Fractal dimension of domain walls in two-dimensional Ising spin glasses

We study domain walls in 2d Ising spin glasses in terms of a minimum-weight path problem. Using this approach, large systems can be treated exactly. Our focus is on the fractal dimension $d_f$ of domain walls, which describes via \simL^{d_f} the growth of the average domain-wall length with %% systems size $L\times L$. %% 20.07.07 OM %% Exploring systems up to L=320 we yield $d_f=1.274(2)$ for the case of Gaussian disorder, i.e. a much higher accuracy compared to previous studies. For the case of bimodal disorder, where many equivalent domain walls exist due to the degeneracy of this model, we obtain a true lower bound $d_f=1.095(2)$ and a (lower) estimate $d_f=1.395(3)$ as upper bound. Furthermore, we study the distributions of the domain-wall lengths. Their scaling with system size can be described also only by the exponent $d_f$, i.e. the distributions are monofractal. Finally, we investigate the growth of the domain-wall width with system size (``roughness'') and find a linear behavior.Comment: 8 pages, 8 figures, submitted to Phys. Rev. B; v2: shortened versio

Parallel String Sample Sort

We discuss how string sorting algorithms can be parallelized on modern multi-core shared memory machines. As a synthesis of the best sequential string sorting algorithms and successful parallel sorting algorithms for atomic objects, we propose string sample sort. The algorithm makes effective use of the memory hierarchy, uses additional word level parallelism, and largely avoids branch mispredictions. Additionally, we parallelize variants of multikey quicksort and radix sort that are also useful in certain situations.Comment: 34 pages, 7 figures and 12 table

One-variable word equations in linear time

In this paper we consider word equations with one variable (and arbitrary many appearances of it). A recent technique of recompression, which is applicable to general word equations, is shown to be suitable also in this case. While in general case it is non-deterministic, it determinises in case of one variable and the obtained running time is O(n + #_X log n), where #_X is the number of appearances of the variable in the equation. This matches the previously-best algorithm due to D\k{a}browski and Plandowski. Then, using a couple of heuristics as well as more detailed time analysis the running time is lowered to O(n) in RAM model. Unfortunately no new properties of solutions are shown.Comment: submitted to a journal, general overhaul over the previous versio

Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model

We study ground-state properties of the two-dimensional random-bond Ising model with couplings having a concentration $p\in[0,1]$ of antiferromagnetic and $(1-p)$ of ferromagnetic bonds. We apply an exact matching algorithm which enables us the study of systems with linear dimension $L$ up to 700. We study the behavior of the domain-wall energies and of the magnetization. We find that the paramagnet-ferromagnet transition occurs at $p_c \sim 0.103$ compared to the concentration $p_n\sim 0.109$ at the Nishimory point, which means that the phase diagram of the model exhibits a reentrance. Furthermore, we find no indications for an (intermediate) spin-glass ordering at finite temperature.Comment: 7 pages, 12 figures, revTe

Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D ±J\pm J Random-Bond Ising Model

The statistics of the ground-state and domain-wall energies for the two-dimensional random-bond Ising model on square lattices with independent, identically distributed bonds of probability $p$ of $J_{ij}= -1$ and $(1-p)$ of $J_{ij}= +1$ are studied. We are able to consider large samples of up to $320^2$ spins by using sophisticated matching algorithms. We study $L \times L$ systems, but we also consider $L \times M$ samples, for different aspect ratios $R = L / M$. We find that the scaling behavior of the ground-state energy and its sample-to-sample fluctuations inside the spin-glass region ($p_c \le p \le 1 - p_c$) are characterized by simple scaling functions. In particular, the fluctuations exhibit a cusp-like singularity at $p_c$. Inside the spin-glass region the average domain-wall energy converges to a finite nonzero value as the sample size becomes infinite, holding $R$ fixed. Here, large finite-size effects are visible, which can be explained for all $p$ by a single exponent $\omega\approx 2/3$, provided higher-order corrections to scaling are included. Finally, we confirm the validity of aspect-ratio scaling for $R \to 0$: the distribution of the domain-wall energies converges to a Gaussian for $R \to 0$, although the domain walls of neighboring subsystems of size $L \times L$ are not independent.Comment: 11 pages with 15 figures, extensively revise

