scholarly journals EFFICIENT ALGORITHMS FOR HIGHLY COMPRESSED DATA: THE WORD PROBLEM IN HIGMAN'S GROUP IS IN P

2012 ◽  
Vol 22 (08) ◽  
pp. 1240008 ◽  
Author(s):  
VOLKER DIEKERT ◽  
JÜRN LAUN ◽  
ALEXANDER USHAKOV
Keyword(s):  
Word Problem ◽  
Time Complexity ◽  
Efficient Algorithms ◽  
Reduction Procedure ◽  
Algorithmic Algebra ◽  
Practical Algorithm ◽  
Power Circuits ◽  
The One ◽  
New Applications ◽  
Compressed Data

Power circuits are data structures which support efficient algorithms for highly compressed integers. Using this new data structure it has been shown recently by Myasnikov, Ushakov and Won that the Word Problem of the one-relator Baumslag group is in P. Before that the best known upper bound was non-elementary. In the present paper we provide new results for power circuits and we give new applications in algorithmic algebra and algorithmic group theory: (1) We define a modified reduction procedure on power circuits which runs in quadratic time, thereby improving the known cubic time complexity. The improvement is crucial for our other results. (2) We improve the complexity of the Word Problem for the Baumslag group to cubic time, thereby providing the first practical algorithm for that problem. (The algorithm has been implemented and is available in the CRAG library.) (3) The main result is that the Word Problem of Higman's group is decidable in polynomial time. The situation for Higman's group is more complicated than for the Baumslag group and forced us to advance the theory of power circuits.

scholarly journals Computing the Atom Graph of a Graph and the Union Join Graph of a Hypergraph

Algorithms ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 347
Author(s):  
Anne Berry ◽  
Geneviève Simonet
Keyword(s):  
Real Number ◽  
Time Complexity ◽  
Matrix Multiplication ◽  
Efficient Algorithms ◽  
Join Graph ◽  
Current Value ◽  
Minimal Separator

The atom graph of a graph is a graph whose vertices are the atoms obtained by clique minimal separator decomposition of this graph, and whose edges are the edges of all possible atom trees of this graph. We provide two efficient algorithms for computing this atom graph, with a complexity in O(min(nωlogn,nm,n(n+m¯)) time, where n is the number of vertices of G, m is the number of its edges, m¯ is the number of edges of the complement of G, and ω, also denoted by α in the literature, is a real number, such that O(nω) is the best known time complexity for matrix multiplication, whose current value is 2,3728596. This time complexity is no more than the time complexity of computing the atoms in the general case. We extend our results to α-acyclic hypergraphs, which are hypergraphs having at least one join tree, a join tree of an hypergraph being defined by its hyperedges in the same way as an atom tree of a graph is defined by its atoms. We introduce the notion of union join graph, which is the union of all possible join trees; we apply our algorithms for atom graphs to efficiently compute union join graphs.

scholarly journals On new applications of fractional calculus

2017 ◽  
Vol 37 (3) ◽  
pp. 113-118 ◽  
Author(s):  
Shilpi Jain ◽  
Praveen Agarwal
Keyword(s):  
Fractional Calculus ◽  
Special Functions ◽  
Leibniz Rule ◽  
The One ◽  
New Applications ◽  
Paper Author

In the present paper author derive a number of integrals concerning various special functions which are applications of the one of Osler result. Osler provided extensions to the familiar Leibniz rule for the nth derivative of product of two functions.

How can health professionals contribute to the internet of things body of knowledge

2019 ◽  
Vol 49 (2) ◽  
pp. 229-240 ◽  
Author(s):  
Mehdi Dadkhah ◽  
Mohammad Lagzian ◽  
Gabriele Santoro
Keyword(s):  
Internet Of Things ◽  
Health Professionals ◽  
Design Methodology ◽  
Content Type ◽  
Technological Paradigm ◽  
Body Of Knowledge ◽  
The One ◽  
New Applications ◽  
Technical People ◽  
The Internet Of Things

Purpose Internet of Things (IoT) as the new technological paradigm has found many applications in different domains. Nowadays, more than 30,000 records related to IoT research can be accessed in Scopus (Scopus.com). Health care is the one of domains which benefits from IoT. However, observations indicate that most active researchers in this area are technical people not health professionals. The purpose of this paper is to understand how health professionals can contribute to the IoT body of knowledge. Design/methodology/approach IoT professionals are asked to provide their views regarding research concerns, and the collected data are analyzed by phenomenography research methodology. Findings Findings indicate that health professionals can contribute through providing information, requirement or standards for developing IoT systems or devices. They can also introduce new applications or domains for which IoT is fit. Originality/value This paper tries to fill the gap concerning the lack of attention to undertaking IoT-related research from health professionals’ side and highlights ways that health professionals can contribute IoT body of knowledge.

