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This class of digraphs represent ... [more ▼]In this research note we introduce St-Nicolas graphs, i.e. circulant digraphs showing exactly n maximal independent sets, isomorph under the digraph’s automorphisms group. This class of digraphs represent a generalisation of Andrásfai graphs with interesting links to finite group theory. [less ▲]Detailed reference viewed: 15 (1 UL) On means and ends: Goal orientation and goal focus across adulthoodFreund, Alexandra M.; Hennecke, Marie; Mustafic, Maida in Ryan, R. M. (Ed.) The Oxford handbook of human motivation (2012)Personal goals guide behavior toward a desired outcome, motivate behavior over time and across situations, provide direction and meaning, and contribute to the acquisition of skills and subjective well ... [more ▼]Personal goals guide behavior toward a desired outcome, motivate behavior over time and across situations, provide direction and meaning, and contribute to the acquisition of skills and subjective well-being. The adaptiveness of goals, however, might vary with dimensions such as their orientation toward the achievement of gains, maintenance of functioning, or the avoidance of losses. We argue that goal orientation is most adaptive when it corresponds to the availability of resources and the ubiquity of losses. In line with this argument, younger adults show a predominant orientation toward the promotion of gains, whereas goal orientation shifts toward maintenance and avoidance of loss across adulthood. This shift in goal orientation seems adaptive both regarding subjective well-being as well as engagement in goal pursuit. A second goal dimension that has been largely overlooked in the literature is the cognitive representation of goal pursuit primarily in terms of its means (i.e., process focus) or its ends (i.e., outcome focus). This chapter investigates the antecedents and consequences of goal focus. In particular, it highlights the importance of factors related to chronological age (i.e., the availability of resources, future time perspective, goal orientation, motivational phase) for the preference for and adaptiveness of an outcome or process focus. Finally, we posit that a process focus leads to more adaptive behavioral and affective reactions when people encounter failure during goal pursuit. [less ▲]Detailed reference viewed: 81 (17 UL) On measuring and testing the ordinal correlation between bipolar outranking relationsBisdorff, Raymond Scientific Conference (2012, November 15)Detailed reference viewed: 23 (4 UL) On microfoundations of the cityPicard, Pierre M. ; Tabuchi, Takatoshiin Journal of Economic Theory (2013), 148(6), 2561-2582This paper considers the spatial structure of a city subject to final demand and vertical linkages. Individuals consume differentiated goods (or services) and firms purchase differentiated inputs (or ... [more ▼]This paper considers the spatial structure of a city subject to final demand and vertical linkages. Individuals consume differentiated goods (or services) and firms purchase differentiated inputs (or services) in product (or service) markets where firms compete under monopolistic competition. Workers rent their residential lots in an urban land market and contribute to the production of differentiated goods and inputs. We show that firms and workers co-agglomerate and endogenously form a city. We characterize and discuss the spatial distribution of firms and consumers in such cities on one- and two-dimensional spaces. We show that final demand and vertical linkages raise the urban density and reduce the city spread. [less ▲]Detailed reference viewed: 183 (121 UL) On minimal realisations of dynamical structure functionsYuan, Ye; Glover, Keith; Goncalves, Jorge in Automatica (2015), 55Motivated by the fact that transfer functions do not contain structural information about networks, dynamical structure functions were introduced to capture causal relationships between measured nodes in ... [more ▼]Motivated by the fact that transfer functions do not contain structural information about networks, dynamical structure functions were introduced to capture causal relationships between measured nodes in networks. From the dynamical structure functions, a) we show that the actual number of hidden states can be larger than the number of hidden states estimated from the corresponding transfer function; b) we can obtain partial information about the true state-space equation, which cannot in general be obtained from the transfer function. Based on these properties, this paper proposes algorithms to find minimal realisations for a given dynamical structure function. This helps to estimate the minimal number of hidden