scholarly journals The computation of factorization invariants for affine semigroups

2019 ◽  
Vol 18 (01) ◽  
pp. 1950019 ◽  
Author(s):  
Pedro A. García-Sánchez ◽  
Christopher O’Neill ◽  
Gautam Webb
Keyword(s):  
Commutative Algebra ◽  
Improved Method ◽  
Dynamic Algorithm ◽  
Delta Set ◽  
Affine Semigroups ◽  
Affine Semigroup ◽  
Combinatorial Commutative Algebra ◽  
Theoretical Results ◽  
New Algorithms ◽  
Standard Techniques

We present several new algorithms for computing factorization invariant values over affine semigroups. In particular, we give (i) the first known algorithm to compute the delta set of any affine semigroup, (ii) an improved method of computing the tame degree of an affine semigroup, and (iii) a dynamic algorithm to compute catenary degrees of affine semigroup elements. Our algorithms rely on theoretical results from combinatorial commutative algebra involving Gröbner bases, Hilbert bases, and other standard techniques. Implementation in the computer algebra system GAP is discussed.

scholarly journals A review of turbulence measurements using ground-based wind lidars

2013 ◽  
Vol 6 (11) ◽  
pp. 3147-3167 ◽  
Author(s):  
A. Sathe ◽  
J. Mann
Keyword(s):  
Turbulence Model ◽  
Isotropic Turbulence ◽  
Lidar Data ◽  
Turbulence Statistics ◽  
Probe Volume ◽  
Turbulence Measurements ◽  
Lidar Measurements ◽  
Processing Algorithms ◽  
New Algorithms ◽  
Standard Techniques

Abstract. A review of turbulence measurements using ground-based wind lidars is carried out. Works performed in the last 30 yr, i.e., from 1972–2012 are analyzed. More than 80% of the work has been carried out in the last 15 yr, i.e., from 1997–2012. New algorithms to process the raw lidar data were pioneered in the first 15 yr, i.e., from 1972–1997, when standard techniques could not be used to measure turbulence. Obtaining unfiltered turbulence statistics from the large probe volume of the lidars has been and still remains the most challenging aspect. Until now, most of the processing algorithms that have been developed have shown that by combining an isotropic turbulence model with raw lidar measurements, we can obtain unfiltered statistics. We believe that an anisotropic turbulence model will provide a more realistic measure of turbulence statistics. Future development in algorithms will depend on whether the unfiltered statistics can be obtained without the aid of any turbulence model. With the tremendous growth of the wind energy sector, we expect that lidars will be used for turbulence measurements much more than ever before.

Combinatorial Commutative Algebra

2004 ◽  
pp. 1703-1746
Author(s):  
Irena Peeva ◽  
Volkmar Welker
Keyword(s):  
Commutative Algebra ◽  
Combinatorial Commutative Algebra

On the structure of simplicial affine semigroups

2000 ◽  
Vol 130 (5) ◽  
pp. 1017-1028 ◽  
Author(s):  
J. C. Rosales ◽  
P. A. García-Sánchez
Keyword(s):  
Upper Bound ◽  
Structure Theorem ◽  
Semigroup Rings ◽  
Affine Semigroups ◽  
Affine Semigroup

We give a structure theorem for simplicial affine semigroups. From this result we deduce characterizations of some properties of semigroup rings of simplicial affine semigroups. We also compute an upper bound for the cardinality of a minimal presentation of a simplicial affine semigroup.

scholarly journals FACTORIZATION INVARIANTS IN HALF-FACTORIAL AFFINE SEMIGROUPS

2013 ◽  
Vol 23 (01) ◽  
pp. 111-122 ◽  
Author(s):  
P. A. GARCÍA SÁNCHEZ ◽  
I. OJEDA ◽  
A. SÁNCHEZ-R.-NAVARRO
Keyword(s):  
Upper Bound ◽  
Affine Semigroups ◽  
Affine Semigroup ◽  
Catenary Degree

Let [Formula: see text] be the monoid generated by [Formula: see text] We introduce the homogeneous catenary degree of [Formula: see text] as the smallest N ∈ ℕ with the following property: for each [Formula: see text] and any two factorizations u, v of a, there exist factorizations u = w1,…,wt = v of a such that, for every k, d (wk,wk+1) ≤ N, where d is the usual distance between factorizations, and the length of wk, |wk|, is less than or equal to max{|u|, |v|}. We prove that the homogeneous catenary degree of [Formula: see text] improves the monotone catenary degree as upper bound for the ordinary catenary degree, and we show that it can be effectively computed. We also prove that for half-factorial monoids, the tame degree and the ω-primality coincide, and that all possible catenary degrees of the elements of an affine semigroup of this kind occur as the catenary degree of one of its Betti elements.

