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Individual versus superensemble forecasts of seasonal influenza outbreaks in the United States
Teresa K. Yamana ,
Roles Conceptualization, Formal analysis, Investigation, Methodology, Software, Visualization, Writing – original draft, Writing – review & editing
* E-mail: tky2104@cumc.columbia.edu
Affiliation Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York, New York, United States of America
Sasikiran Kandula,
Roles Data curation, Investigation, Software, Writing – review & editing
Jeffrey Shaman
Roles Conceptualization, Formal analysis, Funding acquisition, Supervision, Writing – review & editing
Teresa K. Yamana,
Version 2 Version 1 Uncorrected Proof
https://doi.org/10.1371/journal.pcbi.1005801
Teresa K. Yamana Sasikiran Kandula Jeffrey Shaman
Recent research has produced a number of methods for forecasting seasonal influenza outbreaks. However, differences among the predicted outcomes of competing forecast methods can limit their use in decision-making. Here, we present a method for reconciling these differences using Bayesian model averaging. We generated retrospective forecasts of peak timing, peak incidence, and total incidence for seasonal influenza outbreaks in 48 states and 95 cities using 21 distinct forecast methods, and combined these individual forecasts to create weighted-average superensemble forecasts. We compared the relative performance of these individual and superensemble forecast methods by geographic location, timing of forecast, and influenza season. We find that, overall, the superensemble forecasts are more accurate than any individual forecast method and less prone to producing a poor forecast. Furthermore, we find that these advantages increase when the superensemble weights are stratified according to the characteristics of the forecast or geographic location. These findings indicate that different competing influenza prediction systems can be combined into a single more accurate forecast product for operational delivery in real time.
Timely forecasts of infectious disease transmission can help public health officials, health care providers, and individuals better prepare for and respond to disease outbreaks. Work in recent years has led to the development of a number of forecast systems. These systems provide important information on future disease incidence; however, all forecasting systems contain inaccuracies, or error. This error can be reduced by combining information from multiple forecasting systems into a superensemble using Bayesian averaging methods. Here we compare 21 forecasting systems for seasonal influenza outbreaks and use them together to create superensemble forecasts. The superensemble produces more accurate forecasts than the individual systems, improving our ability to predict the timing and severity of seasonal influenza outbreaks.
Citation: Yamana TK, Kandula S, Shaman J (2017) Individual versus superensemble forecasts of seasonal influenza outbreaks in the United States. PLoS Comput Biol 13(11): e1005801. https://doi.org/10.1371/journal.pcbi.1005801
Editor: Justin Lessler, Johns Hopkins Bloomberg School of Public Health, UNITED STATES
Received: January 3, 2017; Accepted: September 29, 2017; Published: November 6, 2017
Copyright: © 2017 Yamana et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are provided within the paper and its Supporting Information files.
Funding: This work was supported by United States National Institute of General Medical Sciences (https://www.nigms.nih.gov/) grants GM100467 and GM110748, as well as National Institute of Environmental Health Sciences (https://www.niehs.nih.gov/) Center grant ES009089. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: I have read the journal's policy and the authors of this manuscript have the following competing interests: JS declares partial ownership of SK Analytics. TKY and SK declare no competing interests.
In the United States, seasonal influenza outbreaks occur every winter; however, the timing and severity of these seasonal outbreaks vary considerably from year to year. Accurate forecast of key characteristics of influenza outbreaks would allow public health agencies to better prepare for and respond to epidemics and pandemics. To this end, there has been significant work in recent years to develop forecasts of seasonal influenza outbreaks[1–5]. Proposed forecast methods include a range of statistical and mechanistic models, and incorporate data sources including syndromic and viral surveillance data, meteorological information, and internet search queries[3]. A comparison of coordinated influenza forecasts for the 2013–2014 season showed substantial disagreement in predicted outbreak characteristics among forecast methods[1]. This disagreement presents a barrier to the use of forecasts in decision-making.
While some forecast methods may be consistently superior to others, the relative performance of individual forecast methods can also vary according to the specifics of the population, location, or outbreak of interest. For example, a forecast method developed for a densely populated urban area may be less accurate in a sparse rural setting. Alternatively, some forecast methods may be better suited for prediction of outbreaks that are smaller or larger than typically observed. The optimal forecast method may also depend on when in the season the forecast is being generated.
Previous comparisons of subsets of the individual forecast methods used in this study have indeed revealed differences in forecast performance. Yang et al. [5] compared the performance of six filtering methods coupled with a mathematic model of disease transmission in retrospective forecasting of influenza epidemics. The relative performance of the filter methods varied by the timing of the forecast, the location being forecast, and the number of observed peaks in the outbreak. In retrospective forecasts of dengue fever, the relative accuracy of a model-filter forecasting system and two statistical methods varied by forecast timing, forecast target of interest (i.e. timing of outbreak peak, maximum incidence and total incidence), and the similarity between the outbreak being forecast and previously observed outbreaks[6].
In weather and climate forecasting, discordant forecasts from competing models are combined into superensemble forecasts in order to offset the biases of each individual model. The resulting superensemble forecasts are more accurate than forecasts from any one model form [7–9]. Recent work has shown this superensemble approach to be effective in improving the accuracy of forecasts of dengue outbreaks[6] and influenza [10, 11].
Here, we compare the accuracy of a suite of 21 competing forecast methods, as well as a superensemble forecast, in retrospective forecasts of influenza epidemics (See Methods and S1 Appendix). We group the 21 individual forecasts into three categories: ensemble filter systems; particle filter systems; and a statistical model. The ensemble-based filter systems include three types of filters: Ensemble Kalman Filter (EKF), Ensemble adjustment Kalman Filter, (EAKF) and Rank Histogram Filter (RHF). Two particle filters are used: a basic particle filter (PF) and a particle Markov Chain Monte Carlo method (pMCMC). The five filter methods are each coupled with four standard compartmental models of disease transmission: SIR, SEIR, SIRS and SEIRS (see Methods). For the final individual forecast method, we use a statistical model called Bayesian Weighted Outbreaks (BWO).
We find that the superensemble forecasts are more accurate than any individual forecast system, and that this advantage increases when superensemble weights are stratified according to the characteristics of the forecast, or by geographic location.
Comparison of individual forecasts
For the ensemble and particle filter systems, observations of influenza incidence from the beginning of the season to the week of forecast initiation are used to optimize each of the 4 mathematical models. The optimized model is then run to the end of the season to generate a weekly forecast of influenza incidence, as measured by ILI+, an estimate of influenza positive patients per 100 patient visits to outpatient health care providers (see Methods). For the BWO, only the most recent 8 weeks are used for training. A forecast is then generated as a weighted average of historical ILI+ epidemic trajectories (see Methods).
Thus, each individual forecast method produces a weekly estimate of ILI+ from the time of forecast through the end of the influenza season. These trajectories were used to calculate key characteristics of each outbreak: the peak incidence, peak timing, and total incidence. Forecast skill was assessed based on the mean absolute error (MAE) in predictions of each of these metrics.
Distributions of seasonal influenza outbreak peak timing, peak ILI+ and total ILI+ across 48 states and 97 cities are shown in Fig 1. The overall error of each of the 21 individual forecast methods (see Methods for names and descriptions of each forecast system) used to predict these observed outbreak characteristics is shown in Fig 2, relative to the MAE of the Baseline superensemble as a reference value (discussed below in Superensemble results). Forecast MAE ranged from 1.8 weeks to 3.5 weeks for peak timing. Individual forecast MAEs for peak incidence ranged from 1.2 to 3.5 ILI+, and from 0.5 to 1.0 ILI+ for total incidence. Among individual forecast methods, the lowest MAEs for peak timing and total incidence were generated by the dynamical models that included an exposed compartment (i.e. the SEIR and SEIRS structures) coupled with ensemble filters. However, the advantage of the exposed compartment was less clear in forecasts of peak incidence. Rather, the EKF model-filter systems produced the most accurate forecasts of peak incidence. Ensemble filter methods and BWO consistently outperformed particle filter methods for peak week and peak incidence; for total incidence, several particle-filter forecast systems performed comparably to ensemble methods. The pMCMC-SEIR and pMCMC-SEIRS forecast systems had exceptionally large errors for peak and total incidence.
Fig 1. Distributions of observed outbreak peak timing, peak ILI+ and total ILI+ by season.
Boxplots show the range of metric values observed each season across 97 cities and 48 states. ILI+ measures the number of influenza positive patients per 100 visits to outpatient visits to health care providers.
https://doi.org/10.1371/journal.pcbi.1005801.g001
Fig 2. Ratio of individual forecast MAE to baseline level MAE.
The baseline level MAE for each metric is the corresponding score of the baseline superensemble forecast (listed in Table 1). The three colors show the three target metrics. Note the abbreviated y-axis; the black line indicates a ratio of 1.
