61.
Operator Topologies And Reflexive Representability Of Groups
- Michael Megrelishvili
Using the concept of fragmentability, we show that weakly continuous
group representations are frequently strongly continuous. We show that if a Banach
(or, even, Frechet) space X has the Radon-Nikodym property (RNP), then the weak
and strong operator topologies coincide on every bounded (respectively, equicontinuous)
subgroup G of GL(X). We also strengthen a result of Shtern on reflexive
representability of topological groups. We show that three natural problems become
closely related: a problem of Ruppert about the existence of sufficiently many
wap functions, Archangelskii's problem on the existence of sufficiently many minimal
topological groups, and a question about the existence of uniformly universal
reflexive Banach spaces.
62.
U-monad Topologies of Hyperfinite Time Lines
- Renling Jin
In an ! 1 #saturated nonstandard universe a cut is an initial segment of the
hyperintegers, which is closed under addition. Keisler and Leth in #KL# introduced,
for each given cut U , a corresponding U#topology on the hyperintegers
by letting O be U,open if for any x 2 O there is a y greater than all the elements
in U such that the interval #x,y;x+y# # O. Let U be a cut in a hyper#-
nite time line H, whichisahyper#nite initial segment of the hyperintegers. The
U,monad topology of H is the quotient topology of the U,topological space
H modulo U . In this paper we...
63.
Sample Path Large Deviations In Finer Topologies
- Peter Eichelsbacher
. In this paper we present sufficient conditions for sample path large
deviation principles to be extended to finer topologies. We consider extensions
of the uniform topology by Orlicz functionals and we consider Lipschitz spaces:
the former are concerned with cumulative path behaviour while the latter are
more sensitive to extremes in local variation. We also consider sample paths
indexed by the half line, where the usual projective limit topologies are not
strong enough for many applications.
1. Introduction
Let Z be a topological space. A good rate function is a lower semi-continuous
function I : Z ! lR + , with compact level sets fz : I(z) ffg....
64.
Transitive Relations, Topologies and Partial Orders
- Steven Finch
by Steven R. Finch. All rights reserved.
Figure 1: There are 19 labeled posets with 3 elements, that is, P 3 =19.
correspondence between the topologies on S and the quasi-orders on S; hence Q n =
U n .
A partial order on S is a quasi-order that is antisymmetric as well. Let P n
denote the number of such relations. We usually write x # y if (x, y) # R and,
moreover, x
65.
Transverse Momentum as a Measure of Colour Topologies
- E. Norrbin
Several distinct colour flow topologies are possible in multiparton configurations.
A method is proposed to find the correct topology, based on a
minimization of the total transverse momentum of produced particles. This
method is studied for three-jet Z
0
! qqg and four-jet W
+
W
Gamma
! q 1 q 2 q 3 q 4
events. It is shown how the basic picture is smeared, especially by partonshower
activity. The method therefore may not be sufficient on its own, but
could still be a useful complement to others, and e.g. help provide some
handle on colour rearrangement effects.
1
emanuel@thep.lu.se
2
torbjorn@thep.lu.se
When high-energy processes produce multiparton states, it is generally believed that
the confinement property of QCD...
66.
Transverse Momentum as a Measure of Colour Topologies
- E. Norrbin
Several distinct colour flow topologies are possible in multiparton configurations.
A method is proposed to find the correct topology, based on a
minimization of the total transverse momentum of produced particles. This
method is studied for three-jet Z
0
! qqg and four-jet W
+
W
Gamma
! q 1 q 2 q 3 q 4
events. It is shown how the basic picture is smeared, especially by partonshower
activity. The method therefore may not be sufficient on its own, but
could still be a useful complement to others, and e.g. help provide some
handle on colour rearrangement effects.
1
emanuel@thep.lu.se
2
torbjorn@thep.lu.se
When high-energy processes produce multiparton states, it is generally believed that
the confinement property of QCD...
67.
Bohr Topologies and Compact Function Spaces
- Joan E. Hart
We consider (discrete) structures, A, for a countable language.
A
#
denotes A with its Bohr topology. Let Y be a compact Hausdor
space. Then Y is homeomorphic to a subspace of some A
#
i Y is
Talagrand compact.
1 Introduction
1.1 Summary
The results of this paper use the theory of compact function spaces to characterize
the possible compact subspaces of topological structures endowed
with the Bohr topology. We begin by reviewing some background on Bohr
topologies, and then explain how this relates to function spaces.
