Variational methods for finding periodic orbits in the incompressible Navier–Stokes equations

Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier–Stokes equations, based on variations of an integral objective functional, and using traditional gradient-based optimisation strategies. Different approaches for handling the incompressibility condition are considered. The variational methods are applied to the specific case of periodic, two-dimensional Kolmogorov flow and compared against existing Newton iteration-based shooting methods. While computationally slow, our methods converge from very inaccurate initial guesses.<br/

Tumor-homing cytotoxic human induced neural stem cells for cancer therapy

Engineered neural stem cells (NSCs) are a promising approach to treating glioblastoma (GBM). The ideal NSC drug carrier for clinical use should be easily isolated and autologous to avoid immune rejection. We transdifferentiated (TD) human fibroblasts into tumor-homing early-stage induced NSCs (h-iNSCTE), engineered them to express optical reporters and different therapeutic gene products, and assessed the tumor-homing migration and therapeutic efficacy of cytotoxic h-iNSCTE in patient-derived GBM models of surgical and nonsurgical disease. Molecular and functional analysis revealed that our single-factor SOX2 TD strategy converted human skin fibroblasts into h-iNSCTE that were nestin+ and expressed pathways associated with tumor-homing migration in 4 days. Time-lapse motion analysis showed that h-iNSCTE rapidly migrated to human GBM cells and penetrated human GBM spheroids, a process inhibited by blockade of CXCR4. Serial imaging showed that h-iNSCTE delivery of the proapoptotic agent tumor necrosis factor-A-related apoptosis-inducing ligand (TRAIL) reduced the size of solid human GBM xenografts 250-fold in 3 weeks and prolonged median survival from 22 to 49 days. Additionally, h-iNSCTE thymidine kinase/ganciclovir enzyme/prodrug therapy (h-iNSCTE-TK) reduced the size of patient-derived GBM xenografts 20-fold and extended survival from 32 to 62 days. Mimicking clinical NSC therapy, h-iNSCTE-TK therapy delivered into the postoperative surgical resection cavity delayed the regrowth of residual GBMs threefold and prolonged survival from 46 to 60 days. These results suggest that TD of human skin into h-iNSCTE is a platform for creating tumor-homing cytotoxic cell therapies for cancer, where the potential to avoid carrier rejection could maximize treatment durability in human trials

Coupled oscillators as models of phantom and scalar field cosmologies

We study a toy model for phantom cosmology recently introduced in the literature and consisting of two oscillators, one of which carries negative kinetic energy. The results are compared with the exact phase space picture obtained for similar dynamical systems describing, respectively, a massive canonical scalar field conformally coupled to the spacetime curvature, and a conformally coupled massive phantom. Finally, the dynamical system describing exactly a minimally coupled phantom is studied and compared with the toy model.Comment: 18 pages, LaTeX, to appear in Physical Review

Classical self-forces in a space with a dispiration

We derive the gravitational and electrostatic self-energies of a particle at rest in the background of a cosmic dispiration (topological defect), finding that the particle may experience potential steps, well potentials or potential barriers depending on the nature of the interaction and also on certain properties of the defect. The results may turn out to be useful in cosmology and condensed matter physics.Comment: 5 pages, 4 figures, revtex4 fil

Back reaction in the formation of a straight cosmic string

A simple model for the formation of a straight cosmic string, wiggly or unperturbed is considered. The gravitational field of such string is computed in the linear approximation. The vacuum expectation value of the stress tensor of a massless scalar quantum field coupled to the string gravitational field is computed to the one loop order. Finally, the back-reaction effect on the gravitational field of the string is obtained by solving perturbatively the semiclassical Einstein's equations.Comment: 29 pages, LaTeX, no figures. A postcript version can be obtained from anonymous ftp at ftp://ftp.ifae.es/preprint.f

Integrated analysis of RNA and DNA from the phase III trial CALGB 40601 identifies predictors of response to trastuzumab-based neoadjuvant chemotherapy in HER2-positive breast cancer

