Spherically symmetric equilibria for self-gravitating kinetic or fluid models in the non-relativistic and relativistic case - A simple proof for finite extension

We consider a self-gravitating collisionless gas as described by the Vlasov-Poisson or Einstein-Vlasov system or a self-gravitating fluid ball as described by the Euler-Poisson or Einstein-Euler system. We give a simple proof for the finite extension of spherically symmetric equilibria, which covers all these models simultaneously. In the Vlasov case the equilibria are characterized by a local growth condition on the microscopic equation of state, i.e., on the dependence of the particle distribution on the particle energy, at the cut-off energy E_0, and in the Euler case by the corresponding growth condition on the equation of state p=P(\rho) at \rho=0. These purely local conditions are slight generalizations to known such conditions.Comment: 20 page

Mott Insulator to Superfluid transition in Bose-Bose mixtures in a two-dimensional lattice

We perform a numeric study (Worm algorithm Monte Carlo simulations) of ultracold two-component bosons in two-dimensional optical lattices. We study how the Mott insulator to superfluid transition is affected by the presence of a second superfluid bosonic species. We find that, at fixed interspecies interaction, the upper and lower boundaries of the Mott lobe are differently modified. The lower boundary is strongly renormalized even for relatively low filling factor of the second component and moderate (interspecies) interaction. The upper boundary, instead, is affected only for large enough filling of the second component. Whereas boundaries are renormalized we find evidence of polaron-like excitations. Our results are of interest for current experimental setups.Comment: 4 pages, 3 figures, accepted as PRA Rapid Communicatio

Gauge and Averaging in Gravitational Self-force

A difficulty with previous treatments of the gravitational self-force is that an explicit formula for the force is available only in a particular gauge (Lorenz gauge), where the force in other gauges must be found through a transformation law once the Lorenz gauge force is known. For a class of gauges satisfying a ``parity condition'' ensuring that the Hamiltonian center of mass of the particle is well-defined, I show that the gravitational self-force is always given by the angle-average of the bare gravitational force. To derive this result I replace the computational strategy of previous work with a new approach, wherein the form of the force is first fixed up to a gauge-invariant piece by simple manipulations, and then that piece is determined by working in a gauge designed specifically to simplify the computation. This offers significant computational savings over the Lorenz gauge, since the Hadamard expansion is avoided entirely and the metric perturbation takes a very simple form. I also show that the rest mass of the particle does not evolve due to first-order self-force effects. Finally, I consider the ``mode sum regularization'' scheme for computing the self-force in black hole background spacetimes, and use the angle-average form of the force to show that the same mode-by-mode subtraction may be performed in all parity-regular gauges. It appears plausible that suitably modified versions of the Regge-Wheeler and radiation gauges (convenient to Schwarzschild and Kerr, respectively) are in this class

Critical entropies for magnetic ordering in bosonic mixtures on a lattice

We perform a numeric study (worm algorithm Monte Carlo simulations) of ultracold two-component bosons in two- and three-dimensional optical lattices. At strong enough interactions and low enough temperatures the system features magnetic ordering. We compute critical temperatures and entropies for the disappearance of the Ising antiferromagnetic and the xy-ferromagnetic order and find that the largest possible entropies per particle are ~0.5kB. We also estimate (optimistically) the experimental hold times required to reach equilibrium magnetic states to be on a scale of seconds. Low critical entropies and long hold times render the experimental observations of magnetic phases challenging and call for increased control over heating sources.Comment: 6 pages, 6 figure

