A nilpotent IP polynomial multiple recurrence theorem

We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibman's result that polynomial mappings into a nilpotent group form a group and a multiparameter version of the nilpotent Hales-Jewett theorem due to Bergelson and Leibman.Comment: v4: switch to TeXlive 2016 and biblate

Simultaneous dense and nondense orbits for commuting maps

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We show that, for two commuting automorphisms of the torus and for two elements of the Cartan action on compact higher rank homogeneous spaces, many points have drastically different orbit structures for the two maps. Specifically, using measure rigidity, we show that the set of points that have dense orbit under one map and nondense orbit under the second has full Hausdorff dimension.V. B. acknowledges support received from the National Science Foundation via Grant DMS-1162073 M. E. acknowledges support by the SNF (200021-152819). J. T. acknowledges the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. 291147

Simultaneous dense and nondense orbits for commuting maps

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We show that, for two commuting automorphisms of the torus and for two elements of the Cartan action on compact higher rank homogeneous spaces, many points have drastically different orbit structures for the two maps. Specifically, using measure rigidity, we show that the set of points that have dense orbit under one map and nondense orbit under the second has full Hausdorff dimension.V. B. acknowledges support received from the National Science Foundation via Grant DMS-1162073 M. E. acknowledges support by the SNF (200021-152819). J. T. acknowledges the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. 291147

Rigidity and Non-recurrence along Sequences

Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main focus in this article is to characterize explicitly the structural properties of sequences which can be rigidity sequences or non-recurrent sequences for some weakly mixing dynamical system. For ergodic transformations generally and for weakly mixing transformations in particular there are both parallels and distinctions between the class of rigid sequences and the class of non-recurrent sequences. A variety of classes of sequences with various properties are considered showing the complicated and rich structure of rigid and non-recurrent sequences

An Extension of Weyl’s Equidistribution Theorem to Generalized Polynomials and Applications

Author's accepted manuscript.This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Bergelson, V., Knutson, I. J. H. & Son, Y. (2020). An Extension of Weyl’s Equidistribution Theorem to Generalized Polynomials and Applications. International Mathematics Research Notices, 2021(19), 14965-15018 is available online at: https://academic.oup.com/imrn/article/2021/19/14965/5775499 and https://doi.org/10.1093/imrn/rnaa035.Generalized polynomials are mappings obtained from the conventional polynomials by the use of the operations of addition and multiplication and taking the integer part. Extending the classical theorem of Weyl on equidistribution of polynomials, we show that a generalized polynomial q(n) has the property that the sequence (q(n)λ)n∈Z is well-distributed mod1 for all but countably many λ∈R if and only if lim|n|→∞n∉J|q(n)|=∞ for some (possibly empty) set J having zero natural density in Z⁠. We also prove a version of this theorem along the primes (which may be viewed as an extension of classical results of Vinogradov and Rhin). Finally, we utilize these results to obtain new examples of sets of recurrence and van der Corput sets.publishedVersio

Nonconventional Large Deviations Theorems

We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation

Retargeting the Coxsackievirus and Adenovirus Receptor to the Apical Surface of Polarized Epithelial Cells Reveals the Glycocalyx as a Barrier to Adenovirus-Mediated Gene Transfer

Lumenal delivery of adenovirus vectors (AdV) results in inefficient gene transfer to human airway epithelium. The human coxsackievirus and adenovirus receptor (hCAR) was detected by immunofluorescence selectively at the basolateral surfaces of freshly excised human airway epithelial cells, suggesting that the absence of apical hCAR constitutes a barrier to adenovirus-mediated gene delivery in vivo. In transfected polarized Madin-Darby canine kidney cells, wild-type hCAR was expressed selectively at the basolateral membrane, whereas hCAR lacking the transmembrane and/or cytoplasmic domains was expressed on both the basolateral and apical membranes. Cells expressing apical hCAR still were not efficiently transduced by AdV applied to the apical surface. However, after the cells were treated with agents that remove components of the apical surface glycocalyx, AdV transduction occurred. These results indicate that adenovirus can infect via receptors located at the apical cell membrane but that the glycocalyx impedes interaction of AdV with apical receptors

