A Min-Max . . . Functions and Its Implications

A. Huber and V. Kolmogorov (ISCO 2012) introduced a concept of k-submodular function as a generalization of ordinary submodular (set) functions and bisubmodular functions and obtained a min-max theorem for minimization of k-submodular functions. Also F. Kuivinen (2011) considered submodular functions on (product lattices of) diamonds and showed a min-max theorem for minimization of submodular functions on diamonds. In the present paper we consider a common generalization of k-submodular functions and submodular functions on diamonds, which we call a transversal submodular function (or a t-submodular function, for short). We show a min-max theorem for minimization of t-submodular functions in terms of a new norm composed of ℓ1 and ℓ ∞ norms. This reveals a relationship between the obtained min-max theorem and that for minimization of ordinary submodular set functions due to J. Edmonds (1970). We also show how our min-max theorem for t-submodular functions can be used to prove the min-max theorem for k-submodular functions by Huber and Kolmogorov and that for submodular functions on diamonds by Kuivinen. Moreover, we show a counterexample to a characterization, given by Huber and Kolmogorov (ISCO 2012), of extreme points of the k-submodular polyhedron and make it a correct one by fixing a flaw therein

EFFECTS OF MOVIE OBSERVATION AND MOTOR IMAGERY ON PERFORMANCE AND JOINT KINETICS DURING TAKE-OFF IN DROP JUMP

The aim of this study was to investigate the effects of movie observation and motor imagery intervention during the pre-set phase (prior to jumping off the platform), on drop jump (DJ) performance and the variables of lower leg kinetics. Three male jumpers performed the DJ under three different conditions (Normal, Movie, and Imagery) from a drop height of 0.3 m. The performance variables and joint kinetics were measured. The DJ performance tended to improve with the intervention of movie and imagery condition. Moreover, the negative ankle joint and positive hip joint kinetics variables (power and work) tended to improve with the intervention of movie and imagery condition. Therefore, it was suggested that movie observation and motor imagery intervention could improve DJ performance and the force exerted by lower leg, which affects performance

THE THREE-DIMENTIONAL PELVIC MOTION IN THE ACCELERATION AND MAXIMUM PHASES

The purpose of this study was to investigate the mechanism of pelvic motion in the acceleration and maximum velocity phases. Eleven male sprinters performed 30 m and 60 m sprints at maximal effort and captured sprint movement at 15 m and 50 m. The contact time was significantly longer, and the angular displacement of pelvic elevation on the frontal plane was significantly greater in the acceleration phase than in the maximum velocity phase. Additionally, the angular displacement of pelvic elevation on the frontal plane showed a significantly positive correlation with the contact time and the stance length in the acceleration phase. These findings suggest that the greater pelvic frontal plane motion in the acceleration phase could increase the contact time and longer stance length

CHANGE OF DIRECTION MOTION DURING THE DEFENSIVE PHASE IN SOCCER PLAYERS

The purpose of the this study was to the change of direction (COD) movement in the backward direction during the defensive phase. Thirteen male soccer players performed the reactive agility test (RAT) and sprint running. Analysis classified the players to two groups according to the RAT time. There was no significant difference in sprint times, but RAT of the fast group was significantly faster than that of the slow group. Before and after COD of RAT, the fast group had made a deceleration quickly by high-step frequency. In the COD movement, the fast group performed the movement with their body tilted backward while lowering their center of gravity with the hip of the COD foot bent before COD and smaller knee flexion displacement during COD support phase. These findings seem to be a basic knowledge for evaluation and training of COD in soccer

