共查询到20条相似文献,搜索用时 46 毫秒
1.
Bayesian networks have become one of the major models used for statistical inference. In this paper we discuss the properties
of the inner product spaces and concept class induced by some special Bayesian networks and the problem whether there exists
a Bayesian network such that lower bound on dimensional inner product space just is some positive integer. We focus on two-label
classification tasks over the Boolean domain. As main results we show that lower bound on the dimension of the inner product
space induced by a class of Bayesian networks without v-structures is
where m
i
denotes the number of parents for ith variable. As the variable’s number of Bayesian network is n≤5, we also show that for each integer m∈[n+1,2
n
−1] there is a Bayesian network
such that VC dimension of concept class and lower bound on dimensional inner product space induced by
all are m.
This work was supported by National Natural Science Foundation of China (60574075). 相似文献
2.
Bent functions have many applications in the fields of coding theory, communications and cryptography. This paper studies
the constructions of bent functions having the form
for odd n and
for even n, over the finite field
of odd characteristic p, where
. Based on the irreducibility of some polynomials on
, we focus on characterizing the bent functions for n=p
v
q
r
and n=2p
v
q
r
, where
is an odd prime and p a primitive root modulo q
2. Moreover, the enumerations of those functions are also considered.
Partially supported by the NSF of China under Grants No. 60603012 and No. 60573053. 相似文献
3.
We are studying the Diophantine exponent μ
n,l
defined for integers 1≤l<n and a vector α∈ℝ
n
by letting
where is the scalar product, denotes the distance to the nearest integer and is the generalised cone consisting of all vectors with the height attained among the first l coordinates. We show that the exponent takes all values in the interval [l+1,∞), with the value n attained for almost all α. We calculate the Hausdorff dimension of the set of vectors α with μ
n,l
(α)=μ for μ≥n. Finally, letting w
n
denote the exponent obtained by removing the restrictions on , we show that there are vectors α for which the gaps in the increasing sequence μ
n,1(α)≤...≤μ
n,n-1(α)≤w
n
(α) can be chosen to be arbitrary. 相似文献
4.
A. Krajka 《Acta Appl Math》2007,96(1-3):327-338
Let
be a probability space with a nonatomic measure P and let (S,ρ) be a separable complete metric space. Let {N
n
,n≥1} be an arbitrary sequence of positive-integer valued random variables. Let {F
k
,k≥1} be a family of probability laws and let X be some random element defined on
and taking values in (S,ρ).
In this paper we present necessary and sufficient conditions under which one can construct an array of random elements {X
n,k
,n,k≥1} defined on the same probability space and taking values in (S,ρ), and such that
, and moreover
as n→∞. Furthermore, we consider the speed of convergence
to X as n→∞.
相似文献
5.
We prove that the Banach space (?n=1¥lpn)lq(\bigoplus_{n=1}^{\infty}\ell_{p}^{n})_{\ell_{q}}, which is isomorphic to certain Besov spaces, has a greedy basis whenever 1≤p≤∞ and 1<q<∞. Furthermore, the Banach spaces (?n=1¥lpn)l1(\bigoplus_{n=1}^{\infty}\ell _{p}^{n})_{\ell_{1}}, with 1<p≤∞, and (?n=1¥lpn)c0(\bigoplus_{n=1}^{\infty}\ell_{p}^{n})_{c_{0}}, with 1≤p<∞, do not have a greedy basis. We prove as well that the space (?n=1¥lpn)lq(\bigoplus_{n=1}^{\infty}\ell _{p}^{n})_{\ell_{q}} has a 1-greedy basis if and only if 1≤p=q≤∞. 相似文献
6.
Ilwoo Cho 《Acta Appl Math》2007,95(2):95-134
In this paper, we will define a graph von Neumann algebra over a fixed von Neumann algebra M, where G is a countable directed graph, by a crossed product algebra = M ×
α
, where is the graph groupoid of G and α is the graph-representation. After defining a certain conditional expectation from onto its M-diagonal subalgebra we can see that this crossed product algebra is *-isomorphic to an amalgamated free product
where = vN(M ×
α
where is the subset of consisting of all reduced words in {e, e
–1} and M ×
α
is a W
*-subalgebra of as a new graph von Neumann algebra induced by a graph G
e
. Also, we will show that, as a Banach space, a graph von Neumann algebra is isomorphic to a Banach space ⊕
where is a certain subset of the set E(G)* of all words in the edge set E(G) of G.
The author really appreciates to Prof F. Radulescu and Prof P. Jorgensen for the valuable discussion and kind advice. Also,
he appreciates all supports from St. Ambrose Univ.. In particular, he thanks to Prof T. Anderson and Prof V. Vega for the
useful conversations and suggestions. 相似文献
7.
