Index problems for game automata

For a given regular language of infinite trees, one can ask about the minimal number of priorities needed to recognize this language with a non-deterministic, alternating, or weak alternating parity automaton. These questions are known as, respectively, the non-deterministic, alternating, and weak Rabin-Mostowski index problems. Whether they can be answered effectively is a long-standing open problem, solved so far only for languages recognizable by deterministic automata (the alternating variant trivializes). We investigate a wider class of regular languages, recognizable by so-called game automata, which can be seen as the closure of deterministic ones under complementation and composition. Game automata are known to recognize languages arbitrarily high in the alternating Rabin-Mostowski index hierarchy; that is, the alternating index problem does not trivialize any more. Our main contribution is that all three index problems are decidable for languages recognizable by game automata. Additionally, we show that it is decidable whether a given regular language can be recognized by a game automaton

What Is “The Word of God” in Sacred Scripture?

This article addresses the interdependence of the terms “word of God” and “Sacred Scripture,” as used in the doctrine of biblical inspiration, in the context of the Pontifical Biblical Commission’s 2014 document The Inspiration and Truth of Sacred Scripture: The Word that Comes from God and Speaks of God for the Salvation of the World. In the article, the essential features of the definition and function of Sacred Scripture are presented, and the understanding of the word of God in the context of the Old and New Testaments is demonstrated. In the concluding section, an attempt is made to answer the question of under what circumstances it is appropriate to equate the above two terms.Jakie „słowo Boże” w Piśmie Świętym? W niniejszym artykule zostaje podjęty problem wzajemnej zależności obecnych w naukach o natchnieniu biblijnym określeń „słowo Boże” oraz „Pismo Święte”, w kontekście wydanego przez Papieską Komisję Biblijną dokumentu pt. „Natchnienie i prawda Pisma Świętego. Słowo, które od Boga pochodzi i mówi o Bogu, aby zbawić świat” z 2014 roku. Po przedstawieniu istotnych cech definicji oraz funkcji Pisma Świętego zostaje wykazane rozumienie słowa Bożego w kontekście Starego i Nowego Testamentu. Ostatecznie zostaje podjęta próba udzielenia odpowiedzi na pytanie w jakich okolicznościach właściwe jest postawienie znaku równości między wspomnianymi wyżej terminami

Neural networks reconstruction of the dense-matter equation of state from neutron-star parameters

Aims: The aim of this work is to study the application of the artificial neural networks guided by the autoencoder architecture as a method for precise reconstruction of the neutron star equation of state, using their observable parameters: masses, radii and tidal deformabilities. In addition we study how well the neutron star radius can be reconstructed using the gravitational-wave only observations of tidal deformability, i.e. quantities which are not related in a straightforward way. Methods: Application of artificial neural network in the equation of state reconstruction exploits the non-linear potential of this machine learning model. Since each neuron in the network is basically a non-linear function, it is possible to create a complex mapping between the input sets of observations and the output equation of state table. Within the supervised training paradigm, we construct a few hidden layer deep neural network on a generated data set, consisting of a realistic equation of state for the neutron star crust connected with a piecewise relativistic polytropes dense core, with parameters representative to the state-of-the art realistic equations of state. Results: We demonstrate the performance of our machine learning implementation with respect to the simulated cases with varying number of observations and measurement uncertainties. Furthermore we study the impact of the neutron star mass distributions on the results. Finally, we test the reconstruction of the equation of state trained on parametric polytropic training set using the simulated mass--radius and mass--tidal-deformability sequences based on realistic equations of state. Neural networks trained with a limited data set are able to generalize the mapping between global parameters and equation of state input tables for realistic models.Comment: 8, pages, 7 figures, accepted in Astronomy and Astrophysic

Successive Halving Top-k Operator

We propose a differentiable successive halving method of relaxing the top-k operator, rendering gradient-based optimization possible. The need to perform softmax iteratively on the entire vector of scores is avoided by using a tournament-style selection. As a result, a much better approximation of top-k with lower computational cost is achieved compared to the previous approach.Comment: Work in progres

Aberration-corrected time aperture of an electro-optic time lens

Recently, there has been renewed interest in electro-optic time lenses due to their favorable properties for quantum photonic applications. Here, we propose a new analytical approach to estimate the chirp rate of a time lens implemented using an electro-optic phase modulator driven with a single-tone radio frequency voltage. Our approach is based on a user-defined time aperture for the time lens. We observe that the temporal aberrations depend on the amplitude of the phase modulation and the effective time aperture of the time lens. We derive an analytical expression for the maximum phase error that will allow the user to choose the maximal aberration-limited time aperture of the time lens. We apply our formalism to a Fourier-time lens system for the spectral compression of Gaussian pulses and find the optimal parameters of the setup. Our approach will provide a handy tool for efficient temporal system design based on electro-optical time lenses.Comment: 7 pages, 5 figure