TY - JOUR
T1 - Approximate Controllability for Navier–Stokes Equations in 3D Rectangles Under Lions Boundary Conditions
AU - Phan, Duy
AU - Rodrigues, Sérgio S.
PY - 2019/7
Y1 - 2019/7
N2 - The 3D Navier–Stokes system, under Lions boundary conditions, is proven to be approximately controllable provided a suitable saturating set does exist. An explicit saturating set for 3D rectangles is given.
AB - The 3D Navier–Stokes system, under Lions boundary conditions, is proven to be approximately controllable provided a suitable saturating set does exist. An explicit saturating set for 3D rectangles is given.
KW - Approximate controllability
KW - Navier–Stokes equations
KW - Saturating set
U2 - 10.1007/s10883-018-9412-0
DO - 10.1007/s10883-018-9412-0
M3 - Article
VL - 25
SP - 351
EP - 376
JO - Journal of Dynamical and Control Systems
JF - Journal of Dynamical and Control Systems
SN - 1079-2724
IS - 3
ER -
TY - JOUR
T1 - Integral kernels for k-hypermonogenic functions
AU - Vuojamo, Vesa
AU - Eriksson, Sirkka-Liisa
N1 - EXT="Eriksson, Sirkka-Liisa"
PY - 2017
Y1 - 2017
N2 - We consider the modified Cauchy–Riemann operator (Formula presented.) in the universal Clifford algebra (Formula presented.) with the basis (Formula presented.). The null-solutions of this operator are called k-hypermonogenic functions. We calculate the k-hyperbolic harmonic fundamental solutions, i.e. solutions to (Formula presented.), and use these solutions to find k-hypermonogenic kernels for a Cauchy-type integral formula in the upper half-space.
AB - We consider the modified Cauchy–Riemann operator (Formula presented.) in the universal Clifford algebra (Formula presented.) with the basis (Formula presented.). The null-solutions of this operator are called k-hypermonogenic functions. We calculate the k-hyperbolic harmonic fundamental solutions, i.e. solutions to (Formula presented.), and use these solutions to find k-hypermonogenic kernels for a Cauchy-type integral formula in the upper half-space.
KW - Cauchy integral formula
KW - Clifford algebra
KW - hyperbolic Laplace–Beltrami
KW - k-hyperbolic harmonic
KW - k-hypermonogenic
U2 - 10.1080/17476933.2016.1250402
DO - 10.1080/17476933.2016.1250402
M3 - Article
VL - 62
SP - 1
EP - 12
JO - Complex Variables and Elliptic Equations
JF - Complex Variables and Elliptic Equations
SN - 1747-6933
IS - 9
ER -
TY - GEN
T1 - Simulation of photon-photon resonance enhanced direct modulation bandwidth of DFB lasers
AU - Dumitrescu, M.
AU - Uusitalo, T.
AU - Virtanen, H.
AU - Laakso, A.
AU - Bardella, P.
AU - Montrosset, I.
N1 - EXT="Laakso, A."
PY - 2016/8/17
Y1 - 2016/8/17
N2 - Simulations and experimental results of high-frequency photon-photon resonance are used to examine the possibilities to extend the direct modulation bandwidth in dual-mode distributed feedback lasers beyond the conventional limit set by the carrier-photon resonance.
AB - Simulations and experimental results of high-frequency photon-photon resonance are used to examine the possibilities to extend the direct modulation bandwidth in dual-mode distributed feedback lasers beyond the conventional limit set by the carrier-photon resonance.
U2 - 10.1109/NUSOD.2016.7547075
DO - 10.1109/NUSOD.2016.7547075
M3 - Conference contribution
SP - 147
EP - 148
BT - 16th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2016
PB - IEEE
ER -
TY - GEN
T1 - Simulation studies of DFB laser longitudinal structures for narrow linewidth emission
AU - Virtanen, Heikki
AU - Uusitalo, Topi
AU - Dumitrescu, Mihail
PY - 2016/8/17
Y1 - 2016/8/17
N2 - Simulation studies targeting high-power narrow-linewidth emission from DFB lasers are presented. The linewidth and output power calculations take into account the mirror losses, including the grating and the facets, as well as spontaneous emission noise, effective refractive index, power and carrier density variations inside the cavity. The longitudinal power and carrier density distributions have been evaluated and their effects on longitudinal spatial hole burning and possible side mode lasing are discussed.
