Micromechanical theory of strain-stiffening of biopolymer networks

Filamentous bio-materials such as fibrin or collagen networks exhibit an enormous stiffening of their elastic moduli upon large deformations. This pronounced nonlinear behavior stems from a significant separation between the stiffnesses scales associated with bending vs. stretching the material's constituent elements. Here we study a simple model of such materials - floppy networks of hinged rigid bars embedded in an elastic matrix - in which the effective ratio of bending to stretching stiffnesses vanishes identically. We introduce a theoretical framework and build upon it to construct a numerical method with which the model's micro- and macro-mechanics can be carefully studied. Our model, numerical method and theoretical framework allow us to robustly observe and fully understand the critical properties of the athermal strain-stiffening transition that underlies the nonlinear mechanical response of a broad class of biomaterials

A Review of Best Practices for Monitoring and Improving Inpatient Pediatric Patient Experiences.

ContextAchieving high-quality patient-centered care requires assessing patient and family experiences to identify opportunities for improvement. With the Child Hospital Consumer Assessment of Healthcare Providers and Systems Survey, hospitals can assess performance and make national comparisons of inpatient pediatric experiences. However, using patient and family experience data to improve care remains a challenge.ObjectiveWe reviewed the literature on best practices for monitoring performance and undertaking activities aimed at improving pediatric patient and family experiences of inpatient care.Data sourcesWe searched PubMed, Cumulative Index to Nursing and Allied Health Literature, and PsychINFO.Study selectionWe included (1) English-language peer-reviewed articles published from January 2000 to April 2019; (2) articles based in the United States, United Kingdom, or Canada; (3) articles focused on pediatric inpatient care; (4) articles describing pediatric patient and family experiences; and (5) articles including content on activities aimed at improving patient and family experiences. Our review included 25 articles.Data extractionTwo researchers reviewed the full article and abstracted specific information: country, study aims, setting, design, methods, results, Quality Improvement (QI) initiatives performed, internal reporting description, best practices, lessons learned, barriers, facilitators and study implications for clinical practice, patient-experience data collection, and QI activities. We noted themes across samples and care settings.ResultsWe identified 10 themes of best practice. The 4 most common were (1) use evidence-based approaches, (2) maintain an internal system that communicates information and performance on patient and family experiences to staff and hospital leadership, (3) use experience survey data to initiate and/or evaluate QI interventions, and (4) identify optimal times (eg, discharge) and modes (eg, print) for obtaining patient and family feedback. These correspond to adult inpatient best practices.ConclusionsBoth pediatric and adult inpatient best practices rely on common principles of culture change (such as evidence-based clinical practice), collaborative learning, multidisciplinary teamwork, and building and/or supporting a QI infrastructure that requires time, money, collaboration, data tracking, and monitoring. QI best practices in both pediatric and adult inpatient settings commonly rely on identifying drivers of overall ratings of care, rewarding staff for successful implementation, and creating easy-to-use and easy-to-access planning and QI tools for staff

A new characterization of the Muckenhoupt Ap weights through an extension of the Lorentz-Shimogaki theorem

Given any quasi-Banach function space X over Rn it is defined an index αX that coincides with the upper Boyd index αX when the space X is rearrangement-invariant. This new index is defined by means of the local maximal operator mλf . It is shown then that the Hardy-Littlewood maximal operator M is bounded on X if and only if αX < 1 providing an extension of the classical theorem of Lorentz and Shimogaki for rearrangement-invariant X. As an application it is shown a new characterization of the Muckenhoupt Ap class of weights: u ∈ Ap if and only if for any ε > 0 there is a constant c such that for any cube Q and any measurable subset E ⊂ Q, |E| |Q| logε |Q| |E| ≤ c u(E) u(Q)!1/p. The case ε = 0 is false corresponding to the class Ap,1. Other applications are given, in particular within the context of the variable Lp spaces.Ministerio de Educación y Cienci

