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Register a new userOn the generation of probabilistic forecasts from deterministic models
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Most of the methods that produce space weather forecasts are based on deterministic models. In order to generate a probabilistic forecast, a model needs to be run several times sampling the input parameter space, in order to generate an ensemble from which the distribution of outputs can be inferred. However, ensemble simulations are costly and often preclude the possibility of real-time forecasting. We introduce a simple and robust method to generate uncertainties from deterministic models, that does not require ensemble simulations. The method is based on the simple consideration that a probabilistic forecast needs to be both accurate and well-calibrated (reliable). We argue that these two requirements are equally important, and we introduce the Accuracy-Reliability cost function that quantitatively measures the trade-off between accuracy and reliability. We then define the optimal uncertainties as the standard deviation of the Gaussian distribution that minimizes the cost function. We demonstrate that this simple strategy, implemented here by means of a regularized deep neural network, produces accurate and well-calibrated forecasts, showing examples both on synthetic and real-world space weather data.
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It is well-known that wireless channel reciprocity together with fading can be exploited to generate a common secret key between two legitimate communication partners. This can be achieved by exchanging known deterministic pilot signals between both partners from which the random fading gains can be estimated and processed. However, the entropy and thus quality of the generated key depends on the channel coherence time. This can result in poor key generation rates in a low mobility environment, where the fading gains are nearly constant. Therefore, wide-spread deployment of wireless channel-based secret key generation is limited. To overcome these issues, we follow up on a recent idea which uses unknown random pilots and enables on-the-fly key generation. In addition, the scheme is able to incorporate local sources of randomness but performance bounds are hard to obtain with standard methods. In this paper, we analyse such a scheme analytically and derive achievable key rates in the Alice-Bob-Eve setting. For this purpose, we develop a novel approximation model which is inspired by the linear deterministic and the lower triangular deterministic model. Using this model, we can derive key rates for specific scenarios. We claim that our novel approach provides an intuitive and clear framework to analyse similar key generation problems.
Probabilistic forecasts in the form of probability distributions over future events have become popular in several fields including meteorology, hydrology, economics, and demography. In typical applications, many alternative statistical models and data sources can be used to produce probabilistic forecasts. Hence, evaluating and selecting among competing methods is an important task. The scoringRules package for R provides functionality for comparative evaluation of probabilistic models based on proper scoring rules, covering a wide range of situations in applied work. This paper discusses implementation and usage details, presents case studies from meteorology and economics, and points to the relevant background literature.
Electromagnetic cyclotron waves (ECWs) near the proton cyclotron frequency are frequently observed in the solar wind, yet their generation mechanism is still an open question. Based on the Wind data during the years 2005$-$2015, this paper carries out a statistical study on plasma characteristics associated with the occurrence of ECWs. The probability density distributions (PDDs) of proton temperature anisotropy ($T_perp/T_parallel$) and proton parallel beta ($beta_parallel$) are investigated, where $perp$ and $parallel$ refer to perpendicular and parallel to the background magnetic field, respectively. The PDDs depend on solar wind types as well as wave polarizations, and those for ECWs with left-handed (LH) polarization exhibit considerable differences from the PDDs for ambient solar winds. The distributions of occurrence rates of LH ECWs in ($beta_parallel$, $T_perp/T_parallel$) space show a tendency that the occurrence rates increase with proton temperature anisotropies. The $beta_parallel$ with maximum of occurrence rates is near 0.1 when $T_perp/T_parallel > 1$ while it is around 1 when $T_perp/T_parallel < 1$. The presence of alpha$-$proton differential flow with large kinetic energy corresponds to a much high occurrence rate as well as the domination of LH polarization of ECWs. Based on these observations and existing theories, we propose that the proton cyclotron and parallel firehose instabilities with effects of alpha$-$proton differential flow are likely responsible for the local generation of LH ECWs in the solar wind. The generation mechanism of right-handed ECWs seems to be complicated and more discussions are needed in future researches.
We consider the emergent behavior of viral spread when agents in a large population interact with each other over a contact network. When the number of agents is large and the contact network is a complete graph, it is well known that the population behavior -- that is, the fraction of susceptible, infected and recovered agents -- converges to the solution of an ordinary differential equation (ODE) known as the classical SIR model as the population size approaches infinity. In contrast, we study interactions over contact networks with generic topologies and derive conditions under which the population behavior concentrates around either the classic SIR model or other deterministic models. Specifically, we show that when most vertex degrees in the contact network are sufficiently large, the population behavior concentrates around an ODE known as the network SIR model. We then study the short and intermediate-term evolution of the network SIR model and show that if the contact network has an expander-type property or the initial set of infections is well-mixed in the population, the network SIR model reduces to the classical SIR model. To complement these results, we illustrate through simulations that the two models can yield drastically different predictions, hence use of the classical SIR model can be misleading in certain cases.
Effectus theory is a relatively new approach to categorical logic that can be seen as an abstract form of generalized probabilistic theories (GPTs). While the scalars of a GPT are always the real unit interval [0,1], in an effectus they can form any effect monoid. Hence, there are quite exotic effectuses resulting from more pathological effect monoids. In this paper we introduce sigma-effectuses, where certain countable sums of morphisms are defined. We study in particular sigma-effectuses where unnormalized states can be normalized. We show that a non-trivial sigma-effectus with normalization has as scalars either the two-element effect monoid 0,1 or the real unit interval [0,1]. When states and/or predicates separate the morphisms we find that in the 0,1 case the category must embed into the category of sets and partial functions (and hence the category of Boolean algebras), showing that it implements a deterministic model, while in the [0,1] case we find it embeds into the category of Banach order-unit spaces and of Banach pre-base-norm spaces (satisfying additional properties), recovering the structure present in GPTs. Hence, from abstract categorical and operational considerations we find a dichotomy between deterministic and convex probabilistic models of physical theories.
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