Love's Notation http://web.ics.purdue.edu/~nowack/geos557/lecture8-dir/lecture8.htm PurdueUniversity EAS 557 Introduction to Seismology Robert L. Nowack Lecture 8 Constitutive Relations We have so far not specified the relationship between displacement and forces in the continuum.The relationship between (strain) and (stress) is termed a constitutive relation.Constitutive relations can be {linear/nonlinear}, {time dependent/time independent}, {reversible/nonreversible}. In general terms, the behavior of a solid under stress can be roughly characterized by a stress-strain relation having some, or all, of the following features 1) linear elastic (i.e., Hookean ) = linear function of e ij reversible process (recoverable strain energy) slope of gives elastic constants 2) nonlinear elastic is a nonlinear function of reversible – strain energy recoverable characteristic of soils 3)yield region ~ beyond the yield point or elastic limit, ductile region, plastic flow energy is dissipated unloading leaves permanent offset - grain sliding and rotation - microfracturing This could be accompanied by dilatancy which is an increase in specific volume resulting in a decrease of seismic velocities.In the 1970’s, this was thought to have great potential for predicting earthquakes. strain hardening 4) failure ~ region beyond ultimate strength of the material proceeds catastrophically to failure The condition can be very unstable ranging over a cascade of distance scales Viscoelasticity – This refers to time dependent constitutive relations The Earth primarily acts at short time scales as an elastic body, but at long times, it can flow or creep without obvious faulting.Strain rate is then proportional to applied stress. There are a number of simple models for viscoelastic materials. Viscoelastic Rheological Models 1)Elastic Material where F is a force, is the elastic constant (or spring constant), and u is the displacement.For a continuum, this would be 2)Viscous Material where for example this could represent the pulling ofa plate through a fluid in a dashpot.Then, where F is the applied force, = viscosity, and is the particle velocity.For a continuum, this would be For this case, a constant stress results in a constant strain rate. Units of viscosity are in poise where 1 poise = 1 dyne -s/cm 2 .In SI units, viscosity is in Pascal-sec where 1 poise = 0.1 Pa-s. 3)Maxwell solid where this shows a spring and dashpot in series.Then, The material is elastic at short times and viscous at long times 4) Voight (Kelvin solid) In this model, the spring and dashpot are in parallel. Then, In the frequency domain, this can be written as where is a complex elastic modulus, and and are the Fourier transforms of and . In elastic wave problems, slight dissipation can be modeled using complex elastic constants and the same equation as for the elastic case can be used.This is called the correspondence principle. In the Earth, observations indicating a dissipation loss mechanism, include Attenuation of seismic waves as measured by a “Q” value Damping of the Earth’s Chandler wobble Nonhydrostatic figure of the Earth Uplift and subsidence of land masses ( Fennoscandia )(Hawaii) For seismic wave propagation, linear elasticity works to an excellent degree away from the source region.Seismic attenuation (not including scattering) can also be included using a Q value related to the imaginary part of the elastic constant.Below, we will focus on linear elasticity with real elastic constants. We consider, in the seismic wave propagation context, linear elasticity and infinitesimal strain.Assume a Hooke’s Law relation where are the elastic constants which has 3 4 or 81 components (each index going from 1 to 3). We now apply various constraints on to reduce the number of elastic constants: 1)From the symmetry of and then This reduces the number of independent elastic constants from 81 to 36. 2)From existence of strain energy function, where W = internal energy per unit volume, then by energy considerations of an adiabatic reversible process From linear elasticity , , and W can be written as a quadratic and homogeneous function of by symmetry Thus, The number of independent elastic constants then reduces from 36 components to 21. In Love’s notation or where L = 1,6 and M = 1,6.The relation between C LM and c ijkl is given by L ( ij ) 1 11 2 22 3 33 4 23 or 32 5 13 or 31 6 12 or 21 For example, C 66 = c 1212 = c 2112 = c 1221 For various crystal symmetries, the 21 independent elastic constants can be progressively reduced in number, ultimately reaching 2 constants for a perfectly