Profile Likelihood Biclustering

Biclustering, the process of simultaneously clustering the rows and columns of a data matrix, is a popular and effective tool for finding structure in a high-dimensional dataset. Many biclustering procedures appear to work well in practice, but most do not have associated consistency guarantees. To address this shortcoming, we propose a new biclustering procedure based on profile likelihood. The procedure applies to a broad range of data modalities, including binary, count, and continuous observations. We prove that the procedure recovers the true row and column classes when the dimensions of the data matrix tend to infinity, even if the functional form of the data distribution is misspecified. The procedure requires computing a combinatorial search, which can be expensive in practice. Rather than performing this search directly, we propose a new heuristic optimization procedure based on the Kernighan-Lin heuristic, which has nice computational properties and performs well in simulations. We demonstrate our procedure with applications to congressional voting records, and microarray analysis.Comment: 40 pages, 11 figures; R package in development at https://github.com/patperry/biclustp

Minimax rank estimation for subspace tracking

Rank estimation is a classical model order selection problem that arises in a variety of important statistical signal and array processing systems, yet is addressed relatively infrequently in the extant literature. Here we present sample covariance asymptotics stemming from random matrix theory, and bring them to bear on the problem of optimal rank estimation in the context of the standard array observation model with additive white Gaussian noise. The most significant of these results demonstrates the existence of a phase transition threshold, below which eigenvalues and associated eigenvectors of the sample covariance fail to provide any information on population eigenvalues. We then develop a decision-theoretic rank estimation framework that leads to a simple ordered selection rule based on thresholding; in contrast to competing approaches, however, it admits asymptotic minimax optimality and is free of tuning parameters. We analyze the asymptotic performance of our rank selection procedure and conclude with a brief simulation study demonstrating its practical efficacy in the context of subspace tracking.Comment: 10 pages, 4 figures; final versio

Direct Evidence for the Source of Reported Magnetic Behavior in "CoTe"

In order to unambiguously identify the source of magnetism reported in recent studies of the Co-Te system, two sets of high-quality, epitaxial CoTe$_x$ films (thickness $\simeq$ 300 nm) were prepared by pulse laser deposition (PLD). X-ray diffraction (XRD) shows that all of the films are epitaxial along the [001] direction and have the hexagonal NiAs structure. There is no indication of any second phase metallic Co peaks (either $fcc$ or $hcp$) in the XRD patterns. The two sets of CoTe$_x$ films were grown on various substrates with PLD targets having Co:Te in the atomic ratio of 50:50 and 35:65. From the measured lattice parameters $c = 5.396 \AA$ for the former and $c = 5.402\AA$ for the latter, the compositions CoTe$_{1.71}$ (63.1% Te) and CoTe$_{1.76}$ (63.8% Te), respectively, are assigned to the principal phase. Although XRD shows no trace of metallic Co second phase, the magnetic measurements do show a ferromagnetic contribution for both sets of films with the saturation magnetization values for the CoTe$_{1.71}$ films being approximately four times the values for the CoTe$_{1.76}$ films. $^{59}$Co spin-echo nuclear magnetic resonance (NMR) clearly shows the existence of metallic Co inclusions in the films. The source of weak ferromagnetism reported in several recent studies is due to the presence of metallic Co, since the stoichiometric composition "CoTe" does not exist.Comment: 19 pages, 7 figure

Tumors in von Hippel–Lindau Syndrome: From Head to Toe—Comprehensive State-of-the-Art Review

Von Hippel–Lindau syndrome (VHL) is an autosomal-dominant hereditary tumor disease that arises owing to germline mutations in the VHL gene, located on the short arm of chromosome 3. Patients with VHL may develop multiple benign and malignant tumors involving various organ systems, including retinal hemangioblastomas (HBs), central nervous system (CNS) HBs, endolymphatic sac tumors, pancreatic neuroendocrine tumors, pancreatic cystadenomas, pancreatic cysts, clear cell renal cell carcinomas, renal cysts, pheochromocytomas, paragangliomas, and epididymal and broad ligament cystadenomas. The VHL/hypoxia-inducible factor pathway is believed to play a key role in the pathogenesis of VHL-related tumors. The diagnosis of VHL can be made clinically when the characteristic clinical history and findings have manifested, such as the presence of two or more CNS HBs. Genetic testing for heterozygous germline VHL mutation may also be used to confirm the diagnosis of VHL. Imaging plays an important role in the diagnosis and surveillance of patients with VHL. Familiarity with the clinical and imaging manifestations of the various VHL-related tumors is important for early detection and guiding appropriate management. The purpose of this article is to discuss the molecular cytogenetics and clinical manifestations of VHL, review the characteristic multimodality imaging features of the various VHL-related tumors affecting multiple organ systems, and discuss the latest advances in management of VHL, including current recommendations for surveillance and screening

Partition Functions, the Bekenstein Bound and Temperature Inversion in Anti-de Sitter Space and its Conformal Boundary

We reformulate the Bekenstein bound as the requirement of positivity of the Helmholtz free energy at the minimum value of the function L=E- S/(2\pi R), where R is some measure of the size of the system. The minimum of L occurs at the temperature T=1/(2\pi R). In the case of n-dimensional anti-de Sitter spacetime, the rather poorly defined size R acquires a precise definition in terms of the AdS radius l, with R=l/(n-2). We previously found that the Bekenstein bound holds for all known black holes in AdS. However, in this paper we show that the Bekenstein bound is not generally valid for free quantum fields in AdS, even if one includes the Casimir energy. Some other aspects of thermodynamics in anti-de Sitter spacetime are briefly touched upon.Comment: Latex, 32 page

On two dimensional coupled bosons and fermions

We study complex bosons and fermions coupled through a generalized Yukawa type coupling in the large-N_c limit following ideas of Rajeev [Int. Jour. Mod. Phys. A 9 (1994) 5583]. We study a linear approximation to this model. We show that in this approximation we do not have boson-antiboson and fermion-antifermion bound states occuring together. There is a possibility of having only fermion-antifermion bound states. We support this claim by finding distributional solutions with energies lower than the two mass treshold in the fermion sector. This also has implications from the point of view of scattering theory to this model. We discuss some aspects of the scattering above the two mass treshold of boson pairs and fermion pairs. We also briefly present a gauged version of the same model and write down the linearized equations of motion.Comment: 25 pages, no figure