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An instance of the marriage problem is given by a graph G = (A boolean OR B, E), together with, for each vertex of G, a strict preference order over its neighbors. A matching M of G is popular in the marriage instance if M does not lose a head-to-head election against any matching where vertices are voters. Every stable matching is a min-size popular matching; another subclass of popular matchings that always exists and can be easily computed is the set of dominant matchings. A popular matching M is dominant if M wins the head-to-head election against any larger matching. Thus, every dominant matching is a max-size popular matching, and it is known that the set of dominant matchings is the linear image of the set of stable matchings in an auxiliary graph. Results from the literature seem to suggest that stable and dominant matchings behave, from a complexity theory point of view, in a very similar manner within the class of popular matchings. The goal of this paper is to show that there are instead differences in the tractability of stable and dominant matchings and to investigate further their importance for popular matchings. First, we show that it is easy to check if all popular matchings are also stable; however, it is co-NP hard to check if all popular matchings are also dominant. Second, we show how some new and recent hardness results on popular matching problems can be deduced from the NP-hardness of certain problems on stable matchings, also studied in this paper, thus showing that stable matchings can be employed to show not only positive results on popular matchings (as is known) but also most negative ones. Problems for which we show new hardness results include finding a min-size (resp., max-size) popular matching that is not stable (resp., dominant). A known result for which we give a new and simple proof is the NP-hardness of finding a popular matching when G is nonbipartite.
In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of agents, who mutually prefer each other to their respective partner. Ties in the preferences allow for three different definitions for a stable matching: weak, strong and super-stability. Besides this, acceptable pairs in the instance can be restricted in their ability of blocking a matching or being part of it, which again generates three categories of restrictions on acceptable pairs. Forced pairs must be in a stable matching, forbidden pairs must not appear in it, and lastly, free pairs cannot block any matching.
Our computational complexity study targets the existence of a stable solution for each of the three stability definitions, in the presence of each of the three types of restricted pairs. We solve all cases that were still open. As a byproduct, we also derive that the maximum size weakly stable matching problem is hard even in very dense graphs, which may be of independent interest.
This study investigates whether number dissimilarities on subject and object DPs facilitate the comprehension of subject-and object-extracted centre-embedded relative clauses in children with Grammatical Specific Language Impairment (G-SLI). We compared the performance of a group of English-speaking children with G-SLI (mean age: 12; 11) with that of two groups of younger typically developing (TD) children, matched on grammar and receptive vocabulary, respectively. All groups were more accurate on subject-extracted relative clauses than object-extracted ones and, crucially, they all showed greater accuracy for sentences with dissimilar number features (i.e., one singular, one plural) on the head noun and the embedded DP. These findings are interpreted in the light of current psycholinguistic models of sentence comprehension in TD children and provide further insight into the linguistic nature of G-SLI.
Population models in ecology are often not good at predictions, even if they are complex and seem to be realistic enough. The reason for this might be that Occam's razor, which is key for minimal models exploring ideas and concepts, has been too uncritically adopted for more realistic models of systems. This can tic models too closely to certain situations, thereby preventing them from predicting the response to new conditions. We therefore advocate a new kind of parsimony to improve the application of Occam's razor. This new parsimony balances two contrasting strategies for avoiding errors in modeling: avoiding inclusion of nonessential factors (false inclusions) and avoiding exclusion of sometimes-important factors (false exclusions). It involves a synthesis of traditional modeling and analysis, used to describe the essentials of mechanistic relationships, with elements that arc included in a model because they have been reported to be or can arguably be assumed to be important under certain conditions. The resulting models should be able to reflect how the internal organization of populations change and thereby generate representations of the novel behavior necessary for complex predictions, including regime shifts.
Think logarithmically!
(2015)
We discuss here a number of algorithmic topics which we
use in our teaching and in learning of mathematics and informatics to
illustrate and document the power of logarithm in designing very efficient
algorithms and computations – logarithmic thinking is one of the
most important key competencies for solving real world practical problems.
We demonstrate also how to introduce logarithm independently
of mathematical formalism using a conceptual model for reducing a
problem size by at least half. It is quite surprising that the idea, which
leads to logarithm, is present in Euclid’s algorithm described almost
2000 years before John Napier invented logarithm.
Business process models are used within a range of organizational initiatives, where every stakeholder has a unique perspective on a process and demands the respective model. As a consequence, multiple process models capturing the very same business process coexist. Keeping such models in sync is a challenge within an ever changing business environment: once a process is changed, all its models have to be updated. Due to a large number of models and their complex relations, model maintenance becomes error-prone and expensive. Against this background, business process model abstraction emerged as an operation reducing the number of stored process models and facilitating model management. Business process model abstraction is an operation preserving essential process properties and leaving out insignificant details in order to retain information relevant for a particular purpose. Process model abstraction has been addressed by several researchers. The focus of their studies has been on particular use cases and model transformations supporting these use cases. This thesis systematically approaches the problem of business process model abstraction shaping the outcome into a framework. We investigate the current industry demand in abstraction summarizing it in a catalog of business process model abstraction use cases. The thesis focuses on one prominent use case where the user demands a model with coarse-grained activities and overall process ordering constraints. We develop model transformations that support this use case starting with the transformations based on process model structure analysis. Further, abstraction methods considering the semantics of process model elements are investigated. First, we suggest how semantically related activities can be discovered in process models-a barely researched challenge. The thesis validates the designed abstraction methods against sets of industrial process models and discusses the method implementation aspects. Second, we develop a novel model transformation, which combined with the related activity discovery allows flexible non-hierarchical abstraction. In this way this thesis advocates novel model transformations that facilitate business process model management and provides the foundations for innovative tool support.
During the last few years there was a tremendous growth of scientific activities in the fields related to both Physics and Control theory: nonlinear dynamics, micro- and nanotechnologies, self-organization and complexity, etc. New horizons were opened and new exciting applications emerged. Experts with different backgrounds starting to work together need more opportunities for information exchange to improve mutual understanding and cooperation. The Conference "Physics and Control 2007" is the third international conference focusing on the borderland between Physics and Control with emphasis on both theory and applications. With its 2007 address at Potsdam, Germany, the conference is located for the first time outside of Russia. The major goal of the Conference is to bring together researchers from different scientific communities and to gain some general and unified perspectives in the studies of controlled systems in physics, engineering, chemistry, biology and other natural sciences. We hope that the Conference helps experts in control theory to get acquainted with new interesting problems, and helps experts in physics and related fields to know more about ideas and tools from the modern control theory.