Using network-flow techniques to solve an optimization problem from surface-physics

The solid-on-solid model provides a commonly used framework for the description of surfaces. In the last years it has been extended in order to investigate the effect of defects in the bulk on the roughness of the surface. The determination of the ground state of this model leads to a combinatorial problem, which is reduced to an uncapacitated, convex minimum-circulation problem. We will show that the successive shortest path algorithm solves the problem in polynomial time.Comment: 8 Pages LaTeX, using Elsevier preprint style (macros included

Lower Critical Dimension of Ising Spin Glasses

Exact ground states of two-dimensional Ising spin glasses with Gaussian and bimodal (+- J) distributions of the disorder are calculated using a ``matching'' algorithm, which allows large system sizes of up to N=480^2 spins to be investigated. We study domain walls induced by two rather different types of boundary-condition changes, and, in each case, analyze the system-size dependence of an appropriately defined ``defect energy'', which we denote by DE. For Gaussian disorder, we find a power-law behavior DE ~ L^\theta, with \theta=-0.266(2) and \theta=-0.282(2) for the two types of boundary condition changes. These results are in reasonable agreement with each other, allowing for small systematic effects. They also agree well with earlier work on smaller sizes. The negative value indicates that two dimensions is below the lower critical dimension d_c. For the +-J model, we obtain a different result, namely the domain-wall energy saturates at a nonzero value for L\to \infty, so \theta = 0, indicating that the lower critical dimension for the +-J model exactly d_c=2.Comment: 4 pages, 4 figures, 1 table, revte

No spin-glass transition in the "mobile-bond" model

The recently introduced ``mobile-bond'' model for two-dimensional spin glasses is studied. The model is characterized by an annealing temperature T_q. On the basis of Monte Carlo simulations of small systems it has been claimed that this model exhibits a non-trivial spin-glass transition at finite temperature for small values of T_q. Here the model is studied by means of exact ground-state calculations of large systems up to N=256^2. The scaling of domain-wall energies is investigated as a function of the system size. For small values T_q<0.95 the system behaves like a (gauge-transformed) ferromagnet having a small fraction of frustrated plaquettes. For T_q>=0.95 the system behaves like the standard two-dimensional +-J spin-glass, i.e. it does NOT exhibit a phase transition at T>0.Comment: 4 pages, 5 figures, RevTe

Dynamics of the Wang-Landau algorithm and complexity of rare events for the three-dimensional bimodal Ising spin glass

We investigate the performance of flat-histogram methods based on a multicanonical ensemble and the Wang-Landau algorithm for the three-dimensional +/- J spin glass by measuring round-trip times in the energy range between the zero-temperature ground state and the state of highest energy. Strong sample-to-sample variations are found for fixed system size and the distribution of round-trip times follows a fat-tailed Frechet extremal value distribution. Rare events in the fat tails of these distributions corresponding to extremely slowly equilibrating spin glass realizations dominate the calculations of statistical averages. While the typical round-trip time scales exponential as expected for this NP-hard problem, we find that the average round-trip time is no longer well-defined for systems with N >= 8^3 spins. We relate the round-trip times for multicanonical sampling to intrinsic properties of the energy landscape and compare with the numerical effort needed by the genetic Cluster-Exact Approximation to calculate the exact ground state energies. For systems with N >= 8^3 spins the simulation of these rare events becomes increasingly hard. For N >= 14^3 there are samples where the Wang-Landau algorithm fails to find the true ground state within reasonable simulation times. We expect similar behavior for other algorithms based on multicanonical sampling.Comment: 9 pages, 12 figure

Prostate-Specific Ets (PSE) factor: a novel marker for detection of metastatic breast cancer in axillary lymph nodes

