A Review of Mathematical Models for the Formation of\ud Vascular Networks

Mainly two mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former consists of the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter consists of the sprouting of new vessels from an existing capillary or post-capillary venule. Similar phenomena are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis.\ud \ud A number of mathematical approaches have analysed these phenomena. This paper reviews the different modelling procedures, with a special emphasis on their ability to reproduce the biological system and to predict measured quantities which describe the overall processes. A comparison between the different methods is also made, highlighting their specific features

A note on heat and mass transfer from a sphere in Stokes\ud flow at low Péclet number

We consider the low Péclet number, Pe ≪ 1, asymptotic solution for steady-state heat and mass transfer from a sphere immersed in Stokes flow with a Robin boundary condition on its surface, representing Newton cooling or a first-order chemical reaction. The application of van Dyke’s rule up to terms of O(Pe3) shows that the O(Pe3 log Pe) terms in the expression for the average Nusselt/Sherwood number are double those previously derived in the literature. Inclusion of the O(Pe3) terms is shown to increase significantly the range of validity of the expansion

Generation of N-qubit W state with rf-SQUID qubits by adiabatic passage

A simple scheme is presented to generate n-qubit W state with rf-superconducting quantum interference devices (rf-SQUIDs) in cavity QED through adiabatic passage. Because of the achievable strong coupling for rf-SQUID qubits embedded in cavity QED, we can get the desired state with high success probability. Furthermore, the scheme is insensitive to position inaccuracy of the rf-SQUIDs. The numerical simulation shows that, by using present experimental techniques, we can achieve our scheme with very high success probability, and the fidelity could be eventually unity with the help of dissipation.Comment: to appear in Phys. Rev.

Improving Small Object Proposals for Company Logo Detection

Many modern approaches for object detection are two-staged pipelines. The first stage identifies regions of interest which are then classified in the second stage. Faster R-CNN is such an approach for object detection which combines both stages into a single pipeline. In this paper we apply Faster R-CNN to the task of company logo detection. Motivated by its weak performance on small object instances, we examine in detail both the proposal and the classification stage with respect to a wide range of object sizes. We investigate the influence of feature map resolution on the performance of those stages. Based on theoretical considerations, we introduce an improved scheme for generating anchor proposals and propose a modification to Faster R-CNN which leverages higher-resolution feature maps for small objects. We evaluate our approach on the FlickrLogos dataset improving the RPN performance from 0.52 to 0.71 (MABO) and the detection performance from 0.52 to 0.67 (mAP).Comment: 8 Pages, ICMR 201

Exact renormalization group equations and the field theoretical approach to critical phenomena

After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as the continuum limit and the renormalizability and the presence of singularities in the perturbative series are discussed.Comment: 15 pages, 7 figures, to appear in the Proceedings of the 2nd Conference on the Exact Renormalization Group, Rome 200

Prolific pair production with high-power lasers

Prolific electron-positron pair production is possible at laser intensities approaching 10^{24} W/cm^2 at a wavelength of 1 micron. An analysis of electron trajectories and interactions at the nodes (B=0) of two counter-propagating, circularly polarised laser beams shows that a cascade of gamma-rays and pairs develops. The geometry is generalised qualitatively to linear polarisation and laser beams incident on a solid target.Comment: 4 pages, 1 figure, minor revisions, accepted for publication in Physical Review Letter

Propagation of spatially entangled qudits through free space

We show the propagation of entangled states of high-dimensional quantum systems. The qudits states were generated using the transverse correlation of the twin photons produced by spontaneous parametric down-conversion. Their free-space distribution was performed at the laboratory scale and the propagated states maintained a high-fidelity with their original form. The use of entangled qudits allow an increase in the quantity of information that can be transmitted and may also guarantee more privacy for communicating parties. Therefore, studies about propagating entangled states of qudits are important for the effort of building quantum communication networks.Comment: 5 Pages, 4 Figures, REVTeX

Extended Representations of Observables and States for a Noncontextual Reinterpretation of QM

A crucial and problematical feature of quantum mechanics (QM) is nonobjectivity of properties. The ESR model restores objectivity reinterpreting quantum probabilities as conditional on detection and embodying the mathematical formalism of QM into a broader noncontextual (hence local) framework. We propose here an improved presentation of the ESR model containing a more complete mathematical representation of the basic entities of the model. We also extend the model to mixtures showing that the mathematical representations of proper mixtures does not coincide with the mathematical representation of mixtures provided by QM, while the representation of improper mixtures does. This feature of the ESR model entails that some interpretative problems raising in QM when dealing with mixtures are avoided. From an empirical point of view the predictions of the ESR model depend on some parameters which may be such that they are very close to the predictions of QM in most cases. But the nonstandard representation of proper mixtures allows us to propose the scheme of an experiment that could check whether the predictions of QM or the predictions of the ESR model are correct.Comment: 17 pages, standard latex. Extensively revised versio

Diffuse Galactic Gamma Rays from Shock-Accelerated Cosmic Rays

A shock-accelerated particle flux \propto p^-s, where p is the particle momentum, follows from simple theoretical considerations of cosmic-ray acceleration at nonrelativistic shocks followed by rigidity-dependent escape into the Galactic halo. A flux of shock-accelerated cosmic-ray protons with s ~ 2.8 provides an adequate fit to the Fermi-LAT gamma-ray emission spectra of high-latitude and molecular cloud gas when uncertainties in nuclear production models are considered. A break in the spectrum of cosmic-ray protons claimed by Neronov, Semikoz, & Taylor (PRL, 108, 051105, 2012) when fitting the gamma-ray spectra of high-latitude molecular clouds is a consequence of using a cosmic-ray proton flux described by a power law in kinetic energy.Comment: Version to correspond to published letter in PRL; corrected Fig.

Qubit-portraits of qudit states and quantum correlations

The machinery of qubit-portraits of qudit states, recently presented, is consider here in more details in order to characterize the presence of quantum correlations in bipartite qudit states. In the tomographic representation of quantum mechanics, Bell-like inequalities are interpreted as peculiar properties of a family of classical joint probability distributions which describe the quantum state of two qudits. By means of the qubit-portraits machinery a semigroup of stochastic matrices can be associated to a given quantum state. The violation of the CHSH inequalities is discussed in this framework with some examples, we found that quantum correlations in qutrit isotropic states can be detected by the suggested method while it cannot in the case of qutrit Werner states.Comment: 12 pages, 4 figure