Formal theory building for the avalanche game: explaining counter-intuitive behaviour of a complex system using geometrical and human behavioural/physiological effects

In 'Avalanche', an object is lowered, players staying in contact throughout. Normally the task is easily accomplished. However, with larger groups counter-intuitive behaviours appear. The paper proposes a formal theory for the underlying causal mechanisms. The aim is to not only provide an explicit, testable hypothesis for the source of the observed modes of behaviour-but also to exemplify the contribution that formal theory building can make to understanding complex social phenomena. Mapping reveals the importance of geometry to the Avalanche game; each player has a pair of balancing loops, one involved in lowering the object, the other ensuring contact. For more players, sets of balancing loops interact and these can allow dominance by reinforcing loops, causing the system to chase upwards towards an ever-increasing goal. However, a series of other effects concerning human physiology and behaviour (HPB) is posited as playing a role. The hypothesis is therefore rigorously tested using simulation. For simplicity a 'One Degree of Freedom' case is examined, allowing all of the effects to be included whilst rendering the analysis more transparent. Formulation and experimentation with the model gives insight into the behaviours. Multi-dimensional rate/level analysis indicates that there is only a narrow region in which the system is able to move downwards. Model runs reproduce the single 'desired' mode of behaviour and all three of the observed 'problematic' ones. Sensitivity analysis gives further insight into the system's modes and their causes. Behaviour is seen to arise only when the geometric effects apply (number of players greater than degrees of freedom of object) in combination with a range of HPB effects. An analogy exists between the co-operative behaviour required here and various examples: conflicting strategic objectives in organizations; Prisoners' Dilemma and integrated bargaining situations. Additionally, the game may be relatable in more direct algebraic terms to situations involving companies in which the resulting behaviours are mediated by market regulations. Finally, comment is offered on the inadequacy of some forms of theory building and the case is made for formal theory building involving the use of models, analysis and plausible explanations to create deep understanding of social phenomena.

The counter-propagating Rossby-wave perspective on baroclinic instability. I: Mathematical basis

It is shown that Bretherton's view of baroclinic instability as the interaction of two counter-propagating Rossby waves (CRWs) can be extended to a general zonal flow and to a general dynamical system based on material conservation of potential vorticity (PV). The two CRWs have zero tilt with both altitude and latitude and are constructed from a pair of growing and decaying normal modes. One CRW has generally large amplitude in regions of positive meridional PV gradient and propagates westwards relative to the flow in such regions. Conversely, the other CRW has large amplitude in regions of negative PV gradient and propagates eastward relative to the zonal flow there. Two methods of construction are described. In the first, more heuristic, method a ‘home-base’ is chosen for each CRW and the other CRW is defined to have zero PV there. Consideration of the PV equation at the two home-bases gives ‘CRW equations’ quantifying the evolution of the amplitudes and phases of both CRWs. They involve only three coefficients describing the mutual interaction of the waves and their self-propagation speeds. These coefficients relate to PV anomalies formed by meridional fluid displacements and the wind induced by these anomalies at the home-bases. In the second method, the CRWs are defined by orthogonality constraints with respect to wave activity and energy growth, avoiding the subjective choice of home-bases. Using these constraints, the same form of CRW equations are obtained from global integrals of the PV equation, but the three coefficients are global integrals that are not so readily described by ‘PV-thinking’ arguments. Each CRW could not continue to exist alone, but together they can describe the time development of any flow whose initial conditions can be described by the pair of growing and decaying normal modes, including the possibility of a super-modal growth rate for a short period. A phase-locking configuration (and normal-mode growth) is possible only if the PV gradient takes opposite signs and the mean zonal wind and the PV gradient are positively correlated in the two distinct regions where the wave activity of each CRW is concentrated. These are easily interpreted local versions of the integral conditions for instability given by Charney and Stern and by Fjørtoft.

The counter-propagating Rossby-wave perspective on baroclinic instability. II: Application to the Charney model

The constant-density Charney model describes the simplest unstable basic state with a planetary-vorticity gradient, which is uniform and positive, and baroclinicity that is manifest as a negative contribution to the potential-vorticity (PV) gradient at the ground and positive vertical wind shear. Together, these ingredients satisfy the necessary conditions for baroclinic instability. In Part I it was shown how baroclinic growth on a general zonal basic state can be viewed as the interaction of pairs of ‘counter-propagating Rossby waves’ (CRWs) that can be constructed from a growing normal mode and its decaying complex conjugate. In this paper the normal-mode solutions for the Charney model are studied from the CRW perspective. Clear parallels can be drawn between the most unstable modes of the Charney model and the Eady model, in which the CRWs can be derived independently of the normal modes. However, the dispersion curves for the two models are very different; the Eady model has a short-wave cut-off, while the Charney model is unstable at short wavelengths. Beyond its maximum growth rate the Charney model has a neutral point at finite wavelength (r=1). Thereafter follows a succession of unstable branches, each with weaker growth than the last, separated by neutral points at integer r—the so-called ‘Green branches’. A separate branch of westward-propagating neutral modes also originates from each neutral point. By approximating the lower CRW as a Rossby edge wave and the upper CRW structure as a single PV peak with a spread proportional to the Rossby scale height, the main features of the ‘Charney branch’ (0

