FINDING APPROXIMATE LANGUAGE PATTERNS
Samuel W. K. Chan
Dept. of Decision Sciences, The Chinese University of Hong Kong, Hong Kong
Keywords: Bio-inspired language parsing, semantic labelling.
Abstract: A two-phase annotation method for semantic labeling based on the edit distance is proposed. This dynamic
programming approach stresses on a non-exact string matching technique that takes full advantage of the
underlying grammatical structure of 65,000 parse trees in a Treebank. It is based on the assumption that
human language understanding is relevant to concrete past language experiences rather than any abstract
linguistic rules. This shallow technique is inspired by the research in the area of bio-molecular sequences
analysis which advocates high sequence similarity usually implies significant function or structural
similarity. Experimental results for recognizing various labels in 10,000 sentences are used to justify its
significances.
1 INTRODUCTION
Automatic information extraction has received a
great deal of attention in the latest development of
information retrieval. While a plethora of issues
relating to questions of accuracy and efficiency have
been thoroughly discussed, the problem of extracting
meaning from natural language has scarcely been
addressed. When the size and quantity of documents
available on the Internet are considered, the demand
for a highly efficient system that identifies the
semantic meaning is clear. Case frame is one of the
most important structures that are used to represent
the meaning of sentences (Fillmore, 1968). One
could consider a case frame to be a special, or
distinguishing, form of knowledge structure about
sentences. Although several criteria for recognizing
case frames in sentences have been considered in the
past, none of the criteria serves as a completely
adequate decision procedure. Most of the studies in
natural language processing (NLP) do not provide
any hints on how to map input sentences into case
frames automatically. As a result, both the efficiency
and robustness of the techniques used in information
extraction is highly in doubt when they are applied
to real world applications.
The objective of this research is twofold. First,
a shallow but effective sentence chunking process is
developed. The process is to extract all the phrases
from the input sentences, without being bogged
down into deep semantic parsing and understanding.
Second, a novel semantic labeling technique that is
based on the syntactic and semantic tags of the latest
Treebank is being constructed (CKIP, 2004). One of
our primary goals in this research is to design a
shallow but robust mechanism which can annotate
sentences using a set of semantic labels. While the
classical syntactic and semantic analysis is
extremely difficult, if not impossible, to systematize
the current research in NLP, our approach does not
require any deep linguistic analysis to be formalized.
The annotation will provide piecemeal the
underlying semantic labels of the sentence. The
organization of the paper is as follows. The related
work in semantic labeling and sentence chunking are
first described in Section 2. In this research, each
word in sentences has two attributes, i.e. part-of-
speech (POS) and semantic classes (SC). Any input
sentence is first transformed into a feature-enhanced
string. A two-phase feature-enhanced string
matching algorithm which is based on the edit
distance is devised. Section 3 shows how the
algorithm can be applied in the semantic labeling
using 65,000 parse trees in a Treebank. The system
has already been implemented using Java language.
In order to demonstrate the capability of our system,
an experiment with 10,000 sentences is conducted.
A detailed evaluation is explained in Section 4
followed by a conclusion.
295
W. K. Chan S. (2008).
FINDING APPROXIMATE LANGUAGE PATTERNS.
In Proceedings of the First International Conference on Bio-inspired Systems and Signal Processing, pages 295-301
DOI: 10.5220/0001063802950301
Copyright
c
 SciTePress

2 RELATED WORK
Following the framework of case grammar which is
originally proposed by Fillmore in 1968, it has been
accepted that every nominal constituent in every
language bears a single syntactic–semantic case
relation (Jackendoff, 1983; Dowty, 1991). In earlier
systems, Somers describes a prototype computer
program that attempts to map surface strings of
English onto a formalism representing one level of a
deep structure (Somers, 1982). Weischedel et al.
(1993) predict the intended interpretation of an
utterance when more than one interpretation satisfies
all known syntactic and semantic constraints, and
ascertain its semantic labels. It is on the basis that
semantic features inherent in the main verb of a
sentence can be used to infer the potential semantic
labels of the sentence. Utsuro et al. (1993) describe a
method for acquiring surface semantic labels of
Japanese verbs from bilingual corpora. They make
use of translation examples in two distinct languages
that have quite different syntactic structures and
word meanings. Similarly, Kurohashi and Nagao
(1994) have developed a powerful parser for
Japanese sentences based on the case frames
encoded in a verb dictionary. The dictionary
contains some typical example sentences for each
case frame. The dictionary then tags the proper case
frame for an input sentence based on the sentence
similarities.
