Systematic Differential Renormalization to All Orders

We present a systematic implementation of differential renormalization to all orders in perturbation theory. The method is applied to individual Feynamn graphs written in coordinate space. After isolating every singularity. which appears in a bare diagram, we define a subtraction procedure which consists in replacing the core of the singularity by its renormalized form givenby a differential formula. The organizationof subtractions in subgraphs relies in Bogoliubov's formula, fulfilling the requirements of locality, unitarity and Lorentz invariance. Our method bypasses the use of an intermediate regularization andautomatically delivers renormalized amplitudes which obey renormalization group equations.Comment: TEX, 20 pages, UB-ECM-PF 93/4, 1 figureavailable upon reques

Studies of NGC 6720 with Calibrated HST WFC3 Emission-Line Filter Images--I: Structure and Evolution

We have performed a detailed analysis of the Ring Nebula (NGC 6720) using HST WFC3 images and derived a new 3-D model. Existing high spectral resolution spectra played an important supplementary role in our modeling. It is shown that the Main Ring of the nebula is an ionization-bounded irregular non-symmetric disk with a central cavity and perpendicular extended lobes pointed almost towards the observer. The faint outer halos are determined to be fossil radiation, i.e. radiation from gas ionized in an earlier stage of the nebula when it was not ionization bounded. The narrow-band WFC3 filters that isolate some of the emission-lines are affected by broadening on their short wavelength side and all the filters were calibrated using ground-based spectra. The filter calibration results are presented in an appendix.Comment: Accepted for publication by the Astronomical Journa

Studies of NGC 6720 with Calibrated HST WFC3 Emission-Line Filter Images--II:Physical Conditions

We have performed a detailed analysis of the electron temperature and density in the the Ring Nebula using the calibrated HST WFC3 images described in the preceding paper. The electron temperature (Te) determined from [N II] and [O III] rises slightly and monotonically towards the central star. The observed equivalent width (EW) in the central region indicates that Te rises as high as 13000 K. In contrast, the low EW's in the outer regions are largely due to scattered diffuse Galactic radiation by dust. The images allowed determination of unprecedented small scale variations in Te. These variations indicate that the mean square area temperature fluctuations are significantly higher than expected from simple photoionization. The power producing these fluctuations occurs at scales of less than 3.5E15 cm. This scale length provides a strong restriction on the mechanism causing the large t^2 values observed.Comment: Accepted for publication in the Astronomical Journa

Measurements and Information in Spin Foam Models

We present a problem relating measurements and information theory in spin foam models. In the three dimensional case of quantum gravity we can compute probabilities of spin network graphs and study the behaviour of the Shannon entropy associated to the corresponding information. We present a general definition, compute the Shannon entropy of some examples, and find some interesting inequalities.Comment: 15 pages, 3 figures. Improved versio

Color superconducting matter in a magnetic field

We investigate the effect of a magnetic field on cold dense three-flavor quark matter using an effective model with four-Fermi interactions with electric and color neutrality taken into account. The gap parameters Delta_1, Delta_2, and Delta_3 representing respectively the predominant pairing between down and strange (d-s) quarks, strange and up (s-u) quarks, and up and down (u-d) quarks, show the de Haas-van Alphen effect, i.e. oscillatory behavior as a function of the modified magnetic field B that can penetrate the color superconducting medium. Without applying electric and color neutrality we find Delta_2 \approx Delta_3 >> Delta_1 for 2 e B / mu_q^2, where e is the modified electromagnetic coupling constant and mu_q is one third of the baryon chemical potential. Because the average Fermi surface for each pairing is affected by taking into account neutrality, the gap structure changes drastically in this case; we find Delta_1 >> Delta_2 \approx Delta_3 for 2 e B > mu_q^2. We point out that the magnetic fields as strong as presumably existing inside magnetars might induce significant deviations from the gap structure Delta_1 \approx Delta_2 \approx Delta_3 at zero magnetic field.Comment: 5 pages, 3 figure

