2,503 research outputs found
Distances on the tropical line determined by two points
Let . Write if is a multiple of
. Two different points and in uniquely
determine a tropical line , passing through them, and stable under
small perturbations. This line is a balanced unrooted semi--labeled tree on
leaves. It is also a metric graph.
If some representatives and of and are the first and second
columns of some real normal idempotent order matrix , we prove that the
tree is described by a matrix , easily obtained from . We also
prove that is caterpillar. We prove that every vertex in
belongs to the tropical linear segment joining and . A vertex, denoted
, closest (w.r.t tropical distance) to exists in . Same for
. The distances between pairs of adjacent vertices in and the
distances \dd(p,pq), \dd(qp,q) and \dd(p,q) are certain entries of the
matrix . In addition, if and are generic, then the tree
is trivalent. The entries of are differences (i.e., sum of principal
diagonal minus sum of secondary diagonal) of order 2 minors of the first two
columns of .Comment: New corrected version. 31 pages and 9 figures. The main result is
theorem 13. This is a generalization of theorem 7 to arbitrary n. Theorem 7
was obtained with A. Jim\'enez; see Arxiv 1205.416
Tropical conics for the layman
We present a simple and elementary procedure to sketch the tropical conic
given by a degree--two homogeneous tropical polynomial. These conics are trees
of a very particular kind. Given such a tree, we explain how to compute a
defining polynomial.
Finally, we characterize those degree--two tropical polynomials which are
reducible and factorize them. We show that there exist irreducible degree--two
tropical polynomials giving rise to pairs of tropical lines.Comment: 19 pages, 4 figures. Major rewriting of formerly entitled paper
"Metric invariants of tropical conics and factorization of degree--two
homogeneous tropical polynomials in three variables". To appear in Idempotent
and tropical mathematics and problems of mathematical physics (vol. II), G.
Litvinov, V. Maslov, S. Sergeev (eds.), Proceedings Workshop, Moscow, 200
Producción de planta de alcornoque y otras quercineas para repoblación forestal en la almoraima (Cádiz)
Hartree-Fock dynamics in highly excited quantum dots
Time-dependent Hartree-Fock theory is used to describe density oscillations
of symmetry-unrestricted two-dimensional nanostructures. In the small amplitude
limit the results reproduce those obtained within a perturbative approach such
as the linearized time-dependent Hartree-Fock one. The nonlinear regime is
explored by studying large amplitude oscillations in a non-parabolic potential,
which are shown to introduce a strong coupling with internal degrees of
freedom. This excitation of internal modes, mainly of monopole and quadrupole
character, results in sizeable modifications of the dipole absorption.Comment: 4 pages, 4 embedded figure
On the design of a high-performance adaptive router for CC-NUMA multiprocessors
Copyright © 2003 IEEEThis work presents the design and evaluation of an adaptive packet router aimed at supporting CC-NUMA traffic. We exploit a simple and efficient packet injection mechanism to avoid deadlock, which leads to a fully adaptive routing by employing only three virtual channels. In addition, we selectively use output buffers for implementing the most utilized virtual paths in order to reduce head-of-line blocking. The careful implementation of these features has resulted in a good trade off between network performance and hardware cost. The outcome of this research is a High-Performance Adaptive Router (HPAR), which adequately balances the needs of parallel applications: minimal network latency at low loads and high throughput at heavy loads. The paper includes an evaluation process in which HPAR is compared with other adaptive routers using FIFO input buffering, with or without additional virtual channels to reduce head-of-line blocking. This evaluation contemplates both the VLSI costs of each router and their performance under synthetic and real application workloads. To make the comparison fair, all the routers use the same efficient deadlock avoidance mechanism. In all the experiments, HPAR exhibited the best response among all the routers tested. The throughput gains ranged from 10 percent to 40 percent in respect to its most direct rival, which employs more hardware resources. Other results shown that HPAR achieves up to 83 percent of its theoretical maximum throughput under random traffic and up to 70 percent when running real applications. Moreover, the observed packet latencies were comparable to those exhibited by simpler routers. Therefore, HPAR can be considered as a suitable candidate to implement packet interchange in next generations of CC-NUMA multiprocessors.Valentín Puente, José-Ángel Gregorio, Ramón Beivide, and Cruz Iz
- …