Any high level language understanding process,
such as semantic labeling, must involve chunking
sentences into segments. Motivated by the
psycholinguistic evidence which demonstrates that
intonation changes or pauses would affect the
language understanding processes in humans (Gee &
Grosjean, 1983), Abney (1991) proposes the concept
of text chunking as a first step in the full parsing. A
typical chunk of a text is defined as consisting of a
single content word surrounded by a constellation of
function words, matching a fixed template. Church
also uses a simple model for finding base non-
recursive NPs in sequence of POS tags (Church,
1988). Turning sentence chunking into a bracketing
problem, Church calculates the probability of
inserting both the open and close brackets between
POS tags. Each chunking alternative is ranked and
the best alternative is selected. Using
transformation-based learning with rule-template
referring to neighboring words, POS tags and chunk
tags, Ramshaw & Marcus (1995) identify essentially
the initial portions of non-recursive noun phrases up
to the head, including determiners. These chunks are
extracted from the Treebank parses, by selecting
NPs that contain no nested NPs. While the above
approaches have been proposed to recognize
common subsequences and to produce some forms
of chunked representation of an input sentence, the
recognized structures do not include any recursively
embedded NPs. As the result, the resultant fragments
bear little resemblance to the kind of phrase
structures that normally appear in our languages.
While it may be too computationally
demanding to have a full syntactic and semantic
analysis of every sentence in every text, Sima’an
(2000) presents a Tree-gram model which integrates
bilexical dependencies, and conditions its
substitutions based on the structural relations of the
trees that are involved. The Tree-gram model is a
typical example of data-oriented parsing (DOP)
advocated by Bod et al. (2003). The basic ideas of
the Tree-gram model are to (i) take a corpus of
utterances annotated with labeled trees; (ii)
decompose every corpus tree into the bag of all its
subtrees; (iii) treat the union of all these subtree bags
as a stochastic tree substitution grammar, where the
substitution probability of each subtree is estimated
as the relative frequency of this subtree among the
subtrees with the same root label. Inspired by the
Tree-gram model, in this research, we propose a
mechanism in shallow semantic labeling as well as
sentence chunking by matching any input sentence
with the trees in a Treebank through a two-phase
feature-enhanced string matching. Different from the
stochastic tree substitution grammar proposed in the
Tree-gram model, our approach, characterized by an
optimization technique, looks for a transformation
with a minimum cost, or called edit distance. While
the concept of edit distance is commonly found in
the conventional pattern matching techniques
(Gusfield, 1997; Tsay & Tsai, 1989), we take a step
further in applying the technique in shallow
semantic labeling. The detailed discussion of the
algorithm is shown as follows.
3 TWO-PHASE
FEATURE-ENHANCED STRING
MATCHING ALGORITHM
Our labeling is defined as a two-phase feature-
enhanced string matching using the edit operations.
For every input sentence, a coarse-grained syntactic
matching is conducted in our first phase of matching.
The matching relies on a set of coarse-grained but
global part-of-speech (POS) tags. The major
objective of this phase is to shortlist all the potential
trees among 65,000 parse trees in the CKIP
Treebank, which are relevant to the input sentence,
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296

without getting bogged down into computational
complexity with other linguistic details. The second
phase of the matching is followed to compute the
dissimilarity measure between the input sentence
and every short-listed candidate that is identified in
the first phase. Detailed POS and semantic class (SC)
tags will be employed. As a result, a candidate tree
which has the minimum dissimilarity with the input
sentence will be identified. The underlying semantic
labels and phrases of the candidate tree are used to
determine the shallow language patterns of the input
sentence. The details of the two-phase matching are
explained in the following.
3.1 Coarse-Grained Syntactic
Matching
In the first phase of matching, each word is
represented by its corresponding POS. Let S be an
input sentence and the T be a tree in a Treebank, s
i
and t
j
be two tokens in S and T with attribute POS
i
and POS
j
respectively. We define the cost function
for the change operation in the traditional edit
operations (Wagner & Fischer, 1974) s
i
→ t
j
to be
(
)
),(
jiji
POSPOSutsR =→
(1)
where u(POS
i
, POS
j
) defines the cost due to the
difference between the POS of the two tokens. The
POS tags from the Chinese Knowledge Information
Processing Group (CKIP) of Academia Sinica are
employed (Chen et al., 1996). The tags are
subdivided into 46 major POS classes which are
further refined into more than 150 subtypes.
