Road traffic: A case study of flow and path-dependency in weighted directed networks

How much can we tell about flows through networks just from their topological properties? Whereas flow distributions of river basins, trees or cardiovascular systems come naturally to mind, more complex topologies are not so immediate, especially if the network is large and heterogeneously directed. Our study is motivated by the question of how the distribution of path-dependent trails in directed networks is correlated to the distribution of network flows. As an example we have studied the path-dependencies in closed trails in four metropolitan areas in England and the USA and computed their global and spatial correlations with measured traffic flows. We have found that the heterogeneous distribution of traffic intensity is mirrored by the distribution of agglomerate path-dependency and that high traffic roads are packed along corridors at short-to-medium trail lengths from the ensemble of nodes.     

Hong-Ou-Mandel characterization of multiply charged Levitons

We review and develop recent results regarding Leviton excitations generated in topological states of matter – such as integer and fractional quantum Hall edge channels – and carrying a charge multiple of the electronic one. The peculiar features associated with these clean and robust emerging excitations can be detected through current correlation measurements. In particular, relevant information can be extracted from the noise signal in generalized Hong-Ou-Mandel experiments, where Levitons with different charges collide against each other at a quantum point contact. We describe this quantity both in the framework of the photo-assisted noise formalism and in terms of a very interesting and transparent picture based on wave-packet overlap.     

Bottleneck Problems: An Information and Estimation-Theoretic View

Information bottleneck (IB) and privacy funnel (PF) are two closely related optimization problems which have found applications in machine learning, design of privacy algorithms, capacity problems (e.g., Mrs. Gerber’s Lemma), and strong data processing inequalities, among others. In this work, we first investigate the functional properties of IB and PF through a unified theoretical framework. We then connect them to three information-theoretic coding problems, namely hypothesis testing against independence, noisy source coding, and dependence dilution. Leveraging these connections, we prove a new cardinality bound on the auxiliary variable in IB, making its computation more tractable for discrete random variables. In the second part, we introduce a general family of optimization problems, termed “bottleneck problems”, by replacing mutual information in IB and PF with other notions of mutual information, namely f-information and Arimoto’s mutual information. We then argue that, unlike IB and PF, these problems lead to easily interpretable guarantees in a variety of inference tasks with statistical constraints on accuracy and privacy. While the underlying optimization problems are non-convex, we develop a technique to evaluate bottleneck problems in closed form by equivalently expressing them in terms of lower convex or upper concave envelope of certain functions. By applying this technique to a binary case, we derive closed form expressions for several bottleneck problems.     

DFT Calculations and Synthesis Reveal: Key Intermediates,Omitted Mechanisms,and Unsymmetrical Bimane Products

Theoretical and experimental mixed approaches are complementary and valuable. Our DFT calculations support the mechanism suggested by Kosower, adding to it a key diaziridine intermediate that determines the relative product distribution of this reaction. Our results are consistent with the formation of the diazoketene intermediate as the rate-limiting step. Based on curve fittings, first or second-order kinetics cannot be ruled out. This may indicate that more than one mechanism is simultaneously at play in this transformation. This unexpected outcome led us to study an alternative cyclopropenone intermediate. Although cyclopropenone is not likely to be formed under thermal conditions, adding it to the reaction mixture results in bimane structures. The most staggering finding from this investigation was the unanticipated generation of the unsymmetrical anti-(Me,Me)(Ph,Ph)bimane. The optimization of this route towards unsymmetrical bimanes will require additional investigation.