Automatic Synchronization of Multi-User Photo Galleries

In this paper we address the issue of photo galleries synchronization, where pictures related to the same event are collected by different users. Existing solutions to address the problem are usually based on unrealistic assumptions, like time consistency across photo galleries, and often heavily rely on heuristics, limiting therefore the applicability to real-world scenarios. We propose a solution that achieves better generalization performance for the synchronization task compared to the available literature. The method is characterized by three stages: at first, deep convolutional neural network features are used to assess the visual similarity among the photos; then, pairs of similar photos are detected across different galleries and used to construct a graph; eventually, a probabilistic graphical model is used to estimate the temporal offset of each pair of galleries, by traversing the minimum spanning tree extracted from this graph. The experimental evaluation is conducted on four publicly available datasets covering different types of events, demonstrating the strength of our proposed method. A thorough discussion of the obtained results is provided for a critical assessment of the quality in synchronization.Comment: ACCEPTED to IEEE Transactions on Multimedi

"Magic" numbers in Smale's 7th problem

Smale's 7-th problem concerns N-point configurations on the 2-dim sphere which minimize the logarithmic pair-energy V_0(r) = -ln r averaged over the pairs in a configuration; here, r is the chordal distance between the points forming a pair. More generally, V_0(r) may be replaced by the standardized Riesz pair-energy V_s(r)= (r^{-s} -1)/s, which becomes - ln r in the limit s to 0, and the sphere may be replaced by other compact manifolds. This paper inquires into the concavity of the map from the integers N>1 into the minimal average standardized Riesz pair-energies v_s(N) of the N-point configurations on the 2-sphere for various real s. It is known that v_s(N) is strictly increasing for each real s, and for s<2 also bounded above, hence "overall concave." It is (easily) proved that v_{-2}(N) is even locally strictly concave, and that so is v_s(2n) for s<-2. By analyzing computer-experimental data of putatively minimal average Riesz pair-energies v_s^x(N) for s in {-1,0,1,2,3} and N in {2,...,200}, it is found that {v}_{-1}^x(N) is locally strictly concave, while v_s^x(N) is not always locally strictly concave for s in {0,1,2,3}: concavity defects occur whenever N in C^{x}_+(s) (an s-specific empirical set of integers). It is found that the empirical map C^{x}_+(s), with s in {-2,-1,0,1,2,3}, is set-theoretically increasing; moreover, the percentage of odd numbers in C^{x}_+(s), s in {0,1,2,3}, is found to increase with s. The integers in C^{x}_+(0) are few and far between, forming a curious sequence of numbers, reminiscent of the "magic numbers" in nuclear physics. It is conjectured that the "magic numbers" in Smale's 7-th problem are associated with optimally symmetric optimal-energy configurations.Comment: 109 pages, of which 30 are numerical data tables. Thoroughly revised version, to appear in J. Stat. Phys. under the different title: `Optimal N point configurations on the sphere: "Magic" numbers and Smale's 7th problem

Entrepreneurial intention: An analysis of the role of Student‑Led Entrepreneurial Organizations

Although a great deal of attention has been paid to entrepreneurship education, only a few studies have analysed the impact of extra-curricular entrepreneurial activities on students’ entrepreneurial intention. The aim of this study is to fill this gap by exploring the role played by Student-Led Entrepreneurial Organizations (SLEOs) in shaping the entrepreneurial intention of their members. The analysis is based on a survey that was conducted in 2016 by one of the largest SLEOs in the world: the Junior Enterprises Europe (JEE). The main result of the empirical analysis is that the more time students spent on JEE and the higher the number of events students attended, the greater their entrepreneurial intention was. It has been found that other important drivers also increase students’ entrepreneurial intention, that is, the Science and Technology field of study and the knowledge of more than two foreign languages. These results confirm that SLEOs are able to foster students’ entrepreneurial intention. The findings provide several theoretical, practical and public policy implications. SLEOs are encouraged to enhance their visibility and lobbying potential in order to be recognized more as drivers of student entrepreneurship. In addition, it is advisable for universities and policy makers to support SLEOs by fostering their interactions with other actors operating in the entrepreneurial ecosystem, who promote entrepreneurship and technology transfer activities. Lastly, this paper advises policy makers to assist SLEOs’ activities inside and outside the university context