Gabor Duality Theory for Morita Equivalent C∗C^*-algebras

The duality principle for Gabor frames is one of the pillars of Gabor analysis. We establish a far-reaching generalization to Morita equivalent $C^*$-algebras where the equivalence bimodule is a finitely generated projective Hilbert $C^*$-module. These Hilbert $C^*$-modules are equipped with some extra structure and are called Gabor bimodules. We formulate a duality principle for standard module frames for Gabor bimodules which reduces to the well-known Gabor duality principle for twisted group $C^*$-algebras of a lattice in phase space. We lift all these results to the matrix algebra level and in the description of the module frames associated to a matrix Gabor bimodule we introduce $(n,d)$-matrix frames, which generalize superframes and multi-window frames. Density theorems for $(n,d)$-matrix frames are established, which extend the ones for multi-window and super Gabor frames. Our approach is based on the localization of a Hilbert $C^*$-module with respect to a trace.Comment: 36 page

Symmetry Breaking for Matter Coupled to Linearized Supergravity From the Perspective of the Current Supermultiplet

We consider a generic supersymmetric matter theory coupled to linearized supergravity, and analyze scenarios for spontaneous symmetry breaking in terms of vacuum expectation values of components of the current supermultiplet. When the vacuum expectation of the energy momentum tensor is zero, but the scalar current or pseudoscalar current gets an expectation, evaluation of the gravitino self energy using the supersymmetry current algebra shows that there is an induced gravitino mass term. The structure of this term generalizes the supergravity action with cosmological constant to theories with CP violation. When the vacuum expectation of the energy momentum tensor is nonzero, supersymmetry is broken; requiring cancellation of the cosmological constant gives the corresponding generalized gravitino mass formula.Comment: 11 page

Understanding Perceptions of Problematic Facebook Use: When People Experience Negative Life Impact and a Lack of Control

While many people use social network sites to connect with friends and family, some feel that their use is problematic, seriously affecting their sleep, work, or life. Pairing a survey of 20,000 Facebook users measuring perceptions of problematic use with behavioral and demographic data, we examined Facebook activities associated with problematic use as well as the kinds of people most likely to experience it. People who feel their use is problematic are more likely to be younger, male, and going through a major life event such as a breakup. They spend more time on the platform, particularly at night, and spend proportionally more time looking at profiles and less time browsing their News Feeds. They also message their friends more frequently. While they are more likely to respond to notifications, they are also more likely to deactivate their accounts, perhaps in an effort to better manage their time. Further, they are more likely to have seen content about social media or phone addiction. Notably, people reporting problematic use rate the site as more valuable to them, highlighting the complex relationship between technology use and well-being. A better understanding of problematic Facebook use can inform the design of context-appropriate and supportive tools to help people become more in control.Comment: CHI 201

Nonrenormalization of Flux Superpotentials in String Theory

Recent progress in understanding modulus stabilization in string theory relies on the existence of a non-renormalization theorem for the 4D compactifications of Type IIB supergravity which preserve N=1 supersymmetry. We provide a simple proof of this non-renormalization theorem for a broad class of Type IIB vacua using the known symmetries of these compactifications, thereby putting them on a similar footing as the better-known non-renormalization theorems of heterotic vacua without fluxes. The explicit dependence of the tree-level flux superpotential on the dilaton field makes the proof more subtle than in the absence of fluxes.Comment: 16 pages, no figures. Final version, to appear in JHEP. Arguments for validity of R-symmetry made more explicit. Minor extra comments and references adde

Data-based estimates of the ocean carbon sink variability – First results of the Surface Ocean pCO2 Mapping intercomparison (SOCOM)

Using measurements of the surface-ocean CO2 partial pressure (pCO2) and 14 different pCO2 mapping methods recently collated by the Surface Ocean pCO2 Mapping intercomparison (SOCOM) initiative, variations in regional and global sea–air CO2 fluxes are investigated. Though the available mapping methods use widely different approaches, we find relatively consistent estimates of regional pCO2 seasonality, in line with previous estimates. In terms of interannual variability (IAV), all mapping methods estimate the largest variations to occur in the eastern equatorial Pacific. Despite considerable spread in the detailed variations, mapping methods that fit the data more closely also tend to agree more closely with each other in regional averages. Encouragingly, this includes mapping methods belonging to complementary types – taking variability either directly from the pCO2 data or indirectly from driver data via regression. From a weighted ensemble average, we find an IAV amplitude of the global sea–air CO2 flux of 0.31 PgC yr−1 (standard deviation over 1992–2009), which is larger than simulated by biogeochemical process models. From a decadal perspective, the global ocean CO2 uptake is estimated to have gradually increased since about 2000, with little decadal change prior to that. The weighted mean net global ocean CO2 sink estimated by the SOCOM ensemble is −1.75 PgC yr−1 (1992–2009), consistent within uncertainties with estimates from ocean-interior carbon data or atmospheric oxygen trend

Equilibrium configurations of two charged masses in General Relativity

An asymptotically flat static solution of Einstein-Maxwell equations which describes the field of two non-extreme Reissner - Nordstr\"om sources in equilibrium is presented. It is expressed in terms of physical parameters of the sources (their masses, charges and separating distance). Very simple analytical forms were found for the solution as well as for the equilibrium condition which guarantees the absence of any struts on the symmetry axis. This condition shows that the equilibrium is not possible for two black holes or for two naked singularities. However, in the case when one of the sources is a black hole and another one is a naked singularity, the equilibrium is possible at some distance separating the sources. It is interesting that for appropriately chosen parameters even a Schwarzschild black hole together with a naked singularity can be "suspended" freely in the superposition of their fields.Comment: 4 pages; accepted for publication in Phys. Rev.

Motional Squashed States

We show that by using a feedback loop it is possible to reduce the fluctuations in one quadrature of the vibrational degree of freedom of a trapped ion below the quantum limit. The stationary state is not a proper squeezed state, but rather a ``squashed'' state, since the uncertainty in the orthogonal quadrature, which is larger than the standard quantum limit, is unaffected by the feedback action.Comment: 8 pages, 2 figures, to appear in the special Issue "Quantum Correlations and Fluctuations" of J. Opt.

Coupled coarse graining and Markov Chain Monte Carlo for lattice systems

We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models, capable of handling correctly long and short-range particle interactions. The proposed method is a Metropolis-type algorithm with the proposal probability transition matrix based on the coarse-grained approximating measures introduced in a series of works of M. Katsoulakis, A. Majda, D. Vlachos and P. Plechac, L. Rey-Bellet and D.Tsagkarogiannis,. We prove that the proposed algorithm reduces the computational cost due to energy differences and has comparable mixing properties with the classical microscopic Metropolis algorithm, controlled by the level of coarsening and reconstruction procedure. The properties and effectiveness of the algorithm are demonstrated with an exactly solvable example of a one dimensional Ising-type model, comparing efficiency of the single spin-flip Metropolis dynamics and the proposed coupled Metropolis algorithm.Comment: 20 pages, 4 figure

Charged Particles in a 2+1 Curved Background

The coupling to a 2+1 background geometry of a quantized charged test particle in a strong magnetic field is analyzed. Canonical operators adapting to the fast and slow freedoms produce a natural expansion in the inverse square root of the magnetic field strength. The fast freedom is solved to the second order. At any given time, space is parameterized by a couple of conjugate operators and effectively behaves as the `phase space' of the slow freedom. The slow Hamiltonian depends on the magnetic field norm, its covariant derivatives, the scalar curvature and presents a peculiar coupling with the spin-connection.Comment: 22 page