Structured matrices, continued fractions, and root localization of polynomials

We give a detailed account of various connections between several classes of objects: Hankel, Hurwitz, Toeplitz, Vandermonde and other structured matrices, Stietjes and Jacobi-type continued fractions, Cauchy indices, moment problems, total positivity, and root localization of univariate polynomials. Along with a survey of many classical facts, we provide a number of new results.Comment: 79 pages; new material added to the Introductio

Local asymptotic normality for qubit states

We consider n identically prepared qubits and study the asymptotic properties of the joint state \rho^{\otimes n}. We show that for all individual states \rho situated in a local neighborhood of size 1/\sqrt{n} of a fixed state \rho^0, the joint state converges to a displaced thermal equilibrium state of a quantum harmonic oscillator. The precise meaning of the convergence is that there exist physical transformations T_{n} (trace preserving quantum channels) which map the qubits states asymptotically close to their corresponding oscillator state, uniformly over all states in the local neighborhood. A few consequences of the main result are derived. We show that the optimal joint measurement in the Bayesian set-up is also optimal within the pointwise approach. Moreover, this measurement converges to the heterodyne measurement which is the optimal joint measurement of position and momentum for the quantum oscillator. A problem of local state discrimination is solved using local asymptotic normality.Comment: 16 pages, 3 figures, published versio

Electron Accumulation and Emergent Magnetism in LaMnO3/SrTiO3 Heterostructures

Emergent phenomena at polar-nonpolar oxide interfaces have been studied intensely in pursuit of next-generation oxide electronics and spintronics. Here we report the disentanglement of critical thicknesses for electron reconstruction and the emergence of ferromagnetism in polar-mismatched LaMnO3/SrTiO3 (001) heterostructures. Using a combination of element-specific X-ray absorption spectroscopy and dichroism, and first-principles calculations, interfacial electron accumulation and ferromagnetism have been observed within the polar, antiferromagnetic insulator LaMnO3. Our results show that the critical thickness for the onset of electron accumulation is as thin as 2 unit cells (UC), significantly thinner than the observed critical thickness for ferromagnetism of 5 UC. The absence of ferromagnetism below 5 UC is likely induced by electron over-accumulation. In turn, by controlling the doping of the LaMnO3, we are able to neutralize the excessive electrons from the polar mismatch in ultrathin LaMnO3 films and thus enable ferromagnetism in films as thin as 3 UC, extending the limits of our ability to synthesize and tailor emergent phenomena at interfaces and demonstrating manipulation of the electronic and magnetic structures of materials at the shortest length scales.Comment: Accepted by Phys. Rev. Let

Tensor completion in hierarchical tensor representations

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the reconstruction of tensors of low multi-linear rank in recently introduced hierarchical tensor formats from a small number of measurements. Hierarchical tensors are a flexible generalization of the well-known Tucker representation, which have the advantage that the number of degrees of freedom of a low rank tensor does not scale exponentially with the order of the tensor. While corresponding tensor decompositions can be computed efficiently via successive applications of (matrix) singular value decompositions, some important properties of the singular value decomposition do not extend from the matrix to the tensor case. This results in major computational and theoretical difficulties in designing and analyzing algorithms for low rank tensor recovery. For instance, a canonical analogue of the tensor nuclear norm is NP-hard to compute in general, which is in stark contrast to the matrix case. In this book chapter we consider versions of iterative hard thresholding schemes adapted to hierarchical tensor formats. A variant builds on methods from Riemannian optimization and uses a retraction mapping from the tangent space of the manifold of low rank tensors back to this manifold. We provide first partial convergence results based on a tensor version of the restricted isometry property (TRIP) of the measurement map. Moreover, an estimate of the number of measurements is provided that ensures the TRIP of a given tensor rank with high probability for Gaussian measurement maps.Comment: revised version, to be published in Compressed Sensing and Its Applications (edited by H. Boche, R. Calderbank, G. Kutyniok, J. Vybiral

Effective Interactions and Volume Energies in Charged Colloids: Linear Response Theory

