An Efficient Representation of Partitions of Integers

Composition of weighted finite transducers in MapReduce

Journal Of Big Data ◽

10.1186/s40537-020-00397-4 ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Bilal Elghadyry ◽

Faissal Ouardi ◽

Sébastien Verel

Keyword(s):

Speech Processing ◽

Large Scale ◽

Large Scale Data ◽

Finite State Transducers ◽

Wide Range ◽

Finite State ◽

Common Operation ◽

Efficient Representation ◽

Weighted Finite State Transducers ◽

Np Hardness

AbstractWeighted finite-state transducers have been shown to be a general and efficient representation in many applications such as text and speech processing, computational biology, and machine learning. The composition of weighted finite-state transducers constitutes a fundamental and common operation between these applications. The NP-hardness of the composition computation problem presents a challenge that leads us to devise efficient algorithms on a large scale when considering more than two transducers. This paper describes a parallel computation of weighted finite transducers composition in MapReduce framework. To the best of our knowledge, this paper is the first to tackle this task using MapReduce methods. First, we analyze the communication cost of this problem using Afrati et al. model. Then, we propose three MapReduce methods based respectively on input alphabet mapping, state mapping, and hybrid mapping. Finally, intensive experiments on a wide range of weighted finite-state transducers are conducted to compare the proposed methods and show their efficiency for large-scale data.

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An Invitation to Combinatorics

10.1017/9781108568708 ◽

2021 ◽

Author(s):

Shahriar Shahriari

Keyword(s):

Stirling Numbers ◽

Exclusion Principle ◽

Open Problems ◽

Warm Up ◽

Calculus Sequence ◽

Award Winning ◽

Self Study ◽

Conversational Style ◽

The Subject ◽

Partitions Of Integers

Active student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author – an award-winning teacher – writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.

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Interface Reduction in Craig-Bampton Component Mode Synthesis by Orthogonal Polynomial Series

Volume 7B: Structures and Dynamics ◽

10.1115/gt2017-64583 ◽

2017 ◽

Author(s):

Luigi Carassale ◽

Mirko Maurici

Keyword(s):

Degrees Of Freedom ◽

Axial Compressor ◽

Component Mode Synthesis ◽

Reduction Techniques ◽

Interface Reduction ◽

Reduction Methods ◽

Interface Displacement ◽

Polynomial Series ◽

Efficient Representation

The component mode synthesis based on the Craig-Bampton method has two strong limitations that appear when the number of the interface degrees of freedom is large. First, the reduced-order model obtained is overweighed by many unnecessary degrees of freedom. Second, the reduction step may become extremely time consuming. Several interface reduction techniques addressed successfully the former problem, while the latter remains open. In this paper we tackle this latter problem through a simple interface-reduction technique based on an a-priory choice of the interface modes. An efficient representation of the interface displacement field is achieved adopting a set of orthogonal basis functions determined by the interface geometry. The proposed method is compared with other existing interface reduction methods on a case study regarding a rotor blade of an axial compressor.

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