periodic patterns
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Abstract We report the existence of periodic structures in the transitional and chaotic regimes in bi-parameter spaces of a predator-prey system. A model is constructed taking into consideration of two important effects: namely, the prey refuge and fear of predation risk. The fixed points, their existence and stability behaviors are analyzed. The Neimark-Sacker bifurcation in the neighborhood of the interior fixed point is shown selecting refuge strength as a bifurcation parameter. The complex dynamical behaviors are explored in the biparameter space with the help of the largest Lyapunov exponent and isoperiodic diagrams. The period-bubbling transitional patterns, and triple heterogeneous attractors resulting in qualitative unpredictability are identified in the present system. The Wada basin sets for the triple coexisting attractors are found. The study reveals that the oscillations of the populations in certain control parameter regions are highly dependent upon the initial densities of the populations.

The Green-Naghdi equations are a shallow water waves model which play important roles in nonlinear wave fields. By using the trial equation method and the Complete discrimination system for the polynomial we obtained the classification of travelling wave patterns. Among those patterns, new singular patterns and double periodic patterns are obtained in the first time. And we draw the graphs which help us to understand the dynamics behaviors of the Green-Naghdi model intuitionally.

The timing of neuronal responses is considered to be important for information transferring and communication across individual neurons. However, the sources of variabilities in the timing of neuronal responses are not well understood and sometimes over-interpreted. A systematic variability in the response latencies of the primary visual cortex has been reported in presence of drifting grating stimulus. Whereas the response latencies are systematically dependent on stimulus orientation. To understand the underlying mechanism of these systematic latencies, we recorded the neuronal response of the cat visual cortex, area 17, and simulated the response latency of V1 neurons, with two geometric models. We showed that outputs of these two models significantly predict the response latencies of the electrophysiology recording during orientation tasks. The periodic patterns created in the raster plots were dependent on the relative position of the stimulus rotation center and the receptive-field sub-regions. We argue the position of stimulus is contributing to systematic response latencies, dependent on drifting orientation. Therefore, we provide a toolbox based on our geometrical model for determining the exact location of RF sub-regions. Our result indicates that a major source of neuronal variability is the lack of fine-tuning in the task parameters. Considering the simplicity of the orientation selectivity task, we argue fine-tuning of stimulus properties is crucial for deduction of neural variability in higher-order cortical areas and understanding their neural dynamics.

Historical Islamic ornaments include a fantastic treasury of geometric and mathematical algorithms. Inevitably, restoration of these ornaments in periodic patterns consisting of repeated elements has been faced following and substituting the other available similar ingredients instead of vanished parts. Still, the prediction of parametric, quasi, or non-periodic patterns, where components are not identical, needs to be carried out in a more challenging process than the periodic ones due to shape, scale, or angle of rotation alteration. Intelligent restoration could facilitate the forecasting of damaged parts in such geometric patterns that an algorithm has changed their geometric characteristics. In some architectural heritage, geometric patterns include a parametric algorithm like parametric patterns in the ceiling of Sheikh Lotfollahmosque in Isfahan, Iran, and the dominant structure of Persian domes Karbandi. In this article, the aim is to propose a new method for the smart restoration of the parametric geometric patterns in which, by having access to the image of the existing patterns, the vanished parts could be reconstructed spontaneously. Our approach is based on image processing by detecting boundaries of deterioration, finding every individual element, and extracting features of detected individual patterns via Zernike moments. The order of individual patterns starts from the farthest pattern to detected deterioration. Then by creating a time series, the Back-propagation neural network would be trained by extracted features, and the vanished patterns’ features could be predicted and reconstructed. Eventually, the reconstructed and real patterns are compared to determine differences between them by mean-squared error and to evaluate the performance of our method. To validate the process, a parametric geometric pattern is designed by the assumption that some parts are disappeared. The proposed method’s results, in this case, hold an efficient performance with the accuracy of 92.99%. Furthermore, Sheikh Lotfollah’s patterns and Naseredin Mirza mansion’s patterns as two real cases are tested by the proposed method, representing reliable and suitable performance results.

