A Toom rule that increases the thickness of sets

Toom's north-east-self voting cellular automaton rule R is known to suppress small minorities. A variant which we call R^+ is also known to turn an arbitrary initial configuration into a homogenous one (without changing the ones that were homogenous to start with). Here we show that R^+ always increases a certain property of sets called thickness. This result is intended as a step towards a proof of the fast convergence towards consensus under R^+. The latter is observable experimentally, even in the presence of some noise.Comment: 16 pages, 8 figure

The macroeconomic conditions of EU-inspired employment policies

With its impulses and coordination initiatives the EU makes efforts to influence the employment and labour policies in its Member States. Here the principal instruments are the European Employment Strategy and its main constituent, the Employment Guidelines. The latter, while based on modern professional ideas about the institutional determinants of the labour market, have been incomplete up to 2005: due to departmentalism reflected in the tensions between the EU institutions responsible for employment and macro-policies crucial fields were kept out of the employment guidelines such as wage-setting policies, the wage bargaining system as well as the budgetary implications of active labour market policies. The macroeconomic support of the EU-inspired employment policies is theoretically not sound. An example of this is the objective of the Lisbon Process of simultaneous ambitions improvement of both macro-level productivity and employment. This target ignores the trade-off between these two factors prevailing even in the long term. The division and inconsistency between the philosophy and operation of various EU institutions is reflected in the moderate, but disturbing inconsistencies between the mid-term macroeconomic and employment strategies of the Hungarian government (the Convergence Programme and the National Action Plan for Employment). There are, however, possibilities for the member countries, including Hungary, to prepare and carry out employment policies in the EU framework that are supported by sound macro-policies: they have to be less slavish abiding by specific EU recommendations, have to take into account the domestic conditions realistically, and get rid of detrimental institutional divisions, at least in their indigenous administration.European integration, employment strategy, coordination of policies

Stable Multi-Level Monotonic Eroders

Eroders are monotonic cellular automata with a linearly ordered state set that eventually wipe out any finite island of nonzero states. One-dimensional eroders were studied by Gal'perin in the 1970s, who presented a simple combinatorial characterization of the class. The multi-dimensional case has been studied by Toom and others, but no such characterization has been found. We prove a similar characterization for those one-dimensional monotonic cellular automata that are eroders even in the presence of random noise.Comment: 32 pages, 9 figure

Randomness on computable probability spaces - A dynamical point of view

We extend the notion of randomness (in the version introduced by Schnorr) to computable probability spaces and compare it to a dynamical notion of randomness: typicality. Roughly, a point is typical for some dynamic, if it follows the statistical behavior of the system (Birkhoff’s pointwise ergodic theorem). We prove that a point is Schnorr random if and only if it is typical for every mixing computable dynamics. To prove the result we develop some tools for the theory of computable probability spaces (for example, morphisms) that are expected to have other applications

An extension of Chaitin's halting probability \Omega to a measurement operator in an infinite dimensional quantum system

This paper proposes an extension of Chaitin's halting probability \Omega to a measurement operator in an infinite dimensional quantum system. Chaitin's \Omega is defined as the probability that the universal self-delimiting Turing machine U halts, and plays a central role in the development of algorithmic information theory. In the theory, there are two equivalent ways to define the program-size complexity H(s) of a given finite binary string s. In the standard way, H(s) is defined as the length of the shortest input string for U to output s. In the other way, the so-called universal probability m is introduced first, and then H(s) is defined as -log_2 m(s) without reference to the concept of program-size. Mathematically, the statistics of outcomes in a quantum measurement are described by a positive operator-valued measure (POVM) in the most general setting. Based on the theory of computability structures on a Banach space developed by Pour-El and Richards, we extend the universal probability to an analogue of POVM in an infinite dimensional quantum system, called a universal semi-POVM. We also give another characterization of Chaitin's \Omega numbers by universal probabilities. Then, based on this characterization, we propose to define an extension of \Omega as a sum of the POVM elements of a universal semi-POVM. The validity of this definition is discussed. In what follows, we introduce an operator version \hat{H}(s) of H(s) in a Hilbert space of infinite dimension using a universal semi-POVM, and study its properties.Comment: 24 pages, LaTeX2e, no figures, accepted for publication in Mathematical Logic Quarterly: The title was slightly changed and a section on an operator-valued algorithmic information theory was adde

