USEFULNESS OF DIRECTED ACYCLIC SUBWORD GRAPHS IN PROBLEMS RELATED TO STANDARD STURMIAN WORDS

2009 ◽  
Vol 20 (06) ◽  
pp. 1005-1023 ◽  
Author(s):  
PAWEŁ BATURO ◽  
MARCIN PIATKOWSKI ◽  
WOJCIECH RYTTER
Keyword(s):  
Linear Time ◽  
Regular Structure ◽  
Special Structure ◽  
Graph Properties ◽  
Alternative Graph ◽  
Simple Alternative ◽  
Sturmian Words ◽  
Special Factors ◽  
Exponential Size ◽  
Standard Word

The class of finite Sturmian words consists of words having particularly simple compressed representation, which is a generalization of the Fibonacci recurrence for Fibonacci words. The subword graphs of these words (especially their compacted versions) have a very special regular structure. In this paper we investigate this structure in more detail than in previous papers and show how several syntactical properties of Sturmian words follow from their graph properties. Consequently simple alternative graph-based proofs of several known facts are presented. The very special structure of subword graphs leads also to special easy algorithms computing some parameters of Sturmian words: the number of subwords, the critical factorization point, lexicographically maximal suffixes, occurrences of subwords of a fixed length, and right special factors. These algorithms work in linear time with respect to n, the size of the compressed representation of the standard word, though the words themselves can be of exponential size with respect to n. Some of the computed parameters can be also of exponential size, however we provide their linear size compressed representations. We introduce also a new concept related to standard words: Ostrowski automata.

scholarly journals The Maximal Number of Runs in Standard Sturmian Words

10.37236/2473 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Paweł Baturo ◽  
Marcin Piątkowski ◽  
Wojciech Rytter
Keyword(s):  
Explicit Formula ◽  
Special Class ◽  
Linear Time ◽  
Infinite Sequence ◽  
Integer Sequence ◽  
Sturmian Word ◽  
Compact Representations ◽  
Sturmian Words ◽  
Standard Word

We investigate some repetition problems for a very special class $\mathcal{S}$ of strings called the standard Sturmian words, which  have very compact representations in terms of sequences of integers. Usually the size of this word is exponential with respect to the size of its integer sequence, hence we are dealing with repetition problems in compressed strings. An explicit formula is given for the number $\rho(w)$ of runs in a standard word $w$. We show that $\rho(w)/|w|\le 4/5$ for each $w\in S$, and  there is an infinite sequence of strictly growing words $w_k\in {\mathcal{S}}$ such that $\lim_{k\rightarrow \infty} \frac{\rho(w_k)}{|w_k|} = \frac{4}{5}$. Moreover, we show how to compute the number of runs in a standard Sturmian word in linear time with respect to the size of its compressed representation.

scholarly journals Greedy Transition-Based Dependency Parsing with Stack LSTMs

2017 ◽  
Vol 43 (2) ◽  
pp. 311-347 ◽  
Author(s):  
Miguel Ballesteros ◽  
Chris Dyer ◽  
Yoav Goldberg ◽  
Noah A. Smith
Keyword(s):  
Neural Networks ◽  
Short Term Memory ◽  
Linear Time ◽  
Training Data ◽  
Test Time ◽  
Continuous Space ◽  
Look Ahead ◽  
History Of ◽  
Morphologically Rich Languages ◽  
Standard Word

We introduce a greedy transition-based parser that learns to represent parser states using recurrent neural networks. Our primary innovation that enables us to do this efficiently is a new control structure for sequential neural networks—the stack long short-term memory unit (LSTM). Like the conventional stack data structures used in transition-based parsers, elements can be pushed to or popped from the top of the stack in constant time, but, in addition, an LSTM maintains a continuous space embedding of the stack contents. Our model captures three facets of the parser's state: (i) unbounded look-ahead into the buffer of incoming words, (ii) the complete history of transition actions taken by the parser, and (iii) the complete contents of the stack of partially built tree fragments, including their internal structures. In addition, we compare two different word representations: (i) standard word vectors based on look-up tables and (ii) character-based models of words. Although standard word embedding models work well in all languages, the character-based models improve the handling of out-of-vocabulary words, particularly in morphologically rich languages. Finally, we discuss the use of dynamic oracles in training the parser. During training, dynamic oracles alternate between sampling parser states from the training data and from the model as it is being learned, making the model more robust to the kinds of errors that will be made at test time. Training our model with dynamic oracles yields a linear-time greedy parser with very competitive performance.

scholarly journals Graph properties checkable in linear time in the number of vertices

