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Register a new userWhy we live in hierarchies: a quantitative treatise
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This book is concerned with the various aspects of hierarchical collective behaviour which is manifested by most complex systems in nature. From the many of the possible topics, we plan to present a selection of those that we think are useful from the point of shedding light from very different directions onto our quite general subject. Our intention is to both present the essential contributions by the existing approaches as well as go significantly beyond the results obtained by traditional methods by applying a more quantitative approach then the common ones (there are many books on qualitative interpretations). In addition to considering hierarchy in systems made of similar kinds of units, we shall concentrate on problems involving either dominance relations or the process of collective decision-making from various viewpoints.
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In the context of string theory we argue that higher dimensional Dp-branes unwind and evaporate so that we are left with D3-branes embedded in a (9+1)-dimensional bulk. One of these D3-branes plays the role of our Universe. Within this picture, the evaporation of the higher dimensional Dp-branes provides the entropy of our Universe.
What happens when you slow down part of an ultrafast network that is operating quicker than the blink of an eye, e.g. electronic exchange network, navigational systems in driverless vehicles, or even neuronal processes in the brain? This question just adopted immediate commercial, legal and political importance following U.S. financial regulators decision to allow a new network node to intentionally introduce delays of microseconds. Though similar requests are set to follow, there is still no scientific understanding available to policymakers of the likely system-wide impact of such delays. Giving academic researchers access to (so far prohibitively expensive) microsecond exchange data would help rectify this situation. As a by-product, the lessons learned would deepen understanding of instabilities across myriad other networks, e.g. impact of millisecond delays on brain function and safety of driverless vehicle navigation systems beyond human response times.
I cast doubt upon the desired consistency between the anthropic principle and modern cosmology.
The Susceptible-Infected-Susceptible model is a canonical model for emerging disease outbreaks. Such outbreaks are naturally modeled as taking place on networks. A theoretical challenge in network epidemiology is the dynamic correlations coming from that if one node is occupied, or infected (for disease spreading models), then its neighbors are likely to be occupied. By combining two theoretical approaches---the heterogeneous mean-field theory and the effective degree method---we are able to include these correlations in an analytical solution of the SIS model. We derive accurate expressions for the average prevalence (fraction of infected) and epidemic threshold. We also discuss how to generalize the approach to a larger class of stochastic population models.
We propose that the constants of Nature we observe (which appear as parameters in the classical action) are quantum observables in a kinematical Hilbert space. When all of these observables commute, our proposal differs little from the treatment given to classical parameters in quantum information theory, at least if we were to inhabit a constants eigenstate. Non-commutativity introduces novelties, due to its associated uncertainty and complementarity principles, and it may even preclude hamiltonian evolution. The system typically evolves as a quantum superposition of hamiltonian evolutions resulting from a diagonalization process, and these are usually quite distinct from the original one (defined in terms of the non-commuting constants). We present several examples targeting $G$, $c$ and $Lambda $, and the dynamics of homogeneous and isotropic Universes. If we base our construction on the Heisenberg algebra and the quantum harmonic oscillator, the alternative dynamics tends to silence matter (effectively setting $G$ to zero), and make curvature and the cosmological constant act as if their signs are reversed. Thus, the early Universe expands as a quantum superposition of different Milne or de Sitter expansions for all material equations of state, even though matter nominally dominates the density, $rho $, because of the negligible influence of $Grho $ on the dynamics. A superposition of Einstein static universes can also be obtained. We also investigate the results of basing our construction on the algebra of $SU(2)$, into which we insert information about the sign of a constant of Nature, or whether its action is switched on or off. In this case we find examples displaying quantum superpositions of bounces at the initial state for the Universe.
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