Counting and sampling paths in graphs

Since Euler began studying paths in graphs, graph theory has become an important branch of mathematics. With all of the research into graph theoretic problems, however, counting – exactly or approximately – the number of simple paths in finite graphs has been neglected. This thesis investigates an approximation technique known as Markov chain Monte Carlo (MCMC) for the specific purpose of approximating the number of simple paths in graphs. Due to the paucity of research into the subject, the thesis will make the conjecture that this cannot be done exactly in an efficient manner (assuming that the longstanding conjecture P 6= NP holds). To this end, the thesis focuses on the relationship between counting and sampling in both weighted and unweighted complete graphs, trees, and directed acyclic graphs (DAGs). This includes both positive and negative results for sampling, as well as demonstrating how counting and sampling are intimately related problems

Vergeet de begunstiging krachtens levensverzekering niet! Erfstelling en begunstiging gaan ‘hand in hand’ (II)

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Pascalovska stava politike: pripombe k Badiouju in Lacanu

Badioujevo zanimanje za Pascala je posledica načina, kako slednji misli skupaj um in vero, namesto da bi ju preprosto zoperstavljal. Um mora ne le spoznati svoje lastne omejitve, ampak tudi pripoznati presežek, ki deluje hkrati kot ovira in kot poriv njegovega delovanja. Badiou je očitno naklonjen pascalovskemu subjektu, ki veruje, ne da bi bila njegova vera zunanja in zoperstavljena umu. A vseeno se zdi, da Badiou spregleda poseben kontekst Pascalove misli in zato ostaja slep za problematičen značaj pascalovskega, s tem pa tudi svojega lastnega militantnega subjekta. Na kratko rečeno: politični militant zase morda misli, da je subjekt postopka resnice, a da bi to naposled tudi postal, se bo moral izogniti vsaj temu, da postane objekt temačnega, okrutnega in nehvaležnega Boga. Tu nam prav Lacanovo branje Pascala omogoči izdelati bolj rafinirano teorijo subjekta, ki je hkrati svarilo pred krščansko, »perverzno« eksploatacijo tega subjekta. Sodoben primer tovrstne eksploatacije je mogoče videti v neoliberalizmu, ki od nas pričakuje, da dejansko ljubimo sistem, ki nam v zameno ne dolguje ničesar

Tickle your catastrophe! Imagining catastrophe in art, architecture and philosophy

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