Growing Networks: Limit in-degree distribution for arbitrary out-degree one

We compute the stationary in-degree probability, $P_{in}(k)$, for a growing network model with directed edges and arbitrary out-degree probability. In particular, under preferential linking, we find that if the nodes have a light tail (finite variance) out-degree distribution, then the corresponding in-degree one behaves as $k^{-3}$. Moreover, for an out-degree distribution with a scale invariant tail, $P_{out}(k)\sim k^{-\alpha}$, the corresponding in-degree distribution has exactly the same asymptotic behavior only if $2<\alpha<3$ (infinite variance). Similar results are obtained when attractiveness is included. We also present some results on descriptive statistics measures %descriptive statistics such as the correlation between the number of in-going links, $D_{in}$, and outgoing links, $D_{out}$, and the conditional expectation of $D_{in}$ given $D_{out}$, and we calculate these measures for the WWW network. Finally, we present an application to the scientific publications network. The results presented here can explain the tail behavior of in/out-degree distribution observed in many real networks.Comment: 12 pages, 6 figures, v2 adds a section on descriptive statistics, an analisis on www network, typos adde

Emergent complex neural dynamics

A large repertoire of spatiotemporal activity patterns in the brain is the basis for adaptive behaviour. Understanding the mechanism by which the brain's hundred billion neurons and hundred trillion synapses manage to produce such a range of cortical configurations in a flexible manner remains a fundamental problem in neuroscience. One plausible solution is the involvement of universal mechanisms of emergent complex phenomena evident in dynamical systems poised near a critical point of a second-order phase transition. We review recent theoretical and empirical results supporting the notion that the brain is naturally poised near criticality, as well as its implications for better understanding of the brain

Ultrashort filaments of light in weakly-ionized, optically-transparent media

Modern laser sources nowadays deliver ultrashort light pulses reaching few cycles in duration, high energies beyond the Joule level and peak powers exceeding several terawatt (TW). When such pulses propagate through optically-transparent media, they first self-focus in space and grow in intensity, until they generate a tenuous plasma by photo-ionization. For free electron densities and beam intensities below their breakdown limits, these pulses evolve as self-guided objects, resulting from successive equilibria between the Kerr focusing process, the chromatic dispersion of the medium, and the defocusing action of the electron plasma. Discovered one decade ago, this self-channeling mechanism reveals a new physics, widely extending the frontiers of nonlinear optics. Implications include long-distance propagation of TW beams in the atmosphere, supercontinuum emission, pulse shortening as well as high-order harmonic generation. This review presents the landmarks of the 10-odd-year progress in this field. Particular emphasis is laid to the theoretical modeling of the propagation equations, whose physical ingredients are discussed from numerical simulations. Differences between femtosecond pulses propagating in gaseous or condensed materials are underlined. Attention is also paid to the multifilamentation instability of broad, powerful beams, breaking up the energy distribution into small-scale cells along the optical path. The robustness of the resulting filaments in adverse weathers, their large conical emission exploited for multipollutant remote sensing, nonlinear spectroscopy, and the possibility to guide electric discharges in air are finally addressed on the basis of experimental results.Comment: 50 pages, 38 figure

Retrieving the structure of probabilistic sequences of auditory stimuli from EEG data

Using a new probabilistic approach we model the relationship between sequences of auditory stimuli generated by stochastic chains and the electroencephalographic (EEG) data acquired while 19 participants were exposed to those stimuli. The structure of the chains generating the stimuli are characterized by rooted and labeled trees whose leaves, henceforth called contexts, represent the sequences of past stimuli governing the choice of the next stimulus. A classical conjecture claims that the brain assigns probabilistic models to samples of stimuli. If this is true, then the context tree generating the sequence of stimuli should be encoded in the brain activity. Using an innovative statistical procedure we show that this context tree can effectively be extracted from the EEG data, thus giving support to the classical conjecture.Comment: 16 pages, 7 figure

Towards affordable biomarkers of frontotemporal dementia: A classification study via network's information sharing

Developing effective and affordable biomarkers for dementias is critical given the difficulty to achieve early diagnosis. In this sense, electroencephalographic (EEG) methods offer promising alternatives due to their low cost, portability, and growing robustness. Here, we relied on EEG signals and a novel information-sharing method to study resting-state connectivity in patients with behavioral variant frontotemporal dementia (bvFTD) and controls. To evaluate the specificity of our results, we also tested Alzheimer's disease (AD) patients. The classification power of the ensuing connectivity patterns was evaluated through a supervised classification algorithm (support vector machine). In addition, we compared the classification power yielded by (i) functional connectivity, (ii) relevant neuropsychological tests, and (iii) a combination of both. BvFTD patients exhibited a specific pattern of hypoconnectivity in mid-range frontotemporal links, which showed no alterations in AD patients. These functional connectivity alterations in bvFTD were replicated with a low-density EEG setting (20 electrodes). Moreover, while neuropsychological tests yielded acceptable discrimination between bvFTD and controls, the addition of connectivity results improved classification power. Finally, classification between bvFTD and AD patients was better when based on connectivity than on neuropsychological measures. Taken together, such findings underscore the relevance of EEG measures as potential biomarker signatures for clinical settings

Collapse of solitary waves near transition from supercritical to subcritical bifurcations

We study both analytically and numerically the nonlinear stage of the instability of one-dimensional solitons in a small vicinity of the transition point from supercritical to subcritical bifurcations in the framework of the generalized nonlinear Schr\"{o}dinger equation. It is shown that near the collapsing time the pulse amplitude and its width demonstrate the self-similar behavior with a small asymmetry at the pulse tails due to self-steepening. This theory is applied to both solitary interfacial deep-water waves and envelope water waves with a finite depth and short optical pulses in fibers as well

Retrospective study investigating naloxone prescribing and cost in US Medicaid and Medicare patients

Background Opioid overdoses in the USA have increased to unprecedented levels. Administration of the opioid antagonist naloxone can prevent overdoses. Objective This study was conducted to reveal the pharmacoepidemiologic patterns in naloxone prescribing to Medicaid patients from 2018 to 2021 as well as Medicare in 2019. Design Observational pharmacoepidemiologic study Setting US Medicare and Medicaid naloxone claims Intervention The Medicaid State Drug Utilisation Data File was utilised to extract information on the number of prescriptions and the amount prescribed of naloxone at a national and state level. The Medicare Provider Utilisation and Payment was also utilised to analyse prescription data from 2019. Outcome measures States with naloxone prescription rates that were outliers of quartile analysis were noted. Results The number of generic naloxone prescriptions per 100 000 Medicaid enrollees decreased by 5.3%, whereas brand naloxone prescriptions increased by 245.1% from 2018 to 2021. There was a 33.1-fold difference in prescriptions between the highest (New Mexico=1809.5) and lowest (South Dakota=54.6) states in 2019. Medicare saw a 30.4-fold difference in prescriptions between the highest (New Mexico) and lowest states (also South Dakota) after correcting per 100 000 enrollees. Conclusions This pronounced increase in the number of naloxone prescriptions to Medicaid patients from 2018 to 2021 indicates a national response to this widespread public health emergency. Further research into the origins of the pronounced state-level disparities is warranted