Short disjoint cycles in graphs with degree constraints

AbstractWe show that each finite undirected graph G = (V, E), |V| = n, |E|= m with minimum degree δ(G) ⩾ 3 and maximum degree Δ = Δ(G) contains at least n/[4(Δ − 1)log2n] pairwise vertex-disjoint cycles of length at most 4(Δ − 1)log2n. Furthermore collections of such cycles can be determined within O(n(n + m)) steps. For constant Δ this means Ω(n/log n) cycles of length O(log n). This bound is also an optimum.A similar approach yields similar bounds for subgraphs with more edges than vertices instead of cycles. Furthermore also collections of many small pairwise disjoint induced subgraphs of this type can be determined within O(n(n + m)) steps similarly as for cycles

The cardiorespiratory network in healthy first-degree relatives of schizophrenic patients

Impaired heart rate- and respiratory regulatory processes as a sign of an autonomic dysfunction seems to be obviously present in patients suffering from schizophrenia. Since the linear and non-linear couplings within the cardiorespiratory system with respiration as an important homeostatic control mechanism are only partially investigated so far for those subjects, we aimed to characterize instantaneous cardiorespiratory couplings by quantifying the casual interaction between heart rate (HR) and respiration (RESP). Therefore, we investigated causal linear and non-linear cardiorespiratory couplings of 23 patients suffering from schizophrenia (SZO), 20 healthy first-degree relatives (REL) and 23 healthy subjects, who were age-gender matched (CON). From all participants’ heart rate (HR) and respirations (respiratory frequency, RESP) were investigated for 30 min under resting conditions. The results revealed highly significant increased HR, reduced HR variability, increased respiration rates and impaired cardiorespiratory couplings in SZO in comparison to CON. SZO were revealed bidirectional couplings, with respiration as the driver (RESP → HR), and with weaker linear and non-linear coupling strengths when RESP influencing HR (RESP → HR) and with stronger linear and non-linear coupling strengths when HR influencing RESP (HR → RESP). For REL we found only significant increased HR and only slightly reduced cardiorespiratory couplings compared to CON. These findings clearly pointing to an underlying disease-inherent genetic component of the cardiac system for SZO and REL, and those respiratory alterations are only clearly present in SZO seem to be connected to their mental emotional states

Observation of giant two-level systems in a granular superconductor

Disordered thin films are a common choice of material for superconducting, high impedance circuits used in quantum information or particle detector physics. A wide selection of materials with different levels of granularity are available, but, despite low microwave losses being reported for some, the high degree of disorder always implies the presence of intrinsic defects. Prominently, quantum circuits are prone to interact with two-level systems (TLS), typically originating from solid state defects in the dielectric parts of the circuit, like surface oxides or tunneling barriers. We present an experimental investigation of TLS in granular aluminum thin films under applied mechanical strain and electric fields. The analysis reveals a class of strongly coupled TLS having electric dipole moments up to 30 eA, an order of magnitude larger than dipole moments commonly reported for solid state defects. Notably, these large dipole moments appear more often in films with a higher resistivity. Our observations shed new light on granular superconductors and may have implications for their usage as a quantum circuit material.Comment: 12 pages, 8 figure

Multivariate linear and nonlinear central-cardiorespiratory coupling pathways in healthy subjects

Postprint (published version

Altered causal coupling pathways within the central-autonomic-network in patients suffering from schizophrenia

The multivariate analysis of coupling pathways within physiological (sub)systems focusing on identifying healthy and diseased conditions. In this study, we investigated a part of the central-autonomic-network (CAN) in 17 patients suffering from schizophrenia (SZO) compared to 17 age–gender matched healthy controls (CON) applying linear and nonlinear causal coupling approaches (normalized short time partial directed coherence, multivariate transfer entropy). Therefore, from all subjects continuous heart rate (successive beat-to-beat intervals, BBI), synchronized maximum successive systolic blood pressure amplitudes (SYS), synchronized calibrated respiratory inductive plethysmography signal (respiratory frequency, RESP), and the power PEEG of frontal EEG activity were investigated for 15 min under resting conditions. The CAN revealed a bidirectional coupling structure, with central driving towards blood pressure (SYS), and respiratory driving towards PEEG. The central-cardiac, central-vascular, and central-respiratory couplings are more dominated by linear regulatory mechanisms than nonlinear ones. The CAN showed significantly weaker nonlinear central-cardiovascular and central-cardiorespiratory coupling pathways, and significantly stronger linear central influence on the vascular system, and on the other hand significantly stronger linear respiratory and cardiac influences on central activity in SZO compared to CON, and thus, providing better understanding of the interrelationship of central and autonomic regulatory mechanisms in schizophrenia might be useful as a biomarker of this diseas

Correlation between autonomic dysfunction and impaired microcirculation in patients with schizophrenia

Patients suffering from schizophrenia have an increased mortality risk due to cardiovascular events that might be associated with cardiac autonomic dysfunction. The aim of this study was to analyse the interdependencies between indices of autonomic regulation from heart rate and blood pressure variability, and spectral indices of Laser-Doppler-Flowmetry signals, reflecting the condition of the microcirculatory system. Therefore, we compared the correlation between indices in controls with indices in schizophrenic patients. We found that short term interaction between autonomic regulation and microcirculation decreases in schizophrenic patients compared to healthy controls while the permanently increased heart rate in patients is highly correlated with a periphery endothelial and sympathetic activation