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Item type: Publication , Access status: Metadata only , A Geometric Perspective on Fusing Gaussian Distributions on Lie Groups(2024) Ge, Yixiao; Van Goor, Pieter; Mahony, RobertStochastic inference on Lie groups plays a key role in state estimation problems such as; inertial navigation, visual inertial odometry, pose estimation in virtual reality, etc. A key problem is fusing independent concentrated Gaussian distributions defined at different reference points on the group. In this letter we approximate distributions at different points in the group in a single set of exponential coordinates and then use classical Gaussian fusion to obtain the fused posteriori in those coordinates. We consider several approximations including the exact Jacobian of the change of coordinate map, first and second order Taylor's expansions of the Jacobian, and parallel transport with and without curvature correction associated with the underlying geometry of the Lie group. Preliminary results on SO(3) demonstrate that a novel approximation using parallel transport with curvature correction achieves similar accuracy to the state-of-the-art optimization based algorithms at a fraction of the computational cost.Item type: Publication , Access status: Metadata only , Seed dynamics and factors limiting recruitment of the mallee Eucalyptus incrassata, in semi-arid, south-eastern Australia.(1985) Wellington, A. B.; Noble, I. R.(1) Seedlings of mallee eucalypts occur infrequently after fire and are absent from long-unburnt stands. In this study, seedling recruitment in long-unburnt stands of yellow mallee, Eucalyptus incrassata, was found to be limited by a low availability of viable seed in the soil and by the inability of new seedlings to survive. (2) Despite a large reserve of seeds retained in woody capsules in the canopy for several years (maximum seed load of 8.0 (S.D. = 1.0) × 106 seeds ha-1 and a seed rain of up to $2.1 (S.D. = 0.9) \times 10^6 \text{seeds} ha^{-1} \text{year}^{-1}$, there was little or no storage of seed in the soil. Seed-harvesting ants rapidly removed 65-100% of newly-fallen seed. The exponential half-life of an isolated seed on the soil surface was 5.2 days. Seed harvesting activity was spatially and temporally variable. Naturally-fallen seeds were occasionally present at low densities on the soil surface. (3) The hypothesis that fire-induced mass release of seed may facilitate recruitment through the establishment of a seed bank in the soil was tested and supported. The experimental addition of seeds to the soil surface of an unburnt stand at likely post-fire densities (300 seeds m-2) resulted in an increased store of seed in the soil. Seeds remained viable in the soil for at least 300 days. Depletion of surface-added seed was gradual, indicating that high seed densities may have satiated the seed predator populations. The rate of field germination of this surface-added seed was similar to that of natural recruitment (10 000 seedlings ha-1) following a fire in December 1977. (4) Sufficient numbers of seedlings germinated in unburnt stands during the winter of 1980 to maintain population densities, despite the activities of seed-harvesting ants. However, all seedlings, both natural and induced, had died by the late spring of 1980, indicating that the conditions were not suitable for establishment. The successful establishment after fire, and the general absence of seedlings from unburnt stands, strongly suggest that the effects of fire in modifying environmental factors are crucial for seedling recruitment of mallees.Item type: Publication , Access status: Metadata only , Democracy in an age of tragedy: Democracy, tragedy and paradox(2010) Chou, MarkDemocracy and tragedy captured a delicate poise in ancient Athens. While many today perceive democracy as a finite, unquestionable and almost procedural form of governance that glorifies equality and liberty for their own sake, the Athenians saw it as so much more. Beyond the burgeoning equality and liberty, which were but fronts for a deeper goal, finitude, unimpeachability and procedural norms were constantly contradicted by boundlessness, subversion and disarray. In such a world, where certainty and immortality were luxuries beyond the reach of humankind, tragedy gave comfort and inspired greatness. The purpose of this article is to draw explicit links between democracy, tragedy and paradox. Given that tragedy's political ascendancy coincided with the birth of democracy in ancient Athens, we may assume that democracy was somehow, if not implicitly, tragic. But what was it that made democracy and tragedy speak so intimately to each other and to the Athenians who created them? The answer, at least the one which this article entertains, is paradox.Item type: Publication , Access status: Metadata only , Dramatizing war: George Packer and the democratic potential of Verbatim Theater(2010) Chou, Mark; Bleiker, RolandTimes of war are often times when democratic debates are under siege. The apparent necessity to ward off an enemy and secure the nation's survival can trigger a state of exception: a partial suspension of crucial democratic rights and practices for the sake of national security. The purpose of this essay is to examine the potential and limits of theater to offer an alternative forum for public debate in contexts where freedom of speech is limited. To do so, the authors systematically analyze the content and context of one play: George Packer's 2008 award-winning play, Betrayed. Through their analysis, they make two key arguments about the democratic potential of theater. First, that theater has the potential to sidestep political censorship during a time of war. And second, that theater can give voice to a multitude of real characters and under-represented perspectives.Item type: Publication , Access status: Metadata only , Democrats against democracy(2014-07-01) Chou, MarkIn late 2011, the Wall Street Journal published a curiously titled editorial, “Democrats against Democracy.” Written by James Taranto, one of the Journal’s conservative columnists, the piece documented a disturbing trend besetting democracy in America. Taranto claimed that American Democrats, or those who identified themselves as liberal and progressive, were increasingly turning their backs on democracy. Taranto was apprehensive that still more democrats would begin turning against democracy, spurred on by those on the American political left and by popular political movements like Occupy. In this essay, I take up and extend Taranto’s claim by exploring how democrats against democracy is manifesting in America beyond the relative minority who took to the streets as part of movements like Occupy. Basing my analysis on the Netflix series House of Cards, and the recent works of Sheldon Wolin and Henry Giroux, I demonstrate how standard it has become for democrats, broadly conceived, to use democracy as a means of producing antidemocratic and inequitable outcomes. I argue that Taranto’s analysis, though important, is tainted by his conservative outlook and, as such, misses the most pernicious and dystopic aspects of America’s democratic system, which not only permits but requires democrats to use democracy for their own ends. Here, it is not just left-leaning progressives and Democratic Party faithfuls we need to concern ourselves with. Private citizens, elected political representatives of all stripes, and the corporate and media elite are all engaged in the deceit, which has as its end point the decapitation of democracy.