Application of Two-Phase Regression to Geotechnical Data

2000 Mathematics Subject Classification: 62F10, 62J05, 62P30A method for estimating a transition parameter in two-phase regression is described. The two phases are fitted and simultaneously the transition point is estimated. Practical application of the method is demonstrated on the data for determining soil hydraulic properties.Partly supported by projects FOR 444, Deutsche Forschungsgemeinschaft, Germany, MM1301/2003, National Science Fund, Bulgaria, and PRO-ENBIS: GTC1-2001-43031

Universal spectral properties of spatially periodic quantum systems with chaotic classical dynamics

We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on whether the chain is disordered or invariant under lattice translations. In the disordered case, the spectrum is dominated by Anderson localization whereas in the periodic case, the spectrum is arranged in bands. We investigate the special features in the spectral statistics for a periodic chain. For finite N, we define spectral form factors involving correlations both for identical and non-identical Bloch numbers. The short-time regime is treated within the semiclassical approximation, where the spectral form factor can be expressed in terms of a coarse-grained classical propagator which obeys a diffusion equation with periodic boundary conditions. In the long-time regime, the form factor decays algebraically towards an asymptotic constant. In the limit $N\to\infty$, we derive a universal scaling function for the form factor. The theory is supported by numerical results for quasi one-dimensional periodic chains of coupled Sinai billiards.Comment: 33 pages, REVTeX, 13 figures (eps

Combinatorial identities for binary necklaces from exact ray-splitting trace formulae

Based on an exact trace formula for a one-dimensional ray-splitting system, we derive novel combinatorial identities for cyclic binary sequences (P\'olya necklaces).Comment: 15 page

Can One Hear the Shape of a Graph?

We show that the spectrum of the Schrodinger operator on a finite, metric graph determines uniquely the connectivity matrix and the bond lengths, provided that the lengths are non-commensurate and the connectivity is simple (no parallel bonds between vertices and no loops connecting a vertex to itself). That is, one can hear the shape of the graph! We also consider a related inversion problem: A compact graph can be converted into a scattering system by attaching to its vertices leads to infinity. We show that the scattering phase determines uniquely the compact part of the graph, under similar conditions as above.Comment: 9 pages, 1 figur

Periodic-Orbit Theory of Anderson Localization on Graphs

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an a-periodic Kronig-Penney model in one dimension. The exact expression for the probability to return of an initially localized state is computed in terms of classical trajectories. It saturates to a finite value due to localization, while the diagonal approximation decays diffusively. Our theory is based on the identification of families of isometric orbits. The coherent periodic-orbit sums within these families, and the summation over all families are performed analytically using advanced combinatorial methods.Comment: 4 pages, 3 figures, RevTe

Transport and dynamics on open quantum graphs

We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular we consider extended open graphs whose classical dynamics generate a diffusion process. The transport properties of the classical system are revealed in the scattering resonances and in the time evolution of the quantum system.Comment: 42 pages, 13 figures, submitted to PR

Shot noise from action correlations

We consider universal shot noise in ballistic chaotic cavities from a semiclassical point of view and show that it is due to action correlations within certain groups of classical trajectories. Using quantum graphs as a model system we sum these trajectories analytically and find agreement with random-matrix theory. Unlike all action correlations which have been considered before, the correlations relevant for shot noise involve four trajectories and do not depend on the presence of any symmetry.Comment: 4 pages, 2 figures (a mistake in version 1 has been corrected

Self-directed passive-aggressive behaviour as an essential component of depression: findings from two cross-sectional observational studies

Background: The self-control model of depression suggests depressive symptoms to derive from distorted self-monitoring, dysfunctional self-evaluation and reduced self-reward as well as increased self-punishment. Building on this model a relationship between self-directed passive-aggressive behaviour, that is, harmful inactivity, and depression has been assumed. This association has been supported by a recent study in an inpatient sample. However, it remains unclear if patients with depressive disorders report more self-directed passive-aggressive behaviour than patients without depressive disorders and if self-directed passive aggression mediates the associations between distorted selfmonitoring and dysfunctional self-evaluation with depressive symptoms. Methods: Study 1 compared self-directed passive-aggressive behaviour levels between 220 psychotherapy outpatients with (n=140; 67.9% female; Mage=40.0) and without (n=80; 65.0% female; Mage=36.2) depressive disorders. Diagnoses were made based on the Structured Clinical Interview for DSM-IV. Study 2 examined self-directed passiveaggressive behaviour as a mediator of the relationship between distorted self-monitoring and dysfunctional selfevaluation and self-reported depressive symptoms in 200 undergraduate Psychology students. Results: Compared to outpatients without depressive disorders, outpatients with depressive disorder reported signifcantly more self-directed passive aggression (d=0.51). Furthermore, Study 2 verifed self-directed passiveaggressive behaviour as a partial mediator of the relationship between dysfunctional attitudes (abcs=.22, 95%-CI: .14, .31), attributional style (abcs=.20, 95%-CI: .13, .27), ruminative response style (abcs=.15, 95%-CI: .09, .21) and depressive symptoms. Conclusion: Self-directed passive-aggressive behaviour partially mediates the association between distorted selfmonitoring and dysfunctional self-evaluation with depressive symptoms. Future longitudinal studies need to examine a potential causal relationship that would form a base to include interventions targeting self-directed passive-aggressive behaviour in prevention and treatment of depression. Trial registration: Both studies were preregistered at the German Clinical Trials Register (DRKS00014005 and DRKS00019020)

Three-point correlations for quantum star graphs

We compute the three point correlation function for the eigenvalues of the Laplacian on quantum star graphs in the limit where the number of edges tends to infinity. This extends a work by Berkolaiko and Keating, where they get the 2-point correlation function and show that it follows neither Poisson, nor random matrix statistics. It makes use of the trace formula and combinatorial analysis.Comment: 10 pages, 2 figure