Non-commutative symbolic coding

We give a non-commutative generalization of classical symbolic coding in the presence of a synchronizing word. This is done by a scattering theoretical approach. Classically, the existence of a synchronizing word turns out to be equivalent to asymptotic completeness of the corresponding Markov process. A criterion for asymptotic completeness in general is provided by the regularity of an associated extended transition operator. Commutative and non-commutative examples are analysed.

The disk-percolation model on graphs

We study a long-range percolation model whose dynamics describe the spreading of an infection on an infinite graph. We obtain a sufficient condition for phase transition and prove all upper bound for the critical parameter of spherically symmetric trees. (C) 2008 Elsevier B.V. All rights reserved.

Turning collegial governance on its head : symbolic violence, hegemony and the academic board

This article draws on Bourdieu’s theorisation of domination and Gramsci’s notions of hegemony within the context of a larger empirical study of Australian university academic governance, and of academic boards (also known as academic senates or faculty senates) in particular. Reporting data that suggest a continued but radically altered form of collegial governance in which hegemony is exercised by management rather than by the professor, it theorises the domination of academic boards within western democratic universities. However, traditional collegial governance is also dependent upon a community of scholars, a role historically played by the academic board. In view of the suggested transition in collegial governance and the resultant convergence of academic work and management, the article concludes with questions about whether academic boards can continue to serve as communities of scholars in future.

Valuing practice over theory: How beginning teachers re-orient their practice in the transition from the university to the workplace

This paper is about the experiences of beginning teachers in turning theory learned in universities into practice in the workplace. The research is situated in the context of a pre-service teacher education programme that explicitly and deliberately seeks to bridge the theory-practice gap in teacher education. The paper argues that, despite long-standing awareness of the theory-practice gap as a central issue faced by beginning teachers, attempts by teacher educators to address this issue remain thwarted. The argument draws on interview and focus group data collected via a study of 1st year graduate teachers of an Australian pre-service teacher education programme. The theoretical perspective of symbolic interactionism is used to focus on the meanings that graduates have of their experiences of turning theory into practice. The data suggest that prospective teachers during pre-service training value both the theory that they learn on campus and the practice that they observe in schools. However, once they become practitioners, they privilege the latter. Upon entry to the workplace, graduates come to associate good practice with that of the veteran teacher, whose practice and cache of resources they seek to emulate.

Valuing practice over theory : how beginning teachers re-orient their practice in the transition from the university to the workplace

This paper is about the experiences of beginning teachers in turning theory learned in universities into practice in the workplace. The research is situated in the context of a preservice teacher education program that explicitly and deliberately seeks to bridge the theory-practice gap in teacher education. The paper argues that, despite long-standing awareness of the theory-practice gap as a central issue faced by beginning teachers, attempts by teacher educators to address this issue remain thwarted. The argument draws on interview and focus group data collected via a study of 1st year graduate teachers of an Australian preservice teacher education program. The theoretical perspective of symbolic interactionism is used to focus on the meanings that graduates have of their experiences of turning theory into practice. The data suggest that prospective teachers during preservice training value both the theory that they learn on campus and the practice that they observe in schools. However, once they become practitioners, they privilege the latter. Upon entry to the workplace, graduates come to associate good practice with that of the veteran teacher, whose practice and cache of resources they seek to emulate. The paper concludes that background knowledge and occupational socialization remain key influences on teacher development and continue to play a key role in ensuring the continued transmittal of the cultural heritage. In particular, it proposes the need for innovative disruptions to the conventional model of teacher education.

Signal-flow graphs: Direct method of reduction and MATLAB implementation

Block diagrams and signal-flow graphs are used to represent and to obtain the transfer function of interconnected systems. The reduction of signal-flow graphs is considered simpler than the reduction of block diagrams for systems with complex interrelationships. Signal-flow graphs reduction can be made without graphic manipulations of diagrams, and it is attractive for a computational implementation. In this paper the authors propose a computational method for direct reduction of signal-flow graphs. This method uses results presented in this paper about the calculation of literal determinants without symbolic mathematics tools. The Cramer's rule is applied for the solution of a set of linear equations, A program in MATLAB language for reduction of signal-flow graphs with the proposed method is presented.

Complex Transition to Cooperative Behavior in a Structured Population Model

Cooperation plays an important role in the evolution of species and human societies. The understanding of the emergence and persistence of cooperation in those systems is a fascinating and fundamental question. Many mechanisms were extensively studied and proposed as supporting cooperation. The current work addresses the role of migration for the maintenance of cooperation in structured populations. This problem is investigated in an evolutionary perspective through the prisoner's dilemma game paradigm. It is found that migration and structure play an essential role in the evolution of the cooperative behavior. The possible outcomes of the model are extinction of the entire population, dominance of the cooperative strategy and coexistence between cooperators and defectors. The coexistence phase is obtained in the range of large migration rates. It is also verified the existence of a critical level of structuring beyond that cooperation is always likely. In resume, we conclude that the increase in the number of demes as well as in the migration rate favor the fixation of the cooperative behavior.

