Temporal stability of network partitions

We present a method to find the best temporal partition at any time-scale and rank the relevance of partitions found at different time-scales. This method is based on random walkers coevolving with the network and as such constitutes a generalization of partition stability to the case of temporal networks. We show that, when applied to a toy model and real datasets, temporal stability uncovers structures that are persistent over meaningful time-scales as well as important isolated events, making it an effective tool to study both abrupt changes and gradual evolution of a network mesoscopic structures.Comment: 15 pages, 12 figure

PP-persistent homology of finite topological spaces

Let $P$ be a finite poset. We will show that for any reasonable $P$-persistent object $X$ in the category of finite topological spaces, there is a $P-$ weighted graph, whose clique complex has the same $P$-persistent homology as $X$

Developing Indicators for Regional Economic Integration and Cooperation

We develop indicators to measure the degree of economic integration and cooperation among East Asian economies and compare these with similar measures for other regions. Our indicators cover regional integration in trade, investment, financial assets, and people-to-people exchange. We also analyze measures of regional cooperation such as the density of free trade agreements and official policy dialogues. We find that in various Asian groupings, and especially in a group of 16 integrating Asian economies, interdependence in trade, direct investment, financial flows, and other forms of economic and social exchange has increased significantly over time, and now approaches that in the European Union. Nonetheless, Asia’s official cooperation remains weak and formal regional institutions remain relatively underdeveloped. To provide insight into the causes of this discrepancy, we also develop quantitative measures of political and cultural similarity of nations, and find that Asian countries have relatively low levels of political and cultural proximity compared to regions such as Europe. The diversity of political interests and cultural values may have hindered more intense cooperation among Asian economies in the past. But if regional economic and social interactions continue to grow, requirements for joint decision-making are also likely to expand, leading to stronger frameworks of official cooperation.Regional integration; economic cooperation; East Asia

Construction of and efficient sampling from the simplicial configuration model

Simplicial complexes are now a popular alternative to networks when it comes to describing the structure of complex systems, primarily because they encode multi-node interactions explicitly. With this new description comes the need for principled null models that allow for easy comparison with empirical data. We propose a natural candidate, the simplicial configuration model. The core of our contribution is an efficient and uniform Markov chain Monte Carlo sampler for this model. We demonstrate its usefulness in a short case study by investigating the topology of three real systems and their randomized counterparts (using their Betti numbers). For two out of three systems, the model allows us to reject the hypothesis that there is no organization beyond the local scale.Comment: 6 pages, 4 figure

P-persistent homology of finite topological spaces

Let P be a finite poset. We will show that for any reasonable P-persistent object X in the category of finite topological spaces, there is a P− weighted graph, whose clique complex has the same P-persistent homology as X

the shape of collaborations

Abstract The structure of scientific collaborations has been the object of intense study both for its importance for innovation and scientific advancement, and as a model system for social group coordination and formation thanks to the availability of authorship data. Over the last years, complex networks approach to this problem have yielded important insights and shaped our understanding of scientific communities. In this paper we propose to complement the picture provided by network tools with that coming from using simplicial descriptions of publications and the corresponding topological methods. We show that it is natural to extend the concept of triadic closure to simplicial complexes and show the presence of strong simplicial closure. Focusing on the differences between scientific fields, we find that, while categories are characterized by different collaboration size distributions, the distributions of how many collaborations to which an author is able to participate is conserved across fields pointing to underlying attentional and temporal constraints. We then show that homological cycles, that can intuitively be thought as hole in the network fabric, are an important part of the underlying community linking structure

Persistent Homology analysis of Phase Transitions

Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called XY-mean field model and by the phi^4 lattice model, respectively. For both models the relationship between phase transitions and the topological properties of certain submanifolds of configuration space are exactly known. It turns out that these a-priori known facts are clearly retrieved by persistent homology analysis of dynamically sampled submanifolds of configuration space.Comment: 10 pages; 10 figure

Developing Indicators for Regional Economic Integration and Cooperation

We develop indicators to measure the degree of economic integration and cooperation among East Asian economies and compare these with similar measures for other regions. Our indicators cover regional integration in trade, investment, financial assets, and people-to-people exchange. We also analyze measures of regional cooperation such as the density of free trade agreements and official policy dialogues. We find that in various Asian groupings, and especially in a group of 16 integrating Asian economies, interdependence in trade, direct investment, financial flows, and other forms of economic and social exchange has increased significantly over time, and now approaches that in the European Union. Nonetheless, Asia’s official cooperation remains weak and formal regional institutions remain relatively underdeveloped. To provide insight into the causes of this discrepancy, we also develop quantitative measures of political and cultural similarity of nations, and find that Asian countries have relatively low levels of political and cultural proximity compared to regions such as Europe. The diversity of political interests and cultural values may have hindered more intense cooperation among Asian economies in the past. But if regional economic and social interactions continue to grow, requirements for joint decision-making are also likely to expand, leading to stronger frameworks of official cooperation

On Non-Gaussianity of the Cosmological Perturbation

The primordial curvature perturbation (ζ), generated during or at the end of Inflation, is the seed of present structures. Non Gaussianity in ζ is an efficient tool to discriminate among the different theoretical mechanisms which are thought to be generating ζ. We study the effects of including high order loop corrections of a λφ^4 massless scalar field theory during a de Sitter stage in the prediction of non Gaussianity in the trispectrum, i.e.the 4-point correlation function