states, to better understand the complexity of the network, and to identify potential targets for new measurements. [less ▲]Detailed reference viewed: 147 (15 UL) On mod $p$ representations which are defined over $\Bbb F_p$: IIKilford, L. J. P.; Wiese, Gabor in Glasgow Mathematical Journal (2010), 52(2), 391--400The behaviour of Hecke polynomials modulo p has been the subject of some study. In this note we show that, if p is a prime, the set of integers N such that the Hecke polynomials T^{N,\chi}_{l,k} for all ... [more ▼]The behaviour of Hecke polynomials modulo p has been the subject of some study. In this note we show that, if p is a prime, the set of integers N such that the Hecke polynomials T^{N,\chi}_{l,k} for all primes l, all weights k>1 and all characters \chi taking values in {+1,-1} splits completely modulo p has density 0, unconditionally for p=2 and under the Cohen-Lenstra heuristics for odd p. The method of proof is based on the construction of suitable dihedral modular forms. [less ▲]Detailed reference viewed: 33 (0 UL) On Modelling Communication in Ubiquitous Computing Systems using Algebraic Higher Order NetsGottmann, Susann ; Nachtigall, Nico ; Hoffmann, Kathrinin Electronic Communications of the EASST (2012)Ubiquitous computing systems (UCSs) are designed to participate almost imperceptibly in everyday life. To ensure a solid operation, a UCS heavily depends on a reliable and efficient communication between ... [more ▼]Ubiquitous computing systems (UCSs) are designed to participate almost imperceptibly in everyday life. To ensure a solid operation, a UCS heavily depends on a reliable and efficient communication between its distributed computing components. Moreover components can join and leave the system at any time. In order to guarantee high quality systems, the use of models is inevitable especially at an early stage of the development process where models are the only possibility to address a system which does not yet exist in reality. Petri nets and graph transformation systems are established, theoretically well-founded concepts for modelling and analysing complex systems. This paper presents a formal approach for modelling core aspects of the communication in UCSs by using Algebraic Higher Order Nets with Individual Tokens and graph transformation. The approach is suitable to cover the different aspects of communication and enables the analysis of specific properties. The approach and its suitability are illustrated based on a running example. The easibility of embedding the approach in a broader context of modelling is demonstrated in applying it to a real world system: the Living Place Hamburg. [less ▲]Detailed reference viewed: 58 (8 UL) On modular decompositions of system signaturesMarichal, Jean-Luc ; Mathonet, Pierre; Spizzichino, Fabioin Journal of Multivariate Analysis (2015), 134Considering a semicoherent system made up of $n$ components having i.i.d. continuous lifetimes, Samaniego defined its structural signature as the $n$-tuple whose $k$-th coordinate is the probability that ... [more ▼]Considering a semicoherent system made up of $n$ components having i.i.d. continuous lifetimes, Samaniego defined its structural signature as the $n$-tuple whose $k$-th coordinate is the probability that the $k$-th component failure causes the system to fail. This $n$-tuple, which depends only on the structure of the system and not on the distribution of the component lifetimes, is a very useful tool in the theoretical analysis of coherent systems. It was shown in two independent recent papers how the structural signature of a system partitioned into two disjoint modules can be computed from the signatures of these modules. In this work we consider the general case of a system partitioned into an arbitrary number of disjoint modules organized in an arbitrary way and we provide a general formula for the signature of the system in terms of the signatures of the modules. The concept of signature was recently extended to the general case of semicoherent systems whose components may have dependent lifetimes. The same definition for the $n$-tuple gives rise to the probability signature, which may depend on both the structure of the system and the probability distribution of the component lifetimes. In this general setting, we show how under a natural condition on the distribution of the lifetimes, the probability signature of the system can be expressed in terms of the probability signatures of the modules. We finally discuss a few situations where this condition holds in the non-i.i.d. and nonexchangeable cases and provide some applications of the main results. [less ▲]Detailed reference viewed: 109 (9 UL) On modular forms and the inverse Galois