Temporal Ordered Clustering in Dynamic Networks: Unsupervised and Semi-supervised Learning Algorithms

In temporal ordered clustering, given a single snapshot of a dynamic network in which nodes arrive at distinct time instants, we aim at partitioning its nodes into $K$ ordered clusters $\mathcal{C}_1 \prec \cdots \prec \mathcal{C}_K$ such that for $i<j$, nodes in cluster $\mathcal{C}_i$ arrived before nodes in cluster $\mathcal{C}_j$, with $K$ being a data-driven parameter and not known upfront. Such a problem is of considerable significance in many applications ranging from tracking the expansion of fake news to mapping the spread of information. We first formulate our problem for a general dynamic graph, and propose an integer programming framework that finds the optimal clustering, represented as a strict partial order set, achieving the best precision (i.e., fraction of successfully ordered node pairs) for a fixed density (i.e., fraction of comparable node pairs). We then develop a sequential importance procedure and design unsupervised and semi-supervised algorithms to find temporal ordered clusters that efficiently approximate the optimal solution. To illustrate the techniques, we apply our methods to the vertex copying (duplication-divergence) model which exhibits some edge-case challenges in inferring the clusters as compared to other network models. Finally, we validate the performance of the proposed algorithms on synthetic and real-world networks.Comment: 14 pages, 9 figures, and 3 tables. This version is submitted to a journal. A shorter version of this work is published in the proceedings of IEEE International Symposium on Information Theory (ISIT), 2020. The first two authors contributed equall

Fine structure of helium-like ions and determination of the fine structure constant

We report a calculation of the fine structure splitting in light helium-like atoms, which accounts for all quantum electrodynamical effects up to order \alpha^5 Ry. For the helium atom, we resolve the previously reported disagreement between theory and experiment and determine the fine structure constant with an accuracy of 31 ppb. The calculational results are extensively checked by comparison with the experimental data for different nuclear charges and by evaluation of the hydrogenic limit of individual corrections.Comment: 4 pages, 3 tables, with a typo in Eq. (9) correcte

Strong-coupling solution of the bosonic dynamical mean-field theory

We derive an approximate analytical solution of the self-consistency equations of the bosonic dynamical mean-field theory (B-DMFT) in the strong-coupling limit. The approach is based on a linked-cluster expansion in the hybridization function of normal bosons around the atomic limit. The solution is used to compute the phase diagram of the bosonic Hubbard model for different lattices. We compare our results with numerical solutions of the B-DMFT equations and numerically exact methods, respectively. The very good agreement with those numerical results demonstrates that our approach captures the essential physics of correlated bosons both in the Mott insulator and in the superfluid phase. Close to the transition into the superfluid phase the momentum distribution function at zero momentum is found to be strongly enhanced already in the normal phase. The linked-cluster expansion also allows us to compute dynamical properties such as the spectral function of bosons. The evolution of the spectral function across the transition from the normal to the superfluid phase is seen to be characteristically different for the interaction driven and density driven transition, respectively.Comment: 8 pages, 6 figure

Diffractive production of electroweak vector bosons at the LHC

We analyse diffractive electroweak vector boson production in hadronic collisions and show that the single diffractive W boson production asymmetry in rapidity is a particularly good observable at the LHC to test the concept of the flavour symmetric pomeron parton distributions. It may also provide an additional constraint for the parton distribution functions in the proton.Comment: 7 pages, 5 figure

CP-nets and Nash equilibria

We relate here two formalisms that are used for different purposes in reasoning about multi-agent systems. One of them are strategic games that are used to capture the idea that agents interact with each other while pursuing their own interest. The other are CP-nets that were introduced to express qualitative and conditional preferences of the users and which aim at facilitating the process of preference elicitation. To relate these two formalisms we introduce a natural, qualitative, extension of the notion of a strategic game. We show then that the optimal outcomes of a CP-net are exactly the Nash equilibria of an appropriately defined strategic game in the above sense. This allows us to use the techniques of game theory to search for optimal outcomes of CP-nets and vice-versa, to use techniques developed for CP-nets to search for Nash equilibria of the considered games.Comment: 6 pages. in: roc. of the Third International Conference on Computational Intelligence, Robotics and Autonomous Systems (CIRAS '05). To appea

Coulomb Gas Representation of the SU(2) WZW Correlators at Higher Genera

We express the correlation functions of the SU(2) WZW conformal field theory on Riemann surfaces of genus >1 by finite dimensional integrals.Comment: 9 pages, late