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 - Asymptotics for periodic systems
AU - Paunonen, Lassi
AU - Seifert, David
PY - 2019/5
Y1 - 2019/5
N2 - This paper investigates the asymptotic behaviour of solutions of periodic evolution equations. Starting with a general result concerning the quantified asymptotic behaviour of periodic evolution families we go on to consider a special class of dissipative systems arising naturally in applications. For this class of systems we analyse in detail the spectral properties of the associated monodromy operator, showing in particular that it is a so-called Ritt operator under a natural ‘resonance’ condition. This allows us to deduce from our general result a precise description of the asymptotic behaviour of the corresponding solutions. In particular, we present conditions for rational rates of convergence to periodic solutions in the case where the convergence fails to be uniformly exponential. We illustrate our general results by applying them to concrete problems including the one-dimensional wave equation with periodic damping.
AB - This paper investigates the asymptotic behaviour of solutions of periodic evolution equations. Starting with a general result concerning the quantified asymptotic behaviour of periodic evolution families we go on to consider a special class of dissipative systems arising naturally in applications. For this class of systems we analyse in detail the spectral properties of the associated monodromy operator, showing in particular that it is a so-called Ritt operator under a natural ‘resonance’ condition. This allows us to deduce from our general result a precise description of the asymptotic behaviour of the corresponding solutions. In particular, we present conditions for rational rates of convergence to periodic solutions in the case where the convergence fails to be uniformly exponential. We illustrate our general results by applying them to concrete problems including the one-dimensional wave equation with periodic damping.
KW - Damped wave equation
KW - Evolution family
KW - Non-autonomous system
KW - Periodic
KW - Rates of convergence
KW - Ritt operator
U2 - 10.1016/j.jde.2018.11.028
DO - 10.1016/j.jde.2018.11.028
M3 - Article
VL - 266
SP - 7152
EP - 7172
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 11
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 - Optimal energy decay for the wave-heat system on a rectangular domain
AU - Batty, Charles
AU - Paunonen, Lassi
AU - Seifert, David
PY - 2019
Y1 - 2019
N2 - We study the rate of energy decay for solutions of a coupled wave-heat system on a rectangular domain. Using techniques from the theory of C 0 -semigroups, and in particular a well-known result due to Borichev and Tomilov, we prove that the energy of classical solutions decays like t - 2/ 3 as t \rightarrow \infty . This rate is moreover shown to be sharp. Our result implies in particular that a general estimate in the literature, which predicts at least logarithmic decay and is known to be best possible in general, is suboptimal in the special case under consideration here. Our strategy of proof involves direct estimates based on separation of variables and a refined version of the technique developed in our earlier paper for a one-dimensional wave-heat system.
AB - We study the rate of energy decay for solutions of a coupled wave-heat system on a rectangular domain. Using techniques from the theory of C 0 -semigroups, and in particular a well-known result due to Borichev and Tomilov, we prove that the energy of classical solutions decays like t - 2/ 3 as t \rightarrow \infty . This rate is moreover shown to be sharp. Our result implies in particular that a general estimate in the literature, which predicts at least logarithmic decay and is known to be best possible in general, is suboptimal in the special case under consideration here. Our strategy of proof involves direct estimates based on separation of variables and a refined version of the technique developed in our earlier paper for a one-dimensional wave-heat system.
KW - C -semigroups
KW - Coupled
KW - Energy
KW - Heat equation
KW - Rates of decay
KW - Rectangular domain
KW - Resolvent estimates
KW - Wave equation
U2 - 10.1137/18M1195796
DO - 10.1137/18M1195796
M3 - Article
VL - 51
SP - 808
EP - 819
JO - SIAM JOURNAL ON MATHEMATICAL ANALYSIS
JF - SIAM JOURNAL ON MATHEMATICAL ANALYSIS
SN - 0036-1410
IS - 2
ER -
TY - JOUR
T1 - On derivatives of hypergeometric functions and classical polynomials with respect to parameters
AU - Sofotasios, P. C.