problemDieulefait, Luis; Wiese, Gabor in Transactions of the American Mathematical Society (2011), 363(9), 4569--4584In this article new cases of the Inverse Galois Problem are established. The main result is that for a fixed integer n, there is a positive density set of primes p such that PSL_2(F_{p^n}) occurs as the ... [more ▼]In this article new cases of the Inverse Galois Problem are established. The main result is that for a fixed integer n, there is a positive density set of primes p such that PSL_2(F_{p^n}) occurs as the Galois group of some finite extension of the rational numbers. These groups are obtained as projective images of residual modular Galois representations. Moreover, families of modular forms are constructed such that the images of all their residual Galois representations are as large as a priori possible. Both results essentially use Khare's and Wintenberger's notion of good-dihedral primes. Particular care is taken in order to exclude nontrivial inner twists. [less ▲]Detailed reference viewed: 82 (2 UL) On modular Galois representations modulo prime powersWiese, Gabor Presentation (2012, May 30)Detailed reference viewed: 42 (1 UL) On modular Galois representations modulo prime powersChen, Imin; Kiming, Ian; Wiese, Gabor in International Journal of Number Theory (2013), 9(1), 91--113We study modular Galois representations mod p^m. We show that there are three progressively weaker notions of modularity for a Galois representation mod p^m: we have named these strongly', weakly', and ... [more ▼]We study modular Galois representations mod p^m. We show that there are three progressively weaker notions of modularity for a Galois representation mod p^m: we have named these strongly', weakly', and dc-weakly' modular. Here, dc' stands for divided congruence' in the sense of Katz and Hida. These notions of modularity are relative to a fixed level M. Using results of Hida we display a stripping-of-powers of p away from the level' type of result: A mod p^m strongly modular representation of some level Np^r is always dc-weakly modular of level N (here, N is a natural number not divisible by p). We also study eigenforms mod p^m corresponding to the above three notions. Assuming residual irreducibility, we utilize a theorem of Carayol to show that one can attach a Galois representation mod p^m to any `dc-weak' eigenform, and hence to any eigenform mod p^m in any of the three senses. We show that the three notions of modularity coincide when m=1 (as well as in other, particular cases), but not in general. [less ▲]Detailed reference viewed: 116 (4 UL) On modular symbols and the cohomology of Hecke triangle surfacesWiese, Gabor in International Journal of Number Theory (2009), 5(1), 89--108The aim of this article is to give a concise algebraic treatment of the modular symbols formalism, generalised from modular curves to Hecke triangle surfaces. A sketch is included of how the modular ... [more ▼]The aim of this article is to give a concise algebraic treatment of the modular symbols formalism, generalised from modular curves to Hecke triangle surfaces. A sketch is included of how the modular symbols formalism gives rise to the standard algorithms for the computation of holomorphic modular forms. Precise and explicit connections are established to the cohomology of Hecke triangle surfaces and group cohomology. In all the note a general commutative ring is used as coefficient ring in view of applications to the computation of modular forms over rings different from the complex numbers. [less ▲]Detailed reference viewed: 97 (0 UL) On monopolistic competition and optimal product diversity: workers' rents also matterPicard, Pierre M. ; Toulemonde, Ericin Canadian Journal of Economics (2009), 42(4), 1347-1360In the Dixit-Stiglitz model of monopolistic competition, entry of rms is socially too small. Other authors have shown that excess entry is also a possibility with other preferences for diversity. We show ... [more ▼]In the Dixit-Stiglitz model of monopolistic competition, entry of rms is socially too small. Other authors have shown that excess entry is also a possibility with other preferences for diversity. We show that workers rents also contribute to explain excess entry through a general equilibrium mechanism. Larger wages indeed raises the aggregate earnings and rms sales and pro ts, which entices too many rms to enter. We discuss the possibility of over-provision of varieties by comparing the equilibrium to unconstrained and constrained social optima and to other regulatory framework where wages are not controlled. [less ▲]Detailed reference viewed: 68 (5 UL) On Mpc-structures and symplectic Dirac operatorsCahen, Michel; Gutt, Simone; La Fuente-Gravy, Laurent