Rigidity of Frameworks Supported on Surfaces

A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in \bR^2. A more general theory is developed for frameworks in \bR^3 whose vertices are constrained to move on a two-dimensional smooth submanifold \M. Furthermore, when \M is a union of concentric spheres, or a union of parallel planes or a union of concentric cylinders, necessary and sufficient combinatorial conditions are obtained for the minimal rigidity of generic frameworks.Comment: Final version, 28 pages, with new figure

Measuring Uncertainty in Games: Design and Preliminary Validation

Uncertainty is an important element of game play, which is widely believed to act as a precondition for player experience (PX). To investigate the concept and examine its relation to other PX concepts, we should be able to measure it. We present the design and preliminary results of the validation of the Player Uncertainty in Games (PUG) questionnaire. Based on various sources from games user research and work done with regards to searching digital archives, we designed a questionnaire that measures the experience of uncertainty in games. The scale was refined down to 66 items via interviews with players and expert reviews, which was then validated and further refined based on data gathered from gamers in an online survey. The Principal Component Analysis showed high level of internal consistency for the scale and each of its four factors: Disorientation, Exploration, Prospect, and Randomness. This work demonstrates the initial findings towards a validated tool for measuring uncertainty of players in digital games

Reflexivity of the translation-dilation algebras on L^2(R)

The hyperbolic algebra A_h, studied recently by Katavolos and Power, is the weak star closed operator algebra on L^2(R) generated by H^\infty(R), as multiplication operators, and by the dilation operators V_t, t \geq 0, given by V_t f(x) = e^{t/2} f(e^t x). We show that A_h is a reflexive operator algebra and that the four dimensional manifold Lat A_h (with the natural topology) is the reflexive hull of a natural two dimensional subspace.Comment: 10 pages, no figures To appear in the International Journal of Mathematic

I feel good, therefore I am real: testing the causal influence of mood on state authenticity

Although the literature has focused on individual differences in authenticity, recent findings suggest that authenticity is sensitive to context; that is, it is also a state. We extended this perspective by examining whether incidental affect influences authenticity. In three experiments, participants felt more authentic when in a relatively positive than negative mood. The causal role of affect in authenticity was consistent across a diverse set of mood inductions, including explicit (Experiments 1 and 3) and implicit (Experiment 2) methods. The link between incidental affect and state authenticity was not moderated by ability to down-regulate negative affect (Experiments 1 and 3) nor was it explained by negative mood increasing private self-consciousness or decreasing access to the self system (Experiment 3). The results indicate that mood is used as information to assess one’s sense of authenticity

Mass of Clusters in Simulations

We show that dark matter haloes, in n--body simulations, have a boundary layer (BL) with precise features. In particular, it encloses all dynamically stable mass while, outside it, dynamical stability is lost soon. Particles can pass through such BL, which however acts as a confinement barrier for dynamical properties. BL is set by evaluating kinetic and potential energies (T(r) and W(r)) and calculating R=-2T/W. Then, on BL, R has a minimum which closely approaches a maximum of w= -dlog W/dlog r. Such $Rw$ ``requirement'' is consistent with virial equilibrium, but implies further regularities. We test the presence of a BL around haloes in spatially flat CDM simulations, with or without cosmological constant. We find that the mass M_c, enclosed within the radius r_c, where the $Rw$ requirement is fulfilled, closely approaches the mass M_{dyn}, evaluated from the velocities of all particles within r_c, according to the virial theorem. Using r_c we can then determine an individual density contrast Delta_c for each virialized halo, which can be compared with the "virial" density contrast $\Delta_v ~178 \Omega_m^{0.45}$ (Omega_m: matter density parameter) obtained assuming a spherically symmetric and unperturbed fluctuation growth. The spread in Delta_c is wide, and cannot be neglected when global physical quantities related to the clusters are calculated, while the average Delta_c is ~25 % smaller than the corresponding Delta_v; moreover if $M_{dyn}$ is defined from the radius linked to Delta_v, we have a much worse fit with particle mass then starting from {\it Rw} requirement.Comment: 4 pages, 5 figures, contribution to the XXXVIIth Rencontres de Moriond, The Cosmological Model, Les Arc March 16-23 2002, to appear in the proceeding

Heat Capacity Mapping Mission

The Tasman Front was delineated by airborne expendable bathythermograph survey; and an Heat Capacity Mapping Mission (HCMM) IR image on the same day shows the same principal features as determined from ground-truth. It is clear that digital enhancement of HCMM images is necessary to map ocean surface temperatures and when done, the Tasman Front and other oceanographic features can be mapped by this method, even through considerable scattered cloud cover

Scaling Symmetries of Scatterers of Classical Zero-Point Radiation

Classical radiation equilibrium (the blackbody problem) is investigated by the use of an analogy. Scaling symmetries are noted for systems of classical charged particles moving in circular orbits in central potentials V(r)=-k/r^n when the particles are held in uniform circular motion against radiative collapse by a circularly polarized incident plane wave. Only in the case of a Coulomb potential n=1 with fixed charge e is there a unique scale-invariant spectrum of radiation versus frequency (analogous to zero-point radiation) obtained from the stable scattering arrangement. These results suggest that non-electromagnetic potentials are not appropriate for discussions of classical radiation equilibrium.Comment: 13 page