21,374 research outputs found
A Probabilistic Analysis of the Power of Arithmetic Filters
The assumption of real-number arithmetic, which is at the basis of
conventional geometric algorithms, has been seriously challenged in recent
years, since digital computers do not exhibit such capability.
A geometric predicate usually consists of evaluating the sign of some
algebraic expression. In most cases, rounded computations yield a reliable
result, but sometimes rounded arithmetic introduces errors which may invalidate
the algorithms. The rounded arithmetic may produce an incorrect result only if
the exact absolute value of the algebraic expression is smaller than some
(small) varepsilon, which represents the largest error that may arise in the
evaluation of the expression. The threshold varepsilon depends on the structure
of the expression and on the adopted computer arithmetic, assuming that the
input operands are error-free.
A pair (arithmetic engine,threshold) is an "arithmetic filter". In this paper
we develop a general technique for assessing the efficacy of an arithmetic
filter. The analysis consists of evaluating both the threshold and the
probability of failure of the filter.
To exemplify the approach, under the assumption that the input points be
chosen randomly in a unit ball or unit cube with uniform density, we analyze
the two important predicates "which-side" and "insphere". We show that the
probability that the absolute values of the corresponding determinants be no
larger than some positive value V, with emphasis on small V, is Theta(V) for
the which-side predicate, while for the insphere predicate it is Theta(V^(2/3))
in dimension 1, O(sqrt(V)) in dimension 2, and O(sqrt(V) ln(1/V)) in higher
dimensions. Constants are small, and are given in the paper.Comment: 22 pages 7 figures Results for in sphere test inproved in
cs.CG/990702
Further Results on Arithmetic Filters for Geometric Predicates
An efficient technique to solve precision problems consists in using exact
computations. For geometric predicates, using systematically expensive exact
computations can be avoided by the use of filters. The predicate is first
evaluated using rounding computations, and an error estimation gives a
certificate of the validity of the result. In this note, we studies the
statistical efficiency of filters for cosphericity predicate with an assumption
of regular distribution of the points. We prove that the expected value of the
polynomial corresponding to the in sphere test is greater than epsilon with
probability O(epsilon log 1/epsilon) improving the results of a previous paper
by the same authors.Comment: 7 pages 2 figures presented at the 15th European Workshop Comput.
Geom., 113--116, 1999 improve previous results (in other paper
Strange pulsation modes in luminous red giants
We show that the spectrum of radial pulsation modes in luminous red giants
consists of both normal modes and a second set of modes with periods similar to
those of the normal modes. These additional modes are the red giant analogues
of the strange modes found in classical Cepheids and RR Lyrae variables. Here,
we describe the behaviour of strange and normal modes in luminous red giants
and discuss the dependence of both the strange and normal modes on the outer
boundary conditions. The strange modes always appear to be damped, much more so
than the normal modes. They should never be observed as self-excited modes in
real red giants but they may be detected in the spectrum of solar-like
oscillations. A strange mode with a period close to that of a normal mode can
influence both the period and growth rate of the normal mode.Comment: 6 pages, 5 figures, accepted by MNRA
Quantization of the Jackiw-Teitelboim model
We study the phase space structure of the Jackiw-Teitelboim model in its
connection variables formulation where the gauge group of the field theory is
given by local SL(2,R) (or SU(2) for the Euclidean model), i.e. the de Sitter
group in two dimensions. In order to make the connection with two dimensional
gravity explicit, a partial gauge fixing of the de Sitter symmetry can be
introduced that reduces it to spacetime diffeomorphisms. This can be done in
different ways. Having no local physical degrees of freedom, the reduced phase
space of the model is finite dimensional. The simplicity of this gauge field
theory allows for studying different avenues for quantization, which may use
various (partial) gauge fixings. We show that reduction and quantization are
noncommuting operations: the representation of basic variables as operators in
a Hilbert space depend on the order chosen for the latter. Moreover, a
representation that is natural in one case may not even be available in the
other leading to inequivalent quantum theories.Comment: Published version, a short note (not present in the published
version) on the quantization of the null sector has been adde
The CMB Quadrupole in a Polarized Light
The low quadrupole of the cosmic microwave background (CMB), measured by COBE
and confirmed by WMAP, has generated much discussion recently. We point out
that the well-known correlation between temperature and polarization
anisotropies of the CMB further constrains the low multipole anisotropy data.