Purpose: Response to a complex trastuzumab-based regimen is affected by multiple features of the tumor and its microenvironment. Developing a predictive algorithm is key to optimizing HER2-targeting therapy. Experimental Design: We analyzed 137 pretreatment tumors with mRNA-seq and DNA exome sequencing from CALGB 40601, a neoadjuvant phase III trial of paclitaxel plus trastuzumab with or without lapatinib in stage II to III HER2-positive breast cancer. We adopted an Elastic Net regularized regression approach that controls for covarying features within high-dimensional data. First, we applied 517 known gene expression signatures to develop an Elastic Net model to predict pCR, which we validated on 143 samples from four independent trials. Next, we performed integrative analyses incorporating clinicopathologic information with somatic mutation status, DNA copy number alterations (CNA), and gene signatures. Results: The Elastic Net model using only gene signatures predicted pCR in the validation sets (AUC ¼ 0.76). Integrative analyses showed that models containing gene signatures, clinical features, and DNA information were better pCR predictors than models containing a single data type. Frequently selected variables from the multiplatform models included amplifications of chromosome 6p, TP53 mutation, HER2-enriched subtype, and immune signatures. Variables predicting resistance included Luminal/ERþ features. Conclusions: Models using RNA only, as well as integrated RNA and DNA models, can predict pCR with improved accuracy over clinical variables. Somatic DNA alterations (mutation, CNAs), tumor molecular subtype (HER2E, Luminal), and the microenvironment (immune cells) were independent predictors of response to trastuzumab and paclitaxel-based regimens. This highlights the complexity of predicting response in HER2-positive breast cancer

Forecasting the underlying potential governing the time series of a dynamical system

Copyright © 2013 The Authors. Published by Elsevier B.V. All rights reserved.We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal approximation of the empirical probability distribution and extrapolate them in order to forecast the future probability distribution of data. The method is tested on artificial data, used for hindcasting observed climate data, and then applied to forecast Arctic sea-ice time series. The proposed methodology completes a framework for ‘potential analysis’ of tipping points which altogether serves anticipating, detecting and forecasting nonlinear changes including bifurcations using several independent techniques of time series analysis. Although being applied to climatological series in the present paper, the method is very general and can be used to forecast dynamics in time series of any origin.NERCAXA Research FundEuropean Commissio

LCCC 1025: a phase II study of everolimus, trastuzumab, and vinorelbine to treat progressive HER2-positive breast cancer brain metastases

Purpose: HER2 + breast cancer (BC) is an aggressive subtype with high rates of brain metastases (BCBM). Two-thirds of HER2 + BCBM demonstrate activation of the PI3K/mTOR pathway driving resistance to anti-HER2 therapy. This phase II study evaluated everolimus (E), a brain-permeable mTOR inhibitor, trastuzumab (T), and vinorelbine (V) in patients with HER2 + BCBM. Patients and methods: Eligible patients had progressive HER2 + BCBM. The primary endpoint was intracranial response rate (RR); secondary objectives were CNS clinical benefit rate (CBR), extracranial RR, time to progression (TTP), overall survival (OS), and targeted sequencing of tumors from enrolled patients. A two-stage design distinguished intracranial RR of 5% versus 20%. Results: 32 patients were evaluable for toxicity, 26 for efficacy. Intracranial RR was 4% (1 PR). CNS CBR at 6 mos was 27%; at 3 mos 65%. Median intracranial TTP was 3.9 mos (95% CI 2.2–5). OS was 12.2 mos (95% CI 0.6–20.2). Grade 3–4 toxicities included neutropenia (41%), anemia (16%), and stomatitis (16%). Mutations in TP53 and PIK3CA were common in BCBM. Mutations in the PI3K/mTOR pathway were not associated with response. ERBB2 amplification was higher in BCBM compared to primary BC; ERBB2 amplification in the primary BC trended toward worse OS. Conclusion: While intracranial RR to ETV was low in HER2 + BCBM patients, one-third achieved CNS CBR; TTP/OS was similar to historical control. No new toxicity signals were observed. Further analysis of the genomic underpinnings of BCBM to identify tractable prognostic and/or predictive biomarkers is warranted. Clinical Trial: (NCT01305941)

The graviton one-loop effective action in cosmological space-times with constant deceleration

We consider the quantum Friedmann equations which include one-loop vacuum fluctuations due to gravitons and scalar field matter in a FLRW background with constant $\epsilon=-{\dot{H}}/{H^2}$. After several field redefinitions, to remove the mixing between the gravitational and matter degrees of freedom, we can construct the one loop correction to the Friedmann equations. Due to cosmological particle creation, the propagators needed in such a calculation are typically infrared divergent. In this paper we construct the graviton and matter propagators, making use of the recent construction of the infrared finite scalar propagators calculated on a compact spatial manifold in \cite{Janssen:2008px}. The resulting correction to the Friedman equations is suppressed with respect to the tree level contribution by a factor of $H^2/m_p^2$ and shows no secular growth.Comment: 37 pages, 1 figure. Revised version, including a proper treatment of the infrared secto