Exploring a string-like landscape

We explore inflationary trajectories within randomly-generated two-dimensional potentials, considered as a toy model of the string landscape. Both the background and perturbation equations are solved numerically, the latter using the two-field formalism of Peterson and Tegmark which fully incorporates the effect of isocurvature perturbations. Sufficient inflation is a rare event, occurring for only roughly one in $10^5$ potentials. For models generating sufficient inflation, we find that the majority of runs satisfy current constraints from WMAP. The scalar spectral index is less than 1 in all runs. The tensor-to-scalar ratio is below the current limit, while typically large enough to be detected by next-generation CMB experiments and perhaps also by Planck. In many cases the inflationary consistency equation is broken by the effect of isocurvature modes.Comment: 24 pages with 8 figures incorporated, matches version accepted by JCA

Corrections to the Central Limit Theorem for Heavy-Tailed Probability Densities

Classical Edgeworth expansions provide asymptotic correction terms to the Central Limit Theorem (CLT) up to an order that depends on the number of moments available. In this paper, we provide subsequent correction terms beyond those given by a standard Edgeworth expansion in the general case of regularly varying distributions with diverging moments (beyond the second). The subsequent terms can be expressed in a simple closed form in terms of certain special functions (Dawson's integral and parabolic cylinder functions), and there are qualitative differences depending on whether the number of moments available is even, odd or not an integer, and whether the distributions are symmetric or not. If the increments have an even number of moments, then additional logarithmic corrections must also be incorporated in the expansion parameter. An interesting feature of our correction terms for the CLT is that they become dominant outside the central region and blend naturally with known large-deviation asymptotics when these are applied formally to the spatial scales of the CLT

A note on spin-s duality

Duality is investigated for higher spin ($s \geq 2$), free, massless, bosonic gauge fields. We show how the dual formulations can be derived from a common "parent", first-order action. This goes beyond most of the previous treatments where higher-spin duality was investigated at the level of the equations of motion only. In D=4 spacetime dimensions, the dual theories turn out to be described by the same Pauli-Fierz (s=2) or Fronsdal ($s \geq 3$) action (as it is the case for spin 1). In the particular s=2 D=5 case, the Pauli-Fierz action and the Curtright action are shown to be related through duality. A crucial ingredient of the analysis is given by the first-order, gauge-like, reformulation of higher spin theories due to Vasiliev.Comment: Minor corrections, reference adde

Digital Imaging and Analysis of Dusty Plasmas

Dust particles immersed within a plasma environment, such as those found in planetary rings or cometary environments, will acquire an electric charge. If the ratio of interparticle potential energy to average kinetic energy is high enough the particles will form either a 'liquid' structure with short-range ordering or a crystalline structure with long-range ordering. Since their discovery in laboratory environments in 1994, such crystals have been the subject of a variety of experimental, theoretical, and numerical investigations. Laboratory experiments analyzing the behavior of dust grains in a plasma rely on optical diagnostics to provide data about the system in a non-perturbative manner. In the past, capturing, imaging, and analyzing crystalline structure in dusty plasmas has been a non-trivial problem. Utilizing digital imaging and analysis systems, data capture, image formatting, and analysis can be done quickly. Following data capture, image analysis is conducted using modified Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) algorithms. The data extracted is then used to construct Voronoi diagrams, calculate particle density, inter-particle spacing, pair correlation functions, and thermal energy. From this data other dust plasma parameters can be inferred such as inter-particle forces and grain charges.Comment: 6 pages, Presented at COSPAR '0

The resistive state in a superconducting wire: Bifurcation from the normal state

We study formally and rigorously the bifurcation to steady and time-periodic states in a model for a thin superconducting wire in the presence of an imposed current. Exploiting the PT-symmetry of the equations at both the linearized and nonlinear levels, and taking advantage of the collision of real eigenvalues leading to complex spectrum, we obtain explicit asymptotic formulas for the stationary solutions, for the amplitude and period of the bifurcating periodic solutions and for the location of their zeros or "phase slip centers" as they are known in the physics literature. In so doing, we construct a center manifold for the flow and give a complete description of the associated finite-dimensional dynamics

Survival, pathologic response, and genomics in CALGB 40601 (Alliance), a neoadjuvant Phase III trial of paclitaxel-trastuzumab with or without lapatinib in HER2-positive breast cancer

PURPOSE CALGB 40601 assessed whether dual versus single human epidermal growth factor receptor 2 (HER2) -targeting drugs added to neoadjuvant chemotherapy increased pathologic complete response (pCR). Here, we report relapse-free survival (RFS), overall survival (OS), and gene expression signatures that predict pCR and survival. PATIENTS AND METHODS Three hundred five women with untreated stage II and III HER2-positive breast cancer were randomly assigned to receive weekly paclitaxel combined with trastuzumab plus lapatinib (THL), trastuzumab (TH), or lapatinib (TL). The primary end point was pCR, and secondary end points included RFS, OS, and gene expression analyses. mRNA sequencing was performed on 264 pretreatment samples. RESULTS One hundred eighteen patients were randomly allocated to THL, 120 to TH, and 67 to TL. At more than 7 years of follow-up, THL had significantly better RFS and OS than did TH (RFS hazard ratio, 0.32; 95% CI, 0.14 to 0.71; P 5.005; OS hazard ratio, 0.34; 95% CI, 0.12 to 0.94; P 5.037), with no difference between TH and TL. Of 688 previously described gene expression signatures, significant associations were found in 215 with pCR, 45 with RFS, and only 22 with both pCR and RFS (3.2%). Specifically, eight immune signatures were significantly correlated with a higher pCR rate and better RFS. Among patients with residual disease, the immunoglobulin G signature was an independent, good prognostic factor, whereas the HER2-enriched signature, which was associated with a higher pCR rate, showed a significantly shorter RFS. CONCLUSION In CALGB 40601, dual HER2-targeting resulted in significant RFS and OS benefits. Integration of intrinsic subtype and immune signatures allowed for the prediction of pCR and RFS, both overall and within the residual disease group. These approaches may provide means for rational escalation and de-escalation treatment strategies in HER2-positive breast cancer

