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 - A graph theoretic approach to construct desired cryptographic boolean functions
AU - Ghorbani, Modjtaba
AU - Dehmer, Matthias
AU - Taghvayi-Yazdelli, Vahid
AU - Emmert-Streib, Frank
PY - 2019/6/1
Y1 - 2019/6/1
N2 - In this paper, we present four product operations to construct cryptographic boolean functions from smaller ones with predictableWalsh spectrum. A lot of cryptographic properties of boolean functions can be presented by theirWalsh spectrum. In our method, we use the product of Cayley graphs to present new boolean functions with desiredWalsh spectrum and investigate their non-linearity, algebraic and correlation immunity.
AB - In this paper, we present four product operations to construct cryptographic boolean functions from smaller ones with predictableWalsh spectrum. A lot of cryptographic properties of boolean functions can be presented by theirWalsh spectrum. In our method, we use the product of Cayley graphs to present new boolean functions with desiredWalsh spectrum and investigate their non-linearity, algebraic and correlation immunity.
KW - Algebraic immunity
KW - Boolean functions
KW - Cayley graphs
KW - Non-linearity
KW - Walsh spectrum
U2 - 10.3390/axioms8020040
DO - 10.3390/axioms8020040
M3 - Article
VL - 8
JO - Axioms
JF - Axioms
SN - 2075-1680
IS - 2
M1 - 40
ER -
TY - JOUR
T1 - A note on distance-based entropy of dendrimers
AU - Ghorbani, Modjtaba
AU - Dehmer, Matthias
AU - Zangi, Samaneh
AU - Mowshowitz, Abbe
AU - Emmert-Streib, Frank
PY - 2019
Y1 - 2019
N2 - This paper introduces a variant of entropy measures based on vertex eccentricity and applies it to all graphs representing the isomers of octane. Taking into account the vertex degree as well (degree-ecc-entropy), we find a good correlation with the acentric factor of octane isomers. In particular, we compute the degree-ecc-entropy for three classes of dendrimer graphs.
AB - This paper introduces a variant of entropy measures based on vertex eccentricity and applies it to all graphs representing the isomers of octane. Taking into account the vertex degree as well (degree-ecc-entropy), we find a good correlation with the acentric factor of octane isomers. In particular, we compute the degree-ecc-entropy for three classes of dendrimer graphs.
KW - Dendrimer
KW - Graph entropy
KW - Vertex eccentricity
U2 - 10.3390/axioms8030098
DO - 10.3390/axioms8030098
M3 - Article
VL - 8
JO - Axioms
JF - Axioms
SN - 2075-1680
IS - 3
M1 - 98
ER -
TY - JOUR
T1 - On the spectral and Frobenius norm of a generalized Fibonacci r-circulant matrix
AU - Merikoski, Jorma K.
AU - Haukkanen, Pentti
AU - Mattila, Mika
AU - Tossavainen, Timo
PY - 2018/1/1
Y1 - 2018/1/1
N2 - Consider the recursion g0 = a, g1 = b, gn = gn-1 + gn-2, n = 2, 3, . . . . We compute the Frobenius norm of the r-circulant matrix corresponding to g0, . . . , gn-1. We also give three lower bounds (with equality conditions) for the spectral norm of this matrix. For this purpose, we present three ways to estimate the spectral norm from below in general.
AB - Consider the recursion g0 = a, g1 = b, gn = gn-1 + gn-2, n = 2, 3, . . . . We compute the Frobenius norm of the r-circulant matrix corresponding to g0, . . . , gn-1. We also give three lower bounds (with equality conditions) for the spectral norm of this matrix. For this purpose, we present three ways to estimate the spectral norm from below in general.
KW - Euclidean norm
KW - Frobenius norm
KW - generalized Fibonacci numbers
KW - r-circulant matrix
KW - spectral norm
U2 - 10.1515/spma-2018-0003
DO - 10.1515/spma-2018-0003
M3 - Article
VL - 6
SP - 23
EP - 36
JO - Special Matrices
JF - Special Matrices
SN - 2300-7451
IS - 1
ER -
TY - JOUR
T1 - Toward measuring network aesthetics based on symmetry
AU - Chen, Zengqiang
AU - Dehmer, Matthias
AU - Emmert-Streib, Frank
AU - Mowshowitz, Abbe
AU - Shi, Yongtang
PY - 2017/6/1
Y1 - 2017/6/1
N2 - In this exploratory paper, we discuss quantitative graph-theoretical measures of network aesthetics. Related work in this area has typically focused on geometrical features (e.g., line crossings or edge bendiness) of drawings or visual representations of graphs which purportedly affect an observer's perception. Here we take a very different approach, abandoning reliance on geometrical properties, and apply information-theoretic measures to abstract graphs and networks directly (rather than to their visual representaions) as a means of capturing classical appreciation of structural symmetry. Examples are used solely to motivate the approach to measurement, and to elucidate our symmetry-based mathematical theory of network aesthetics.
