Guiding contact by coupling the taus of gaps

Animals control contact with surfaces when locomoting, catching prey, etc. This requires sensorily guiding the rate of closure of gaps between effecters such as the hands, feet or jaws and destinations such as a ball, the ground and a prey. Control is generally rapid, reliable and robust, even with small nervous systems: the sensorimotor processes are therefore probably rather simple. We tested a hypothesis, based on general tau theory, that closing two gaps simultaneously, as required in many actions, might be achieved simply by keeping the taus of the gaps coupled in constant ratio. tau of a changing gap is defined as the time-to-closure of the gap at the current closure-rate. General tau theory shows that tau of a gap could, in principle, be directly sensed without needing to sense either the gap size or its rate of closure. In our experiment, subjects moved an effector (computer cursor) to a destination zone indicated on the computer monitor, to stop in the zone just as a moving target cursor reached it. The results indicated the subjects achieved the task by keeping tau of the gap between effector and target coupled to tau of the gap between the effector and the destination zone. Evidence of tau -coupling has also been found, for example, in bats guiding landing using echolocation. Thus, it appears that a sensorimotor process used by different species for coordinating the closure of two or more gaps between effecters and destinations entails constantly sensing the taus of the gaps and moving so as to keep the taus coupled in constant ratio.

Detecting motor abnormalities in preterm infants

As a consequence of the fragility of various neural structures, preterm infants born at a low gestation and/or birthweight are at an increased risk of developing motor abnormalities. The lack of a reliable means of assessing motor integrity prevents early therapeutic intervention. In this paper, we propose a new method of assessing neonatal motor performance, namely the recording and subsequent analysis of intraoral sucking pressures generated when feeding nutritively. By measuring the infant's control of sucking in terms of a new development of tau theory, normal patterns of intraoral motor control were established for term infants. Using this same measure, the present study revealed irregularities in sucking control of preterm infants. When these findings were compared to a physiotherapist's assessment six months later, the preterm infants who sucked irregularly were found to be delayed in their motor development. Perhaps a goal-directed behaviour such as sucking control that can be measured objectively at a very young age, could be included as part of the neurological assessment of the preterm infant. More accurate classification of a preterm infant's movement abnormalities would allow for early therapeutic interventions to be realised when the infant is still acquiring the most basic of motor functions. (C) Springer-Verlag 2000.

Sensory and intrinsic coordination of movement

A recently generalized theory of perceptual guidance (general tau theory) was used to analyse coordination in skilled movement. The theory posits that (i) guiding movement entails controlling closure of spatial and/or force gaps between effecters and goals, by sensing and regulating the tau s of the gaps (the time-to-closure at current closure rate), (ii) a principal way of coordinating movements is keeping the rs of different gaps in constant ratio (known as tau-coupling), and (iii) intrinsically paced movements are guided and coordinated by tau-coupling onto a tau-guide, tau(g), generated in the nervous system and described by the equation tau(g) = 0.5(t-T-2/t) where T is the duration of the body movement and t is the time from the start of the movement. Kinematic analysis of hand to mouth movements by human adults, with eyes open or closed, indicated that hand guidance was achieved by maintaining, during 80-85% of the movement, the tau-couplings tau(alpha)-tau(t) and tau(t)-tau(g), where tau(t) is tau of the hand-mouth gap, tau(alpha) is tau of the angular gap to be closed by steering the hand and tau(g) is an intrinsic tau-guide.

Judging the ‘passability’ of dynamic gaps in a virtual rugby environment

Affordances have recently been proposed as a guiding principle in perception–action research in sport (Fajen, Riley, & Turvey, 2009). In the present study, perception of the ’passability’ affordance of a gap between two approaching defenders in rugby is explored. A simplified rugby gap closure scenario was created using immersive, interactive virtual reality technology where 14 novice participants (attacker) judged the passability of the gap between two virtual defenders via a perceptual judgment (button press) task. The scenario was modeled according to tau theory (Lee, 1976) and a psychophysical function was fitted to the response data. Results revealed that a tau-based informational quantity could account for 82% of the variance in the data. Findings suggest that the passability affordance in this case, is defined by this variable and participants were able to use it in order to inform prospective judgments as to passability. These findings contribute to our understanding of affordances and how they may be defined in this particular sporting scenario; however, some limitations regarding methodology, such as decoupling perception and action are also acknowledged.

