Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled activation subunits, while the DA was modeled using uncoupled activation subunits. Implementations of DA with coupled subunits, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable - allowing an easy and efficient DA implementation. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods.Comment: 32 text pages, 10 figures, 1 supplementary text + figur

Tipping points in the dynamics of speciation.

Speciation can be gradual or sudden and involve few or many genetic changes. Inferring the processes generating such patterns is difficult, and may require consideration of emergent and non-linear properties of speciation, such as when small changes at tipping points have large effects on differentiation. Tipping points involve positive feedback and indirect selection stemming from associations between genomic regions, bi-stability due to effects of initial conditions and evolutionary history, and dependence on modularity of system components. These features are associated with sudden 'regime shifts' in other cellular, ecological, and societal systems. Thus, tools used to understand other complex systems could be fruitfully applied in speciation research

Evolution of active galactic nuclei

[Abriged] Supermassive black holes (SMBH) lurk in the nuclei of most massive galaxies, perhaps in all of them. The tight observed scaling relations between SMBH masses and structural properties of their host spheroids likely indicate that the processes fostering the growth of both components are physically linked, despite the many orders of magnitude difference in their physical size. This chapter discusses how we constrain the evolution of SMBH, probed by their actively growing phases, when they shine as active galactic nuclei (AGN) with luminosities often in excess of that of the entire stellar population of their host galaxies. Following loosely the chronological developments of the field, we begin by discussing early evolutionary studies, when AGN represented beacons of light probing the most distant reaches of the universe and were used as tracers of the large scale structure. This early study turned into AGN "Demography", once it was realized that the strong evolution (in luminosity, number density) of the AGN population hindered any attempt to derive cosmological parameters from AGN observations directly. Following a discussion of the state of the art in the study of AGN luminosity functions, we move on to discuss the "modern" view of AGN evolution, one in which a bigger emphasis is given to the physical relationships between the population of growing black holes and their environment. This includes observational and theoretical efforts aimed at constraining and understanding the evolution of scaling relations, as well as the resulting limits on the evolution of the SMBH mass function. Physical models of AGN feedback and the ongoing efforts to isolate them observationally are discussed next. Finally, we touch upon the problem of when and how the first black holes formed and the role of black holes in the high-redshift universe.Comment: 75 pages, 35 figures. Modified version of the chapter accepted to appear in "Planets, Stars and Stellar Systems", vol 6, ed W. Keel (www.springer.com/astronomy/book/978-90-481-8818-5). The number of references is limited upon request of the editors. Original submission to Springer: June 201

The use of a standardized order set reduces systemic corticosteroid dose and length of stay for individuals hospitalized with acute exacerbations of COPD: a cohort study

Swati Gulati,1–3 Aline N Zouk,1–3 Jonathan P Kalehoff,4 Christopher S Wren,5 Peter N Davison,6 Denay Porter Kirkpatrick,1–3 Surya P Bhatt,1–3 Mark T Dransfield,1–3,7 James Michael Wells1–3,7 1Department of Medicine, University of Alabama at Birmingham (UAB), Birmingham, AL, USA; 2Division of Pulmonary, Allergy, and Critical Care Medicine, University of Alabama at Birmingham (UAB), Birmingham, AL, USA; 3UAB Lung Health Center, Birmingham, AL, USA; 4Division of Internal Medicine, University of Alabama at Birmingham (UAB), Birmingham, AL, USA; 5Harrison School of Pharmacy, Auburn University, Auburn, AL, USA; 6University of Alabama at Birmingham School of Medicine, Birmingham, AL, USA; 7Birmingham VA Medical Center, Birmingham, AL, USA Background: Systemic corticosteroids (SC) are an integral part of managing acute exacerbations of COPD (AECOPD). However, the optimal dose and duration vary widely in clinical practice. We hypothesized that the use of a “PowerPlan” order set in the electronic health system (EHS) that includes a 5-day SC order would be associated with a reduced steroid dose and length of stay (LOS) for individuals hospitalized with AECOPD. Patients and methods: We conducted a retrospective cohort study of Medicare recipients discharged with an AECOPD diagnosis from our University Hospital from 2014 to 2016. Our EHS-based “COPD PowerPlan” order set included admission, laboratory, pharmacy, and radiology orders for managing AECOPD. The default SC option included intravenous methylprednisolone for 24 hours followed by oral prednisone for 4 days. The primary endpoint was the difference in cumulative steroid dose between the PowerPlan and the usual care group. Secondary endpoints included hospital LOS and readmission rates. Results: The 250 patients included for analysis were 62±11 years old, 58% male, with an FEV1 55.1%±23.6% predicted. The PowerPlan was used in 72 (29%) patients. Cumulative steroid use was decreased by 31% in the PowerPlan group (420±224 vs 611±462 mg, P<0.001) when compared with usual care. PowerPlan use was independently associated with decreased LOS (3 days; IQR 2–4 days vs 4 days; IQR 3–6 days, P=0.022) without affecting 30- and 90-day readmission rates. Conclusion: Use of a standardized EHS-based order set to manage AECOPD was associated with a reduction in steroid dose and hospital LOS. Keywords: COPD exacerbation, treatment, corticosteroid, electronic order se

Statistical Machine Learning and Combinatorial Optimization

In this work we apply statistical learning methods in the context of combinatorial optimization, which is understood as nding a binary string minimizing a given cost function. We rst consider probability densities over binary strings and we dene two dierent statistical criteria. Then we recast the initial problem as the problem of nding a density minimizing one of the two criteria. We restrict ourselves to densities described by a small number of parameters and solve the new problem by means of gradient techniques. This results in stochastic algorithms which iteratively update density parameters. We apply these algorithms to two families of densities, the Bernoulli model and the Gaussian model. The algorithms have been implemented and some experiments are reported. 1 Introduction In this work, we apply statistical learning methods in the context of combinatorial optimization, which is understood as nding a binary string minimizing a given cost function. We transform t..