We extend the classical results on the symmetry inheritance of the canonical electromagnetic fields, described by the Maxwell's Lagrangian, to a much wider class of models, which include those of the Born-Infeld, power Maxwell and the Euler-Heisenberg type. Symmetry inheriting fields allow the introduction of electromagnetic scalar potentials and these are proven to be constant on the Killing horizons. Finally, using the relations obtained along the analysis, we generalize and simplify the recent proof for the symmetry inheritance of the 3-dimensional case, as well as give the first constraint for the higher dimensional electromagnetic fields.
Motivated by the many diverse responses of different countries to the COVID-19 emergency, here we develop a toy model of the dependence of the epidemics spreading on the availability of tests for disease. Our model, that we call SUDR+K, grounds on the usual SIR model, with the difference of splitting the total fraction of infected individuals in two components: patients that are still undetected and patients that have been already detected through tests. Moreover, we assume that available tests increase at a constant rate from the beginning of epidemics but are consumed to detect infected individuals. Strikingly, we find a bi-stable behavior between a phase with a giant fraction of infected and a phase with a very small fraction. We show that the separation between these two regimes is governed by a match between the rate of testing and a rate of infection spread at given time. We also show that the existence of two phases does not depend on the mathematical choice of the form of the term describing the rate at which undetected individuals are tested and detected. Presented research implies that a vigorous early testing activity, before the epidemics enters its giant phase, can potentially keep epidemics under control, and that even a very small change of the testing rate around the bi-stable point can determine a fluctuation of the size of the whole epidemics of various orders of magnitude. For the real application of realistic model to ongoing epidemics, we would gladly collaborate with field epidemiologists in order to develop quantitative models of testing process.
We present the first symmetry inheritance analysis of fields nonminimally coupled to gravity. In this work we are focused on the real scalar field φ with nonminimal coupling of the form ξφ 2 R. Possible cases of the symmetry noninheriting fields are constrained by the properties of the Ricci tensor and the scalar potential. Examples of such spacetimes can be found among those which are "dressed" with the stealth scalar field, a nontrivial scalar field configuration with the vanishing energymomentum tensor. We classify the scalar field potentials which allow the symmetry noninheriting stealth field configurations on top of the exact solutions of the Einstein's gravitational field equation with the cosmological constant.
In this paper, we analyze the time-series of minute price returns on the Bitcoin market through the statistical models of generalized autoregressive conditional heteroskedasticity (GARCH) family. Several mathematical models have been proposed in finance, to model the dynamics of price returns, each of them introducing a different perspective on the problem, but none without shortcomings. We combine an approach that uses historical values of returns and their volatilities -GARCH family of models, with a so-called "Mixture of Distribution Hypothesis", which states that the dynamics of price returns are governed by the information flow about the market. Using time-series of Bitcoin-related tweets and volume of transactions as external information, we test for improvement in volatility prediction of several GARCH model variants on a minute level Bitcoin price time series. Statistical tests show that the simplest GARCH(1,1) reacts the best to the addition of external signal to model volatility process on out-of-sample data.
Motivated by the problem of detection of cascades of defaults in economy, we developed a detection framework for an endogenous spreading based on causal motifs we define in this paper. We assume that the change of state of a vertex can be triggered either by an endogenous (related to the network) or an exogenous (unrelated to the network) event, that the underlying network is directed and that times when vertices changed their states are available. After simulating default cascades driven by different stochastic processes on different synthetic networks, we show that some of the smallest causal motifs can robustly detect endogenous spreading events. Finally, we apply the method to the data of defaults of Croatian companies and observe the time window in which an endogenous cascade was likely happening.
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