Exact Metric Research Articles

Collective Influence Maximization in Mobile Social Networks

The omnipresence of information cascading process in mobile social networking applications makes the identification of a small set <inline-formula><tex-math notation="LaTeX">$S$</tex-math></inline-formula> of influential users, which is widely believed to trigger the information outbreak, always an crucial issue in various applications such as the mobile advertising and viral marketing. Formulated as Influence maximization (IM) in 2003, this NP-hard problem has received a multitude of studies with diverse angles. However, these works often unable to provide reliable solutions, due to the loss of an exact metric for evaluating users’ contributions on information cascading in the state-of-the-art sampling based IM schemes. In this paper, we evaluate users in IM based on the collective influence (CI), a metric on the structural features of the users in network graph that reflects the contributions of the users’ neighborhoods on shaping collective dynamics of the users over the whole network. For conducting the influencer identification under probabilistic diffusion model based on the CI, we specify a quantified structural feature of the most influential users from the scope of diffusion over the whole network, and reveal that the structural influence power (CI value) of each user is a weighted cumulation of the diffusion probabilities from neighbors within certain hops. Utilizing CI, we design a novel algorithm which identifies the influencers via iteratively choosing the users with top CI values. Moreover, we point out that directly computing CI values requires to traverse the network which is originally represented by a high-dimensional matrix, and leads to huge complexity of influencer identification. To improve scalability, we further trade precision for efficiency by incorporating network embedding, a dimensionality reduction technology for networks, into algorithm design, and propose a minor variant, where CI is jointly recapitulated by low-dimensional user representations and user degrees. The superiority of our algorithms is empirically validated over 8 datasets, with an increment in influence size up to 50 percent and a comparable or even less running time comparing with existing baselines.

Kerr–Schild form of the exact metric for a constantly moving Kerr black hole and null gravitational deflection

The exact metric of a moving Kerr black hole with an arbitrary constant velocity is derived in Kerr–Schild coordinates. We then calculate the null equatorial gravitational deflection caused by a radially moving Kerr source up to the second post-Minkowskian order, acting as an application of the weak-field limit of the metric. The bending angle of light is found to be consistent with the result given in the previous works.

Gravitational Deflection of Massive Particles by a Schwarzschild Black Hole in Radiation Gauge**Supported by the National Natural Science Foundation of China under Grant No. 11647314 and the Research Foundation of Education Department of Hunan Province under Grant No. 18C0427

The exact metric of a Schwarzschild black hole in the true radiation gauge was recently reported. In this work, we base on this gravity and calculate the gravitational deflection of relativistic massive particles up to the fourth post-Minkowskian order. It is found that the result is consistent with the previous formulations for both the case of dropping the fourth-order contribution and the case of light deflection. Our result might be helpful for future high-accuracy observations.

Homographic p-norms: Metrics of homographic image transformation

Images often need to be aligned in a single coordinate system, and homography is one of the most efficient geometric models to align images. This paper presents homographic p-norms, scalar metrics of homographic image transformation, and to the best of our knowledge these are the most rigorous definition of scalar metrics quantifying homographic image transformations. We first define a metric between two homography matrices, and show it satisfies metric properties. Then we propose metrics of a single homography matrix for a general planar region, and ones for a usual rectangle image. For use of the proposed metrics, we provide useful homographic 2-norm expressions derived from the definition of the metrics, and compare the approximation errors of the metrics with respect to the exact metric. As a result, the discrete version of the metric obtained by pixel-wise computation is greatly close to the exact metric. The proposed metrics can be applied to evaluation of transformation magnitude, image closeness estimation, evaluation of camera pose difference, selection of image pair in stereo vision, panoramic image mosaic, and deblurring. Experimental results show the efficacy of the proposed metrics.

Neutron star structure in the presence of conformally coupled scalar fields

Neutron star models are studied in the context of scalar–tensor theories of gravity in the presence of a conformally coupled scalar field, using two different numerical equations of state (EoS) representing different degrees of stiffness. In both cases we obtain a complete solution by matching the interior numerical solution of the coupled Einstein-scalar field hydrostatic equations, with an exact metric on the surface of the star. These are then used to find the effect of the scalar field and its coupling to geometry, on the neutron star structure, particularly the maximum neutron star mass and radius. We show that in the presence of a conformally coupled scalar field, neutron stars are less dense and have smaller masses and radii than their counterparts in the minimally coupled case, and the effect increases with the magnitude of the scalar field at the center of the star.

A NONSINGULAR PERFECT FLUID CLASSICAL LEPTON MODEL OF ARBITRARILY SMALL RADIUS

We exhibit a classical lepton model based on a perfect fluid that reproduces leptonic charges and masses in arbitrarily small volumes without metric singularities or pressure discontinuities. This solution is the first of this kind to our knowledge, because to date the only classical general relativistic models that have reproduced leptonic charges and masses in arbitrarily small volumes are based on imperfect (anisotopic) fluids or perfect fluids with electric field discontinuities. We use a Maxwell–Einstein exact metric for a spherically symmetric static perfect fluid in a region in which the pressure vanishes at a boundary, beyond which the metric is of the Reissner–Nordström form. This construction models lepton mass and charge in the limit as the boundary → 0.