AB - Simulation studies targeting high-power narrow-linewidth emission from DFB lasers are presented. The linewidth and output power calculations take into account the mirror losses, including the grating and the facets, as well as spontaneous emission noise, effective refractive index, power and carrier density variations inside the cavity. The longitudinal power and carrier density distributions have been evaluated and their effects on longitudinal spatial hole burning and possible side mode lasing are discussed.
U2 - 10.1109/NUSOD.2016.7547078
DO - 10.1109/NUSOD.2016.7547078
M3 - Conference contribution
SP - 153
EP - 154
BT - 16th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2016
PB - IEEE
ER -
TY - GEN
T1 - Transverse structure optimization of laterally-coupled ridge waveguide DFB lasers
AU - Uusitalo, Topi
AU - Virtanen, Heikki
AU - Dumitrescu, Mihail
PY - 2016/8/17
Y1 - 2016/8/17
N2 - A new figure of merit for single transverse mode operation and an accurate procedure for calculating the coupling coefficient in distributed feedback lasers with laterally-coupled ridge waveguide surface grating structures are introduced. Based on the difference in optical confinement between the pumped and un-pumped regions in the transverse plane, the single transverse mode figure of merit is effective and easy to calculate, while the improved coupling coefficient calculation procedure gives experimentally confirmed better results than the standard calculation approaches.
AB - A new figure of merit for single transverse mode operation and an accurate procedure for calculating the coupling coefficient in distributed feedback lasers with laterally-coupled ridge waveguide surface grating structures are introduced. Based on the difference in optical confinement between the pumped and un-pumped regions in the transverse plane, the single transverse mode figure of merit is effective and easy to calculate, while the improved coupling coefficient calculation procedure gives experimentally confirmed better results than the standard calculation approaches.
U2 - 10.1109/NUSOD.2016.7547038
DO - 10.1109/NUSOD.2016.7547038
M3 - Conference contribution
SP - 79
EP - 80
BT - 16th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2016
PB - IEEE
ER -
TY - JOUR
T1 - Geometric solution strategy of Laplace problems with free boundary
AU - Poutala, Arto
AU - Tarhasaari, Timo
AU - Kettunen, Lauri
PY - 2016/3/9
Y1 - 2016/3/9
N2 - This paper introduces a geometric solution strategy for Laplace problems. Our main interest and emphasis is on efficient solution of the inverse problem with a boundary with Cauchy condition and with a free boundary. This type of problem is known to be sensitive to small errors. We start from the standard Laplace problem and establish the geometric solution strategy on the idea of deforming equipotential layers continuously along the field lines from one layer to another. This results in exploiting ordinary differential equations to solve any boundary value problem that belongs to the class of Laplace's problem. Interpretation in terms of a geometric flow will provide us with stability considerations. The approach is demonstrated with several examples.
AB - This paper introduces a geometric solution strategy for Laplace problems. Our main interest and emphasis is on efficient solution of the inverse problem with a boundary with Cauchy condition and with a free boundary. This type of problem is known to be sensitive to small errors. We start from the standard Laplace problem and establish the geometric solution strategy on the idea of deforming equipotential layers continuously along the field lines from one layer to another. This results in exploiting ordinary differential equations to solve any boundary value problem that belongs to the class of Laplace's problem. Interpretation in terms of a geometric flow will provide us with stability considerations. The approach is demonstrated with several examples.
