Spectral asymptotics of periodic elliptic operators

We demonstrate that the structure of complex second-order strongly elliptic operators $H$ on ${\bf R}^d$ with coefficients invariant under translation by ${\bf Z}^d$ can be analyzed through decomposition in terms of versions $H_z$, $z\in{\bf T}^d$, of $H$ with $z$-periodic boundary conditions acting on $L_2({\bf I}^d)$ where ${\bf I}=[0,1>$. If the semigroup $S$ generated by $H$ has a H\"older continuous integral kernel satisfying Gaussian bounds then the semigroups $S^z$ generated by the $H_z$ have kernels with similar properties and $z\mapsto S^z$ extends to a function on ${\bf C}^d\setminus\{0\}$ which is analytic with respect to the trace norm. The sequence of semigroups $S^{(m),z}$ obtained by rescaling the coefficients of $H_z$ by $c(x)\to c(mx)$ converges in trace norm to the semigroup $\hat{S}^z$ generated by the homogenization $\hat{H}_z$ of $H_z$. These convergence properties allow asymptotic analysis of the spectrum of $H$.Comment: 27 pages, LaTeX article styl

Proof of Bose-Einstein Condensation for Interacting Gases with a One-Particle Spectral Gap

Using a specially tuned mean-field Bose gas as a reference system, we establish a positive lower bound on the condensate density for continuous Bose systems with superstable two-body interactions and a finite gap in the one-particle excitations spectrum, i.e. we prove for the first time standard homogeneous Bose-Einstein condensation for such interacting systems

A Global Analysis of the Relationship Between Urbanization and Fatalities in Earthquake-Prone Areas

Urbanization can be a challenge and an opportunity for earthquake risk mitigation. However, little is known about the changes in exposure (for example, population and urban land) to earthquakes in the context of global urbanization, and their impacts on fatalities in earthquake-prone areas. We present a global analysis of the changes in population size and urban land area in earthquake-prone areas from 1990 to 2015, and their impacts on earthquake-related fatalities. We found that more than two thirds of population growth (or 70% of total population in 2015) and nearly three quarters of earthquake-related deaths (or 307,918 deaths) in global earthquake-prone areas occurred in developing countries with an urbanization ratio (percentage of urban population to total population) between 20 and 60%. Holding other factors constant, population size was significantly and positively associated with earthquake fatalities, while the area of urban land was negatively related. The results suggest that fatalities increase for areas where the urbanization ratio is low, but after a ratio between 40 and 50% occurs, earthquake fatalities decline. This finding suggests that the resistance of building and infrastructure is greater in countries with higher urbanization ratios and highlights the need for further investigation. Our quantitative analysis is extended into the future using Shared Socioeconomic Pathways to reveal that by 2050, more than 50% of the population increase in global earthquake-prone areas will take place in a few developing countries (Pakistan, India, Afghanistan, and Bangladesh) that are particularly vulnerable to earthquakes. To reduce earthquake-induced fatalities, enhanced resilience of buildings and urban infrastructure generally in these few countries should be a priority

Multi‐scale heterogeneity in vegetation and soil carbon in exurban residential land of southeastern Michigan, USA

Exurban residential land (one housing unit per 0.2–16.2 ha) is growing in importance as a human‐dominated land use. Carbon storage in the soils and vegetation of exurban land is poorly known, as are the effects on C storage of choices made by developers and residents. We studied C storage in exurban yards in southeastern Michigan, USA, across a range of parcel sizes and different types of neighborhoods. We divided each residential parcel into ecological zones (EZ) characterized by vegetation, soil, and human behavior such as mowing, irrigation, and raking. We found a heterogeneous mixture of trees and shrubs, turfgrasses, mulched gardens, old‐field vegetation, and impervious surfaces. The most extensive zone type was turfgrass with sparse woody vegetation (mean 26% of parcel area), followed by dense woody vegetation (mean 21% of parcel area). Areas of turfgrass with sparse woody vegetation had trees in larger size classes (> 50 cm dbh) than did areas of dense woody vegetation. Using aerial photointerpretation, we scaled up C storage to neighborhoods. Varying C storage by neighborhood type resulted from differences in impervious area (8–26% of parcel area) and area of dense woody vegetation (11–28%). Averaged and multiplied across areas in differing neighborhood types, exurban residential land contained 5240 ± 865 g C/m2 in vegetation, highly sensitive to large trees, and 13 800 ± 1290 g C/m2 in soils (based on a combined sampling and modeling approach). These contents are greater than for agricultural land in the region, but lower than for mature forest stands. Compared with mature forests, exurban land contained more shrubs and less downed woody debris and it had similar tree size‐class distributions up to 40 cm dbh but far fewer trees in larger size classes. If the trees continue to grow, exurban residential land could sequester additional C for decades. Patterns and processes of C storage in exurban residential land were driven by land management practices that affect soil and vegetation, reflecting the choices of designers, developers, and residents. This study provides an example of human‐mediated C storage in a coupled human–natural system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/122437/1/eap1313.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/122437/2/eap1313_am.pd

How often should we monitor for reliable detection of atrial fibrillation recurrence? Efficiency considerations and implications for study design

