A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics

We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the Relative Entropy Rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of suitable observables in path space for the Relative Entropy Rate and the corresponding Fisher Information Matrix. The stationary regime is crucial for stochastic dynamics and here allows us to address the sensitivity analysis of complex systems, including examples of processes with complex landscapes that exhibit metastability, non-reversible systems from a statistical mechanics perspective, and high-dimensional, spatially distributed models. All these systems exhibit, typically non-gaussian stationary probability distributions, while in the case of high-dimensionality, histograms are impossible to construct directly. Our proposed methods bypass these challenges relying on the direct Monte Carlo simulation of rigorously derived observables for the Relative Entropy Rate and Fisher Information in path space rather than on the stationary probability distribution itself. We demonstrate the capabilities of the proposed methodology by focusing here on two classes of problems: (a) Langevin particle systems with either reversible (gradient) or non-reversible (non-gradient) forcing, highlighting the ability of the method to carry out sensitivity analysis in non-equilibrium systems; and, (b) spatially extended Kinetic Monte Carlo models, showing that the method can handle high-dimensional problems

Large deviations for the macroscopic motion of an interface

We study the most probable way an interface moves on a macroscopic scale from an initial to a final position within a fixed time in the context of large deviations for a stochastic microscopic lattice system of Ising spins with Kac interaction evolving in time according to Glauber (non-conservative) dynamics. Such interfaces separate two stable phases of a ferromagnetic system and in the macroscopic scale are represented by sharp transitions. We derive quantitative estimates for the upper and the lower bound of the cost functional that penalizes all possible deviations and obtain explicit error terms which are valid also in the macroscopic scale. Furthermore, using the result of a companion paper about the minimizers of this cost functional for the macroscopic motion of the interface in a fixed time, we prove that the probability of such events can concentrate on nucleations should the transition happen fast enough

Genomic Testing in Localized Prostate Cancer Can Identify Subsets of African Americans With Aggressive Disease

BACKGROUND: Personalized genomic classifiers have transformed the management of prostate cancer (PCa) by identifying the most aggressive subsets of PCa. Nevertheless, the performance of genomic classifiers to risk classify African American men is thus far lacking in a prospective setting. METHODS: This is a prospective study of the Decipher genomic classifier for National Comprehensive Cancer Network low- and intermediate-risk PCa. Study-eligible non-African American men were matched to African American men. Diagnostic biopsy specimens were processed to estimate Decipher scores. Samples accrued in NCT02723734, a prospective study, were interrogated to determine the genomic risk of reclassification (GrR) between conventional clinical risk classifiers and the Decipher score. RESULTS: The final analysis included a clinically balanced cohort of 226 patients with complete genomic information (113 African American men and 113 non-African American men). A higher proportion of African American men with National Comprehensive Cancer Network-classified low-risk (18.2%) and favorable intermediate-risk (37.8%) PCa had a higher Decipher score than non-African American men. Self-identified African American men were twice more likely than non-African American men to experience GrR (relative risk [RR] = 2.23, 95% confidence interval [CI] = 1.02 to 4.90; P = .04). In an ancestry-determined race model, we consistently validated a higher risk of reclassification in African American men (RR = 5.26, 95% CI = 1.66 to 16.63; P = .004). Race-stratified analysis of GrR vs non-GrR tumors also revealed molecular differences in these tumor subtypes. CONCLUSIONS: Integration of genomic classifiers with clinically based risk classification can help identify the subset of African American men with localized PCa who harbor high genomic risk of early metastatic disease. It is vital to identify and appropriately risk stratify the subset of African American men with aggressive disease who may benefit from more targeted interventions

A Detailed Dosimetric Analysis of Spinal Cord Tolerance in High-Dose Spine Radiosurgery.

OBJECTIVE: Dose-volume tolerance of the spinal cord (SC) in spinal stereotactic radiosurgery (SRS) is difficult to define because radiation myelitis rates are low, and published reports document cases of myelopathy but do not account for the total number of patients treated at given dose-volume combinations who do not have myelitis. This study reports SC toxicity from single-fraction spinal SRS and presents a comprehensive atlas of the incidence of adverse events to examine dose-volume predictors. METHODS AND MATERIALS: A prospective database of all patients undergoing single-fraction spinal SRS at our institution between 2004 and 2011 was reviewed. SC toxicity was defined by clinical myelitis with accompanying magnetic resonance imaging (MRI) signal changes that were not attributable to tumor progression. Dose-volume histogram (DVH) atlases were created for these endpoints. Rates of adverse events with 95% confidence limits and probabilities that rates of adverse events were RESULTS: Information about DVH and myelitis was available for 228 patients treated at 259 sites. The median follow-up time was 14.6 months (range, 0.1-138.3 months). The median prescribed dose to the planning treatment volume was 24 Gy (range, 18-24 Gy). There were 2 cases of radiation myelitis (rate r=0.7%) with accompanying MRI signal changes. Myelitis occurred in 2 patients, with Dmax \u3e13.33 Gy, and minimum doses to the hottest 0.1, 0.2, 0.5, and 1 cc were \u3e10.66, 10.9, and 8 Gy, respectively; however, both myelitis cases occurred below the 34th percentile for Dmax and there were 194 DVHs in total with Dmax \u3e13.33 Gy. CONCLUSIONS: A median SC Dmax of 13.85 Gy is safe and supports that a Dmax limit of 14 Gy carries a lo

Parametrizing coarse grained models for molecular systems at equilibrium

Hierarchical coarse graining of atomistic molecular systems at equilibrium has been an intensive research topic over the last few decades. In this work we (a) review theoretical and numerical aspects of different parametrization methods (structural-based, force matching and relative entropy) to derive the effective interaction potential between coarse-grained particles. All methods approximate the many body potential of mean force; resulting, however, in different optimization problems. (b) We also use a reformulation of the force matching method by introducing a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (E. Kalligiannaki, et al., J. Chem. Phys. 2015). We apply and compare these methods to: (a) a benchmark system of two isolated methane molecules; (b) methane liquid; (c) water; and (d) an alkane fluid. Differences between the effective interactions, derived from the various methods, are found that depend on the actual system under study. The results further reveal the relation of the various methods and the sensitivities that may arise in the implementation of numerical methods used in each case