Density classification on infinite lattices and trees

Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic) cellular automaton or a finite-range interacting particle system that evolves on this graph and decides whether p is smaller or larger than 1/2. Precisely, the trajectories should converge to the uniform configuration with only 0's if p1/2. We present solutions to that problem on the d-dimensional lattice, for any d>1, and on the regular infinite trees. For Z, we propose some candidates that we back up with numerical simulations

Alternatív növekedési stratégiák és pályák az EU csatlakozás után: Vizsgálatok a csatlakozó országok központhoz való közeledésének illetve perifériára szorulásának esélyeiről a modern növekedési elméletek és a közgazdasági földrajz alapján = Alternative development strategies and growth paths after the EU accession: Investigations about the chances of the accession countries for approaching the growth centers or staying in peripheries based on modern growth theories and economic geography

A magyar gazdaság növekedését az elmúlt másfél évtizedben fokozódó mértékben a világgazdasági keretek és a regionális integráció erői határozzák meg. A folyamatosan változó feltételek új lehetőségeket nyitnak, ugyanakkor sokszor kiszámíthatatlan vagy irracionális kötöttségeket jelentenek a nemzetgazdaságok, így a magyar gazdaság számára. Ezek felismerése és tudatos átgondolása segít a gazdasági fejlődés alternatív pályáinak felvázolásában. Három témát vizsgáltunk: 1. Értelmeztük a gazdasági globalizáció fogalmát, s a főbb dimenziókban méréseket végeztünk az EU-tagországok, köztük Magyarország és jelentősebb feltörekvő gazdaságok nemzetközi integráltságára, az eredményeket értékeltük, s mérlegeltük a szakpolitika beavatkozási lehetőségeit. 2. Kritikai módon értékeltük az EU átfogó fejlesztési és reformstratégiáját, a lisszaboni folyamatot, s a legfontosabb koordinált európai politika, az Európai Foglalkoztatási Stratégia potenciális szerepét az összehangolt nemzeti fejlesztési stratégiában. 3. A szokásosnál dezaggregáltabb szektorális bontásban, növekedési elszámolási keretben azt vizsgáltuk, hogy mely főbb gazdasági szektoroknak tulajdonítható az elmaradottabb országok termelékenységi lemaradása a fejlettekhez képest. Azt kaptuk, hogy a lemaradás a kereskedelem tárgyát képező feldolgozóipari beruházási és fogyasztási javak előállítása területén a legnagyobb, míg a fogyasztási szolgáltatások illetve az építési tevékenység terén az elmaradás lényegesen kisebb. | In recent years, growth in the Hungarian economy has been determined increasingly by global developments as well as forces of regional integration. These changing conditions imply both new opportunities and incalculable or irrational constraints for the national economies. The identification and analysis of these opportunities and risks help in drawing up alternative paths of economic development. Three themes were studied: (1) We defined and analyzed the concept of economic globalization, and measured the extent of international integration of the EU members states (including Hungary) and major emerging economies in the main aspects of globalization. Results were evaluated, and various forms of policy interventions analyzed. (2) The comprehensive reform-strategy of the EU, the Lisbon Process was scrutinized, and the most important EU policy, the European Employment Strategy was analyzed from the point of view that what potential role it could play in a harmonized national development strategy. (3) In a development accounting framework and in a detailed sectoral disaggregation we investigated the question that which sectors are mainly responsible for the low aggregate total factor productivity of poor countries compared to that of the more advanced economies. The results showed that lagging behind by the by poor countries is due mostly to the production of tradable equipment and consumption goods, while it is much less due to the provision of services and construction