Transfer operator analysis of the parallel dynamics of disordered Ising chains

We study the synchronous stochastic dynamics of the random field and random bond Ising chain. For this model the generating functional analysis methods of De Dominicis leads to a formalism with transfer operators, similar to transfer matrices in equilibrium studies, but with dynamical paths of spins and (conjugate) fields as arguments, as opposed to replicated spins. In the thermodynamic limit the macroscopic dynamics is captured by the dominant eigenspace of the transfer operator, leading to a relative simple and transparent set of equations that are easy to solve numerically. Our results are supported excellently by numerical simulations.Comment: 2 figures, 10 pages, submitted to Philosophical Magazin

Replica analysis of overfitting in regression models for time-to-event data

Overfitting, which happens when the number of parameters in a model is too large compared to the number of data points available for determining these parameters, is a serious and growing problem in survival analysis. While modern medicine presents us with data of unprecedented dimensionality, these data cannot yet be used effectively for clinical outcome prediction. Standard error measures in maximum likelihood regression, such as p-values and z-scores, are blind to overfitting, and even for Cox's proportional hazards model (the main tool of medical statisticians), one finds in literature only rules of thumb on the number of samples required to avoid overfitting. In this paper we present a mathematical theory of overfitting in regression models for time-to-event data, which aims to increase our quantitative understanding of the problem and provide practical tools with which to correct regression outcomes for the impact of overfitting. It is based on the replica method, a statistical mechanical technique for the analysis of heterogeneous many-variable systems that has been used successfully for several decades in physics, biology, and computer science, but not yet in medical statistics. We develop the theory initially for arbitrary regression models for time-to-event data, and verify its predictions in detail for the popular Cox model.Comment: 37 pages, 9 figure

Importance of controlling the degree of saturation in soil compaction

n the typical conventional fill compaction, the dry density ρd and the water content w are controlled in relation to (ρd)max and wopt determined by laboratory compaction tests using a representative sample at a certain compaction energy level CEL. Although CEL and actual soil type affect significantly the values of (ρd)max and wopt, they change inevitably in a given earthwork project while CEL in the field may not match the value used in the laboratory compaction tests. Compaction control based on the stiffness of compacted soil in the field has such a drawback that the stiffness drops upon wetting more largely as the degree of saturation, Sr, of compacted soil becomes lower than the optimum degree of saturation (Sr)opt defined as Sr when (ρd)max is obtained for a given CEL. In comparison, the value of (Sr)opt and the ρd/(ρd)max vs. Sr - (Sr)opt relation of compacted soil are rather insensitive to variations in CEL and soil type, while the strength and stiffness of unsoaked and soaked compacted soil is controlled by ρd and “Sr at the end of compaction”. It is proposed to control not only w and ρd but also Sr so that Sr becomes (Sr)opt and ρd becomes large enough to ensue soil properties required in design.Fundação para a Ciência e Tecnologia (FCT)info:eu-repo/semantics/publishedVersio

Improved resection margins in breast-conserving surgery using Terahertz Pulsed imaging data

New statistical methods were employed to improve the ability to distinguish benign from malignant breast tissue ex vivo in a recent study. The ultimately aim was to improve the intraoperative assessment of positive tumour margins in breast-conserving surgery (BCS), potentially reducing patient re-operation rates. A multivariate Bayesian classifier was applied to the waveform samples produced by a Terahertz Pulsed Imaging (TPI) handheld probe system in order to discriminate tumour from benign breast tissue, obtaining a sensitivity of 96% and specificity of 95%. We compare these results to traditional and to state-of-the-art methods for determining resection margins. Given the general nature of the classifier, it is expected that this method can be applied to other tumour types where resection margins are also critical

Interpolating the Sherrington-Kirkpatrick replica trick

The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally implemented into the cavity field technique, or its variants as the stochastic stability or the random overlap structures. However the first and most famous approach to mean field statistical mechanics with quenched disorder is the replica trick. Among the models where these methods have been used (namely, dealing with frustration and complexity), probably the best known is the Sherrington-Kirkpatrick spin glass: In this paper we are pleased to apply the interpolation scheme to the replica trick framework and test it directly to the cited paradigmatic model: interestingly this allows to obtain easily the replica-symmetric control and, synergically with the broken replica bounds, a description of the full RSB scenario, both coupled with several minor theorems. Furthermore, by treating the amount of replicas $n\in(0,1]$ as an interpolating parameter (far from its original interpretation) this can be though of as a quenching temperature close to the one introduce in off-equilibrium approaches and, within this viewpoint, the proof of the attended commutativity of the zero replica and the infinite volume limits can be obtained.Comment: This article is dedicated to David Sherrington on the occasion of his seventieth birthda