The Hungarian Economic Elite After the Political Transition

Erzsebet Szalai (Hungary). The Hungarian Economic Elite after the Political Transition. Ms. Szalai is a research fellow in the Institute of Political Sciences in Budapest and worked on this project from July 1996 to June 1998. In the period following the political changes of 1989, the leading forces of the economic elite have gained increasing superiority over the political and cultural elites, with the clear ambition of putting the latter to their service. The power relations within the economic elite were characterised by "a war of all against all". The desire to gain precedence over others became an openly declared value. The formation of estates and the intensification of competition became embodied in a multitude of lobbies which cropped up to assert short-term interests. After the state socialist period, possession of at least two of the social, economic and cultural forms of capital is necessary to join one of the three segments of the elite: political, cultural or economic. What defines the ability of the members of the three elite groups to assert their interests is their ability to convert any of the three types of capital into another. That is to say, the basis on which they can retain and extend their position is "symbolic capital" as interpreted by Bourdieu. The concept of symbolic capital is useful for describing the power relations following the collapse of state socialist systems and societies. In the state-socialist system, the political, economic and cultural spheres are tightly interwoven, and this interpenetration slackens only slowly after the system's disintegration. A close institutional relationship between the three spheres continues to make it easier for power actors to convert social, economic and cultural capital from one type to another. Symbolic capital, or the easy transfer between the three spheres, in turn reproduces the institutional relationship, or more precisely, complicates the separation of the three spheres after the fall of state socialism.

Quasiperiodic graphs at the onset of chaos

We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers

Formal verification of ASM designs using the MDG tool

In this paper, we present a formal hardware verification framework linking ASM with MDG. ASM (Abstract State Machine) is a state based language for describing transition systems. MDG (Multiway Decision Graphs) provides symbolic representation of transition systems with support of abstract sorts and functions. We implemented a transformation tool that automatically generates MDG models from ASM specifications, then formal verification techniques provided by the MDG tool, such as model checking or equivalence checking, can be applied on the generated models. We support this work with a case study of an Island Tunnel Controller, which behavior and structure were specified in ASM then using our ASM-MDG tool successfully verified within the MDG tool.

On Graph-Based Cryptography and Symbolic Computations

We have been investigating the cryptographical properties of in nite families of simple graphs of large girth with the special colouring of vertices during the last 10 years. Such families can be used for the development of cryptographical algorithms (on symmetric or public key modes) and turbocodes in error correction theory. Only few families of simple graphs of large unbounded girth and arbitrarily large degree are known. The paper is devoted to the more general theory of directed graphs of large girth and their cryptographical applications. It contains new explicit algebraic constructions of in finite families of such graphs. We show that they can be used for the implementation of secure and very fast symmetric encryption algorithms. The symbolic computations technique allow us to create a public key mode for the encryption scheme based on algebraic graphs.

Shortest node-disjoint paths on random graphs

A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to process global information and distribute paths optimally. Statistical properties such as scaling with system size and number of paths, average path-length and the transition to the frustrated regime are analyzed. The performance of the suggested algorithm is evaluated through a comparison against a greedy algorithm. © 2014 IOP Publishing Ltd and SISSA Medialab srl.

Random walk with restart over dynamic graphs

Random Walk with Restart (RWR) is an appealing measure of proximity between nodes based on graph structures. Since real graphs are often large and subject to minor changes, it is prohibitively expensive to recompute proximities from scratch. Previous methods use LU decomposition and degree reordering heuristics, entailing O(|V|^3) time and O(|V|^2) memory to compute all (|V|^2) pairs of node proximities in a static graph. In this paper, a dynamic scheme to assess RWR proximities is proposed: (1) For unit update, we characterize the changes to all-pairs proximities as the outer product of two vectors. We notice that the multiplication of an RWR matrix and its transition matrix, unlike traditional matrix multiplications, is commutative. This can greatly reduce the computation of all-pairs proximities from O(|V|^3) to O(|delta|) time for each update without loss of accuracy, where |delta| (<<|V|^2) is the number of affected proximities. (2) To avoid O(|V|^2) memory for all pairs of outputs, we also devise efficient partitioning techniques for our dynamic model, which can compute all pairs of proximities segment-wisely within O(l|V|) memory and O(|V|/l) I/O costs, where 1<=l<=|V| is a user-controlled trade-off between memory and I/O costs. (3) For bulk updates, we also devise aggregation and hashing methods, which can discard many unnecessary updates further and handle chunks of unit updates simultaneously. Our experimental results on various datasets demonstrate that our methods can be 1–2 orders of magnitude faster than other competitors while securing scalability and exactness.

Symbolic dynamics generated by a hybrid chaotic systems

We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.