Stochastic linear scaling for metals and non metals

Total energy electronic structure calculations, based on density functional theory or on the more empirical tight binding approach, are generally believed to scale as the cube of the number of electrons. By using the localisaton property of the high temperature density matrix we present exact deterministic algorithms that scale linearly in one dimension and quadratically in all others. We also introduce a stochastic algorithm that scales linearly with system size. These results hold for metallic and non metallic systems and are substantiated by numerical calculations on model systems.Comment: 9 pages, 2 figure

Linear scaling electronic structure calculations and accurate sampling with noisy forces

Numerical simulations based on electronic structure calculations are finding ever growing applications in many areas of physics. A major limiting factor is however the cubic scaling of the algorithms used. Building on previous work [F. R. Krajewski and M. Parrinello, Phys.Rev. B71, 233105 (2005)] we introduce a novel statistical method for evaluating the inter-atomic forces which scales linearly with system size and is applicable also to metals. The method is based on exact decomposition of the fermionic determinant and on a mapping onto a field theoretical expression. We solve exactly the problem of sampling the Boltzmann distribution with noisy forces. This novel approach can be used in such diverse fields as quantum chromodynamics, quantum Monte Carlo or colloidal physics.Comment: 5 pages, 2 figure

Quantum creep and quantum creep transitions in 1D sine-Gordan chains

Discrete sine-Gordon (SG) chains are studied with path-integral molecular dynamics. Chains commensurate with the substrate show the transition from collective quantum creep to pinning at bead masses slightly larger than those predicted from the continuous SG model. Within the creep regime, a field-driven transition from creep to complete depinning is identified. The effects of disorder in the external potential on the chain's dynamics depend on the potential's roughness exponent $H$, i.e., quantum and classical fluctuations affect the current self-correlation functions differently for $H = 1/2$.Comment: 4 pages, 3 figure

Selecting the Best Candidates for Cisplatin-based Adjuvant Chemotherapy After Radical Cystectomy Among Patients with pN+ Bladder Cancer

: A trend towards greater benefit from adjuvant chemotherapy (ACT) in pN+ bladder cancer (BCa) has been observed in multiple randomized controlled trials. However, it is still unclear which patients might benefit the most from this approach. We retrospectively analyzed a multicenter cohort of 1381 patients with pTany pN1-3 cM0 R0 urothelial BCa treated with radical cystectomy (RC) with or without cisplatin-based ACT. The main endpoint was overall survival (OS) after RC. We performed 1:1 propensity score matching to adjust for baseline characteristics and conducted a classification and regression tree (CART) analysis to assess postoperative risk groups and Cox regression analyses to predict OS. Overall, 391 patients (28%) received cisplatin-based ACT. After matching, two cohorts of 281 patients with pN+ BCa were obtained. CART analysis stratified patients into three risk groups: favorable prognosis (≤pT2 and positive lymph node [PLN] count ≤2; odds ratio [OR] 0.43), intermediate prognosis (≥pT3 and PLN count ≤2; OR 0.92), and poor prognosis (pTany and PLN count ≥3; OR 1.36). Only patients with poor prognosis benefitted from ACT in terms of OS (HR 0.51; p < 0.001). We created the first algorithm that stratifies patients with pN+ BCa into prognostic classes and identified patients with pTany BCa with PLN ≥3 as the most suitable candidates for cisplatin-based ACT. PATIENT SUMMARY: We found that overall survival among patients with bladder cancer and evidence of lymph node involvement depends on cancer stage and the number of positive lymph nodes. Patients with more than three nodes affected by metastases seem to experience the greatest overall survival benefit from cisplatin-based chemotherapy after bladder removal. Our study suggests that patients with the highest risk should be prioritized for cisplatin-based chemotherapy after bladder removal