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

Psychiatric disturbances regulate the innate immune system in CSF of conscious mice

Environment may affect brain activity through cerebrospinal fluid (CSF) only if there are regulatory molecules or cascades in CSF that are sensitive to external stimuli. This study was designed to identify regulatory activity present in CSF, better elucidating environmental regulation of brain function. By using cannulation-based sequential CSF sampling coupled with mass spectrometry-based identification and quantification of proteins, we show that the naive mouse CSF harbors, among 22 other pathways, the innate immune system as a main pathway, which was downregulated and upregulated, respectively, by acute stressor (AS) and acute cocaine (AC) administrations. Among novel processes and molecular functions, AS also regulated schizophrenia-associated proteins. Furthermore, AC upregulated exosome-related proteins with a false discovery rate of 1.0 × 10−16. These results suggest that psychiatric disturbances regulate the neuroimmune system and brain disorder-related proteins, presenting a sensitive approach to investigating extracellular mechanisms in conscious and various mouse models of psychiatric disorders

Spin-Boson Hamiltonian and Optical Absorption of Molecular Dimers

An analysis of the eigenstates of a symmetry-broken spin-boson Hamiltonian is performed by computing Bloch and Husimi projections. The eigenstate analysis is combined with the calculation of absorption bands of asymmetric dimer configurations constituted by monomers with nonidentical excitation energies and optical transition matrix elements. Absorption bands with regular and irregular fine structures are obtained and related to the transition from the coexistence to a mixing of adiabatic branches in the spectrum. It is shown that correlations between spin states allow for an interpolation between absorption bands for different optical asymmetries.Comment: 15 pages, revTeX, 8 figures, accepted for publication in Phys. Rev.

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)