Multiplicative processes and power laws

[Takayasu et al., Phys. Rev.Lett. 79, 966 (1997)] revisited the question of stochastic processes with multiplicative noise, which have been studied in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with multiplicative noise produce intermittency of a special kind, characterized by a power law probability density distribution. We briefly explain the physical mechanism leading to a power law pdf and provide a list of references for these results dating back from a quarter of century. We explain how the formulation in terms of the characteristic function developed by Takayasu et al. can be extended to exponents $\mu >2$, which explains the ``reason of the lucky coincidence''. The multidimensional generalization of (\ref{eq1}) and the available results are briefly summarized. The discovery of stretched exponential tails in the presence of the cut-off introduced in \cite{Taka} is explained theoretically. We end by briefly listing applications.Comment: Extended version (7 pages). Phys. Rev. E (to appear April 1998

Assessment of left ventricular ejection fraction in patients eligible for ICD therapy: Discrepancy between cardiac magnetic resonance imaging and 2D echocardiography

OBJECTIVE: Implantable cardioverter defibrillators (ICD) and cardiac resynchronisation therapy (CRT) have substantially improved the survival of patients with cardiomyopathy. Eligibility for this therapy requires a left ventricular ejection fraction (LVEF) <35 %. This is largely based on studies using echocardiography. Cardiac magnetic resonance imaging (CMR) is increasingly utilised for LVEF assessment, but several studies have shown differences between LVEF assessed by CMR and echocardiography. The present study compared LVEF assessment by CMR and echocardiography in a heart failure population and evaluated effects on eligibility for device therapy. METHODS: 152 patients (106 male, mean age 65.5 ± 9.9 years) referred for device therapy were included. During evaluation of eligibility they underwent both CMR and echocardiographic LVEF assessment. CMR volumes were computed from a stack of short-axis images. Echocardiographic volumes were computed using Simpson’s biplane method. RESULTS: The study population demonstrated an underestimation of end-diastolic volume (EDV) and end-systolic volume (ESV) by echocardiography of 71 ± 53 ml (mean ± SD) and 70 ± 49 ml, respectively. This resulted in an overestimation of LVEF of 6.6 ± 8.3 % by echocardiography compared with CMR (echocardiographic LVEF 31.5 ± 8.7 % and CMR LVEF 24.9 ± 9.6 %). 28 % of patients had opposing outcomes of eligibility for cardiac device therapy depending on the imaging modality used. CONCLUSION: We found EDV and ESV to be underestimated by echocardiography, and LVEF assessed by CMR to be significantly smaller than by echocardiography. Applying an LVEF cut-off value of 35 %, CMR would significantly increase the number of patients eligible for device implantation. Therefore, LVEF cut-off values might need reassessment when using CMR

Parameterized Compilation Lower Bounds for Restricted CNF-formulas

We show unconditional parameterized lower bounds in the area of knowledge compilation, more specifically on the size of circuits in decomposable negation normal form (DNNF) that encode CNF-formulas restricted by several graph width measures. In particular, we show that - there are CNF formulas of size $n$ and modular incidence treewidth $k$ whose smallest DNNF-encoding has size $n^{\Omega(k)}$, and - there are CNF formulas of size $n$ and incidence neighborhood diversity $k$ whose smallest DNNF-encoding has size $n^{\Omega(\sqrt{k})}$. These results complement recent upper bounds for compiling CNF into DNNF and strengthen---quantitatively and qualitatively---known conditional low\-er bounds for cliquewidth. Moreover, they show that, unlike for many graph problems, the parameters considered here behave significantly differently from treewidth

Modification of maleic anhydride grafted polyethylene with 1,4-diaminobutane in near critical propane

Granules of high density polyethylene grafted with 0.17 wt.% maleic anhydride (PEMA) were modified with an excess of 1,4-diaminobutane (DAB) by impregnation from near critical propane. After formation of amic acid groups, the excess of diaminobutane was extracted with a near critical propane–ethanol mixture (95/5 wt.%). Finally, the obtained PEMA–DAB was imidised quantitatively to the corresponding imide (PEMI) in the melt. The obtained PEMI showed no increased gel content with respect to the PEMA. The presence of primary amine groups was indirectly proven by selective extraction experiments. It appeared that PEMI samples had reacted with the anhydride groups of styrene-MA copolymer (SMA) during melt blending of SMA with PEMI, while the PEMA had not reacted. SMA/PEMI 80/20 blends consisted of a continuous SMA phase and PEMI droplets with a diameter of less than 1 μm. SMA/PEMA 80/20 blends showed a course morphology of PEMA strings in a continuous SMA phase. With this article we have shown that this new technique for the chemical modification of swollen HDPE particles in near critical propane has proven to be much better than the conventional modification in the melt, when it comes to avoiding crosslinking

