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Here we give further evidences to support our scaling relation described in our previous paper [cond-mat/0006459, Phys. Rev. Lett. Vol.85, pp.1238 (2000)].
Using data from computer databases of scientific papers in physics, biomedical research, and computer science, we have constructed networks of collaboration between scientists in each of these disciplines. In these networks two scientists…
I introduce new Langlands duality conjectures concerning skein modules of 3-manifolds, which we have made recently with David Ben-Zvi, Sam Gunningham, and Pavel Safronov. I recount some historical motivation and some recent special cases…
We introduce the pro-tensor network, a categorification of the tensor network, as a fully rigorous yet graphically transparent framework for studying the collection of many many-body theories, which we dub many-many-body theory. We provide…
We reprove and extend a result of David Krebes (J. Knot Theory Ramif. 8 (1999), 321-352) giving an obstruction to embedding a tangle T into a link L. Closing the tangle up in the two obvious ways gives rise to two links, the numerator and…
Networks represent relationships between entities in many complex systems, spanning from online social interactions to biological cell development and brain connectivity. In many cases, relationships between entities are unambiguously…
Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…
An intuitive overview of the scalability of a variety of types of wireless networks is presented. Simple heuris- tic arguments are demonstrated here for scaling laws presented in other works, as well as for conditions not previously…
This expository article delves into the Greenlees-May Duality Theorem which is widely thought of as a far-reaching generalization of the Grothendieck's Local Duality Theorem. This theorem is not addressed in the literature as it merits and…
We introduce a model of polarization in networks as a unifying framework for the measurement of polarization that covers a wide range of applications. We consider a sufficiently general setup for this purpose: node- and edge-weighted,…
Invited discussion on the paper "Hybrid Semiparametric Bayesian Networks" by David Atienza, Pedro Larranaga and Concha Bielza (TEST, 2022).
With regard to the recently published article, ``Y.-Q. Wang, et al., Physical mechanism of equiprobable exclusion network with heterogeneous interactions in phase transitions: Analytical analyses of steady state evolving from initial state,…
We prove that, for a link $L$ in a rational homology 3--sphere, the link Floer homology detects the Thurston norm of its complement. This generalizes the previous results due to Ozsv\'ath, Szab\'o and the author.
Signed networks appear naturally in contexts where conflict or animosity is apparent. In this book chapter we review some of the literature on signed networks, especially in the context of partitioning. Most of the work is founded in what…
News Articles provides crucial information about various events happening in the society but they unfortunately come with different kind of biases. These biases can significantly distort public opinion and trust in the media, making it…
Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we…
Misinformation is still a major societal problem and the arrival of Large Language Models (LLMs) only added to it. This paper analyzes synthetic, false, and genuine information in the form of text from spectral analysis, visualization, and…
The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.
Knowledge networks have become increasingly important as a changing repository of data which can be represented, studied and modeled by using complex networks concepts and methodologies. Here we report a study of knowledge networks…
The structural properties of the network generated by the editorial activities of the members of the boards of "Information Science & Library Science" journals are explored through network analysis techniques. The crossed presence of…