Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions

The implications of conformal invariance, as relevant in quantum field theories at a renormalisation group fixed point, are analysed with particular reference to results for correlation functions involving conserved currents and the energy momentum tensor. Ward identities resulting from conformal invariance are discussed. Explicit expressions for two and three point functions, which are essentially determined by conformal invariance, are obtained. As special cases we consider the three point functions for two vector and an axial current in four dimensions, which realises the usual anomaly simply and unambiguously, and also for the energy momentum tensor in general dimension $d$. The latter is shown to have two linearly independent forms in which the Ward identities are realised trivially, except if $d = 4$, when the two forms become degenerate. This is necessary in order to accommodate the two independent forms present in the trace of the energy momentum tensor on curved space backgrounds for conformal field theories in four dimensions. The coefficients of the two trace anomaly terms are related to the three parameters describing the general energy momentum tensor three point function. The connections with gravitational effective actions depending on a background metric are described. A particular form due to Riegert is shown to be unacceptable. Conformally invariant expressions for the effective action in four dimensions are obtained using the Green function for a differential operator which has simple properties under local rescalings of the metric.Comment: 44 pages uses harvmac, version to be published in Nuclear Physics, some additions, misprints corrected and extra reference

Predicting colorectal cancer risk from adenoma detection via a two-type branching process model.

Despite advances in the modeling and understanding of colorectal cancer development, the dynamics of the progression from benign adenomatous polyp to colorectal carcinoma are still not fully resolved. To take advantage of adenoma size and prevalence data in the National Endoscopic Database of the Clinical Outcomes Research Initiative (CORI) as well as colorectal cancer incidence and size data from the Surveillance Epidemiology and End Results (SEER) database, we construct a two-type branching process model with compartments representing adenoma and carcinoma cells. To perform parameter inference we present a new large-size approximation to the size distribution of the cancer compartment and validate our approach on simulated data. By fitting the model to the CORI and SEER data, we learn biologically relevant parameters, including the transition rate from adenoma to cancer. The inferred parameters allow us to predict the individualized risk of the presence of cancer cells for each screened patient. We provide a web application which allows the user to calculate these individual probabilities at https://ccrc-eth.shinyapps.io/CCRC/. For example, we find a 1 in 100 chance of cancer given the presence of an adenoma between 10 and 20mm size in an average risk patient at age 50. We show that our two-type branching process model recapitulates the early growth dynamics of colon adenomas and cancers and can recover epidemiological trends such as adenoma prevalence and cancer incidence while remaining mathematically and computationally tractable

The long term dynamical stability of the known Neptune Trojans

The Neptune Trojans are a population of small bodies that librate around the L4 and L5 Lagrange points of Neptune’s orbit. Shortly after the discovery of the first such object, 2001 QR322, simulations suggested that the body moved on a dynamically stable orbit. Following this, further discovered objects were generally assumed to also be stable. In recent years, the situation has proved to be more complicated than previously thought. Two of Neptune’s Trojans have been found to exhibit orbital instability on billion year timescales, with another being revealed as a temporarily captured interloper. Here, the results of detailed dynamical simulations of the orbital evolution of the eleven known Neptunian Trojans are presented, examining the influence of their initial orbital semi-major axes and eccentricities on their stability. The results reveal the importance of considering the orbital stability of newly discovered objects on a case-by-case basis, with some members showing highly unstable behaviour, whilst others seem likely to be primordial in nature. The earlier finding that 2001 QR322 and 2008 LC18 are primordial in nature but unstable on billion year timescales are confirmed. In both cases, their stability is a strong function of their semi-major axis, with the two lying on the boundary between stable and unstable regions. In addition we reveal the stability of eight other Neptune Trojans. Six of the known Trojans move on highly stable orbits. In contrast, two objects, 2004 KV18 and 2010 EN65, are confirmed to be temporarily captured members of the Neptune's Trojan population. While one, 2012 GX17, is found to be a misidentified Trans-Neptunian Object