Fig 3 shows the MAE of each individual forecast method by forecast lead time and influenza season. Lead time refers to timing of the forecast relative to the outbreak peak, in weeks, with negative values indicating forecasts made prior to the peak and positive values for forecasts made after the peak. There were clear differences in relative forecast accuracy when discriminating by these factors. For example, the ensemble filters and BWO generally outperformed the particle filters in forecasts of peak ILI+ and total ILI+, with the exception of 2007–2008 and 2012–2013, two years with relatively large outbreaks. The particle filters produced the most accurate forecasts of peak week 1 to 5 weeks before the peak, but were among the worst performers following the peak. Inaccurate predictions of outbreak peak are possible even after the true peak has passed, as the models may predict a continued increase in incidence resulting in a later peak. The pMCMC-SEIR and pMCMC-SEIRS systems were especially prone to this type of error. Unlike the other filter methods, the pMCMC requires the same set of parameters be used to fit the entire observed time series [5]. As a result, the filter is less able to adapt to shifts in outbreak dynamics during an influenza season. This can result in poor forecasts, particularly for multi-peak outbreaks.
Fig 3. Forecast MAE grouped by forecast lead (left column) and season (right column).
Line plots show MAE for forecast peak week (top row), peak ILI+ (middle row) and total ILI+ (bottom row), averaged over all locations. Each line shows the MAE of an individual forecast method. For the model-filter systems, colors indicate groupings by filter type.
Superensemble results
For the initial baseline set of superensemble forecasts, a single set of weights for each target metric was applied to the competing individual forecasts each season (Fig 4). Each season, a new set of superensemble weights were computed using training data from all previous years. As such, we expected increased stability in the weights as more years were used to generate the weights. For all target metrics, the BWO forecast was typically assigned large weight, ranging from .10 to .53 for peak week, .10 to .32 for peak ILI+, and .03 to .33 for total incidence. However, note that the BWO approach is the most dissimilar among the forecast approaches. If a subgroup of forecasts predicts similar outcomes, the superensemble weights, which sum to one, are expected to be split among that subgroup. The contribution of the individual model-filter forecasts, which share filter methods and model structures, may thus be diluted among similar forecasts. This circumstance may explain the heavy weighting of the BWO forecast, despite its larger than average MAEs among individual forecasts. The twelve ensemble filter systems contributed a total weight of .29 to .68 for peak week, .49 to .68 for peak incidence, and .36 to .69 for total incidence. The eight particle filter systems contributed a total weight of .14 to .31 for peak week, .14 to .21 for peak incidence., and .26 to .43 for total incidence.
Fig 4. Contribution of each individual forecast to the baseline superensemble forecast for peak week (top), peak incidence (middle), and total incidence (bottom) by year.
The colors indicate the weight assigned to an individual forecast system specified by the horizontal axes and the influenza season specified by the vertical axes. For example, the upper-right square in each subplot shows the weight assigned to the EAKF-SEIR forecast system for the 2005–2006 influenza season.
The MAEs of superensemble forecasts are shown in Table 1. On average, the baseline superensemble forecasts were more accurate at predicting the timing of the outbreak peak than any of the individual forecasts, with the exception of the EKF-SEIRS (Fig 2). Baseline superensemble forecasts of peak and total incidence had smaller MAE than all individual forecasts.
Table 1. Mean absolute error for superensemble forecasts.
Forecast error averaged over all seasons, forecast weeks, and locations.
https://doi.org/10.1371/journal.pcbi.1005801.t001
We then stratified the weights by geographical region, forecast week, lead time relative to predicted peak, lead time relative to observed outbreak peak, population size and population density. These variables were pre-specified on the basis of previous work indicating that they may influence the accuracy of individual forecast methods (for example [5, 6]). The MAEs of the stratified superensemble forecasts are shown in Table 1. For both peak timing and peak incidence, stratifying by lead time relative to observed peak led to the greatest improvements in forecast performance, decreasing MAE by 0.4 weeks for peak timing and 0.06 ILI+ for peak incidence compared to the baseline superensemble forecast. On average, this forecast outperformed individual forecasts of peak timing and peak incidence at all times during the course of the outbreak (Fig 5). In contrast, several individual forecasts were more accurate in forecasting peak timing than the baseline superensemble early in the season, while others outperformed the baseline superensemble late in the season (Fig 5).
Fig 5. Performance of superensemble forecasts compared to individual forecasts stratified by lead time.
Each line shows the results of one forecast, with grey dotted lines representing the 21 individual forecasts and colored lines representing superensemble forecasts. SE-baseline refers to the baseline superensemble forecast, while SE-week, SE-region, SE-forlead and SE-actlead refer to superensemble forecasts with weights stratified by forecast week, HHS region, lead relative to predicted peak, and lead relative to observed peak, respectively.
Averaged within influenza seasons, the superensemble forecasts generally outperformed individual forecasts (S1 Fig) The most notable single seasonal exception was the set of forecasts of total incidence in 2012–2013, the year with unusually high influenza incidence.
Stratifying superensemble weights by forecast week or lead time relative to predicted peak, which can serve as real-time proxies for actual lead time, led to decreases in MAE for peak timing, but had only a small effect on forecasts of peak and total incidence. Meanwhile, stratifying by geographical region and population density led to small decreases in MAE for peak incidence, but degraded forecast accuracy for peak timing (Table 1, Fig 5). Stratifying weights by geographical region led to the lowest MAE for total incidence, but the improvement over the baseline forecast was small (0.02 ILI+).
We further assessed the accuracy of superensemble forecast credible intervals by determining the fraction of observations falling within the credible intervals specified by each forecast. In a well-calibrated forecast, we would expect this fraction to correspond to the value of the credible intervals; for example, 95% of observed outcomes should fall within the 95% credible intervals of a forecast method. Overall, the forecasts were well-calibrated. The calibration varied between the three target metrics, as well as between choices of stratification variable for superensemble weighting (S2 and S3 Figs) Forecasts of peak week and peak ILI+ were well calibrated at 90% and 95% credible intervals but somewhat overdispersed at lower confidence intervals. Forecast coverage for total ILI+ was well calibrated for 50%, but underdispersed at 95% and 99% credible intervals.
Forecast rankings
In addition to comparing forecast errors averaged over many forecasts, we also compiled a ranking of individual forecast outcomes. For each forecast, we ranked the 21 point-estimates from the individual forecasts and the resulting baseline superensemble forecast from 1 (lowest absolute error) through 22 (highest absolute error) and summed the frequency of each ranking (Fig 6). For peak week and peak incidence, we restrain the analysis to forecasts made prior to the observed forecast peak, as most forecasts report the true peak values after the peak has been observed, resulting in equal ranking.
Fig 6. Heat map of forecast rankings.
The colors indicate the frequency of each forecast ranking, with rank 1 assigned to the most accurate forecast and rank 22 assigned to the least accurate forecast. More optimal forecasts have a higher frequency of top rankings (warm colors on the left) and a lower frequency of bottom rankings (cold colors on the right). The upper image shows peak week, the middle shows peak incidence, and the bottom shows total incidence. This analysis includes all forecasts of total season incidence (n = 22640), and all forecasts made at or prior to the observed outbreak peak for peak week and peak incidence (n = 15187). Forecasts made after the peak had been observed were excluded from the ranking, as were forecasts where all 22 forecasts predicted the same outcome.
The superensemble gave the most accurate forecast 8.6% of the time for peak timing, which was more frequently than 12 of the individual forecast methods, but less frequently than BWO and most models-filter combinations using SEIR and SEIRS models. While the BWO, pMCMC-SEIR and pMCMC-SEIRS forecasts of peak timing had the most frequent first place rankings, they also produced many predictions that received the lowest rankings. In contrast, the superensemble forecast, as well as the SEIR and SEIRS models coupled with EAKF, EKF, and RHF ensemble filter methods, had few low rankings. When superensemble weights were stratified by lead time of forecast relative to the observed outbreak peak, the resulting forecast rankings dramatically improved, with 54.3% of superensemble forecasts receiving a rank of 1 through 4, surpassing all individual forecast methods (S4 Fig).
In forecasts of peak incidence, the baseline superensemble forecast gave the best prediction 10.8% of the time, which was more frequent than all individual forecasts except BWO, which was the highest ranked method for 17.1% of predictions. The superensemble was among the 4 worst forecasts less than 0.5% of the time, compared to 17.7% of BWO forecasts (Fig 6). The proportion of high to low ranking forecasts increases when superensemble weights are stratified by lead time of forecast (S4 Fig). These results indicate that the superensemble provides a consistent advantage in forecasts of peak incidence, both in aggregate, as well as for any given prediction.
For forecasts of total incidence, the baseline superensemble forecast had an average number of first place forecasts (5%), and was most often ranked between 7 and 13. However, as with the other two metrics, the superensemble had far fewer low rankings than any individual method. Among individual ensemble models, those using the SEIRS structure were ranked highest. BWO, pMCMC-SEIR, pMCMC-SEIRS, PF-SEIR and PF-SEIRS had frequent rankings in both the top 4 and the bottom 4.
