All scale-free networks are sparse

We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse.Comment: 4 pages, 2 figure

Network Inoculation: Heteroclinics and phase transitions in an epidemic model

In epidemiological modelling, dynamics on networks, and in particular adaptive and heterogeneous networks have recently received much interest. Here we present a detailed analysis of a previously proposed model that combines heterogeneity in the individuals with adaptive rewiring of the network structure in response to a disease. We show that in this model qualitative changes in the dynamics occur in two phase transitions. In a macroscopic description one of these corresponds to a local bifurcation whereas the other one corresponds to a non-local heteroclinic bifurcation. This model thus provides a rare example of a system where a phase transition is caused by a non-local bifurcation, while both micro- and macro-level dynamics are accessible to mathematical analysis. The bifurcation points mark the onset of a behaviour that we call network inoculation. In the respective parameter region exposure of the system to a pathogen will lead to an outbreak that collapses, but leaves the network in a configuration where the disease cannot reinvade, despite every agent returning to the susceptible class. We argue that this behaviour and the associated phase transitions can be expected to occur in a wide class of models of sufficient complexity.Comment: 26 pages, 11 figure

Two-dimensional macroscopic quantum dynamics in YBCO Josephson junctions

We theoretically study classical thermal activation (TA) and macroscopic quantum tunneling (MQT) for a YBCO Josephson junction coupled with an LC circuit. The TA and MQT escape rate are calculated by taking into account the two-dimensional nature of the classical and quantum phase dynamics. We find that the MQT escape rate is largely suppressed by the coupling to the LC circuit. On the other hand, this coupling leads to the slight reduction of the TA escape rate. These results are relevant for the interpretation of a recent experiment on the MQT and TA phenomena in YBCO bi-epitaxial Josephson junctions.Comment: 9 pages, 2 figure

Transdiagnostic treatment of bipolar disorder and comorbid anxiety using the Unified Protocol for Emotional Disorders: A pilot feasibility and acceptability trial

BACKGROUND Comorbid anxiety in bipolar disorder (BD) is associated with greater illness severity, reduced treatment response, and greater impairment. Treating anxiety in the context of BD is crucial for improving illness course and outcomes. The current study examined the feasibility, acceptability and preliminary efficacy of the Unified Protocol (UP), a transdiagnostic cognitive behavioral therapy, as an adjunctive treatment to pharmacotherapy for BD and comorbid anxiety disorders. METHODS Twenty-nine patients with BD and at least one comorbid anxiety disorder were randomized to pharmacotherapy treatment-as-usual (TAU) or TAU with 18 sessions of the UP (UP+TAU). All patients completed assessments every four weeks to track symptoms, functioning, emotion regulation and temperament. Linear mixed-model regressions were conducted to track symptom changes over time and to examine the relationship between emotion-related variables and treatment response. RESULTS Satisfaction ratings were equivalent for both treatment groups. Patients in the UP+TAU group evidenced significantly greater reductions over time in anxiety and depression symptoms (Cohen's d's>0.80). Baseline levels of neuroticism, perceived affective control, and emotion regulation ability predicted magnitude of symptom change for the UP+TAU group only. Greater change in perceived control of emotions and emotion regulation skills predicted greater change in anxiety related symptoms. LIMITATIONS This was a pilot feasibility and acceptability trial; results should be interpreted with caution. CONCLUSIONS Treatment with the UP+TAU was rated high in patient satisfaction, and resulted in significantly greater improvement on indices of anxiety and depression relative to TAU. This suggests that the UP may be a feasible treatment approach for BD with comorbid anxiety.This work was supported by a Postdoctoral National Research Service Award from the National Institutes of Health [F32 MH098490] to K. Ellard. (F32 MH098490 - Postdoctoral National Research Service Award from the National Institutes of Health)Accepted manuscrip

Neurocognitive Predictors of Treatment Response to Randomized Treatment in Adults with Tic Disorders

