Construction of N-body initial data sets in general relativity

Given a collection of N solutions of the (3+1) vacuum Einstein constraint equations which are asymptotically Euclidean, we show how to construct a new solution of the constraints which is itself asymptotically Euclidean, and which contains specified sub-regions of each of the N given solutions. This generalizes earlier work which handled the time-symmetric case, thus providing a construction of large classes of initial data for the many body problem in general relativity

The Relative Pricing of Sovereign Credit Risk After the Eurozone Crisis

The paper analyses the relative pricing between sovereign CDS spreads and sovereign bond yields, for European countries, during and after the sovereign debt crisis of 2010-2012. In particular, we focus on the cross-sectional relationship between CDS spreads and bond yields across the European countries, and we investigate whether the differences across countries in terms of default risk, priced in the CDS spreads, are consistently priced in the cross-section of the bond yields. We show that an inconsistent cross-sectional relationship between CDS spreads and bond yields emerges during the crisis period for all the European countries, while after the announcement of the Outright Monetary Transaction (OMT) Programme, by the European Central Bank, the consistent cross-sectional relationship between default risk and bond yields is restored for the Eurozone countries only

Default risk premium in credit and equity markets

The default risk premium expresses the difference between the actual default risk of a company and the default risk implied by the securities issued by the company. In this paper, we study the simultaneous relationship between the dynamics of the default risk premium and both the dynamics of the stock price and the CDS (Credit Default Swap) spread of a company. We show that an increase in the default risk premium can be associated, at the same time, to either an increase in the stock price and a decrease in the CDS spread, or to a decrease in the stock price and an increase in the CDS spread. We document that the first type of relationship features securities belonging to a consistent risk-return framework, while the second type of relationship describes securities following a counterintuitive risk-return puzzle. We show this result theoretically end empirically, by adopting a contingent claim model. We estimate the model with a non-linear Kalman filter in conjunction with quasimaximum likelihood, and we shed light on the relationship over time between the default risk premium and both the equity value and the CDS spreads for a sample of non-financial firms

Novel schedule for treatment of inflammatory breast cancer

Inflammatory breast cancer (IBC) is the most aggressive form of this tumor, with the clinical and biological characteristics of a rapidly proliferating disease. This tumor is always diagnosed at advanced stages, atleast stage IIIB (locally advanced), so its management requires an integrated multidisciplinary approach with a systemic therapy followed by surgery and radiation therapy. Patients with IBC usually have a worse prognosis but the achievement of a pathologic complete response after neoadjuvant chemotherapy may have good rates of overall survival. We present the case of a 47 year old women with IBC, luminal B and with high proliferative index; she was successfully treated with a sequential schedule of chemotherapy (anthracyclines dose-dense/carboplatin+ taxane/Cyclophosphamide Methotrexate Fluorouracil), hormone-therapy, complementary radiotherapy and finally surgery until the achievement of a complete clinical and pathological response. Luminal B inflammatory breast cancer with high proliferation index can benefit from sequential schedules of neoadjuvant chemotherapy and hormonal treatment and this can result in pathological complete response

Positive mass theorems for asymptotically AdS spacetimes with arbitrary cosmological constant

We formulate and prove the Lorentzian version of the positive mass theorems with arbitrary negative cosmological constant for asymptotically AdS spacetimes. This work is the continuation of the second author's recent work on the positive mass theorem on asymptotically hyperbolic 3-manifolds.Comment: 17 pages, final version, to appear in International Journal of Mathematic

Gluing construction of initial data with Kerr-de Sitter ends

We construct initial data sets which satisfy the vacuum constraint equa- tions of General Relativity with positive cosmologigal constant. More pre- silely, we deform initial data with ends asymptotic to Schwarzschild-de Sitter to obtain non-trivial initial data with exactly Kerr-de Sitter ends. The method is inspired from Corvino's gluing method. We obtain here a extension of a previous result for the time-symmetric case by Chru\'sciel and Pollack.Comment: 27 pages, 3 figure

Splenic Artery Pseudoaneurysms: The Role of ce-CT for Diagnosis and Treatment Planning

Splenic artery pseudoaneurysm (PSA) is a contained vascular wall lesion associated with a high mortality rate, generally related to pancreatitis, trauma, malignancy, iatrogenic injury, and segmental arterial mediolysis. Computed tomography angiography allows us to visualize the vascular anatomy, differentiate a PSA from an aneurysm, and provide adequate information for endovascular/surgical treatment. The present review reports on the main state-of-the-art splenic artery PSA diagnosis, differentiating between the pros and cons of the imaging methods and about the endovascular treatment

Perturbative Solutions of the Extended Constraint Equations in General Relativity

The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on $Z$, and are equivalent to the usual constraint equations that $Z$ satisfies as a spacelike hypersurface in a spacetime satisfying Einstein's vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the `classical' method of Lichnerowicz and York that is used to solve the usual constraint equations.Comment: This third and final version has been accepted for publication in Communications in Mathematical Physic