KW - Bernoulli problem
KW - Cauchy condition
KW - Differential equations
KW - Elliptic partial differential equations
KW - Equipotential layers
KW - Field lines
KW - Inverse problem
KW - Laplace problem
KW - Mean curvature
KW - Shape design
U2 - 10.1002/nme.4988
DO - 10.1002/nme.4988
M3 - Article
VL - 105
SP - 723
EP - 746
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 10
ER -
TY - JOUR
T1 - Target tracking via combination of particle filter and optimisation techniques
AU - Hosseini, Seyyed Soheil Sadat
AU - Jamali, Mohsin M.
AU - Astola, Jaakko
AU - Gorsevski, Peter V.
PY - 2016
Y1 - 2016
N2 - Particle filters (PFs) have been used for the nonlinear estimation for a number of years. However, they suffer from the impoverishment phenomenon. It is brought by resampling which intends to prevent particle degradation, and therefore becomes the inherent weakness of this technique. To solve the problem of sample impoverishment and to improve the performance of the standard particle filter we propose a modification to this method by adding a sampling mechanism inspired by optimisation techniques, namely, the pattern search, particle swarm optimisation, differential evolution and Nelder-Mead algorithms. In the proposed methods, the true state of the target can be better expressed by the optimised particle set and the number of meaningful particles can be grown significantly. The efficiency of the proposed particle filters is supported by a truck-trailer problem. Simulations show that the hybridised particle filter with Nelder-Mead search is better than other optimisation approaches in terms of particle diversity.
AB - Particle filters (PFs) have been used for the nonlinear estimation for a number of years. However, they suffer from the impoverishment phenomenon. It is brought by resampling which intends to prevent particle degradation, and therefore becomes the inherent weakness of this technique. To solve the problem of sample impoverishment and to improve the performance of the standard particle filter we propose a modification to this method by adding a sampling mechanism inspired by optimisation techniques, namely, the pattern search, particle swarm optimisation, differential evolution and Nelder-Mead algorithms. In the proposed methods, the true state of the target can be better expressed by the optimised particle set and the number of meaningful particles can be grown significantly. The efficiency of the proposed particle filters is supported by a truck-trailer problem. Simulations show that the hybridised particle filter with Nelder-Mead search is better than other optimisation approaches in terms of particle diversity.
KW - Differential evolution
KW - Nelder-Mead
KW - Particle filter
KW - Particle swarm optimisation
KW - Pattern search
KW - PSO
KW - Target tracking
U2 - 10.1504/IJMMNO.2016.077068
DO - 10.1504/IJMMNO.2016.077068
M3 - Article
VL - 7
SP - 212
EP - 229
JO - International Journal of Mathematical Modelling and Numerical Optimization
JF - International Journal of Mathematical Modelling and Numerical Optimization
SN - 2040-3607
IS - 2
ER -
TY - JOUR
T1 - A comparative analysis of multidimensional features of objects resembling sets of graphs
AU - Dehmer, Matthias
AU - Emmert-Streib, Frank
AU - Gesell, Tanja
PY - 2008/2/15
Y1 - 2008/2/15
N2 - In the present paper, we introduce a notion of a style representing abstract, complex objects having characteristics that can be represented as structured objects. Furthermore, we provide some mathematical properties of such styles. As a main result, we present a novel approach to perform a meaningful comparative analysis of such styles by defining and using graph-theoretic measures. We compare two styles by comparing the underlying feature sets representing sets of graph structurally. To determine the structural similarity between the underlying graphs, we use graph similarity measures that are computationally efficient. More precisely, in order to compare styles, we map each feature set to a so-called median graph and compare the resulting median graphs. As an application, we perform an experimental study to compare special styles representing sets of undirected graphs and present numerical results thereof.
AB - In the present paper, we introduce a notion of a style representing abstract, complex objects having characteristics that can be represented as structured objects. Furthermore, we provide some mathematical properties of such styles. As a main result, we present a novel approach to perform a meaningful comparative analysis of such styles by defining and using graph-theoretic measures. We compare two styles by comparing the underlying feature sets representing sets of graph structurally. To determine the structural similarity between the underlying graphs, we use graph similarity measures that are computationally efficient. More precisely, in order to compare styles, we map each feature set to a so-called median graph and compare the resulting median graphs. As an application, we perform an experimental study to compare special styles representing sets of undirected graphs and present numerical results thereof.
