Network-based ranking in social systems: three challenges

Ranking algorithms are pervasive in our increasingly digitized societies, with important real-world applications including recommender systems, search engines, and influencer marketing practices. From a network science perspective, network-based ranking algorithms solve fundamental problems related to the identification of vital nodes for the stability and dynamics of a complex system. Despite the ubiquitous and successful applications of these algorithms, we argue that our understanding of their performance and their applications to real-world problems face three fundamental challenges: (i) Rankings might be biased by various factors; (2) their effectiveness might be limited to specific problems; and (3) agents' decisions driven by rankings might result in potentially vicious feedback mechanisms and unhealthy systemic consequences. Methods rooted in network science and agent-based modeling can help us to understand and overcome these challenges.Comment: Perspective article. 9 pages, 3 figure

Multiplet Structures of BPS Solitons

There exist simple single-charge and multi-charge BPS p-brane solutions in the D-dimensional maximal supergravities. From these, one can fill out orbits in the charge vector space by acting with the global symmetry groups. We give a classification of these orbits, and the associated cosets that parameterise them.Comment: Latex, 34 pages, comments and reference adde

Massive Three-Dimensional Supergravity From R+R^2 Action in Six Dimensions

We obtain a three-parameter family of massive N=1 supergravities in three dimensions from the 3-sphere reduction of an off-shell N=(1,0) six-dimensional Poincare supergravity that includes a curvature squared invariant. The three-dimensional theory contains an off-shell supergravity multiplet and an on-shell scalar matter multiplet. We then generalise this in three dimensions to an eight-parameter family of supergravities. We also find a duality relationship between the six-dimensional theory and the N=(1,0) six-dimensional theory obtained through a T^4 reduction of the heterotic string effective action that includes the higher-order terms associated with the supersymmetrisation of the anomaly-cancelling \tr(R\wedge R) term.Comment: Latex, 32 Pages, an equation is corrected, a few new equations and a number of clarifying remarks are adde

Spherically Symmetric Solutions in Higher-Derivative Gravity

Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantised gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type `no-hair' theorem. From a Frobenius analysis of the asymptotic small-radius behaviour, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analysed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match on to an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to `vacuum' solutions. In addition to the three families identified from near-origin behaviour, there are solutions that may be identified as `wormholes', which can match symmetrically on to another sheet of spacetime at finite radius.Comment: 57 pages, 6 figures; version appearing in journal; minor corrections and clarifications to v

f(R) Theories of Supergravities and Pseudo-supergravities

We present f(R) theories of ten-dimensional supergravities, including the fermionic sector up to the quadratic order in fermion fields. They are obtained by performing the conformal scaling on the usual supergravities to the f(R) frame in which the dilaton becomes an auxiliary field and can be integrated out. The f(R) frame coincides with that of M-theory, D2-branes or NS-NS 5-branes. We study various BPS p-brane solutions and their near-horizon AdS \times sphere geometries in the context of the f(R) theories. We find that new solutions emerge with global structures that do not exist in the corresponding solutions of the original supergravity description. In lower dimensions, We construct the f(R) theory of N=2, D=5 gauged supergravity with a vector multiplet, and that for the four-dimensional U(1)^4 gauged theory with three vector fields set equal. We find that some previously-known BPS singular "superstars" become wormholes in the f(R) theories. We also construct a large class of f(R) (gauged) pseudo-supergravities. In addition we show that the breathing mode in the Kaluza-Klein reduction of Gauss-Bonnet gravity on S^1 is an auxiliary field and can be integrated out.Comment: Latex, 46 page

From p-branes to Cosmology

We study the relationship between static p-brane solitons and cosmological solutions of string theory or M-theory. We discuss two different ways in which extremal p-branes can be generalised to non-extremal ones, and show how wide classes of recently discussed cosmological models can be mapped into non-extremal p-brane solutions of one of these two kinds. We also extend previous discussions of cosmological solutions to include some that make use of cosmological-type terms in the effective action that can arise from the generalised dimensional reduction of string theory or M-theory.Comment: Latex, 24 pages, no figur

Pseudo-Killing Spinors, Pseudo-supersymmetric p-branes, Bubbling and Less-bubbling AdS Spaces

We consider Einstein gravity coupled to an n-form field strength in D dimensions. Such a theory cannot be supersymmetrized in general, we nevertheless propose a pseudo-Killing spinor equation and show that the AdS X Sphere vacua have the maximum number of pseudo-Killing spinors, and hence are fully pseudo-supersymmetric. We show that extremal p-branes and their intersecting configurations preserve fractions of the pseudo-supersymmetry. We study the integrability condition for general (D,n) and obtain the additional constraints that are required so that the existence of the pseudo-Killing spinors implies the Einstein equations of motion. We obtain new pseudo-supersymmetric bubbling AdS_5 X S^5 spaces that are supported by a non-self-dual 5-form. This demonstrates that non-supersymmegtric conformal field theories may also have bubbling states of arbitrary droplets of free fermions in the phase space. We also obtain an example of less-bubbling AdS geometry in D=8, whose bubbling effects are severely restricted by the additional constraint arising from the integrability condition.Comment: typos corrected, extra comments and references added, version appeared in JHE

Gauged Six-dimensional Supergravity from Massive Type IIA

We obtain the complete non-linear Kaluza-Klein ansatz for the reduction of the bosonic sector of massive type IIA supergravity to the Romans F(4) gauged supergravity in six dimensions. The latter arises as a consistent warped S^4 reduction.Comment: Latex, 7 page

Cosmological Solutions in String Theories

We obtain a large class of cosmological solutions in the toroidally-compactified low energy limits of string theories in $D$ dimensions. We consider solutions where a $p$-dimensional subset of the spatial coordinates, parameterising a flat space, a sphere, or an hyperboloid, describes the spatial sections of the physically-observed universe. The equations of motion reduce to Liouville or $SL(N+1,R)$ Toda equations, which are exactly solvable. We study some of the cases in detail, and find that under suitable conditions they can describe four-dimensional expanding universes. We discuss also how the solutions in $D$ dimensions behave upon oxidation back to the $D=10$ string theory or $D=11$ M-theory.Comment: Latex, 21 pages, a reference adjuste

Fibre Bundles and Generalised Dimensional Reduction

We study some geometrical and topological aspects of the generalised dimensional reduction of supergravities in D=11 and D=10 dimensions, which give rise to massive theories in lower dimensions. In these reductions, a global symmetry is used in order to allow some of the fields to have a non-trivial dependence on the compactifying coordinates. Global consistency in the internal space imposes topological restrictions on the parameters of the compactification as well as the structure of the space itself. Examples that we consider include the generalised reduction of the type IIA and type IIB theories on a circle, and also the massive ten-dimensional theory obtained by the generalised reduction of D=11 supergravity.Comment: 23 pages, Late