Likelihood ratio tests for equality of shape under varying degrees of orientation invariance

We consider a problem from image cytometry where the objective is to describe possible changes in the shape and orientation of cellular nuclei after treatment with a toxin. The shapes of nuclei are represented by individual ellipses. It is argued that the shape comparison problem can be formulated as a generalization of a hypothesis test for the equality of covariance matrices. For many cell types, the test statistic should be invariant with respect to orientations of the cells. For other cell types, the test statistic should be equivariant with respect to orientations of the cells, but invariant with respect to orientations of the images. Likelihood ratio tests (LRTs) are derived under a Wishart model. The likelihood maximization uses a new result about the minimization of the determinant of a sum of matrices under individual rotations. The applicability and limitations of these LRTs are demonstrated by means of simulation experiments. The reference distributions of the test statistics under the null hypothesis are obtained using unrestricted and restricted randomization procedures. Justification for the Wishart model is provided using a residual diagnostic method. The scientific implications of the results are considered.57N25 47N60 58J70 Shape analysis Likelihood ratio test Orientation invariance

Regularized reconstruction of water surfaces from noisy gradient information via plane-wave superposition

International audienceRefraction-based imaging systems, used in wave tank facilities, provide measurements of local water surface gradients. The reconstruction of wave height fields from this information is considered. Utilizing the convenient approximation of target wave height fields by superposition of simple plane waves, we explore the possibility of adaptive plane-wave approximation for computation of the regularized solutions to the wave height reconstruction problem. A greedy algorithm is employed. The method developed allows for non-parametric estimation of wave-front shapes and their periodicities. Regularization forces a natural inverse relation between the smoothness of wave-front shapes and their periodicities. A generalized cross-validation statistic based on a novel tomographic approximation to the model degrees of freedom is developed to assess the regularization parameter. The approximation technique would appear to have wider utility in multi-dimensional smoothing via regularization. The methodology is illustrated by application to real and synthetic data associated with an operational imaging system. Generalization of the approach to the nonlinear problem of reconstructing water surfaces from reflectance data is also considered and some preliminary results for Lambertian reflection are provided. The approach is found to offer substantial potential for this class of reconstruction problems

Dissecting the gene dose-effects of the APOE ε4 and ε2 alleles on hippocampal volumes in aging and Alzheimer's disease.

To investigate whether there is a specific dose-dependent effect of the Apolipoprotein E (APOE) ε4 and ε2 alleles on hippocampal volume, across the cognitive spectrum, from normal aging to Alzheimer's Disease (AD).We analyzed MR and genetic data on 662 patients from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database-198 cognitively normal controls (CN), 321 mild-cognitive impairment (MCI) subjects, and 143 AD subjects-looking for dose-dependent effects of the ε4 and ε2 alleles on hippocampal volumes. Volumes were measured using a fully-automated algorithm applied to high resolution T1-weighted MR images. Statistical analysis consisted of a multivariate regression with repeated-measures model.There was a dose-dependent effect of the ε4 allele on hippocampal volume in AD (p = 0.04) and MCI (p = 0.02)-in both cases, each allele accounted for loss of >150 mm(3) (approximately 4%) of hippocampal volume below the mean volume for AD and MCI subjects with no such alleles (Cohen's d = -0.16 and -0.19 for AD and MCI, respectively). There was also a dose-dependent, main effect of the ε2 allele (p<0.0001), suggestive of a moderate protective effect on hippocampal volume-an approximately 20% per allele volume increase as compared to CN with no ε2 alleles (Cohen's d = 0.23).Though no effect of ε4 was seen in CN subjects, our findings confirm and extend prior data on the opposing effects of the APOE ε4 and ε2 alleles on hippocampal morphology across the spectrum of cognitive aging

Tcrd Rearrangement Redirects a Processive Tcra Recombination Program to Expand the Tcra Repertoire

Adaptive immunity depends on diverse T cell receptor repertoires generated by variable, diversity, and joining (V[D]J) recombination. Here, we define the principles by which combinatorial diversity is generated in the murine Tcra repertoire. Tcra and Tcrd gene segments share the Tcra-Tcrd locus, with interspersed Vα and Vδ segments undergoing Vδ-Dδ-Jδ rearrangement in CD4−CD8− thymocytes and then multiple rounds of Vα-Jα rearrangement in CD4+CD8+ thymocytes. We document stepwise, highly coordinated proximal-to-distal progressions of Vα and Jα use on individual Tcra alleles, limiting combinatorial diversity. This behavior is supported by an extended chromatin conformation in CD4+CD8+ thymocytes, with only nearby Vα and Jα segments contacting each other. Tcrd rearrangements can use distal Vδ segments due to a contracted Tcra-Tcrd conformation in CD4−CD8− thymocytes. These rearrangements expand the Tcra repertoire by truncating the Vα array to permit otherwise disfavored Vα-Jα combinations. Therefore, recombination events at two developmental stages with distinct chromatin conformations synergize to promote Tcra repertoire diversity