Neonatal control of sucking pressures

Human newborns appear to regulate sucking pressure when bottle feeding by employing, with similar precision, the same principle of control evidenced by adults in skilled behavior, such as reaching (Lee et al., 1998a). In particular, the present study of 12 full-term newborn infants indicated that the intraoral sucking pressures followed an internal dynamic prototype - an intrinsic tau-guide. The intrinsic tau-guide, a recent hypothesis of general tau theory is a time-varying quantity, tau(g), assumed to be generated within the nervous system. It corresponds to some quantity (e.g., electrical charge), chang ing with a constant second-order temporal derivative from a rest level to a goal level, in the sense that tau(g) equals tau of the gap between the quantity and its goal level at each time t. (tau of a gap is the rime-to-closure of the gap at the current closure-rate.) According to the hypoth esis, the infant senses tau(p), the tau of the gap between the current intraoral pressure and its goal level, and regulates intraoral pressure so that tau(p) and tau(g) remain coupled in a constant ratio, k; i.e., tau(p) = k tau(g). With k in the range 0-1, the tau-coupling would result in a bell-shaped rate of change pressure profile, as was, in fact, found. More specifically, the high mean r(2) values obtained when regressing tau(p) on tau(g), for both the increasing and decreasing suction periods of the infants' suck, supported a strong tau-coupling between tau(p) and tau(g). The mean k values were significantly higher In the Increasing suction period, indicating that the ending of the movement was more forceful, a finding which makes sense given the different functions of the two periods of the suck.

Detecting Deceptive Movement in 1 vs. 1 Based on Global Body Displacement of a Rugby Player

A key to success in many sports stems from the ability to anticipate what a player is going to do next. In sporting duels such as a 1 vs. 1 in rugby, the attacker can try and beat the defender by using deceptive movement. Those strategies involve an evolution of the centre of mass (COM) in the medio-lateral plane, from a minimal state to maximal displacement just before the final reorientation. The aim of this work is to consider this displacement as a motion-gap, as outlined in Tau theory, as a potential variable that may specify deceptive movement and as a means of comparing anticipatory performance between mid-level players and novices in rugby. Using a virtual reality set-up, 8 mid-level rugby players (ML) and 8 novices (NOV) observed deceptive (DM) and non-deceptive movements (NDM). The global framework used an occlusion time paradigm with four occlusion times. Participants had to judge the final direction of the attacker after the different cuts-off. For each movement and at each occlusion time, we coupled the ability to predict the good final direction with the value of the COM displacement in the medio-lateral (COM M/L) plane or with the Tau of this parameter (Tau COM). Firstly, results show that the Tau COM is a more predictive optical variable than the simple COM M/L. Secondly, this optical variable Tau COM is used by both groups, and finally, with a specific methodology we showed that mid-level players have significantly better anticipatory ability than the novice group.

Temporal guidance of musicians’ performance movement is an acquired skill

The ancillary (non-sounding) body movements made by expert musicians during performance have been shown to indicate expressive, emotional, and structural features of the music to observers, even if the sound of the performance is absent. If such ancillary body movements are a component of skilled musical performance, then it should follow that acquiring the temporal control of such movements is a feature of musical skill acquisition. This proposition is tested using measures derived from a theory of temporal guidance of movement, “General Tau Theory” (Lee in Ecol Psychol 10:221–250, 1998; Lee et al. in Exp Brain Res 139:151–159, 2001), to compare movements made during performances of intermediate-level clarinetists before and after learning a new piece of music. Results indicate that the temporal control of ancillary body movements made by participants was stronger in performances after the music had been learned and was closer to the measures of temporal control found for an expert musician’s movements. These findings provide evidence that the temporal control of musicians’ ancillary body movements develops with musical learning. These results have implications for other skillful behaviors and nonverbal communication.

Bio-inspired autonomous visual vertical control of a quadrotor UAV

Near ground maneuvers, such as hover, approach and landing, are key elements of autonomy in unmanned aerial vehicles. Such maneuvers have been tackled conventionally by measuring or estimating the velocity and the height above the ground often using ultrasonic or laser range finders. Near ground maneuvers are naturally mastered by flying birds and insects as objects below may be of interest for food or shelter. These animals perform such maneuvers efficiently using only the available vision and vestibular sensory information. In this paper, the time-to-contact (Tau) theory, which conceptualizes the visual strategy with which many species are believed to approach objects, is presented as a solution for Unmanned Aerial Vehicles (UAV) relative ground distance control. The paper shows how such an approach can be visually guided without knowledge of height and velocity relative to the ground. A control scheme that implements the Tau strategy is developed employing only visual information from a monocular camera and an inertial measurement unit. To achieve reliable visual information at a high rate, a novel filtering system is proposed to complement the control system. The proposed system is implemented on-board an experimental quadrotor UAV and shown not only to successfully land and approach ground, but also to enable the user to choose the dynamic characteristics of the approach. The methods presented in this paper are applicable to both aerial and space autonomous vehicles.

