A solution to the weighted procrustes problem in which the transformation is in agreement with the loss function

This paper provides a generalization of the Procrustes problem in which the errors are weighted from the right, or the left, or both. The solution is achieved by having the orthogonality constraint on the transformation be in agreement with the norm of the least squares criterion. This general principle is discussed and illustrated by the mathematics of the weighted orthogonal Procrustes problem.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45737/1/11336_2005_Article_BF02296976.pd

Origin of the butterfly magnetoresistance in a Dirac nodal-line system

We report a study on the magnetotransport properties and on the Fermi surfaces (FS) of the ZrSi(Se,Te) semimetals. Density Functional Theory (DFT) calculations, in absence of spin orbit coupling (SOC), reveal that both the Se and the Te compounds display Dirac nodal lines (DNL) close to the Fermi level $\varepsilon_F$ at symmorphic and non-symmorphic positions, respectively. We find that the geometry of their FSs agrees well with DFT predictions. ZrSiSe displays low residual resistivities, pronounced magnetoresistivity, high carrier mobilities, and a butterfly-like angle-dependent magnetoresistivity (AMR), although its DNL is not protected against gap opening. As in Cd$_3$As$_2$, its transport lifetime is found to be 10$^2$ to 10$^3$ times larger than its quantum one. ZrSiTe, which possesses a protected DNL, displays conventional transport properties. Our evaluation indicates that both compounds most likely are topologically trivial. Nearly angle-independent effective masses with strong angle dependent quantum lifetimes lead to the butterfly AMR in ZrSiSe

Detailed study of the Fermi surfaces of the type-II Dirac semimetallic candidates XTe2 (X =Pd, Pt)

We present a detailed quantum oscillatory study on the Dirac type-II semimetallic candidates PdTe2 and PtTe2 via the temperature and the angular dependence of the de Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) effects. In high quality single crystals of both compounds, i.e. displaying carrier mobilities between 10 3 and 10 4 cm 2 /Vs, we observed a large non-saturating magnetoresistivity (MR) which in PtTe 2 at a temperature T = 1. 3 K, leads to an increase in the resistivity up to 5 × 10 4 % under a magnetic field μ 0 H = 62 T. These high mobilities correlate with their light effective masses in the range of 0.04 to 1 bare electron mass according to our measurements. For PdTe2 the experimentally determined Fermi surface cross-sectional areas show an excellent agreement with those resulting from band-structure calculations. Surprisingly, this is not the case for PtTe2 whose agreement between calculations and experiments is relatively poor even when electronic correlations are included in the calculations. Therefore, our study provides a strong support for the existence of a Dirac type-II node in PdTe 2 and probably also for PtTe2. Band structure calculations indicate that the topologically non-trivial bands of PtTe2 do not cross the Fermi-level (εF). In contrast, for PdTe2 the Dirac type-II cone does intersect εF, although our calculations also indicate that the associated cyclotron orbit on the Fermi surface is located in a distinct kz plane with respect to the one of the Dirac type-II node. Therefore it should yield a trivial Berry-phase

Anomalous metamagnetism in the low carrier density Kondo lattice YbRh3Si7

We report complex metamagnetic transitions in single crystals of the new low carrier Kondo antiferromagnet YbRh3Si7. Electrical transport, magnetization, and specific heat measurements reveal antiferromagnetic order at T_N = 7.5 K. Neutron diffraction measurements show that the magnetic ground state of YbRh3Si7 is a collinear antiferromagnet where the moments are aligned in the ab plane. With such an ordered state, no metamagnetic transitions are expected when a magnetic field is applied along the c axis. It is therefore surprising that high field magnetization, torque, and resistivity measurements with H||c reveal two metamagnetic transitions at mu_0H_1 = 6.7 T and mu_0H_2 = 21 T. When the field is tilted away from the c axis, towards the ab plane, both metamagnetic transitions are shifted to higher fields. The first metamagnetic transition leads to an abrupt increase in the electrical resistivity, while the second transition is accompanied by a dramatic reduction in the electrical resistivity. Thus, the magnetic and electronic degrees of freedom in YbRh3Si7 are strongly coupled. We discuss the origin of the anomalous metamagnetism and conclude that it is related to competition between crystal electric field anisotropy and anisotropic exchange interactions.Comment: 23 pages and 4 figures in the main text. 7 pages and 5 figures in the supplementary materia

