The Generalized Good Cut Equation

The properties of null geodesic congruences (NGCs) in Lorentzian manifolds are a topic of considerable importance. More specifically NGCs with the special property of being shear-free or asymptotically shear-free (as either infinity or a horizon is approached) have received a great deal of recent attention for a variety of reasons. Such congruences are most easily studied via solutions to what has been referred to as the 'good cut equation' or the 'generalization good cut equation'. It is the purpose of this note to study these equations and show their relationship to each other. In particular we show how they all have a four complex dimensional manifold (known as H-space, or in a special case as complex Minkowski space) as a solution space.Comment: 12 page

Asymptotically Stationary and Static Space-times and Shear-free Null Geodesic Congruences

In classical electromagnetic theory, one formally defines the complex dipole moment (the electric plus 'i' magnetic dipole) and then computes (and defines) the complex center of charge by transforming to a complex frame where the complex dipole moment vanishes. Analogously in asymptotically flat space-times it has been shown that one can determine the complex center of mass by transforming the complex gravitational dipole (mass dipole plus 'i' angular momentum) (via an asymptotic tetrad trasnformation) to a frame where the complex dipole vanishes. We apply this procedure to such space-times which are asymptotically stationary or static, and observe that the calculations can be performed exactly, without any use of the approximation schemes which must be employed in general. In particular, we are able to exactly calculate complex center of mass and charge world-lines for such space-times, and - as a special case - when these two complex world-lines coincide, we recover the Dirac value of the gyromagnetic ratio.Comment: 11 page

The Real Meaning of Complex Minkowski-Space World-Lines

In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.Comment: 16 page

Color Fields on the Light-Shell

We study the classical color radiation from very high energy collisions that produce colored particles. In the extreme high energy limit, the classical color fields are confined to a light-shell expanding at $c$ and are associated with a non-linear $\sigma$-model on the 2D light-shell with specific symmetry breaking terms. We argue that the quantum version of this picture exhibits asymptotic freedom and may be a useful starting point for an effective light-shell theory of the structure between the jets at a very high energy collider.Comment: 11 pages, no figure

Twistors, Harmonics and Holomorphic Chern-Simons

We show that the off-shell N=3 action of N=4 super Yang-Mills can be written as a holomorphic Chern-Simons action whose Dolbeault operator is constructed from a complex-real (CR) structure of harmonic space. We also show that the local space-time operators can be written as a Penrose transform on the coset SU(3)/(U(1) \times U(1)). We observe a strong similarity to ambitwistor space constructions.Comment: 34 pages, 3 figures, v2: replaced with published version, v3: Added referenc

Safety and activity of trastuzumab-containing therapies for the treatment of metastatic breast cancer: our long-term clinical experience (GOIM study).

Background: Trastuzumab is widely used as the treatment of choice for HER2-positive metastatic breast cancer (MBC). Patients and methods: Seventy patients, median age 57 years and range 31–81 years, were included in our retrospective analysis with the aim to evaluate safety and activity of trastuzumab-containing therapies. Results: We observed for first-line treatment response rate (RR) 41%, stable disease (SD) 47% and time to progression (TTP) 8 months (range 1–44). Corresponding numbers for second line were RR 23%, SD 62% and (TTP) 9 months (range 3–23) and beyond second line RR 22%, SD 78% and (TTP) 9 months (range 4–19). Overall survival was 19.2 months (3–62 months). The median cumulative dose of trastuzumab administrated was 5286 mg (464–17 940 mg). Trastuzumab was well tolerated. Median left ventricular ejection function (LVEF) at baseline was 62% and at the end of treatment was 59%. The more relevant adverse events consisted of an asymptomatic decrease in LVEF to 40% (baseline 60%) and a grade 3 symptomatic increase in bilirubin. Conclusion: Trastuzumab-containing therapies in MBC show a good safety and toxicity profile and a remarkable activity even in heavily pretreated women. Patients should benefit from continued trastuzumab therapy, as shown by the maintenance of (TTP) even beyond second-line treatment

CHY representations for gauge theory and gravity amplitudes with up to three massive particles

We show that a wide class of tree-level scattering amplitudes involving scalars, gauge bosons, and gravitons, up to three of which may be massive, can be expressed in terms of a Cachazo-He-Yuan representation as a sum over solutions of the scattering equations. These amplitudes, when expressed in terms of the appropriate kinematic invariants, are independent of the masses and therefore identical to the corresponding massless amplitudes.Comment: 20 pages, 1 figure; v2: minor typos corrected, published versio

Correlation functions, null polygonal Wilson loops, and local operators

We consider the ratio of the correlation function of n+1 local operators over the correlator of the first n of these operators in planar N=4 super-Yang-Mills theory, and consider the limit where the first n operators become pairwise null separated. By studying the problem in twistor space, we prove that this is equivalent to the correlator of a n-cusp null polygonal Wilson loop with the remaining operator in general position, normalized by the expectation value of the Wilson loop itself, as recently conjectured by Alday, Buchbinder and Tseytlin. Twistor methods also provide a BCFW-like recursion relation for such correlators. Finally, we study the natural extension where n operators become pairwise null separated with k operators in general position. As an example, we perform an analysis of the resulting correlator for k=2 and discuss some of the difficulties associated to fixing the correlator completely in the strong coupling regime.Comment: 34 pages, 6 figures. v2: typos corrected and references added; v3: published versio

The Risk of Toxicities from Trastuzumab, Alone or in Combination, in an Elderly Breast Cancer Population

Abstract Background: Breast cancer in the elderly is associated with high recurrence and death rates, due mostly to undertreatment. Human epidermal growth factor receptor type 2 (HER2) overexpression is infrequent in older patients. Trastuzumab- based chemotherapy is often withheld from elderly patients because of its cardiotoxicity. Patients and Methods: Medical records of consecutive HER2-positive breast cancer patients aged 65 70 years old treated between 2005 and 2010 in the participating centers were retrospectively reviewed. All patients underwent multidimensional geriatric assessment (MGA). Results: Among 59 patients identified, 51 patients were evaluable (median age 76 years). The rate of any adverse event was 20% (10/51). The most relevant cardiac adverse event consisted of symptomatic congestive heart failure (CHF; n = 1, 2%) followed by asymptomatic decreases of left ventricular ejection fraction (LVEF; n = 6, 12%). Other toxicities included moderate hypersensitivity reactions during trastuzumab infusions (n = 3, 6%). Hypertension, obesity, prior anthracyclines exposure and concurrent chemotherapy were associated with a higher incidence of toxic events. Previous radiotherapy, concurrent endocrine therapy and different trastuzumab-based regimens did not seem to influence toxicity. Conclusions: Our data suggest that trastuzumab has a good safety profile in nonfrail women aged 70 years and older. These favorable findings may be related to a limited number of anthracycline pretreatments, patient selection and a close cardiologic monitoring