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We adapt Forman’s discretization of Ricci curvature to the case of undirected networks, both weighted and unweighted, and investigate the measure in a variety of model and real-world networks. We find that most nodes and edges in model and real networks have a negative curvature. Furthermore, the distribution of Forman curvature of nodes and edges is narrow(More)
We have recently introduced Forman’s discretization of Ricci curvature to the realm of complex networks. Forman curvature is an edge-based measure whose mathematical definition elegantly encapsulates the weights of nodes and edges in a complex network. In this contribution, we perform a comparative analysis of Forman curvature with other edge-based measures(More)
One of the most celebrated theorems of differential geometry is the 1929 theorem of Lusternik and Schnirelmann, which states that for every riemannian metric on the 2-sphere there exist at least three simple closed geodesies. Jurgen Jost [J] (following important work of Pitts [P] and Simon and Smith [SS]) has recently generalized this result by showing that(More)
Quansheng Ren, Kiran M. Kolwankar, 2 Areejit Samal, 3 and Jürgen Jost 4 Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany Department of Physics, Ramniranjan Jhunjhunwala College, Ghatkopar (W), Mumbai 400 086, India Laboratoire de Physique Théorique et Modèles Statistiques, CNRS and Univ Paris-Sud, UMR 8626,(More)
In previous articles we have investigated the firing properties of the standard Hodgkin-Huxley (HH) systems of ordinary and partial differential equations in response to input currents composed of a drift (mean) and additive Gaussian white noise. For certain values of the mean current, as the noise amplitude increased from zero, the firing rate exhibited a(More)
We define and study periodic strategies in two player finite strategic form games. This concept can arise from some epistemic analysis of the rationalizability concept of Bernheim and Pearce. We analyze in detail the pure strategies and mixed strategies cases. In the pure strategies case, we prove that every two player finite action game has at least one(More)
Areejit Samal, R.P. Sreejith, Jiao Gu, Shiping Liu, ∗ Emil Saucan, 5, † and Jürgen Jost 7, ‡ The Institute of Mathematical Sciences, Homi Bhabha National Institute, Chennai, India Jiangnan University, Wuxi, P.R. China School of Mathematical Sciences, University of Science and Technology of China, Hefei, P.R. China Department of Applied Mathematics, ORT(More)