Bulk fermi surface of the Weyl type-II semimetallic candidate γ−MoTe2

The electronic structure of WTe$_2$ and orthorhombic $\gamma-$MoTe$_2$, are claimed to contain pairs of Weyl type-II points. A series of ARPES experiments claim a broad agreement with these predictions. We synthesized single-crystals of MoTe$_2$ through a Te flux method to validate these predictions through measurements of its bulk Fermi surface (FS) \emph{via} quantum oscillatory phenomena. We find that the superconducting transition temperature of $\gamma-$MoTe$_2$ depends on disorder as quantified by the ratio between the room- and low-temperature resistivities, suggesting the possibility of an unconventional superconducting pairing symmetry. Similarly to WTe$_2$, the magnetoresistivity of $\gamma-$MoTe$_2$ does not saturate at high magnetic fields and can easily surpass $10^{6}$ \%. Remarkably, the analysis of the de Haas-van Alphen (dHvA) signal superimposed onto the magnetic torque, indicates that the geometry of its FS is markedly distinct from the calculated one. The dHvA signal also reveals that the FS is affected by the Zeeman-effect precluding the extraction of the Berry-phase. A direct comparison between the previous ARPES studies and density-functional-theory (DFT) calculations reveals a disagreement in the position of the valence bands relative to the Fermi level $\varepsilon_F$. Here, we show that a shift of the DFT valence bands relative to $\varepsilon_F$, in order to match the ARPES observations, and of the DFT electron bands to explain some of the observed dHvA frequencies, leads to a good agreement between the calculations and the angular dependence of the FS cross-sectional areas observed experimentally. However, this relative displacement between electron- and hole-bands eliminates their crossings and, therefore, the Weyl type-II points predicted for $\gamma-$MoTe$_2$.Comment: 13 pages, 7 figures, supplementary file not included (in press

Factor analysis for gene regulatory networks and transcription factor activity profiles

BACKGROUND: Most existing algorithms for the inference of the structure of gene regulatory networks from gene expression data assume that the activity levels of transcription factors (TFs) are proportional to their mRNA levels. This assumption is invalid for most biological systems. However, one might be able to reconstruct unobserved activity profiles of TFs from the expression profiles of target genes. A simple model is a two-layer network with unobserved TF variables in the first layer and observed gene expression variables in the second layer. TFs are connected to regulated genes by weighted edges. The weights, known as factor loadings, indicate the strength and direction of regulation. Of particular interest are methods that produce sparse networks, networks with few edges, since it is known that most genes are regulated by only a small number of TFs, and most TFs regulate only a small number of genes. RESULTS: In this paper, we explore the performance of five factor analysis algorithms, Bayesian as well as classical, on problems with biological context using both simulated and real data. Factor analysis (FA) models are used in order to describe a larger number of observed variables by a smaller number of unobserved variables, the factors, whereby all correlation between observed variables is explained by common factors. Bayesian FA methods allow one to infer sparse networks by enforcing sparsity through priors. In contrast, in the classical FA, matrix rotation methods are used to enforce sparsity and thus to increase the interpretability of the inferred factor loadings matrix. However, we also show that Bayesian FA models that do not impose sparsity through the priors can still be used for the reconstruction of a gene regulatory network if applied in conjunction with matrix rotation methods. Finally, we show the added advantage of merging the information derived from all algorithms in order to obtain a combined result. CONCLUSION: Most of the algorithms tested are successful in reconstructing the connectivity structure as well as the TF profiles. Moreover, we demonstrate that if the underlying network is sparse it is still possible to reconstruct hidden activity profiles of TFs to some degree without prior connectivity information

Modelling the perceptual similarity of facial expressions from image statistics and neural responses

The ability to perceive facial expressions of emotion is essential for effective social communication. We investigated how the perception of facial expression emerges from the image properties that convey this important social signal, and how neural responses in face-selective brain regions might track these properties. To do this, we measured the perceptual similarity between expressions of basic emotions, and investigated how this is reflected in image measures and in the neural response of different face-selective regions. We show that the perceptual similarity of different facial expressions (fear, anger, disgust, sadness, happiness) can be predicted by both surface and feature shape information in the image. Using block design fMRI, we found that the perceptual similarity of expressions could also be predicted from the patterns of neural response in the face-selective posterior superior temporal sulcus (STS), but not in the fusiform face area (FFA). These results show that the perception of facial expression is dependent on the shape and surface properties of the image and on the activity of specific face-selective regions

A stochastic multidimensional scaling procedure for the empirical determination of convex indifference curves for preference/choice analysis

The vast majority of existing multidimensional scaling (MDS) procedures devised for the analysis of paired comparison preference/choice judgments are typically based on either scalar product (i.e., vector) or unfolding (i.e., ideal-point) models. Such methods tend to ignore many of the essential components of microeconomic theory including convex indifference curves, constrained utility maximization, demand functions, et cetera. This paper presents a new stochastic MDS procedure called MICROSCALE that attempts to operationalize many of these traditional microeconomic concepts. First, we briefly review several existing MDS models that operate on paired comparisons data, noting the particular nature of the utility functions implied by each class of models. These utility assumptions are then directly contrasted to those of microeconomic theory. The new maximum likelihood based procedure, MICROSCALE, is presented, as well as the technical details of the estimation procedure. The results of a Monte Carlo analysis investigating the performance of the algorithm as a number of model, data, and error factors are experimentally manipulated are provided. Finally, an illustration in consumer psychology concerning a convenience sample of thirty consumers providing paired comparisons judgments for some fourteen brands of over-the-counter analgesics is discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45748/1/11336_2005_Article_BF02294463.pd