Photonic realization of a quantum finite automaton

We describe a physical implementation of a quantum finite automaton that recognizes a well-known family of periodic languages. The realization exploits the polarization degree of freedom of single photons and their manipulation through linear optical elements. We use techniques of confidence amplification to reduce the acceptance error probability of the automaton. It is worth remarking that the quantum finite automaton we physically realize is not only interesting per se but it turns out to be a crucial building block in many quantum finite automaton design frameworks theoretically settled in the literature

Basics and Applications in Quantum Optics

Quantum optics has received a lot of attention in recent decades due to the handiness and versatility of optical systems, which have been exploited both to study the foundations of quantum mechanics and for various applications. In this Special Issue, we collect some articles and a review focusing on some research activities that show the potential of quantum optics in the advancement of quantum technologies

Models of self-organization in biological development

Bibliography: p. 297-320.In this thesis we thus wish to consider the concept of self-organization as an overall paradigm within which various theoretical approaches to the study of development may be described and evaluated. In the process, an attempt is made to give a fair and reasonably comprehensive overview of leading modelling approaches in developmental biology, with particular reference to self-organization. The work proceeds from a physical or mathematical perspective, but not unduly so - the major mathematical derivations and results are relegated to appendices - and attempts to fill a perceived gap in the extant review literature, in its breadth and attempted impartiality of scope. A characteristic of the present account is its markedly interdisciplinary approach: it seeks to place self-organization models that have been proposed for biological pattern formation and morphogenesis both within the necessary experimentally-derived biological framework, and in the wider physical context of self-organization and the mathematical techniques that may be employed in its study. Hence the thesis begins with appropriate introductory chapters to provide the necessary background, before proceeding to a discussion of the models themselves. It should be noted that the work is structured so as to be read sequentially, from beginning to end; and that the chapters in the main text were designed to be understood essentially independently of the appendices, although frequent references to the latter are given. In view of the vastness of the available information and literature on developmental biology, a working knowledge of embryological principles must be assumed. Consequently, rather than attempting a comprehensive introduction to experimental embryology, chapter 2 presents just a few biological preliminaries, to 'set the scene', outlining some of the major issues that we are dealing with, and sketching an indication of the current status of knowledge and research on development. The chapter is aimed at furnishing the necessary biological, experimental background, in the light of which the rest of the thesis should be read, and which should indeed underpin and motivate any theoretical discussions. We encounter the different hierarchical levels of description in this chapter, as well as some of the model systems whose experimental study has proved most fruitful, some of the concepts of experimental embryology, and a brief reference to some questions that will not be addressed in this work. With chapter 3, we temporarily move away from developmental biology, and consider the wider physical and mathematical concepts related to the study of self-organization. Here we encounter physical and chemical examples of spontaneous structure formation, thermodynamic considerations, and different approaches to the description of complexity. Mathematical approaches to the dynamical study of self-organization are also introduced, with specific reference to reaction-diffusion equations, and we consider some possible chemical and biochemical realizations of self-organizing kinetics. The chapter may be read in conjunction with appendix A, which gives a somewhat more in-depth study of reaction-diffusion equations, their analysis and properties, as an example of the approach to the analysis of self-organizing dynamical systems and mathematically-formulated models. Appendix B contains a more detailed discussion of the Belousov-Zhabotinskii reaction, which provides a vivid chemical paradigm for the concepts of symmetry-breaking and self-organization. Chapter 3 concludes with a brief discussion of a model biological system, the cellular slime mould, which displays rudimentary development and has thus proved amenable to detailed study and modelling. The following two chapters form the core of the thesis, as they contain discussions of the detailed application of theoretical concepts and models, largely based on self-organization, to various developmental situations. We encounter a diversity of models which has arisen largely in the last quarter century, each of which attempts to account for some aspect of biological pattern formation and morphogenesis; an aim of the discussion is to assess the extent of the underlying unity of these models in terms of the self-organization paradigm. In chapter 4 chemical pre-patterns and positional information are considered, without the overt involvement of cells in the patterning. In chapter 5, on the other hand, cellular interactions and activities are explicitly taken into account; this chapter should be read together with appendix C, which contains a brief introduction to the mathematical formulation and analysis of some of the models discussed. The penultimate chapter, 6, considers two other approaches to the study of development; one of these has faded away, while the other is still apparently in the ascendant. The assumptions underlying catastrophe theory, the value of its applications to developmental biology and the reasons for its decline in popularity, are considered. Lastly, discrete approaches, including the recently fashionable cellular automata, are dealt with, and the possible roles of rule-based interactions, such as of the so-called L-systems, and of fractals and chaos are evaluated. Chapter 7 then concludes the thesis with a brief assessment of the value of the self-organization concept to the study of biological development

A complex systems approach to education in Switzerland

The insights gained from the study of complex systems in biological, social, and engineered systems enables us not only to observe and understand, but also to actively design systems which will be capable of successfully coping with complex and dynamically changing situations. The methods and mindset required for this approach have been applied to educational systems with their diverse levels of scale and complexity. Based on the general case made by Yaneer Bar-Yam, this paper applies the complex systems approach to the educational system in Switzerland. It confirms that the complex systems approach is valid. Indeed, many recommendations made for the general case have already been implemented in the Swiss education system. To address existing problems and difficulties, further steps are recommended. This paper contributes to the further establishment complex systems approach by shedding light on an area which concerns us all, which is a frequent topic of discussion and dispute among politicians and the public, where billions of dollars have been spent without achieving the desired results, and where it is difficult to directly derive consequences from actions taken. The analysis of the education system's different levels, their complexity and scale will clarify how such a dynamic system should be approached, and how it can be guided towards the desired performance

Quantum finite automata : advances on Bertoni's ideas

We first outline main steps and achievements along Bertoni's research path in quantum finite automata theory - from the very basic definitions of the models of quantum finite automata throughout the investigation of their computational and descriptional power. Next, we choose to focus on Bertoni's studies on quantum finite automata descriptional complexity. In particular, we expand on a statistical framework for the synthesis of succinct quantum finite automata, discussing its adaptation to the case of multiperiodic events and languages. We then improve such a framework to obtain even more succinct quantum finite automata for some multiperiodic languages. Finally, we introduce some promise problems for multiperiodic inputs, showing that even on this class of problems the descriptional power of quantum finite automata greatly outperforms that of equivalent classical finite automata

Quantum automata for some multiperiodic languages

We exhibit small size measure-once one-way quantum finite automata (mo-1qfa’s) inducing multiperiodic stochastic events. Moreover, for certain classes of multiperiodic languages, we exhibit: (i) isolated cut point mo-1qfa’s whose size logarithmically depends on the periods; (ii) Monte Carlo mo-1qfa’s whose size logarithmically depends on the periods and polynomially on the inverse of the error probability