Prostate Specific Ets factor is a recently identified transcriptional activator that is overexpressed in prostate cancer. To determine whether this gene is overexpressed in breast cancer, we performed a virtual Northern blot using data available online at the Cancer Genome Anatomy Project website. Ninety-five SAGE libraries were probed with a unique sequence tag to the Prostate Specific Ets gene. The results indicate that Prostate Specific Ets is expressed in 14 out of 15 breast cancer libraries (93%), nine out of 10 prostate cancer libraries (90%), three out of 40 libraries from other cancers (7.5%), and four out of 30 normal tissue libraries (13%). To determine the possibility that the Prostate Specific Ets gene is a novel marker for detection of metastatic breast cancer in axillary lymph nodes, quantitative real-time RT–PCR analyses were performed. The mean level of Prostate Specific Ets expression in lymph nodes containing metastatic breast cancer (n=22) was 410-fold higher than in normal lymph node (n=51). A receiver operator characteristic curve analysis indicated that Prostate Specific Ets was overexpressed in 18 out of 22 lymph nodes containing metastatic breast cancer (82%). The receiver operator characteristic curve analysis also indicated that the diagnostic accuracy of the Prostate Specific Ets gene for detection of metastatic breast cancer in axillary lymph nodes was 0.949. These results provide evidence that Prostate Specific Ets is a potentially informative novel marker for detection of metastatic breast cancer in axillary lymph nodes, and should be included in any study that involves molecular profiling of breast cancer

Generating droplets in two-dimensional Ising spin glasses by using matching algorithms

We study the behavior of droplets for two dimensional Ising spin glasses with Gaussian interactions. We use an exact matching algorithm which enables study of systems with linear dimension L up to 240, which is larger than is possible with other approaches. But the method only allows certain classes of droplets to be generated. We study single-bond, cross and a category of fixed volume droplets as well as first excitations. By comparison with similar or equivalent droplets generated in previous works, the advantages but also the limitations of this approach are revealed. In particular we have studied the scaling behavior of the droplet energies and droplet sizes. In most cases, a crossover of the data can be observed such that for large sizes the behavior is compatible with the one-exponent scenario of the droplet theory. Only for the case of first excitations, no clear conclusion can be reached, probably because even with the matching approach the accessible system sizes are still too small.Comment: 11 pages, 16 figures, revte

HRAS is a therapeutic target in malignant chemo-resistant adenomyoepithelioma of the breast

Abstract Malignant adenomyoepithelioma (AME) of the breast is an exceptionally rare form of breast cancer, with a significant metastatic potential. Chemotherapy has been used in the management of advanced AME patients, however the majority of treatments are not effective. Recent studies report recurrent mutations in the HRAS Q61 hotspot in small series of AMEs, but there are no preclinical or clinical data showing H-Ras protein as a potential therapeutic target in malignant AMEs. We performed targeted sequencing of tumours’ samples from new series of 13 AMEs, including 9 benign and 4 malignant forms. Samples from the breast tumour and the matched axillary metastasis of one malignant HRAS mutated AME were engrafted and two patient-derived xenografts (PDX) were established that reproduced the typical AME morphology. The metastasis-derived PDX was treated in vivo by different chemotherapies and a combination of MEK and BRAF inhibitors (trametinib and dabrafenib). All malignant AMEs presented a recurrent mutation in the HRAS G13R or G12S hotspot. Mutation of PIK3CA were found in both benign and malignant AMEs, while AKT1 mutations were restricted to benign AMEs. Treatment of the PDX by the MEK inhibitor trametinib, resulted in a marked anti-tumor activity, in contrast to the BRAF inhibitor and the different chemotherapies that were ineffective. Overall, these findings further expand on the genetic features of AMEs and suggest that patients carrying advanced HRAS-mutated AMEs could potentially be treated with MEK inhibitors

Ground states of 2d +-J Ising spin glasses via stationary Fokker-Planck sampling

We investigate the performance of the recently proposed stationary Fokker-Planck sampling method considering a combinatorial optimization problem from statistical physics. The algorithmic procedure relies upon the numerical solution of a linear second order differential equation that depends on a diffusion-like parameter D. We apply it to the problem of finding ground states of 2d Ising spin glasses for the +-J-Model. We consider square lattices with side length up to L=24 with two different types of boundary conditions and compare the results to those obtained by exact methods. A particular value of D is found that yields an optimal performance of the algorithm. We compare this optimal value of D to a percolation transition, which occurs when studying the connected clusters of spins flipped by the algorithm. Nevertheless, even for moderate lattice sizes, the algorithm has more and more problems to find the exact ground states. This means that the approach, at least in its standard form, seems to be inferior to other approaches like parallel tempering.Comment: v1: 13 pages, 7 figures; v2: extended tex