Nonparametric regression for multiple heterogeneous networks

We study nonparametric methods for the setting where multiple distinct networks are observed on the same set of nodes. Such samples may arise in the form of replicated networks drawn from a common distribution, or in the form of heterogeneous networks, with the network generating process varying from one network to another, e.g. dynamic and cross-sectional networks. Nonparametric methods for undirected networks have focused on estimation of the graphon model. While the graphon model accounts for nodal heterogeneity, it does not account for network heterogeneity, a feature specific to applications where multiple networks are observed. To address this setting of multiple networks, we propose a multi-graphon model which allows node-level as well as network-level heterogeneity. We show how information from multiple networks can be leveraged to enable estimation of the multi-graphon via standard nonparametric regression techniques, e.g. kernel regression, orthogonal series estimation. We study theoretical properties of the proposed estimator establishing recovery of the latent nodal positions up to negligible error, and convergence of the multi-graphon estimator to the normal distribution. Finite sample performance are investigated in a simulation study and application to two real-world networks--a dynamic contact network of ants and a collection of structural brain networks from different subjects--illustrate the utility of our approach

Inference of tissue relative proportions of the breast epithelial cell types luminal progenitor, basal, and luminal mature

Single-cell analysis has revolutionised genomic science in recent years. However, due to cost and other practical considerations, single-cell analyses are impossible for studies based on medium or large patient cohorts. For example, a single-cell analysis usually costs thousands of euros for one tissue sample from one volunteer, meaning that typical studies using single-cell analyses are based on very few individuals. While single-cell genomic data can be used to examine the phenotype of individual cells, cell-type deconvolution methods are required to track the quantities of these cells in bulk-tissue genomic data. Hormone receptor negative breast cancers are highly aggressive, and are thought to originate from a subtype of epithelial cells called the luminal progenitor. In this paper, we show how to quantify the number of luminal progenitor cells as well as other epithelial subtypes in breast tissue samples using DNA and RNA based measurements. We find elevated levels of cells which resemble these hormone receptor negative luminal progenitor cells in breast tumour biopsies of hormone receptor negative cancers, as well as in healthy breast tissue samples from BRCA1 (FANCS) mutation carriers. We also find that breast tumours from carriers of heterozygous mutations in non-BRCA Fanconi Anaemia pathway genes are much more likely to be hormone receptor negative. These findings have implications for understanding hormone receptor negative breast cancers, and for breast cancer screening in carriers of heterozygous mutations of Fanconi Anaemia pathway genes

Local linear graphon estimation using covariates

We consider local linear estimation of the graphon function which determines probabilities of pairwise edges between nodes within an unlabeled network. Real world networks are typically characterized by node heterogeneity with different nodes exhibiting different degrees of interaction. Existing approaches to graphon estimation are limited to local constant approximations, and are not designed to estimate heterogeneity across the full network. In this paper, we show how continuous node covariates can be employed to estimate heterogeneity in the network via a local linear graphon estimator. We derive the bias and variance of an oracle based local linear graphon estimator and thus obtain the mean integrated squared error optimal bandwidth rule. We also provide a plug-in bandwidth selection procedure, making local linear estimation for unlabeled networks practically feasible. Finite sample performance is investigated in a simulation study. We apply our method to a school friendship network and an email network to illustrate the advantages offered by our approach over existing methods

Picosecond polarized fluorescence studies of anisotropic fluid media. I. Theory

Recent work has demonstrated the production of substantial molecular alignment in a free ethylene glycol jet. Using variably polarized photoselection, a range of initial nonequilibrium orientational distributions can be prepared and their subsequent relaxation monitored via polarization resolved time correlated single photon counting. The imposition of order in a fluid is seen to have a profound effect on molecular motion and a strong anisotropy in theta and phi diffusion is indicated. In this work (Papers I and II) we describe a detailed investigation of this phenomenon. Here (Paper I) we develop the formalism necessary to describe the interaction of polarized laser pulses with an anisotropic medium, allowing a full description of the initially photoselected distribution. The relaxation of the nonequilibrium distributions is considered via a perturbation treatment of the anisotropic rotational diffusion equation. New "selection rules" for orientational relaxation can be deduced from symmetry arguments and the form of the cylindrically symmetric (theta diffusion) and asymmetric alignment decays (phi diffusion) are predicted. (C) 2000 American Institute of Physics. [S0021-9606(00)00117-3]

Picosecond polarized fluorescence studies of anisotropic fluid media. II. Experimental studies of molecular order and motion in jet aligned rhodamine 6G and resorufin solutions