Tourette\u27s disorder (TS) and chronic tic disorder (CTD) are neurodevelopmental disorders characterized by involuntary vocal and motor tics. Consequently, TS/CTD have been conceptualized as disorders of cognitive and motor inhibitory control. However, most neurocognitive studies have found comparable or superior inhibitory capacity among individuals with TS/CTD relative to healthy controls. These findings have led to the hypothesis that individuals with TS/CTD develop increased inhibitory control due to the constant need to inhibit tics. However, the role of cognitive control in TS/CTD is not yet understood, particularly in adults. To examine the role of inhibitory control in TS/CTD, the present study investigated this association by assessing the relationship between inhibitory control and treatment response in a large sample of adults with TS/CTD. As part of a large randomized trial comparing behavior therapy versus supportive psychotherapy for TS/CTD, a battery of tests, including tests of inhibitory control was administered to 122 adults with TS/CTD at baseline. We assessed the association between neuropsychological test performance and change in symptom severity, as well as compared the performance of treatment responders and non-responders as defined by the Clinical Global Impression Scale. Results indicated that change in symptoms, and treatment response were not associated with neuropsychological performance on tests of inhibitory control, intellectual ability, or motor function, regardless of type of treatment. The finding that significant change in symptom severity of TS/CTD patients is not associated with impairment or change in inhibitory control regardless of treatment type suggests that inhibitory control may not be a clinically relevant facet of these disorders in adults

Disorder Induced Stripes in d-Wave Superconductors

Stripe phases are observed experimentally in several copper-based high-Tc superconductors near 1/8 hole doping. However, the specific characteristics may vary depending on the degree of dopant disorder and the presence or absence of a low- temperature tetragonal phase. On the basis of a Hartree-Fock decoupling scheme for the t-J model we discuss the diverse behavior of stripe phases. In particular the effect of inhomogeneities is investigated in two distinctly different parameter regimes which are characterized by the strength of the interaction. We observe that small concen- trations of impurities or vortices pin the unidirectional density waves, and dopant disorder is capable to stabilize a stripe phase in parameter regimes where homogeneous phases are typically favored in clean systems. The momentum-space results exhibit universal features for all coexisting density-wave solutions, nearly unchanged even in strongly disordered systems. These coexisting solutions feature generically a full energy gap and a particle-hole asymmetry in the density of states.Comment: 28 pages, 8 figure

Dark matter within high surface brightness spiral galaxies

We present results from a detailed dynamical analysis of five high surface brightness, late type spirals, studied with the aim to quantify the luminous-to-dark matter ratio inside their optical radii. The galaxies' stellar light distribution and gas kinematics have been observed and compared to hydrodynamic gas simulations, which predict the 2D gas dynamics arising in response to empirical gravitational potentials, which are combinations of differing stellar disk and dark halo contributions. The gravitational potential of the stellar disk was derived from near-infrared photometry, color-corrected to constant (M/L); the dark halo was modelled by an isothermal sphere with a core. Hydrodynamic gas simulations were performed for each galaxy for a sequence of five different mass fractions of the stellar disk and for a wide range of spiral pattern speeds. These two parameters mainly determine the modelled gas distribution and kinematics. The agreement between the non-axisymmetric part of the simulated and observed gas kinematics permitted us to conclude that the galaxies with the highest rotation velocities tend to possess near-maximal stellar disks. In less massive galaxies, with v_max<200 km/s, the mass of the dark halo at least equals the stellar mass within 2-3 R_disk. The simulated gas morphology provides a powerful tool to determine the dominant spiral pattern speed. The corotation radius for all galaxies was found to be constant at R_corotation ~ 3 R_disk and encloses the strong part of the stellar spiral in all cases.Comment: 28 pages, 7 figures; to appear in the Astrophysical Journal, Vol. 586, March 200

Adaptive self-organization in a realistic neural network model

Information processing in complex systems is often found to be maximally efficient close to critical states associated with phase transitions. It is therefore conceivable that also neural information processing operates close to criticality. This is further supported by the observation of power-law distributions, which are a hallmark of phase transitions. An important open question is how neural networks could remain close to a critical point while undergoing a continual change in the course of development, adaptation, learning, and more. An influential contribution was made by Bornholdt and Rohlf, introducing a generic mechanism of robust self-organized criticality in adaptive networks. Here, we address the question whether this mechanism is relevant for real neural networks. We show in a realistic model that spike-time-dependent synaptic plasticity can self-organize neural networks robustly toward criticality. Our model reproduces several empirical observations and makes testable predictions on the distribution of synaptic strength, relating them to the critical state of the network. These results suggest that the interplay between dynamics and topology may be essential for neural information processing.Comment: 6 pages, 4 figure