Measuring Online Social Bubbles

Social media have quickly become a prevalent channel to access information, spread ideas, and influence opinions. However, it has been suggested that social and algorithmic filtering may cause exposure to less diverse points of view, and even foster polarization and misinformation. Here we explore and validate this hypothesis quantitatively for the first time, at the collective and individual levels, by mining three massive datasets of web traffic, search logs, and Twitter posts. Our analysis shows that collectively, people access information from a significantly narrower spectrum of sources through social media and email, compared to search. The significance of this finding for individual exposure is revealed by investigating the relationship between the diversity of information sources experienced by users at the collective and individual level. There is a strong correlation between collective and individual diversity, supporting the notion that when we use social media we find ourselves inside "social bubbles". Our results could lead to a deeper understanding of how technology biases our exposure to new information

Elliptic Thermal Correlation Functions and Modular Forms in a Globally Conformal Invariant QFT

Global conformal invariance (GCI) of quantum field theory (QFT) in two and higher space-time dimensions implies the Huygens' principle, and hence, rationality of correlation functions of observable fields (see Commun. Math. Phys. 218 (2001) 417-436; hep-th/0009004). The conformal Hamiltonian $H$ has discrete spectrum assumed here to be finitely degenerate. We then prove that thermal expectation values of field products on compactified Minkowski space can be represented as finite linear combinations of basic (doubly periodic) elliptic functions in the conformal time variables (of periods 1 and $\tau$) whose coefficients are, in general, formal power series in $q^{1/2}=e^{i\pi\tau}$ involving spherical functions of the "space-like" fields' arguments. As a corollary, if the resulting expansions converge to meromorphic functions, then the finite temperature correlation functions are elliptic. Thermal 2-point functions of free fields are computed and shown to display these features. We also study modular transformation properties of Gibbs energy mean values with respect to the (complex) inverse temperature $\tau$ ($Im(\tau)=\beta/(2\pi)>0$). The results are used to obtain the thermodynamic limit of thermal energy densities and correlation functions.Comment: LaTex. 56 pages. The concept of global conformal invariance set in a historical perspective (new Sect. 1.1 in the Introduction), references added; minor corrections in the rest of the pape

Entire curves avoiding given sets in C^n

Let $F\subset\Bbb C^n$ be a proper closed subset of $\Bbb C^n$ and $A\subset\Bbb C^n\setminus F$ at most countable ($n\geq 2$). We give conditions of $F$ and $A$, under which there exists a holomorphic immersion (or a proper holomorphic embedding) $\phi:\Bbb C\to\Bbb C^n$ with $A\subset\phi(\Bbb C)\subset\Bbb C^n\setminus F$.Comment: 10 page

Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

Self-consistent tilted-axis-cranking study of triaxial strongly deformed bands in 158^{158}Er at ultrahigh spin

Stimulated by recent experimental discoveries, triaxial strongly deformed (TSD) states in $^{158}$Er at ultrahigh spins have been studied by means of the Skyrme-Hartree-Fock model and the tilted-axis-cranking method. Restricting the rotational axis to one of the principal axes -- as done in previous cranking calculations -- two well-defined TSD minima in the total Routhian surface are found for a given configuration: one with positive and another with negative triaxial deformation $\gamma$. By allowing the rotational axis to change direction, the higher-energy minimum is shown to be a saddle point. This resolves the long-standing question of the physical interpretation of the two triaxial minima at a very similar quadrupole shape obtained in the principal axis cranking approach. Several TSD configurations have been predicted, including a highly deformed band expected to cross lesser elongated TSD bands at the highest spins. Its transitional quadrupole moment $Q_t \approx 10.5$\,eb is close to the measured value of $\sim$11\,eb; hence, it is a candidate for the structure observed in experiment.Comment: 5 pages, 5 figure

Optimizing the photoassociation of cold atoms by use of chirped laser pulses

Photoassociation of ultracold atoms induced by chirped picosecond pulses is analyzed in a non-perturbative treatment by following the wavepackets dynamics on the ground and excited surfaces. The initial state is described by a Boltzmann distribution of continuum scattering states. The chosen example is photoassociation of cesium atoms at temperature T=54 $\mu K$ from the $a^3 \Sigma_u^+(6s,6s)$ continuum to bound levels in the external well of the $0_g^-(6s+6p_{3/2})$ potential. We study how the modification of the pulse characteristics (carrier frequency, duration, linear chirp rate and intensity) can enhance the number of photoassociated molecules and suggest ways of optimizing the production of stable molecules.Comment: 40 pages, 12 figures, submitted to Eur. Phys. J.

Comparison of boreal ecosystem model sensitivity to variability in climate and forest site parameters

Ecosystem models are useful tools for evaluating environmental controls on carbon and water cycles under past or future conditions. In this paper we compare annual carbon and water fluxes from nine boreal spruce forest ecosystem models in a series of sensitivity simulations. For each comparison, a single climate driver or forest site parameter was altered in a separate sensitivity run. Driver and parameter changes were prescribed principally to be large enough to identify and isolate any major differences in model responses, while also remaining within the range of variability that the boreal forest biome may be exposed to over a time period of several decades. The models simulated plant production, autotrophic and heterotrophic respiration, and evapotranspiration (ET) for a black spruce site in the boreal forest of central Canada (56°N). Results revealed that there were common model responses in gross primary production, plant respiration, and ET fluxes to prescribed changes in air temperature or surface irradiance and to decreased precipitation amounts. The models were also similar in their responses to variations in canopy leaf area, leaf nitrogen content, and surface organic layer thickness. The models had different sensitivities to certain parameters, namely the net primary production response to increased CO2 levels, and the response of soil microbial respiration to precipitation inputs and soil wetness. These differences can be explained by the type (or absence) of photosynthesis-CO2 response curves in the models and by response algorithms of litter and humus decomposition to drying effects in organic soils of the boreal spruce ecosystem. Differences in the couplings of photosynthesis and soil respiration to nitrogen availability may also explain divergent model responses. Sensitivity comparisons imply that past conditions of the ecosystem represented in the models\u27 initial standing wood and soil carbon pools, including historical climate patterns and the time since the last major disturbance, can be as important as potential climatic changes to prediction of the annual ecosystem carbon balance in this boreal spruce forest

Spin Squeezing as a Probe of Emergent Quantum Orders

Nuclear magnetic resonance (NMR) experiments can reveal local properties in materials, but are often limited by the low signal-to-noise ratio. Spin squeezed states have an improved resolution below the Heisenberg limit in one of the spin components, and have been extensively used to improve the sensitivity of atomic clocks, for example. Interacting and entangled spin ensembles with non-linear coupling are a natural candidate for implementing squeezing. Here, we propose measurement of the spin-squeezing parameter that itself can act as a local probe of emergent orders in quantum materials. In particular, we demonstrate how to investigate an anisotropic electric field gradient via its coupling to the nuclear quadrupole moment. While squeezed spin states are pure, the squeezing parameter can be estimated for both pure and mixed states. We evaluate the range of fields and temperatures for which a thermal-equilibrium state is sufficient to improve the resolution in an NMR experiment and probe relevant parameters of the quadrupole Hamiltonian, including its anisotropy