AU - Brychkov, Yu A.
PY - 2018/11/2
Y1 - 2018/11/2
N2 - Closed expressions are obtained for derivatives of symbolic order with respect to parameters for the hypergeometric functions, Laguerre, Gegenbauer, Jacobi and some other polynomial.
AB - Closed expressions are obtained for derivatives of symbolic order with respect to parameters for the hypergeometric functions, Laguerre, Gegenbauer, Jacobi and some other polynomial.
KW - 33C20
KW - 33C45
KW - Bessel polynomial
KW - C33
KW - Charlier polynomial
KW - continuous Hahn polynomial
KW - differentiation
KW - Gegenbauer polynomial
KW - Hahn polynomial
KW - hypergeometric functions
KW - Jacobi polynomial
KW - Krawtchouk polynomial
KW - Laguerre polynomial
KW - Legendre function
KW - Meixner polynomial
KW - Special functions
U2 - 10.1080/10652469.2018.1504042
DO - 10.1080/10652469.2018.1504042
M3 - Article
VL - 29
SP - 852
EP - 865
JO - Integral Transforms and Special Functions
JF - Integral Transforms and Special Functions
SN - 1065-2469
IS - 11
ER -
TY - JOUR
T1 - Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time
AU - Paunonen, Lassi
AU - Seifert, David
PY - 2018/6
Y1 - 2018/6
N2 - This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time.
AB - This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time.
KW - $C_0$-semigroups
KW - Asymptotic behaviour
KW - Power-boundeness
KW - Rates of convergence
KW - Recurrence relations
KW - Spectral theory
KW - System
U2 - 10.1007/s10884-016-9547-1
DO - 10.1007/s10884-016-9547-1
M3 - Article
VL - 30
SP - 433
EP - 445
JO - JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
JF - JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
SN - 1040-7294
IS - 2
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 - GEN
T1 - Output Regulation of Infinite-Dimensional Time-Delay Systems
AU - Paunonen, Lassi
PY - 2017/5
Y1 - 2017/5
N2 - We study output tracking and disturbance rejection for linear infinite-dimensional time-delay systems using dynamic error feedback controllers with state delays. The class of systems covers many partial differential equations with state, input, and output delays. As our main result we characterize the solvability of the control problem in terms of the solvability of the associated regulator equations.
AB - We study output tracking and disturbance rejection for linear infinite-dimensional time-delay systems using dynamic error feedback controllers with state delays. The class of systems covers many partial differential equations with state, input, and output delays. As our main result we characterize the solvability of the control problem in terms of the solvability of the associated regulator equations.
U2 - 10.23919/ACC.2017.7963438
DO - 10.23919/ACC.2017.7963438
M3 - Conference contribution
T3 - Proceedings of the American Control Conference
SP - 3189
EP - 3193
BT - American Control Conference (ACC), 2017
PB - IEEE
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 - Asymptotic Behaviour of Platoon Systems
AU - Paunonen, Lassi
AU - Seifert, David
PY - 2016/7
Y1 - 2016/7
N2 - In this paper we study the asymptotic behaviour of various platoon-type systems using the general theory developed by the authors in a recent article. The aim is to steer an infinite number of vehicles towards a target configuration in which each vehicle has a prescribed separation from its neighbour and all vehicles are moving at a given velocity. More specifically, we study systems in which state feedback is possible, systems in which observer-based dynamic output feedback is required, and also a situation in which the control objective is modified to allow the target separations to depend on the vehicles’ velocities. We show that in the first and third cases the objective can be achieved, but that in the second case the system is unstable in the sense that the associated semigroup is not uniformly bounded. We also present some quantified results concerning the rate of convergence of the platoon to its limit state when the limit exists.
