A distance-based dynamical transition analysis of time series signals and application to biological systems

Abstract

This study demonstrates an application of distance-based numerical measures to the phase space of time series signals, in order to obtain a temporal analysis of complex dynamical systems. This method is capable of detecting alterations appearing in the characters of the deterministic dynamical systems and provides a simple tool for the real-time analysis of time series data obtained from a complex dynamical system even with black box functionality. The study presents a possible application of the method in the dynamical transition analysis of real EEG records from epilepsy patients.

Theoretical demonstration of the hybrid focusing points of sonic crystal flat lenses and possible applications

“…Figure 2(a) shows the ray-trace analysis of a crystal slab with a single source. [24][25][26] The intersection of beams indicates a wave focusing at the intersection point. In the case of a point source array placed near to a negative refractive sonic crystal, there appear several focusing points due to the intersections of the beams coming from different wave source couples (s x , s y ), as shown in Fig.…”

“…Metamaterials have been implemented by using artificial crystal structures for a wide range of wave spectra. Photonic crystals, [1][2][3][4][5][6][7][8][9][10][11][12] phononic crystals, [13][14][15][16][17][18][19][20][21][22][23] and sonic crystals [24][25][26][27][28] were developed for their technological potentials such as wave focusing, [24][25][26][27][28][29][30][31] wave isolation, [16][17][18]21] wave absorption, [10,22] and wave guiding. [2][3][4]32,33] The realization of flat lenses from crystal structures is one of the promising applications of metamaterials.…”

“…Negative refraction and the wave focusing effects of negative refractive crystal slabs have been well studied in the last decade. [24][25][26][27][28] Those studies mainly addressed the focusing effect of single point source configurations. Reports indicated that flat lenses made of negative refractive crystals exhibited superior focusing properties, such as sub-wavelength focusing [31] and the ideal imaging effect.…”

“…The previous works extensively studied the pure focusing points for single-point source cases. [24][25][26][27] This paper specifically investigates multi-point source configurations that lead to the occurrences of hybrid focusing points. The shape of the focusing point constellation corresponds to two situations listed below.…”