Let I be a finite interval, s ∈ ℕ0, and r,ν,n ∈ ℕ. Given a set M, of functions defined on I, denote by
M the subset of all functions y ∈ M such that the s-difference is nonnegative on I, ∀τ > 0. Further, denote by the Sobolev class of functions x on I with the seminorm . Also denote by Σ
ν,n
, the manifold of all piecewise polynomials of order ν and with n – 1 knots in I. If ν ≥ max {r,s}, 1 ≤ p,q ≤ ∞, and (r,p,q) ≠ (1,1,∞), then we give exact orders of the best unconstrained approximation and of the best s-monotonicity preserving approximation .
Part of this work was done while the first author visited Tel Aviv University in May 2003 and in March 2004. 相似文献
8.
Elton Pasku 《Semigroup Forum》2008,76(3):427-468
If a monoid S is given by some finite complete presentation ℘, we construct inductively a chain of CW-complexes
such that Δ
n
has dimension n, for every 2≤m≤n, the m-skeleton of Δ
n
is Δ
m
, and p
m
are critical (m+1)-cells with 1≤m≤n−2. For every 2≤m≤n−1, the following is an exact sequence of (ℤS,ℤS)-bimodules
where
if m=2. We then use these sequences to obtain a free finitely generated bimodule partial resolution of ℤS. Also we show that for groups properties FDT and FHT coincide. 相似文献
9.
We investigate the correlation between the constants K(ℝn) and
, where
is the exact constant in a Kolmogorov-type inequality, ℝ is the real straight line,
, L
l
p, p
(G
n) is the set of functions ƒ ∈ L
p
(G
n
) such that the partial derivative
belongs to L
p
(G
n
),
, 1 ≤ p ≤ ∞, l ∈ ℕn, α ∈ ℕ
0
n
= (ℕ ∪ 〈0〉)n, D
α
f is the mixed derivative of a function ƒ, 0 < μi < 1,
, and ∑
i=0
n
. If G
n
= ℝ, then μ0=1−∑
i=0
n
(α
i
/l
i
), μi = αi/l
i
,
if
, then μ0=1−∑
i=0
n
(α
i
/l
i
) − ∑
i=0
n
(λ/l
i
), μi = αi/ l
i
+ λ/l
i
,
, λ ≥ 0. We prove that, for λ = 0, the equality
is true.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 597–606, May, 2006. 相似文献
10.
11.
S. Pirzada Merajuddin T. A. Naikoo 《分析论及其应用》2007,23(4):363-374
Let D(U, V, W) be an oriented 3-partite graph with |U|=p, |V|=q and |W|= r. For any vertex x in D(U, V, W), let d x and d-x be the outdegree and indegree of x respectively. Define aui (or simply ai) = q r d ui - d-ui, bvj(or simply bj) = p r d vj - d-vj and Cwk (or simply ck) = p q d wk - d-wk as the scores of ui in U, vj in V and wk in Wrespectively. The set A of distinct scores of the vertices of D(U, V, W) is called its score set. In this paper, we prove that if a1 is a non-negative integer, ai(2≤i≤n - 1) are even positive integers and an is any positive integer, then for n≥3, there exists an oriented 3-partite graph with the score set A = {a1,2∑i=1 ai,…,n∑i=1 ai}, except when A = {0,2,3}. Some more results for score sets in oriented 3-partite graphs are obtained. 相似文献
12.
The minimisation problem for a functional
is considered, where
is an ℝ
n
-valued stochastic process, defined on some filtered probability space
, and P is an admissible probability measure in the sense that it obeys (1) some uniform equivalence condition with respect to the given measure ℙ
on Γ, and (2) a finite number (possibly zero) of arbitrarily given other conditions that require the expectation (with respect
to P) of some continuous bounded function φ of
, for t
1,…,t
k
∈[0,1], to lie within some closed set. We assume that u can be formulated through finite compositions of conditional expectations and bounded continuous functions.
Under the assumption of |φ| being uniformly bounded from below and some condition on the dimension of
, the existence of a solution on hyperfinite adapted probability spaces, as well as its minimality among admissible measures
on any other adapted probability space, is proven. Also, a coarseness result for the Loeb operation is established.
The main result of this paper, however, is a “standard result”: It does not include any reference to nonstandard analysis
and can be perfectly understood without any familiarity with nonstandard analysis.
相似文献
13.
The method of cyclic relaxation for the minimization of a function depending on several variables cyclically updates the value
of each of the variables to its optimum subject to the condition that the remaining variables are fixed.
We present a simple and transparent proof for the fact that cyclic relaxation converges linearly to an optimum solution when
applied to the minimization of functions of the form
for a
i,j
,b
i
,c
i
∈ℝ≥0 with max {min {b
1,b
2,…,b
n
},min {c
1,c
2,…,c
n
}}>0 over the n-dimensional interval [l
1,u
1]×[l
2,u
2]×⋅⋅⋅×[l
n
,u
n
] with 0<l
i
<u
i
for 1≤i≤n. Our result generalizes several convergence results that have been observed for algorithms applied to gate- and wire-sizing
problems that arise in chip design. 相似文献
14.