F as in Fat: How Obesity Threatens America’s Future 2012

https://www.rwjf.org/content/dam/farm/reports/reports/2012/rwjf40131

Conformal Partial Waves and the Operator Product Expansion

By solving the two variable differential equations which arise from finding the eigenfunctions for the Casimir operator for $O(d,2)$ succinct expressions are found for the functions, conformal partial waves, representing the contribution of an operator of arbitrary scale dimension $\Delta$ and spin $\ell$ together with its descendants to conformal four point functions for $d=4$, recovering old results, and also for $d=6$. The results are expressed in terms of ordinary hypergeometric functions of variables $x,z$ which are simply related to the usual conformal invariants. An expression for the conformal partial wave amplitude valid for any dimension is also found in terms of a sum over two variable symmetric Jack polynomials which is used to derive relations for the conformal partial waves.Comment: 17 pages, uses harvmac, v2 correction to eq. 2.2

Systems-Based Design of Bi-Ligand Inhibitors of Oxidoreductases: Filling the Chemical Proteomic Toolbox

Genomics-driven growth in the number of enzymes of unknown function has created a need for better strategies to characterize them. Since enzyme inhibitors have traditionally served this purpose, we present here an efficient systems-based inhibitor design strategy, enabled by bioinformatic and NMR structural developments. First, we parse the oxidoreductase gene family into structural subfamilies termed pharmacofamilies, which share pharmacophore features in their cofactor binding sites. Then we identify a ligand for this site and use NMR-based binding site mapping (NMR SOLVE) to determine where to extend a combinatorial library, such that diversity elements are directed into the adjacent substrate site. The cofactor mimic is reused in the library in a manner that parallels the reuse of cofactor domains in the oxidoreductase gene family. A library designed in this manner yielded specific inhibitors for multiple oxidoreductases

Identification of transcription factor and microRNA binding sites in responsible to fetal alcohol syndrome

This is a first report, using our MotifModeler informatics program, to simultaneously identify transcription factor (TF) and microRNA (miRNA) binding sites from gene expression microarray data. Based on the assumption that gene expression is controlled by combinatorial effects of transcription factors binding in the 5'-upstream regulatory region and miRNAs binding in the 3'-untranslated region (3'-UTR), we developed a model for (1) predicting the most influential cis-acting elements under a given biological condition, and (2) estimating the effects of those elements on gene expression levels. The regulatory regions, TF and miRNA, which mediate the differential genes expression in fetal alcohol syndrome were unknown; microarray data from alcohol exposure paradigm was used. The model predicted strong inhibitory effects of 5' cis-acting elements and stimulatory effects of 3'-UTR under alcohol treatment. Current predictive model derived a key hypothesis for the first time a novel role of miRNAs in gene expression changes associated with abnormal mouse embryo development after alcohol exposure. This suggests that disturbance of miRNA functions may contribute to the alcohol-induced developmental deficiencies

The brain recovery core: Building a system of organized stroke rehabilitation and outcomes assessment across the continuum of care

none10siThis Special Interest article describes a multidisciplinary, interinstitutional effort to build an organized system of stroke rehabilitation and outcomes measurement across the continuum of care. This system is focused on a cohort of patients who are admitted with the diagnosis of stroke to our acute facility, are discharged to inpatient and/or outpatient rehabilitation at our free-standing facility, and are then discharged to the community. This article first briefly explains the justification, goals, and purpose of the Brain Recovery Core system. The next sections describe its development and implementation, with details on the aspects related to physical therapy. The article concludes with an assessment of how the Brain Recovery Core system has changed and improved delivery of rehabilitation services. It is hoped that the contents of this article will be useful in initiating discussions and potentially facilitating similar efforts among other centers.mixedLang, Catherine E.; Bland, Marghuretta D.; Connor, Lisa Tabor; Fucetola, Robert; Whitson, Michelle; Edmiaston, Jeff; Karr, Clayton; Sturmoski, Audra; Baty, Jack; Corbetta, MaurizioLang, Catherine E.; Bland, Marghuretta D.; Connor, Lisa Tabor; Fucetola, Robert; Whitson, Michelle; Edmiaston, Jeff; Karr, Clayton; Sturmoski, Audra; Baty, Jack; Corbetta, Maurizi