Developmental trajectories of infants born at less than 30 weeks' gestation on the Bayley-III Scales

OBJECTIVE: To describe the cognitive, language and motor developmental trajectories of children born very preterm and to identify perinatal factors that predict the trajectories. DESIGN: Data from a cohort of 1142 infants born at <30 weeks' gestation who were prospectively assessed on the Bayley Scales of Infant and Toddler Development, third edition (Bayley-III) at 3, 6, 12 and 24 months corrected age, were analysed using the Super Imposition by Translation and Rotation (SITAR) growth curve analysis model. MAIN OUTCOME MEASURES: Developmental trajectory SITAR models for Bayley-III cognitive, language (receptive and expressive communication subscales) and motor (fine and gross motor subscales) scores. RESULTS: The successfully fitted SITAR models explained 62% of variance in cognitive development, 68% in receptive communication, 53% in fine motor and 68% in the gross motor development. There was too much variation in the expressive communication subscale to fit a SITAR model. The rate of development (gradient of the curve) best explains the variation in trajectories of development in all domains. Lower gestational age, lower birth weight and male sex significantly predicted a slower rate of development. CONCLUSION: The rate of development, rather than single time point developmental assessment, best predicts the very preterm infant's developmental trajectory and should be the focus for monitoring and early intervention

Pathways from speech illusions to psychotic symptoms in subjects at Ultra-High Risk for psychosis: combining an experimental measure of aberrant experiences with network analysis

Background One of the oldest and most influential theories of psychosis formation states that delusions arise in an attempt to explain unusual experiences, including perceptual aberrations. The White Noise Task by Galdos et al (2011) was developed as an experimental task to assess the tendency to attribute meaning to random perceptual stimuli: speech illusions in white noise. Studies to date have demonstrated that speech illusions as assessed with the White Noise Task are associated with a composite measure of positive symptoms in patients with psychotic disorders (Galdos et al, 2011; Catalan et al, 2014). However, findings in non-clinical samples have been inconsistent: one study found an association with a composite measure of subclinical positive symptoms, including support for a relation with familial psychosis liability (Galdos et al, 2011), whereas other studies did not find any association in non-clinical samples or only partly (Catalan et al, 2014; Rimvall et al, 2016; Pries et al, 2017). The current study aims to further examine whether speech illusions as assessed with the White Noise Task are indicative of psychosis liability and to explore specific symptomatic pathways. Methods We conducted symptom-based network analyses in Ultra-High Risk (UHR) subjects participating in the European network of national networks studying gene-environment interactions in schizophrenia project (EU-GEI, 2014; www.eu-gei.eu). Psychotic symptoms were assessed with the Brief Psychiatric Rating Scale (BPRS). Transition to clinical psychosis was assessed with the Comprehensive Assessment of At Risk Mental State (CAARMS). We used a conservative measure of speech illusions, as described in Catalan et al (2014). Results The current sample consisted of 339 UHR subjects, of which 9.1% (N=31) experienced speech illusions. Preliminary network analyses in cross-sectional baseline data showed potential pathways from speech illusions to delusional ideation, through hallucinatory experiences. We also found evidence of prospective relations between speech illusions at baseline and transition to clinical psychosis. Pathways ran via baseline psychotic symptoms and affective symptoms, as well as a ‘direct’ pathway. Discussion As far as we are aware, this is the first study combining an experimental measure of aberrant experiences with symptom-based network analysis. Although the current reported findings are preliminary and exploratory, they tentatively support a relation between speech illusions as assessed with the White Noise Task and psychosis liability. This relation may be dependent on sample composition, and not generalizable to the general population as a whole. Future studies may benefit from focusing on more detailed trajectories of both susceptibility to speech illusions and course of (sub)clinical psychotic symptom severity in subjects with increased risk for psychosis, with use of more frequent, short assessment periods and inclusion of environmental risk factors for transition to clinical disorder