AB - In this paper we study the asymptotic behaviour of various platoon-type systems using the general theory developed by the authors in a recent article. The aim is to steer an infinite number of vehicles towards a target configuration in which each vehicle has a prescribed separation from its neighbour and all vehicles are moving at a given velocity. More specifically, we study systems in which state feedback is possible, systems in which observer-based dynamic output feedback is required, and also a situation in which the control objective is modified to allow the target separations to depend on the vehicles’ velocities. We show that in the first and third cases the objective can be achieved, but that in the second case the system is unstable in the sense that the associated semigroup is not uniformly bounded. We also present some quantified results concerning the rate of convergence of the platoon to its limit state when the limit exists.
KW - Vehicle platoon
KW - ordinary differential equations
KW - asymptotic behaviour
KW - state feedback
KW - rates of convergence
M3 - Conference contribution
SP - 830
EP - 836
BT - Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems
PB - University of Minnesota
ER -
TY - JOUR
T1 - Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel
AU - Sandev, Trifce
AU - Chechkin, Aleksei
AU - Kantz, Holger
AU - Metzler, Ralf
PY - 2015/8/1
Y1 - 2015/8/1
N2 - We consider anomalous stochastic processes based on the renewal continuous time random walk model with different forms for the probability density of waiting times between individual jumps. In the corresponding continuum limit we derive the generalized diffusion and Fokker-Planck- Smoluchowski equations with the corresponding memory kernels. We calculate the qth order moments in the unbiased and biased cases, and demonstrate that the generalized Einstein relation for the considered dynamics remains valid. The relaxation of modes in the case of an external harmonic potential and the convergence of the mean squared displacement to the thermal plateau are analyzed.
AB - We consider anomalous stochastic processes based on the renewal continuous time random walk model with different forms for the probability density of waiting times between individual jumps. In the corresponding continuum limit we derive the generalized diffusion and Fokker-Planck- Smoluchowski equations with the corresponding memory kernels. We calculate the qth order moments in the unbiased and biased cases, and demonstrate that the generalized Einstein relation for the considered dynamics remains valid. The relaxation of modes in the case of an external harmonic potential and the convergence of the mean squared displacement to the thermal plateau are analyzed.
KW - anomalous diffusion
KW - continuous time random walk (CTRW)
KW - Fokker- Planck-Smoluchowski equation
KW - Mittag-Leffler functions
KW - multi-scaling
UR - http://www.scopus.com/inward/record.url?scp=84939133175&partnerID=8YFLogxK
U2 - 10.1515/fca-2015-0059
DO - 10.1515/fca-2015-0059
M3 - Article
VL - 18
SP - 1006
EP - 1038
JO - Fractional Calculus and Applied Analysis
JF - Fractional Calculus and Applied Analysis
SN - 1311-0454
IS - 4
ER -
TY - JOUR
T1 - A general framework for island systems
AU - Foldes, S.
AU - Horváth, Eszter K.
AU - Radeleczki, Sándor
AU - Waldhauser, Tamás
PY - 2015
Y1 - 2015
N2 - The notion of an island defined on a rectangular board is an elementary combinatorial concept that occurred first in [3]. Results of [3] were starting points for investigations exploring several variations and various aspects of this notion. In this paper we introduce a general framework for islands that subsumes all earlier studied concepts of islands on finite boards, moreover we show that the prime implicants of a Boolean function, the formal concepts of a formal context, convex subgraphs of a simple graph, and some particular subsets of a projective plane also fit into this framework. We axiomatize those cases where islands have the property of being pairwise comparable or disjoint, or they are distant, introducing the notion of a connective island domain and of a proximity domain, respectively. In the general case the maximal systems of islands are characterised by using the concept of an admissible system. We also characterise all possible island systems in the case of connective island domains and proximity domains.
