Self-similar parabolic optical solitary waves

We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.

A dynamic model of the hypoxia-inducible factor 1α (HIF-1α) network

Activation of the hypoxia-inducible factor (HIF) pathway is a critical step in the transcriptional response to hypoxia. Although many of the key proteins involved have been characterised, the dynamics of their interactions in generating this response remain unclear. In the present study, we have generated a comprehensive mathematical model of the HIF-1a pathway based on core validated components and dynamic experimental data, and confirm the previously described connections within the predicted network topology. Our model confirms previous work demonstrating that the steps leading to optimal HIF-1a transcriptional activity require sequential inhibition of both prolyl- and asparaginyl-hydroxylases. We predict from our model (and confirm experimentally) that there is residual activity of the asparaginyl-hydroxylase FIH (factor inhibiting HIF) at low oxygen tension. Furthermore, silencing FIH under conditions where prolyl-hydroxylases are inhibited results in increased HIF-1a transcriptional activity, but paradoxically decreases HIF-1a stability. Using a core module of the HIF network and mathematical proof supported by experimental data, we propose that asparaginyl hydroxylation confers a degree of resistance upon HIF-1a to proteosomal degradation. Thus, through in vitro experimental data and in silico predictions, we provide a comprehensive model of the dynamic regulation of HIF-1a transcriptional activity by hydroxylases and use its predictive and adaptive properties to explain counter-intuitive biological observations.

Concatenated all-optical loop mirror switches

Synthesis of a sharp switching characteristic is experimentally demonstrated by concatenation of nonlinear optical loop mirrors. A novel configuration has been used which results in three terminal operation of the device. This device can be used as a logic gate and for pulse shaping to produce square pulses. © 1993 Taylor and Francis Ltd.

Self-similar parabolic optical solitary waves

We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.

Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations. © 2005 Springer Science+Business Media, Inc.

An activity theory approach to strategy as practice

This chapter introduces activity theory as an approach for studying strategy as practice. Activity theory conceptualizes the ongoing construction of activity as a product of activity systems, comprising the actor, the community with which that actor interacts and those symbolic and material tools that mediate between actors, their community and their pursuit of activity. The focus on the mediating role of tools and cultural artefacts in human activity seems especially promising for advancing the strategy-as-practice agenda, for example as a theoretical resource for the growing interest in sociomateriality and the role of tools and artefacts in (strategy) practice (for example, Balogun et al. 2014; Lanzara 2009; Nicolini 2009; Spee and Jarzabkowski 2009; Stetsenko 2005). Despite its potential, in a recent review Vaara and Whittington (2012) identified only three strategy-as-practice articles explicitly applying an activity theory lens. In the wider area of practice-based studies in organizations, activity theory has been slightly more popular (for example, Blackler 1993; 1995; Blackler, Crump and McDonald 2000; Engeström, Kerosuo and Kajamaa 2007; Groleau 2006; Holt 2008; Miettinen and Virkkunen 2005). It still lags behind its potential, however, primarily because of its origins as a social psychology theory developed in Russia with little initial recognition outside the Russian context, particularly in the area of strategy and organization theory, until recently (Miettinen, Samra-Fredericks and Yanow 2009). This chapter explores activity theory as a resource for studying strategy as practice as it is socially accomplished by individuals in interaction with their wider social group and the artefacts of interaction. In particular, activity theory’s focus on actors as social individuals provides a conceptual basis for studying the core question in strategy-as-practice research: what strategy practitioners do. The chapter is structured in three parts. First, an overview of activity theory is provided. Second, activity theory as a practice-based approach to studying organizational action is introduced and an activity system conceptual framework is developed. Third, the elements of the activity system are explained in more detail and explicitly linked to each of the core SAP concepts: practitioners, practices and praxis. In doing so, links are made to existing strategy-as-practice research, with brief empirical examples of topics that might be addressed using activity theory. Throughout the chapter, we introduce key authors in the development of activity theory and its use in management and adjacent disciplinary fields, as further resources for those wishing to make greater use of activity theory.

Isomerism as Manifestation of Intrinsic Symmetry of Molecules: Lunn–Senior’s Theory

This article presents the principal results of the doctoral thesis “Isomerism as internal symmetry of molecules” by Valentin Vankov Iliev (Institute of Mathematics and Informatics), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 15 December, 2008.

From icon to naturalised icon:a linguistic analysis of media representations of the BP Deepwater Horizon crisis

This research explores how news media reports construct representations of a business crisis through language. In an innovative approach to dealing with the vast pool of potentially relevant texts, media texts concerning the BP Deepwater Horizon oil spill are gathered from three different time points: immediately after the explosion in 2010, one year later in 2011 and again in 2012. The three sets of 'BP texts' are investigated using discourse analysis and semi-quantitative methods within a semiotic framework that gives an account of language at the semiotic levels of sign, code, mythical meaning and ideology. The research finds in the texts three discourses of representation concerning the crisis that show a movement from the ostensibly representational to the symbolic and conventional: a discourse of 'objective factuality', a discourse of 'positioning' and a discourse of 'redeployment'. This progression can be shown to have useful parallels with Peirce's sign classes of Icon, Index and Symbol, with their implied movement from a clear motivation by the Object (in this case the disaster events), to an arbitrary, socially-agreed connection. However, the naturalisation of signs, whereby ideologies are encoded in ways of speaking and writing that present them as 'taken for granted' is at its most complete when it is least discernible. The findings suggest that media coverage is likely to move on from symbolic representation to a new kind of iconicity, through a fourth discourse of 'naturalisation'. Here the representation turns back towards ostensible factuality or iconicity, to become the 'naturalised icon'. This work adds to the study of media representation a heuristic for understanding how the meaning-making of a news story progresses. It offers a detailed account of what the stages of this progression 'look like' linguistically, and suggests scope for future research into both language characteristics of phases and different news-reported phenomena.