Disagreement between competing forecasts of infectious disease outbreaks presents an obstacle to the interpretation and utilization of such forecasts. Here, we have presented a method for reconciling the disagreement among forecasts, while simultaneously improving overall forecast accuracy. We have shown that overall forecast accuracy for the timing and magnitude of peak influenza transmission is improved by combining individual forecasts into weighted-average superensemble forecasts. These superensemble forecasts were, on average, more accurate than any individual forecast method. In particular, the superensemble was less prone to producing a poor forecast. The advantage of the superensemble approach increases in circumstances where the relative accuracy of individual forecasts varies according to characteristics of the outbreak, or the location being forecast.
The 21 individual forecast methods compared in this study varied in their performance, as well as their reliability. The SEIRS dynamical model coupled with the EKF, EAKF and RHF ensemble filter methods were consistently among the better individual forecasts. Other forecast methods, namely pMCMC-SEIRS and pMCMC-SEIR, and to a lesser extent, BWO, performed inconsistently in that predictions were either among the best or the worst of the competing forecasts. This type of inconsistent performance presents a challenge to the superensemble approach, as the good forecasts can cause the forecast to receive a relatively high weighting in the superensemble; however, by identifying the circumstances that lead to differences in relative forecast performance, adaptive weighting can then be employed to variably weight an individual forecast method highly when it is prone to perform well and discount it in other circumstances. Here we found that the performance of individual forecast methods varied according to geographic location, influenza season, and the timing of the forecast.
We found that the timing of the forecast with respect to the outbreak peak was an important factor in determining relative forecast accuracy; consequently, stratifying superensemble weights by the actual lead time of the forecasts led to improvements in superensemble forecast accuracy. This improvement outweighed the gains made by simply eliminating the two most inconsistent forecast methods (pMCMC-SEIR and pMCMC-SEIRS). While the idealized process of weighting individual forecasts by actual forecast lead is not possible in real time, stratifying weights by forecast-predicted lead or simply calendar week, which can serve as real-time proxies for actual forecast lead, proved beneficial in improving forecast accuracy.
Stratifying superensemble weights by HHS region improved forecasts of peak and total incidence. This benefit may be related to regional differences in baseline and seasonal levels of influenza activity, or could be reflective of differences in the progression of influenza among regions. These findings provide a robust methodology for generating superensemble forecasts of influenza and other infectious diseases; however, the superensemble weights and the optimal stratification partitioning must be continually reevaluated and updated as new years of data become available, or as the geographical scale or resolution are altered.
While this study focused on the forecast of point estimate outcomes, the superensemble approach can also be used to produce probability distribution functions of target metrics. For example, the superensemble forecasts presented here were associated with reasonable credible intervals, which were influenced by the choice of stratification variable (S3 Fig). The calibration of individual and superensemble probabilistic forecasts remains an area of ongoing research.
The algorithm used to create the superensemble is flexible, and can combine any number and any type of individual forecast method, provided retrospective forecasts are available for superensemble training. These findings can thus be applied operationally to competing forecasts of infectious disease in order to improve forecast accuracy, and to present a streamlined prediction to public health decision-makers.
Observations of influenza activity
Regional influenza activity is monitored by the U.S. Centers for Disease Control and Prevention (CDC) through the U.S. Outpatient Influenza- like Illness Surveillance Network (ILINet). The CDC provides weekly near real-time estimates of regional influenza-like illness (ILI), defined as the number of patients with flu-like symptoms (fever with sore throat and/or with cough) divided by the total number of patient visits at ILINet outpatient healthcare facilities in order to account for temporal and spatial variability in patient volume and reporting rates of health care providers [1]. At the city and state level, ILI was estimated by Google Flu Trends (GFT), which used a statistical model relating weekly CDC ILI data to Google internet search queries[12]. GFT estimates are available for up to 115 cities and 50 states, from 2003 until the program was discontinued in 2015.
ILI is not specific to influenza, as it encompasses a range of respiratory infections. The World Health Organization and National Respiratory and Enteric Virus Surveillance System (NREVSS) provide weekly reports of the proportion of laboratory-confirmed positive tests for influenza virus. A more specific estimate of influenza activity can be obtained by multiplying ILI with corresponding weekly regional viral isolation information, resulting in a measure we refer to as ILI+, defined as the number of influenza positive patients per 100 patient visits. As in our previous studies, we use city and state level GFT ILI estimates multiplied by regional NREVSS viral isolation rates to obtain ILI+, as the metric of observed influenza incidence [5].
Forecast targets
We produced weekly forecasts of three target metrics for each influenza outbreak: the highest observed weekly ILI+ (peak incidence); the week during which peak ILI+ occurred (peak week); and the total ILI+ over the influenza season, which we define as a 20-week period beginning on the 45th calendar week of the year (total incidence).
Forecast methods
Weekly forecasts of influenza outbreak trajectories, outbreak peak ILI+, total ILI+ and outbreak peak timing were produced using 21 different forecast methods. Of the 21 methods, 20 are variations of a mathematical model of disease transmission coupled with a data assimilation, or filtering, method, and 1 is a statistical model based on historically observed outbreaks. We generated retrospective forecasts for 95 cities and the 48 contiguous United States with available records during the 2005–2006 through 2014–2015 influenza seasons, excluding the pandemic seasons of 2008–2009 and 2009–2010. Pandemic seasons were excluded because the individual forecast systems used in this study were designed specifically for seasonal outbreaks. While the model-filter forecasts could be adapted to forecast pandemics or irregularly timed outbreaks (for example [13–15]), the Bayesian Weighted Outbreaks method in particular is not appropriate for forecasting pandemics as it relies on the assumption that the outbreak in progress will be similar in timing and magnitude to previously observed outbreaks.
Mathematical models of disease transmission.
Our previous studies using model-filter forecasts of influenza feature a humidity-forced Susceptible-Infectious-Recovered-Susceptible (SIRS) model to simulate influenza transmission [2, 5, 16]. This model assumes a perfectly-mixed population and is described by the following equations. (1) (2) where N is the population size, S and I are, respectively, the number of susceptible and infectious individuals in the population, and N-S-I is the number of recovered (immune) individuals. The model parameters are: D, the mean duration of infection; β(t), the transmission rate at time t, L, the mean duration of immunity; and α, the rate of travel-related imported influenza into the model domain.
The transmission rate β(t) is related to the basic reproductive number, β(t) = R0 (t)/D. R0(t) is modulated daily based on the empirical relationship between absolute humidity and viral transmission[17]: (3) where R0min and R0max are the minimum and maximum daily basic reproductive numbers, respectively, and q(t) is time-varying daily average specific humidity.
In addition to the SIRS model, we consider three alternate model structures: Susceptible-Infectious-Recovered (SIR); Susceptible-Exposed-Infectious-Recovered (SEIR); and Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS). The Exposed compartment in the SEIR and SEIRS models represent a latent period of infection. The equations describing these additional model structures are provided in S1 Appendix.
Filter methods.
The mathematical models described above are coupled with filter methods for the weekly assimilation of ILI+ observations and optimization of the model state variables and parameters. These filters use Bayesian inference to calculate the posterior conditional distribution of parameters and state variables given observed ILI+, based on the prior distribution of the model ensemble and the conditional distribution of observed ILI+ given model parameters and state variables.
Five different data assimilation methods were used with each of the four model structures. These consist of three ensemble filter methods—the ensemble Kalman filter (EKF)[18], the ensemble adjustment Kalman filter (EAKF)[19] and the rank histogram filter (RHF)[20], and two particle filter methods—a basic particle filter (PF) with resampling and regularization[21] and the particle Markov chain Monte Carlo (pMCMC) method[22]. A description of each filter method is provided in S1 Appendix. For full filter details, we refer readers to the original texts referenced above.
The combined model-filter system recursively updates the model state variable and parameter estimates with each new weekly ILI+ observation. Through this process, these estimates of the observed and unobserved variables and parameters values are nudged closer to their true values. Following the assimilation of the most recent weekly ILI+ observation, the optimized set of model simulations is propagated forward in free simulation through the remainder of the season, producing a forecast of future ILI+ observations, from which we calculate the predicted timing and magnitude of peak influenza incidence, and total incidence.
Bayesian weighted outbreaks.
The final forecast method, which we call Bayesian weighted outbreaks (BWO), is a statistical method that uses Bayesian model averaging to describe the trajectory of ILI+ for the outbreak of interest as a weighted average of outbreak trajectories from prior seasons. This method has been used in weather forecasting[23], and has previously been adapted to forecast dengue outbreaks[6]. The weights assigned to candidate trajectories are determined based on the likelihood of the ILI+ values observed for the outbreak in progress given ILI+ during the same time period (weeks t-7 through t) in the candidate trajectories (see [6] for further details). The forecast trajectory of ILI+ obtained by taking the weighted average is used to predict peak timing, peak incidence and total incidence in the outbreak of interest.
