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1.
Abstract We obtain a multivariate extension of a classical result of Schoenberg on cardinal spline interpolation. Specifically, we
prove the existence of a unique function in
, polyharmonic of order p on each strip
,
, and periodic in its last n variables, whose restriction to the parallel hyperplanes
,
, coincides with a prescribed sequence of n-variate periodic data functions satisfying a growth condition in
. The constructive proof is based on separation of variables and on Micchelli’s theory of univariate cardinal
-splines.
Keywords: cardinal
-splines, polyharmonic functions, multivariable interpolation
Mathematics Subject Classification (2000): 41A05, 41A15, 41A63 相似文献
2.
An algorithm that performs asynchronous backtracking on distributed
, with dynamic ordering of agents is proposed,
. Agents propose reorderings of lower priority agents and send these proposals whenever they send assignment messages. Changes
of ordering triggers a different computation of
. The dynamic ordered asynchronous backtracking algorithm uses polynomial space, similarly to standard
. The
algorithm with three different ordering heuristics is compared to standard
on randomly generated
. A Nogood-triggered heuristic, inspired by dynamic backtracking, is found to outperform static order
by a large factor in run-time and improve the network load. 相似文献
3.
In 1999 Nakano, Olariu, and Schwing in [20], they showed that the permutation routing of n items pretitled on a mobile ad hoc network (MANET for short) of p stations (p known) and k channels (MANET{(n, p, k)) with k < p, can be carried out in
broadcast rounds if k p and if each station has a
-memory locations. And if k
and if each station has a
-memory locations, the permutations of these n pretitled items can be done also in
broadcast rounds. They used two assumptions: first they suppose that each station of the mobile ad hoc network has an identifier beforehand. Secondly, the stations are partitioned into k groups such that each group has
stations, but it was not shown how this partition can be obtained. In this paper, the stations have not identifiers beforehand and p is unknown. We develop a protocol which first names the stations, secondly gives the value of p, and partitions stations in groups of
stations. Finally we show that the permutation routing problem can be solved on it in
broadcast rounds in the worst case. It can be solved in
broadcast rounds in the better case. Note that our approach does not impose any restriction on k. 相似文献
4.
Coupling and self-stabilization 总被引:1,自引:0,他引:1
A randomized self-stabilizing algorithm
is an algorithm that, whatever the initial configuration is, reaches a set
of М legal configurations} in finite time with probability 1. The proof of convergence towards
is generally done by exhibiting a potential function
, which measures the “vertical” distance of any configuration to
, such that
decreases with non-null probability at each step of
. We propose here a method, based on the notion of coupling, which makes use of a “horizontal” distance
between any pair of configurations, such that
decreases in expectation at each step of
. In contrast with classical methods, our coupling method does not require the knowledge of
. In addition to the proof of convergence, the method allows us to assess the convergence rate according to two different
measures. Proofs produced by the method are often simpler or give better upper bounds than their classical counterparts, as
examplified here on Herman's mutual exclusion and Iterated Prisoner's Dilemma algorithms in the case of cyclic graphs. 相似文献
5.
R. F. Streater 《Open Systems & Information Dynamics》2004,11(4):359-375
Let H0 be a selfadjoint operator such that Tr
is of trace class for some
, and let
denote the set of ε-bounded forms, i.e.,
for some
0 $$" align="middle" border="0">
. Let χ := Span
. Let
denote the underlying set of the quantum information manifold of states of the form
. We show that if Tr
,
Presented at the 36th Symposium on Mathematical Physics, ‘Open Systems & Quantum Information’, Toruń, Poland, June 9-12, 2004. 相似文献
1. | the map Φ,
| |
2. | The Orlicz space defined by Φ is the tangent space of at ρ0; its affine structure is defined by the (+1)-connection of Amari | |
3. | The subset of a ‘hood of ρ0, consisting of p-nearby states (those obeying for some 1$$" align="middle" border="0"> ) admits a flat affine connection known as the (-1) connection, and the span of this set is part of the cotangent space of | |
4. | These dual structures extend to the completions in the Luxemburg norms. |
6.
7.
Dai, Li, and Wu proposed Rule k, a localized approximation algorithm that attempts to find a small connected dominating
set in a graph. In this paper we consider the "average-case" performance of two closely related versions of Rule k for the
model of random unit disk graphs constructed from n random points in an
square. We show that if
and
then for both versions of Rule k, the expected size of the Rule k dominating set is
as
It follows that, for
in a suitable range, the expected size of the Rule k dominating sets are within a constant factor of the optimum. 相似文献
8.
Agent Communication Languages (ACLs) have been developed to provide a way for agents to communicate with each other supporting
cooperation in Multi-Agent Systems (MAS). In the past few years many ACLs have been proposed for MAS and new standards are
emerging such as the ACL developed by the Foundation for Intelligent Physical Agents (FIPA). Despite these efforts, an important
issue in the research on ACLs is still open and concerns how these languages should deal with failures of agents in asynchronous MAS. The Fault Tolerant Agent Communication Language (
-
) presented in this paper addresses this issue dealing with crash failures of agents.
-
provides high-level communication primitives which support a fault-tolerant anonymous interaction protocol designed for open
MAS. We present a formal semantics for
-
and a formal specification of the underlying agent architecture. This formal framework allows us to prove that the ACL satisfies
a set of well defined knowledge-level programming requirements. To illustrate the language features we show how
-
can be effectively used to write high-level executable specifications of fault tolerant protocols, such as the Contract Net
one. 相似文献
9.
Abstract We present nonconforming, rectangular mixed finite element methods based on the Hellinger-Reissner variational principle in both two and three dimensions and show stability and convergence. An optimal error estimate of
is obtained for the displacement, along with a suboptimal,
, error estimate for the stress, in both dimensions. 相似文献
10.