Reduced-Complexity Robust MIMO Decoders

We propose a robust near maximum-likelihood (ML) decoding metric that is robust to channel estimation errors and is near optimal with respect to symbol error rate (SER). The solution involves an exhaustive search through all possible transmitted signal vectors; this search has exponential complexity, which is undesirable in practical systems. Hence, we also propose a robust sphere decoder to implement the decoding with substantially lower computational complexity. For a real 4 x 4 MIMO system with 256-QAM modulation and at SER of 10^{-3}, our proposed robust sphere decoder has a coding loss of only 0.5 dB while searching through 2360 nodes (or less) compared to a 65536 node search using the exact ML metric. This translates to up to 228 times fewer real multiplications and additions in the implementation. We derive analytical upper bounds on the pairwise codeword error rate and symbol error rate of our robust sphere decoder and validate these bounds via simulation.

Unveiling the metric structure of internal representations of space

How are neuronal representations of space organized in the hippocampus? The self-organization of such representations, thought to be driven in the CA3 network by the strong randomizing input from the Dentate Gyrus, appears to run against preserving the topology and even less the exact metric of physical space. We present a way to assess this issue quantitatively, and find that in a simple neural network model of CA3, the average topology is largely preserved, but the local metric is loose, retaining e.g., 10% of the optimal spatial resolution.

Effective world-sheet theory for non-Abelian semilocal strings inN=2supersymmetric QCD

We consider non-Abelian semilocal strings (vortices, or vortex-strings) arising in N=2 supersymmetric U(N) gauge theory with Nf=N+\~N matter hypermultiplets in the fundamental representation (quarks), and a Fayet-Iliopoulos term {\xi}. We present, for the first time ever, a systematic field-theoretic derivation of the world-sheet theory for such strings, describing dynamics of both, orientational and size zero modes. Our derivation is complete in the limit, ln(L)\rightarrow \infty, where L is an infrared (IR) regulator in the transverse plane. In this limit the world-sheet theory is obtained exactly. It is presented by a so far unknown N=2 two-dimensional sigma model, to which we refer as the zn model, with or without twisted masses. Alternative formulations of the zn model are worked out: conventional and extended gauged formulations and a geometric formulation. We compare the exact metric of the zn model with that of the weighted CP(Nf-1) model conjectured by Hanany and Tong, through D-branes, as the world-sheet theory for the non-Abelian semilocal strings. The Hanany-Tong set-up has no parallel for the field-theoretic IR parameter and metrics of the weighted CP(Nf-1) model and zn model are different. Still their quasiclassical excitation spectra coincide.

GEOMETRIC DUALITY AND CHERN–SIMONS MODIFIED GRAVITY

We consider a theory which involves an extension of general relativity known as Chern–Simons modified gravity (CSMG). In this theory the standard Einstein–Hilbert action is extended with a gravitational Pontryagin density that is obtained from a divergence of a Chern–Simons topological current. The extended theory has the standard Schwarzchild metric as solution, however, only a perturbed Kerr metric holds solution. From the exact Kerr metric we construct dual metrics to search for rotating black hole solutions. The conditions on the Killing tensors associated with dual metrics entail nontrivial solutions to CSMG.

Gyromagnetic ratio of charged Kerr–anti-de Sitter black holes

We examine the gyromagnetic ratios of rotating and charged AdS black holes in four and higher spacetime dimensions. We compute the gyromagnetic ratio for Kerr–AdS black holes with an arbitrary electric charge in four dimensions and show that it corresponds to g = 2 irrespective of the AdS nature of the spacetime. We also compute the gyromagnetic ratio for Kerr–AdS black holes with a single angular momentum and with a test electric charge in all higher dimensions. The gyromagnetic ratio crucially depends on the dimensionless ratio of the rotation parameter to the curvature radius of the AdS background. At the critical limit, when the boundary Einstein universe is rotating at the speed of light, it exhibits a striking feature leading to g = 2 regardless of the spacetime dimension. Next, we extend our consideration to include the exact metric for five-dimensional rotating charged black holes in minimal gauged supergravity. We show that the value of the gyromagnetic ratio found in the ‘test-charge’ approach remains unchanged for these black holes.

Observing the Geometry of Warped Compactification via Cosmic Inflation

Using Dirac-Born-Infeld inflation as an example, we demonstrate that the detailed geometry of warped compactification can leave an imprint on the cosmic microwave background. We compute cosmic microwave background observables for Dirac-Born-Infeld inflation in a generic class of warped throats and find that the results (such as the sign of the tilt of the scalar perturbations and its running) depend sensitively on the precise shape of the warp factor. In particular, we analyze the warped deformed conifold and find that the results can differ from those of other warped geometries, even when these geometries approximate well the exact metric of the warped deformed conifold.