isotropic material. Ex)A triclinic crystalline substance has 21 elastic constants Ex)A monoclinic crystal has symmetry with respect to one plane and has 13 independent elastic constants Ex)Orthorhombic symmetry has symmetry with respect to three planes and has 9 independent elastic constants Ex)Hexagonal symmetry has 5 independent elastic constants For example, “transverse isotropy is common in seismology and has symmetry in a plane perpendicular to the z axis.This is common in seismology related to stacks of thin layers with a vertical axis of symmetry.In general, hexagonal symmetry can have an arbitrary axis of symmetry and can result from crystal symmetry, a stack of thin layers in a sedimentary rock, or a crack network in a rock. The Love matrix for hexagonal symmetry is An excellent survey of wave propagation in general anisotropic materials is given by Auld (1990).Applications of seismic anisotropy in the Earth are given by Babuska and Cara (1991). Proceeding in this way, we come to the case where the constants are invariant to an arbitrary rotation of the coordinate axes.This is called isotropy.Although no crystal has this symmetry, it is the most common one used in elasticity and seismology.It is appropriate for fine-grained materials with grains with random orientations. The Love matrix for an isotropic material is The Lamé constants for an isotropic material are which is called the shear modulus, and .Then, In full index notation, the isotropic elastic constants can be written as where Expressing the stress-strain relation for a linear elastic solid as , then for an isotropic material For each component, this can be written as In addition to and , other isotropic elastic constants are sometimes easier to measure in the lab. 1)Young’s Modulus Consider a bar under uniaxial compression (or tension ) , then For this case, where E is called Young’s Modulus and is measured as the ratio of uniaxial stress to strain. 2)Poisson’s ratio = Poisson’s ratio is the ratio of contraction in the direction of applied stress to the expansion in directions perpendicular to the applied stress.Thus, ( is not viscosity here!) where L 2 is a direction perpendicular to the direction of applied stress.Then, The two constants can be used to describe the isotropic elastic properties in a similar manner as and are easier to measure. Now, we want to relate to .For uniaxial compression, Then, a) b) From these, we can find relations between and as Now consider a bar under hydrostatic stress where , ( recall pressure is positive in compression). Now, find the forces in the different coordinate directions and relate to the strain in the x 1 direction. a) forces in x 1 b) forces in x 2 c) forces in x 3 where is the Poisson’s ratio and E is Young’s Modulus.Then, the total change length in the x 1 direction from all applied stresses is The change of volume can then be written as Thus, K is called the bulk modulus relating an applied hydrostatic pressure to a change of volume. Under an applied shear stress, say , with all other stresses being zero, then Thus, shear modulus is related to the ratio of shear stress to shear strain.Note, with our definitions of stress, there is also a factor of 2. We can relate K to as .Thus, we could also use as the independent elastic parameters for an isotropic material. The coefficients and are related to the more commonly measured elastic coefficients by = G = shear modulus E = Young’s modulus = = Poisson’s ratio = K = Bulk modulus = A complete set of relations for an isotropic medium is given in the box below from Stein and Wysession (2003). Poisson’s ratio is a very important diagnostic property of an isotropic elastic material.It can vary from -1 to +.5.For a perfectly rigid material, = 0.For an incompressible fluid, = .5 and . When under uniaxial compression, a material with a Poisson’s ratio of zero won’t come out on the sides.An example of this type of material is cork which is used as a bottle stopper.A material with a negative Poisson’s ratio would come in on the sides under uniaxial compression.But, it is important to remember that Poisson’s ratio is an isotropic and not anisotropic concept. The solid part of the Earth (coast to mantle) has a Poisson’s ratio that varies between .25 to .30 .For a Poisson solid, we choose and for this case .This relation is assumed in a great number of seismic studies of the solid parts of the Earth.In the Earth’s liquid outer core , .In the inner core, which is in a solid state, ~ 0.40-0.45. That is, the inner core can support shear, but is quite different from the mantle material.