Hierarchical matrices (
-matrices) approximate matrices in a data-sparse way, and the approximate arithmetic for
-matrices is almost optimal. In this paper we present an algebraic approach for constructing
-matrices which combines multilevel clustering methods with
-matrix arithmetic to compute the
-inverse,
-LU, and the
-Cholesky factors of a matrix. Then the
-inverse,
-LU or
-Cholesky factors can be used as preconditioners in iterative methods to solve systems of linear equations. The numerical
results show that this method is efficient and greatly speeds up convergence compared to other approaches, such as JOR or
AMG, for solving some large, sparse linear systems, and is comparable to other
-matrix constructions based on Nested Dissection. 相似文献
11.
12.
All the results given in the paper hold true. In the proof of Theorem 1, change steps IV, V, and VI to IV. for every
, add
to P; V. for every
, add
,
,
,
,
,
to P; VI. for every
, add
to P. 相似文献
13.
We construct a linear interval system Ax = b with a 4 × 4 interval matrix whose all proper interval coefficients (there are also some noninterval ones) are of the form [–, ]. It is proved that for each > 0, the interval hull
and interval hull of the midpoint preconditioned system
satisfy
and
, hence midpoint preconditioning produces a 100% overestimation of
independently of in this case. The example was obtained as a result of an extensive MATLAB search. 相似文献
14.
Eric Allender Anna Bernasconi Carsten Damm Joachim von zur Gathen Michael Saks Igor Shparlinski 《Computational Complexity》2003,12(1-2):23-47
We study various combinatorial complexity measures of
Boolean functions related to some natural arithmetic problems about
binary polynomials, that is, polynomials over
.
In particular, we consider
the Boolean function deciding whether a given polynomial over
is squarefree. We obtain an exponential lower bound on the size of a
decision tree for this function, and derive an asymptotic formula, having
a linear main term, for its average sensitivity. This allows us to estimate
other complexity characteristics such as the formula size, the average decision
tree depth and the degrees of exact and approximative polynomial
representations of this function. Finally, using a different method, we
show that testing squarefreeness and irreducibility of polynomials over
cannot be done in
for any odd prime p. Similar results are
obtained for deciding coprimality of two polynomials over
as well. 相似文献
15.
We study the problem of computing the k maximum sum subsequences. Given a sequence of real numbers
and an integer parameter k,
the problem involves finding the k largest values of
for
The problem for fixed k = 1, also known as the maximum sum subsequence problem, has received much attention in the literature
and is linear-time solvable. Recently, Bae and Takaoka presented a
-time algorithm for the k maximum sum subsequences problem. In this paper we design an efficient algorithm that solves the
above problem in
time in the worst case. Our algorithm is optimal for
and improves over the previously best known result for any value of the user-defined parameter k < 1. Moreover, our results
are also extended to the multi-dimensional versions of the k maximum sum subsequences problem; resulting in fast algorithms
as well. 相似文献
17.
Martin Ziegler 《Theory of Computing Systems》2007,41(1):177-206
By the sometimes so-called Main Theorem of Recursive Analysis, every computable real function is necessarily continuous. We
wonder whether and which kinds of hypercomputation allow for the effective evaluation of also discontinuous
. More precisely the present work considers the following three super-Turing notions of real function computability: - relativized
computation; specifically given oracle access to the Halting Problem
or its jump
; - encoding input
and/or output y = f(x) in weaker ways also related to the Arithmetic Hierarchy; - nondeterministic computation. It turns
out that any
computable in the first or second sense is still necessarily continuous whereas the third type of hypercomputation provides
the required power to evaluate for instance the discontinuous Heaviside function. 相似文献
18.
19.
Celina M.H. de Figueiredo Guilherme D. da Fonseca Vinicius G.P. de Sa Jeremy Spinrad 《Algorithmica》2006,46(2):149-180
A homogeneous set is a non-trivial module of a graph, i.e. a non-empty,
non-unitary, proper subset of a graph's vertices such that all its elements
present exactly the same outer neighborhood. Given two graphs
the Homogeneous Set Sandwich Problem (HSSP) asks whether there
exists a sandwich graph
which
has a homogeneous set. In 2001 Tang et al. published
an all-fast
algorithm which was recently proven wrong, so that the HSSP's known upper bound would have been reset
thereafter at the former
determined by Cerioli et al. in 1998. We present, notwithstanding, new deterministic
algorithms which have it established at
We give as
well two even faster
randomized algorithms, whose simplicity might
lend them didactic usefulness. We believe that, besides providing efficient
easy-to-implement procedures to solve it, the study of these new approaches
allows a fairly thorough understanding of the problem. 相似文献
20.
Emanuele Viola 《Computational Complexity》2005,13(3-4):147-188
We study the complexity of constructing pseudorandom generators (PRGs) from hard functions, focussing on constant-depth circuits. We show that, starting from a function
computable in alternating time O(l) with O(1) alternations that is hard on average (i.e. there is a constant
such that every circuit of size
fails to compute f on at least a 1/poly(l) fraction of inputs) we can construct a
computable by DLOGTIME-uniform constant-depth circuits of size polynomial in n. Such a PRG implies
under DLOGTIME-uniformity. On the negative side, we prove that starting from a worst-case hard function
(i.e. there is a constant
such that every circuit of size
fails to compute f on some input) for every positive constant
there is no black-box construction of a
computable by constant-depth circuits of size polynomial in n. We also study worst-case hardness amplification, which is the related problem of producing an average-case hard function starting from a worst-case hard one. In particular, we deduce that there is no blackbox worst-case hardness amplification within the polynomial time hierarchy. These negative results are obtained by showing that polynomialsize constant-depth circuits cannot compute good extractors and listdecodable codes. 相似文献