et alin Journal of Geometry and Physics (2014), 86We prove that the kernels of the restrictions of the symplectic Dirac operator and one of the two symplectic Dirac–Dolbeault operators on natural sub-bundles of polynomial valued spinor fields are finite ... [more ▼]We prove that the kernels of the restrictions of the symplectic Dirac operator and one of the two symplectic Dirac–Dolbeault operators on natural sub-bundles of polynomial valued spinor fields are finite dimensional on a compact symplectic manifold. We compute these kernels explicitly for complex projective spaces and show that the remaining Dirac–Dolbeault operator has infinite dimensional kernels on these finite rank sub-bundles. We construct injections of subgroups of the symplectic group (the pseudo-unitary group and the stabiliser of a Lagrangian subspace) in the Mpc group and classify G-invariant Mpc-structures on symplectic manifolds with a G-action. We prove a variant of Parthasarathy’s formula for the commutator of two symplectic Dirac-type operators on general symmetric symplectic spaces. [less ▲]Detailed reference viewed: 15 (0 UL) On Multifaceted Commonality. Theories of Social Pedagogy in GermanySandermann, Philipp; Neumann, Sascha in International Journal of Social Pedagogy (2014), 3(1), 15-29This paper makes an attempt to interpret the German debate on social pedagogy as a multifaceted perspective that nonetheless shows a striking commonality. To exemplify this, we intentionally focus on ... [more ▼]This paper makes an attempt to interpret the German debate on social pedagogy as a multifaceted perspective that nonetheless shows a striking commonality. To exemplify this, we intentionally focus on dominant theories of social pedagogy in Germany, which declaredly aim to directly answer the question of what social pedagogy is. However, to contribute to a clearer understanding of social pedagogy as a theoretical phenomenon, it is not sufficient to only describe these theories and the various ideas of social pedagogy they generate. Instead, it is essential to deconstruct how exactly these theories objectify their numerous assumptions on social pedagogy. We will therefore argue that it is worthwhile to focus not too narrowly on what dominant theories of social pedagogy in Germany objectify as social pedagogy. Instead, we suggest a careful analysis of how social pedagogy is commonly being objectified. Our hypothesis is that prominent theories of social pedagogy in Germany reify social pedagogy by using a distinct ontological mode of objectification. This mode we see as a common structure, regardless of the different objects of social pedagogy that the respective approaches end up with. Beyond mere critique, we intend to also explain this mode at the end of our paper, and raise the question whether it might point to a broader concept of how theories of social pedagogy and social work are usually being generated in Germany and beyond. [less ▲]Detailed reference viewed: 114 (4 UL) On multistability of delayed genetic regulatory networks with multivariable regulation functionsPan, Wei ; Wang, Z.; Gao, H. et alin Mathematical Biosciences (2010), 228(1), 100-109Many genetic regulatory networks (GRNs) have the capacity to reach different stable states. This capacity is defined as multistability which is an important regulation mechanism. Multiple time delays and ... [more ▼]Many genetic regulatory networks (GRNs) have the capacity to reach different stable states. This capacity is defined as multistability which is an important regulation mechanism. Multiple time delays and multivariable regulation functions are usually inevitable in such GRNs. In this paper, multistability of GRNs is analyzed by applying the control theory and mathematical tools. This study is to provide a theoretical tool to facilitate the design of synthetic gene circuit with multistability in the perspective of control theory. By transforming such GRNs into a new and uniform mathematical formulation, we put forward a general sector-like regulation function that is capable of quantifying the regulation effects in a more precise way. By resorting to up-to-date techniques, a novel Lyapunov–Krasovskii functional (LKF) is introduced for achieving delay dependence to ensure less conservatism. New conditions are then proposed to ensure the multistability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the delays. Our multistability conditions are applicable to several frequently used regulation functions especially the multivariable ones. Two examples are employed to illustrate the applicability and usefulness of the developed theoretical results. [less ▲]Detailed reference viewed: 56 (0 UL) On n-ary Lie Algebras of Type (r, l)Vishnyakova, Elizaveta