We prove the Minimum Vertex Cover problem to be NP-hard to approximate to within a factor of 1.3606, extending on previous PCP and hardness of approximation technique. To that end, one needs to develop a new proof framework, and to borrow and extend ideas from several ﬁelds. 1. Introduction The basic purpose of computational complexity theory is to classify computational problems according to the amount of resources required to solve them. In particular, the most basic task is to classify computational problems to those that are eﬃciently solvable and those that are not. ...
We prove that the classical Oka property of a complex manifold Y, concerning the existence and homotopy classiﬁcation of holomorphic mappings from Stein manifolds to Y, is equivalent to a Runge approximation property for holomorphic maps from compact convex sets in Euclidean spaces to Y . Introduction Motivated by the seminal works of Oka  and Grauert (, , ) we say that a complex manifold Y enjoys the Oka property if for every Stein manifold X, every compact O(X)-convex subset K of X and every continuous map f0 : X → Y which is holomorphic in an...
Sums of two squares near perfect squares
by R. C. Vaughan∗∗∗ In memory of Pritish Limani (1983–2003) Abstract Let C be a nondegenerate planar curve and for a real, positive decreasing function ψ let C(ψ) denote the set of simultaneously ψ-approximable points lying on C. We show that C is of Khintchine type for divergence; i.e. if a certain sum diverges then the one-dimensional Lebesgue measure on C of C(ψ) is full. We also obtain the Hausdorﬀ measure analogue of the divergent Khintchine type result. ...
This paper proposes a new method for approximate string search, speciﬁcally candidate generation in spelling error correction, which is a task as follows. Given a misspelled word, the system ﬁnds words in a dictionary, which are most “similar” to the misspelled word. The paper proposes a probabilistic approach to the task, which is both accurate and efﬁcient. The approach includes the use of a log linear model, a method for training the model, and an algorithm for ﬁnding the top k candidates. ...
Although adequate models of human language for syntactic analysis and semantic interpretation are of at least contextfree complexity, for applications such as speech processing in which speed is important finite-state models are often preferred. These requirements may be reconciled by using the more complex grammar to automatically derive a finite-state approximation which can then be used as a filter to guide speech recognition or to reject many hypotheses at an early stage of processing.
This paper describes the conversion of a Hidden Markov Model into a sequential transducer that closely approximates the behavior of the stochastic model. This transformation is especially advantageous for part-of-speech tagging because the resulting transducer can be composed with other transducers that encode correction rules for the most frequent tagging errors. The speed of tagging is also improved. The described methods have been implemented and successfully tested on six languages.
We present a novel PCFG-based architecture for robust probabilistic generation based on wide-coverage LFG approximations (Cahill et al., 2004) automatically extracted from treebanks, maximising the probability of a tree given an f-structure. We evaluate our approach using stringbased evaluation. We currently achieve coverage of 95.26%, a BLEU score of 0.7227 and string accuracy of 0.7476 on the Penn-II WSJ Section 23 sentences of length ≤20. grammar for generation.
This paper shows how ﬁnite approximations of long distance dependency (LDD) resolution can be obtained automatically for wide-coverage, robust, probabilistic Lexical-Functional Grammar (LFG) resources acquired from treebanks. We extract LFG subcategorisation frames and paths linking LDD reentrancies from f-structures generated automatically for the Penn-II treebank trees and use them in an LDD resolution algorithm to parse new text.
This paper describes how to construct a finite-state machine (FSM) approximating a 'unification-based' grammar using a left-corner grammar transform. The approximation is presented as a series of grammar transforms, and is exact for left-linear and rightlinear CFGs, and for trees up to a user-specified depth of center-embedding.
In this paper we extend the maximum spanning tree (MST) dependency parsing framework of McDonald et al. (2005c) to incorporate higher-order feature representations and allow dependency structures with multiple parents per word. We show that those extensions can make the MST framework computationally intractable, but that the intractability can be circumvented with new approximate parsing algorithms. We conclude with experiments showing that discriminative online learning using those approximate algorithms achieves the best reported parsing accuracy for Czech and Danish. ...
This book presents a mathematical development of a recent approach to
the modeling and simulation of turbulent flows based on methods for
the approximate solution of inverse problems. The resulting Approximate
Deconvolution Models or ADMs have some advantages (as well as some
disadvantages) over more commonly used turbulence models:
ADMs are supported by a mathematically rigorous theoretical foundation.
ADMs are a family of models of increasing accuracy O(δ2N+2), where δ is
the averaging (or filter) radius...
We present a novel framework for automated extraction and approximation of numerical object attributes such as height and weight from the Web. Given an object-attribute pair, we discover and analyze attribute information for a set of comparable objects in order to infer the desired value. This allows us to approximate the desired numerical values even when no exact values can be found in the text.
We present a linguistically-motivated algorithm for reconstructing nonlocal dependency in broad-coverage context-free parse trees derived from treebanks. We use an algorithm based on loglinear classiﬁers to augment and reshape context-free trees so as to reintroduce underlying nonlocal dependencies lost in the context-free approximation. We ﬁnd that our algorithm compares favorably with prior work on English using an existing evaluation metric, and also introduce and argue for a new dependency-based evaluation metric. ...
Phrase-structure grammars are an effective representation for important syntactic and semantic aspects of natural languages, but are computationally too demanding for use as language models in real-time speech recognition. An algorithm is described that computes finite-state approximations for context-free grammars and equivalent augmented phrase-structure grammar formalisms. The approximation is exact for certain contextfree grammars generating regular languages, including all left-linear and right-linear context-free grammars. ...
We introduce cube summing, a technique that permits dynamic programming algorithms for summing over structures (like the forward and inside algorithms) to be extended with non-local features that violate the classical structural independence assumptions. It is inspired by cube pruning (Chiang, 2007; Huang and Chiang, 2007) in its computation of non-local features dynamically using scored k-best lists, but also maintains additional residual quantities used in calculating approximate marginals. ...
This chapter examines methods of deriving approximate solutions to problems or of approximating exact solutions, which allow us to develop concise and precise estimates of quantities of interest when analyzing algorithms.
Top 200 Words in the GRE and other words which are related or similar in meaning to them are grouped together so that you can learn it easier. The words are given along with it's meaning, a sentence in which it is used and also the words similar in meaning are given. A total of approximately 1500 words will be covered in just this one article. You must learn this if you want to do well...
ABATE: to reduce in amount, degree, or severity
As the hurricane's force ABATED, the winds dropped and the sea became calm.
Words with similar meanings:
EBB LAPSE LET...
Many problems of practical significance are NPcomplete
but are too important to abandon merely
because obtaining an optimal solution is intractable
(khó). If a problem is NP-complete, we are unlikely to find
a polynomial time algorithm for solving it exactly, but
it may still be possible to find near-optimal solution
in polynomial time.
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Optimality Conditions for Approximate Solutions in Multiobjective Optimization Problems