AB - In this exploratory paper, we discuss quantitative graph-theoretical measures of network aesthetics. Related work in this area has typically focused on geometrical features (e.g., line crossings or edge bendiness) of drawings or visual representations of graphs which purportedly affect an observer's perception. Here we take a very different approach, abandoning reliance on geometrical properties, and apply information-theoretic measures to abstract graphs and networks directly (rather than to their visual representaions) as a means of capturing classical appreciation of structural symmetry. Examples are used solely to motivate the approach to measurement, and to elucidate our symmetry-based mathematical theory of network aesthetics.
KW - Aesthetical theory
KW - Aesthetics
KW - Entropy
KW - Network aesthetics
KW - Networks
U2 - 10.3390/axioms6020012
DO - 10.3390/axioms6020012
M3 - Article
VL - 6
JO - Axioms
JF - Axioms
SN - 2075-1680
IS - 2
M1 - 12
ER -
TY - JOUR
T1 - On homomorphisms between products of median algebras
AU - Couceiro, Miguel
AU - Foldes, Stephan
AU - Meletiou, Gerasimos C.
PY - 2017
Y1 - 2017
N2 - Homomorphisms of products of median algebras are studied with particular attention to the case when the codomain is a tree. In particular, we show that all mappings from a product (Formula presented.) of median algebras to a median algebra (Formula presented.) are essentially unary whenever the codomain (Formula presented.) is a tree. In view of this result, we also characterize trees as median algebras and semilattices by relaxing the defining conditions of conservative median algebras.
AB - Homomorphisms of products of median algebras are studied with particular attention to the case when the codomain is a tree. In particular, we show that all mappings from a product (Formula presented.) of median algebras to a median algebra (Formula presented.) are essentially unary whenever the codomain (Formula presented.) is a tree. In view of this result, we also characterize trees as median algebras and semilattices by relaxing the defining conditions of conservative median algebras.
U2 - 10.1007/s00012-017-0468-6
DO - 10.1007/s00012-017-0468-6
M3 - Article
VL - 78
SP - 545
EP - 553
JO - Algebra Universalis
JF - Algebra Universalis
SN - 0002-5240
IS - 4
ER -
TY - JOUR
T1 - Constructing Minimal Coverability Sets
AU - Piipponen, Artturi
AU - Valmari, Antti
PY - 2016/3/4
Y1 - 2016/3/4
N2 - This publication addresses two bottlenecks in the construction of minimal coverability sets of Petri nets: the detection of situations where the marking of a place can be converted to ω, and the manipulation of the set A of maximal ω-markings that have been found so far. For the former, a technique is presented that consumes very little time in addition to what maintaining A consumes. It is based on Tarjan's algorithm for detecting maximal strongly connected components of a directed graph. For the latter, a data structure is introduced that resembles BDDs and Covering Sharing Trees, but has additional heuristics designed for the present use. Results from a few experiments are shown. They demonstrate significant savings in running time and varying savings in memory consumption compared to an earlier state-of-the-art technique.
AB - This publication addresses two bottlenecks in the construction of minimal coverability sets of Petri nets: the detection of situations where the marking of a place can be converted to ω, and the manipulation of the set A of maximal ω-markings that have been found so far. For the former, a technique is presented that consumes very little time in addition to what maintaining A consumes. It is based on Tarjan's algorithm for detecting maximal strongly connected components of a directed graph. For the latter, a data structure is introduced that resembles BDDs and Covering Sharing Trees, but has additional heuristics designed for the present use. Results from a few experiments are shown. They demonstrate significant savings in running time and varying savings in memory consumption compared to an earlier state-of-the-art technique.
KW - antichain data structure
KW - coverability set
KW - Tarjan's algorithm
U2 - 10.3233/FI-2016-1319
DO - 10.3233/FI-2016-1319
M3 - Article
VL - 143
SP - 393
EP - 414
JO - Fundamenta Informaticae
JF - Fundamenta Informaticae
SN - 0169-2968
IS - 3-4
ER -
TY - JOUR
T1 - Application and theory of Petri nets and other models of concurrency
T2 - Special issue of selected papers from Petri Nets 2015
AU - Devillers, Raymond
AU - Valmari, Antti
AU - Penczek, Wojciech
PY - 2016/9/13
Y1 - 2016/9/13
U2 - 10.3233/FI-2016-1373
DO - 10.3233/FI-2016-1373
M3 - Editorial
VL - 146
SP - v-vi
JO - Fundamenta Informaticae
JF - Fundamenta Informaticae
SN - 0169-2968
IS - 1
ER -