This correlation originates from the fact that the low-multipole polarization
signal is sourced by the CMB quadrupole as seen by free electrons during the
relatively recent cosmic history. Consequently, the large-angle temperature
anisotropy data make restrictive predictions for the large-angle polarization
anisotropy, which depend primarily on the optical depth for electron scattering
after cosmological recombination, tau. We show that if current cosmological
models for the generation of large angle anisotropy are correct and the
COBE/WMAP data are not significantly contaminated by non-CMB signals, then the
observed C_te amplitude on the largest scales is discrepant at the 99.8% level
with the observed C_tt for the concordance LCDM model with tau=0.10. Using
tau=0.17, the preferred WMAP model-independent value, the discrepancy is at the
level of 98.5%.Comment: 6 pages, 6 figures, ApJ in pres
Separation probabilities for products of permutations
We study the mixing properties of permutations obtained as a product of two
uniformly random permutations of fixed cycle types. For instance, we give an
exact formula for the probability that elements are in distinct
cycles of the random permutation of obtained as product of two
uniformly random -cycles
On the simulation of interactive non-verbal behaviour in virtual humans
Development of virtual humans has focused mainly in two broad areas - conversational agents and computer game characters. Computer game characters have traditionally been action-oriented - focused on the game-play - and conversational agents have been focused on sensible/intelligent conversation. While virtual humans have incorporated some form of non-verbal behaviour, this has been quite limited and more importantly not connected or connected very loosely with the behaviour of a real human interacting with the virtual human - due to a lack of sensor data and no system to respond to that data. The interactional aspect of non-verbal behaviour is highly important in human-human interactions and previous research has demonstrated that people treat media (and therefore virtual humans) as real people, and so interactive non-verbal behaviour is also important in the development of virtual humans. This paper presents the challenges in creating virtual humans that are non-verbally interactive and drawing corollaries with the development history of control systems in robotics presents some approaches to solving these challenges - specifically using behaviour based systems - and shows how an order of magnitude increase in response time of virtual humans in conversation can be obtained and that the development of rapidly responding non-verbal behaviours can start with just a few behaviours with more behaviours added without difficulty later in development
Establishing the behavioural limits for countershaded camouflage
Countershading is a ubiquitous patterning of animals whereby the side that typically faces the highest illumination is darker. When tuned to specific lighting conditions and body orientation with respect to the light field, countershading minimizes the gradient of light the body reflects by counterbalancing shadowing due to illumination, and has therefore classically been thought of as an adaptation for visual camouflage. However, whether and how crypsis degrades when body orientation with respect to the light field is non-optimal has never been studied. We tested the behavioural limits on body orientation for countershading to deliver effective visual camouflage. We asked human participants to detect a countershaded target in a simulated three-dimensional environment. The target was optimally coloured for crypsis in a reference orientation and was displayed at different orientations. Search performance dramatically improved for deviations beyond 15 degrees. Detection time was significantly shorter and accuracy significantly higher than when the target orientation matched the countershading pattern. This work demonstrates the importance of maintaining body orientation appropriate for the displayed camouflage pattern, suggesting a possible selective pressure for animals to orient themselves appropriately to enhance crypsis
Is countershading camouflage robust to lighting change due to weather?
Countershading is a pattern of coloration thought to have evolved in order to implement camouflage. By adopting a pattern of coloration that makes the surface facing towards the sun darker and the surface facing away from the sun lighter, the overall amount of light reflected off an animal can be made more uniformly bright. Countershading could hence contribute to visual camouflage by increasing background matching or reducing cues to shape. However, the usefulness of countershading is constrained by a particular pattern delivering ‘optimal’ camouflage only for very specific lighting conditions. In this study, we test the robustness of countershading camouflage to lighting change due to weather, using human participants as a ‘generic’ predator. In a simulated three-dimensional environment, we constructed an array of simple leaf-shaped items and a single ellipsoidal target ‘prey’. We set these items in two light environments: strongly directional ‘sunny’ and more diffuse ‘cloudy’. The target object was given the optimal pattern of countershading for one of these two environment types or displayed a uniform pattern. By measuring detection time and accuracy, we explored whether and how target detection depended on the match between the pattern of coloration on the target object and scene lighting. Detection times were longest when the countershading was appropriate to the illumination; incorrectly camouflaged targets were detected with a similar pattern of speed and accuracy to uniformly coloured targets. We conclude that structural changes in light environment, such as caused by differences in weather, do change the effectiveness of countershading camouflage
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