2004 ◽  
Vol 68 (3) ◽  
pp. 546-597 ◽  
Author(s):  
Etienne Grandjean ◽  
Frédéric Olive
Keyword(s):  
Linear Time ◽  
Graph Properties

Special factors, periodicity, and an application to Sturmian words

2000 ◽  
Vol 36 (12) ◽  
pp. 983-1006 ◽  
Author(s):  
Arturo Carpi ◽  
Aldo de Luca
Keyword(s):  
Sturmian Words ◽  
Special Factors

scholarly journals Consensus of Noisy Multiagent Systems with Markovian Switching Topologies and Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Multiagent Systems ◽  
Linear Time ◽  
Design Method ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Graph Properties ◽  
Linear Time Invariant Systems ◽  
Necessary And Sufficient ◽  
Time Invariant

Stochastic multiagent systems have attracted much attention during the past few decades. This paper concerns the continuous-time consensus of a network of agents under directed switching communication topologies governed by a time-homogeneous Markovian process. The agent dynamics are described by linear time-invariant systems, with random noises as well as time-varying delays. Two types of network-induced delays are considered, namely, delays affecting only the output of the agents’ neighbors and delays affecting both the agents’ own output and the output of their neighbors. We present necessary and sufficient consensus conditions for these two classes of multiagent systems, respectively. The design method of consensus gains allows for decoupling the design problem from the graph properties. Numerical simulations are implemented to test the effectiveness of our obtained results as well as the tightness of necessary/sufficient conditions.

Interrelationship of the cellular distribution and secretion of regular structure (RS) protein in Bacillus licheniformis nm 105

1992 ◽  
Vol 50 (1) ◽  
pp. 712-713
Author(s):  
Xiaorong Zhu ◽  
Richard McVeigh ◽  
Bijan K. Ghosh
Keyword(s):  
Alkaline Phosphatase ◽  
Bacillus Licheniformis ◽  
Self Assembly ◽  
Gel Electrophoresis ◽  
Culture Supernatant ◽  
Regular Structure ◽  
The Self ◽  
Cellular Distribution ◽  
Structural Protein ◽  
Laboratory Cultures

A mutant of Bacillus licheniformis 749/C, NM 105 exhibits some notable properties, e.g., arrest of alkaline phosphatase secretion and overexpression and hypersecretion of RS protein. Although RS is known to be widely distributed in many microbes, it is rarely found, with a few exceptions, in laboratory cultures of microorganisms. RS protein is a structural protein and has the unusual properties to form aggregate. This characteristic may have been responsible for the self assembly of RS into regular tetragonal structures. Another uncommon characteristic of RS is that enhanced synthesis and secretion which occurs when the cells cease to grow. Assembled RS protein with a tetragonal structure is not seen inside cells at any stage of cell growth including cells in the stationary phase of growth. Gel electrophoresis of the culture supernatant shows a very large amount of RS protein in the stationary culture of the B. licheniformis. It seems, Therefore, that the RS protein is cotranslationally secreted and self assembled on the envelope surface.

A Real Time Control Architecture for Continuously Managing Patients in a Care Unit

1995 ◽  
Vol 34 (05) ◽  
pp. 475-488
Author(s):  
B. Seroussi ◽  
J. F. Boisvieux ◽  
V. Morice
Keyword(s):  
Real Time ◽  
Linear Time ◽  
Treatment Plan ◽  
Control Architecture ◽  
Real Time Control ◽  
Time Representation ◽  
Time Control ◽  
Continuous Support ◽  
Definition Of ◽  
Computerized System

Abstract:The monitoring and treatment of patients in a care unit is a complex task in which even the most experienced clinicians can make errors. A hemato-oncology department in which patients undergo chemotherapy asked for a computerized system able to provide intelligent and continuous support in this task. One issue in building such a system is the definition of a control architecture able to manage, in real time, a treatment plan containing prescriptions and protocols in which temporal constraints are expressed in various ways, that is, which supervises the treatment, including controlling the timely execution of prescriptions and suggesting modifications to the plan according to the patient’s evolving condition. The system to solve these issues, called SEPIA, has to manage the dynamic, processes involved in patient care. Its role is to generate, in real time, commands for the patient’s care (execution of tests, administration of drugs) from a plan, and to monitor the patient’s state so that it may propose actions updating the plan. The necessity of an explicit time representation is shown. We propose using a linear time structure towards the past, with precise and absolute dates, open towards the future, and with imprecise and relative dates. Temporal relative scales are introduced to facilitate knowledge representation and access.

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