Classification of factorial generalized down-up algebras

We determine when a generalized down-up algebra is a Noetherian unique factorisation domain or a Noetherian unique factorisation ring

Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation

We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our approach enables to control the error in the computation of the displacement and stress fields around the needle tip and needle shaft by suitably refining the mesh, whilst maintaining a coarser mesh in other parts of the domain. We demonstrate through academic and practical examples that our approach increases the accuracy of the displacement and stress fields around the needle without increasing the computational expense. This enables real-time simulations. The proposed methodology has direct implications to increase the accuracy and control the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anesthesia, or cryotherapy and can be essential to the development of robotic guidance.Comment: 21 pages, 14 figure

Leland & Pyle Meet Foreign Aid? Adverse Selection and the Procyclicality of Financial Aid Flows

Official development assistance (grants and subsidized loans from foreign aid agencies) is the main source of external finance in developing countries. These financial aid flows are positively correlated with the recipients' business cycles, which is puzzling because it reinforces already strong and costly macroeconomic fluctuations in the recipient countries. We propose an explanation related to a familiar corporate finance theory of inside equity commitments. We assume that donor agencies and recipient governments value projects differently, and that donors know less than recipients do about projects. We show that donors can make an aid recipient idientify high-return projects by conditioning aid on the recipient's committing some of its own funds to the selected projects. This commitment makes recommending bad projects costly. Contributing "counterpart funds" is more difficult during economic downturns, however - which leads to aid procyclicality. This simple model of investment financing and aid provision produces aid contracts consistent with those used by aid agencies, rationalizes observed aid flow patterns, and yields a rich set of testable empirical predictions.Aid, Altruism, Adverse selection, Counterpart funds, Capital flow procyclicality

A model-independent dark energy reconstruction scheme using the geometrical form of the luminosity-distance relation

We put forward a new model-independent reconstruction scheme for dark energy which utilises the expected geometrical features of the luminosity-distance relation. The important advantage of this scheme is that it does not assume explicit ansatzes for cosmological parameters but only some very general cosmological properties via the geometrical features of the reconstructed luminosity-distance relation. Using the recently released supernovae data by the Supernova Legacy Survey together with a phase space representation, we show that the reconstructed luminosity-distance curves best fitting the data correspond to a slightly varying dark energy density with the Universe expanding slightly slower than the Lambda CDM model. However, the Lambda CDM model fits the data at 1 sigma significance level and the fact that our best fitting luminosity-distance curve is lower than that of the corresponding Lambda CDM model could be due to systematics. The transition from an accelerating to a decelerating expansion occurs at a redshift larger than z=0.35. Interpreting the dark energy as a minimally coupled scalar field we also reconstruct the scalar field and its potential. We constrain $\Omega_{m_0}$ using the baryon acoustic oscillation peak in the SDSS luminous red galaxy sample and find that the best fit is obtained with $\Omega_{m_0}=0.27$, in agreement with the CMB data.Comment: 10 pages, 18 figure

Haldane's Fractional Statistics and the Riemann-Roch Theorem

The new definition of fractional statistics given by Haldane can be understood in some special cases in terms of the Riemann-Roch theorem.Comment: 38050 Povo, Trento and Division de Physique Th\'eorique, IPN, 91406 Orsay Cedex, 19 pages, IPNO/TH 94-11, SISSA/27/94/EP,UFT/32

Interaction Quench in Nonequilibrium Luttinger Liquids

We study the relaxation dynamics of a nonequilibrium Luttinger liquid after a sudden interaction switch-on ("quench"), focussing on a double-step initial momentum distribution function. In the framework of the non-equilibrium bosonization, the results are obtained in terms of singular Fredholm determinants that are evaluated numerically and whose asymptotics are found analytically. While the quasi-particle weights decay exponentially with time after the quench, this is not a relaxation into a thermal state, in view of the integrability of the model. The steady-state distribution emerging at infinite times retains two edges which support Luttinger-liquid-like power-law singularities smeared by dephasing. The obtained critical exponents and the dephasing length are found to depend on the initial nonequilibrium state.Comment: 11 pages, 5 figure

Spatial coherence and stability in a disordered organic polariton condensate

Although only a handful of organic materials have shown polariton condensation, their study is rapidly becoming more accessible. The spontaneous appearance of long-range spatial coherence is often recognized as a defining feature of such condensates. In this work, we study the emergence of spatial coherence in an organic microcavity and demonstrate a number of unique features stemming from the peculiarities of this material set. Despite its disordered nature, we find that correlations extend over the entire spot size and we measure $g^{(1)}(r,r')$ values of nearly unity at short distances and of 50% for points separated by nearly 10 $\mu$m. We show that for large spots, strong shot to shot fluctuations emerge as varying phase gradients and defects, including the spontaneous formation of vortices. These are consistent with the presence of modulation instabilities. Furthermore, we find that measurements with flat-top spots are significantly influenced by disorder and can, in some cases, lead to the formation of mutually incoherent localized condensates.Comment: Revised versio