Polynomial combinatorial algorithms for skew-bisubmodular function minimization

Huber et al. (SIAM J Comput 43:1064–1084, 2014) introduced a concept of skew bisubmodularity, as a generalization of bisubmodularity, in their complexity dichotomy theorem for valued constraint satisfaction problems over the three-value domain, and Huber and Krokhin (SIAM J Discrete Math 28:1828–1837, 2014) showed the oracle tractability of minimization of skew-bisubmodular functions. Fujishige et al. (Discrete Optim 12:1–9, 2014) also showed a min–max theorem that characterizes the skew-bisubmodular function minimization, but devising a combinatorial polynomial algorithm for skew-bisubmodular function minimization was left open. In the present paper we give first combinatorial (weakly and strongly) polynomial algorithms for skew-bisubmodular function minimization

SPRINT STEP-TYPE SPECIFIC CHARACTERISTICS OF ANTHROPOMETRIC AND KINEMATIC VARIABLES IN SPRINTING ACCELERATION

The purpose of this study was to compare the anthropometric and the kinematic characteristics during the acceleration phase between stride frequency (SF)-type and stride length (SL)-type sprinters. Seventeen sprinters participated in this study. The maximal 60-m sprints and anthropometric measures were obtained from subjects. Two sprints were recorded by using high-speed cameras. Sprint velocity, SL, SF and their underlying kinematic variables were calculated. Cluster analysis was used to classify the subjects into the SF or SL -type groups (step-type) as indicated by the ratio of the SF and SL at maximum velocity. The SF-type group showed shorter lower limbs length, flight time, lower the height of center of mass at takeoff, smaller swing motion and faster forward rotation of the shank and foot segments than the SL-type group. This study showed the noticeable differences between SFtype and SL-type sprinters were not only in swing motion but also in push-off motion

世界陸上ロンドン大会観戦雑感

The purpose of this paper is to offer alternative ways in the instruction of the Nature of Science (NOS), while making connections with areas of knowledge outside the natural sciences. It focuses on the teaching of NOS in the Theory of Knowledge (TOK) course of the International Baccalaureate Organization, which is a curriculum that connects NOS with other areas of knowledges. To fulfil the purpose of this research, I analyzed two TOK course textbooks from two points of view. The first of these points refers to the question of what are the tenets of NOS that relate to other areas of knowledge. The second one explores the role of NOS in those cases in which natural sciences connect with other areas of knowledge. After pondering these two questions, I extracted an example from educational materials, and analyzed in detail the role of NOS..

LOWER LIMB KINETIC CHARACTERISTICS OF THE SIDE-HOP TEST IN HEALTHY INDIVIDUALS

The purpose of this study was to investigate the relationship between the kinetics of lower limb joints and the side-hop test (SHT) time in healthy individuals and to clarify the factors that may influence performance on the SHT. Twenty male athletes performed the SHT. The SHT time and lower limb joint torque (hip, knee, and ankle) were calculated to explore the relationship between the two variables. The relationship between the SHT time and joint torque was found specifically at the medial and lateral contact phases of the SHT. These results suggest that hip joint function may be important in the medial contact phase. In the knee joint, it was suggested that the load at the frontal plane of the knee joint increases with shorter SHT time. We have provided these results for researchers/clinicians who consider the performance characteristics related to shorter times in the SHT

TYPE-SPECIFIC STEP CHARACTERISTICS OF SPRINTERS DURING ACCELERATION PHASE OF 100-M RACE

The purpose of this study was to show the type-specific step characteristics during acceleration phase (0?30 m) of a 100-m race. Fifty-nine male varsity sprinters (10.68 ± 0.22 s) were recorded running in 100-m races using 10 high-speed cameras, and step variables in 0?30 m and maximum speed phase (MSP, 30?60 m) were calculated. Cluster analysis was used to classify the subjects into the step-frequency (SF) or -length (SL) reliant group (i.e., type-specific) as indicators for the ratio of the SF and SL in the MSP. Then, each group was divided into two sub-groups according to the mean speed in MSP (good and poor sprinters). As a result, the sprinters were classified into SL-, SF-, and Mid-groups. In SL-group, good sprinters showed a longer SL from the 7th step to MSP than the poor sprinters. In SF-group, good sprinters showed a higher SF from the 7th step to MSP than the poor sprinters