Common and Unique Network Dynamics in Football Games

The sport of football is played between two teams of eleven players each using a spherical ball. Each team strives to score by driving the ball into the opposing goal as the result of skillful interactions among players. Football can be regarded from the network perspective as a competitive relationship between two cooperative networks with a dynamic network topology and dynamic network node. Many complex large-scale networks have been shown to have topological properties in common, based on a small-world network and scale-free network models. However, the human dynamic movement pattern of this network has never been investigated in a real-world setting. Here, we show that the power law in degree distribution emerged in the passing behavior in the 2006 FIFA World Cup Final and an international “A” match in Japan, by describing players as vertices connected by links representing passes. The exponent values are similar to the typical values that occur in many real-world networks, which are in the range of , and are larger than that of a gene transcription network, . Furthermore, we reveal the stochastically switched dynamics of the hub player throughout the game as a unique feature in football games. It suggests that this feature could result not only in securing vulnerability against intentional attack, but also in a power law for self-organization. Our results suggest common and unique network dynamics of two competitive networks, compared with the large-scale networks that have previously been investigated in numerous works. Our findings may lead to improved resilience and survivability not only in biological networks, but also in communication networks

高齢者に対する膀胱留置カテーテル抜去後の排尿管理 : 超音波膀胱内尿量測定の有効性

膀胱留置カテーテル抜去後の高齢者の排尿自立に向けた援助を検討するために、手術目的等で膀胱内留置カテーテルを留置した７名の高齢患者を対象に、カテーテル抜去後に超音波膀胱内尿量測定器「ゆりりん」による残尿測定を行った。留置期間が１～5日の場合、抜去後6時間以内に自然排尿があり、残尿は少なかった。留置期間が9日、23日となった患者では抜去後6時間以内の自然排尿がなく、「ゆりりん」での測定で残尿を認め、導尿を行った。3名の「ゆりりん」による測定値と導尿による尿量を比較した結果、誤差は20ml～70ml、誤差率5％～26％であったことから、超音波膀胱内尿量測定」はカテーテル抜去後の残尿測定において有用であることが示唆された

A Switching Hybrid Dynamical System: Toward Understanding Complex Interpersonal Behavior

Complex human behavior, including interlimb and interpersonal coordination, has been studied from a dynamical system perspective. We review the applications of a dynamical system approach to a sporting activity, which includes continuous, discrete, and switching dynamics. Continuous dynamics identified switching between in- and anti-phase synchronization, controlled by an interpersonal distance of 0.1 m during expert kendo matches, using a relative phase analysis. In the discrete dynamical system, return map analysis was applied to the time series of movements during kendo matches. Offensive and defensive maneuvers were classified as six coordination patterns, that is, attractors and repellers. Furthermore, these attractors and repellers exhibited two discrete states. Then, state transition probabilities were calculated based on the two states, which clarified the coordination patterns and switching behavior. We introduced switching dynamics with temporal inputs to clarify the simple rules underlying the complex behavior corresponding to switching inputs in a striking action as a non-autonomous system. As a result, we determined that the time evolution of the striking action was characterized as fractal-like movement patterns generated by a simple Cantor set rule with rotation. Finally, we propose a switching hybrid dynamics to understand both court-net sports, as strongly coupled interpersonal competition, and weakly coupled sports, such as martial arts

A novel Fuzy Internal Model Controller (FIMC)

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Scene selection.

<p>(<b>A</b>) Kendo match. (<b>B</b>) Trajectories of two players during a kendo match over a 5-min period in a two-dimensional plane (). (<b>C</b>) Time series of interpersonal distance (IPD) for one match. (<b>D</b>) Time series of IPD for one sequence eliminating unrelated scenes. (<b>E</b>) Time series of IPD for one scene that begins with the contestants at the greatest distance from one another and ends with them coming together in a striking action.</p

Well fitted scenes switching between different functions in each scene.

<p>The numbers show the different functions in each scene.</p

State transition diagrams.

<p>(<b>A, B</b>) Return maps were plotted using observed points as four different linear functions of an attractor (red) and a repeller (blue) for expert and intermediate competitors respectively. The circles show crossing points with the line of identity, . (C, D) Red, blue, and black lines show histograms of crossing points for an attractor, a repeller, and the sum of these respectively. (E, F) Second-order state transition diagrams with the conditional probabilities consisted of the “farthest apart” high velocity state (F) and the “nearest together” low velocity state (N) for expert and intermediate competitors, respectively. (G, H) The third-order state transition diagrams comprised four second-order sub-states.</p

Trajectories of six functions and return map analysis.

<p>(<b>a–d</b>) Linear functions, , with four different slopes for and , respectively. (<b>e</b>) Exponential function, . (<b>f</b>) Logarithmic function, . (<b>a</b>) Asymptotic trajectory to the attractive fixed point as a series of points, which corresponds to the movement of decreasing IPD by the step-towards motion shown in (<b>A</b>). (<b>a’</b>) Observed series of points in a scene from to , approaching an attractor with . (<b>b</b>) Rotational trajectory to the attractor, which corresponds to the movement of decreasing IPD by alternating step-towards and step-away motions shown in (<b>B</b>). (<b>b’</b>) Observed series of points in a scene from to , approaching an attractor with . (<b>c</b>) Diverging from the repellent fixed point asymptotically, decreasing IPD by the step-towards motions shown in (<b>C</b>). (<b>c’</b>) Series of points ( to ), diverging from repeller with . (<b>d</b>) Diverging from the repeller rotationally, increasing IPD by alternating step-towards and step-away motions shown in (<b>D</b>). (<b>d’</b>) Series of points ( to ), diverging from a repeller with . (<b>e</b>) Approaching and diverging trajectories around the attractor and/or the repeller exponentially, increasing IPD by step-away motions shown in (<b>E</b>). (<b>e’</b>) Series of points ( to ), diverging from a repeller with . (<b>f</b>) Logarithmically approaching and diverging trajectories around an attractor, decreasing IPD by step-towards from motions shown in (<b>F</b>). (<b>f’</b>) Series of points ( to ) approaching an attractor and diverging from a repeller ( to ) with .</p