However, in this coarse-grained matching, only the
major POS classes will be considered. To figure out
the cost function u(⋅,⋅) in the coarse-grained
matching, all the major POS tags are organized into
a hierarchical structure with an associated hard-
coded cost function. Figure 1 shows the structure of
notional words and describes the relative distances
between the adjectives (A), verbs (V), status-verbs
(VH), measure-words (Nf), nouns (N), position-
words (Ng), time-words (Nd) and place-words (Nc).
All notional words have definite meanings in the
language. The cost function is based on their
interchangeability, the degree of flexibility in
placement in the syntax, and the similarity of their
acceptable modifiers. For example, Chinese verbs
and adjectives share a lot of common features
syntactically, i.e. both can be predicates or modified
by adverbs and the word, not. All these features fail
to appear in nouns. The abbreviations in bracket
indicate the original POS tags marked by the CKIP.
The corresponding tree structure of the XML is
shown in Figure 2.
<Head toll="5">
<NodeB toll="2">
<NodeC toll="2">
<Adjective toll="5"/>
<Verb toll="5"/>
</NodeC>
<Status-Verb toll="7"/>
</NodeB>
<NodeD toll="2">
<Measure-Word toll="7"/>
<NodeE toll="2">
<Noun toll="5"/>
<NodeF toll="2">
<Position-word toll="3"/>
<NodeG toll="1">
<Time-word toll="2"/>
<Place-word toll="2"/>
...
</Head>
Figure 1: XML illustrating the relative distances between
8 different types of POS.
Head
B D
C
G
(A)
(V)
(Nd) (Nc)
5 5
2
2
2
1
2
2
(VH)
E
(Nf) (Ng) (N)
F
3
5
7
2
2
7
Figure 2: Corresponding tree structure of the XML shown
in Figure1.
The cost function u(⋅,⋅) reflects the difference
based on the tag toll encoded in the XML as
shown in Figure 1. The function also indicates the
degree of alignment between the syntactic structure
of the input sentence and the trees in the Treebank.
Although two feature-enhanced strings with the
same POS sequence do not imply they will share the
same syntactic structure, this coarse-grained
syntactic matching shortlists the potential trees by
imposing a necessary, even not sufficient, constraint
on its syntactic structure and limits the potential
search space in the subsequent stage of semantic
matching.
FINDING APPROXIMATE LANGUAGE PATTERNS
297

3.2 Computation of Semantic
Dissimilarity
What this second phase matching basically does is to
make a detailed comparison between the input
sentence and the short-listed trees in its earlier stage.
In this phase, each Chinese token has two attributes,
i.e. a detailed part-of-speech (POS) and semantic
class (SC). Similar to the approach in Section 3.1,
we define the cost function for the change operation
s
i
→ t
j
to be
(
)
(
)
),(),,(
jijiji
SCSCvPOSPOSuftsR =→
(2)
where the function f is the dissimilarity function
relied on two major components. The first
component u(POS
i
, POS
j
) defines the partial cost
due to the difference between the detailed POS of
the words. The detailed POS tags are organized in
XML format, similar to the approach demonstrated
in Figure 1. Figure 3 shows the further breakdown of
the nouns (Na) which is divided into in-collective
(Nae) and collective (Na1) nouns. The collective
nouns are then subdivided into in-collective concrete
uncountable nouns (Naa), in-collective concrete
countable nouns (Nab), in-collective abstract
countable nouns (Nac), in-collective abstract
uncountable nouns (Nad). The figure associated
with the arcs in the Figure 3 illustrates the cost
function.
Na
Na1 Nae
Naa
Nab
Nac
Nad
Naea Naeb
1 1 1 1
1
1
2
1
1
2
Figure 3: Tree structure of Nouns (Na) based on the CKIP
Academia Sinica.
The second term in Eqn. (2) defines another
partial cost due to the semantic differences. In our
approach, the words in the input sentences and the
trees are identified using a bilingual thesaurus
similar to the Roget’s Thesaurus. The is-a hierarchy
in the bilingual thesaurus, shown the underlying
ontology, can be viewed as a directed acyclic graph
with a single root. Figure 4 shows one of the is-a
hierarchies in the thesaurus using our Tree Editor.
