Multiscale fractal dimension applied to tactical analysis in football: A novel approach to evaluate the shapes of team organization on the pitch

The aim of this study was to evaluate different shape descriptors applied to images of polygons that represent the organization of football teams on the pitch. The effectiveness of different shape descriptors (area/perimeter, fractal area, circularity, maximum fractal, rectangularity, multiscale fractal curve—MFC), and the concatenation of all shape descriptors (except MFC), denominated Alldescriptors (AllD)) was evaluated and applied to polygons corresponding to the shapes represented by the convex hull obtained from players’ 2D coordinates. A content-based image retrieval system (CBIR) was applied for 25 users (mean age of 31.9 ± 8.4 years) to evaluate the relevant images. Measures of effectiveness were used to evaluate the shape descriptors (P@n and R@n). The MFD (P@5, 0.46±0.37 and P@10, 0.40±0.31, p < 0.001; R@5, 0.14±0.13 and R@10, 0.24±0.19, p < 0.001) and AllD (P@5 = 0.43±0.36 and P@10 = 0.39±0.32, p < 0.001; R@5 = 0.13±0.11 and R@10 = 0.24±0.20, p < 0.001) descriptors presented higher values of effectiveness. As a practical demonstration, the best evaluated shape descriptor (MFC) was applied for tactical analysis of an official match. K-means clustering technique was applied, and different shapes of organization could be identified throughout the match. The MFC was the most effective shape descriptor in relation to all others, making it possible to apply this descriptor in the analysis of professional football matches.

Meander And Koch Hybrid Fractal Curve Based Dual Hexagonal Radiating Patch Antenna For Quad Band Wireless Applications

A unique dual hexagonal-shaped radiating patch design with hybrid fractal curves (Meander and Koch) is presented for quad-band wireless applications. Initially, the antenna from 0th to 2nd iteration of hybrid fractal curves with PGP (Partial Ground Plane) is designed and investigated. Further, to get better results of the designed antenna in respect of Bandwidth (BW) and coefficient of reflection these hybrid curves are superimposed on the limited ground plane of 1st and 2nd iteration of the antenna, and the generated antennas are designated as Antenna – 1 and Antenna – 2. A comparison between both the antennas has been made and it is observed that antenna -2 shows better results in respect of improved BW and coefficient of reflection. The proposed antenna exhibits four resonant frequency bands 1.6, 4.8, 6.9, and 8.8GHz with improved corresponding impedance BW of 2.09, 1.36, 0.86, and 1.51GHz. The designed antenna is simulated and made on FR4 glass epoxy substrate with an overall size of 20×40×1.6 mm3. The fabricated proposed antenna is tested experimentally for the authentication of simulated results with experimental results and these are compatible with each other. The other performance indicators like radiation pattern, peak realized gain, and radiation efficiency are also determined for the proposed Hybrid Fractal Antenna (HFA) and all are found satisfactory. Due to the improved operational parameters, the designed HFA can be considered as a suitable applicant for distinct wireless applications in anticipated operational frequency ranges.

Planar Sensor for Material Characterization Based on the Sierpinski Fractal Curve

This paper presents a planar and compact microwave resonator sensor to characterize materials. The geometry of the resonator is based on the Sierpinski fractal curve and has four poles in the frequency range from 0.5 GHz to 5.5 GHz. Any of the four poles can be used to measure samples with low permittivity values, where the first pole is suitable for samples with high permittivity values. The sensitivity of the poles and return losses of the sensor are presented and obtained using a full-wave 3D simulator software. The device is manufactured and validated through a comparison between simulated and measured results.

Koch Infinite Fractal Curve Implementation for the Space Filling Problem in Manufacturing

Space-?filling problem has been one of the most intriguing problems in the domain of manufacturing science and engineering. Several approaches have been applied to solve the problem, ranging from in?finite curves (Gospel Curve) to straight-line approaches. This paper introducesa new approach of space fi?lling using fractal curves. Fractal curves are de?ned as mathematical curves whose shape retains the same general pattern of irregularity, regardless of how much magnifi?ed the shape has been considered, basically the shape of a fractal. These curves are widespread in nature and hence using the same, a novel method has been prepared for generating a fractal curve to be implemented in the additive manufacturing process.

Compact quintuple notched-band UWB BPF with high selectivity and wide bandwidth

In this paper, a compact quintuple notched-band ultra-wideband bandpass filter with high selectivity and wide bandwidth is proposed. The filter adopts an approximate closed-loop C-shaped stepped impedance resonator to generate triple notched bands, and uses Hilbert fractal curve slit and L-shaped resonator to create single notched band, respectively. Multiple notched-band are centered at 5.29, 6.61, 7.92, 8.95, and 9.93 GHz to eliminate undesired interference from coexisting wireless services of WLAN, C-band, and X-band. Additionally, two transmission zeros are introduced to enhance the sharp skirt selectivity up to 0.944. This filter could exhibit high sharp selectivity and wider bandwidth simultaneously. The filter is fabricated on a RT/Duroid 5880 substrate (ɛ r = 2.2 and thickness = 0.787 mm) and measured to verify the simulation results. Both simulation and measurement are in well agreement, showing the good performance of the filter.

Compact Circular CSRR Loaded Koch Fractal Inspired Frequency Band Reconfigurable Antenna

A compact frequency band reconfigurable dual-mode antenna utilizing both Koch fractal geometry and circular complementary split ring resonators (CSRRs) is presented in this paper. The proposed antenna can be electrically switched into both dual- and single-band resonance modes. A Koch curve derivative novel fractal curve is used to design the patch boundary of the antenna. Two optimized circular CSRRs are loaded inside the antenna geometry to achieve double-band resonance. The antenna operates at both 5.1[Formula: see text]GHz (upper WLAN band) and 9.6[Formula: see text]GHz ([Formula: see text]-band) in dual resonance mode and resonates only at 8[Formula: see text]GHz ([Formula: see text]-band) in single resonance mode. A properly biased RF-range PIN diode placed at the slotted ground plane reconfigures the antenna in two operating modes by switching into its ON–OFF states. The antenna is fabricated on cost-efficient epoxy (FR-4) substrate consuming the maximum dimension of [Formula: see text] which is much more compact than the conventional rectangular patch antennas designed for similar bands. Stable radiation characteristics with reduced cross-polarization are achieved at all the resonant bands of the antenna. A prototype of the proposed antenna is fabricated and measured. The simulated results are in good agreement with the measured ones.