155,810 research outputs found
Hitting minors, subdivisions, and immersions in tournaments
The Erd\H{o}s-P\'osa property relates parameters of covering and packing of
combinatorial structures and has been mostly studied in the setting of
undirected graphs. In this note, we use results of Chudnovsky, Fradkin, Kim,
and Seymour to show that, for every directed graph (resp.
strongly-connected directed graph ), the class of directed graphs that
contain as a strong minor (resp. butterfly minor, topological minor) has
the vertex-Erd\H{o}s-P\'osa property in the class of tournaments. We also prove
that if is a strongly-connected directed graph, the class of directed
graphs containing as an immersion has the edge-Erd\H{o}s-P\'osa property in
the class of tournaments.Comment: Accepted to Discrete Mathematics & Theoretical Computer Science.
Difference with the previous version: use of the DMTCS article class. For a
version with hyperlinks see the previous versio
Bidding combinatorial games
Combinatorial Game Theory is a branch of mathematics and theoretical computer
science that studies sequential 2-player games with perfect information. Normal
play is the convention where a player who cannot move loses. Here, we
generalize the classical alternating normal play to infinitely many game
families, by means of discrete Richman auctions (Develin et al. 2010, Larsson
et al. 2021, Lazarus et al. 1996). We generalize the notion of a perfect play
outcome, and find an exact characterization of outcome feasibility. As a main
result, we prove existence of a game form for each such outcome class; then we
describe their lattice structures. By imposing restrictions to the general
families, such as impartial and {\em symmetric termination}, we find surprising
analogies with alternating play.Comment: 5 figure
Attribute Exploration of Gene Regulatory Processes
This thesis aims at the logical analysis of discrete processes, in particular
of such generated by gene regulatory networks. States, transitions and
operators from temporal logics are expressed in the language of Formal Concept
Analysis. By the attribute exploration algorithm, an expert or a computer
program is enabled to validate a minimal and complete set of implications, e.g.
by comparison of predictions derived from literature with observed data. Here,
these rules represent temporal dependencies within gene regulatory networks
including coexpression of genes, reachability of states, invariants or possible
causal relationships. This new approach is embedded into the theory of
universal coalgebras, particularly automata, Kripke structures and Labelled
Transition Systems. A comparison with the temporal expressivity of Description
Logics is made. The main theoretical results concern the integration of
background knowledge into the successive exploration of the defined data
structures (formal contexts). Applying the method a Boolean network from
literature modelling sporulation of Bacillus subtilis is examined. Finally, we
developed an asynchronous Boolean network for extracellular matrix formation
and destruction in the context of rheumatoid arthritis.Comment: 111 pages, 9 figures, file size 2.1 MB, PhD thesis University of
Jena, Germany, Faculty of Mathematics and Computer Science, 2011. Online
available at http://www.db-thueringen.de/servlets/DocumentServlet?id=1960
A survey on algorithmic aspects of modular decomposition
The modular decomposition is a technique that applies but is not restricted
to graphs. The notion of module naturally appears in the proofs of many graph
theoretical theorems. Computing the modular decomposition tree is an important
preprocessing step to solve a large number of combinatorial optimization
problems. Since the first polynomial time algorithm in the early 70's, the
algorithmic of the modular decomposition has known an important development.
This paper survey the ideas and techniques that arose from this line of
research
Self-Evaluation Applied Mathematics 2003-2008 University of Twente
This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008
Curriculum Guidelines for Undergraduate Programs in Data Science
The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program
met for the purpose of composing guidelines for undergraduate programs in Data
Science. The group consisted of 25 undergraduate faculty from a variety of
institutions in the U.S., primarily from the disciplines of mathematics,
statistics and computer science. These guidelines are meant to provide some
structure for institutions planning for or revising a major in Data Science
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