Bayesian Two-Way Analysis of High-Dimensional Collinear Metabolomics Data

Kaksisuuntainen tehtävänasettelu on yleinen bioinformatiikan alalla. Tässä diplomityössä esitellään uusi bayesilaisen mallinnuksen menetelmä kaksisuuntaisen havaintoaineiston analysointiin. Menetelmä toimii myös vähän näytteitä sisältävillä korkeaulotteisilla havaintoaineistoilla. Havaintoaineiston oletetaan jakautuvan populaatioihin kovariaattien mukaan, jotka tyypillisessä biologisessa kokeessa ovat yksilön terveydentila, sukupuoli, lääketieteellinen hoito sekä yksilön ikä. Esiteltävä menetelmä on suunniteltu arvioimaan näiden kovariaattien vaikutus havaintoaineiston kontrolliryhmän perustasoon verrattuna. Menetelmä perustuu olettamukseen siitä, että havaintoaineiston piirteet muodostavat ryhmiä, joiden sisällä piirteet ovat voimakkaasti kollineaarisia. Tämä olettamus mahdollistaa piilomuuttajamalliin perustuvan dimensionaalisuuden pudotuksen, jonka ansiosta menetelmä on toimiva myös pienen näytemäärän havaintoaineistoille. Menetelmä käsittelee havaintoaineistoa täysin bayesilaisittain, Gibbsin otannan avulla. Bayesilainen lähestymistapa tuottaa arvion sekä mallin ja havaintoaineiston yhteisjakaumalle että mallin jokaisen parametrin marginaalijakaumalle. Tämä mahdollistaa tulosten epävarmuuden arvioinnin sekä vertailun toisiin malleihin. Uuden menetelmän toimivuutta esitellään metabolomiikan alalta olevan havaintoaineiston avulla. Aineisto sisältää lipidiprofiileja, jotka on mitattu terveistä lapsista ja lapsista, jotka myöhemmin sairastuvat tyypin 1 diabetekseen. Kahdessa erillisessä analyysissä tutkitaan sairauden ja sukupuolen sekä sairauden ja iän vaikutusta lipidiprofiileihin.Two-way experimental designs are common in bioinformatics. In this thesis, a new Bayesian model is proposed for the analysis of two-way data. The method also works for small sample-size data with a high number of features. The data set is assumed to be divided into populations according to covariates, which in the case of a typical biological experiment are the health status, the gender, the medical treatment and the age of the individual. The proposed method is designed to estimate the effect of these covariates compared to the ground level of a control group of the data. The method is based on the assumption that features of the data form groups that are highly collinear. This allows the use of a latent variable-based dimensionality reduction, which makes inference possible also for small sample-size data sets. The method treats the data in a completely Bayesian way, which produces an estimate for the joint distribution of the model and the data, and marginal posterior distributions of all model parameters. This allows one to evaluate the signicance and uncertainty of the results and to compare it to other models. Inference is carried out with Gibbs sampling. The performance of the new method is demonstrated with a metabolomic data set by comparing lipidomic profiles from children who remain healthy to those who will later develop type 1 diabetes. In two separate studies, the effect of the disease and gender, and the effect of the disease and time, are estimated

Transverse Momentum Broadening and the Jet Quenching Parameter, Redux

We use Soft Collinear Effective Theory (SCET) to analyze the transverse momentum broadening, or diffusion in transverse momentum space, of an energetic parton propagating through quark-gluon plasma. Since we neglect the radiation of gluons from the energetic parton, we can only discuss momentum broadening, not parton energy loss. The interaction responsible for momentum broadening in the absence of radiation is that between the energetic (collinear) parton and the Glauber modes of the gluon fields in the medium. We derive the effective Lagrangian for this interaction, and we show that the probability for picking up transverse momentum k_\perp is given by the Fourier transform of the expectation value of two transversely separated light-like path-ordered Wilson lines. This yields a field theoretical definition of the jet quenching parameter \hat q, and shows that this can be interpreted as a diffusion constant. We close by revisiting the calculation of \hat q for the strongly coupled plasma of N=4 SYM theory, showing that previous calculations need some modifications that make them more straightforward and do not change the result.Comment: 18 pages, 7 figures; v2, minor revisions, references added; v3, version to appear in Phys. Rev. D: Feynman rules corrected, improved explanations of the gauge invariance of our calculation and of how the scaling of SCET operators differs from that in other contexts in the literature; no changes to any result

Topological solitons in highly anisotropic two dimensional ferromagnets

e study the solitons, stabilized by spin precession in a classical two--dimensional lattice model of Heisenberg ferromagnets with non-small easy--axis anisotropy. The properties of such solitons are treated both analytically using the continuous model including higher then second powers of magnetization gradients, and numerically for a discrete set of the spins on a square lattice. The dependence of the soliton energy $E$ on the number of spin deviations (bound magnons) $N$ is calculated. We have shown that the topological solitons are stable if the number $N$ exceeds some critical value $N_{\rm{cr}}$. For $N < N_{\rm{cr}}$ and the intermediate values of anisotropy constant $K_{\mathrm{eff}} <0.35J$ ($J$ is an exchange constant), the soliton properties are similar to those for continuous model; for example, soliton energy is increasing and the precession frequency $\omega (N)$ is decreasing monotonously with $N$ growth. For high enough anisotropy $K_{\mathrm{eff}} > 0.6 J$ we found some fundamentally new soliton features absent for continuous models incorporating even the higher powers of magnetization gradients. For high anisotropy, the dependence of soliton energy E(N) on the number of bound magnons become non-monotonic, with the minima at some "magic" numbers of bound magnons. Soliton frequency $\omega (N)$ have quite irregular behavior with step-like jumps and negative values of $\omega$ for some regions of $N$. Near these regions, stable static soliton states, stabilized by the lattice effects, exist.Comment: 17 page