We describe a multi-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of the corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions and the corresponding photon statistics are discussed. Some applications to quantum optics, cavity quantum electrodynamics and superfocusing in channelling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.
Background
In 2015, the Zika arbovirus (ZIKV) began circulating in the Americas, rapidly expanding its global geographic range in explosive outbreaks. Unusual among mosquito-borne diseases, ZIKV has been shown to also be sexually transmitted, although sustained autochthonous transmission due to sexual transmission alone has not been observed, indicating the reproduction number (R0) for sexual transmission alone is less than 1. Critical to the assessment of outbreak risk, estimation of the potential attack rates, and assessment of control measures, are estimates of the basic reproduction number, R0.
Methods
We estimated the R0 of the 2015 ZIKV outbreak in Barranquilla, Colombia, through an analysis of the exponential rise in clinically identified ZIKV cases (n = 359 to the end of November, 2015).
Findings
The rate of exponential rise in cases was ρ = 0.076 days[superscript −1], with 95% CI [0.066,0.087] days[superscript −1]. We used a vector-borne disease model with additional direct transmission to estimate the R0; assuming the R0 of sexual transmission alone is less than 1, we estimated the total R0 = 3.8 [2.4,5.6], and that the fraction of cases due to sexual transmission was 0.23 [0.01,0.47] with 95% confidence.
Interpretation
This is among the first estimates of R0 for a ZIKV outbreak in the Americas, and also among the first quantifications of the relative impact of sexual transmission.
Antiviral resistance in influenza is rampant and has the possibility of causing major morbidity and mortality. Previous models have identified treatment regimes to minimize total infections and keep resistance low. However, the bulk of these studies have ignored stochasticity and heterogeneous contact structures. Here we develop a network model of influenza transmission with treatment and resistance, and present both standard mean-field approximations as well as simulated dynamics. We find differences in the final epidemic sizes for identical transmission parameters (bistability) leading to different optimal treatment timing depending on the number initially infected. We also find, contrary to previous results, that treatment targeted by number of contacts per individual (node degree) gives rise to more resistance at lower levels of treatment than non-targeted treatment. Finally we highlight important differences between the two methods of analysis (mean-field versus stochastic simulations), and show where traditional mean-field approximations fail. Our results have important implications not only for the timing and distribution of influenza chemotherapy, but also for mathematical epidemiological modeling in general. Antiviral resistance in influenza may carry large consequences for pandemic mitigation efforts, and models ignoring contact heterogeneity and stochasticity may provide misleading policy recommendations.
Community associated methicillin-resistant Staphylococcus aureus (CA-MRSA) has become a major cause of skin and soft tissue infections (SSTIs) in the US. We developed an age-structured compartmental model to study the spread of CA-MRSA at the population level and assess the effect of control intervention strategies. We used Monte-Carlo Markov Chain (MCMC) techniques to parameterize our model using monthly time series data on SSTIs incidence in children (≤19 years) during January 2004 -December 2006 in Maricopa County, Arizona. Our model-based forecast for the period January 2007–December 2008 also provided a good fit to data. We also carried out an uncertainty and sensitivity analysis on the control reproduction number, Rc which we estimated at 1.3 (95% CI [1.2,1.4]) based on the model fit to data. Using our calibrated model, we evaluated the effect of typical intervention strategies namely reducing the contact rate of infected individuals owing to awareness of infection and decolonization strategies targeting symptomatic infected individuals on both and the long-term disease dynamics. We also evaluated the impact of hypothetical decolonization strategies targeting asymptomatic colonized individuals. We found that strategies focused on infected individuals were not capable of achieving disease control when implemented alone or in combination. In contrast, our results suggest that decolonization strategies targeting the pediatric population colonized with CA-MRSA have the potential of achieving disease elimination.
A data set of observed daily precipitation, maximum and minimum temperature, gridded to a 1/16° (~6 km) resolution, is described that spans the entire country of Mexico, the conterminous U.S. (CONUS), and regions of Canada south of 53° N for the period 1950-2013. The dataset improves previous products in spatial extent, orographic precipitation adjustment over Mexico and parts of Canada, and reduction of transboundary discontinuities. The impacts of adjusting gridded precipitation for orographic effects are quantified by scaling precipitation to an elevation-aware 1981-2010 precipitation climatology in Mexico and Canada. Differences are evaluated in terms of total precipitation as well as by hydrologic quantities simulated with a land surface model. Overall, orographic correction impacts total precipitation by up to 50% in mountainous regions outside CONUS. Hydrologic fluxes show sensitivities of similar magnitude, with discharge more sensitive than evapotranspiration and soil moisture. Because of the consistent gridding methodology, the current product reduces transboundary discontinuities as compared with a commonly used reanalysis product, making it suitable for estimating large-scale hydrometeorologic phenomena.