Throughout this paper, a language, L, is a countable (possibly nite) set
of function and constant symbols. Then, a structure A for L is a non-empty
set A,...
68.
Deflection routing in regular MNA topologies
- Jacek Maitan
: We introduce MNA (Multigrid Network Architecture)---a networking concept aimed at applications calling for very high transmission rates (of the order of gigabits per second). An MNA network is a collection of photonic switches linked by optical channels. A switch is responsible for relaying incoming packets along the best available routes to their destinations. Packets that cannot be relayed optimally are deflected, i.e., relayed along suboptimal paths. The technology for building MNA switches has been developed in Lockheed Palo Alto Research Lab [20, 21, 22]. In this paper, we discuss the logical aspects of MNA, present a model for investigating...
69.
On Different Topologies for Set-Indexing Collections
- Giacomo Aletti
We underline some topological properties of set-indexing collections
in order to give new assumptions for set-indexed stochastic processes.
We show that this topological assumption is equivalent to another
one used in set-indexed framework and replaces metric assumption
for some stopping results. We give an example that modelizes
birth-and-growth processes.
Key words: Set-indexed processes, topological space, Birth-and-growth
processes
AMS subject classication. Primary: 60g05; Secondary: 60g07, 06a05,
60g40
1 Set-indexing framework
The aim of this paper is to study the topologies generated by set-indexing collection
in order to give more natural topological assumptions for set-indexed
stochastic processes. Condition SHAPE, introduced by Ivano and Merzbach
(see [2]) is one of the widest assumption in set-indexed theory, but...
70.
Modal Logics For Products Of Topologies
- J. Van Benthem,G. Bezhanishvili,B. Ten Cate,D. Sarenac
We introduce the horizontal and vertical topologies on the product
of topological spaces, and study their relationship with the standard product
topology. We show that the modal logic of products of topological spaces with
horizontal and vertical topologies is the fusion S4
S4. We axiomatize the
modal logic of products of topological spaces with horizontal, vertical, and
standard product topologies. We prove that both of these logics are complete
for the product of rational numbers Q
Q with the appropriate topologies.
71.
Measuring ISP Topologies with Rocketfuel
- Neil Spring,Ratul Mahajan,David Wetherall
To date, realistic ISP topologies have not been accessible to the research community, leaving work that depends on topology on an uncertain footing. In this paper, we present new Internet mapping techniques that have enabled us to directly measure router-level ISP topologies. Our techniques reduce the number of required traces compared to a brute-force, all-to-all approach by three orders of magnitude without a significant loss in accuracy. They include the use of BGP routing tables to focus the measurements, exploiting properties of IP routing to eliminate redundant measurements, better alias resolution, and the use of DNS to divide each map...
72.
Measuring ISP Topologies with Rocketfuel
- Neil Spring,Ratul Mahajan,David Wetherall,Thomas Anderson
To date, realistic ISP topologies have not been accessible to the research
community, leaving work that depends on topology on an uncertain footing.
In this paper, we present new Internet mapping techniques that have enabled
us to measure router-level ISP topologies. Our techniques reduce the
number of required traces compared to a brute-force, all-to-all approach
by three orders of magnitude without a significant loss in accuracy. They
include the use of BGP routing tables to focus the measurements, the elimination
of redundant measurements by exploiting properties of IP routing,
better alias resolution, and the use of DNS to divide each map into POPs
and backbone. We collect maps from...
73.
Measuring ISP Topologies with Rocketfuel
- Neil Spring,Ratul Mahajan,David Wetherall,Thomas Anderson
To date, realistic ISP topologies have not been accessible to the research
community, leaving work that depends on topology on an uncertain footing.
In this paper, we present new Internet mapping techniques that have enabled
us to measure router-level ISP topologies. Our techniques reduce the
number of required traces compared to a brute-force, all-to-all approach
by three orders of magnitude without a significant loss in accuracy. They
include the use of BGP routing tables to focus the measurements, the elimination
of redundant measurements by exploiting properties of IP routing,
better alias resolution, and the use of DNS to divide each map into POPs
and backbone. We collect maps from...
74.
