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1.
By combining the prototype theory and random set theory interpretations of vague concepts, a novel structure named information
cell and a combined structure named information cell mixture model are proposed to represent the semantics of vague concepts.
An information cell L
i
on the domain Ω has a transparent cognitive structure ‘L
i
=about
P
i
’ which is mathematically formalized by a 3-tuple 〈P
i
,d
i
,δ
i
〉 comprising a prototype set P
i
(⊆Ω), a distance function d
i
on Ω and a density function δ
i
on [0,+∞). An information cell mixture model on domain Ω is actually a set of weighted information cells L
i
s. A positive neighborhood function of the information cell mixture model is introduced in this paper to reflect the belief
distribution of positive neighbors of the underlying concept. An information cellularization algorithm is also proposed to
learn the information cell mixture model from a training data set, which is a direct application of the k-means and EM algorithms. Information cell mixture models provide some tools for information coarsening and concept modelling,
and have potential applications in uncertain reasoning and classification. 相似文献
2.
I. E. Simonova 《Journal of Mathematical Sciences》1995,75(2):1536-1539
A wide class of reliability theory models or lifetime data can be described as follows. Assume that the lifetime distribution
function is F(t, θ)=F0(λ(θ)t), where θ is the parameter characterizing some inner properties of a product and λ(θ) is an unknown increasing function.
The paper deals with methods of estimation of λ(θ) from the sample (t
i
,θ
i
),i = 1, ...,n, for the case of exponentialF
0.
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 46–51, Perm, 1991. 相似文献
3.
We consider an overloaded multi-server multi-class queueing model where customers may abandon while waiting to be served.
For class i, service is provided at rate μ
i
, and abandonment occurs at rate θ
i
. In a many-server fluid regime, we show that prioritizing the classes in decreasing order of c
i
μ
i
/θ
i
asymptotically minimizes an ergodic holding cost, where c
i
denotes the equivalent holding cost per unit time for class i. 相似文献
4.
Robert J. Aumann 《International Journal of Game Theory》1999,28(3):301-314
Formal Interactive Epistemology deals with the logic of knowledge and belief when there is more than one agent or “player.”
One is interested not only in each person's knowledge and beliefs about substantive matters, but also in his knowledge and
beliefs about the others' knowledge and beliefs. This paper examines two parallel approaches to the subject. The first is
the semantic, in which knowledge and beliefs are represented by a space Ω of states of the world, and for each player i, partitions ℐi of Ω and probability distributions πi(·; ω) on Ω for each state ω of the world. The atom of ℐi containing a given state ω represents i's knowledge at that state – the set of those other states that i cannot distinguish from ω; the probability distributions πi(·; ω) represents i's beliefs at the state ω. The second is the syntactic approach, in which beliefs are embodied in sentences constructed according to certain syntactic rules. This paper examines
the relation between the two approaches, and shows that they are in a sense equivalent.
In game theory and economics, the semantic approach has heretofore been most prevalent. A question that often arises in this
connection is whether, in what sense, and why the space Ω, the partitions ℐi, and the probability distributions πi(·; ω) can be taken as given and commonly known by the players. An answer to this question is provided by the syntactic approach. 相似文献
5.
Kurt Johansson 《Arkiv f?r Matematik》2010,48(1):79-95
We show that the transition probability of the Markov chain (G(i,1),...,G(i,n))
i≥1, where the G(i,j)’s are certain directed last-passage times, is given by a determinant of a special form. An analogous formula has recently
been obtained by Warren in a Brownian motion model. Furthermore we demonstrate that this formula leads to the Meixner ensemble
when we compute the distribution function for G(m,n). We also obtain the Fredholm determinant representation of this distribution, where the kernel has a double contour integral
representation. 相似文献
6.
Given convex bodies K
1,…,K
d
in ℝ
d
and numbers α
1,…,α
d
∈[0,1], we give a sufficient condition for existence and uniqueness of an (oriented) halfspace H with Vol (H∩K
i
)=α
i
⋅Vol K
i
for every i. The result is extended from convex bodies to measures. 相似文献
7.
S. Reshetov 《Journal of Mathematical Sciences》2010,167(4):537-542
We consider the problem of estimating a vector θ = (θ1, θ2,…) ∈ Θ ⊂ l
2 from observations y
i
= θ
i
+ σ
i
x
i
, i = 1, 2,…, where the random values x
i
are N(0, 1), independent, and identically distributed, the parametric set Θ is compact, orthosymmetric, convex, and quadratically
convex. We show that in that case, the minimax risk is not very different from sup?L( P) \sup {\Re_L}\left( \Pi \right) , where ?L( P) {\Re_L}\left( \Pi \right) is the minimax linear risk in the same problem with parametric set Π, and sup is taken over all the hyperrectangles Π ⊂ Θ.