Reduction of Two-Dimensional Dilute Ising Spin Glasses

The recently proposed reduction method is applied to the Edwards-Anderson model on bond-diluted square lattices. This allows, in combination with a graph-theoretical matching algorithm, to calculate numerically exact ground states of large systems. Low-temperature domain-wall excitations are studied to determine the stiffness exponent y_2. A value of y_2=-0.281(3) is found, consistent with previous results obtained on undiluted lattices. This comparison demonstrates the validity of the reduction method for bond-diluted spin systems and provides strong support for similar studies proclaiming accurate results for stiffness exponents in dimensions d=3,...,7.Comment: 7 pages, RevTex4, 6 ps-figures included, for related information, see http://www.physics.emory.edu/faculty/boettcher

Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems

We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields in near-linear time solutions as well as upper bounds. Using various computational tools, we get solutions within considerably less than 1% of the optimum. An interesting feature of our approach is that, even though an FWP is hard to compute in theory and Edmonds' algorithm for maximum weighted matching yields a polynomial solution for the MWMP, the practical behavior is just the opposite, and we can solve the FWP with high accuracy in order to find a good heuristic solution for the MWMP.Comment: 20 pages, 14 figures, Latex, to appear in Journal of Experimental Algorithms, 200

SUPREME-HN: a retrospective biomarker study assessing the prognostic value of PD-L1 expression in patients with recurrent and/or metastatic squamous cell carcinoma of the head and neck

Biomarcador; Carcinoma de células escamosas de cabeza y cuello; PD-L1Biomarker; Head and neck squamous cell carcinoma; PD-L1Biomarcador; Carcinoma de cèl·lules escamoses de cap i coll; PD-L1Background Programmed cell death ligand-1 (PD-L1) expression on tumor cells (TCs) is associated with improved survival in patients with head and neck squamous cell carcinoma (HNSCC) treated with immunotherapy, although its role as a prognostic factor is controversial. This study investigates whether tumoral expression of PD-L1 is a prognostic marker in patients with recurrent and/or metastatic (R/M) HNSCC treated with standard chemotherapy. Methods This retrospective, multicenter, noninterventional study assessed PD-L1 expression on archival R/M HNSCC tissue samples using the VENTANA PD-L1 (SP263) Assay. PD-L1 high was defined as PD-L1 staining of ≥ 25% TC, with exploratory scoring at TC ≥ 10% and TC ≥ 50%. The primary objective of this study was to estimate the prognostic value of PD-L1 status in terms of overall survival (OS) in patients with R/M HNSCC. Results 412 patients (median age, 62.0 years; 79.9% male; 88.2% Caucasian) were included from 19 sites in seven countries. 132 patients (32.0%) had TC ≥ 25% PD-L1 expression; 199 patients (48.3%) and 85 patients (20.6%) had TC ≥ 10% and ≥ 50%, respectively. OS did not differ significantly across PD-L1 expression (at TC ≥ 25% cutoff median OS: 8.2 months vs TC < 25%, 10.1 months, P = 0.55) or the ≥ 10% and ≥ 50% cutoffs (at TC ≥ 10%, median OS: 9.6 months vs TC < 10%, 9.4 months, P = 0.32, and at TC ≥ 50%, median OS 7.9 vs TC < 50%, 10.0 months, P = 0.39, respectively). Conclusions PD-L1 expression, assessed using the VENTANA PD-L1 (SP263) Assay, was not prognostic of OS in patients with R/M HNSCC treated with standard of care chemotherapies.This study was sponsored by AstraZeneca. The protocol for this study was developed by the sponsor (AstraZeneca) and advisors. Data were collected collaboratively by the sponsor and clinical investigators. Statisticians employed by the sponsor analyzed the data. All authors participated in the preparation, review, and approval of the manuscript; and decision to submit the manuscript for publication