Effective models for strong electronic correlations at graphene edges

We describe a method for deriving effective low-energy theories of electronic interactions at graphene edges. Our method is applicable to general edges of honeycomb lattices (zigzag, chiral, and even disordered) as long as localized low-energy states (edge states) are present. The central characteristic of the effective theories is a dramatically reduced number of degrees of freedom. As a consequence, the solution of the effective theory by exact diagonalization is feasible for reasonably large ribbon sizes. The quality of the involved approximations is critically assessed by comparing the correlation functions obtained from the effective theory with numerically exact quantum Monte-Carlo calculations. We discuss effective theories of two levels: a relatively complicated fermionic edge state theory and a further reduced Heisenberg spin model. The latter theory paves the way to an efficient description of the magnetic features in long and structurally disordered graphene edges beyond the mean-field approximation.Comment: 13 pages, 9 figure

Dynamic programming algorithm for the vehicle routing problem with time windows and EC social legislation

In practice, apart from the problem of vehicle routing, schedulers also face the problem of nding feasible driver schedules complying with complex restrictions on drivers' driving and working hours. To address this complex interdependent problem of vehicle routing and break scheduling, we propose a dynamic programming approach for the vehicle routing problem with time windows including the EC social legislation on drivers' driving and working hours. Our algorithm includes all optional rules in these legislations, which are generally ignored in the literature. To include the legislation in the dynamic programming algorithm we propose a break scheduling method that does not increase the time-complexity of the algorithm. This is a remarkable eect that generally does not hold for local search methods, which have proved to be very successful in solving less restricted vehicle routing problems. Computational results show that our method finds solutions to benchmark instances with 18% less vehicles and 5% less travel distance than state of the art approaches. Furthermore, they show that including all optional rules of the legislation leads to an additional reduction of 4% in the number of vehicles and of 1.5%\ud regarding the travel distance. Therefore, the optional rules should be exploited in practice

Push-Pull Control of Motor Output

Inhibition usually decreases input–output excitability of neurons. If, however, inhibition is coupled to excitation in a push–pull fashion, where inhibition decreases as excitation increases, neuron excitability can be increased. Although the presence of push–pull organization has been demonstrated in single cells, its functional impact on neural processing depends on its effect on the system level. We studied push–pull in the motor output stage of the feline spinal cord, a system that allows independent control of inhibitory and excitatory components. Push–pull organization was clearly present in ankle extensor motoneurons, producing increased peak-to-peak modulation of synaptic currents. The effect at the system level was equally strong. Independent control of the inhibitory component showed that the stronger the background of inhibition, the greater the peak force production. This illustrates the paradox at the heart of push–pull organization: increased force output can be achieved by increasing background inhibition to provide greater disinhibition

Exact diagonalization study of the tunable edge magnetism in graphene

The tunable magnetism at graphene edges with lengths of up to 48 unit cells is analyzed by an exact diagonalization technique. For this we use a generalized interacting one-dimensional model which can be tuned continuously from a limit describing graphene zigzag edge states with a ferromagnetic phase, to a limit equivalent to a Hubbard chain, which does not allow ferromagnetism. This analysis sheds light onto the question why the edge states have a ferromagnetic ground state, while a usual one-dimensional metal does not. Essentially we find that there are two important features of edge states: (a) umklapp processes are completely forbidden for edge states; this allows a spin-polarized ground state. (b) the strong momentum dependence of the effective interaction vertex for edge states gives rise to a regime of partial spin-polarization and a second order phase transition between a standard paramagnetic Luttinger liquid and ferromagnetic Luttinger liquid.Comment: 11 pages, 8 figure

Classical Antiferromagnetism in Kinetically Frustrated Electronic Models

We study the infinite U Hubbard model with one hole doped away half-filling, in triangular and square lattices with frustrated hoppings that invalidate Nagaoka's theorem, by means of the density matrix renormalization group. We find that these kinetically frustrated models have antiferromagnetic ground states with classical local magnetization in the thermodynamic limit. We identify the mechanism of this kinetic antiferromagnetism with the release of the kinetic energy frustration as the hole moves in the established antiferromagnetic background. This release can occurs in two different ways: by a non-trivial spin-Berry phase acquired by the hole or by the effective vanishing of the hopping amplitude along the frustrating loops.Comment: 12 pages and 4 figures, with Supplementary Material. To be published in Phys. Rev. Let