The scope of this work is to consolidate research dealing with the vibroacoustics of periodic media. This investigation aims at developing and validating tools for the design and characterization of global vibroacoustic treatments based on foam cores with embedded periodic patterns, which allow passive control of acoustic paths in layered concepts. Firstly, a numerical test campaign is carried out by considering some perfectly rigid inclusions in a 3D-modeled porous structure; this causes the excitation of additional acoustic modes due to the periodic nature of the meta-core itself. Then, through the use of the Delany–Bazley–Miki equivalent fluid model, some design guidelines are provided in order to predict several possible sets of characteristic parameters (that is unit cell dimension and foam airflow resistivity) that, constrained by the imposition of the total thickness of the acoustic package, may satisfy the target functions (namely, the frequency at which the first Transmission Loss (TL) peak appears, together with its amplitude). Furthermore, when the Johnson–Champoux–Allard model is considered, a characterization task is performed, since the meta-material description is used in order to determine its response in terms of resonance frequency and the TL increase at such a frequency. Results are obtained through the implementation of machine learning algorithms, which may constitute a good basis in order to perform preliminary design considerations that could be interesting for further generalizations.

Big Data is a generic term that involves the storing and processing of a large amount of data. This large amount of data has been promoted by technologies such as mobile applications, Internet of Things (IoT), and Geographic Information Systems (GIS). An example of GIS is a Spatio-Temporal Database (STDB). A complex problem to address in terms of processing time is pattern searching on STDB. Nowadays, high information processing capacity is available everywhere. Nevertheless, the pattern searching problem on STDB using traditional Data Mining techniques is complex because the data incorporate the temporal aspect. Traditional techniques of pattern searching, such as time series, do not incorporate the spatial aspect. For this reason, traditional algorithms based on association rules must be adapted to find these patterns. Most of the algorithms take exponential processing times. In this paper, a new efficient algorithm (named Minus-F1) to look for periodic patterns on STDB is presented. Our algorithm is compared with Apriori, Max-Subpattern, and PPA algorithms on synthetic and real STDB. Additionally, the computational complexities for each algorithm in the worst cases are presented. Empirical results show that Minus-F1 is not only more efficient than Apriori, Max-Subpattern, and PAA, but also it presents a polynomial behavior.

A method for improving the brazing joining strength of Titanium alloy/Stainless steel fabricated through fibre laser surface texturing is introduced because it is a simple process that does not require the fabrication of complicated interlayers. However, previous research shows that a milimeter scale was fabricated by surface modification for dissimilar brazing join, yielding insignificant results and limiting the application and degree of enhancement. Fiber laser ablation was used in this study to create microscale periodic patterns (grooves) on a stainless steel surface. No defect or damage induced during laser surface texturing process. The groove dimension was tunable by controlling the laser parameters. Vacuum brazing of Ti6Al4V to 316L stainless steel with surface texturing, the average joint strength was 22.1 MPa, 34% of increase of joining strength compared to unprocessed flat surface. The combination of laser surface texturing and brazing proven effectively on joining strength enhancement.

The basic building blocks for rhythmic structure in music are widely believed to be universally confined to small-integer ratios. In particular, basic metric processes such as pulse perception are assumed to depend on the recognition and anticipation of even, categorically equivalent durations or inter-onset intervals, which are related by the ratio of 1:1 (isochrony). Correspondingly, uneven (non-isochronous) beat subdivisions are theorized as instances of expressive microtiming variation, i.e. as performance deviations from some underlying, categorically isochronous temporal structure. By contrast, ethnographic experience suggests that the periodic patterns of uneven beat subdivision timing in various styles of music from Mali themselves constitute rhythmic and metric structures. The present chapter elaborates this hypothesis and surveys a series of empirical research projects that have found evidence for it. These findings have implications for metric theory as well as for our broader understanding of how human perception relates to cultural environments. They suggest that the bias towards isochrony, which according to many accounts of rhythm and metre underlies pulse perception, is culturally specific rather than universal. Claims regarding cultural diversity in the study of music typically concern styles and meanings of performance practices. In this chapter, I will claim that basic structures of perception can vary across cultural groups too.