Donoho, Liu, and McGibbon (1990) have obtained this result for the case of equal σ
i
, i = 1, 2,…. Bibliography: 4 titles. 相似文献
8.
Pekka Tukia 《Journal d'Analyse Mathématique》2004,92(1):137-189
A classical Teichmüller sequence is a sequence of quasiconformal mapsf
i with complex dilatations of the form
, where φ is a quadratic differential and 0≤k
i<1 are numbers such thatk
i→1 asi→∞. This situation occurs in the Teichmüller theory when one moves along a Teichmüller geodesic toward the boundary. The central
result is that if τ is a vertical trajectory associated to φ, then there is often, for instance if the sequence is normalized
so thatf
i fix 3 points, a subsequence such thatf
i tend either toward a constant or an injective map of τ (Theorem 4.1). If the limit is injective, it is an embedding of τ
if τ does not contain points such that τ returns infinitely often to every neighborhood of the point. The main idea is to
composef
i locally with a map ϱi so that the composed mapf
iϱi is conformal and coincides withf
i on τ. Normal family arguments are applied to the sequencef
iϱi. Various extensions are presented.
The research for this paper has been supported by the project 51749 of the Academy of Finland. 相似文献
9.
10.
Zineb Mimouni René Limage 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,18(1):569-574
Within the framework of the study of the fibrillation mechanism in an electrorheological (ER) suspension, this work presents
a comparison between the self similar solutions when the kernel is Ki,j ~ (i−1 + j−1) and the behaviour of the chains growth. Till now, the field induced chains formation has only been studied by numerical
or experimental methods. The work of Fournier and Lauren?ot (Communications in Mathematical Physics 256 2005) on the Smoluchowski’s
equation allows us to present an analytical solution for the field induced pearl chains in a colloidal ER suspension. 相似文献
11.
For a natural number k, define an oriented site percolation on ℤ2 as follows. Let x
i
, y
j
be independent random variables with values uniformly distributed in {1, …, k}. Declare a site (i, j) ∈ℤ2
closed if x
i
= y
j
, and open otherwise. Peter Winkler conjectured some years ago that if k≥ 4 then with positive probability there is an infinite oriented path starting at the origin, all of whose sites are open.
I.e., there is an infinite path P = (i
0, j
0)(i
1, j
1) · · · such that 0 = i
0≤i
1≤· · ·, 0 = j
0≤j
1≤· · ·, and each site (i
n
, j
n
) is open. Rather surprisingly, this conjecture is still open: in fact, it is not known whether the conjecture holds for any value of k. In this note, we shall prove the weaker result that the corresponding assertion holds in the unoriented case: if k≤ 4 then the probability that there is an infinite path that starts at the origin and consists only of open sites is positive.
Furthermore, we shall show that our method can be applied to a wide variety of distributions of (x
i
) and (y
j
). Independently, Peter Winkler [14] has recently proved a variety of similar assertions by different methods.
Received: 4 March 1999 / Revised version: 27 September 1999 / Published online: 21 June 2000 相似文献
12.
Highest weight representations of a Lie algebra of Block type 总被引:2,自引:0,他引:2
Yue-zhu WU & Yu-cai SU Department of Mathematics Shanghai Jiaotong University Shanghai China Department of Mathematics Qufu Normal University Qufu China Department of Mathematics University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2007,50(4):549-560
For a field F of characteristic zero and an additive subgroup G of F, a Lie algebra B(G) of the Block type is defined with the basis {Lα,i, c|α∈G, -1≤i∈Z} and the relations [Lα,i,Lβ,j] = ((i 1)β- (j 1)α)Lα β,i j αδα,-βδi j,-2c,[c, Lα,i] = 0. Given a total order (?) on G compatible with its group structure, and anyα∈B(G)0*, a Verma B(G)-module M(A, (?)) is defined, and the irreducibility of M(A,(?)) is completely determined. Furthermore, it is proved that an irreducible highest weight B(Z )-module is quasifinite if and only if it is a proper quotient of a Verma module. 相似文献
13.