Much of the socioeconomic life in the United States occurs in its urban areas. While an urban economy is defined to a large extent by its network of occupational specializations, an examination of this important network is absent from the considerable body of work on the determinants of urban economic performance. Here we develop a structure-based analysis addressing how the network of interdependencies among occupational specializations affects the ease with which urban economies can transform themselves. While most occupational specializations exhibit positive relationships between one another, many exhibit negative ones, and the balance between the two partially explains the productivity of an urban economy. The current set of occupational specializations of an urban economy and its location in the occupation space constrain its future development paths. Important tradeoffs exist between different alternatives for altering an occupational specialization pattern, both at a single occupation and an entire occupational portfolio levels.
Background: Hemorrhagic fever with renal syndrome (HFRS), a rodent-borne infectious disease, is one of the most serious public health threats in China. Increasing our understanding of the spatial and temporal patterns of HFRS infections could guide local prevention and control strategies.
Methodology/Principal Findings: We employed statistical models to analyze HFRS case data together with environmental data from the Dongting Lake district during 2005–2010. Specifically, time-specific ecologic niche models (ENMs) were used to quantify and identify risk factors associated with HFRS transmission as well as forecast seasonal variation in risk across geographic areas. Results showed that the Maximum Entropy model provided the best predictive ability (AUC = 0.755). Time-specific Maximum Entropy models showed that the potential risk areas of HFRS significantly varied across seasons. High-risk areas were mainly found in the southeastern and southwestern areas of the Dongting Lake district. Our findings based on models focused on the spring and winter seasons showed particularly good performance. The potential risk areas were smaller in March, May and August compared with those identified for June, July and October to December. Both normalized difference vegetation index (NDVI) and land use types were found to be the dominant risk factors.
Conclusions/Significance: Our findings indicate that time-specific ENMs provide a useful tool to forecast the spatial and temporal risk of HFRS.
Background:
Pandemic influenza is said to 'shift mortality' to younger age groups; but also to spare a subpopulation of the elderly population. Does one of these effects dominate? Might this have important ramifications?
Methods: We estimated age-specific excess mortality rates for all-years for which data were available in the 20th century for Australia, Canada, France, Japan, the UK, and the USA for people older than 44 years of age. We modeled variation with age, and standardized estimates to allow direct comparison across age groups and countries. Attack rate data for four pandemics were assembled.
Results: For nearly all seasons, an exponential model characterized mortality data extremely well. For seasons of emergence and a variable number of seasons following, however, a subpopulation above a threshold age invariably enjoyed reduced mortality. 'Immune escape', a stepwise increase in mortality among the oldest elderly, was observed a number of seasons after both the A(H2N2) and A(H3N2) pandemics. The number of seasons from emergence to escape varied by country. For the latter pandemic, mortality rates in four countries increased for younger age groups but only in the season following that of emergence. Adaptation to both emergent viruses was apparent as a progressive decrease in mortality rates, which, with two exceptions, was seen only in younger age groups. Pandemic attack rate variation with age was estimated to be similar across four pandemics with very different mortality impact.
Conclusions: In all influenza pandemics of the 20th century, emergent viruses resembled those that had circulated previously within the lifespan of then-living people. Such individuals were relatively immune to the emergent strain, but this immunity waned with mutation of the emergent virus. An immune subpopulation complicates and may invalidate vaccine trials. Pandemic influenza does not 'shift' mortality to younger age groups; rather, the mortality level is reset by the virulence of the emerging virus and is moderated by immunity of past experience. In this study, we found that after immune escape, older age groups showed no further mortality reduction, despite their being the principal target of conventional influenza vaccines. Vaccines incorporating variants of pandemic viruses seem to provide little benefit to those previously immune. If attack rates truly are similar across pandemics, it must be the case that immunity to the pandemic virus does not prevent infection, but only mitigates the consequences.
In this paper, we present a visual analytics approach that provides decision makers with a proactive and predictive environment in order to assist them in making effective resource allocation and deployment decisions. The challenges involved with such predictive analytics processes include end-users' understanding, and the application of the underlying statistical algorithms at the right spatiotemporal granularity levels so that good prediction estimates can be established. In our approach, we provide analysts with a suite of natural scale templates and methods that enable them to focus and drill down to appropriate geospatial and temporal resolution levels. Our forecasting technique is based on the Seasonal Trend decomposition based on Loess (STL) method, which we apply in a spatiotemporal visual analytics context to provide analysts with predicted levels of future activity. We also present a novel kernel density estimation technique we have developed, in which the prediction process is influenced by the spatial correlation of recent incidents at nearby locations. We demonstrate our techniques by applying our methodology to Criminal, Traffic and Civil (CTC) incident datasets.