- Topology Seminar
- Mathematical Biology and Ecology Seminar
A joint History of Mathematics/Egyptology and Ancient Near Eastern Studies Seminar
In the hieratic Egyptian mathematical texts, which are extant from the periods of the Middle Kingdom and the Second Intermediate Period, the verb form sdm.hr.f has its most numerous attestations. This verb form has been recognized to express a necessary consequence from a previously stated situation, e.g. in indicating the result of a previously stated arithmetic operation. Therefore one might expect this form to be similarly (frequently) used in Egyptian laws to express the consequences of wrongdoing. Only few collections of laws from pharaonic times are extant, of which the earliest are the Great Edict of Haremhab and the Nauri Decree of Sethos I. both from the beginning of the Ramesside Period. These sources, however, show no use of this form. In this respect then, the Egyptian concept of rational practice is different from its Mesopotamian neighbour, where a connection between mathematical and legal procedure texts has been shown by Jim Ritter based on their verbal structure. Using examples from several Egyptian genres of texts, I would like to document that in ancient Egypt, too, this relation existed, and explore how it was expressed.
- History of Mathematics
We consider random graph models where graphs are generated by connecting not only pairs of nodes by edges but also larger subsets of
nodes by copies of small atomic subgraphs of arbitrary topology. More specifically we consider canonical and microcanonical ensembles
corresponding to constraints placed on the counts and distributions of atomic subgraphs and derive general expressions for the entropy of such
models. We also introduce a procedure that enables the distributions of multiple atomic subgraphs to be combined resulting in more coarse
grained models. As a result we obtain a general class of models that can be parametrized in terms of basic building blocks and their
distributions that includes many widely used models as special cases. These models include random graphs with arbitrary distributions of subgraphs (Karrer & Newman PRE 2010, Bollobas et al. RSA 2011), random hypergraphs, bipartite models, stochastic block models, models of multilayer networks and their degree corrected and directed versions. We show that the entropy expressions for all these models can be derived from a single expression that is characterized by the symmetry groups of their atomic subgraphs.
- Networks Seminar
- Mathematical and Computational Finance internal seminar