The pool of candidate trajectories used in the BWO retrospective forecasts included ILI+ observations from all 145 locations (48 states and 97 cities) available for the seasons prior to the season being forecast (e.g. retrospective forecasts of the 2005–2006 season considered ILI+ trajectories from 2003–2004 and 2004–2005—seasons 1 and 2), excluding the pandemic years of 2008–2009 and 2009–2010. More generally, retrospective BWO forecasts of influenza season N use candidate trajectories from seasons 1 through N-1.
Superensemble model averaging algorithm
Superensemble forecasts were created for the 2005–2006 through 2014–2015 influenza seasons (excluding the pandemic seasons 2008–2009 and 2009–2010) by taking the weighted average of the 21 individual weekly forecasts for each location. The superensemble weights, which dictate the contribution of each individual forecast to the superensemble, are determined using maximum likelihood estimation of the conditional probability distribution function (PDF) over a selected number of training forecasts: (4) where the left hand side of the equation is the probability distribution of the superensemble forecast, and the right hand side is the weighted sum of the 21 individual forecast distributions, gk(y'|f'k,m). More formally, y' is the true value of the training outbreak metric m (peak timing, peak incidence or total incidence), wk,m is the probability that individual forecast method k is the most accurate method, and gk(y'|f'k,m) is the PDF of y', conditional on training forecast f'k,m, given that f'k,m is the most accurate forecast of y'm. This conditional PDF is assumed to be normal with mean f'k,m and standard deviation σ. For simplicity, σ is assumed equal for all individual forecasts, and is determined through the maximum likelihood estimation of Eq 4 to obtain wk,m, which serve as the superensemble weights (see Raftery et al.[23] for full details).
Superensemble weights for season N are trained using individual forecasts from 2003–2004 through season N-1. The set of BWO training forecasts, f'BWO,m, are produced using a leave-one-out approach for training seasons 1 through N-1. That is, training forecasts for each season from 1 through N-1 were constructed using trajectories using all other seasons between 1 and N-1. The number and diversity of candidate trajectories increases over time, as each subsequent year adds 145 additional ILI+ trajectories to the pool. The model-filter forecasts do not use historical observations, and thus do not require a leave-one-out approach for training forecasts.
The superensemble weights wk,m are then applied to the point estimates of the target metric from the 21 individual forecasts, fk, for the time t, location l, and metric m of interest to obtain the superensemble forecast, SE: (5)
The probability distribution function of the superensemble forecast obtained from Eq 4 is used to determine credible intervals around each forecast (for example, S2 Fig). The width of the credible intervals is a function of both the spread of the point estimates from the 21 individual forecast methods, as well as the estimated variance of each individual forecast over the training period (σ2) [23].
Superensemble weighting schemes
The baseline superensemble forecasts were made by applying a single set of superensemble weights across all locations and times within an influenza season. However, based on previous analyses of individual forecast system performance (e.g. [2, 5, 6]), we hypothesized that superensemble performance would improve if superensemble weights were stratified by the following variables: calendar week of forecast, lead time relative to forecast peak (weeks between the week of forecast initiation and the predicted peak), geographic region, population size, and population density.
A final set of forecasts was produced by stratifying superensemble weights by lead time relative to the actual peak (weeks between the week of forecast initiation and the week of the true peak). While this weighting scheme could not be implemented in an operational real-time forecast, it is useful to know how the superensemble would perform under this idealized condition, as this may represent an upper bound to improvements that can be achieved using a weighting scheme based on forecast timing.
The method for stratifying superensemble weights consisted of dividing forecasts into bins according to the variable of interest. We then obtained weights for each bin by including only training forecasts falling into that bin in the algorithm described in Eq 4. In setting the bin sizes for each variable, our objective was to resolve potential differences in forecast performance. This objective was balanced by the need to include sufficient training forecasts in each bin to avoid over-fitting.
Forecasts stratified by lead time (actual or predicted) were grouped using the following bin edges, where negative values indicate weeks prior to the peak and positive numbers are weeks after the peak: [<-8, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5–8, 9–12, >12]. We selected a fine resolution of 1 week around peak, with wider bins at either end, as fewer outbreaks have lead times in these categories. Actual lead time is simply the week of the forecast minus the week that peak is eventually observed. Forecast predicted lead time is calculated by taking the mean prediction of peak week from the 21 individual forecasts, and subtracting this mean value from the week of forecast.
Geographic regions were grouped according to the ten US Health and Human Services Regions, as these are the standard geographical groupings used by the CDC to describe influenza activity. Calendar week groupings were delineated by individual weeks. Population density and populations size were arbitrarily binned into quintiles for cities and terciles for states.
S1 Appendix. Additional details on forecast methods.
https://doi.org/10.1371/journal.pcbi.1005801.s001
S1 Fig. Performance of superensemble forecasts compared to individual forecasts by influenza season.
Each line shows the results of one forecast, with grey dotted lines representing the 21 individual forecasts and colored lines representing superensemble forecasts. SE-baseline refers to the baseline superensemble forecast, whereas SE-week, SE-region, SE-forlead and SE-actlead refer to superensemble forecasts with weights stratified by forecast week, HHS region, lead relative to predicted peak, and lead relative to observed peak, respectively.
S2 Fig. Sample superensemble forecast with 95% credible intervals.
The weekly SE-baseline and SE-week forecasts are shown for a sample outbreak. 95% credible intervals are indicated by the shaded areas.
S3 Fig. Coverage of forecast credible intervals.
The points on the graph show the percent of observations falling within the specified credible intervals of the superensemble forecasts.
S4 Fig. Heat map of forecast rankings.
Same as Fig 6 in main text of paper, but with superensemble weights stratified by lead time of forecast relative to observed outbreak peak.
1. Biggerstaff M, Alper D, Dredze M, Fox S, Fung IC, Hickmann KS, et al. Results from the centers for disease control and prevention's predict the 2013–2014 Influenza Season Challenge. BMC Infect Dis. 2016;16(1):357. pmid:27449080.
2. Shaman J, Karspeck A, Yang W, Tamerius J, Lipsitch M. Real-time influenza forecasts during the 2012–2013 season. Nature communications. 2013;4:2837. pmid:24302074.
3. Chretien JP, George D, Shaman J, Chitale RA, McKenzie FE. Influenza forecasting in human populations: a scoping review. PLoS One. 2014;9(4):e94130. pmid:24714027.
4. Brooks LC, Farrow DC, Hyun S, Tibshirani RJ, Rosenfeld R. Flexible Modeling of Epidemics with an Empirical Bayes Framework. PLoS computational biology. 2015;11(8):e1004382. pmid:26317693.
5. Yang W, Karspeck A, Shaman J. Comparison of filtering methods for the modeling and retrospective forecasting of influenza epidemics. PLoS computational biology. 2014;10(4):e1003583. Epub 2014/04/26. pmid:24762780.
6. Yamana TK, Kandula S, Shaman J. Superensemble forecasts of dengue outbreaks. Journal of The Royal Society Interface. 2016;13(123):20160410.
7. Yun W, Stefanova L, Krishnamurti T. Improvement of the multimodel superensemble technique for seasonal forecasts. Journal of Climate. 2003;16(22):3834–40.
8. Krishnamurti TN, Surendran S, Shin DW, Correa-Torres RJ, Kumar TSVV, Williford E, et al. Real-time multianalysis-multimodel superensemble forecasts of precipitation using TRMM and SSM/I products. Monthly Weather Review. 2001;129(12):2861–83.
9. Krishnamurti TN, Kishtawal C, Zhang Z, LaRow T, Bachiochi D, Williford E, et al. Multimodel ensemble forecasts for weather and seasonal climate. Journal of Climate. 2000;13(23):4196–216.
10. Chakraborty P, Khadivi P, Lewis B, Mahendiran A, Chen J, Butler P, et al., editors. Forecasting a moving target: Ensemble models for ILI case count predictions. Proceedings of the 2014 SIAM international conference on data mining; 2014: SIAM.
11. Ray EL, Reich NG. Prediction of infectious disease epidemics via weighted density ensembles. arXiv preprint arXiv:170310936. 2017.
12. Ginsberg J, Mohebbi MH, Patel RS, Brammer L, Smolinski MS, Brilliant L. Detecting influenza epidemics using search engine query data. Nature. 2009;457(7232):1012–4. pmid:19020500
13. Yang W, Lipsitch M, Shaman J. Inference of seasonal and pandemic influenza transmission dynamics. Proceedings of the National Academy of Sciences of the United States of America. 2015;112(9):2723–8. pmid:25730851.
14. Yang W, Cowling BJ, Lau EHY, Shaman J. Forecasting Influenza Epidemics in Hong Kong. PLoS computational biology. 2015;11(7):e1004383. pmid:26226185
15. Yang W, Olson DR, Shaman J. Forecasting Influenza Outbreaks in Boroughs and Neighborhoods of New York City. PLoS computational biology. 2016;12(11):e1005201. pmid:27855155
16. Shaman J, Karspeck A. Forecasting seasonal outbreaks of influenza. Proceedings of the National Academy of Sciences. 2012;109(50):20425–30.
17. Shaman J, Kohn M. Absolute humidity modulates influenza survival, transmission, and seasonality. Proceedings of the National Academy of Sciences. 2009;106(9):3243–8.
18. Burgers G, Jan van Leeuwen P, Evensen G. Analysis scheme in the ensemble Kalman filter. Monthly weather review. 1998;126(6):1719–24.
19. Anderson JL. An ensemble adjustment Kalman filter for data assimilation. Monthly weather review. 2001;129(12):2884–903.
20. Anderson JL. A non-Gaussian ensemble filter update for data assimilation. Monthly Weather Review. 2010;138(11):4186–98.
21. Arulampalam MS, Maskell S, Gordon N, Clapp T. A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on signal processing. 2002;50(2):174–88.
22. Andrieu C, Doucet A, Holenstein R. Particle markov chain monte carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2010;72(3):269–342.
23. Raftery AE, Gneiting T, Balabdaoui F, Polakowski M. Using Bayesian model averaging to calibrate forecast ensembles. Monthly Weather Review. 2005;133(5):1155–74.
Is the Subject Area "Influenza" applicable to this article?
Is the Subject Area "Epidemiology" applicable to this article?
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text:
Q: Is this a fragment or a sentence? Is this a sentence:
Seems we could use some shaping from our building practices today.

