Aalto Stochastics and Statistics Seminar is organized by Kalle Kytölä, Lasse Leskelä, and Pauliina Ilmonen. Feel free to contact one of us if you are interested in giving a talk. You may also earn credit points by active participation.
Over the centuries, many claims have been made of numerical patterns of miraculous nature hidden within the text of sacred writings, including the Jewish, Christian and Islamic scriptures. Usually the patterns involve counting of letters and words, or calculations involving numerical equivalents of the letters. Until recently, all such claims were made by people with little mathematical understanding and were easily explained. This situation changed when a highly respected Israeli mathematician Eliyahu Rips and two others published a paper in the academic journal Statistical Science claiming to prove that information about medieval Jewish rabbis was encoded in the Hebrew text of the Book of Genesis. The journal reported that its reviewers were "baffled". The paper in Statistical Science spawned a huge "Bible Codes" industry, complete with best selling books, TV documentaries, and even a romance movie. The talk will reveal the inside story of the Codes and the people behind them, from their inception through to their refutation.
We consider the problem of energy-efficient broadcasting on homogeneous random geometric graphs (RGGs) within a large finite box around the origin. A source node at the origin encodes $k$ data packets of information into $n\ (>k)$ coded packets and transmits them to all its one-hop neighbors. The encoding is such that, any node that receives at least $k$ out of the $n$ coded packets can retrieve the original $k$ data packets. Every other node in the network follows a probabilistic forwarding protocol; upon reception of a previously unreceived packet, the node forwards it with probability $p$ and does nothing with probability $1-p$. We are interested in the minimum forwarding probability which ensures that a large fraction of nodes can decode the information from the source. We deem this a \emph{near-broadcast}. The performance metric of interest is the expected total number of transmissions at this minimum forwarding probability, where the expectation is over both the forwarding protocol as well as the realization of the RGG. In comparison to probabilistic forwarding with no coding, our treatment of the problem indicates that, with a judicious choice of $n$, it is possible to reduce the expected total number of transmissions while ensuring a near-broadcast. Techniques from continuum percolation and ergodic theory are used to characterize the probabilistic broadcast algorithm. Joint work with Navin Kashyap and D. Yogeshwaran
This thesis studies the connectivity of passive random intersection graphs. In addition to this, it studies the connectivity of an intersection between a passive random intersection graph and an ErdősRényi graph. Random intersection graphs can be used to model many real-life phenomena. For example, social networks and communication in sensor networks can be modelled by random intersection graphs. A random intersection graph is a random graph, where nodes are assigned attributes according to some random process. Two nodes are connected by an edge if they have at least one attribute in common. For a passive random intersection graph, each attribute is given a number according to some probability distribution. Each attribute then chooses that number of nodes, uniformly at random from the whole set of nodes. The chosen nodes are given the respective attribute. Two nodes are thus connected, if at least one attribute chooses them both. This thesis presents zero-one laws on passive random intersection graphs being connected and not having isolated nodes. This thesis also presents zero-one laws on the intersection between a passive random intersection graph and an ErdősRényi graph, being connected and not having isolated nodes.
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