The counter-propagating Rossby-wave perspective on baroclinic instability. Part III: Primitive-equation disturbances on the sphere

Baroclinic instability of perturbations described by the linearized primitive quations, growing on steady zonal jets on the sphere, can be understood in terms of the interaction of pairs of counter-propagating Rossby waves (CRWs). The CRWs can be viewed as the basic components of the dynamical system where the Hamiltonian is the pseudoenergy and each CRW has a zonal coordinate and pseudomomentum. The theory holds for adiabatic frictionless flow to the extent that truncated forms of pseudomomentum and pseudoenergy are globally conserved. These forms focus attention on Rossby wave activity. Normal mode (NM) dispersion relations for realistic jets are explained in terms of the two CRWs associated with each unstable NM pair. Although derived from the NMs, CRWs have the conceptual advantage that their structure is zonally untilted, and can be anticipated given only the basic state. Moreover, their zonal propagation, phase-locking and mutual interaction can all be understood by ‘PV-thinking’ applied at only two ‘home-bases’—potential vorticity (PV) anomalies at one home-base induce circulation anomalies, both locally and at the other home-base, which in turn can advect the PV gradient and modify PV anomalies there. At short wavelengths the upper CRW is focused in the mid-troposphere just above the steering level of the NM, but at longer wavelengths the upper CRW has a second wave-activity maximum at the tropopause. In the absence of meridional shear, CRW behaviour is very similar to that of Charney modes, while shear results in a meridional slant with height of the air-parcel displacement-structures of CRWs in sympathy with basic-state zonal angular-velocity surfaces. A consequence of this slant is that baroclinically growing eddies (on jets broader than the Rossby radius) must tilt downshear in the horizontal, giving rise to up-gradient momentum fluxes that tend to accelerate the barotropic component of the jet.

The counter-propagating Rossby-wave perspective on baroclinic instability. Part IV: Nonlinear life cycles

Pairs of counter-propagating Rossby waves (CRWs) can be used to describe baroclinic instability in linearized primitive-equation dynamics, employing simple propagation and interaction mechanisms at only two locations in the meridional plane—the CRW ‘home-bases’. Here, it is shown how some CRW properties are remarkably robust as a growing baroclinic wave develops nonlinearly. For example, the phase difference between upper-level and lower-level waves in potential-vorticity contours, defined initially at the home-bases of the CRWs, remains almost constant throughout baroclinic wave life cycles, despite the occurrence of frontogenesis and Rossby-wave breaking. As the lower wave saturates nonlinearly the whole baroclinic wave changes phase speed from that of the normal mode to that of the self-induced phase speed of the upper CRW. On zonal jets without surface meridional shear, this must always act to slow the baroclinic wave. The direction of wave breaking when a basic state has surface meridional shear can be anticipated because the displacement structures of CRWs tend to be coherent along surfaces of constant basic-state angular velocity, U. This results in up-gradient horizontal momentum fluxes for baroclinically growing disturbances. The momentum flux acts to shift the jet meridionally in the direction of the increasing surface U, so that the upper CRW breaks in the same direction as occurred at low levels

Orde Wingate and the Special Night Squads: A Feasible Policy for Counter-Terrorism?

This article analyses the counter-terrorist operations carried out by Captain (later Major General) Orde Wingate in Palestine in 1938, and considers whether these might inform current operations. Wingate's Special Night Squads were formed from British soldiers and Jewish police specifically to counter terrorist and sabotage attacks. Their approach escalated from interdicting terrorist gangs to pre-emptive attacks on suspected terrorist sanctuaries to reprisal attacks after terrorist atrocities. They continued the British practice of using irregular units in counter-insurgency, which was sustained into the postwar era and contributed to the evolution of British Special Forces. Wingate's methods proved effective in pacifying terrorist-infested areas and could be applied again, but only in the face of 'friction' arising from changes in cultural attitudes since the 1930s, and from the political-strategic context of post-2001 counter-insurgent and counter-terrorist operations. In some cases, however, public opinion might not preclude the use of some of Wingate's techniques.

Orde Wingate, the Iron Wall and Counter-terrorism in Palestine, 1936-1939

A pamphlet published by the British Army's Strategic and Combat Studies Institute on the then Captain Orde Wingate's formation and command of the Anglo-Jewish Special Night Squads in the Palestine Arab revolt of 1936-1939, with a discussion of their long-term strategic and political implications.