AB - The notion of an island defined on a rectangular board is an elementary combinatorial concept that occurred first in [3]. Results of [3] were starting points for investigations exploring several variations and various aspects of this notion. In this paper we introduce a general framework for islands that subsumes all earlier studied concepts of islands on finite boards, moreover we show that the prime implicants of a Boolean function, the formal concepts of a formal context, convex subgraphs of a simple graph, and some particular subsets of a projective plane also fit into this framework. We axiomatize those cases where islands have the property of being pairwise comparable or disjoint, or they are distant, introducing the notion of a connective island domain and of a proximity domain, respectively. In the general case the maximal systems of islands are characterised by using the concept of an admissible system. We also characterise all possible island systems in the case of connective island domains and proximity domains.
KW - Admissible system
KW - CD-independent and CDW-independent sets
KW - Connected subgraph
KW - Convex subgraph
KW - Distant system
KW - Formal concept
KW - Height function
KW - Island domain
KW - Island system
KW - Point-to-set proximity relation
KW - Prime implicant
KW - Projective plane
KW - Proximity domain
UR - http://www.scopus.com/inward/record.url?scp=84938827353&partnerID=8YFLogxK
U2 - 10.14232/actasm-013-279-7
DO - 10.14232/actasm-013-279-7
M3 - Article
VL - 81
SP - 3
EP - 24
JO - Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum
JF - Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum
SN - 0001-6969
IS - 1-2
ER -
TY - CHAP
T1 - On Robustness of Strongly Stable Semigroups with Spectrum on iR
AU - Paunonen, Lassi
PY - 2015
Y1 - 2015
N2 - We study the robustness properties of strong stability of a strongly continuous semigroup on a Hilbert space. We concentrate on a situation where the generator of the unperturbed semigroup has a finite spectral point on the imaginary axis and the resolvent operator is polynomially bounded elsewhere on the imaginary axis. As our main result we present conditions for preservation of the strong stability of the semigroup under bounded perturbations.
AB - We study the robustness properties of strong stability of a strongly continuous semigroup on a Hilbert space. We concentrate on a situation where the generator of the unperturbed semigroup has a finite spectral point on the imaginary axis and the resolvent operator is polynomially bounded elsewhere on the imaginary axis. As our main result we present conditions for preservation of the strong stability of the semigroup under bounded perturbations.
KW - Strongly Continuous Semigroup
KW - Functional Analysis
U2 - 10.1007/978-3-319-12145-1
DO - 10.1007/978-3-319-12145-1
M3 - Chapter
SN - 978-3-319-12144-4
T3 - Springer Proceedings in Mathematics & Statistics
SP - 105
EP - 121
BT - Semigroups of Operators -Theory and Applications
A2 - Banasiak, Jacek
A2 - Bobrowski, Adam
A2 - Lachowicz, Mirosław
PB - Springer International Publishing
ER -
TY - GEN
T1 - On Robust Output Regulation for Continuous-Time Periodic Systems
AU - Paunonen, Lassi
PY - 2015
Y1 - 2015
N2 - We construct a controller to solve robust output tracking problem for a stable linear continuous-time periodic system on a finite-dimensional space. We begin by transforming the time-dependent plant to a time-invariant discrete-time system using the ``lifting technique''. The controller is then designed to achieve robust output tracking for the lifted system. We show that an exact solution to the control problem for a continuous-time periodic system necessarily requires an error feedback controller with an infinite-dimensional internal model. The results are illustrated with an example where robust output tracking is considered for a stable periodic scalar system.
AB - We construct a controller to solve robust output tracking problem for a stable linear continuous-time periodic system on a finite-dimensional space. We begin by transforming the time-dependent plant to a time-invariant discrete-time system using the ``lifting technique''. The controller is then designed to achieve robust output tracking for the lifted system. We show that an exact solution to the control problem for a continuous-time periodic system necessarily requires an error feedback controller with an infinite-dimensional internal model. The results are illustrated with an example where robust output tracking is considered for a stable periodic scalar system.
U2 - 10.1137/1.9781611974072.7
DO - 10.1137/1.9781611974072.7
M3 - Conference contribution
BT - 2015 Proceedings of the SIAM Conference on Control and its Applications
PB - SIAM, Society for Industrial and Applied Mathematics
ER -