@article{9815821bfb1e40b6aea51a94ede090f7, title = "A graph theoretic approach to construct desired cryptographic boolean functions", abstract = "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.", keywords = "Algebraic immunity, Boolean functions, Cayley graphs, Non-linearity, Walsh spectrum", author = "Modjtaba Ghorbani and Matthias Dehmer and Vahid Taghvayi-Yazdelli and Frank Emmert-Streib", year = "2019", month = "6", day = "1", doi = "10.3390/axioms8020040", language = "English", volume = "8", journal = "Axioms", issn = "2075-1680", publisher = "MDPI", number = "2", }
@article{5a51a89709184a2ea5674a77fc0a0dbb, title = "Asymptotics for periodic systems", abstract = "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.", keywords = "Damped wave equation, Evolution family, Non-autonomous system, Periodic, Rates of convergence, Ritt operator", author = "Lassi Paunonen and David Seifert", year = "2019", month = "5", doi = "10.1016/j.jde.2018.11.028", language = "English", volume = "266", pages = "7152--7172", journal = "Journal of Differential Equations", issn = "0022-0396", publisher = "Elsevier", number = "11", }
@article{9e706c1eb0574a70b5db79e4ff273a66, title = "A note on distance-based entropy of dendrimers", abstract = "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.", keywords = "Dendrimer, Graph entropy, Vertex eccentricity", author = "Modjtaba Ghorbani and Matthias Dehmer and Samaneh Zangi and Abbe Mowshowitz and Frank Emmert-Streib", year = "2019", doi = "10.3390/axioms8030098", language = "English", volume = "8", journal = "Axioms", issn = "2075-1680", publisher = "MDPI", number = "3", }
@article{a156383f553e4f85babf7fe95d58d133, title = "Optimal energy decay for the wave-heat system on a rectangular domain", abstract = "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.", keywords = "C -semigroups, Coupled, Energy, Heat equation, Rates of decay, Rectangular domain, Resolvent estimates, Wave equation", author = "Charles Batty and Lassi Paunonen and David Seifert", year = "2019", doi = "10.1137/18M1195796", language = "English", volume = "51", pages = "808--819", journal = "SIAM JOURNAL ON MATHEMATICAL ANALYSIS", issn = "0036-1410", publisher = "Society for Industrial and Applied Mathematics", number = "2", }
@article{8608d4d0e2e04973adab0f206e5f09d8, title = "On derivatives of hypergeometric functions and classical polynomials with respect to parameters", abstract = "Closed expressions are obtained for derivatives of symbolic order with respect to parameters for the hypergeometric functions, Laguerre, Gegenbauer, Jacobi and some other polynomial.", keywords = "33C20, 33C45, Bessel polynomial, C33, Charlier polynomial, continuous Hahn polynomial, differentiation, Gegenbauer polynomial, Hahn polynomial, hypergeometric functions, Jacobi polynomial, Krawtchouk polynomial, Laguerre polynomial, Legendre function, Meixner polynomial, Special functions", author = "Sofotasios, {P. C.} and Brychkov, {Yu A.}", year = "2018", month = "11", day = "2", doi = "10.1080/10652469.2018.1504042", language = "English", volume = "29", pages = "852--865", journal = "Integral Transforms and Special Functions", issn = "1065-2469", publisher = "Taylor & Francis", number = "11", }
@article{1a312ea3e262469f9550e28dd6385c91, title = "Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time", abstract = "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.", keywords = "$C_0$-semigroups, Asymptotic behaviour, Power-boundeness, Rates of convergence, Recurrence relations, Spectral theory, System", author = "Lassi Paunonen and David Seifert", year = "2018", month = "6", doi = "10.1007/s10884-016-9547-1", language = "English", volume = "30", pages = "433--445", journal = "JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS", issn = "1040-7294", publisher = "Springer Verlag", number = "2", }
@article{f350eecd75ee4f83ad40c9f3ca9ba618, title = "Toward measuring network aesthetics based on symmetry", abstract = "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.", keywords = "Aesthetical theory, Aesthetics, Entropy, Network aesthetics, Networks", author = "Zengqiang Chen and Matthias Dehmer and Frank Emmert-Streib and Abbe Mowshowitz and Yongtang Shi", year = "2017", month = "6", day = "1", doi = "10.3390/axioms6020012", language = "English", volume = "6", journal = "Axioms", issn = "2075-1680", publisher = "MDPI", number = "2", }
