23,050 research outputs found
The Boden-Hu conjecture holds precisely up to rank eight
Consider moduli schemes of vector bundles over a smooth projective curve
endowed with parabolic structures over a marked point. Boden and Hu observed
that a slight variation of the weights leads to a desingularisation of the
moduli scheme, and they conjectured that one can always obtain a small
resolution this way. The present text proves this conjecture in some cases
(including all bundles of rank up to eight) and gives counterexamples in all
other cases (in particular in every rank beyond eight). The main tool is a
generalisation of Ext-groups involving more than two quasiparabolic bundles.Comment: 17 page
Decision blocks: A tool for automating decision making in CLIPS
The human capability of making complex decision is one of the most fascinating facets of human intelligence, especially if vague, judgemental, default or uncertain knowledge is involved. Unfortunately, most existing rule based forward chaining languages are not very suitable to simulate this aspect of human intelligence, because of their lack of support for approximate reasoning techniques needed for this task, and due to the lack of specific constructs to facilitate the coding of frequently reoccurring decision block to provide better support for the design and implementation of rule based decision support systems. A language called BIRBAL, which is defined on the top of CLIPS, for the specification of decision blocks, is introduced. Empirical experiments involving the comparison of the length of CLIPS program with the corresponding BIRBAL program for three different applications are surveyed. The results of these experiments suggest that for decision making intensive applications, a CLIPS program tends to be about three times longer than the corresponding BIRBAL program
Optimal Timer Based Selection Schemes
Timer-based mechanisms are often used to help a given (sink) node select the
best helper node among many available nodes. Specifically, a node transmits a
packet when its timer expires, and the timer value is a monotone non-increasing
function of its local suitability metric. The best node is selected
successfully if no other node's timer expires within a 'vulnerability' window
after its timer expiry, and so long as the sink can hear the available nodes.
In this paper, we show that the optimal metric-to-timer mapping that (i)
maximizes the probability of success or (ii) minimizes the average selection
time subject to a minimum constraint on the probability of success, maps the
metric into a set of discrete timer values. We specify, in closed-form, the
optimal scheme as a function of the maximum selection duration, the
vulnerability window, and the number of nodes. An asymptotic characterization
of the optimal scheme turns out to be elegant and insightful. For any
probability distribution function of the metric, the optimal scheme is
scalable, distributed, and performs much better than the popular inverse metric
timer mapping. It even compares favorably with splitting-based selection, when
the latter's feedback overhead is accounted for.Comment: 21 pages, 6 figures, 1 table, submitted to IEEE Transactions on
Communications, uses stackrel.st
Green's Functions and the Adiabatic Hyperspherical Method
We address the few-body problem using the adiabatic hyperspherical
representation. A general form for the hyperangular Green's function in
-dimensions is derived. The resulting Lippmann-Schwinger equation is solved
for the case of three-particles with s-wave zero-range interactions. Identical
particle symmetry is incorporated in a general and intuitive way. Complete
semi-analytic expressions for the nonadiabatic channel couplings are derived.
Finally, a model to describe the atom-loss due to three-body recombination for
a three-component fermi-gas of Li atoms is presented.Comment: 14 pages, 8 figures, 2 table
Three-Body Recombination in One Dimension
We study the three-body problem in one dimension for both zero and finite
range interactions using the adiabatic hyperspherical approach. Particular
emphasis is placed on the threshold laws for recombination, which are derived
for all combinations of the parity and exchange symmetries. For bosons, we
provide a numerical demonstration of several universal features that appear in
the three-body system, and discuss how certain universal features in three
dimensions are different in one dimension. We show that the probability for
inelastic processes vanishes as the range of the pair-wise interaction is taken
to zero and demonstrate numerically that the recombination threshold law
manifests itself for large scattering length.Comment: 15 pages 7 figures Submitted to Physical Review
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