Compression Technologies of Graphic Information

The classification of types of information redundancy in symbolic and graphical forms representation of information is done. The general classification of compression technologies for graphical information is presented as well. The principles of design, tasks and variants for realizations of semantic compression technology of graphical information are suggested.

Experimental Support of Argument-based Syntactic Computation

Linguistic theory, cognitive, information, and mathematical modeling are all useful while we attempt to achieve a better understanding of the Language Faculty (LF). This cross-disciplinary approach will eventually lead to the identification of the key principles applicable in the systems of Natural Language Processing. The present work concentrates on the syntax-semantics interface. We start from recursive definitions and application of optimization principles, and gradually develop a formal model of syntactic operations. The result – a Fibonacci- like syntactic tree – is in fact an argument-based variant of the natural language syntax. This representation (argument-centered model, ACM) is derived by a recursive calculus that generates a mode which connects arguments and expresses relations between them. The reiterative operation assigns primary role to entities as the key components of syntactic structure. We provide experimental evidence in support of the argument-based model. We also show that mental computation of syntax is influenced by the inter-conceptual relations between the images of entities in a semantic space.

Biomedical relation extraction:from binary to complex

Biomedical relation extraction aims to uncover high-quality relations from life science literature with high accuracy and efficiency. Early biomedical relation extraction tasks focused on capturing binary relations, such as protein-protein interactions, which are crucial for virtually every process in a living cell. Information about these interactions provides the foundations for new therapeutic approaches. In recent years, more interests have been shifted to the extraction of complex relations such as biomolecular events. While complex relations go beyond binary relations and involve more than two arguments, they might also take another relation as an argument. In the paper, we conduct a thorough survey on the research in biomedical relation extraction. We first present a general framework for biomedical relation extraction and then discuss the approaches proposed for binary and complex relation extraction with focus on the latter since it is a much more difficult task compared to binary relation extraction. Finally, we discuss challenges that we are facing with complex relation extraction and outline possible solutions and future directions.

Processing of Byzantine Neume Notation in Ancient Historical Manuscripts

This article presents the principal results of the doctoral thesis “Recognition of neume notation in historical documents” by Lasko Laskov (Institute of Mathematics and Informatics at Bulgarian Academy of Sciences), successfully defended before the Specialized Academic Council for Informatics and Mathematical Modelling on 07 June 2010.

PREFACE

The Conference on Partial Differential Equations and Applications, Sofia, September 14–16, 2011 (In honor of 65-th Anniversary of Professor Petar Popivanov) took place in the premises of the Institute of Mathematics and Informatics (IMI) of the Bulgarian Academy of Sciences (BAS). The conference was organized by the Section “Differential Equations and Mathematical Physics” of IMI with the participation of research groups on PDE from Universit`a di Cagliari and Universit`a di Torino (Italy), with the organizing committee – N. Kutev (IMI–BAS) – chair, G. Boyadzhiev (IMI–BAS) – secretary, T. Gramchev (Univ. Cagliari) and A. Oliaro (Univ. Torino) – members, and thefollowing program/scientific committee: T. Gramchev (chair), N. Kutev (IMI–BAS), L. Rodino (Universit`a di Torino), M. Ruzhansky (Imperial College London), A. Slavova (IMI–BAS), C. Van Der Mee (Universit`a di Cagliari).

A Simple Example of Localized Parametric Resonance for the Wave Equation

2000 Mathematics Subject Classification: 35L05, 35P25, 47A40.

On the implementation of the L-Nash bargaining solution in two-person bargaining games

The “Nash program” initiated by Nash (Econometrica 21:128–140, 1953) is a research agenda aiming at representing every axiomatically determined cooperative solution to a game as a Nash outcome of a reasonable noncooperative bargaining game. The L-Nash solution first defined by Forgó (Interactive Decisions. Lecture Notes in Economics and Mathematical Systems, vol 229. Springer, Berlin, pp 1–15, 1983) is obtained as the limiting point of the Nash bargaining solution when the disagreement point goes to negative infinity in a fixed direction. In Forgó and Szidarovszky (Eur J Oper Res 147:108–116, 2003), the L-Nash solution was related to the solution of multiciteria decision making and two different axiomatizations of the L-Nash solution were also given in this context. In this paper, finite bounds are established for the penalty of disagreement in certain special two-person bargaining problems, making it possible to apply all the implementation models designed for Nash bargaining problems with a finite disagreement point to obtain the L-Nash solution as well. For another set of problems where this method does not work, a version of Rubinstein’s alternative offer game (Econometrica 50:97–109, 1982) is shown to asymptotically implement the L-Nash solution. If penalty is internalized as a decision variable of one of the players, then a modification of Howard’s game (J Econ Theory 56:142–159, 1992) also implements the L-Nash solution.