Controlling edge dynamics in complex networks

The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Here we introduce and evaluate a dynamical process defined on the edges of a network, and demonstrate that the controllability properties of this process significantly differ from simple nodal dynamics. Evaluation of real-world networks indicates that most of them are more controllable than their randomized counterparts. We also find that transcriptional regulatory networks are particularly easy to control. Analytic calculations show that networks with scale-free degree distributions have better controllability properties than uncorrelated networks, and positively correlated in- and out-degrees enhance the controllability of the proposed dynamics.Comment: Preprint. 24 pages, 4 figures, 2 tables. Source code available at http://github.com/ntamas/netctr

Hierarchical self-organization of non-cooperating individuals

Hierarchy is one of the most conspicuous features of numerous natural, technological and social systems. The underlying structures are typically complex and their most relevant organizational principle is the ordering of the ties among the units they are made of according to a network displaying hierarchical features. In spite of the abundant presence of hierarchy no quantitative theoretical interpretation of the origins of a multi-level, knowledge-based social network exists. Here we introduce an approach which is capable of reproducing the emergence of a multi-levelled network structure based on the plausible assumption that the individuals (representing the nodes of the network) can make the right estimate about the state of their changing environment to a varying degree. Our model accounts for a fundamental feature of knowledge-based organizations: the less capable individuals tend to follow those who are better at solving the problems they all face. We find that relatively simple rules lead to hierarchical self-organization and the specific structures we obtain possess the two, perhaps most important features of complex systems: a simultaneous presence of adaptability and stability. In addition, the performance (success score) of the emerging networks is significantly higher than the average expected score of the individuals without letting them copy the decisions of the others. The results of our calculations are in agreement with a related experiment and can be useful from the point of designing the optimal conditions for constructing a given complex social structure as well as understanding the hierarchical organization of such biological structures of major importance as the regulatory pathways or the dynamics of neural networks.Comment: Supplementary videos are to be found at http://hal.elte.hu/~nepusz/research/supplementary/hierarchy

Probability current in zero-spin relativistic quantum mechanics

We show that the antisymmetric spinor tensor representation of spin-0 relativistic quantum mechanics provides a conserved current with positive definite timelike component, interpretable as probability density. The construction runs in complete analogy to the spin-1/2 case, and provides an analogously natural one-particle Hilbert space description for spin 0. Except for the free particle, the obtained formulation proves to be inequivalent to the one based on the Klein--Gordon equation. The second quantized version may lead to new field theoretical interaction terms for zero-spin particles.Comment: 9 pages, no figures; material presented at the Zim\'anyi School, December 7-11, 2015, Budapest, Hungar

The nucleolus of directed acyclic graph games

In this paper we consider a natural generalization of standard tree games where the underlying structure is a directed acyclic graph. We analyze the properties of the game and illustrate its relation with other graph based cost games. We show that although the game is not convex its core is always non-empty. Furthermore we provide a painting algorithm for large families of directed acyclic graph games that finds the nucleolus in polynomial time

Taxonomic results of the Bryotrop expedition to Zaïre and Rwanda : 28., Lejeuneaceae ; a ramicolous collection

The treatment of non epiphyllous Lejeuneaceae taxa was published in the first part of the Central African BRYOTROP results (Pócs 1993b). Anyhow, a nice material collected on tiny twigs (partly from fallen canopy branches) from the W edge of Nyungwe Forest Reserve, in a wet type of montane rainforest at 2000 m altitude, remained unidentified

Geometric pluripotential theory on K\"ahler manifolds

Finite energy pluripotential theory accommodates the variational theory of equations of complex Monge-Amp\`ere type arising in K\"ahler geometry. Recently it has been discovered that many of the potential spaces involved have a rich metric geometry, effectively turning the variational problems in question into problems of infinite dimensional convex optimization, yielding existence results for solutions of the underlying complex Monge-Amp\`ere equations. The purpose of this survey is to describe these developments from basic principles

Infrastruktúra: helyzetek, nézetek, szemléletmódok = Infrastructure in Hungary: Situations, Views, Attitudes

Az infrastruktúra háttérbeszorítása kezdetben ideologikus volt, de mindmáig érdekeltségen alapul. A forráselosztás ágazatközi csatáiban az egyes ágazatok felhasználják a csőd kilátásával történő forrás-zsarolás érveit és fegyvereit. Ezek, és az ágazatokon belül működő hasonlóan pazarló és tendenciózus szisztémák megváltoztatása nélkül a piacra hivatkozó „korszerűsítés” is hamis vágányra fog futni. A szerző általános érvényű következtetéseket próbál levonni egy követhető szabályozás kiindulására és elvi kereteire vonatkozóan, az alábbi tézisek szerint. (1) ideologikusan is háttérbe szorult az infrastruktúra, (2) a bajok oka nem a kevés pénz, a megoldás kulcsa sem a „több pénzt az infrastruktúrára” (3) nem „jó” ágazati stratégia a forrás-zsarolás a csőd kilátásával, (4) infrastruktúrán belül is hibás jelszó a „prioritás a termelésnek” (5) az infrastruktúrára is jutott pénz, ha fontosnak tűnt, (6) elosztás helyett több piacot az infrastruktúrában, (7) húzóhatáshoz és motorszerephez is piaci környezet kell, (8) vannak piacosítható infrastruktúrák és vannak externáliák, (9) stabil peremfeltételekre és mozgékony visszajelzésre van szükség, (10) tüneteket kell mérni, és struktúrákat kell építeni. Infrastructure in Hungary: Situations, Views, Attitudes - Tamás Fleischer - In the Central- and Eastern European countries the neglecting of infrastructure first had an ideological basis, but the lack of interest has remained so far. While fighting for resources individual economic branches use the weapons and arguments of threatening with bankruptcy. If this state and the intra-sectoral systems of wastage cannot be changed, "modernisation" even with permanent reference to the market will lead to a wrong direction. The author tries to state the start line and the theoretic frames of a followable regulation along the theses below. (1) The infrastructure was suppressed by ideology, (2) The cause of sickness is not the insufficient amount of money, the solution is not "more money for the infrastructure", (3) Not a useful sector-level strategy is blackmailing for more money by threatening with breakdown (4) Even within the infrastructure "give priority to production" is a mistaken slogan, (5) The infrastructure also got money when it was especially important, (6) Instead of distribution "More market" is needed in the infrastructure, (7) Market environment is required for a real driving effect, for an effective engine role, (8) There are both marketable infrastructures and externalities as well, (9) What we need are stable boundary conditions and flexible feedbacks, (10) We have to measure symptoms and construct structure