A: Formally? No.
It's missing a subject.
But in informal settings it's fine. The subject is elided.
Our department seems we could use some shaping from our building practices today.
or
It seems we could use some shaping from our building practices today.
etc.

redpajama_set_name: RedPajamaStackExchange


Thatched and atmospheric, this parrilla is a popular Paraná choice. Fridays and Saturdays see special fire-roasted options, otherwise just enjoy the usual chargrilled selection and solicitous service. Deep-pan stews are designed to share between three or more. Starters, drinks and the salad bar are overpriced, but the meat comes out to the table in most generous portions.


© Copyright 2018 Orient Semiconductor Electronics, Ltd. All rights reserved.
OSE is one of the world's leading electronics contract manufacturing services (EMS/ECM) providers. We are also one of the few major CMs specializing in high-mix electronics manufacturing. We offer our services from our locations in the US, Taiwan and China.
OSE is a leading IC packaging and testing services provider. We are also a leading Flash Memory Card Manufacturer.


text:
Tunisia intercepts nearly 100 Europe-bound migrants
Tunisia said Tuesday it had foiled several attempts by almost 100 migrants to reach Europe via the Mediterranean Sea since the previous day.
Tunisia and Libya are the main points of departure for migrants trying to reach Europe from Africa. Sea crossing attempts tend to increase during spring and summer.
Tunisia's National Guard said it had prevented five maritime crossings and rescued 80 people, mostly Tunisians and including 35 migrants from sub-Saharan Africa.
It said "preventive operations" were also carried out near Menzel Temime in the north, Mahdia and Kerkennah on the central coast and Zarzis in the south, leading to 11 arrests.
The National Guard said it seized an undisclosed sum of money and an inflatable boat in the operations.
On Monday, maritime and military authorities said 657 people were rescued or prevented from trying to cross in 46 separate incidents between Friday and Monday.
Tunisia is in the throes of political and economic crises, and Libya has been gripped by lawlessness since 2011 that has seen militias turn to people trafficking.
The two countries are the gateway for sub-Saharan Africans hoping for a better life by escaping impoverished and strife-torn countries such as Sudan.
The EU's Frontex border agency said the central Mediterranean route was used by more than 42,500 migrants between January and July, up 44 percent compared with the first seven months of 2021.
Tags: Europe, migrants, Tunisia
Brazil to privatise São Sebastião port
Maersk, Suez Canal sign $500m Port Said development deal

redpajama_set_name: RedPajamaCommonCrawl


text:
Outdoor Gear & Product Reviews
Jackery Fit Portable Battery Charger 10200Mah Package
The Jackery Explorer portable powerstation may be the best option if you need to quickly power small appliances. It does have some limitations. We'll show you how Jackery power stations work and the different ways to use them. These power stations can be used to power a refrigerator, which may surprise you. You don't even need hardwiring! These are just a few of the many benefits that this power station offers.
You can choose from a variety Jackery units depending on your needs. The Explorer 160 is ideally suited for charging mobile devices, while the Explorer 1000 and 1500 are designed for high Wattage devices. The Explorer unit is available in various sizes, and they come with a surge power rating. This rating indicates how long the inverter can run during a spike in power. These surges are usually short-lived.
The Jackery 1500W solar generator comes with four panels, and it can charge from zero to 80% in four hours. The Jackery 500 unit, on the other hand, can be charged from 0% to 80% with one 100W panel. These panels have a limited charging capacity. This depends on how much sun is available and how much power they draw. These two factors can affect the Jackery's ability provide energy for your devices. But if you're not looking to spend time outdoors, the Jackery solar generator is a great choice.
The Jackery battery can last for two to three years, but you'll need to regularly recharge it. The company recommends that you charge your unit every three to six months. As of this writing, the Jackery is still the best portable power station on the market, but it's not the best solution for full-time vanlife. If you need emergency power for a limited time frame, you'll need to find a more powerful battery. The Jackery is not up to the mark despite its many positives.
The Jackery's innovative technology allows you to use solar energy with maximum efficiency. However, the panels can be difficult to use in certain situations. Their foldable design means that they need to be properly angled to receive the sun's rays. This can be challenging, since you'll need to keep adjusting them as the sun moves. Despite the lightweight design of the Jackery solar panels, they can be difficult to unload.
Besides providing electricity, the Jackery's new lineup of portable solar generators has a wide price range. The Entry Mini (E160) can be recharged by a single 60W panel, while the Jackery Explorer 1500 can charge up to two 100W panels in nine hours. Jackery is celebrating their 9th anniversary with a site-wide sale that offers up to 15% off all its products.
The Jackery Explorer 1500 portable power station is solar-ready and promises 1800 watts continuous AC power. Its 1488 watt-hours of power make it an ideal choice for a home office, van, or other applications. There are many charging options and it can be charged from different power sources. There are many different models to choose from, so consider what works best for you. If you're traveling for a long period of time, a portable power station might be the best option for you.
The Explorer 1500 is a top-of-the-line power supply, and the build quality is excellent. It doesn't have sharp corners, which could potentially smack you in the leg. The LCD is clear and easy to read, unlike the previous Explorer 1000 iteration. A high-quality power supply will last a long time. However, if you're not going to use the device often, you may want to consider other options.
The Jackery Explorer 1000 is a great portable power station that will keep your electronics running for hours and days. It is about the same size as a small microwave but it is quieter than a portable gas generator. The Explorer 1000 offers a variety of ports and an intuitive interface. It is small enough to protect electronics from the elements, but strong enough to last.
Jackery Explorer 240 Portable Power Station Reviews
Jackery Giant+ Powerbank
Jackery ソーラー
Jackery Pop 5000Mah Ultra-Slim External Battery
Jackery Gets Hot
Jackery Mini Premium 3350Mah Portable Charger
© 2023 Outdoor Gear & Product Reviews • Built with GeneratePress


Is this Blu-ray going to be released any time soon?
This has finally been released - but will it find many takers with an MRP of Rs 1999?
Can anyone, who was able to procure, report what the quality is like? I don't have a BRD player, hence I did not purchase it.
The rip on the net shows a DNRed image.
tools (pun intended) ruin even the nicest sources.
Last edited by mhafner on Sat May 10, 2014 9:21 am, edited 2 times in total.
The rip on the net shows a DNRed image. I remember the prints had such a nice image from DI data. So this could be a top BD.
I remember the prints had such a nice image from DI data. So this could have been a top BD.
I'll leave this here for you .


While recent manned spaceflight news has been somewhat disappointing, exciting things are still happening with robotic probes in deeper space.
Saturn probe Cassini did its closest pass yet at Enceladus yesterday, one of the stranger moons in the Saturn system. The bright white surface of Enceladus, mostly coated with clean water ice, is smoother and less cratered than most moons like it, with long rifts and valleys wrinkling its face. This would indicate recent geologic activity: tectonics caused by gravitational tidal forces from Saturn, wiping out impact craters and forming cracks and bumps. Enceladus also has a tenuous atmosphere, which might be caused by cryovolcanoes spewing material from underground, covering the moon's surface with icy particles, and replenishing Saturn's E ring with new material. This is all theory, of course: no volcanic plumes have been spotted on Cassini yet.
I'm watching the Enceladus Flyby page for updates, but there haven't been any yet since the scheduled event yesterday. Maybe it was boring. More Enceladus photos by Cassini.
Planetary.org's Rocks Amidst the Rings, a lovely compilation of Cassini photography from Saturn.
Cassini at Saturn, Kokogiak's Flickr photoset of favorite Cassini imagery.
Next post: Deep Impact at Tempel 1: Nought But Dust?


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Fjallraven Debuts the Eco-Friendly Version of Their Marquee Backpack: The Tree Kanken
By James Schiff August 16, 2021
Courtesy of Fjallraven
Even if you had never stepped foot in a Fjallraven store, you'd recognize the Kanken backpack when you saw it. This often brightly colored, boxy backpack is a regular sight on high school and college campuses around the US (and Sweden, of course). And while it remains a perennial favorite, Fjallraven has decided to give their marquee bag a bit of an eco upgrade in the form of their new Tree-Kanken. Fjallraven sent SPY a sample of their new Tree-Kanken for testing and review.
As the name suggests, this version of the Kanken is made from trees. To be more specific, Fjallraven created the backpack with a new material which they call "Pine Weave." Pine Weave, in essence, is wood sourced from Sweden that has been boiled into a pulp and then chemically treated to turn into a sticky cellulose, before being spun into a fiber. This fiber is then used to build the bag, making it a sturdy and sustainable bag that is just as tough as its predecessor. But the base material isn't all that's eco about this backpack. Even the chemicals used to treat the backpack (to help make it water-resistant) are 99.6% recycled.
Fjallraven Tree-Kanken
Though this is the latest eco-turn for the Swedish company, it is by no means their first foray into the eco-space. In fact, just a few months back, Fjallraven debuted their Samlaren collection, a line that utilized the literal scraps on the cutting room floor to create a handful of bags and jackets. But while we enjoyed the creativity in Samlaren, the Tree-Kanken feels much more sustainable. Fjallraven's pine weave technology seems like a first step down a long road of eco-friendly products. And judging by the quality of this bag, we're excited to see what the future brings.
Fjallraven created their Tree-Kanken to be tough. In hand, it looks to be just as durable as the original bag, with the Pine Weave feeling like a dead ringer for waxed canvas. In fact, if I wasn't sure this was made from trees, I might think otherwise. Physically, the Tree-Kanken remains fairly faithful to the original. It still sports its iconic top handle but has done away with its front pouch pocket, in place of MOLLE webbing. This gives the Tree-Kanken more of an outdoor tilt, making it feel like more of a hiking backpack than a college backpack.
In typical Fjallraven fashion, the Tree-Kanken is available in a handful of colors. Though not nearly as bright as their original Kanken, you can still pick up the Tree-Kanken is a pleasant mustard yellow, a cool blue-gray, a piney sage-green and an ashy gray.
Fjallraven will debut their new bag on August 16th on Fjallraven.com, and then on partner sites such as Nordstrom, Urban Outfitters and REI starting in mid-August. If you're looking for a new bag that does right by our planet, the Fjallraven Tree-Kanken should be at the top of your list.
The 30 Best Backpacks for College Students in 2021
Gear Outdoors Back to School Backpacks Best New Product fashion News outdoors spy finds


New! Now 10% more jerky for the same price.
Made from American bison that roam and graze freely on the open prairie, our Buffalo Jerky tastes exactly as it should—pure, robust and delicious. The 100% grass-fed, free-range, antibiotic- and hormone-free buffalo is lightly seasoned and dried for a flavorful, hearty snack that's both portable and nutritious. The unopened package requires no refrigeration and is backpack, boat bag and shelf stable. We love this jerky as a convenient, tasty snack on the go, or as a satisfying supplement to camp meals.
Our Buffalo Jerky comes from the affiliated ranches of Wild Idea Buffalo, which represent more than 50,000 acres of recovering grasslands. Through their light grazing habits, nutrient input and soil-tilling hooves, the free-roaming bison of these ranches are vital to preserving the Great Plains ecosystem. Wild Idea harvests their buffalo in the field and processes them locally, providing jobs for the regional economy. This is a business we're proud to support.


