Finding topological subgraphs is fixed-parameter tractable

We show that for every fixed undirected graph $H$, there is a $O(|V(G)|^3)$ time algorithm that tests, given a graph $G$, if $G$ contains $H$ as a topological subgraph (that is, a subdivision of $H$ is subgraph of $G$). This shows that topological subgraph testing is fixed-parameter tractable, resolving a longstanding open question of Downey and Fellows from 1992. As a corollary, for every $H$ we obtain an $O(|V(G)|^3)$ time algorithm that tests if there is an immersion of $H$ into a given graph $G$. This answers another open question raised by Downey and Fellows in 1992

Programozás struktogramokkal

Programozás struktogramokka

Exponential Time Complexity of the Permanent and the Tutte Polynomial

We show conditional lower bounds for well-studied #P-hard problems: (a) The number of satisfying assignments of a 2-CNF formula with n variables cannot be counted in time exp(o(n)), and the same is true for computing the number of all independent sets in an n-vertex graph. (b) The permanent of an n x n matrix with entries 0 and 1 cannot be computed in time exp(o(n)). (c) The Tutte polynomial of an n-vertex multigraph cannot be computed in time exp(o(n)) at most evaluation points (x,y) in the case of multigraphs, and it cannot be computed in time exp(o(n/polylog n)) in the case of simple graphs. Our lower bounds are relative to (variants of) the Exponential Time Hypothesis (ETH), which says that the satisfiability of n-variable 3-CNF formulas cannot be decided in time exp(o(n)). We relax this hypothesis by introducing its counting version #ETH, namely that the satisfying assignments cannot be counted in time exp(o(n)). In order to use #ETH for our lower bounds, we transfer the sparsification lemma for d-CNF formulas to the counting setting

A bűnben fogant tudomány? Összefoglaló A közgazdaságtan humanizálása c. könyv bemutatójáról

A közgazdaságtan emberképét, az ún. homo oeconomicus-t gyakran vezetik vissza Adam Smithre és a láthatatlan kéz elméletére. A homo oeconomicus racionális és önző. Adam Smith a morálfilozófia skót professzora, akit a klasszikus közgazdaságtan atyjaként is számon tartanak, valóban erkölcstelen tudományt alapozott volna meg? A diszciplína alapítója A nemzetek gazdagsága (1776) előtt írta az Erkölcsi érzelmek elmélete (1759) című könyvét, melyet a filozófusok gyakran összeegyeztethetetlennek látnak a láthatatlan kéz elméletéhez kötött önző emberképpel. Vajon a közgazdaságtan tényleg bűnben fogant és ezért a tudományosságának alapja az erkölcstelenség? Többek között erre a kérdésre is keresi a választ A közgazdaságtan humanizálása2 c. könyv, melynek könyvbemutatóját 2020. augusztus 26-án tartották. A beszélgetést Sárvári Balázs, a Budapesti Corvinus Egyetem oktatója moderálta, beszélgetőpartnerei pedig Neszveda Gábor, a Budapesti Corvinus Egyetem oktatója, valamint Bertók Rózsa, a Pécsi Egyetem egyetemi docense voltak. = What can we learn about people from the economy? The elementary microeconomics books taught us that people are racional entity and selfish. This narrative of people was the mainstream economy from decades. Some other sciences and some new wave economy theories recognised that the human being is more complicated than we can describe with this adjectives. The Humanomics: Moral Sentiments and the Wealth of Nations for the Twenty-First Century book’s aim to show how we can see different ways of the economy actions of people, how we can see the human being as own wholeness and integrity. This article is a summary from the book presentation of this book. Rózsa Bertók Associate Professor in the University of Pécs and Gábor Neszveda Assistant Lecturer in the Corvinus University of Budapest were talking about this book and about the global picture of Smith theoritical job. The moderator was Balázs Sárvári Assistant Professor from the Corvinus Universtiy of Budapest. In the conversation we can see the difference between Adam Smith’s theory and the neoclassical interpretation of this. The starting point was his two books: „The Wealth of Nations” and „The Theory of Moral Sentiments”

Bioverse: The Habitable Zone Inner Edge Discontinuity as an Imprint of Runaway Greenhouse Climates on Exoplanet Demographics

Long-term magma ocean phases on rocky exoplanets orbiting closer to their star than the runaway greenhouse threshold - the inner edge of the classical habitable zone - may offer insights into the physical and chemical processes that distinguish potentially habitable worlds from others. Thermal stratification of runaway planets is expected to significantly inflate their atmospheres, potentially providing observational access to the runaway greenhouse transition in the form of a "habitable zone inner edge discontinuity" in radius-density space. Here, we use Bioverse, a statistical framework combining contextual information from the overall planet population with a survey simulator, to assess the ability of ground- and space-based telescopes to test this hypothesis. We find that the demographic imprint of the runaway greenhouse transition is likely detectable with high-precision transit photometry for sample sizes $\gtrsim 100$ planets if at least ~10 % of those orbiting closer than the habitable zone inner edge harbor runaway climates. Our survey simulations suggest that in the near future, ESA's PLATO mission will be the most promising survey to probe the habitable zone inner edge discontinuity. We determine survey strategies that maximize the diagnostic power of the obtained data and identify as key mission design drivers: 1. A follow-up campaign of planetary mass measurements and 2. The fraction of low-mass stars in the target sample. Observational constraints on the runaway greenhouse transition will provide crucial insights into the distribution of atmospheric volatiles among rocky exoplanets, which may help to identify the nearest potentially habitable worlds.Comment: Accepted for publication in The Planetary Science Journal. For a video abstract, see https://youtu.be/acgKcdTTv9c. 29 pages, 12 figures, 1 table. All source code is available at https://github.com/matiscke/hz-inner-edge-discontinuit

New Challenges in the Education of Managerial Economics

In this article, the authors summarise their panel presentation on the role of education in managerial economics, given at the Danube Cup in April, 2022. The main finding of the article and the presentation is that today's and tomorrow's economists need to think in a so-called global framework. A common commodity and energy policy is becoming an increasingly urgent issue that will significantly change the development path of international institutions and technologies. Therefore, the teaching of economics will also have to adapt to this new trend. Apart from the obvious point - teaching a professional ethos and the importance of international trade - the authors see a constructivist approach as the most viable way forward in pedagogy. According to this approach, secondary and university students should be given the experience of discovery in order to stimulate their interest in economic topics and contexts