http://www.ariosadx.com/about-the-science/Ariosa-Paper-Selective-Analysis-PRENATAL-DIAGNOSIS-2012-1.pdf http://www.sciencedaily.com/releases/2012/06/120605155950.htm =================== Verinata Health Publishes Proof-of-Concept Data Showing Non-invasive Fetal Karyotype Equivalent to Invasive Procedures http://www.verinata.com/verinata-healths-non-invasive-prenatal-testing-position-statement/ http://www.verinata.com/news/verinata-health-publishes-proof-of-concept-data-showing-non-invasive-fetal-karyotype-equivalent-to-invasive-procedures/ 2013 Article Noninvasive Detection of Fetal Subchromosome Abnormalities via Deep Sequencing of Maternal Plasma Anupama Srinivasan1, Diana W. Bianchi2, Hui Huang1, Amy J. Sehnert1, Richard P. Rava1, , 1 Verinata Health, Inc., Redwood City, CA 94063, USA 2 Mother Infant Research Institute at Tufts Medical Center and Tufts University School of Medicine, Boston, MA 02111, USA ============ Illumina Acquires Verinata for $450 Million http://www.burrillreport.com/article-illumina_acquires_verinata_for_450_million.html
http://snpedia.com/index.php/Rs2910164 Rs2910164 is a snp is mentioned by dbSNP rs2910164 PheGenI rs2910164 nextbio rs2910164 hapmap rs2910164 1000 genomes rs2910164 hgdp rs2910164 ensembl rs2910164 gopubmed rs2910164 geneview rs2910164 scholar rs2910164 google rs2910164 pharmgkb rs2910164 gwascentral rs2910164 openSNP rs2910164 23andMe rs2910164 23andMe all rs2910164 SNP Nexus SNPshot rs2910164 SNPdbe rs2910164 MSV3d rs2910164 Gene MIR146A Chromosome 5 Orientation plus GMAF 0.3814 Position 159912418 Reference GRCh37 37.1/131 Max Magnitude 2.5 Geno Mag Summary (C;C) 2.5 higher risk cancer (C;G) higher/earlier cancer likelihood?? (G;G) 0 normal ? (C;C) (C;G) (G;G) 28 (C;C) predisposes to papillary thyroid carcinoma. Among 42 patients with familial breast cancer and 82 patients with ovarian cancer, those with at least one rs2910164(C) SNP tended to have been diagnosed at an earlier age than those with only (G) alleles. For the breast cancer patients, the difference in median age was between 45 vs 56 (p = 0.029) and for ovarian cancer patients, 45 vs 50, (p = 0.014). (G;G) males were two-fold more susceptible to hepatocellular carcinoma (OR = 2.016, 95% CI = 1.056-3.848, P = 0.034) perhaps an ambiguous flip? snp near microRNA ACC MI0000477 ID hsa-mir-146a offset -10 A Functional Genetic Variant in microRNA-196a2 Is Associated with Increased Susceptibility of Lung Cancer in Chinese. Functional variant in microRNA-196a2 contributes to the susceptibility of congenital heart disease in a Chinese population OMIM 610566 Desc MICRO RNA 146A; MIRN146A Variant Related also Evaluation of SNPs in miR-146a, miR196a2 and miR-499 as low-penetrance alleles in German and Italian familial breast cancer cases A functional polymorphism in Pre-miR-146a gene is associated with prostate cancer risk and mature miR-146a expression in vivo Analyses of polymorphisms in the inflammasome-associated NLRP3 and miRNA-146A genes in the susceptibility to and tubal pathology of Chlamydia trachomatis infection Common genetic polymorphisms in pre-microRNAs were associated with increased risk of dilated cardiomyopathy The Role of microRNA-146a (miR-146a) and its Target IL-1R-Associated Kinase (IRAK1) in Psoriatic Arthritis Susceptibility Genetic variants in selected pre-microRNA genes and the risk of squamous cell carcinoma of the head and neck The association between two polymorphisms in pre-miRNAs and breast cancer risk: a meta-analysis A functional varient in microRNA-146a is associated with risk of esophageal squamous cell carcinoma in Chinese Han Genetic variation in microRNA genes and prostate cancer risk in North Indian population Association Study of Common Genetic Variants in Pre-microRNAs in Patients with Ulcerative Colitis A polymorphism in the 3'-UTR of interleukin-1 receptor-associated kinase (IRAK1), a target gene of miR-146a, is associated with rheumatoid arthritis susceptibility Association Between Common Genetic Variants in Pre-microRNAs and Gastric Cancer Risk in Japanese Population Genetic study of two single nucleotide polymorphisms within corresponding