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Studying the real-time dynamics of strongly correlated systems poses significant challenges, which have recently become more manageable thanks to advances in density matrix renormalization group (DMRG) and tensor network methods. A notable…
A novel approach to analyzing time series generated by complex systems, such as markets, is presented. The basic idea of the approach is the {\it Law of Self-Similar Evolution}, according to which any complex system develops self-similarly.…
We consider Markov jump processes describing structured populations with interactions via density dependance. We propose a Markov construction with a distinguished individual which allows to describe the random tree and random sample at a…
In the last years different studies have revealed the usefulness of a microcanonical analysis of finite systems when dealing with phase transitions. In this approach the quantities of interest are exclusively expressed as derivatives of the…
In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…
Many practical approximations in physics and engineering invoke a relatively long physical domain with a relatively thin cross-section. In this scenario we typically expect the system to have structures that vary slowly in the long…
Time evolution of macroscopic systems is re-examined primarily through further analysis and extension of the equation of motion for the density matrix $\rho(t)$. Because $\rho$ contains both classical and quantum-mechanical probabilities it…
Master equations describing open quantum dynamics are typically first order differential equations. When such dynamics brings the trajectories in state space of more than one initial state to the same point at finite instants in time, the…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
We apply the event-chain Monte Carlo algorithm to classical continuum spin models on a lattice and clarify the condition for its validity. In the two-dimensional XY model, it outperforms the local Monte Carlo algorithm by two orders of…
We present a strategy for solving time-dependent problems on grids with local refinements in time using different time steps in different regions of space. We discuss and analyze two conservative approximations based on finite volume with…
A general dynamical process model of psychiatric disorders is proposed that specifies the basic cognitive processes involved in the transition from beliefs about self, others and world that are normal and adaptive, to beliefs that are…
It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of the…
Open effective field theories provide a systematic framework for describing systems coupled to an environment, where dissipation, noise, and modified conservation laws naturally arise. Working within the Schwinger-Keldysh formalism, we…
We present the applications of variational--wavelet approach to nonlinear (rational) model for spin-orbital motion: orbital dynamics and Thomas-BMT equations for classical spin vector. We represent the solution of this dynamical system in…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
The dynamical behaviours of a kinetically constrained spin model (Fredrickson-Andersen model) on a Bethe lattice are investigated by a perturbation analysis that provides exact final states above the nonergodic transition point. It is…
It has been speculated that gravity could be an emergent phenomenon, with classical general relativity as an effective, macroscopic theory, valid only for classical systems at large temporal and spatial scales. As in classical continuum…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider a model for spin-orbital motion: orbital…
The study of toy models in loop quantum gravity (LQG), defined as truncations of the full theory, is relevant to both the development of the LQG phenomenology, in cosmology and astrophysics, and the progress towards the resolution of the…