Radiation-induced pulmonary fibrosis (RIPF) results from thoracic radiotherapy and severely limits the use of radiotherapy. Recent studies suggest that epithelium-to-mesenchymal transition (EMT) contributes to pulmonary fibrosis. Although miRNA dysregulation participates in a variety of pathophysiologic processes, their roles in fibrotic lung diseases and EMT are unclear. In this study, we aimed to identify key miRNAs involved in this process using a mouse model of RIPF previously established by irradiation with a single dose (20 Gy) of 60Co γ-rays. At 2-weeks post-irradiation, a set of significantly upregulated miRNAs was identified in lung tissue by miRNA array analysis. This included miR-21, which has been reported to contribute to the pulmonary fibrotic response induced by stereotactic body radiotherapy. Here, we showed that miR-21 expression increased in parallel with EMT progression in the lungs of irradiated mice. Ectopic miR-21 expression promoted EMT progression in lung epithelial cells. Furthermore, downregulation of miR-21 expression by transfection of its inhibitor inhibited ionizing radiation (IR)-induced EMT. Knockdown of PTEN, which is the functional target of miR-21, reversed the attenuation of IR-induced EMT mediated by miR-21 downregulation. Radiation treatment decreased PTEN expression and increased Akt phosphorylation; these effects were abolished by the miR-21 inhibitor. MiR-21 overexpression in lung epithelial cell also downregulated PTEN expression and upregulated Akt phosphorylation. In conclusion, we have demonstrated that miR-21 functions as a key regulator of IR-induced EMT in lung epithelial cells via the PTEN/Akt pathway. Targeting miR-21 is implicated as a novel therapeutic strategy for the prevention of RIPF.


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Aliko Dangote Hosts LBS at Dangote Lekki Refinery
President/CEO, Dangote Group, Aliko Dangote hosted students, participants and staff of Lagos Business School (LBS) at the Dangote Lekki refinery, recently.
This is the second year in a row that students from LBS will be visiting the Dangote Refinery for an experiential leg of their study programme. Ifeanyi Obiorah, Director, Executive Education LBS stated that the visit to the refinery was an experiential learning experience conducted for the participants of the Owner Manager Programme with the aim of exposing them to unique opportunities that can inspire them to scale their businesses and transform the Nigerian economy." The purpose of the visit was to give the Owner Manager's an experiential learning experience by allowing them the opportunity to interact with an inspiring entrepreneur who started a business just like themselves and has greatly contributed to the Nigerian economy and grown his business from a Nigerian brand to a global brand" he said.
Dangote delivered a lecture which stressed the importance of the diversification of the Nigerian economy. He stated that there is a dire need for Nigeria to diversify the economy and focus on other revenue pulling streams other than oil. "It is extremely crucial for us to ensure Nigeria is a diversified economy, we need to invest in other things apart from oil, if we do not invest there will be no growth, what will take us out of recession is growth" he said.
Dangote further stated that Nigeria should focus on agriculture as it is a sure way of boosting the Nigerian economy and attracting foreign exchange and exports. "If I knew one thing now I did not know back then, is the importance of agriculture. Nigeria needs to focus more on agriculture. We do not have food security because a large percentage of our food is imported. Agriculture is very important; the people from rural areas are not concerned about recession, because they are very into agriculture" he said.
The participants present which included the Owner Managers Programme (OMP), the Chief Executive Programme (CEP) and the MBA programme appreciated Alhaji Aliko Dangote for the lecture and engaged him with questions which led to healthy discussions bordering on how to take advantage of the current economic situation of the country which will enable them take their careers and various businesses to the next level.
The visit to the refinery came to a close with a guided tour of the ongoing construction of the Dangote refinery grounds which includes a petrochemical project, gas pipeline project and a fertiliser project.
Tolu Omoyeni
Lagos Business School announces new Director of Executive Education
The graduate school of Pan-Atlantic University, Lagos Business School, has announced the appointment of Victor Banjo as its new Director of Executive Education.
Lagos Business School MBA students shine at 2020 Africa Business Ethics Conference
First-year students of the Lagos Business School Full-time MBA (MBA 19) have taken the lead at the 2020 Africa Business Ethics Conference pitch awards by emerging in the 1st, 2nd, 4th and 5th positions.
Lagos Business School appoints Olayinka David-West as Associate Dean
Professor of Information Systems, Olayinka David-West has been appointed Associate Dean of Lagos Business School.
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This post is to let everyone know that we have added a 3rd DNS server to provide an extra level of redundancy in our DNS systems.
This DNS server will only be used if you add it to your domains at their registrar, so we recommend that you do so wherever you can. It's not critical, but extra levels of protection against downtime never hurt.
[note, versions without the "HOSTED.BY" are also available, but we prefer that you use the fully spelled out version so it is clear to anyone who looks that your sites are our customers not properties].
Hey guys! It's been a while, but the time has come for a new Vae feature. And we think this one is huge. We're proud to announce that Vae now has full support for a separation of Staging and Production environments on your website.
Once you opt-in to Vae's Production Environment feature for one of your domains by going to the Domains tab under the Vae tab, Vae will create a Production Environment for that website. FTP will be directed to the Staging Environment, which can be browsed at http://<;site>.vaesite.com/. Any changes made to the FTP will be instantly reflected there. However, they will not be reflected on the main domain until perform a 'release'.
You can release your site to the production environment from the new Production Environment tab under the Site tab.
5 previous releases are stored, and you may roll back to them at any time. This provides an awesome recovery option if you accidentally release a bad copy of the site.
You may also make a new release by using the Vae Local Development Environment. Simply type verb release to make a new release to production. Or type vae stagerelease to update the Staging Environment and Production Environment with the current copy from Subversion.
The best part of all: there is no additional cost for this feature. It's just one more thing that we're doing to make Vae the most powerful and unique shared hosting environment in existence. Thanks for your support!
If you have any questions, please direct them to support@actionvae.com.
Today we're showing you how to dynamically create zip files using Vae's <v:zip> tag. For more videos and examples, check out our Documentation and Integration Center.
Permalinks keep your address bar clean, is good for SEO, and is easy to implement with Vae. As always, check out our Documentation and Integration Center for more videos and tutorials.
As you may know, <v:rss> makes it easy to quickly create an RSS feed from any Collection in your site. Vae also takes this a step further by making it easy to create an RSS feed that can be submitted to Google Product Search, so potential customers can locate your items when querying this search engine. In this mini tutorial, we'll create an RSS feed that's ready to submit to Google Product Search.
<v:rss> works with any Collection, so you can quickly create RSS feeds from your existing Collections.
If our customers wanted to easily stay up-to-date on what records we have for sale, they could subscribe to this RSS feed using any browser or RSS client. Since we can use <v:rss> to output the contents of any Collection, we could just as easily create an RSS file for our blog or any other Collection our customers might want to subscribe to.
Since we integrated the Google Base Tags into our RSS feed, it's ready to be submitted to Google Product Search [just follow Google's instructions]. After we submit it, our records will appear in Google Product Search results, and we'll have increased traffic to our website without much effort.


