How soccer players head the ball: a test of optic acceleration cancellation theory with virtual reality

We measured the movements of soccer players heading a football in a fully immersive virtual reality environment. In mid-flight the ball’s trajectory was altered from its normal quasi-parabolic path to a linear one, producing a jump in the rate of change of the angle of elevation of gaze (α) from player to ball. One reaction time later the players adjusted their speed so that the rate of change of α increased when it had been reduced and reduced it when it had been increased. Since the result of the player’s movement was to regain a value of the rate of change close to that before the disturbance, the data suggest that the players have an expectation of, and memory for, the pattern that the rate of change of α will follow during the flight. The results support the general claim that players intercepting balls use servo control strategies and are consistent with the particular claim of Optic Acceleration Cancellation theory that the servo strategy is to allow α to increase at a steadily decreasing rate.

Some theory for constructing minimum aberration fractional factorial designs

Minimum aberration is the most established criterion for selecting a regular fractional factorial design of maximum resolution. Minimum aberration designs for n runs and n/2 less than or equal to m < n factors have previously been constructed using the novel idea of complementary designs. In this paper, an alternative method of construction is developed by relating the wordlength pattern of designs to the so-called 'confounding between experimental runs'. This allows minimum aberration designs to be constructed for n runs and 5n/16 less than or equal to m less than or equal to n/2 factors as well as for n/2 less than or equal to m < n.

Self-consistent field theory for diblock copolymers grafted to a sphere

An efficient numerical self-consistent field theory (SCFT) algorithm is developed for treating structured polymers on spherical surfaces. The method solves the diffusion equations of SCFT with a pseudospectral approach that combines a spherical-harmonics expansion for the angular coordinates with a modified real-space Crank–Nicolson method for the radial direction. The self-consistent field equations are solved with Anderson-mixing iterations using dynamical parameters and an alignment procedure to prevent angular drift of the solution. A demonstration of the algorithm is provided for thin films of diblock copolymer grafted to the surface of a spherical core, in which the sequence of equilibrium morphologies is predicted as a function of diblock composition. The study reveals an array of interesting behaviors as the block copolymer pattern is forced to adapt to the finite surface area of the sphere.

Atrocities in theory and practice: An introduction

Classical counterinsurgency theory – written before the 19th century – has generally strongly opposed atrocities, as have theoreticians writing on how to conduct insurgencies. For a variety of reasons – ranging from pragmatic to religious or humanitarian – theoreticians of both groups have particularly argued for the lenient treatment of civilians associated with the enemy camp, although there is a marked pattern of exceptions, for example, where heretics or populations of cities refusing to surrender to besieging armies are concerned. And yet atrocities – defined here as acts of violence against the unarmed (non-combatants, or wounded or imprisoned enemy soldiers), or needlessly painful and/or humiliating treatment of enemy combatants, beyond any action needed to incapacitate or disarm them – occur frequently in small wars. Examples abound where these exhortations have been ignored, both by forces engaged in an insurgency and by forces trying to put down a rebellion. Why have so many atrocities been committed in war if so many arguments have been put forward against them? This is the basic puzzle for which the individual contributions to this special issue are seeking to find tentative answers, drawing on case studies.

Beyond description to pattern: The contribution of Batesonian epistemology to critical realist research

This paper proposes a limitation to epistemological claims to theory building prevalent in critical realist research. While accepting the basic ontological and epistemological positions of the perspective as developed by Roy Bhaskar, it is argued that application in social science has relied on sociological concepts to explain the underlying generative mechanisms, and that in many cases this has been subject to the effects of an anthropocentric constraint. A novel contribution to critical realist research comes from the work and ideas of Gregory Bateson. This is in service of two central goals of critical realism, namely an abductive route to theory building and a commitment to interdisciplinarity. Five aspects of Bateson’s epistemology are introduced: (1) difference, (2) logical levels of abstraction, (3) recursive causal loops, (4) the logic of metaphor, and (5) Bateson’s theory of mind. The comparison between Bateson and Bhaskar’s ideas is seen as a form of double description, illustrative of the point being raised. The paper concludes with an appeal to critical realists to start exploring the writing and outlook of Bateson himself.