Nickel(II) complexes of terdentate or symmetrical tetradentate Schiff bases: Evidence of the influence of the counter anions in the hydrolysis of the imine bond in Schiff base complexes

Two sets of ligands, set-1 and set-2, have been prepared by mixing 1,3-diaminopentane and carbonyl compounds (2-acetylpyridine or pyridine-2-carboxaldehyde) in 1:1 and 1:2 ratios, respectively, and employed for the synthesis of complexes with Ni(II) perchlorate, Ni(II) thiocyanate and Ni(II) chloride. Ni(II) perchlorate yields the complexes having general formula [NiL2](ClO4)(2)(L = L-1 [N-3-(1-pyridin-2-yl-ethylidene)-pentane-1,3-diamine] for complex 1 or L-2[N-3-pyridin-2-ylmethylene-pentane-1,3-diamine] for complex 2) in which the Schiff bases are monocondensed terdentate, whereas Ni(II) thiocyanate results in the formation of tetradentate Schiff base complexes, [NiL(SCN)(2)] (L = L-3[N,N'-bis-(1-pyridin-2- yl-ethylidine)-pentane-1,3-diamine] for complex 3 or L-4 [N,N'-bis(pyridin-2-ylmethyline)-pentane-1,3- diamine] for complex 4) irrespective of the sets of ligands used. Complexes 5 {[NiL3(N-3)(2)]} and 6 {[NiL4(N-3)(2)]} are prepared by adding sodium azide to the methanol solution of complexes 1 and 2. Addition of Ni(II) chloride to the set-1 or set-2 ligands produces [Ni(pn)(2)]Cl-2, 7, as the major product, where pn = 1,3-diaminopentane. Formation of the complexes has been explained by the activation of the imine bond by the counter anion and thereby favouring the hydrolysis of the Schiff base. All the complexes have been characterized by elemental analyses and spectral data. Single crystal X-ray diffraction studies con. firm the structures of three representative members, 1, 4 and 7; all of them have distorted octahedral geometry around Ni(II). The bis-complex of terdentate ligands, 1, is the mer isomer, and complexes 4 and 7 possess trans geometry. (C) 2008 Elsevier B. V. All rights reserved.

Influence of counter anions on the structures and magnetic properties of trinuclear Cu(II) complexes containing a mu(3)-OH core and Schiff base ligands

Four trinuclear Cu(II) complexes, [(CuL1)(3)(mu(3)-OH)](NO3)(2) (1), [(CuL2)(3)(mu(3)-OH)](I)(2)center dot H2O (2), [(CuL3)(3)(mu(3)-OH)](I)(2) (3) and [(CuL1)(3)(mu(3)-OH)][(CuI3)-I-1] (4), where HL1 (8-amino-4-methyl-5-azaoct-3-en-2-one), HL2 [7-amino-4-methyl-5-azaoct-3-en-2-one] and HL3 [7-amino-4-methyl-5-azahept-3-en-2- one] are the three tridentate Schiff bases, have been synthesized and structurally characterized by X-ray crystallography. All four complexes contain a partial cubane core, [(CuL)(3)(mu(3)-OH)](2+) in which the three [CuL] subunits are interconnected through two types of oxygen bridges afforded by the oxygen atoms of the ligands and the central OH- group. The copper(II) ions are in a distorted square-pyramidal environment. The equatorial plane consists of the bridging oxygen of the central OH- group together with three atoms (N, N, O) from the Schiff base. The oxygen atom of the Schiff base also coordinates to the axial position of Cu(II) of another subunit to form the cyclic trimer. Magnetic susceptibilities have been determined for these complexes over the temperature range of 2-300 K. The isotropic Hamiltonian, H = -J(12)S(1)S(2) - J(13)S(1)S(3) - J(23)S(2)S(3) has been used to interpret the magnetic data. The best fit parameters obtained are: J = - 54.98 cm(-1) g = 2.24 for 1; J = - 56.66 cm(-1), g = 2.19 for 2; J = -44.39 cm(-1), g = 2.16 for 3; J = - 89.92 cm(-1), g = 2.25 for 4. The EPR data at low temperature indicate that the phenomenon of spin frustration occurs for complexes 1-3. (c) 2007 Elsevier B.V. All rights reserved.

Learning to talk to users in participatory design situations

In participatory design situations the competence of the facilitator will influence the opportunities for a user group to become engaged in the process of design. Based on the observation of the conversations from a series of design workshops, the performance of design facilitation expertise by an expert architect is compared with a less experienced architectural graduate. The skills that are the focus of this research are the conversational competences deployed by architects to engage users in the design of an architectural project. The difference between the conversational behaviour of a project architect and a less experienced graduate was observed to illustrate with examples the effect the performance of facilitation had on the opportunity for user engagement in design, and of learning the skill of facilitation that occurred in these situations.