Let X
1, X
2, ... be i.i.d. random variables. The sample range is R
n
= max {X
i
, 1 ≤ i ≤ n} − min {X
i
, 1 ≤ i ≤ n}. If for a non-degenerate distribution G and some sequences (α
k
), (β
k
) then we have
and
almost surely for any continuity point x of G and for any bounded Lipschitz function f: R → R.
相似文献
15.
V. F. Molchanov 《Acta Appl Math》2007,99(3):321-337
We define canonical representations R
λ
,
, for the Lobachevsky space ℒ=G/K of dimension n−1 where G=SO0(n−1,1), K=SO(n−1), as the restriction to G of maximal degenerate series representations of the overgroup
. We determine explicitly the interaction of Lie operators of
with operators intertwining canonical representations and representations of G associated with a cone.
Supported by the Russian Foundation for Basic Research: grants No. 05-01-00074a and No. 05-01-00001a, the Netherlands Organization
for Scientific Research (NWO): grant 047-017-015, the Scientific Program “Devel. Sci. Potent. High. School”: project RNP.2.1.1.351
and Templan No. 1.2.02. 相似文献
16.
A. D. Blinco S. I. El-Zanati G. F. Seelinger P. A. Sissokho L. E. Spence C. Vanden Eynden 《Designs, Codes and Cryptography》2008,48(1):69-77
Let V
n
(q) denote a vector space of dimension n over the field with q elements. A set of subspaces of V
n
(q) is a partition of V
n
(q) if every nonzero vector in V
n
(q) is contained in exactly one subspace in . A uniformly resolvable design is a pairwise balanced design whose blocks can be resolved in such a way that all blocks in a given parallel class have the
same size. A partition of V
n
(q) containing a
i
subspaces of dimension n
i
for 1 ≤ i ≤ k induces a uniformly resolvable design on q
n
points with a
i
parallel classes with block size , 1 ≤ i ≤ k, and also corresponds to a factorization of the complete graph into -factors, 1 ≤ i ≤ k. We present some sufficient and some necessary conditions for the existence of certain vector space partitions. For the partitions
that are shown to exist, we give the corresponding uniformly resolvable designs. We also show that there exist uniformly resolvable
designs on q
n
points where corresponding partitions of V
n
(q) do not exist.
A. D. Blinco—Part of this research was done while the author was visiting Illinois State University. 相似文献
17.
Constant-Sign Solutions for Systems of Fredholm and Volterra Integral Equations: The Singular Case 总被引:1,自引:0,他引:1
We consider the system of Fredholm integral equations
and also the system of Volterra integral equations
where T>0 is fixed and the nonlinearities h
i
(t,u
1,u
2,…,u
n
) can be singular at t=0 and u
j
=0 where j∈{1,2,…,n}. Criteria are offered for the existence of constant-sign solutions, i.e., θ
i
u
i
(t)≥0 for t∈[0,1] and 1≤i≤n, where θ
i
∈{1,−1} is fixed. We also include examples to illustrate the usefulness of the results obtained.
相似文献
18.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequality holds for 0 < p ≤ 2. Moreover, we prove that if ω0,..., ω
n−1 are the n roots of unity with ω
j
= e
2πij/n
, 0 ≤ j ≤ n − 1, then for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequalities hold for 0 < p ≤ 2. These inequalities, which involve n-tuples of operators, lead to natural generalizations and refinements of some of the classical Clarkson inequalities in the
Schatten p-norms. Extensions of these inequalities to certain convex and concave functions, including the power functions, are olso
optained.
相似文献
19.
We prove a functional law of iterated logarithm for the following kind of anticipating stochastic differential equations
where u>e, W={(W
t
1,…,W
t
k
),0≤t≤1} is a standard k-dimensional Wiener process,
are functions of class
with bounded partial derivatives up to order 2, X
0
u
is a random vector not necessarily adapted and the first integral is a generalized Stratonovich integral.
The work is partially supported by DGES grant BFM2003-01345. 相似文献
20.
LetI be a finite interval andr ∈ ℕ. Denote by △
+
s
L
q
the subset of all functionsy ∈L
q
such that thes-difference △
T
s
y(·) is nonnegative onI, ∀τ>0. Further, denote by △
+
s
W
p
r
the class of functionsx onI with the seminorm ‖x
(r)
‖L
p
≤1, such that △
T
s
x≥0, τ > 0, τ>0. Fors=3,…,r+1, we obtain two-sided estimates of the shape preserving widths
, whereM
n
is the set of all linear manifoldsM
n
inL
q
, dimM
n
≤n, such thatM
n
⋂△
+
s
L
q
≠ 0.
Part of this work was done while the first author visited Tel Aviv University in 2001 and part of it while the second author
was a member of the Industrial Mathematics Institute (IMI), University of South Carolina. 相似文献