in Kielanowski, Piotr; Bieliavsky, Pierre; Odzijewicz, Anatol (Eds.) et al Geometric Methods in Physics (2015)These notes are devoted to the multiple generalization of a Lie algebra introduced by A.M. Vinogradov and M.M. Vinogradov. We compare definitions of such algebras in the usual and invariant case ... [more ▼]These notes are devoted to the multiple generalization of a Lie algebra introduced by A.M. Vinogradov and M.M. Vinogradov. We compare definitions of such algebras in the usual and invariant case. Furthermore, we show that there are no simple n-ary Lie algebras of type (n - 1, l) for l > 0. [less ▲]Detailed reference viewed: 22 (0 UL) On Nature-based tourismOlafsdottir, Gunnthora in Tourist Studies (2013), 13(2), 127-138Detailed reference viewed: 66 (0 UL) On non-parametric models for detecting outages in the mobile networkFalk, Eric ; Camino, Ramiro Daniel ; State, Radu et alin Integrated Network and Service Management 2017 (2017, May)The wireless/cellular communications network is composed of a complex set of interconnected computation units that form the mobile core network. The mobile core network is engineered to be fault tolerant ... [more ▼]The wireless/cellular communications network is composed of a complex set of interconnected computation units that form the mobile core network. The mobile core network is engineered to be fault tolerant and redundant; small errors that manifest themselves in the network are usually resolved automatically. However, some errors remain latent, and if discovered early enough can provide warnings to the network operator about a pending service outage. For mobile network operators, it is of high interest to detect these minor anomalies near real-time. In this work we use performance data from a 4G-LTE network carrier to train two parameter-free models. A first model relies on isolation forests, and the second is histogram based. The trained models represent the data characteristics for normal periods; new data is matched against the trained models to classify the new time period as being normal or abnormal. We show that the proposed methods can gauge the mobile network state with more subtlety than standard success/failure thresholds used in real-world networks today. [less ▲]Detailed reference viewed: 87 (8 UL) On noncommutative deformations, cohomology of color-commutative algebras and formal smoothnessGohr, Aron Samuel Doctoral thesis (2009)The main topic under study in the present work is the deformation theory of color algebras. Color algebras are generalized analogues of associative superalgebras, where the underlying grading can be over ... [more ▼]The main topic under study in the present work is the deformation theory of color algebras. Color algebras are generalized analogues of associative superalgebras, where the underlying grading can be over an arbitrary abelian group and the Koszul sign is replaced by a bicharacter from the group into the base ring. A special case of particular interest are color-commutative algebras, which satisfy a commutation identity similar to (but much more general than) supercommutative algebras. Examples of color-commutative algebras include commutative and supercommutative superalgebras, the quaternions and para-quaternions, full matrix algebras over suitable base rings, Clifford algebras, and group rings over certain nonabelian groups. In the present work, Gerstenhaber-type formal deformations of these algebras are studied. In doing so, we extend previous work by Scheunert and provide a different approach to noncommutative deformation theory as introduced by Pinczon and Nadaud. In preparation of developing deformation theory for color algebras, we adapt a number of tools from ungraded Hochschild theory to our setting: among them, we derive an adapted Ext-functor, a color Gerstenhaber bracket, twisted graded versions of pre-Lie-algebras and pre-Lie-systems and colored analogs of the classical results linking infinitesimal deformations and obstructions to extension of deformations to second and third Hochschild cohomology. Additionally, we discuss the impact of some decisions in the construction of the trivial deformation object (color power series rings of given degree) on the resulting deformation theory. Finally, color-commutative deformations of color-commutative algebras are discussed and a suitable version of Harrison cohomology is developed. Also, the problem of classifying the color-commutative structures compatible with a given ungraded algebra is discussed and one nontrivial example is studied in detail. In support of all of these efforts, a number of structure theorems about color-commutative algebras are shown. [less ▲]Detailed reference viewed: 111 (7 UL)