@inproceedings{b533dd1628de46cf8cc3b55f17d09dc6, title = "Output Regulation of Infinite-Dimensional Time-Delay Systems", abstract = "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.", author = "Lassi Paunonen", year = "2017", month = "5", doi = "10.23919/ACC.2017.7963438", language = "English", series = "Proceedings of the American Control Conference", publisher = "IEEE", pages = "3189--3193", booktitle = "American Control Conference (ACC), 2017", }
@article{b82d3e0b038a4b38a1b1768502f4e2a7, title = "Integral kernels for k-hypermonogenic functions", abstract = "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.", keywords = "Cauchy integral formula, Clifford algebra, hyperbolic Laplace–Beltrami, k-hyperbolic harmonic, k-hypermonogenic", author = "Vesa Vuojamo and Sirkka-Liisa Eriksson", note = "EXT={"}Eriksson, Sirkka-Liisa{"}", year = "2017", doi = "10.1080/17476933.2016.1250402", language = "English", volume = "62", pages = "1--12", journal = "Complex Variables and Elliptic Equations", issn = "1747-6933", publisher = "Taylor & Francis", number = "9", }
@inproceedings{ff44a5a442cc4b8bad3100093fab1400, title = "Asymptotic Behaviour of Platoon Systems", abstract = "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.", keywords = "Vehicle platoon, ordinary differential equations, asymptotic behaviour, state feedback, rates of convergence", author = "Lassi Paunonen and David Seifert", year = "2016", month = "7", language = "English", pages = "830--836", booktitle = "Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems", publisher = "University of Minnesota", address = "United States", }
@article{edefde71dbed4e74bafc3ff080cfd2e0, title = "Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel", abstract = "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.", keywords = "anomalous diffusion, continuous time random walk (CTRW), Fokker- Planck-Smoluchowski equation, Mittag-Leffler functions, multi-scaling", author = "Trifce Sandev and Aleksei Chechkin and Holger Kantz and Ralf Metzler", year = "2015", month = "8", day = "1", doi = "10.1515/fca-2015-0059", language = "English", volume = "18", pages = "1006--1038", journal = "Fractional Calculus and Applied Analysis", issn = "1311-0454", publisher = "Springer Science + Business Media", number = "4", }
@article{79867c2a35fe406aabf309b7c9899a62, title = "A general framework for island systems", abstract = "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.", keywords = "Admissible system, CD-independent and CDW-independent sets, Connected subgraph, Convex subgraph, Distant system, Formal concept, Height function, Island domain, Island system, Point-to-set proximity relation, Prime implicant, Projective plane, Proximity domain", author = "S. Foldes and Horv{\'a}th, {Eszter K.} and S{\'a}ndor Radeleczki and Tam{\'a}s Waldhauser", year = "2015", doi = "10.14232/actasm-013-279-7", language = "English", volume = "81", pages = "3--24", journal = "Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum", issn = "0001-6969", publisher = "University of Szeged", number = "1-2", }
@inbook{05da41f175614320baf6abbedbedbb15, title = "On Robustness of Strongly Stable Semigroups with Spectrum on iR", abstract = "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.", keywords = "Strongly Continuous Semigroup, Functional Analysis", author = "Lassi Paunonen", year = "2015", doi = "10.1007/978-3-319-12145-1", language = "English", isbn = "978-3-319-12144-4", series = "Springer Proceedings in Mathematics & Statistics", publisher = "Springer International Publishing", pages = "105--121", editor = "Jacek Banasiak and Adam Bobrowski and Mirosław Lachowicz", booktitle = "Semigroups of Operators -Theory and Applications", }
@inproceedings{c2fa4b539a30465f8d348d5f5c2778a9, title = "On Robust Output Regulation for Continuous-Time Periodic Systems", abstract = "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.", author = "Lassi Paunonen", year = "2015", doi = "10.1137/1.9781611974072.7", language = "English", booktitle = "2015 Proceedings of the SIAM Conference on Control and its Applications", publisher = "SIAM, Society for Industrial and Applied Mathematics", }