OBJECTIVE: Although atrial fibrillation (AF) recurrence is unpredictable in terms of onset and duration, current intermittent rhythm monitoring (IRM) diagnostic modalities are short-termed and discontinuous. The aim of the present study was to investigate the necessary IRM frequency required to reliably detect recurrence of various AF recurrence patterns. METHODS: The rhythm histories of 647 patients (mean AF burden: 12±22% of monitored time; 687 patient-years) with implantable continuous monitoring devices were reconstructed and analyzed. With the use of computationally intensive simulation, we evaluated the necessary IRM frequency to reliably detect AF recurrence of various AF phenotypes using IRM of various durations. RESULTS: The IRM frequency required for reliable AF detection depends on the amount and temporal aggregation of the AF recurrence (p<0.0001) as well as the duration of the IRM (p<0.001). Reliable detection (>95% sensitivity) of AF recurrence required higher IRM frequencies (>12 24-hour; >6 7-day; >4 14-day; >3 30-day IRM per year; p<0.0001) than currently recommended. Lower IRM frequencies will under-detect AF recurrence and introduce significant bias in the evaluation of therapeutic interventions. More frequent but of shorter duration, IRMs (24-hour) are significantly more time effective (sensitivity per monitored time) than a fewer number of longer IRM durations (p<0.0001). CONCLUSIONS: Reliable AF recurrence detection requires higher IRM frequencies than currently recommended. Current IRM frequency recommendations will fail to diagnose a significant proportion of patients. Shorter duration but more frequent IRM strategies are significantly more efficient than longer IRM durations. CLINICAL TRIAL REGISTRATION URL: Unique identifier: NCT00806689

Viral genotype correlates with distinct liver gene transcription signatures in chronic hepatitis C virus infection

BACKGROUND: Chronic hepatitis C virus (HCV) infection of the liver with either genotype 1 or genotype 3 gives rise to distinct pathologies, and the two viral genotypes respond differently to antiviral therapy. METHODS: To understand these clinical differences, we compared gene transcription profiles in liver biopsies from patients infected with either gt1 or gt3, and uninfected controls. RESULTS: Gt1-infected biopsies displayed elevated levels of transcripts regulated by type I and type III interferons (IFN), including genes that predict response to IFN-α therapy. In contrast, genes controlled by IFN-γ were induced in gt3-infected biopsies. Moreover, IFN-γ levels were higher in gt3-infected biopsies. Analysis of hepatocyte-derived cell lines confirmed that the genes upregulated in gt3 infection were preferentially induced by IFN-γ. The transcriptional profile of gt3 infection was unaffected by IFNL4 polymorphisms, providing a rationale for the reduced predictive power of IFNL genotyping in gt3-infected patients. CONCLUSIONS: The interactions between HCV genotypes 1 and 3 and hepatocytes are distinct. These unique interactions provide avenues to explore the biological mechanisms that drive viral genotype-specific differences in disease progression and treatment response. A greater understanding of the distinct host-pathogen interactions of the different HCV genotypes is required to facilitate optimal management of HCV infection

Eight grand challenges in socio-environmental systems modeling

Modeling is essential to characterize and explore complex societal and environmental issues in systematic and collaborative ways. Socio-environmental systems (SES) modeling integrates knowledge and perspectives into conceptual and computational tools that explicitly recognize how human decisions affect the environment. Depending on the modeling purpose, many SES modelers also realize that involvement of stakeholders and experts is fundamental to support social learning and decision-making processes for achieving improved environmental and social outcomes. The contribution of this paper lies in identifying and formulating grand challenges that need to be overcome to accelerate the development and adaptation of SES modeling. Eight challenges are delineated: bridging epistemologies across disciplines; multi-dimensional uncertainty assessment and management; scales and scaling issues; combining qualitative and quantitative methods and data; furthering the adoption and impacts of SES modeling on policy; capturing structural changes; representing human dimensions in SES; and leveraging new data types and sources. These challenges limit our ability to effectively use SES modeling to provide the knowledge and information essential for supporting decision making. Whereas some of these challenges are not unique to SES modeling and may be pervasive in other scientific fields, they still act as barriers as well as research opportunities for the SES modeling community. For each challenge, we outline basic steps that can be taken to surmount the underpinning barriers. Thus, the paper identifies priority research areas in SES modeling, chiefly related to progressing modeling products, processes and practices

Understanding the acceleration in the ring-opening of lactones delivered by microwave heating

AbstractThis paper reports the first detailed study focussed upon identifying the influence that microwave heating (MWH) has upon the mechanic steps involved in the tin catalysed ring-opening of lactones such as ɛ-caprolactone (CL). Direct comparison of conventional (CH) and microwave (MWH) heated kinetic studies showed that a key factor in the reduction of the polymerisation cycle time with MWH was the elimination of the induction period associated with in situ catalyst manufacture and initiation. NMR studies demonstrated that the most significant mechanistic change contributing to the observed induction time reduction/elimination was faster initiation (i.e., reaction of the initiatior/catalyst complex with the first monomer unit). Consequently, analysis of the dielectric properties of the reaction components predicted that this MWH induced change was related to the selective volumetric heating of both the catalyst and the monomer. Furthermore, this indication of the greater significance of the initiation step in defining the length of the induction period suggests that this is the rate determining step of the process, whether conducted by CH or MWH. Increasing the catalyst concentration was demonstrated to produce significant reductions in reaction heat-up time and to induce a significant (up to 30 °C) overshoot in reaction mixture bulk temperature in with MWH only. Thus supporting the conclusion that selective heating of the organometallic species in the system contributes directly to differences in the reaction conditions and which need to be taken into account when drawing comparisons with CH systems. Consequently, both effects were concluded to be thermally generated from selective volumetric heating