Chemotherapy following radium-223 dichloride treatment in ALSYMPCA

BACKGROUND Radium-223 prolongs overall survival in patients with castration-resistant prostate cancer (CRPC) and symptomatic bone metastases, regardless of prior docetaxel. Whether or not chemotherapy can be safely administered following radium-223 treatment is of clinical importance. An exploratory analysis of prospectively collected data, from the ALSYMPCA (ALpharadin in SYMptomatic Prostate CAncer) patient subgroup who received chemotherapy after radium-223 or placebo treatment, was conducted to evaluate the safety and efficacy of chemotherapy following radium-223. METHODS In ALSYMPCA, CRPC patients with symptomatic bone metastases and no visceral metastases were randomized 2:1 to receive six injections of radium-223 (50 kBq/kg IV) or placebo plus best standard of care, stratified by prior docetaxel, baseline alkaline phosphatase, and current bisphosphonate use. In this exploratory analysis, chemotherapy agents administered following study treatment were identified; timing and duration were calculated. Hematologic safety was reviewed, and overall survival analyzed. RESULTS Overall, 142 radium-223 and 64 placebo patients received subsequent chemotherapy; most common were docetaxel (70% radium-223, 72% placebo) and mitoxantrone (16% radium-223, 20% placebo). The majority of patients (61% radium-223, 58% placebo) had received prior docetaxel. Radium-223 patients started subsequent chemotherapy later than placebo patients; chemotherapy duration was similar between groups. In radium-223 and placebo patients receiving subsequent chemotherapy, median hematologic values (hemoglobin, neutrophils, and platelets) remained nearly constant up to 18 months following start of chemotherapy, regardless of prior docetaxel treatment. A low percentage of patients in both groups had grades 3–4 hematologic values (<10%). Platelet count decline, from last measurement before chemotherapy, was numerically greater in radium-223 versus placebo patients. Median overall survivals from start of chemotherapy were 16.0 and 15.8 months following radium-223 and placebo, respectively. CONCLUSIONS Chemotherapy following radium-223, regardless of prior docetaxel, is feasible and appears to be well tolerated in patients with CRPC and symptomatic bone metastases

The general Leigh-Strassler deformation and integrability

The success of the identification of the planar dilatation operator of N=4 SYM with an integrable spin chain Hamiltonian has raised the question if this also is valid for a deformed theory. Several deformations of SYM have recently been under investigation in this context. In this work we consider the general Leigh-Strassler deformation. For the generic case the S-matrix techniques cannot be used to prove integrability. Instead we use R-matrix techniques to study integrability. Some new integrable points in the parameter space are found.Comment: 22 pages, 8 figures, reference adde

Decoupling limits of N=4 super Yang-Mills on R x S^3

We find new decoupling limits of N=4 super Yang-Mills (SYM) on R x S^3 with gauge group SU(N). These decoupling limits lead to decoupled theories that are much simpler than the full N=4 SYM but still contain many of its interesting features. The decoupling limits correspond to being in a near-critical region, near a point with zero temperature and critical chemical potentials. The new decoupling limits are found by generalizing the limits of hep-th/0605234 to include not only the chemical potentials for the SU(4) R-symmetry of N=4 SYM but also the chemical potentials corresponding to the SO(4) symmetry. In the decoupled theories it is possible to take a strong coupling limit in a controllable manner since the full effective Hamiltonian is known. For planar N=4 SYM on R x S^3 all the decoupled theories correspond to fully integrable spin chains. We study the thermodynamics of the decoupled theories and find the Hagedorn temperature for small and large values of the effective coupling. We find an alternative formulation of the decoupling limits in the microcanonical ensemble. This leads to a characterization of certain regimes of weakly coupled N=4 SYM in which there are string-like states. Finally, we find a similar decoupling limit for pure Yang-Mills theory, which for the planar limit leads to a fully integrable decoupled theory.Comment: 48 pages, 1 figure; added references, published versio

On the Maximum Crossing Number

Research about crossings is typically about minimization. In this paper, we consider \emph{maximizing} the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructing a planar graph on twelve vertices that allows a non-convex drawing with more crossings than any convex one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the maximum number of crossings of a geometric graph and that the weighted geometric case is NP-hard to approximate. We strengthen these results by showing hardness of approximation even for the unweighted geometric case and prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure

Generalized Penner models to all genera

We give a complete description of the genus expansion of the one-cut solution to the generalized Penner model. The solution is presented in a form which allows us in a very straightforward manner to localize critical points and to investigate the scaling behaviour of the model in the vicinity of these points. We carry out an analysis of the critical behaviour to all genera addressing all types of multi-critical points. In certain regions of the coupling constant space the model must be defined via analytical continuation. We show in detail how this works for the Penner model. Using analytical continuation it is possible to reach the fermionic 1-matrix model. We show that the critical points of the fermionic 1-matrix model can be indexed by an integer, $m$, as it was the case for the ordinary hermitian 1-matrix model. Furthermore the $m$'th multi-critical fermionic model has to all genera the same value of $\gamma_{str}$ as the $m$'th multi-critical hermitian model. However, the coefficients of the topological expansion need not be the same in the two cases. We show explicitly how it is possible with a fermionic matrix model to reach a $m=2$ multi-critical point for which the topological expansion has alternating signs, but otherwise coincides with the usual Painlev\'{e} expansion.Comment: 27 pages, PostScrip

On dilatation operator for a renormalizable theory

Given a renormalizable theory we construct the dilatation operator, in the sense of generator of RG flow of composite operators. The generator is found as a differential operator acting on the space of normal symbols of composite operators in the theory. In the spirit of AdS/CFT correspondence, this operator is interpreted as the Hamiltonian of the dual theory. In the case of a field theory with non-abelian gauge symmetry the resulting system is a matrix model. The one-loop case is analyzed in details and it is shown that we reproduce known results from N=4 supersymmetric Yang-Mills theory.Comment: 26 pages, no figure

Integrable Spin Chains with U(1)^3 symmetry and generalized Lunin-Maldacena backgrounds

We consider the most general three-state spin chain with U(1)^3 symmetry and nearest neighbour interaction. Our model contains as a special case the spin chain describing the holomorphic three scalar sector of the three parameter complex deformation of N=4 SYM, dual to type IIB string theory in the generalized Lunin-Maldacena backgrounds discovered by Frolov. We formulate the coordinate space Bethe ansatz, calculate the S-matrix and determine for which choices of parameters the S-matrix fulfills the Yang-Baxter equations. For these choices of parameters we furthermore write down the R-matrix. We find in total four classes of integrable models. In particular, each already known model of the above type is nothing but one in a family of such models.Comment: 16 pages, 3 figures, references correcte

Matching Higher Conserved Charges for Strings and Spins

We demonstrate that the recently found agreement between one-loop scaling dimensions of large dimension operators in N=4 gauge theory and energies of spinning strings on AdS_5 x S^5 extends to the eigenvalues of an infinite number of hidden higher commuting charges. This dynamical agreement is of a mathematically highly intricate and non-trivial nature. In particular, on the gauge side the generating function for the commuting charges is obtained by integrable quantum spin chain techniques from the thermodynamic density distribution function of Bethe roots. On the string side the generating function, containing information to arbitrary loop order, is constructed by solving exactly the Backlund equations of the integrable classical string sigma model. Our finding should be an important step towards matching the integrable structures on the string and gauge side of the AdS/CFT correspondence.Comment: Latex, 33 pages, v2: new section added (completing the analytic proof that the entire infinite towers of commuting gauge and string charges match); references adde

Single impurity operators at critical wrapping order in the beta-deformed N=4 SYM

We study the spectrum of one single magnon in the superconformal beta-deformed N=4 SYM theory in the planar limit. We compute the anomalous dimensions of one-impurity operators O_{1,L}= tr(phi Z^{L-1}), including wrapping contributions at their critical order L.Comment: LaTeX, feynmf, Metapost, 20 pages, 11 figures, v2: results up to 11 loops completed, appendix on integral calculation extende

Beauty and the Twist: The Bethe Ansatz for Twisted N=4 SYM

It was recently shown that the string theory duals of certain deformations of the N=4 gauge theory can be obtained by a combination of T-duality transformations and coordinate shifts. Here we work out the corresponding procedure of twisting the dual integrable spin chain and its Bethe ansatz. We derive the Bethe equations for the complete twisted N=4 gauge theory at one and higher loops. These have a natural generalization which we identify as twists involving the Cartan generators of the conformal algebra. The underlying model appears to be a form of noncommutative deformation of N=4 SYM.Comment: 28 pages, v2: reference flip corrected, v3: some typos in (4.10,4.20,5.5) correcte