Phase transitions in diluted negative-weight percolation models

We investigate the geometric properties of loops on two-dimensional lattice graphs, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of spanning loops of total negative weight. The resulting percolation problem is fundamentally different from conventional percolation, as we have seen in a previous study of this model for the undiluted case. Here, we investigate how the percolation transition is affected by additional dilution. We consider two types of dilution: either a certain fraction of edges exhibit zero weight, or a fraction of edges is even absent. We study these systems numerically using exact combinatorial optimization techniques based on suitable transformations of the graphs and applying matching algorithms. We perform a finite-size scaling analysis to obtain the phase diagram and determine the critical properties of the phase boundary. We find that the first type of dilution does not change the universality class compared to the undiluted case whereas the second type of dilution leads to a change of the universality class.Comment: 8 pages, 7 figure

Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6

We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary conditions in all relevant dimensions from d=2 to the upper critical dimension d=6. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in in the full ensemble of loops with negative weight, i.e. non-trivial (system spanning) loops as well as topologically trivial ("small") loops. The NWP phenomenon refers to the disorder driven proliferation of system spanning loops of total negative weight. While previous studies where focused on the latter loops, we here put under scrutiny the ensemble of small loops. Our aim is to characterize -using this extensive and exhaustive numerical study- the loop length distribution of the small loops right at and below the critical point of the hypercubic setups by means of two independent critical exponents. These can further be related to the results of previous finite-size scaling analyses carried out for the system spanning loops. For the numerical simulations we employed a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allowed us to study here numerically exact very large systems with high statistics.Comment: 7 pages, 4 figures, 2 tables, paper summary available at http://www.papercore.org/Kajantie2000. arXiv admin note: substantial text overlap with arXiv:1003.1591, arXiv:1005.5637, arXiv:1107.174

Nonlinear Dynamics of Parity-Even Tricritical Gravity in Three and Four Dimensions

Recently proposed "multicritical" higher-derivative gravities in Anti de Sitter space carry logarithmic representations of the Anti de Sitter isometry group. While generically non-unitary already at the quadratic, free-theory level, in special cases these theories admit a unitary subspace. The simplest example of such behavior is "tricritical" gravity. In this paper, we extend the study of parity-even tricritical gravity in d = 3, 4 to the first nonlinear order. We show that the would-be unitary subspace suffers from a linearization instability and is absent in the full non-linear theory.Comment: 22 pages; v2: references added, published versio

Avelumab, an Anti-Programmed Death-Ligand 1 Antibody, In Patients With Refractory Metastatic Urothelial Carcinoma: Results From a Multicenter, Phase Ib Study

Purpose We assessed the safety and antitumor activity of avelumab, a fully human anti-programmed death-ligand 1 (PD-L1) IgG1 antibody, in patients with refractory metastatic urothelial carcinoma. Methods In this phase Ib, multicenter, expansion cohort, patients with urothelial carcinoma progressing after platinum-based chemotherapy and unselected for PD-L1 expression received avelumab 10 mg/kg intravenously every 2 weeks. The primary objectives were safety and tolerability. Secondary objectives included confirmed objective response rate (Response Evaluation Criteria in Solid Tumors [RECIST] version 1.1), progression-free survival, overall survival (OS), and PD-L1-associated clinical activity. PD-L1 positivity was defined as expression by immunohistochemistry on ≥ 5% of tumor cells. Results Forty-four patients were treated with avelumab and followed for a median of 16.5 months (interquartile range, 15.8 to 16.7 months). The data cutoff was March 19, 2016. The most frequent treatment-related adverse events of any grade were fatigue/asthenia (31.8%), infusion-related reaction (20.5%), and nausea (11.4%). Grades 3 to 4 treatment-related adverse events occurred in three patients (6.8%) and included asthenia, AST elevation, creatine phosphokinase elevation, and decreased appetite. The confirmed objective response rate by independent central review was 18.2% (95% CI, 8.2% to 32.7%; five complete responses and three partial responses). The median duration of response was not reached (95% CI, 12.1 weeks to not estimable), and responses were ongoing in six patients (75.0%), including four of five complete responses. Seven of eight responding patients had PD-L1-positive tumors. The median progression-free survival was 11.6 weeks (95% CI, 6.1 to 17.4 weeks); the median OS was 13.7 months (95% CI, 8.5 months to not estimable), with a 12-month OS rate of 54.3% (95% CI, 37.9% to 68.1%). Conclusion Avelumab was well tolerated and associated with durable responses and prolonged survival in patients with refractory metastatic UC