microRNAs and susceptibility to tuberculosis in a Chinese Tibetan and Han population The rs2910164:GC SNP in the MIR146A gene is not associated with breast cancer risk in BRCA1 and BRCA2 mutation carriers Effects of Common Polymorphisms rs11614913 in miR-196a2 and rs2910164 in miR-146a on Cancer Susceptibility: A Meta-Analysis A functional polymorphism in the pre-miR-146a gene is associated with risk and prognosis in adult glioma No association of pre-microRNA-146a rs2910164 polymorphism and risk of hepatocellular carcinoma development in Turkish population: A case-control study Association Between Two Genetic Variants in miRNA and Primary Liver Cancer Risk in the Chinese Population Genetic association of miRNA-146a with systemic lupus erythematosus in Europeans through decreased expression of the gene Thyroid cancer susceptibility polymorphisms: confirmation of loci on chromosomes 9q22 and 14q13, validation of a recessive 8q24 locus and failure to replicate a locus on 5q24 Association between the rs2910164 polymorphism in pre-mir-146a and oral carcinoma progression. A Genetic Variant in miR-196a2 Increased Digestive System Cancer Risks: A Meta-Analysis of 15 Case-Control Studies Differential Expression Profile and Genetic Variants of MicroRNAs Sequences in Breast Cancer Patients Increased Risk of Breast Cancer Associated with CC Genotype of Has-miR-146a Rs2910164 Polymorphism in Europeans Lack of Association of miR-146a rs2910164 Polymorphism with Gastrointestinal Cancers: Evidence from 10206 Subjects MiR-146a polymorphism is associated with asthma but not with systemic lupus erythematosus and juvenile rheumatoid arthritis in Mexican patients Genetic variants of miRNA sequences and non-small cell lung cancer survival. Common genetic variants in pre-microRNAs were associated with increased risk of breast cancer in Chinese women. Single nucleotide polymorphisms of microRNA machinery genes modify the risk of renal cell carcinoma. Genetic variations in microRNA-related genes are novel susceptibility loci for esophageal cancer risk. Polymorphic mature microRNAs from passenger strand of pre-miR-146a contribute to thyroid cancer. Signatures of purifying and local positive selection in human miRNAs. MicroRNA polymorphisms: the future of pharmacogenomics, molecular epidemiology and individualized medicine. Comprehensive analysis of the impact of SNPs and CNVs on human microRNAs and their regulatory genes. SNPs in human miRNA genes affect biogenesis and function. Common genetic variants in pre-microRNAs are associated with risk of coal workers' pneumoconiosis. MicroRNA polymorphisms: a giant leap towards personalized medicine. Common genetic variants in pre-microRNAs and risk of gallbladder cancer in North Indian population. Combined effect of miR-146a rs2910164 G/C polymorphism and Toll-like receptor 4 +3725 G/C polymorphism on the risk of severe gastric atrophy in Japanese. Association between hsa-mir-146a genotype and tumor age-of-onset in BRCA1/BRCA2-negative familial breast and ovarian cancer patients. Association of pre-microRNAs genetic variants with susceptibility in systemic lupus erythematosus. Association study of single nucleotide polymorphisms in pre-miRNA and rheumatoid arthritis in a Han Chinese population. Common genetic polymorphisms in pre-microRNAs and risk of cervical squamous cell carcinoma. Investigative role of pre-microRNAs in bladder cancer patients: a case-control study in North India. Polymorphism of the pre-miR-146a is associated with risk of cervical cancer in a Chinese population. Association between single-nucleotide polymorphisms in pre-miRNAs and the risk of asthma in a Chinese population. Association between two single nucleotide polymorphisms at corresponding microRNA and schizophrenia in a Chinese population. Expression and genetic analysis of miRNAs involved in CD4+ cell activation in patients with multiple sclerosis. Genetic variants in miR-146a, miR-149, miR-196a2, miR-499 and their influence on relative expression in lung cancers. Has-miR-146a polymorphism (rs2910164) and cancer risk: a meta-analysis of 19 case-control studies. Association of polymorphisms in pre-miRNA with inflammatory biomarkers in rheumatoid arthritis in the Chinese Han population. Meta-analysis confirms that a common G/C variant in the pre-miR-146a gene contributes to cancer susceptibility and that ethnicity, gender and smoking status are risk factors Evaluation of SNPs in miR-196-a2, miR-27a and miR-146a as risk factors of colorectal cancer Association of pre-miRNA-146a rs2910164 and pre‑miRNA-499 rs3746444 polymorphisms and susceptibility to rheumatoid arthritis