Bulk scalar stabilization of the radion without metric back reaction in the Randall-Sundrum model

Generalizations of the Randall-Sundrum model containing a bulk scalar field $\Phi$ interacting with the curvature $R$ through the general coupling $R f(\Phi)$ are considered. We derive the general form of the effective 4D potential for the spin-zero fields and show that in the mass matrix the radion mixes with the Kaluza-Klein modes of the bulk scalar fluctuations. We demonstrate that it is possible to choose a non-trivial background form $\Phi_0(y)$ (where $y$ is the extra dimension coordinate) for the bulk scalar field such that the exact Randall-Sundrum metric is preserved (i.e. such that there is no back-reaction). We compute the mass matrix for the radion and the KK modes of the excitations of the bulk scalar relative to the background configuration $\Phi_0(y)$ and find that the resulting mass matrix implies a non-zero value for the mass of the radion (identified as the state with the lowest eigenvalue of the scalar mass matrix). We find that this mass is suppressed relative to the Planck scale by the standard warp factor needed to explain the hierarchy puzzle, implying that a mass $\sim 1\tev$ is a natural order of magnitude for the radion mass. The general considerations are illustrated in the case of a model containing an $R\Phi^2$ interaction term.

Rotating deformations of AdS3× S3, the orbifold CFT and strings in the pp-wave limit

We construct an exact metric which at short distances is the metric of massless particles in 5+1 spacetime (moving along a diameter of the sphere) and is AdS 3× S 3 at infinity. We also consider a set of a conical defect spacetimes which are locally AdS 3× S 3 and have the masses and charges of a special set of chiral primaries of the dual orbifold CFT. We find that excitation energies for a scalar field in the latter geometries agree exactly with the excitations in the corresponding CFT state created by twist operators: redshift in the geometry reproduces ‘long circle’ physics in the CFT. We propose a map of string states in AdS 3× S 3× T 4 to states in the orbifold CFT, analogous to the recently discovered map for AdS 5× S 5. The vibrations of the string can be pictured as oscillations of a Fermi sea in the CFT.

N = 4 Supersymmetric (Dyonic) Hypermultiplets in String Theory

In four-dimensional N = 4 supersymmetric gauge theory, we obtain an exact metric on the moduli space of quantum vacua and analyze the spectra of BPS states in weak as well as in strong coupling regions. Identifying the hypermultiplet of the dyonic state as a string stretched between D3-brane probe and a 7-brane, we demonstrate that the two hypermultiplets, which become massless at two singularities in supersymmetric theory, correspond to open strings beginning on the D3-brane and ending on the respective 7-brane.

Exact Metric for the Exterior of a Global String in the Brans-Dicke Theory

We determine in closed form the general static solution with cylindrical symmetry to the Brans-Dicke equations for an energy-momentum tensor corresponding to the one of the straight U(1) global string outside the core radius assuming that the Goldstone boson field takes its asymptotic value

Moduli space of many BPS monopoles for arbitrary gauge groups.

We study the moduli space for an arbitrary number of BPS monopoles in a gauge theory with an arbitrary gauge group that is maximally broken to $U(1)^k$. From the low energy dynamics of well-separated dyons we infer the asymptotic form of the metric for the moduli space. For a pair of distinct fundamental monopoles, the space thus obtained is $R^3 \times(R^1\times {\cal M}_0)/Z$ where ${\cal M}_0$ is the Euclidean Taub-NUT manifold. Following the methods of Atiyah and Hitchin, we demonstrate that this is actually the exact moduli space for this case. For any number of such objects, we show that the asymptotic form remains nonsingular for all values of the intermonopole distances and that it has the symmetries and other characteristics required of the exact metric. We therefore conjecture that the asymptotic form is exact for these cases also.

Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD

We study four dimensional N = 2 supersymmetric gauge theories with matter multiplets. For all such models for which the gauge group is SU(2), we derive the exact metric on the moduli space of quantum vacua and the exact spectrum of the stable massive states. A number of new physical phenomena occur, such as chiral symmetry breaking that is driven by the condensation of magnetic monopoles that carry global quantum numbers. For those cases in which conformal invariance is broken only by mass terms, the formalism automatically gives results that are invariant under electric-magnetic duality. In one instance, this duality is mixed in an interesting way with SO(8) triality.

Matter-ghost mixing and the exact 2D black hole metric

We study a revised version of Witten's 2D black hole, in which the matter and ( b, c) ghosts are mixed. The level of the coset model is still 9 4 . We show that this model is equivalent to that of Mukhi and Vafa, in which the level of the coset model is taken as 3, and the stress tensor is improved. We argue that the exact metric in such a model is just the semi-classical one, quite different from the exact metric in Witten's black hole, being studied by Dijkgraaf, Verlinde and Verlinde. In addition, there appear ghost-related terms as a part of the background in the world sheet action.

Gravitational lensing properties of curved cosmic strings

We examine the effect of a Gaussian wave pulse, propagating along a cosmic string, on both the observed position and redshift of the double images of an object behind the string. We also calculate the effect of the string on a rectangular grid of stars which are located infinitely far behind the string. The calculations are done numerically using the exact metric for a traveling wave recently discovered by Garfinkle.