On the extraction of instantaneous frequencies from ridges in time-frequency representations of signals

The extraction of oscillatory components and their properties from different time-frequency representations, such as windowed Fourier transform and wavelet transform, is an important topic in signal processing. The first step in this procedure is to find an appropriate ridge curve: a sequence of amplitude peak positions (ridge points), corresponding to the component of interest. This is not a trivial issue, and the optimal method for extraction is still not settled or agreed. We discuss and develop procedures that can be used for this task and compare their performance on both simulated and real data. In particular, we propose a method which, in contrast to many other approaches, is highly adaptive so that it does not need any parameter adjustment for the signal to be analysed. Being based on dynamic path optimization and fixed point iteration, the method is very fast, and its superior accuracy is also demonstrated. In addition, we investigate the advantages and drawbacks that synchrosqueezing offers in relation to curve extraction. The codes used in this work are freely available for download.Comment: 13 pages, 7 figures, plus 4 supplementary figure

DOMINANTS OF UKRAINE’S FOREIGN TRADE INTELLECTUALIZATION

The article raises the problem of identifying dominants and assessing the level of international trade intellectualization in the context of the formation of prerequisites for the optimal use of intellectual technologies under integration of Ukraine into the world economy. The purpose of the article is to define key dominants of international trade intellectualization and to assess their development in Ukraine's foreign trade. The applicable estimation is carried out by introduction of the international trade intellectualization index – an integrated index based on the sum of weighted average group indicators. Also, the nature of international trade intellectualization processes is discovered, their forms and peculiarities both in government and business are identified. Current state and problems limiting intellectualization of Ukraine's foreign trade are characterized. The dominants of Ukraine's foreign trade intellectualization and regulatory mechanisms intensifying the export potential of its economy are defined.Tyrimo problema – identifikuoti determinantus ir įvertinti tarptautinės prekybos intelektualizacijos lygį, atsižvelgiant į intelektualinių technologijų naudojimo sąlygas, integruojant Ukrainą į pasaulio ekonomiką. Straipsnio tikslas – apibūdinti pagrindinius tarptautinės prekybos intelektualizacijos dominantus ir įvertinti jų raidą Ukrainos užsienio prekyboje. Įvertinimas atliekamas naudojant autorių pasiūlytas tarptautinės prekybos intelektualizacijos indeksą, pagrįstą vidutinių svertinių grupių rodiklių suma. Straipsnyje atskleidžiamas tarptautinės prekybos intelektualizacijos procesų pobūdis, nustatomos jų formos ir ypatumai tiek Vyriausybėje, tiek versle; apibūdinama intelektualizacijos dabartinė būklė ir problemos bei apribojimai Ukrainos užsienio prekyboje. Apibrėžiami prekybos intelektualizacijos dominantai ir reguliavimo mechanizmai, sustiprinantys prekybos ekonomikos eksporto potencialą

Stationary and Traveling Wave States of the Kuramoto Model with an Arbitrary Distribution of Frequencies and Coupling Strengths

We consider the Kuramoto model of an ensemble of interacting oscillators allowing for an arbitrary distribution of frequencies and coupling strengths. We define a family of traveling wave states as stationary in a rotating frame, and derive general equations for their parameters. We suggest empirical stability conditions which, for the case of incoherence, become exact. In addition to making new theoretical predictions, we show that many earlier results follow naturally from our general framework. The results are applicable in scientific contexts ranging from physics to biology.Comment: 5 pages, 1 figur