HER2-HER3 heterodimer quantification by FRET-FLIM and patient subclass analysis of the COIN colorectal trial

BACKGROUND: The phase 3 MRC COIN trial showed no statistically significant benefit from adding the EGFR-target cetuximab to oxaliplatin-based chemotherapy in first-line treatment of advanced colorectal cancer. This study exploits additional information on HER2-HER3 dimerization to achieve patient stratification and reveal previously hidden subgroups of patients who had differing disease progression and treatment response. METHODS: HER2-HER3 dimerization was quantified by "FLIM Histology" in primary tumor samples from 550 COIN trial patients receiving oxaliplatin and fluoropyrimidine chemotherapy +/-cetuximab. Bayesian latent class analysis (LCA) and covariate reduction was performed to analyze the effects of HER2-HER3 dimer, RAS mutation and cetuximab on progression-free survival (PFS) and overall survival (OS). All statistical tests were two-sided. RESULTS: LCA on a cohort of 398 patients revealed two patient subclasses with differing prognoses (median OS: 1624 days [95%CI=1466-1816] vs 461 [95%CI=431-504]): Class 1 (15.6%) showed a benefit from cetuximab in OS (HR = 0.43 [95%CI=0.25-0.76]; p = 0.004). Class 2 showed an association of increased HER2-HER3 with better OS (HR = 0.64 [95%CI=0.44-0.94]; p = 0.02). A class prediction signature was formed and tested on an independent validation cohort (N = 152) validating the prognostic utility of the dimer assay. Similar subclasses were also discovered in full trial dataset (N = 1,630) based on 10 baseline clinicopathological and genetic covariates. CONCLUSIONS: Our work suggests that the combined use of HER dimer imaging and conventional mutation analyses will be able to identify a small subclass of patients (>10%) who will have better prognosis following chemotherapy. A larger prospective cohort will be required to confirm its utility in predicting the outcome of anti-EGFR treatment

A latent class model for competing risks

Survival data analysis becomes complex when the proportional hazards assumption is violated at population level or when crude hazard rates are no longer estimators of marginal ones. We develop a Bayesian survival analysis method to deal with these situations, on the basis of assuming that the complexities are induced by latent cohort or disease heterogeneity that is not captured by covariates and that proportional hazards hold at the level of individuals. This leads to a description from which risk-specific marginal hazard rates and survival functions are fully accessible, 'decontaminated' of the effects of informative censoring, and which includes Cox, random effects and latent class models as special cases. Simulated data confirm that our approach can map a cohort's substructure and remove heterogeneity-induced informative censoring effects. Application to data from the Uppsala Longitudinal Study of Adult Men cohort leads to plausible alternative explanations for previous counter-intuitive inferences on prostate cancer. The importance of managing cardiovascular disease as a comorbidity in women diagnosed with breast cancer is suggested on application to data from the Swedish Apolipoprotein Mortality Risk Study. Copyright © 2017 John Wiley & Sons, Ltd

The diminishing role of hubs in dynamical processes on complex networks

It is notoriously difficult to predict the behaviour of a complex self-organizing system, where the interactions among dynamical units form a heterogeneous topology. Even if the dynamics of each microscopic unit is known, a real understanding of their contributions to the macroscopic system behaviour is still lacking. Here we develop information-theoretical methods to distinguish the contribution of each individual unit to the collective out-of-equilibrium dynamics. We show that for a system of units connected by a network of interaction potentials with an arbitrary degree distribution, highly connected units have less impact on the system dynamics as compared to intermediately connected units. In an equilibrium setting, the hubs are often found to dictate the long-term behaviour. However, we find both analytically and experimentally that the instantaneous states of these units have a short-lasting effect on the state trajectory of the entire system. We present qualitative evidence of this phenomenon from empirical findings about a social network of product recommendations, a protein-protein interaction network, and a neural network, suggesting that it might indeed be a widespread property in nature.Comment: Published versio