Measuring ISP Topologies with Rocketfuel
- Neil Spring,Ratul Mahajan,David Wetherall
To date, realistic ISP topologies have not been accessible to the research
community, leaving work that depends on topology on an
uncertain footing. In this paper, we present new Internet mapping
techniques that have enabled us to directly measure router-level ISP
topologies. Our techniques reduce the number of required traces
compared to a brute-force, all-to-all approach by three orders of
magnitude without a significant loss in accuracy. They include the
use of BGP routing tables to focus the measurements, exploiting
properties of IP routing to eliminate redundant measurements, better
alias resolution, and the use of DNS to divide each map into
POPs and backbone. We collect maps from ten diverse...
75.
Towards Optimal Load Balancing Topologies
- Thomas Decker,Burkhard Monien,Robert Preis
. Many load balancing algorithms balance the load according to a topology.
Its choice can significantly influence the performance of the algorithm. We
consider the two phase balancing model. The first phase calculates a balancing
flow with respect to this topology by a diffusion scheme. Its time requirement
depends on the maximum node degree and on the number of eigenvalues of the
network. The second phase migrates the load according to this flow. A small flow
volume and a small diameter of the graph keeps the time requirement of this
phase low. We compare and propose several network topologies based on these
measurements. Several experiments on a Cray...
76.
A Modal Logic for Network Topologies
- Rogier M. Van Eijk,Frank S. De Boer
. In this paper, we present a logical framework that combines modality
with a first-order quantification mechanism. The logic differs from standard firstorder
modal logics in that quantification is not performed inside the states of a
model, but the states in the model themselves constitute the domain of quantification.
The locality principle of modal logic is preserved via the requirement that
in each state, the domain of quantification is restricted to a subset of the entire set
of states in the model. We show that the language is semantically characterised
by a generalisation of classical bisimulation, called history-based bisimulation,
consider its decidability and study the application of the...
77.
On Lookahead Routing in Torus Topologies with Random Extra Links
In this paper we present an asymptotic analysis of torus topologies enhanced with additional,
randomly assigned links for a class of scalable routing algorithms. In particular, we consider
algorithms in which each node has knowledge about only a limited number of other nodes. We
call them lookahead algorithms since each node looks only a few hops ahead in order to make a
routing decision. We develop an analytical method for finding asymptotic results for the expected
number of hops which can be applied to any torus topology with random extra links and lookahead
routing. We also present closed form asymptotic results for one dimensional and two-dimensional
torus...
78.
On Lookahead Routing in Torus Topologies with Random Extra Links
In this paper we present an asymptotic analysis of torus topologies enhanced with additional,
randomly assigned links for a class of scalable routing algorithms. In particular, we consider
algorithms in which each node has knowledge about only a limited number of other nodes. We
call them lookahead algorithms since each node looks only a few hops ahead in order to make a
routing decision. We develop an analytical method for finding asymptotic results for the expected
number of hops which can be applied to any torus topology with random extra links and lookahead
routing. We also present closed form asymptotic results for one dimensional and two-dimensional
torus...
79.
Blending Polygonal Shapes With Different Topologies
- Tatiana Surazhsky,Vitaly Surazhsky,Gill Barequet
In this paper, we propose a new method for morphing between two polygonal, possibly non-simply connected, shapes
in the plane. The method is based on reconstructing an xy-monotone surface whose extreme cross-sections coincide with
the given shapes. The surface generated by our algorithm does not contain any self-intersections, does not change the
topologies of the input slices, does not contain any horizontal triangles, and guarantees that all the topology changes
occur at a mid-height which is a degenerate form of both input topologies. All these properties are highly desirable for
blending shapes of di!erent topologies. # 2001 Elsevier Science Ltd. All rights reserved.
Keywords: Metamorphosis; Morphing;...
80.
Blending Polygonal Shapes with Different Topologies
- Tatiana Surazhsky,Vitaly Surazhsky,Gill Barequet,Ayellet Tal
In this paper we propose a new method for morphing between two polygonal, possibly
non-simply-connected, shapes in the plane. The method is based on reconstructing
an xy-monotone surface whose extreme cross-sections coincide with the
given shapes. The surface generated by our algorithm does not contain any selfintersections,
does not change the topologies of the input slices, does not contain
any horizontal triangles, and guarantees that all the topology changes occur at a
mid-height which is a degenerate form of both input topologies. All these properties
are highly desirable for blending shapes of different topologies.