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

Stress corrosion cracking in Al-Zn-Mg-Cu aluminum alloys in saline environments

Copyright 2013 ASM International. This paper was published in Metallurgical and Materials Transactions A, 44A(3), 1230 - 1253, and is made available as an electronic reprint with the permission of ASM International. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplications of any material in this paper for a fee or for commercial purposes, or modification of the content of this paper are prohibited.Stress corrosion cracking of Al-Zn-Mg-Cu (AA7xxx) aluminum alloys exposed to saline environments at temperatures ranging from 293 K to 353 K (20 °C to 80 °C) has been reviewed with particular attention to the influences of alloy composition and temper, and bulk and local environmental conditions. Stress corrosion crack (SCC) growth rates at room temperature for peak- and over-aged tempers in saline environments are minimized for Al-Zn-Mg-Cu alloys containing less than ~8 wt pct Zn when Zn/Mg ratios are ranging from 2 to 3, excess magnesium levels are less than 1 wt pct, and copper content is either less than ~0.2 wt pct or ranging from 1.3 to 2 wt pct. A minimum chloride ion concentration of ~0.01 M is required for crack growth rates to exceed those in distilled water, which insures that the local solution pH in crack-tip regions can be maintained at less than 4. Crack growth rates in saline solution without other additions gradually increase with bulk chloride ion concentrations up to around 0.6 M NaCl, whereas in solutions with sufficiently low dichromate (or chromate), inhibitor additions are insensitive to the bulk chloride concentration and are typically at least double those observed without the additions. DCB specimens, fatigue pre-cracked in air before immersion in a saline environment, show an initial period with no detectible crack growth, followed by crack growth at the distilled water rate, and then transition to a higher crack growth rate typical of region 2 crack growth in the saline environment. Time spent in each stage depends on the type of pre-crack (“pop-in” vs fatigue), applied stress intensity factor, alloy chemistry, bulk environment, and, if applied, the external polarization. Apparent activation energies (E a) for SCC growth in Al-Zn-Mg-Cu alloys exposed to 0.6 M NaCl over the temperatures ranging from 293 K to 353 K (20 °C to 80 °C) for under-, peak-, and over-aged low-copper-containing alloys (~0.8 wt pct), they are typically ranging from 20 to 40 kJ/mol for under- and peak-aged alloys, and based on limited data, around 85 kJ/mol for over-aged tempers. This means that crack propagation in saline environments is most likely to occur by a hydrogen-related process for low-copper-containing Al-Zn-Mg-Cu alloys in under-, peak- and over-aged tempers, and for high-copper alloys in under- and peak-aged tempers. For over-aged high-copper-containing alloys, cracking is most probably under anodic dissolution control. Future stress corrosion studies should focus on understanding the factors that control crack initiation, and insuring that the next generation of higher performance Al-Zn-Mg-Cu alloys has similar longer crack initiation times and crack propagation rates to those of the incumbent alloys in an over-aged condition where crack rates are less than 1 mm/month at a high stress intensity factor

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

Selecting Yield and Nutritional Traits in Sphenostylis stenocarpa Landraces for Food Improvement

Background: Sphenostylis stenocarpa is an underexploited African indigenous food crop that is enriched in nutritional quality. Objective: Exploring the robust genetic base of this landrace can help to maximize the benefit of the agricultural sector on the economy through production that is enhanced by packaging and patent, this as well will increase the quality of food production and promote African campaign on food sustainability. Method: Upon this, this research made use of multiple statistics to identify S. stenocarpa yield and nutritional trait relatedness that supported selection for maximum yield and nutritional trait output. Yield and related traits including protein and oil contents of twenty-three Sphenostylis stenocarpa landraces were studied under a four year planting seasons in Teaching and Research farm of Landmark University, Nigeria. Results: Trait variances from Landrace × Year (L × Y) interaction, Principal Component and Cluster analyses were evaluated and the variation patterns were identified. Some vegetative (maturity phase, height and branching) and yield traits (Pod traits, seed yield and oil content) correlated significantly (P < 0.05) in the L × Y interactions. This suggests the usefulness of these traits in improving S. Stenocarpa grain and oil quality yield. Tuber and nodule yield including protein content did not differ significantly in the variance table. Conclusion: The result indicates that one location trial is insufficient to determine such trait performance. The first four PCs that accounted for 51 per cent of the total variations were traceable to branching, maturity date, pod numbers, seed and oil content as main contributors to yiel