Proof. Assume that T is not 3-colorable and thus it can be colored in four colors. Our proof is an extension of the proof of Lemma 1. We use the same approach to color vertices of a triangulation T of a convex polyomino as in the proof of Lemma 1 until we are forced to use color 4. We will show that either T contains a graph from S as an induced subgraph, or the vertices colored so far can be recolored to avoid color 4; in the later case our arguments can be repeated until eventually it will be shown that T contains a graph from S (otherwise a contradiction would be obtained with T being non-3-colorable). Once again, there are three possible situations that are shown in Figure 12, where the areas of the convex polyomino labeled by A, B and C can possibly contain no other vertices than those shown in the figure colored by 1, 2 and 3. We assume that vertices on the boundary of two areas belong to both areas; in particular, the vertex colored by 2 in the leftmost picture in Figure 12 belongs to all three areas. Finally, we call a vertex in an area internal, if it belongs only to a single area.
The base for our inductive proof is the three graphs, M , N and P in Figure 4.14, which are the only non-isomorphic triangulations of the GC- CG on nine vertices containing no graph in Figure 4.11 as an induced sub- graph. Each of these graphs can be semi-transitively oriented as shown in Figure 4.15. Note that we provide two semi-transitive orientations for the graphs N and P , which is essential in our inductive argument. Also, note that each triangulation of a GCCG with three sectors on less than nine ver- tices can be oriented semi-transitively (just remove the external layer in the graphs in Figure 4.15).
Recently, Akrobotu at el.  proved that a triangulation of the graph G associated with a convex polyomino is word-representable if and only if G is 3-colorable. Inspired by this elegant result, in the paper in hands, we characterized word-representable face subdivisions of triangular grid graphs. The paper is organized as follows. In Section 2 some necessary defini- tions, notation and known results are given. In Section 3 we state and prove our main result (Theorem 3.1) saying that a face subdivision of a triangular grid graph is word-representable if and only if it has no interior cell subdi- vided. Theorem 3.1 is proved using the notion of a smart (semi-transitive) orientation introduced in this paper. Finally, in Section 4 we apply our main result to face subdivisions of triangular grid graphs having equilateral triangle shape and face subdivisions of the Sierpi´ nski gasket graph.
in the leftmost column, because otherwise instead of colour 1 we could use colour 3, and there would be no need to use colour 4 for colouring v. Further, note that in the case when the vertex v is involved in a subgraph presented schematically to the left in Figure 5 (the question marks there indicate that triangulations of respective squares are unknown to us), such a subgraph must be either T 1 or T 2 . Indeed, otherwise, the subgraph must
Manual word sense assignment is difficult for human annotators (Krishnamurthy and Nicholls, 2000). Reported inter-annotator agreement (ITA) for fine-grained word sense assignment tasks has ranged between 69% (Kilgarriff and Rosenzweig, 2000) for a lexical sample using the HECTOR dic- tionary and 78.6.% using WordNet (Landes et al., 1998) in all-words annotation. The use of more coarse-grained senses alleviates the problem: In OntoNotes (Hovy et al., 2006), an ITA of 90% is used as the criterion for the construction of coarse- grained sense distinctions. However, intriguingly, for some high-frequency lemmas such as leave this ITA threshold is not reached even after mul- tiple re-partitionings of the semantic space (Chen and Palmer, 2009). Similarly, the performance of WSD systems clearly indicates that WSD is not easy unless one adopts a coarse-grained approach, and then systems tagging all words at best perform a few percentage points above the most frequent sense heuristic (Navigli et al., 2007). Good perfor- mance on coarse-grained sense distinctions may be more useful in applications than poor perfor- mance on fine-grained distinctions (Ide and Wilks, 2006) but we do not know this yet and there is some evidence to the contrary (Stokoe, 2005).
You might think that excoriate is a combination of ex, cor, and ate, but it isn’t so. The cor in excoriate actually has a very different derivation and only happens to have the same spelling as the cor that we have studied. Look up the etymology of excoriate in a good dictionary and explain why this word is sued to describe extremely abusive denunciation or verbal whipping.
ssssss Older adults tend to suffer a decline in some of their cognitive capabilities, being language one of least affected processes. Word association norms (WAN) also known as free word asso- ciations reflect word-word relations, the participant reads or hears a word and is asked to write or say the first word that comes to mind. Free word associations show how the organization of semantic memory remains almost unchanged with age. We have performed a WAN task with very small samples of older adults with Alzheimer’s disease (AD), vascular dementia (VaD) and mixed dementia (MxD), and also with a control group of typical aging adults, matched by age, sex and education. All of them are native speakers of Mexican Spanish. The results show, as expected, that Alzheimer disease has a very important impact in lexical retrieval, unlike vascular and mixed dementia. This suggests that linguistic tests elaborated from WAN can be also used for detecting AD at early stages.
tions between lexical items collected from dif- ferent sources. Declarative clues can be taken from linguistic resources such as bilingual dic- tionaries. They may also include pre-defined relations between lexical items based on cer- tain features such as parts of speech. Estimated clues are derived from the parallel data using, for example, measures of co-occurrence (e.g. the Dice coefficient (Smadja et al., 1996)), statisti- cal alignment models (e.g. IBM models from statistical machine translation (Brown et al., 1993)), or string similarity measures (e.g. the longest common sub-sequence ratio (Melamed, 1995)). They can also be learned from pre- viously aligned training data using linguistic and contextual features associated with aligned items. Relations between certain word classes with respect to the translational association of words belonging to these classes is one example of such clues that can be learned from aligned training data. In our experiments, for example, we will use clues that indicate relations between lexical items based on their part-of-speech tags and their positions in the sentence relative to each other. They are learned from automati- cally word-aligned training data.