Analysis of flowrates as a basis for the simulation of dry-running rotational positive displacement pumps

2002 ◽  
Vol 216 (12) ◽  
pp. 1197-1205 ◽  
Author(s):  
K Kauder ◽  
D Wenderott
Keyword(s):  
Mass Flow ◽  
Characteristic Number ◽  
Operational Reliability ◽  
Simulation System ◽  
Positive Displacement ◽  
Market Situation ◽  
Flow Through ◽  
The One ◽  
New Applications ◽  
Operational Behaviour

New applications improve the market situation of dry-running positive displacement pumps. The mostly empirically based design of these pumps has to take into account partly competing viewpoints. These viewpoints are energetic process optimization, on the one hand, and operational reliability, on the other hand. A simulation system can be used to solve this problem. The simulation system uses an energy and a mass balance in order to simulate the operational behaviour of the vacuum pumps. Therefore knowledge of the different states of flow through clearances in a vacuum is essential. The experimental examination of the flow is done by flood curve measurements, to describe the mass flow integrally using the characteristic number of the standardized mass flow. The results for some possible plain clearance shapes are discussed.

scholarly journals EXTENDED CONFORMAL GROUP AND DSR VELOCITIES ON THE PHYSICAL SURFACE

2006 ◽  
Vol 21 (13n14) ◽  
pp. 2863-2876
Author(s):  
CARLOS LEIVA
Keyword(s):  
Dimensional Reduction ◽  
Relativistic Particle ◽  
Dimensional Space ◽  
Lorentz Invariance ◽  
Conformal Group ◽  
Reduction Procedure ◽  
Doubly Special Relativity ◽  
Nonlinear Algebra ◽  
Space Dynamics ◽  
The One

The relation between conformal generators and Magueijo–Smolin Doubly Special Relativity term, is achieved. Through a dimensional reduction procedure, it is demonstrated that a massless relativistic particle living in a d-dimensional space, is isomorphic to the one living in a d+2 space with pure Lorentz invariance and to a particle living in a AdS d+1 space. To accomplish these identifications, the conformal group is extended and a nonlinear algebra is obtained. Finally, because the relation between momenta and velocities is known through the dimensional reduction procedure, the problem of position space dynamics is solved.

CONSTRUCTING THE GROUP PRESERVING A SYSTEM OF FORMS

2008 ◽  
Vol 18 (02) ◽  
pp. 227-241 ◽  
Author(s):  
PETER A. BROOKSBANK ◽  
E. A. O'BRIEN
Keyword(s):  
Finite Field ◽  
Vector Space ◽  
Linear Group ◽  
Jacobson Radical ◽  
Matrix Algebra ◽  
General Linear Group ◽  
Efficient Algorithms ◽  
Sesquilinear Forms ◽  
Group Of Units ◽  
Practical Algorithm

We present a practical algorithm to construct the subgroup of the general linear group that preserves a system of bilinear or sesquilinear forms on a vector space defined over a finite field. Components include efficient algorithms to construct the Jacobson radical and the group of units of a matrix algebra.

scholarly journals Foundations of Competitive Intelligence System to form Business Coalitions

2012 ◽  
Vol 2 (2) ◽  
Author(s):  
Olivier Mamawi
Keyword(s):  
Competitive Intelligence ◽  
Business Networks ◽  
Intelligence System ◽  
Industrial Labor ◽  
Dominant Parties ◽  
The One ◽  
New Applications ◽  
Procurement Contracts ◽  
Competitive Intelligence System

This study shows how a business can identify the networks allowing to form coalitions to obtain French procurement contracts. To this end, we have represented, by a graph, the 2008 co-branding system. We have detected, in this graph, 1360 strategic networks of which the organization reveals, on the one hand, identical characteristics within business networks, and on the other hand, the role of the dominant parties as to access to industrial labor. From these results, we propose a network cartography allowing us to consider new applications for competitive intelligence.

scholarly journals Remarks on the A** algorithm

2014 ◽  
Vol 6 (2) ◽  
pp. 190-205
Author(s):  
Tibor Gregorics
Keyword(s):  
Time Complexity ◽  
Search Algorithm ◽  
The Other ◽  
Graph Search ◽  
Path Finding ◽  
A Algorithm ◽  
Other Hand ◽  
The One ◽  
Memory Complexity

Abstract The A** algorithm is a famous heuristic path-finding algorithm. In this paper its different definitions will be analyzed firstly. Then its memory complexity is going to be investigated. On the one hand, the well-known concept of better-information will be extended to compare the different heuristics in the A** algorithm. On the other hand, a new proof will be given to show that there is no deterministic graph-search algorithm having better memory complexity than A**∗. At last the time complexity of A** will be discussed.

Maintaining Constrained Path Problem for Directed Acyclic Graphs

2021 ◽  
Vol 21 (03) ◽  
Author(s):  
Chenying Hao ◽  
Shurong Zhang ◽  
Weihua Yang
Keyword(s):  
Shortest Path ◽  
Time Complexity ◽  
Directed Acyclic Graph ◽  
Shortest Paths ◽  
Directed Acyclic Graphs ◽  
Shortest Path Algorithm ◽  
Acyclic Graphs ◽  
Main Technique ◽  
Number Formula ◽  
The One

In order to restore the faulty path in network more effectively, we propose the maintaining constrained path problem. Give a directed acyclic graph (DAG) [Formula: see text] with some faulty edges, where [Formula: see text], [Formula: see text]. For any positive number [Formula: see text], we give effective maintain algorithm for finding and maintaining the path between source vertex [Formula: see text] and destination [Formula: see text] with length at most [Formula: see text]. In this paper, we consider the parameters [Formula: see text] and [Formula: see text] which are used to measure the numbers of edges and vertices which are influenced by faulty edges, respectively. The main technique of this paper is to define and solve a subproblem called the one to set constrained path problem (OSCPP) which has not been addressed before. On the DAG, compared with the dynamic shortest path algorithm with time complexity [Formula: see text] [16] and the shortest path algorithm with time complexity [Formula: see text] [18], based on the algorithm for OSCPP, we develop a maintaining constrained path algorithm and improve the time complexity to [Formula: see text] in the case that all shortest paths from each vertex [Formula: see text] to [Formula: see text] have been given.

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