinguished and certain measures have been suggested to be suitable for both. We discuss two existing…

At the classical level the electromagnetic field can be well identified at the spatial infinity. Staruszkiewicz pointed out that the quantization of the electromagnetic field at spatial infinity is essentially unique and follows from the…

Massive data collection holds the promise of a better understanding of complex phenomena and, ultimately, better decisions. Representation learning has become a key driver of deep learning applications, as it allows learning latent spaces…

Cosmological perturbation theory is a key tool to study the universe. The linear or first order theory is well understood, however, developing and applying the theory beyond linear order is at the cutting edge of current research in…

The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is…

State-dependent time-impulsive perturbations to a two-dimensional autonomous flow with stable and unstable manifolds are analysed by posing in terms of an integral equation which is valid in both forwards- and backwards-time. The impulses…

Causal inference in brain networks has traditionally relied on regression-based models such as Granger causality, structural equation modeling, and dynamic causal modeling. While effective for identifying directed associations, these…

Quantum trajectory-based descriptions of interference between two coherent stationary waves in a double-slit experiment are presented, as given by the de Broglie-Bohm (dBB) and modified de Broglie-Bohm (MdBB) formulations of quantum…

This tutorial provides a concise introduction to modern causal modeling by integrating potential outcomes and graphical methods. We motivate causal questions such as counterfactual reasoning under interventions and define binary treatments…

By tracking tracer particles at high speeds and for long times, we study the geometric statistics of Lagrangian trajectories in an intensely turbulent laboratory flow. In particular, we consider the distinction between the displacement of…

In the causal learning setting, we wish to learn cause-and-effect relationships between variables such that we can correctly infer the effect of an intervention. While the difference between a cyclic structure and an acyclic structure may…

Black hole perturbation theory beyond second order is not well understood because typically one defines the meaning of gauge invariance order by order which is ambiguous. In this series of works we therefore developed a new approach which…

Causal inference is a central goal across many scientific disciplines. Over the past several decades, three major frameworks have emerged to formalize causal questions and guide their analysis: the potential outcomes framework, structural…