KW - Classification
KW - Object comparison
KW - Similarity
KW - Structural similarity
KW - Structured objects
U2 - 10.1016/j.amc.2007.05.058
DO - 10.1016/j.amc.2007.05.058
M3 - Article
VL - 196
SP - 221
EP - 235
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
IS - 1
ER -
TY - JOUR
T1 - Structural similarity of directed universal hierarchical graphs
T2 - A low computational complexity approach
AU - Dehmer, Matthias
AU - Emmert-Streib, Frank
PY - 2007/12/1
Y1 - 2007/12/1
N2 - In the present paper we mainly introduce an efficient approach to measure the structural similarity of so called directed universal hierarchical graphs. We want to underline that directed universal hierarchical graphs can be obtained from generalized trees which are already introduced. In order to classify these graphs, we state our novel graph similarity method. As a main result we notice that our novel algorithm has low computational complexity.
AB - In the present paper we mainly introduce an efficient approach to measure the structural similarity of so called directed universal hierarchical graphs. We want to underline that directed universal hierarchical graphs can be obtained from generalized trees which are already introduced. In order to classify these graphs, we state our novel graph similarity method. As a main result we notice that our novel algorithm has low computational complexity.
KW - Complexity analysis
KW - Graph classes
KW - Graph classification
KW - Graph similarity
KW - Hierarchical models
KW - Structured objects
UR - http://www.scopus.com/inward/record.url?scp=35648968162&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2007.04.006
DO - 10.1016/j.amc.2007.04.006
M3 - Article
VL - 194
SP - 7
EP - 20
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
IS - 1
ER -
TY - JOUR
T1 - Information theoretic measures of UHG graphs with low computational complexity
AU - Emmert-Streib, Frank
AU - Dehmer, Matthias
PY - 2007/7/15
Y1 - 2007/7/15
N2 - We introduce a novel graph class we call universal hierarchical graphs (UHG) whose topology can be found numerously in problems representing, e.g., temporal, spacial or general process structures of systems. For this graph class we show, that we can naturally assign two probability distributions, for nodes and for edges, which lead us directly to the definition of the entropy and joint entropy and, hence, mutual information establishing an information theory for this graph class. Furthermore, we provide some results under which conditions these constraint probability distributions maximize the corresponding entropy. Also, we demonstrate that these entropic measures can be computed efficiently which is a prerequisite for every large scale practical application and show some numerical examples.
AB - We introduce a novel graph class we call universal hierarchical graphs (UHG) whose topology can be found numerously in problems representing, e.g., temporal, spacial or general process structures of systems. For this graph class we show, that we can naturally assign two probability distributions, for nodes and for edges, which lead us directly to the definition of the entropy and joint entropy and, hence, mutual information establishing an information theory for this graph class. Furthermore, we provide some results under which conditions these constraint probability distributions maximize the corresponding entropy. Also, we demonstrate that these entropic measures can be computed efficiently which is a prerequisite for every large scale practical application and show some numerical examples.
KW - Entropy
KW - Graph classes
KW - Graph measures
KW - Hierarchical graphs
KW - Information theory
UR - http://www.scopus.com/inward/record.url?scp=34250623666&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2007.02.095
DO - 10.1016/j.amc.2007.02.095
M3 - Article
VL - 190
SP - 1783
EP - 1794
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
IS - 2
ER -
TY - JOUR
T1 - Comparing large graphs efficiently by margins of feature vectors
AU - Dehmer, Matthias
AU - Emmert-Streib, Frank
PY - 2007/5/15
Y1 - 2007/5/15
N2 - Measuring the structural similarity of graphs is a challenging and outstanding problem. Most of the classical approaches of the so-called exact graph matching methods are based on graph or subgraph isomorphic relations of the underlying graphs. In contrast to these methods in this paper we introduce a novel approach to measure the structural similarity of directed and undirected graphs that is mainly based on margins of feature vectors representing graphs. We introduce novel graph similarity and dissimilarity measures, provide some properties and analyze their algorithmic complexity. We find that the computational complexity of our measures is polynomial in the graph size and, hence, significantly better than classical methods from, e.g. exact graph matching which are NP-complete. Numerically, we provide some examples of our measure and compare the results with the well-known graph edit distance.