Effects of rapid prey evolution on predator-prey cycles

We study the qualitative properties of population cycles in a predator-prey system where genetic variability allows contemporary rapid evolution of the prey. Previous numerical studies have found that prey evolution in response to changing predation risk can have major quantitative and qualitative effects on predator-prey cycles, including: (i) large increases in cycle period, (ii) changes in phase relations (so that predator and prey are cycling exactly out of phase, rather than the classical quarter-period phase lag), and (iii) "cryptic" cycles in which total prey density remains nearly constant while predator density and prey traits cycle. Here we focus on a chemostat model motivated by our experimental system [Fussmann et al. 2000,Yoshida et al. 2003] with algae (prey) and rotifers (predators), in which the prey exhibit rapid evolution in their level of defense against predation. We show that the effects of rapid prey evolution are robust and general, and furthermore that they occur in a specific but biologically relevant region of parameter space: when traits that greatly reduce predation risk are relatively cheap (in terms of reductions in other fitness components), when there is coexistence between the two prey types and the predator, and when the interaction between predators and undefended prey alone would produce cycles. Because defense has been shown to be inexpensive, even cost-free, in a number of systems [Andersson and Levin 1999, Gagneux et al. 2006,Yoshida et al. 2004], our discoveries may well be reproduced in other model systems, and in nature. Finally, some of our key results are extended to a general model in which functional forms for the predation rate and prey birth rate are not specified.Comment: 35 pages, 8 figure

Barriers and enablers of health system adoption of kangaroo mother care: a systematic review of caregiver perspectives

Background: Despite improvements in child survival in the past four decades, an estimated 6.3 million children under the age of five die each year, and more than 40% of these deaths occur in the neonatal period. Interventions to reduce neonatal mortality are needed. Kangaroo mother care (KMC) is one such life-saving intervention; however it has not yet been fully integrated into health systems around the world. Utilizing a conceptual framework for integration of targeted health interventions into health systems, we hypothesize that caregivers play a critical role in the adoption, diffusion, and assimilation of KMC. The objective of this research was to identify barriers and enablers of implementation and scale up of KMC from caregivers’ perspective. Methods: We searched Pubmed, Embase, Web of Science, Scopus, and WHO regional databases using search terms ‘kangaroo mother care’ or ‘kangaroo care’ or ‘skin to skin care’. Studies published between January 1, 1960 and August 19, 2015 were included. To be eligible, published work had to be based on primary data collection regarding barriers or enablers of KMC implementation from the family perspective. Abstracted data were linked to the conceptual framework using a deductive approach, and themes were identified within each of the five framework areas using Nvivo software. Results: We identified a total of 2875 abstracts. After removing duplicates and ineligible studies, 98 were included in the analysis. The majority of publications were published within the past 5 years, had a sample size less than 50, and recruited participants from health facilities. Approximately one-third of the studies were conducted in the Americas, and 26.5% were conducted in Africa. We identified four themes surrounding the interaction between families and the KMC intervention: buy in and bonding (i.e. benefits of KMC to mothers and infants and perceptions of bonding between mother and infant), social support (i.e. assistance from other people to perform KMC), sufficient time to perform KMC, and medical concerns about mother or newborn health. Furthermore, we identified barriers and enablers of KMC adoption by caregivers within the context of the health system regarding financing and service delivery. Embedded within the broad social context, barriers to KMC adoption by caregivers included adherence to traditional newborn practices, stigma surrounding having a preterm infant, and gender roles regarding childcare. Conclusion: Efforts to scale up and integrate KMC into health systems must reduce barriers in order to promote the uptake of the intervention by caregivers