Higher Order Corrections to the Asymptotic Perturbative Solution of a Schwinger-Dyson Equation

Building on our previous works on perturbative solutions to a Schwinger-Dyson for the massless Wess-Zumino model, we show how to compute 1/n corrections to its asymptotic behavior. The coefficients are analytically determined through a sum on all the poles of the Mellin transform of the one loop diagram. We present results up to the fourth order in 1/n as well as a comparison with numerical results. Unexpected cancellations of zetas are observed in the solution, so that no even zetas appear and the weight of the coefficients is lower than expected, which suggests the existence of more structure in the theory.Comment: 16 pages, 2 figures. Some points clarified, typos corrected, matches the version to be published in Lett. Math. Phy

A Schwinger--Dyson Equation in the Borel Plane: singularities of the solution

We map the Schwinger--Dyson equation and the renormalization group equation for the massless Wess--Zumino model in the Borel plane, where the product of functions get mapped to a convolution product. The two-point function can be expressed as a superposition of general powers of the external momentum. The singularities of the anomalous dimension are shown to lie on the real line in the Borel plane and to be linked to the singularities of the Mellin transform of the one-loop graph. This new approach allows us to enlarge the reach of previous studies on the expansions around those singularities. The asymptotic behavior at infinity of the Borel transform of the solution is beyond the reach of analytical methods and we do a preliminary numerical study, aiming to show that it should remain bounded.Comment: 21 pages, 2 figures, use Tikz New version includes corrections asked by refere

Outcomes in newly diagnosed elderly glioblastoma patients after concomitant temozolomide administration and hypofractionated radiotherapy

This study aimed to analyze the treatment and outcomes of older glioblastoma patients. Forty-four patients older than 70 years of age were referred to the Paul Strauss Center for chemotherapy and radiotherapy. The median age was 75.5 years old (range: 70-84), and the patients included 18 females and 26 males. The median Karnofsky index (KI) was 70%. The Charlson indices varied from 4 to 6. All of the patients underwent surgery. O6-methylguanine-DNA methyltransferase (MGMT) methylation status was determined in 25 patients. All of the patients received radiation therapy. Thirty-eight patients adhered to a hypofractionated radiation therapy schedule and six patients to a normofractionated schedule. Neoadjuvant, concomitant and adjuvant chemotherapy regimens were administered to 12, 35 and 20 patients, respectively. At the time of this analysis, 41 patients had died. The median time to relapse was 6.7 months. Twenty-nine patients relapsed, and 10 patients received chemotherapy upon relapse. The median overall survival (OS) was 7.2 months and the one- and two-year OS rates were 32% and 12%, respectively. In a multivariate analysis, only the Karnofsky index was a prognostic factor. Hypofractionated radiotherapy and chemotherapy with temozolomide are feasible and acceptably tolerated in older patients. However, relevant prognostic factors are needed to optimize treatment proposals

Generalisations of multiple zeta values to rooted forests

We show that any convergent (shuffle) arborified zeta value admits a series representation. This justifies the introduction of a new generalisation to rooted forests of multiple zeta values, and we study its algebraic properties. As a consequence of the series representation, we derive elementary proofs of some results of Bradley and Zhou for Mordell-Tornheim zeta values and give explicit formulas. The series representation for shuffle arborified zeta values also implies that they are conical zeta values. We characterise which conical zeta values are arborified zeta values and evaluate them as sums of multiple zeta values with rational coefficients.Comment: 29 pages. One section added, where tree zeta values are studied. One new author. Change of titl

Batalin–Vilkovisky Formalism as a Theory of Integration for Polyvectors

International audienceThe Batalin–Vilkovisky (BV) formalism is a powerful generalization of the BRST approach of gauge theories and allows to treat more general field theories. We will see how, starting from the case of a finite dimensional configuration space, we can see this formalism as a theory of integration for polyvectors over the shifted cotangent bundle of the configuration space and arrive at a formula that admits a generalization to the infinite dimensional case. The process of gauge fixing and the observables of the theory will be presented

Solving the Dyson–Schwinger equation around its first singularities in the Borel plane

International audienceThe Dyson–Schwinger equation of the massless Wess–Zumino model is written as an equation over the anomalous dimension of the theory. Its asymptotic behavior is derived and the procedure to compute the perturbations of this asymptotic behavior is detailed. This procedure uses ill-defined objects. To solve this, the Dyson–Schwinger equation is rewritten for the Borel plane. It is shown that the illdefined procedure in the physical plane can be applied in the Borel plane. Other results obtained in the Borel plane are stated and the proof for one result is described