Hermite-Padé Approximants for a Pair of Cauchy Transforms with Overlapping Symmetric Supports

Hermite-Padé approximants of type II are vectors of rational functions with a common denominator that interpolate a given vector of power series at infinity with maximal order. We are interested in the situation when the approximated vector is given by a pair of Cauchy transforms of smooth complex measures supported on the real line. The convergence properties of the approximants are rather well understood when the supports consist of two disjoint intervals (Angelesco systems) or two intervals that coincide under the condition that the ratio of the measures is a restriction of the Cauchy transform of a third measure (Nikishin systems). In this work we consider the case where the supports form two overlapping intervals (in a symmetric way) and the ratio of the measures extends to a holomorphic function in a region that depends on the size of the overlap. We derive Szegő-type formulae for the asymptotics of the approximants, identify the convergence and divergence domains (the divergence domains appear for Angelesco systems but are not present for Nikishin systems), and show the presence of overinterpolation (a feature peculiar for Nikishin systems but not for Angelesco systems). Our analysis is based on a Riemann-Hilbert problem for multiple orthogonal polynomials (the common denominator)

Experimental linear-optical implementation of a multifunctional optimal qubit cloner

We present the first experimental implementation of a multifunctional device for the optimal cloning of one to two qubits. Previous implementations have always been designed to optimize the cloning procedure with respect to one single type of a priori information about the cloned state. In contrast, our "all-in-one" implementation is optimal for several prominent regimes such as universal cloning, phase-covariant cloning, and also the first ever realized mirror phase-covariant cloning, when the square of the expected value of Pauli's Z operator is known in advance. In all these regimes the experimental device yields clones with almost maximum achievable average fidelity (97.5% of theoretical limit). Our device has a wide range of possible applications in quantum information processing, especially in quantum communication. For instance, one can use it for incoherent and coherent attacks against a variety of cryptographic protocols, including the Bennett-Brassard 1984 protocol of quantum key distribution through the Pauli damping channels. It can be also applied as a state-dependent photon multiplier in practical quantum networks.Comment: 9 pages, 6 figures, accepted to Phys. Rev. A (Rapid Communications

Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model

We apply the nonlinear steepest descent method to a class of 3x3 Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix random model. The general case of two equilibrium measures supported on an arbitrary number of intervals is considered. In this case, we solve the Riemann-Hilbert problem for the outer parametrix in terms of sections of a spinorial line bundle on a three-sheeted Riemann surface of arbitrary genus and establish strong asymptotic results for the Cauchy biorthogonal polynomials.Comment: 31 pages, 12 figures. V2; typos corrected, added reference

Gehechtheid als beïnvloedende factor van gedrags- en psychologische symptomen bij dementie

De laatste jaren wordt in toenemende mate het belang van hechting op oudere leeftijd erkend. Getuigen daarvan zijn vele onderzoekingen die gebeurden in de voorbije drie decennia. In dit artikel geven we een overzicht van de belangrijkste resultaten met speciale aandacht voor onderzoek naar hechting en dementie. Studies suggereren dat het aantal hechtingsfiguren afneemt op oudere leeftijd. Daarentegen wordt de plaats van volwassen kinderen, een overleden partner en God prominenter. Ook blijkt dat de hechtingsangst daalt naarmate mensen ouder worden, terwijl hechtingsvermijding relatief stabiel blijft. Veilige gehechtheid is verder positief gerelateerd met groter welzijn en een positievere visie op ouder worden in vergelijking met meer onveilig gehechte individuen. Onveilige gehechtheid hangt ook samen met een toename van gedragsen psychologische problemen bij dementerende ouderen. Bij de zorgverlener zijn draaglast en depressiviteit, evenals de wijze waarop zorg opgenomen wordt en het engagement naar de toekomst toe, verschillend afhankelijk van de hechtingsstijl. Conform deze bevindingen lijken hechtingsgebaseerde interventies een positief effect op gedrags- en psychologische symptomen bij dementie te hebben, maar meer onderzoek is hier duidelijk nodig. Tot slot is er nog een weg af te leggen wat betreft uniformisering en validering van meetmethoden voor hechting op oudere leeftijd

Metabolic profiling of a transgenic Caenorhabditis elegans Alzheimer model

Despite decades of research, no early-onset biomarkers are currently available for Alzheimer’s disease, a cureless neurodegenerative disease afflicting millions worldwide. In this study, transgenic Caenorhabditis elegans were used to investigate changes in the metabolome after induced expression of amyloid-β. GC- and LC–MS-based platforms determined a total of 157 differential features. Some of these were identified using in-house (GC–MS) or public libraries (LC–MS), revealing changes in allantoin, cystathionine and tyrosine levels. Since C. elegans is far better suited to metabolomics studies than most other model systems, the accordance of these findings with vertebrate literature is promising and argues for further use of C. elegans as a model of human pathology in the study of AD

Continuous variable private quantum channel

In this paper we introduce the concept of quantum private channel within the continuous variables framework (CVPQC) and investigate its properties. In terms of CVPQC we naturally define a "maximally" mixed state in phase space together with its explicit construction and show that for increasing number of encryption operations (which sets the length of a shared key between Alice and Bob) the encrypted state is arbitrarily close to the maximally mixed state in the sense of the Hilbert-Schmidt distance. We bring the exact solution for the distance dependence and give also a rough estimate of the necessary number of bits of the shared secret key (i.e. how much classical resources are needed for an approximate encryption of a generally unknown continuous-variable state). The definition of the CVPQC is analyzed from the Holevo bound point of view which determines an upper bound of information about an incoming state an eavesdropper is able to get from his optimal measurement.Comment: upper bound on information Eve can get was revised and substantially lowered (chapter IV), part of chapter III rewritten, several typos correcte

Critical behavior in Angelesco ensembles

We consider Angelesco ensembles with respect to two modified Jacobi weights on touching intervals [a,0] and [0,1], for a < 0. As a \to -1 the particles around 0 experience a phase transition. This transition is studied in a double scaling limit, where we let the number of particles of the ensemble tend to infinity while the parameter a tends to -1 at a rate of order n^{-1/2}. The correlation kernel converges, in this regime, to a new kind of universal kernel, the Angelesco kernel K^{Ang}. The result follows from the Deift/Zhou steepest descent analysis, applied to the Riemann-Hilbert problem for multiple orthogonal polynomials.Comment: 32 pages, 9 figure