New polarized time resolved fluorescence techniques are implemented to determine the full angular motion of a probe molecule in an anisotropic environment. Studies of rhodamine 6G and resorufin molecules aligned in a free ethylene glycol jet show that the presence of net molecular order is accompanied by a distinct anisotropy in alignment relaxation following photoselection. Diffusion coefficients for phi and theta motion (D-parallel to and D-perpendicular to) in a jet fixed axis system are determined from the cylindrically symmetric and asymmetric alignment relaxation rates for the isotropic and anisotropic regions of the jet. The presence of net negative molecular alignment as the free jet is formed is seen to correspond to restricted phi motion (D-parallel to < D-perpendicular to), with a net positive steady state alignment the anisotropy in the diffusion dynamics is reversed. The differences in D-parallel to and D-perpendicular to are attributed to anisotropy in the solvent viscosity as a consequence of flow. The combination of linear and circular polarization techniques is seen to provide useful information on cylindrical asymmetry and relaxation dynamics hitherto unobserved by conventional fluorescence polarization techniques. (C) 2000 American Institute of Physics. [S0021-9606(00)00217-8]

Inference of tissue relative proportions of the breast epithelial cell types luminal progenitor, basal, and luminal mature

Single-cell analysis has revolutionised genomic science in recent years. However, due to cost and other practical considerations, single-cell analyses are impossible for studies based on medium or large patient cohorts. For example, a single-cell analysis usually costs thousands of euros for one tissue sample from one volunteer, meaning that typical studies using single-cell analyses are based on very few individuals. While single-cell genomic data can be used to examine the phenotype of individual cells, cell-type deconvolution methods are required to track the quantities of these cells in bulk-tissue genomic data. Hormone receptor negative breast cancers are highly aggressive, and are thought to originate from a subtype of epithelial cells called the luminal progenitor. In this paper, we show how to quantify the number of luminal progenitor cells as well as other epithelial subtypes in breast tissue samples using DNA and RNA based measurements. We find elevated levels of cells which resemble these hormone receptor negative luminal progenitor cells in breast tumour biopsies of hormone receptor negative cancers, as well as in healthy breast tissue samples from BRCA1 (FANCS) mutation carriers. We also find that breast tumours from carriers of heterozygous mutations in non-BRCA Fanconi Anaemia pathway genes are much more likely to be hormone receptor negative. These findings have implications for understanding hormone receptor negative breast cancers, and for breast cancer screening in carriers of heterozygous mutations of Fanconi Anaemia pathway genes

Jaw Morphology and Vertical Facial Types: A Cephalometric Appraisal

Aims and objectives: To evaluate the maxillary and mandibular&nbsp;morphology in different vertical facial types and to implicate the&nbsp;achieved results into diagnosis and treatment planning of patients&nbsp;requiring orthodontic treatment.&nbsp;Materials and methods: The present study is conducted on a&nbsp;sample of 120 subjects comprising of 60 males and 60 females&nbsp;in the age range of 18 to 25 years. The lateral head cephalograms&nbsp;of the subjects were divided into three groups, i.e. group I&nbsp;(hypodivergent), group II (normodivergent) and group III(hyperdivergent) with regard to vertical facial type by using the&nbsp;following three parameters, i.e. SN-MP (facial divergence angle),&nbsp;overbite depth indicator (ODI) and Jarabak ratio or facial height&nbsp;ratio (FHR). Differences among the groups and between genders&nbsp;were assessed by means of variance analysis and Newman-&nbsp;Keuls post hoc test.&nbsp;Results: Maxillary and mandibular anterior alveolar and maxillary&nbsp;postalveolar height was found to be greater for hyperdivergent&nbsp;group in comparison to others. Hyperdivergent facial types posseslong and narrow symphysis along with greater antegonial notch&nbsp;depth whereas hypodivergent showed an opposite tendency.&nbsp;Hyperdivergent facial types generally have a smaller maxillary&nbsp;area as compared to other facial types. However, total mandibular&nbsp;area does not vary among different vertical facial types. Sexual&nbsp;dichotomy was found with maxillary anterior alveolar and basal&nbsp;height, mandibular posterior alveolar and basal height, mandibular&nbsp;length, symphyseal depth, depth of the antegonial notch,&nbsp;symphyseal area and ext/total symphyseal area ratio.&nbsp;Conclusion: Vertical facial type may be related to the&nbsp;morphological and dentoalveolar pattern of both maxilla and&nbsp;mandible. Determination of this relationship may be of great help&nbsp;from diagnostic as well as therapeutic aspects of many vertical&nbsp;malocclusion problems