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Nine Soldiers Officially Named to 2014 U.S. Olympic Team
By Tim Hipps
Army Installation Management Command
COLORADO SPRINGS, Colo., Jan. 27, 2014 - Nine soldiers in the U.S. Army World Class Athlete Program are members of the U.S. Olympic Team that will compete at the 2014 Olympic Winter Games, scheduled for Feb. 7 through 24 in Sochi, Russia.
The U.S. Olympic Committee officially announced the team today.
The soldier-athletes named to Team USA are 2010 Olympic gold medalist in four-man bobsled Sgt. Justin Olsen, 26, of San Antonio; 2010 Olympic bobsledder Capt. Christopher Fogt, 30, of Alpine, Utah; 2010 Olympic bobsledder Sgt. Nick Cunningham, 27, of Monterey, Calif.; bobsledder Sgt. Dallas Robinson, 31, of Georgetown, Ky.; 2006 Olympic luger Sgt. Preston Griffall, 29, of Salt Lake City; and luger Sgt. Matt Mortensen, 28, of Huntington Station, N.Y.
Three WCAP coaches also will represent the U.S. Army in Russia. Team USA luge coach Staff Sgt. Bill Tavares, 50, of Lake Placid, N.Y., will be making his sixth appearance in the Olympics, including once as an athlete and five times as a coach. Team USA skeleton coach Sgt. 1st Class Tuffield "Tuffy" Latour, 45, of Saranac Lake, N.Y., will make his fourth trip to the Olympics. He has coached U.S. and Canadian men's and women's bobsledders to Olympic medals. Team USA assistant bobsled coach 1st Lt. Michael Kohn, 41, of Myrtle Beach, S.C., is a two-time Olympic competitor who will make his Olympic coaching debut at the Sochi Games. He won a bronze medal in four-man bobsled as a WCAP athlete at the 2002 Olympic Winter Games in Salt Lake City.
USA-1 bobsled driver Steven Holcomb, 33, of Park City, Utah, is the reigning Olympic champion in the four-man event. He spent seven years in the U.S. Army World Class Athlete Program.
The 230-member team is comprised of 105 women and 125 men – the largest athlete delegation for any nation in the history of the Olympic Winter Games. The United States will be represented in all 15 disciplines across seven sports, and up to 94 of the 98 medal events that will be contested in Sochi.
"We are thrilled to announce the 230 athletes who will represent Team USA in Sochi," said USOC CEO Scott Blackmun. "This is the largest team we have ever sent to an Olympic Winter Games, and I'd like to commend all of those who helped support our athletes in the pursuit of their Olympic dreams.
"Most of all," he continued, "this is a time to celebrate our athletes, who have made countless sacrifices and dedicated themselves to being their best, both on and off the ice and snow. I am very excited to watch them compete as they represent our nation with excellence and distinction on the world stage."
The 2014 U.S. Olympic Team features 106 returning Olympians – including one five-time Olympian, two four-time Olympians, 10 three-time Olympians and 23 two-time Olympians. Returning from the 2010 Olympic Winter Games in Vancouver, where the U.S. finished first in the overall medal count with 37 medals, are 99 U.S. Olympians. Overall, among the veterans are 49 Olympic medalists, 13 of whom are Olympic champions.
Nordic combined skier Todd Lodwick becomes the first American to compete at six Olympic Winter Games. The two U.S. Olympians headed to their fifth Olympic Games are Billy Demong (Nordic combined) and Bode Miller (alpine skiing). Only four other athletes in U.S. Olympic history, including Lodwick, have competed in five or more Olympic Winter Games.
Additionally, women's bobsled push athletes Lolo Jones – a two-time Olympic hurdler – and Lauryn Williams – a three-time Olympic sprinter – become the ninth and 10th Americans to compete at both the winter and summer editions of the Olympic Games.
Highlighting this list of accomplished U.S. men's athletes are Miller and long track speedskater Shani Davis. A five-time Olympic medalist, Miller needs three medals to match U.S. short track speedskater Apolo Anton Ohno as the most decorated U.S. Olympian in history on the winter side.
Davis is making his fourth Olympic appearance after winning consecutive Olympic gold and silver medals in the 1,000- and 1,500-meter events in 2006 and 2010. Both Davis and snowboarder Shaun White will have the opportunity to become the first American man to win three gold medals in the same event at consecutive Olympic Winter Games.
Headlining the list of U.S. women's athletes are three-time Olympic medalists Julie Chu (ice hockey) and Julia Mancuso (alpine skiing). Mancuso already is the most decorated U.S. Olympic female alpine skier, with one gold medal and two silver medals, while Chu is looking to help Team USA reclaim the top podium spot for the first time since women's ice hockey debuted at the 1998 Olympic Winter Games.
"This distinguished group of athletes represents the largest delegation in the history of the Olympic Winter Games, which is a true testament to the growing number of winter sport opportunities across the United States," said Alan Ashley, chief of the U.S. mission and USOC's chief of sport performance. "With 106 returning Olympians, this year's team is an exceptional blend of youth and experience, and represents the finest our nation has to offer. During the Games, we will continue to support our athletes, coaches and National Governing Bodies in every way possible to succeed."
The 2014 U.S. Olympic Team roster may still be adjusted due to injury, illness or exceptional circumstances up to the technical meetings for each sport.


text:
York Region News
Worms winners at EG biz awards
Cathy's Crawly Composters owner Cathy Nesbitt,
with husband Rick, won the new evironmental award at last week's East Gwillimbury Spirit of Business Awards.
By: Amanda Persico
Who knew creepy crawlers could help an apartment building or a condominium complex go green?
Cathy Nesbitt, owner of Cathy's Crawly Composters, took home the new environmental business award of the year last week for her vermicomposting venture at the East Gwillimbury Spirit of Business awards at Silver Lakes Golf and Country Club.
The new award defines leadership in an area of growing importance, Roberta Fox said, the gala's MC and owner of Fox Group Telecom Consulting, one of the sponsoring companies.
"(Ms Nesbitt) has shown how the lowly worm can help the environment," Ms Fox said.
Ms Nesbitt accepted her award and asked her business peers to think of worms as the romantic type.
"Worms have five hearts. In a pound of worms, there could be four or five thousand hearts," she joked. "So, next Valentine's Day, get a pound of worms."
But worms were not always crawling for Ms Nesbitt's affection.
"I was afraid of worms before I started the business," she said. "They're creepy and slimy. Now, I think they're magic."
The adamant gardener and composter started her wormy business in 2002 when she noticed the group home in which she worked didn't have a composting facility.
"You connect what you do," she said. "If you have lots of food scraps, you have a lot of waste."
Vermicomposting is an on-site solution for composting, especially in areas not being serviced by the green bin program, such as apartments, condominiums and schools, she said.
Every day, red worms eat half their weight in food scraps and shredded paper. Ms Nesbitt recommends a two-to-one ratio, where there is two pounds of worms for every pound of food. The harvested castings is like black gold for the soil, Ms Nesbitt said.
"They produce earth's finest fertilizer," she said. "They return the nutrients and the goodness back into the soil."
This is the first year a business has been recognized for its unique environmental achievement, said East Gwillimbury Chamber president, Cindy Thiele.
Winners of the 2008 East Gwillimbury business awards are:
Excellence in small business: Matthew Clulow, Clulow and Associates
Excellence in large business: Craig Evans, Pheasant Run Golf Club
Young entrepreneur of the year: Dino Kotsikas, Atlas Landscaping
Business community service award: Sharon Bates, Tangles Hair Salon
Best new venture/start up: Dr. Nancy Mehi, Mehi Veterinary Mobile
Environmental business of the year: Cathy Nesbitt, Cathy's Crawly Composters
Entrepreneur of the year: Kim Mortson, Body Design
Goto Awards Picture Gallery


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How to create better ads? Do more of them.
Prince released several hundred songs in his lifetime. Picasso produced many thousands of artworks. Their overwhelming desire to create was matched with a deep understanding that practising their art would make them better. AML Creative Director Richard Germain discusses how exercising their creativity has helped the teams at AML to create stronger ideas, faster.
There are a lot of stairs at AML towers; 82 at the last count (I'm sure they increase by one a week). The tall and narrow nature of 101 St John Street means we have to be smart about how we collaborate with each other. Our building may not be open plan, but our mindset is.
One of the most popular initiatives is our monthly creative showcase, an opportunity for the creatives to present some of the simple ideas for complicated businesses (SIFCBs) they've been working on. This month, they've shown two top campaigns – a brand identity, advertising and a very cool video for a new online financial advice service, and an integrated DM and digital campaign for an international asset manager that involves a time capsule… from the future.
As part of the creative showcase, the creatives also show spec work – speculative ideas that they've worked on in their spare time. They can be for any product, service, charity or brand. The only rule is that the work has a simple idea at its heart. It's fun. But it also serves a vital purpose. I am a fervent believer that creativity is just like a muscle. It needs exercising. Don't, and like a muscle (don't I know it) creativity can waste away. It's estimated that one of my heroes, Picasso, created 50,000 artworks in his lifetime. (Let's just think about that for a moment: that's 1.5 pieces of art every day for 91 years.) Similarly the musician Prince, who died last week, released several hundred songs and 39 studio albums, as well as writing hits for many other artists. Their prolificacy makes others in their fields look like hobbyists. It's also why they were so damn good.
Another way that creativity is like a muscle is that the more you use it the stronger and faster it gets. Steve Jobs said, 'Creativity is just connecting things.' In advertising and its associated disciplines that means connecting brands with emotions, products with needs, words with pictures. So it goes without saying that the faster you can make these connections – and the stronger they are – the more successful your work will be. Gary Player, golfing legend, famously said, "The more I practise, the luckier I become." What he could have said was, '…the luckier I get in tournaments.' Advertising isn't a pastime, it's business. So the more we can practise being creative, the luckier we'll be in pressurised environments like the white-hot cauldron of a global pitch.
So what did the ripped creative muscles of AML's writers, art directors and designers generate this month for our creative showcase? In no particular order of excellence (or litigiousness), their ideas included a poster by copywriter, Matt Evans, suggesting that lodging in a shared house could turn out to be a hairy experience; Head of Art, Chris Walker's brilliant ambient media idea for Pledge polish that literally protects wood, plus an ad warning of the shockingly addictive qualities of sugar (clue: it's worse than cocaine). But our favourite is this poster for the Economist, setting forth what we imagine their view on Donald Trump might be. It was written by art director, Stephen O'Neill aka @typechap. We think David Abbott, legendary copywriter and creator of the original Economist campaign, would approve.


Vienna, March 30 (IANS/WAM) The basket of 12 crude oils of the Organisation of Petroleum Exporting Countries (OPEC) closed at $52.93 a barrel on Friday, compared to $54.55 the previous day, the organisation's secretariat said.
The OPEC Reference Basket of Crudes is made up of Murban (UAE), Saharan Blend (Algeria), Girassol (Angola), Oriente (Ecuador), Iran Heavy (Iran), Basra Light (Iraq), Kuwait Export (Kuwait), Es Sider (Libya), Bonny Light (Nigeria), Qatar Marine (Qatar), Arab Light (Saudi Arabia) and Merey (Venezuela). A barrel equals 159 litres.