Alexander R. Pruss 《Probability Theory and Related Fields》1998,111(3):323-332
Summary. A sequence of random variables X
1,X
2,X
3,… is said to be N-tuplewise independent if X
i
1,X
i
2,…,X
i
N
are independent whenever (i
1,i
2,…,i
N
) is an N-tuple of distinct positive integers. For any fixed N∈ℤ+, we construct a sequence of bounded identically distributed N-tuplewise independent random variables which fail to satisfy the central limit theorem.
Received: 17 May 1996 / In revised form: 28 January 1998 相似文献
14.
The ordered fieldR(M) consists of the realsR with a transcendentalM adjoined, which is larger than any realr ∈R. Given any semi-infinite matrix (s.i.m.) interpreted as linear inequalities:u
tPi≧c
i, ∀
i
∈I, an arbitrary index set, it is also shown that the following are equivalent. (1) For every finiteJ ⊆I the systemu
tPi≧c
i,i ∈J is consistent, and (2) the s.i.m. has a solutionu ∈R(M)
n. Some consequences for “duality gaps” are also given.
These results were obtained as part of the activities of the Management Science Research Group and School of Urban and Public
Affairs, Carnegie-Mellon University. 相似文献
15.
Pekka Tukia 《Journal d'Analyse Mathématique》2006,99(1):35-87
We extend the results of [T2] to the situation where there is a compatibility with the action of a Kleinian group. A classical
Techmüller sequence is a sequence of quasiconformal mapsf
i with complex dilatations of the form
, where ϕ is a quadratic differential and 0<-k
i<1 are numbers such thatk
i→1 asi→∞. We proved in [T2] that if τ is a vertical trajectory associated to ϕ, then there is often, for instance if the sequence
is normalized so thatf
i fix 3 points, a subsequence such thatf
i tend either toward a constant or an injective map of τ. If there is compatibility with the action of a non-elementary finitely
generated Kleinian groupG, we can given a precise characterization which of these cases occurs. Suppose thatf
i induce isomorphisms ϕi ofG onto another Kleinian group and that ϕi have algebraic limit ϕ. If the quadratic differential is defined on a component of the ordinary set ofG, if there are no parabolic elements, and if τ is extended maximally so that all branches coming together at a singular point
are included, then we can state the main result as follows. The limit is a constantc if the stabilizerG
τ of τ is elementary; and, if it is non-elementary, then the limit is injective. In the first case, ϕ(g) is parabolic with fixpointc wheneverg∈G
τ is of infinite order; and in the latter case, the limitf is an embedding of τ in a natural topology of τ, andf embeds τ into a component of the limit set of ϕG whose stabilizer is ϕG
τ. Various extensions and generalizations are presented.
The research for this paper has been supported by the project 51749 of the Academy of Finland. 相似文献
16.
E. Ballico 《Annali dell'Universita di Ferrara》1982,38(1):33-40
Summary Here we prove the following result. Fix integersq, τ,a’, b’, a’
i, 1≤i≤τ,a’, b’, a’
i, 1≤i≤τ; then there is an integerew such that for every integert≥w, for every algebraically closed fieldK for every smooth complete surfaceX with negative Kodaira dimension, irregularityq andK
X
2
=8(1−q)−τ, the following condition holds; ifX→S is a sequence fo τ blowing-downs which gives a relatively minimal model with ruling ρ:S→C, take as basis of the Neron Severi groupNS(X) a smooth rational curve which is the total transform of a fiber ofC, the total transform of a minimal section of ρ and the total transformD
i, 1≤i≤τ, of the exceptional curver; then for everyH andL∈Pic (X) withH ample,H (resp.L) represented by the integersa’, b’, a’
i, (resp.a’, b’, a’
i), 1≤i≤τ, in the chosen basis ofNS(X) the moduli spaceM(ZX, 2,H, L, t) of rank 2H-stable vector bundles onX with determinantL andc
2=t is generically smooth and the number, dimension and ?birational structure? of the irreducible components ofM(X, 2,H, L, t)red do not depend on the choice ofK andX. Furthermore the birational structure of these irreducible components can be loosely described in terms of the birational
structure of the components of suitableM(S, 2,H’, L’, t’)red withS a relatively minimal model ofX.