http://jnci.oxfordjournals.org/content/104/4/311.long A Three-Gene Model to Robustly Identify Breast Cancer Molecular Subtypes Benjamin Haibe-Kains, Christine Desmedt, Sherene Loi, Aedin C. Culhane, Gianluca Bontempi, John Quackenbush and Christos Sotiriou + Author Affiliations Affiliations of authors: Department of Biostatistics and Computational Biology (BH-K, ACC, JQ) and Department of Cancer Biology (JQ), Dana-Farber Cancer Institute, Boston, MA; Department of Biostatistics, Harvard School of Public Health, Boston, MA (BH-K, ACC, JQ); Breast Cancer Translational Research Laboratory J.C. Heuson, Medical Oncology Department, Jules Bordet Institute, Université Libre de Bruxelles, Brussels, Belgium (CD, SL, CS); Machine Learning Group, Computer Science Department, Université Libre de Bruxelles, Brussels, Belgium (GB) Correspondence to: Benjamin Haibe-Kains, PhD, Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, 450 Brookline Ave, Boston, MA 02115 (e-mail: bhaibeka@jimmy.harvard.edu). Received June 23, 2011. Revision received December 13, 2011. Accepted December 14, 2011. Next Section Abstract Background Single sample predictors (SSPs) and Subtype classification models (SCMs) are gene expression–based classifiers used to identify the four primary molecular subtypes of breast cancer (basal-like, HER2-enriched, luminal A, and luminal B). SSPs use hierarchical clustering, followed by nearest centroid classification, based on large sets of tumor-intrinsic genes. SCMs use a mixture of Gaussian distributions based on sets of genes with expression specifically correlated with three key breast cancer genes (estrogen receptor , HER2, and aurora kinase A ). The aim of this study was to compare the robustness, classification concordance, and prognostic value of these classifiers with those of a simplified three-gene SCM in a large compendium of microarray datasets. Methods Thirty-six publicly available breast cancer datasets (n = 5715) were subjected to molecular subtyping using five published classifiers (three SSPs and two SCMs) and SCMGENE, the new three-gene (ER, HER2, and AURKA) SCM. We used the prediction strength statistic to estimate robustness of the classification models, defined as the capacity of a classifier to assign the same tumors to the same subtypes independently of the dataset used to fit it. We used Cohen κ and Cramer V coefficients to assess concordance between the subtype classifiers and association with clinical variables, respectively. We used Kaplan–Meier survival curves and cross-validated partial likelihood to compare prognostic value of the resulting classifications. All statistical tests were two-sided. Results SCMs were statistically significantly more robust than SSPs, with SCMGENE being the most robust because of its simplicity. SCMGENE was statistically significantly concordant with published SCMs (κ = 0.65–0.70) and SSPs (κ = 0.34–0.59), statistically significantly associated with ER (V = 0.64), HER2 (V = 0.52) status, and histological grade (V = 0.55), and yielded similar strong prognostic value. Conclusion Our results suggest that adequate classification of the major and clinically relevant molecular subtypes of breast cancer can be robustly achieved with quantitative measurements of three key genes. CONTEXTS AND CAVEATS Prior knowledge Single sample predictors (SSPs) are molecular classification models that use large sets of genes expressed in different tumors to classify different subtypes of breast cancer. Subtype classification models (SCMs) are based on groups of genes specifically correlated with three key breast cancer genes, estrogen receptor (ER), HER2, and