AB - Measuring the structural similarity of graphs is a challenging and outstanding problem. Most of the classical approaches of the so-called exact graph matching methods are based on graph or subgraph isomorphic relations of the underlying graphs. In contrast to these methods in this paper we introduce a novel approach to measure the structural similarity of directed and undirected graphs that is mainly based on margins of feature vectors representing graphs. We introduce novel graph similarity and dissimilarity measures, provide some properties and analyze their algorithmic complexity. We find that the computational complexity of our measures is polynomial in the graph size and, hence, significantly better than classical methods from, e.g. exact graph matching which are NP-complete. Numerically, we provide some examples of our measure and compare the results with the well-known graph edit distance.
KW - Degree vectors
KW - Directed and undirected graphs
KW - Graph similarity
KW - Similarity measures
UR - http://www.scopus.com/inward/record.url?scp=34248165422&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2006.11.185
DO - 10.1016/j.amc.2006.11.185
M3 - Article
VL - 188
SP - 1699
EP - 1710
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
IS - 2
ER -
TY - JOUR
T1 - Topological mappings between graphs, trees and generalized trees
AU - Emmert-Streib, Frank
AU - Dehmer, Matthias
PY - 2007/3/15
Y1 - 2007/3/15
N2 - We present novel topological mappings between graphs, trees and generalized trees that means between structured objects with different properties. The two major contributions of this paper are, first, to clarify the relation between graphs, trees and generalized trees, a graph class recently introduced. Second, these transformations provide a unique opportunity to transform structured objects into a representation that might be beneficial for a processing, e.g., by machine learning techniques for graph classification.
AB - We present novel topological mappings between graphs, trees and generalized trees that means between structured objects with different properties. The two major contributions of this paper are, first, to clarify the relation between graphs, trees and generalized trees, a graph class recently introduced. Second, these transformations provide a unique opportunity to transform structured objects into a representation that might be beneficial for a processing, e.g., by machine learning techniques for graph classification.
KW - Applied graph theory
KW - Graph transformation
KW - Hierarchical graphs
UR - http://www.scopus.com/inward/record.url?scp=33947616843&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2006.07.162
DO - 10.1016/j.amc.2006.07.162
M3 - Article
VL - 186
SP - 1326
EP - 1333
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
IS - 2
ER -
TY - JOUR
T1 - A similarity measure for graphs with low computational complexity
AU - Dehmer, Matthias
AU - Emmert-Streib, Frank
AU - Kilian, Jürgen
PY - 2006/11/1
Y1 - 2006/11/1
N2 - We present and analyze an algorithm to measure the structural similarity of generalized trees, a new graph class which includes rooted trees. For this, we represent structural properties of graphs as strings and define the similarity of two graphs as optimal alignments of the corresponding property stings. We prove that the obtained graph similarity measures are so called Backward similarity measures. From this we find that the time complexity of our algorithm is polynomial and, hence, significantly better than the time complexity of classical graph similarity methods based on isomorphic relations.
AB - We present and analyze an algorithm to measure the structural similarity of generalized trees, a new graph class which includes rooted trees. For this, we represent structural properties of graphs as strings and define the similarity of two graphs as optimal alignments of the corresponding property stings. We prove that the obtained graph similarity measures are so called Backward similarity measures. From this we find that the time complexity of our algorithm is polynomial and, hence, significantly better than the time complexity of classical graph similarity methods based on isomorphic relations.
KW - Computational complexity
KW - Dynamic programming
KW - Graph similarity
KW - Graph theory
UR - http://www.scopus.com/inward/record.url?scp=33750819438&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2006.04.006
DO - 10.1016/j.amc.2006.04.006
M3 - Article
VL - 182
SP - 447
EP - 459
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
IS - 1
ER -