n of density func- asic assertion con- mmetrized product of strongly orthogonal geminal theory if the expansion of geminals is limited to two- dimensional subspaces. This result is remarkable in the sense that for the first time it is shown that top-down and bottom-up methods for generating density functionals are equivalent. The top-down method is represented by the reduction of an N-particle functional generated from an ansatz wave function such as the antisymmetrized pro- duct of strongly orthogonal geminals. In the bottom-up method a functional is generated by progressive inclusion of N-representability conditions. This example shows that perhaps the unity of quantum theory on many-par- ticle systems can be attained by careful handling of top- down and bottom-up methods.
In order to test the existence of effective hopping pa- rameters and thereby decide the question of noninteract- ing v representability, we set up a trial Hamiltonian ma- trix and use iterative nonlinear optimization techniques to vary the effective on-site energies and nearest-neighbor hopping parameters so as to reproduce as closely as pos- sible the density coefficients of the interacting electron system. Occupation numbers and nearest-neighbor over- lap coefficients are taken into account. Both the potential and the density are thus characterized by two parameters per site. Considering the complete Hamiltonian (21), we can obtain an initial guess by setting U = 0. Table I indicates that the corresponding densities are relatively close and we can therefore safely assume this to be a good starting point. The eigenstates of the one-particle Hamiltonian ˆ H s are calculated by exact diagonalization.
We present finite element methods (FEMs) for elliptic and elasticity problems with interfaces. The FEMs are based on body-fitted meshes with a locally modified triangula- tion. A FEM based on a body-fitted mesh uses a triangulation that is aligned with the interfaces. However, for complicated interfaces it can be difficult and expensive to generate such triangulations. That is why we use a locally modified triangulation based on Cartesian meshes. We first form a Cartesian mesh, then move the grid points near the interfaces to the interfaces. This leads to a locally modified triangulation. We use the standard FEM with the locally modified triangulation to solve the elliptic and elasticity problems with interfaces. By FEM theory, the method is second order accurate in the infinity norm for piecewise smooth solutions. We present some numerical examples to show the second order accuracy of the method.
This paper presents a new word align- ment method which incorporates knowl- edge about Bilingual Multi-Word Expres- sions (BMWEs). Our method of word alignment first extracts such BMWEs in a bidirectional way for a given corpus and then starts conventional word alignment, considering the properties of BMWEs in their grouping as well as their alignment links. We give partial annotation of align- ment links as prior knowledge to the word alignment process; by replacing the max- imum likelihood estimate in the M-step of the IBM Models with the Maximum A Posteriori (MAP) estimate, prior knowl- edge about BMWEs is embedded in the prior in this MAP estimate. In our exper- iments, we saw an improvement of 0.77 Bleu points absolute in JP–EN. Except for one case, our method gave better re- sults than the method using only BMWEs grouping. Even though this paper does not directly address the issues in Cross- Lingual Information Retrieval (CLIR), it discusses an approach of direct relevance to the field. This approach could be viewed as the opposite of current trends in CLIR on semantic space that incorpo- rate a notion of order in the bag-of-words model (e.g. co-occurences).
The results in Table 3 suggest that our modeling approach produces better word alignments. We found that our models not only learned smoother translation models for low frequency words but also ranked the conditional probabilities more ac- curately with respect to the correct translations. To illustrate this, we categorized the alignment links from the Chinese-English low-resource ex- periment into bins with respect to the English source word frequency and individually evaluated them. As shown in Figure 3, the gain for low fre- quency words is particularly large.
The initial word alignments are obtained using the baseline configuration described above. From these, we build two bilingual 1-to-n dictionaries (one for each direction), and the training corpus is updated by repacking the words in the dictionaries, using the method presented in Section 2. As previously men- tioned, this process can be repeated several times; at each step, we can also choose to exploit only one of the two available dictionaries, if so desired. We then extract aligned phrases using the same procedure as for the baseline system; the only difference is the ba- sic unit we are considering. Once the phrases are ex- tracted, we perform the estimation of the features of the log-linear model and unpack the grouped words to recover the initial words. Finally, minimum-error- rate training and decoding are performed.
In addition to merely measuring semantic relat- edness, LSA has been shown to emulate the learn- ing of word meanings from natural language (as can be evidenced by a broad range of applications from synonym tests to automated essay grading), at rates that resemble those of human learners (Laundauer et al, 1997). Landauer and Dumais (1997) have demonstrated empirically that LSA can emulate not only the rate of human language acquisition, but also more subtle phenomena, such as the effects of learning certain words on mean- ing of other words. LSA can model meaning with
proficiency learners. Teachers need to help L2 beginners to acquire at least 3000 word families (Coady, 1997) as the 2 000- and 3 000- word levels contain the high- frequency words that all learners need to know in order to function effectively in English. Since this study includes various aspects of word knowledge, it might help teachers to choose suitable activities based on the aspect of word knowledge they want to focus on.