aurora kinase A (AURKA). Both types of models use large numbers of genes. However, the robustness and prognostic value of these classifiers have not been compared with simplified models containing fewer genes. Study design A simplified SCM (SCMGENE) containing only ER, HER2, and AURKA was compared with three SSPs and two SCMs using data from 36 gene expression datasets in public databases. The models were compared with respect to concordance among themselves as well as association with clinical variables and disease-free survival. Contribution Among the SCMs, SCMGENE with only three genes was statistically more robust than SSPs and as robust and yielded similar prognostic value compared with the published SCMs that use large numbers of genes. Implications Adding more genes to a classification model may not improve the ability to discriminate among breast cancer subtypes. In addition, the complexity of multiple-gene classification models may limit their usefulness and translation into clinic. Limitations The datasets used were retrospectively accrued; therefore, the selection of patients may have resulted in unbalanced distribution of the different molecular subtypes. The gene expression datasets taken from public databases and websites were not renormalized. Software limitations precluded checking or correction for departure from proportional hazards assumptions. From the Editors ============ J Natl Cancer Inst. 2012 Feb 22;104(4):262-3. Epub 2012 Jan 18. Gene signatures revisited. Baker SG. Comment on A three-gene model to robustly identify breast cancer molecular subtypes. PMID: 22262869 PMCID: PMC3283539
poissrnd - Poisson random numbers Syntax R = poissrnd(lambda) R = poissrnd(lambda,m,n,...) R = poissrnd(lambda, ) Description R = poissrnd(lambda) generates random numbers from the Poisson distribution with mean parameter lambda. lambda can be a vector, a matrix, or a multidimensional array. The size of R is the size of lambda. R = poissrnd(lambda,m,n,...) or R = poissrnd(lambda, ) generates an m-by-n-by-... array. The lambda parameter can be a scalar or an array of the same size as R. Examples Generate a random sample of 10 pseudo-observations from a Poisson distribution with λ = 2. lambda = 2; random_sample1 = poissrnd(lambda,1,10) random_sample1 = 1 0 1 2 1 3 4 2 0 0 random_sample2 = poissrnd(lambda, ) random_sample2 = 1 1 1 5 0 3 2 2 3 4 random_sample3 = poissrnd(lambda(ones(1,10))) random_sample3 = 3 2 1 1 0 0 4 0 2 0
http://www.sciencemag.org/content/335/6070/780.1.full.pdf Lonely Chinese researchers isolated by shy- ness and long lab hours now have an online dating service designed just for them. Building 88 (http://www.sciencedate. cn/) aims to become a “soul harbor” for young Chinese scientists, its Web site explains. Spearheaded by Science Times Media Group, which also runs the popular Chinese-language news portal Sciencenet. cn, the service takes its name from a fabled Beijing dormitory that became a meet-up spot for Chinese Academy of Sciences researchers in the 1990s. Today’s scientists lack such gather- ing places, says site coordinator Wu Hao, and thus have a “more intense need” for social interaction than Chinese pursu- ing other careers. “The social circles of young Chinese scientists are often lim- ited to other people in their fi eld,” Wu explains. That may be no accident. A question- naire Science Times distributed to 1243 young scientists revealed roughly 70% of highly educated respondents suffer from social anxiety, Wu says. Building 88 broad- ens the pool of potential paramours for introverts to include Chinese researchers both within China and all over the world. Since its launch in January, the site has grown to 1000 users, most of them between the ages of 20 and 35. Whether an online portal can help draw them out of their shells is still an experiment in progress; many scientists have unusu- ally high standards, Wu notes. And as one 31-year-old Beijing scientist puts it on his Building 88 profi le: “Dating is just like scientifi c research: Only when you’re excited about it do you get results.
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