Interparticle interactions in charge-stabilized colloidal suspensions, of arbitrary salt concentration, are described at the level of effective interactions in an equivalent one-component system. Integrating out from the partition function the degrees of freedom of all microions, and assuming linear response to the macroion charges, general expressions are obtained for both an effective electrostatic pair interaction and an associated microion volume energy. For macroions with hard-sphere cores, the effective interaction is of the DLVO screened-Coulomb form, but with a modified screening constant that incorporates excluded volume effects. The volume energy -- a natural consequence of the one-component reduction -- contributes to the total free energy and can significantly influence thermodynamic properties in the limit of low-salt concentration. As illustrations, the osmotic pressure and bulk modulus are computed and compared with recent experimental measurements for deionized suspensions. For macroions of sufficient charge and concentration, it is shown that the counterions can act to soften or destabilize colloidal crystals.Comment: 14 pages, including 3 figure

Remifentanil in the Horse: Identification and Detection of its Major Urinary Metabolite

Remifentanil (4-methoxycarbonyl-4-[(1-oxopropyl)phyenylamino]-1- piperidinepropionic acid methyl ester) is a μ-opioid receptor agonist with considerable abuse potential in racing horses. The identification of its major equine urinary metabolite, 4-methoxycarbonyl-4-[(1- oxopropyl)phenylamino]-1-piperidinepropionic acid, an ester hydrolysis product of remifentanil is reported. Administration of remifentanil HCl (5 mg, intravenous) produced clear-cut locomotor responses, establishing the clinical efficacy of this dose. ELISA analysis of postadministration urine samples readily detected fentanyl equivalents in these samples. Mass spectrometric analysis, using solid-phase extraction and trimethylsilyl (TMS) derivatization, showed the urine samples contained parent remifentanil in low concentrations, peaking at 1 h. More significantly, a major peak was identified as representing 4-methoxycarbonyl-4-[(1-oxopropyl)phenylamino]-1- piperidinepropionic acid, arising from ester hydrolysis of remifentanil. This metabolite reached its maximal urinary concentrations at 1 h and was present at up to 10-fold greater concentrations than parent remifentanil. Base hydrolysis of remifentanil yielded a carboxylic acid with the same mass spectral characteristics as those of the equine metabolite. In summary, these data indicate that remifentanil administration results in the appearance of readily detectable amounts of 4-methoxycarbonyl-4-[(1-oxopropyl)phenylamino]- 1-piperidinepropionic acid in urine. On this basis, screening and confirmation tests for this equine urinary metabolite should be optimized for forensic control of remifentanil

The relationship between the perception of distributed leadership in secondary schools and teachers' and teacher leaders' job satisfaction and organizational commitment

This study investigates the relation between distributed leadership, the cohesion of the leadership team, participative decision-making, context variables, and the organizational commitment and job satisfaction of teachers and teacher leaders. A questionnaire was administered to teachers and teacher leaders (n=1770) from 46 large secondary schools. Multiple regression analyses and path analyses revealed that the study variables explained significant variance in organizational commitment. The degree of explained variance for job satisfaction was considerably lower compared to organizational commitment. Most striking was that the cohesion of the leadership team and the amount of leadership support was strongly related to organizational commitment, and indirectly to job satisfaction. Decentralization of leadership functions was weakly related to organizational commitment and job satisfaction

Eradication of chronic myeloid leukemia stem cells: a novel mathematical model predicts no therapeutic benefit of adding G-CSF to imatinib

Imatinib mesylate induces complete cytogenetic responses in patients with chronic myeloid leukemia (CML), yet many patients have detectable BCR-ABL transcripts in peripheral blood even after prolonged therapy. Bone marrow studies have shown that this residual disease resides within the stem cell compartment. Quiescence of leukemic stem cells has been suggested as a mechanism conferring insensitivity to imatinib, and exposure to the Granulocyte-Colony Stimulating Factor (G-CSF), together with imatinib, has led to a significant reduction in leukemic stem cells in vitro. In this paper, we design a novel mathematical model of stem cell quiescence to investigate the treatment response to imatinib and G-CSF. We find that the addition of G-CSF to an imatinib treatment protocol leads to observable effects only if the majority of leukemic stem cells are quiescent; otherwise it does not modulate the leukemic cell burden. The latter scenario is in agreement with clinical findings in a pilot study administering imatinib continuously or intermittently, with or without G-CSF (GIMI trial). Furthermore, our model predicts that the addition of G-CSF leads to a higher risk of resistance since it increases the production of cycling leukemic stem cells. Although the pilot study did not include enough patients to draw any conclusion with statistical significance, there were more cases of progression in the experimental arms as compared to continuous imatinib. Our results suggest that the additional use of G-CSF may be detrimental to patients in the clinic