Why Do Cascade Sizes Follow a Power-Law?

We introduce random directed acyclic graph and use it to model the information diffusion network. Subsequently, we analyze the cascade generation model (CGM) introduced by Leskovec et al. [19]. Until now only empirical studies of this model were done. In this paper, we present the first theoretical proof that the sizes of cascades generated by the CGM follow the power-law distribution, which is consistent with multiple empirical analysis of the large social networks. We compared the assumptions of our model with the Twitter social network and tested the goodness of approximation.Comment: 8 pages, 7 figures, accepted to WWW 201

Local Quantum Measurement and No-Signaling Imply Quantum Correlations

We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the tensor product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond quantum mechanics, quantum theory would be invalidated even locally.Comment: Published version. 5 pages, 1 figure

Prompt and delayed secondary excitons in rare gas solids

Direct and indirect creation of excitons in rare gas solids has been investigated with reflectivity and luminescence spectroscopy. For the heavy rare gas solids Kr and Xe, new and more reliable exciton parameters have been deduced. With time-resolved luminescence spectroscopy, fast and delayed secondary-exciton creation has been established and separated. Thermalization of photocarriers and their delayed recombination have been analyzed, including a first attempt to investigate the influence of excitation density on the carrier dynamics. The existence of excitonic side bands of ionization limits Ei (either band gap or inner-shell ionization limits) in prompt secondary exciton creation has been established. The threshold energies of these side bands are given by Eth≈Ei nEex (n is integer, Eex is exciton energy). The side bands are ascribed to the formation of electronic polaron complexes, superimposed to inelastic scattering of photoelectrons

Computability limits non-local correlations

If the no-signalling principle was the only limit to the strength of non-local correlations, we would expect that any form of no-signalling correlation can indeed be realized. That is, there exists a state and measurements that remote parties can implement to obtain any such correlation. Here, we show that in any theory in which some functions cannot be computed, there must be further limits to non-local correlations than the no-signalling principle alone. We proceed to argue that even in a theory such as quantum mechanics in which non-local correlations are already weaker, the question of computability imposes such limits.Comment: 5 pages, 1 figure, revte

Entropy in general physical theories

Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world, our measure reduces to the von Neumann and Shannon entropy respectively. It can even be used in a quantum or classical setting where we are only allowed to perform a limited set of operations. In a world that admits superstrong correlations in the form of non-local boxes, our measure can be used to analyze protocols such as superstrong random access encodings and the violation of `information causality'. However, we also show that in such a world no entropic measure can exhibit all properties we commonly accept in a quantum setting. For example, there exists no`reasonable' measure of conditional entropy that is subadditive. Finally, we prove a coding theorem for some theories that is analogous to the quantum and classical setting, providing us with an appealing operational interpretation.Comment: 20 pages, revtex, 7 figures, v2: Coding theorem revised, published versio

Quantifying methane vibrational and rotational temperature with Raman scattering

This work describes the theoretical basis and implementation of the measurement of vibrational (T vib) and rotational (T rot) temperatures in CH4 by fitting spontaneous Raman scattering spectra in the Pentad region. This method could be applied for thermal equilibrium temperature measurements applications, e.g. in combustion, or vibrational-rotational non-equilibrium applications, such as in plasma chemistry. The method of calculating these temperatures is validated against known temperature thermal equilibrium spectra up to 860 K from published data, giving an estimated relative error of 10%. This demonstrates that both the calculated stick spectrum and the algorithm to determine T vib and T rot for CH4 is robust to 860 K, but we expect it is valid to 1500 K. Additionally, a number of non-equilibrium spectra generated with a pulsed microwave plasma are fitted to find T vib and T rot, further demonstrating the applicability of this method in fitting non-equilibrium spectra.</p

Inference of hidden structures in complex physical systems by multi-scale clustering

We survey the application of a relatively new branch of statistical physics--"community detection"-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the quest of partitioning a complex system involving many elements into optimally decoupled subsets or communities of such elements. We review a multiresolution variant which is used to ascertain structures at different spatial and temporal scales. Significant patterns are obtained by examining the correlations between different independent solvers. Similar to other combinatorial optimization problems in the NP complexity class, community detection exhibits several phases. Typically, illuminating orders are revealed by choosing parameters that lead to extremal information theory correlations.Comment: 25 pages, 16 Figures; a review of earlier work

Epidemic processes in complex networks

In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio

Evidence for a Minimal Eukaryotic Phosphoproteome?

BACKGROUND: Reversible phosphorylation catalysed by kinases is probably the most important regulatory mechanism in eukaryotes. METHODOLOGY/PRINCIPAL FINDINGS: We studied the in vitro phosphorylation of peptide arrays exhibiting the majority of PhosphoBase-deposited protein sequences, by factors in cell lysates from representatives of various branches of the eukaryotic species. We derived a set of substrates from the PhosphoBase whose phosphorylation by cellular extracts is common to the divergent members of different kingdoms and thus may be considered a minimal eukaryotic phosphoproteome. The protein kinases (or kinome) responsible for phosphorylation of these substrates are involved in a variety of processes such as transcription, translation, and cytoskeletal reorganisation. CONCLUSIONS/SIGNIFICANCE: These results indicate that the divergence in eukaryotic kinases is not reflected at the level of substrate phosphorylation, revealing the presence of a limited common substrate space for kinases in eukaryotes and suggests the presence of a set of kinase substrates and regulatory mechanisms in an ancestral eukaryote that has since remained constant in eukaryotic life