While the upward links correspond to generalization,
the specialization is represented in the downward
links. The hierarchies demonstrated in the thesaurus
are based on the idea that linguists classify lexical
items in terms of similarities and differences. They
are used to structure or rank lexical items from more
general to the more special.
Figure 4: is-a hierarchy in the bilingual thesaurus.
Based on the is-a hierarchy in the thesaurus, we
define the conceptual distance d between two
notional words by their shortest path lengths. Given
two words t
1
and t
2
in an is-a hierarchy of the
thesaurus, the semantic distance d between the
tokens is defined as follows:
d(t
1
, t
2
) = minimal number of is-a
relationships in the shortest path
between t
1
and t
2
(3)
The shortest path lengths in is-a hierarchies are
calculated. Initially, a search fans out through the is-
a relationships from the original two nodes to all
nodes pointed to by the originals, until a point of
intersection is found. The paths from the original
two nodes are concatenated to form a continuous
path, which must be a shortest path between the
originals. The number of links in the shortest path is
counted. Since d(t
1
, t
2
) is positive and symmetric,
d(t
1
, t
2
) is a metric which means (i) d(t
1
, t
1
) = 0; (ii)
d(t
1
, t
2
) = d (t
2
, t
1
); (iii) d(t
1
, t
2
) + d(t
2
, t
3
) ≥ d(t
1
, t
3
).
At the same time, the semantic similarity measure
between the items is defined by:
⎩
⎨
⎧
≤
=
otherwise
),(if),(
:),(
MaxInt
dttdttd
ttv
maxjiji
ji
(4)
where d
max
is proportional to the number of lexical
items in the system and MaxInt is a maximum
integer of the system. This semantic similarity
measure defines the degree of relatedness between
the words. Obviously, strong degree of relatedness
exists between the lexical tokens under the same
nodes. On the other hand, for the cost of the insert
and delete operations, we make use the concept of
collocation that measures how likely two words are
to co-occur in a window of text. To better
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298

distinguish statistics based ratios, work in this area is
often presented in terms of the mutual information
(MI), which is defined as
)()(
),(
log),(
1
1
21
jj
jj
jj
tPtP
ttP
ttMI
×
=
−
−
−
(5)
where t
j-1
and t
j
are two adjacent words. While P(x, y)
is the probability of observing x and y together, P(x)
and P(y) are the probabilities of observing x and y
anywhere in the text, whether individually or in
conjunction. Note that tokens that have no
association with each other and co-occur together
according to chance will have a MI value close to
zero. This leads to the cost function for insertion and
deletion shown in Eqns. (6) and (7) respectively.
()
⎩
⎨
⎧
>>×
=→
−
otherwise
0if
MaxInt
zek
tR
z
j
ε
λ
(6)
where z =min {MI(t
j-1
, t
j
), MI(t
j
, t
j+1
)}
()
⎩
⎨
⎧
>>×
=→
+−
−
+−
otherwise
0),(if
11
),(
11
MaxInt
ttMIel
tR
jj
ttMI
j
jj
ε
λ
(7)
where k, l, ε are three constants relied on the size of
the active corpus.
Obviously, the insertion operation will be
penalized if the co-occurrence between the newly
inserted word and its neighbors is low. Similarly, the
deletion operation is most likely to happen if there is
a high co-occurrence between the adjacent pairs
after the deletion. Using the above cost functions for
the three types of edit operations, the tree in the
Treebank with minimum cost is being chosen to be
the best approximation of the input sentence and its
associated semantic labels will be adopted. Shallow
language patterns are then extracted based on the
recursive structures and semantic labels appeared in
the Treebank. The experimental results of the
semantic labeling are shown in the section below.
4 EXPERIMENTAL RESULTS
As mentioned in Eqn. (2), several approaches have
been used to define the dissimilarity function f by
combining the semantic differences and the detailed
POS tags in our second phase feature-enhanced
string matching. In our evaluations, five different
types of dissimilarity function f are applied. They are
(i) f
1
(u, v) = u(POS
i
, POS
j
)
(ii) f
2
(u, v) = v(SC
i
, SC
j
)
(iii) f
3
(u, v) = u(POS
i
, POS
j
) + v(SC
i
, SC
j
)
(iv) f
4
(u, v) = min (u(POS
i
, POS
j
) , v(SC
i
, SC
j
))
(v) f
5
(u, v) = max (u(POS
i
, POS
j
) , v(SC
i
, SC
j
))
Dissimilarity function f
1
(u, v) provides a detailed
version of our coarse-grained syntactic matching.