Sunto SiaX una superficie algebrica liscia completa con dimensione di Kodaira negativa e definita su un campo algebricamente chiusoK; fissiamoH eL∈Pic (X),t∈Z; siaq l’irregolarità diX e τ≔8(1−q)−K X Emphasis>2 ; siaM(X, 2,H, L, t) to schema dei moduli dei fibrati vettorialiH-stabili di rango 2 suX con determinateL ec 2=t. Si dimostra che esiste una costantew che dipende solo daq, da τ e dalla classe numerica diH e diL (ma non da char (K) o dalla classe di isomorphismo diX) tale che per ognit≥w il numero, la dimensione e ?la struttura birazionale? delle componenti irriducibili diM(X, 2,H, L, t)red non dipende dalla scelta di char (K),K eX ma solo daq, τ e dalle classi diH eL inNS(X). Inoltre la ?struttura birazionale? di queste componenti irriducibili può essere grossolanamente descritta in termini delle componenti di opportuni spazi di moduliM(S, 2,H’, L’, t’) (doveS è un modello minimale diX).相似文献
17.
S. Sylvia Chu K. C. S. Pillai 《Annals of the Institute of Statistical Mathematics》1979,31(1):185-205
Power studies of tests of equality of covariance matrices of twop-variate normal populations Σ1=Σ2 against two-sided alternatives have been made based on the following six criteria: 1) Roy's largest root, 2) Hotelling's
trace, 3) Pillai's trace, 4) Wilks' criterion, 5) Roy's largest-smallest roots and 6) modified likelihood ratio. A general
theorem has been proved establishing the local unbiasedness conditions connecting the two critical values for tests 1) to
5). Extensive unbiased power tabulations have been made forp=2, for various values ofn
1,n
2, λ1 and λ2 wheren
i
is the df of the SP matrix from theith sample and λ
i
is theith latent root of Σ1Σ
2
−1
(i=1,2). Further, comparisons of powers of tests 1) to 5) have been made with those of the modified likelihood ratio after obtaining
the exact distribution of the latter forn
2=2n
1 andp=2. Equal tail areas approach has also been used further to compute powers of tests 1) to 4) forp=2 for studying the bias. Again, a separate study has been made to compare the powers of the largest-smallest roots test with
its three biased approximate approaches as well as the largest root. Since the largest root test was observed to have some
advantage over the others, critical values were also obtained for this test in the unbiased as well as equal tail areas case
forp=3.
This research was supported by David Ross Grant from Purdue University.
S. Sylvia Chu is now with Northwestern University. 相似文献
18.
Let X
i
, i∈N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a mapping B→R. Under a central limit theorem assumption, an asymptotic evaluation of Z
n
= E (exp (n
Φ (∑
i
=1
n
X
i
/n))), up to a factor (1 + o(1)), has been gotten in Bolthausen [1]. In this paper, we show that the same asymptotic evaluation can be gotten without
the central limit theorem assumption.
Received: 19 September 1997 / Revised version:22 April 1999 相似文献
19.
Yossi Moshe 《Journal d'Analyse Mathématique》2006,99(1):267-294
Let λ be the upper Lyapunov exponent corresponding to a product of i.i.d. randomm×m matrices (X
i)
i
0/∞
over ℂ. Assume that theX
i's are chosen from a finite set {D
0,D
1...,D
t-1(ℂ), withP(X
i=Dj)>0, and that the monoid generated byD
0, D1,…, Dq−1 contains a matrix of rank 1. We obtain an explicit formula for λ as a sum of a convergent series. We also consider the case
where theX
i's are chosen according to a Markov process and thus generalize a result of Lima and Rahibe [22].
Our results on λ enable us to provide an approximation for the numberN
≠0(F(x)n,r) of nonzero coefficients inF(x)
n.(modr), whereF(x) ∈ ℤ[x] andr≥2. We prove the existence of and supply a formula for a constant α (<1) such thatN
≠0(F(x)n,r) ≈n
α for “almost” everyn.
Supported in part by FWF Project P16004-N05 相似文献
20.
Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type 总被引:17,自引:0,他引:17
W. A. Kirk 《Israel Journal of Mathematics》1974,17(4):339-346
LetX be a Banach space,K a nonempty, bounded, closed and convex subset ofX, and supposeT:K→K satisfies: for eachx∈K, lim sup
i→∞{sup
y∈K
‖t
ix−Tiy∼−‖x−y‖}≦0. IfT
N is continuous for some positive integerN, and if either (a)X is uniformly convex, or (b)K is compact, thenT has a fixed point inK. The former generalizes a theorem of Goebel and Kirk for asymptotically nonexpansive mappings. These are mappingsT:K→K satisfying, fori sufficiently large, ‖Tix−Tiy‖≦k
i‖x−y∼,x,y∈K, wherek
i→1 asi→∞. The precise assumption in (a) is somewhat weaker than uniform convexity, requiring only that Goebel’s characteristic of
convexity, ɛ0 (X), be less than one.
Research supported by National Science Foundation Grant GP 18045. 相似文献