Sharp weighted estimates for classical operators

We give a new proof of the sharp one weight $L^p$ inequality for any operator $T$ that can be approximated by Haar shift operators such as the Hilbert transform, any Riesz transform, the Beurling-Ahlfors operator. Our proof avoids the Bellman function technique and two weight norm inequalities. We use instead a recent result due to A. Lerner to estimate the oscillation of dyadic operators. Our method is flexible enough to prove the corresponding sharp one-weight norm inequalities for some operators of harmonic analysis: the maximal singular integrals associated to $T$, Dyadic square functions and paraproducts, and the vector-valued maximal operator of C. Fefferman-Stein. Also we can derive a very sharp two-weight bump type condition for $T$.Comment: We improve different parts of the first version, in particular we show the sharpness of our theorem for the vector-valued maximal functio

A1 bounds for Calderón-Zygmund operators related to a problem of Muckenhoupt and Wheeden

We obtain an Lp(w) bound for Calderón-Zygmund operators T when w ∈ A1. This bound is sharp both with respect to ∥w∥A1 and with respect to p. As a result, we get a new L1,∞(w) estimate for T related to a problem of Muckenhoupt and Wheeden.Ministerio de Educación y Cienci

Sharp weighted bounds for multilinear maximal functions and Calderón-Zygmund operators

In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function M introduced in [18] A.K. Lerner, S. Ombrosi, C. Pérez, R.H. Torres and R. Trujillo-Gonz´alez, New maximal functions and multiple weights for the multilinear Caldern-Zygmund theory, Advances in Math. 220, 1222-1264 (2009). and for multilinear Calderón-Zygmund operators. In particular we obtain a sharp mixed “Ap − A∞” bound for M, some partial results related to a Buckley-type estimate for M, and a sufficient condition for the boundedness of M between weighted Lp spaces with different weights taking into account the precise bounds. Next we get a bound for multilinear Calderón-Zygmund operators in terms of dyadic positive multilinear operators in the spirit of the recent work [16] A.K. Lerner, On an estimate of Calderón-Zygmund operators by dyadic positive operators, J. Anal. Math. Then we obtain a multilinear version of the “A2 conjecture”. Several open problems are posed

Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden

A well known open problem of Muckenhoupt-Wheeden says that any Calderón-Zygmund singular integral operator T is of weak type (1, 1) with respect to a couple of weights (w, Mw). In this paper we consider a somewhat “dual” problem: sup λ>0 λw x ∈ R n : |T f(x)| Mw > λ ≤ c Z Rn |f| dx. We prove a weaker version of this inequality with M3w instead of Mw. Also we study a related question about the behavior of the constant in terms of the A1 characteristic of w.Ministerio de Educación y Cienci

Medical Transport of Children with Complex Chronic Conditions

One of the most notable trends in child health has been the increase in the number of children with special health care needs, including those with complex chronic conditions. Care of these children accounts for a growing fraction of health care resources. We examine recent developments in health care, especially with regard to medical transport and prehospital care, that have emerged to adapt to this remarkable demographic trend. One such development is the focus on care coordination, including the dissemination of the patient-centered medical home concept. In the prehospital setting, the need for greater coordination has catalyzed the development of the emergency information form. Training programs for prehospital providers now incorporate specific modules for children with complex conditions. Another notable trend is the shift to a family-centered model of care. We explore efforts toward regionalization of care, including the development of specialized pediatric transport teams, and conclude with recommendations for a research agenda

New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory

AbstractA multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller than the m-fold product of the Hardy–Littlewood maximal function is studied. The operator is used to obtain a precise control on multilinear singular integral operators of Calderón–Zygmund type and to build a theory of weights adapted to the multilinear setting. A natural variant of the operator which is useful to control certain commutators of multilinear Calderón–Zygmund operators with BMO functions is then considered. The optimal range of strong type estimates, a sharp end-point estimate, and weighted norm inequalities involving both the classical Muckenhoupt weights and the new multilinear ones are also obtained for the commutators