Detailed POS tags are used as the dissimilarity
measure in the labeling. Similarly, f
2
(u, v) considers
only the semantic class of the words. The other three
combine both syntactic and semantic features in
defining the dissimilarity measures. We have tested
our shallow semantic labeling with 10,000 sentences
with the Treebank. Since this research is concerning
with shallow semantic labeling, we have no
incentive to match the trees/subtrees in the Treebank
with very complicated structures. The average
sentence length is around 13.7 characters per
sentence. Table 1 summarizes the results of our
system evaluation. The third and fourth columns in
the table are number of sentences in each range of
edit distance and their average edit distances. The
edit distance is defined as a minimum cost in
transforming the input sentence with the closest
sentence pattern in the Treebank. In other words, the
smaller the distance, the higher similarity they have.
Table 1: Sentence analysis in the experiment. Edit distance
is defined as a minimum cost in transforming the input
sentence with the closest sentence pattern in the Treebank.
The smaller the distance, the higher similarity they have.
Dissimilarity
function f
Range of
Edit distance
% of
sentences
Average edit
distance
0-25 13.9 19.2
26-50 16.3 40.5
51-75 19.7 63.6
76-100 27.9 89.6
f
1
(u, v)
101-150 22.2 124.9
0-25 11.3 19.3
26-50 15.6 41.4
51-75 17.7 65.2
76-100 29.3 91.8
f
2
(u, v)
101-150 26.1 125.7
0-25 24.1 17.9
26-50 31.6 38.2
51-75 22.7 62.3
76-100 12.8 85.5
f
3
(u, v)
101-150 8.8 121.4
0-25 18.6 19.1
26-50 19.1 41.3
51-75 30.2 64.7
76-100 14.7 88.6
f
4
(u, v)
101-150 17.4 124.2
0-25 20.5 19.6
26-50 22.4 40.9
51-75 26.9 58.2
76-100 15.3 87.9
f
5
(u, v)
101-150 14.9 128.4
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299

If it is considered as a good match where the
edit distances are equal to or less than 50, then it can
be observed, in Table 1, that the dissimilarity
functions f
3
, f
5
and f
4
all produce higher percentage
of sentences with lower edit distance. This reflects
both the information from syntactic tags and
semantic classes provide useful clues in our shallow
semantic labeling. Our experiments are not
conducted with perfect information. It is worthwhile
to mention that more than 530 sentences have
incomplete information which mainly comes from
proper nouns, or out-of-vocabulary (OOV) words.
Both of them have neither defined POS nor semantic
class. All these information will be annotated with a
default value which will certainly induce errors in
our labeling. While it is inevitable to have OOV
words in any real corpus, the performance, due to
the coverage of POS and semantic classes, does not
deteriorate much in our system. The labeling is still
feasible over the sentences with OOV words. This
tolerance ability provides the graceful degradation in
our shallow semantic labeling. While other systems
are brittle and working only in all-or-none basis, the
robustness of our system is guaranteed. At the same
time, while real text tends to have grammatical
mistakes and error-prone, these problems can be
tackled with an acceptable tolerance in our system.
In our second evaluation, we have tested our
algorithm in recognizing several major semantic
labels that appear in our sentences. The semantic
labels include theme, goal, property, range,
agent, predication, location, time. As
with other text analysis, the effectiveness of the
system appears to be dictated by recall and precision
parameters where recall (R) is a percentage of how
many correct labels can be identified while precision
(P) is the percentage of labels, tackled by our system,
which are actually correct. In addition, a common
parameter F is used as a single-figure measure of
performance which combines recall (R) and
precision (P) as in follows,
RP
RP
F
+×
××+
=
2
2
)1(
β
β
(8)
We set
β = 1 to give no special preference to either
recall or precision. The recall, precision and F-score
for the semantic labels in dissimilarity function f
3
are
shown in Table 2.