Bioinspired autonomous visual vertical control of a quadrotor unmanned aerial vehicle

Near-ground maneuvers, such as hover, approach, and landing, are key elements of autonomy in unmanned aerial vehicles. Such maneuvers have been tackled conventionally by measuring or estimating the velocity and the height above the ground, often using ultrasonic or laser range finders. Near-ground maneuvers are naturally mastered by flying birds and insects because objects below may be of interest for food or shelter. These animals perform such maneuvers efficiently using only the available vision and vestibular sensory information. In this paper, the time-tocontact (tau) theory, which conceptualizes the visual strategy with which many species are believed to approach objects, is presented as a solution for relative ground distance control for unmanned aerial vehicles. The paper shows how such an approach can be visually guided without knowledge of height and velocity relative to the ground. A control scheme that implements the tau strategy is developed employing only visual information from a monocular camera and an inertial measurement unit. To achieve reliable visual information at a high rate, a novel filtering system is proposed to complement the control system. The proposed system is implemented onboard an experimental quadrotor unmannedaerial vehicle and is shown to not only successfully land and approach ground, but also to enable the user to choose the dynamic characteristics of the approach. The methods presented in this paper are applicable to both aerial and space autonomous vehicles.

Determination of alpha(s)(M-tau(2)) from improved fixed order perturbation theory

We revisit the extraction of alpha(s)(M-tau(2)) from the QCD perturbative corrections to the hadronic tau branching ratio, using an improved fixed-order perturbation theory based on the explicit summation of all renormalization-group accessible logarithms, proposed some time ago in the literature. In this approach, the powers of the coupling in the expansion of the QCD Adler function are multiplied by a set of functions D-n, which depend themselves on the coupling and can be written in a closed form by iteratively solving a sequence of differential equations. We find that the new expansion has an improved behavior in the complex energy plane compared to that of the standard fixed-order perturbation theory (FOPT), and is similar but not identical to the contour-improved perturbation theory (CIPT). With five terms in the perturbative expansion we obtain in the (MS) over bar scheme alpha(s)(M-tau(2)) = 0.338 +/- 0.010, using as input a precise value for the perturbative contribution to the hadronic width of the tau lepton reported recently in the literature.

DETERMINATION OF THE STRONG COUPLING FROM HADRONIC TAU DECAYS USING RENORMALIZATION GROUP SUMMED PERTURBATION THEORY

Be the strong coupling constant alpha(s) from the tau hadronn width using a renormalization group summed (RGS) expansion of the QCD Adler lunction. The main theoretical uncertainty in the extraction of as is due to the manner in which renormalization group invariance is implemented, and the as yet uncalculated higher order terms in the QCD perturbative series. We show that new expansion exhibits good renormalization group improvement and the behavior of the series is similar to that of the standard RGS expansion. The value of the strong coupling in (MS) over bar scheme obtained with the RCS expansion is alpha(s) (M-tau(2)) = 0.338 +/- 0.010. The convergence properties of the new expansion can be improved by Bond transformation and analytic continuation in t he Bond plane. This is discussed elsewhere in these issues.

Expansions of tau hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling alpha(s) and other QCD parameters from the hadronic decays of the tau lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher-order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called ``reference model,'' including moments that are poorly described by the standard expansions. The results provide additional support for the plausibility of the description of the Adler function in terms of a small number of dominant renormalons.

Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

Ampcalculator (AMPC) is a Mathematica (c) based program that was made publicly available some time ago by Unterdorfer and Ecker. It enables the user to compute several processes at one loop (upto O(p(4))) in SU(3) chiral perturbation theory. They include computing matrix elements and form factors for strong and non-leptonic weak processes with at most six external states. It was used to compute some novel processes and was tested against well-known results by the original authors. Here we present the results of several thorough checks of the package. Exhaustive checks performed by the original authors are not publicly available, and hence the present effort. Some new results are obtained from the software especially in the kaon odd-intrinsic parity non-leptonic decay sector involving the coupling G(27). Another illustrative set of amplitudes at tree level we provide is in the context of tau-decays with several mesons including quark mass effects, of use to the BELLE experiment. All eight meson-meson scattering amplitudes have been checked. The Kaon-Compton amplitude has been checked and a minor error in the published results has been pointed out. This exercise is a tutorial-based one, wherein several input and output notebooks are also being made available as ancillary files on the arXiv. Some of the additional notebooks we provide contain explicit expressions that we have used for comparison with established results. The purpose is to encourage users to apply the software to suit their specific needs. An automatic amplitude generator of this type can provide error-free outputs that could be used as inputs for further simplification, and in varied scenarios such as applications of chiral perturbation theory at finite temperature, density and volume. This can also be used by students as a learning aid in low-energy hadron dynamics.

Pattern clustering using cooperative game theory

In this paper, we approach the classical problem of clustering using solution concepts from cooperative game theory such as Nucleolus and Shapley value. We formulate the problem of clustering as a characteristic form game and develop a novel algorithm DRAC (Density-Restricted Agglomerative Clustering) for clustering. With extensive experimentation on standard data sets, we compare the performance of DRAC with that of well known algorithms. We show an interesting result that four prominent solution concepts, Nucleolus, Shapley value, Gately point and \tau-value coincide for the defined characteristic form game. This vindicates the choice of the characteristic function of the clustering game and also provides strong intuitive foundation for our approach.