scholarly journals A review of turbulence measurements using ground-based wind lidars

2013 ◽  
Vol 6 (4) ◽  
pp. 6815-6871 ◽  
Author(s):  
A. Sathe ◽  
J. Mann
Keyword(s):  
Turbulence Model ◽  
Isotropic Turbulence ◽  
Lidar Data ◽  
Turbulence Statistics ◽  
Probe Volume ◽  
Turbulence Measurements ◽  
Lidar Measurements ◽  
Processing Algorithms ◽  
New Algorithms ◽  
Standard Techniques

Abstract. A review of turbulence measurements using ground-based wind lidars is carried out. Works performed in the last 30 yr, i.e. from 1972–2012 are analyzed. More than 80% of the work has been carried out in the last 15 yr, i.e. from 1997–2012. New algorithms to process the raw lidar data were pioneered in the first 15 yr, i.e. from 1972–1997, where standard techniques could not be used to measure turbulence. Obtaining unfiltered turbulence statistics from the large probe volume of the lidars has been and still remains the most challenging aspect. Until now, most of the processing algorithms that have been developed have shown that by combining an isotropic turbulence model with raw lidar measurements, we can obtain unfiltered statistics. We believe that an anisotropic turbulence model will provide a more realistic measure of a turbulence statistic. Future development in algorithms will depend on whether the unfiltered statistics can be obtained without the aid of any turbulence model. With the tremendous growth of the wind energy sector, we expect that lidars will be used for turbulence measurements much more than ever before.

scholarly journals THE SHORT RESOLUTION OF A SEMIGROUP ALGEBRA

2017 ◽  
Vol 96 (3) ◽  
pp. 400-411 ◽  
Author(s):  
I. OJEDA ◽  
A. VIGNERON-TENORIO
Keyword(s):  
Semigroup Algebra ◽  
Numerical Semigroups ◽  
Frobenius Numbers ◽  
Affine Semigroups ◽  
Affine Semigroup ◽  
Lattice Ideal ◽  
Apéry Sets

This work generalises the short resolution given by Pisón Casares [‘The short resolution of a lattice ideal’, Proc. Amer. Math. Soc.131(4) (2003), 1081–1091] to any affine semigroup. We give a characterisation of Apéry sets which provides a simple way to compute Apéry sets of affine semigroups and Frobenius numbers of numerical semigroups. We also exhibit a new characterisation of the Cohen–Macaulay property for simplicial affine semigroups.

Estimating the varying topology of discrete-time dynamical networks with noise

Open Physics ◽  
2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Chengyi Tu ◽  
Yuhua Cheng ◽  
Kai Chen
Keyword(s):  
Numerical Simulation ◽  
Parameter Estimation ◽  
Discrete Time ◽  
Moving Average ◽  
Improved Method ◽  
Dynamical Networks ◽  
Moving Average Filter ◽  
Influence Of Noise ◽  
Average Filter ◽  
Theoretical Results

AbstractWe propose an improved method to estimate the varying topology of discrete-time dynamical networks using autosynchronization. The networks considered in this paper can be weighted or unweighted and directed or undirected, and the dynamics of each node can be nonuniform. Furthermore, we suggest using a moving-average filter to suppress the influence of noise on parameter estimation. Finally, several examples are illustrated to verify the theoretical results by numerical simulation.

scholarly journals Crime Busting Model Based on Dynamic Ranking Algorithms

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Yang Cao ◽  
Xiaotian Xu ◽  
Zhijing Ye
Keyword(s):  
Social Network ◽  
Large Datasets ◽  
Test Results ◽  
Priority List ◽  
Dynamic Algorithm ◽  
Semantic Learning ◽  
Network Mining ◽  
Ranking Algorithms ◽  
Great Performance ◽  
Theoretical Results

This paper proposed a crime busting model with two dynamic ranking algorithms to detect the likelihood of a suspect and the possibility of a leader in a complex social network. Signally, in order to obtain the priority list of suspects, an advanced network mining approach with a dynamic cumulative nominating algorithm is adopted to rapidly reduce computational expensiveness than most other topology-based approaches. Our method can also greatly increase the accuracy of solution with the enhancement of semantic learning filtering at the same time. Moreover, another dynamic algorithm of node contraction is also presented to help identify the leader among conspirators. Test results are given to verify the theoretical results, which show the great performance for either small or large datasets.

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