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Compacta not embeddable into Cartesian products of curves

100%

Dydak J. , Koyama A.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

tom Vol. 48, no 1

51--56

We prove that an n-dimensional compactum X cannot be embedded into the Cartesian product of n curves if there is a group G such that [H^1] (X;G) = 0 and [H^n](X;G) [is not equal to] O.

Clustering for clarity: improvingword sense disambiguation throughmultilevel analysis

100%

Dubey S. K. , Kohli N.

Computer Science

2024

tom T. 25 (2)

277--300

Existing Word Sense Disambiguation (WSD) techniques have limits in exploring word-context relationships since they only deal with the effective use ofword embedding, lexical-based information via WordNet, or the precision ofclustering algorithms. In order to overcome this limitation, the study suggestsa unique hybrid methodology that makes use of context embedding based on center-embedding in order to capture semantic subtleties and utilizing with atwo-level K-means clustering algorithm. Such generated context embedding,producing centroids that serve as representative points for semantic information inside clusters. Additionally, go with such captured cluster- centres in thenested levels of clustering process, locate groups of linked context words andcategorize them according to their word meanings that effectively manage polysemy/homonymy as well as detect minute differences in meaning. Our proposedapproach offers a substantial improvement over traditional WSD methods byharnessing the power of center-embedding in context representation, enhancingthe precision of clustering and ultimately overcoming existing limitations incontext-based sense disambiguation.

Light classes of generalized stars in polyhedral maps on surfaces

100%

Jendrol' S. , Voss H.-J.

Discussiones Mathematicae Graph Theory

2004

tom 24

nr 1

85-107

A generalized s-star, s ≥ 1, is a tree with a root Z of degree s; all other vertices have degree ≤ 2. $S_i$ denotes a generalized 3-star, all three maximal paths starting in Z have exactly i+1 vertices (including Z). Let 𝕄 be a surface of Euler characteristic χ(𝕄) ≤ 0, and m(𝕄):= ⎣(5 + √{49-24χ(𝕄 )})/2⎦. We prove: (1) Let k ≥ 1, d ≥ m(𝕄) be integers. Each polyhedral map G on 𝕄 with a k-path (on k vertices) contains a k-path of maximum degree ≤ d in G or a generalized s-star T, s ≤ m(𝕄), on d + 2- m(𝕄) vertices with root Z, where Z has degree ≤ k·m(𝕄) and the maximum degree of T∖{Z} is ≤ d in G. Similar results are obtained for the plane and for large polyhedral maps on 𝕄.. (2) Let k and i be integers with k ≥ 3, 1 ≤ i ≤ [k/2]. If a polyhedral map G on 𝕄 with a large enough number of vertices contains a k-path then G contains a k-path or a 3-star $S_i$ of maximum degree ≤ 4(k+i) in G. This bound is tight. Similar results hold for plane graphs.

A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization

100%

Feßler R.

Annales Polonici Mathematici

1995

tom 62

nr 1

45-74

The following problem of Markus and Yamabe is answered affirmatively: Let f be a local diffeomorphism of the euclidean plane whose jacobian matrix has negative trace everywhere. If f(0) = 0, is it true that 0 is a global attractor of the ODE dx/dt = f(x)? An old result of Olech states that this is equivalent to the question if such an f is injective. Here the problem is treated in the latter form by means of an investigation of the behaviour of f near infinity.

Wybrane własności osadzeń weryfikowanych przez nie struktur w Teorii Reprezentacji Dyskursu

84%

Hajnicz E.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

2004

tom Nr 980

1-84

Niniejszy raport stanowi omówienie Teorii Reprezentacji Dyskursu (w skrócie DRT) w postaci przedstawionej przez Kampa i Reylego (1993). Prezentowana jest zarówno podstawowa wersja teorii, jak i dwa jej rozszerzenia: jedno dotyczące reprezentacji liczby mnogiej (znaczniki zbiorowe) i rozszerzonych kwantyfikatorów (DRT_Pl), drugie kwestii związanych z czasem i aspektem (DRT_T). Przedstawiona jest także translacja wersji podstawowej na rachunek predykatów I rzędu. Raport skupia się na analizie własności DRT względem oryginalnej semantyki Kampa i Reylego opartej na pojęciu osadzeń wraz z pokazaniem, które z tych własności przenoszą się na zmodyfikowane wersje teorii DRT_Pl i DRT_T. Wykazujemy także, że wiele tautologii rachunku zdań zachowuje swą ważność po przeformułowaniu ich na język DRT. Na koniec dokonano krótkiego porównania omawianej semantyki z późniejszą semantyką (statyczną) opisaną przez van Eijcka i Kampa (1997).

The present report contains a discussion of Discourse Representation Theory (DRT) as formulated in Kamp and Reyle (1993). Apart form the basie version of the theory, the report deser ibes its two extensions: the first concerning representation of plurals and generalized quan-tifiers (DRTpi), the second concerning tense and aspect (DRTy). A translation of the basie version into the first order predicate calculus is described, too. The main focus of the report is an analysis of the properties of DRT with regard to the original Kamp and Reyle's semantics based on the notion of embeddings. Next, the report shows which of these properties carry over to the two modified versions of the theory, i.e.,DRTp; and DRTx- We show also that many of the tautologies of the propositional calculus arę valid after their transposition to the DRT language. Finally, a short comparison of the DRT semantics considered here with the later (static) semantics discussed by van Eijck and Kamp (1997).