Abstract:
Hungary’s history was as troubled as Eric Hobsbawm stated Europe’s past in Age of Extremes. The Short Twentieth Century, 1914-1991. Dictatorships followed each another right from the end of WWI until the system change in 1989, but among all the authoritarian regimes socialism existed longest. After the thawing atmosphere of the second half in the 1960s, critical tone was articulated in the Neo-Avant-Garde’s “second public sphere”. A form of criticism against any kind of hierar- chical repression arose from performative and intermedial artworks and still didn’t disappear even in postmodern times long after the fall of the wall. The paper will focus on three-dimension of hierarchical bondage: being chained through the other, trough the authorities and through history. All artists’ works (that of El Kazovszkij, Tamás St. Auby and Little Warsaw) are meant to show inner relations between the body, its representation, authoritarian practice of control respectively performance and intermedia art.

Abstract:
Algebraic models are proposed for the description of the shell-like quarteting of the nucleons both on the phenomenologic and on the semimicroscopic levels. In the previous one the quartet is considered as a structureless object, while in the latter one its constituents are treated explicitely. The excitation spectrum is generated by the SU(3) formalism in both cases. An application to the $^{20}$Ne nucleus is presented.

Abstract:
The relation of the shell, collective and cluster models of the atomic nuclei is discussed from the viewpoint of symmetries. In the fifties the U(3) symmetry was found as their common part for a single shell problem. For multi major-shell excitations, considered here, the U(3)$\otimes$U(3) dynamical symmetry turns out to be their intersection.

Abstract:
The stable marriage problem with its extensions is a widely studied subject. In this paper, we combine two topics related to it, setting up new and generalizing known results in both. The stable flow problem extends the well-known stable matching problem to network flows. Restricted edges have some special properties: forced edges must be in the stable solution, while forbidden edges may not be in it. Free edges are not able to block matchings. Here we describe a polynomial algorithm that finds a stable flow with forced and forbidden edges or proves its nonexistence. In contrast to this, we also show that determining whether a stable flow with free edges exists, is NP-complete.

Abstract:
We determine the phenomenological cluster--cluster interactions of the algebraic model corresponding to the most often used effective two--nucleon forces for the $^{16}$O + $\alpha$ system.

Abstract:
A composite symmetry of the nuclear structure, called multichannel dynamical symmetry is established. It can describe different cluster configurations (defined by different reaction channels) in a unified framework, thus it has a considerable predictive power. The two-channel case is presented in detail, and its conceptual similarity to the dynamical supersymmetry is discussed.

Abstract:
The relation of quarteting and clustering in atomic nuclei is discussed based on symmetry-considerations. This connection enables us to predict a complete high-energy cluster spectrum from the description of the low-energy quartet part. As an example the $^{28}$Si nucleus is considered, including its well-established ground-state region, the recently proposed superdeformed band, and the high-lying molecular resonances.

Abstract:
We discuss the role of the broken symmetries in the connection of the shell, collective and cluster models. The cluster-shell competition is described in terms of cold quantum phases. Stable quasi-dynamical U(3) symmetry is found for specific large deformations for a Nilsson-type Hamiltonian.

Abstract:
Given a bipartite graph G = (A u B, E) with strict preference lists and and edge e*, we ask if there exists a popular matching in G that contains the edge e*. We call this the popular edge problem. A matching M is popular if there is no matching M' such that the vertices that prefer M' to M outnumber those that prefer M to M'. It is known that every stable matching is popular; however G may have no stable matching with the edge e* in it. In this paper we identify another natural subclass of popular matchings called "dominant matchings" and show that if there is a popular matching that contains the edge e*, then there is either a stable matching that contains e* or a dominant matching that contains e*. This allows us to design a linear time algorithm for the popular edge problem. We also use dominant matchings to efficiently test if every popular matching in G is stable or not.

Abstract:
The stable allocation problem is one of the broadest extensions of the well-known stable marriage problem. In an allocation problem, edges of a bipartite graph have capacities and vertices have quotas to fill. Here we investigate the case of uncoordinated processes in stable allocation instances. In this setting, a feasible allocation is given and the aim is to reach a stable allocation by raising the value of the allocation along blocking edges and reducing it on worse edges if needed. Do such myopic changes lead to a stable solution? In our present work, we analyze both better and best response dynamics from an algorithmic point of view. With the help of two deterministic algorithms we show that random procedures reach a stable solution with probability one for all rational input data in both cases. Surprisingly, while there is a polynomial path to stability when better response strategies are played (even for irrational input data), the more intuitive best response steps may require exponential time. We also study the special case of correlated markets. There, random best response strategies lead to a stable allocation in expected polynomial time.