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We adapt Formanâ€™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 narrowâ€¦ (More)

A goal in network science is the geometrical characterization of complex networks. In this direction, we have recently introduced the Formanâ€™s discretization of Ricci curvature to the realm of undirected networks. Investigation of this edge-centric network measure, Forman curvature, in diverse model and real-world undirected networks revealed that theâ€¦ (More)

- Anirban Banerjee, J. Jost
- 2007

From the spectral plot of the (normalized) graph Laplacian, the essential qualitative properties of a network can be simultaneously deduced. Given a class of empirical networks, reconstruction schemes for elucidating the evolutionary dynamics leading to those particular data can then be developed. This method is exemplified for protein-protein interactionâ€¦ (More)

We have recently introduced Formanâ€™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 measuresâ€¦ (More)

- Brian T. White, J. Jost
- 2007

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 thatâ€¦ (More)

Quansheng Ren, Kiran M. Kolwankar, 2 Areejit Samal, 3 and JÃ¼rgen 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 ThÃ©orique et ModÃ¨les Statistiques, CNRS and Univ Paris-Sud, UMR 8626,â€¦ (More)

- Henry C. Tuckwell, J. Jost
- 2012

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 aâ€¦ (More)

- V. K. Oikonomou, J. Jost
- 2013

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 oneâ€¦ (More)

- J. Jost, Xianqing Li-Jost
- 1995

We study the bifurcation of closed minimal surfaces in Riemannian manifolds through higher order variations of the area functional and relate it to elementary catastrophes.

Areejit Samal, R.P. Sreejith, Jiao Gu, Shiping Liu, âˆ— Emil Saucan, 5, â€ and JÃ¼rgen Jost 7, â€¡ 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, ORTâ€¦ (More)