As shown in the last row in Table 2, the
precision and recall of all semantic labels are
calculated by considering all the semantic labels that
appear in the sentences, rather than by averaging the
measures for individual semantic labels. It is worth
noting that the greatest differences in performance
are the recall while the precision remains relatively
steady in most semantic labels.
Table 2: Evaluation of different semantic labels in the
dissimilarity function f
3
. Brackets show the results
obtained in the derivation subtrees.
Elementary Subtree (Derivation
b)
Semantic Label Recall Precision F-score
theme 0.79 (0.88) 0.82 (0.85)
0.805
()
goal 0.80 (0.78) 0.79 (0.76)
0.795
()
property 0.89 (0.78) 0.91 (0.83)
0.900
()
range 0.94 (0.93) 0.92 (0.91)
0.930
()
agent 0.92 (0.92) 0.87 (0.85)
0.894
()
predication 0.76 (0.80) 0.81 (0.78)
0.784
()
location 0.92 (0.92) 0.91 (0.89)
0.915
()
Time 0.93 (0.93) 0.95 (0.94)
0.940
()
experiencer 0.87 (0.89) 0.86 (0.88)
0.865
()
manner 0.79 (0.85) 0.84 (0.83)
0.814
()
possessor 0.91 (0.93) 0.88 (0.89)
0.895
()
condition 0.80 (0.84) 0.82 (0.81)
0.810
()
all labels 0.88 (0.84) 0.89 (0.88)
0.885
()
One possible explanation is that the low recall rates
in some labels are due to less complete coverage of
linguistic phenomena. In addition, we define an
elementary subtree that spans only on a sequence of
words, as well as a derivation subtree that contains
at least one branch of elementary subtree. It may be
expected the F-score of the derivation subtrees will
be much worse than its counterpart, however, Table
2 shows surprisingly the differences in the overall
accuracy in two main types of subtrees are not
significant. An explanation is that we have
approached chunking as well as assigning the most
salient semantic label to the chunks based on the
POS and semantic tags. Even though there may be
some misclassification in the terminal nodes, this
will not hinder the system to tag the semantic labels
in the longer chunks. In other words, the longer
chunks are less error prone in our semantic labeling.
This shallow semantic labeling technique produces
an output that abstract away the details but retains
the core semantic structure of the actual sentence.
Pure linguistic theories may well have solutions to
the semantic labeling that tends to be highly theory-
specific with less emphasis on real text. Our shallow
approach does not focus on how well it explains
various structural and interpretive phenomena in
linguistics perceptive, but on how well it predicts the
semantic label of sentences. It aims at theory-neutral
annotation and derives linguistically-plausible
semantic labels or short phrase structures using a
Treebank. We have suggested that semantic labels
can be detected by grouping sequences of words that
occur together more often with high mutual
information. While the approach has been
BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing
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implemented successfully in the Chinese language
as illustrated in our evaluation, the idea delineated
certainly does not limit or tailor-made for any
particular language. Only a minor modification is
needed to apply the technique to other languages.
5 CONCLUSIONS
In this paper, we have illustrated a shallow technique
in which semantic labels are extracted in forms of
chunks of phrases or words using a two-phase
feature-enhanced string matching algorithm. While
the first phase is to shortlist the potential trees in the
Treebank, chunks are further tagged with semantic
labels in the second phase. Based on the linguist’s
conception of phrase structure, our approach does
not require a full syntactic parse to pursue semantic
analysis and the recursively embedded phrases can
also be identified without pain. This shallow
technique is inspired by the research in the area of
bio-molecular sequences analysis which advocates
high sequence similarity usually implies significant
function or structural similarity. It is characteristic
of biological systems that objects have a certain
form that has arisen by evolution from related
objects of similar but not identical form. This
sequence-to-structure mapping is a tractable, though
partly heuristic, way to search for functional or
structural universality in biological systems. With
the support from the results as shown, we conjecture
this sequence-to-structure phenomenon appears in
our sentences. The sentence sequence encodes and
reflects the more complex linguistic structures and
mechanisms described by linguists. While our
system does not claim to deal with all aspects of
language, we suggest an alternate, but plausible, way
to handle the real corpus.
ACKNOWLEDGEMENTS
The work described in this paper was partially
supported by the grants from the Research Grants
Council of the Hong Kong Special Administrative
Region, China (Project Nos. CUHK4438/04H and
CUHK4706/05H).
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