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Part of Consultancy.org Consultancy.uk
BCG acquires London based design consultancy AllofUs
17 October 2019 Consultancy.uk
More news on
Global management consulting giant Boston Consulting Group has announced a deal to acquire AllofUs. The acquisition of the London-based design consultancy is intended to broaden and deepen BCG's overall digital offerings, while strengthening its design capabilities in particular.
Global spending on design services is at an all-time high, at $40.7 billion, with the market for offerings such as product design, model design, user interface and interaction design forecast to grow at a CAGR of 6.4% between 2017 and 2023. As is the case with almost any professional service which provides a foot in the door of a lucrative market, then, the consulting industry has predictably been making moves to buy its way into the design space. McKinsey & Company, for example, recently created a design wing by combining its acquired properties of Lunar, Carbon12 and Veryday.
McKinsey's MBB rival, Boston Consulting Group, has its own answer to this new opportunity, in the shape of BCG Platinion. The IT architecture and solutions unit of the strategy giant, BCG Platinion, sits alongside several other business units BCG has established to broaden its multidisciplinary offering globally. These including BCG Digital Ventures, its digital innovation, incubation and investment arm; and BCG Gamma, an advanced analytics and data science service. Now, as it looks to meet complex design demand from clients, BCG has bolstered its Platinion brand with the purchase of UK origin consultancy AllofUs.
Commenting on the news, Sherif Choudhry, BCG Platinion's Managing Director for digital products and services, said, "Our clients are demanding high-value design and engineering capability, which we are catalyzing in Europe with AllofUs."
Founded in 2003, AllofUs is an independent design consulting and venturing firm with studios in London and San Francisco. Over the last 16 years, the firm has established a reputation across the world for helping blue-chip corporations and disruptive start-ups invent and scale breakthrough products and propositions. Having been one of a handful of pioneering consultancies to help introduce product and human-centred design methods to the digital world, its professionals have used this design methodology to help clients like Sky, Microsoft, Samsung and Ikea develop category-defining propositions.
The purchase follows the earlier acquisition of Pittsburgh-based digital design and innovation firm MAYA by BCG, in 2017, reflecting the rapid growth of BCG's digital activities supporting design and innovation and complementing BCG's Digital Ventures and Gamma teams. The AllofUs team will now become part of BCG Platinion – an integrated part of DigitalBCG offering technology capabilities around design, engineering, architecture, and data and analytics, among other areas – while AllofUs founders Phil Gerrard and Orlando Mathias will join Platinion's leadership group.
On top of the ready-made client base that the purchase of AllofUs opens up for BCG, the firm also has a history of high-profile partnerships in the technology sector. Previous collaborations have seen AllofUs work with the likes of Google and Facebook to deliver design-led transformation initiatives with Doddle, Taylors of Harrogate and Yale University.
Phil Gerrard, an AllofUs Founding Partner and the company's current CEO, said of the move, "Our capabilities in design thinking, coupled with BCG's strength in business strategy, ensure that we are bringing to market an offering that can deliver value and impact for our clients at the highest level."
M&A in consulting news
More M&A in consulting
How buyers in professional services will approach M&A in 2021 Global M&A advisory firm Equiteq has released the 2021 edition of its annual 'Global Buyers Report', outlining key M&A trends among buyers and investors from across the professional services industry
Private equity moving in on KPMG's restructuring division The sale of KPMG UK's restructuring arm is reportedly progressing at pace, just months after the global leadership of Big Four rival Deloitte vetoed similar efforts in its own British wing.
Equiteq advises on four acquisitions in Americas and Asia Equiteq, a London-headquartered global dealmaker for the professional services industry, has in the past two months closed four deals across the Americas and Asia.
Boston Consulting Group news
More Boston Consulting Group
BCG's LGBT+ community Pride@BCG wins Business Equality Award Boston Consulting Group has been commended for its efforts to support LGBT+ rights in the business community.
Mai-Britt Poulsen new leader of Boston Consulting Group in UK Boston Consulting Group has appointed Mai-Britt Poulsen to lead its operations in the UK, Netherlands and Belgium.
BCG seniors paid over £6,000 a day on test and trace project Senior members of Boston Consulting Group have been paid over £6,000 per day to help improve the UK's floundering test and trace project.
About Consultancy.uk


Raising happy and healthy children, confidence and high self-esteem, coping with change and resilience, acceptance of differences, coping with bullies, dealing with difficult parent behaviours, mixed family hassles.
During normal development kids are exposed to situations that challenge their ability to cope. Problems that include anxiety are common when confronted with school, home and social changes that inevitably occur. Anxiety may be due to separation, school commencement, performance concerns such as public speaking and examinations, fears of injury, trauma and acute stress reactions, heights, insects and bullies.
The importance of sleep hygiene, what is normal sleep, dreams and nightmares, depression and early waking, relaxation techniques, and mindfulness, simplifying the bedroom, dealing with fears at night time.
Low mood such as sadness, mood swings, lack of pleasure and enjoyment, risky behaviours, anger reactions.
Explosiveness, rudeness, swearing, aggression, violence, arguments, hyperactivity, poor prosocial behaviours, conduct problems, controlling and manipulative behaviours, vindictive and spiteful actions, poor social interactions, poor sleep and diet hygiene, attention problems, and poor adaptive skills.
Managing fussy eaters, encouraging good dietary behaviours, encouraging healthy toileting, achieving peace and quiet at meal times, bath and shower time hassles.


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Tristan, Seahaven town garrison, Seahaven.
Inamoca, Training Center, the Crag.
Gwendal, Castle Portmeryron, Ashen Hills, Agyn Peninsula.
Lord Kilburn, Yon-Chall Forest, Agyn Peninsula.
Thurmond, Fine Dwarven Armour, New Sorpigal.
Lihua, Elegant Armour, Karthal Harbor district.
Lowell, Black guard training center Karthal slums.
Torsten, Rune and Craft, Seahaven.
Arnod, Vantyr range, Agyn Peninsula.
Brogan, Black guard training center Karthal slums.
Drengi, Navea plains, Agyn Peninsula.
Aldin, Training Center, New Sorpigal.
Mabo, Training Center, the Crag.
John, The Deathmatch, Karthal Harbor district.
Yumiko, Desolate wilds, Agyn Peninsula.
Oscar, Goblin Watchtower New Sorpigal Mabo, Training Center, the Crag.
Yeshtar, at the end of Tomb of thousand Terrors lv5.
Enora, Training Center, New Sorpigal.
Lord Haart, Haart's Mansion, Seahaven.
Guaora, Training Center, the Crag.
Iason, Praetorian garrison Karthal Harbor District.
Maximus, Sorpigal Garrison, New Sorpigal.
Atlas, Dubra Scrubland, Agyn Peninsula.
Every, Everyman's Armour, the crag.
Wysthal, Wyslin Jungle, Agyn Peninsula.
Tamina, Karthal Slums, by the docks.
Hamato, Lighthouse, Tirya Bay, Agyn Peninsula.
Changbo, Vantyr range, Agyn Peninsula.
Arsene, Seahaven town garrison, Seahaven.
Yaksha, Desolate wilds, Agyn Peninsula.
Caldwell, Caldwell's Weapons, New Sorpigal.
Sandor, Desolate Wilds, Agyn Peninsula.
Faris, Arcane Library, New Sorpigal.
Mizuki, Desolate wilds, Agyn Peninsula.
Have to wait about 38 days, for her to train you.
Guaora, the training center, the Crag.
Shiva, Wyslin Jungle, Agyn Peninsula.
Selena, The moon Doe, Seahaven.
Grimbold, Black guard training center Karthal slums.
Ahlam, Arcane Library Karthal Slums, Erunia at the end of Tomb of thousand Terrors lv5.
Luna, Halloth grove, Agyn Peninsula.
Shihab, Ltinerant Merchant, Ashen Hills, Agyn Peninsula.
Caranthir, Yon-Chall forest, Agyn Peninsula.
Geilir, dwarven district of Seahaven.
Erika, Minho Marsh, Agyn Peninsula.
Lisandre, Chapel of Elrath, New Sorpigal.
Umberto, Church of Elrath, Seahaven.
Orna, Navea delta, Agyn Peninsula.
Johara, Johara's charms and talismans, New Sorpigal.
Hypatia, Great Library of Karthal, Harbor district.
Kastore, at the end of Tomb of thousand Terrors lv5.
Nur, Top Floor The Enigma, Nevea delta, Agyn Peninsula.
Ryu, The lock kit, Karthal Harbor district.
Ciele, the fort, the crag.


text:
Q: How to calculate the double sum Let $L$ be an even  lattice and $L'$ its dual lattice . Consider the sum $$\sum_{\delta\in L'/L}\sum_{\mu\in L'/L}e^{-2\pi i (\mu,\delta)},$$ where $(\mu,\delta)=Tr(\overline \mu \delta)=\overline \mu \delta+\mu \overline \delta .$ If $\delta=0$, then the sum is equal to $|L'/L|$. Why is the sum equal to $0$ if $\delta \ne 0$ ? My idea is to consider representatives $r_1,...r_n$ of $L'/L $ and to use the geometric series , but somehow it does not work .
Thanks for the help .

A: For $A\in GL_n(\Bbb{R})$, $L = A \Bbb{Z}^n=\{ Av,v\in \Bbb{Z}^n\}$ is a lattice in $\Bbb{R}^n$, the norm is $ \|Av\|^2= vA^\top Av$,
We assume that $M=A^\top A\in \frac12 M_n(\Bbb{Z})$ and the diagonal coefficients are integers so that $\forall Av\in L,\|Av\|^2\in \Bbb{Z}$. Even lattice means that $M \in M_n(\Bbb{Z})$.
let $$L' = \{ x\in \Bbb{R}^n, \forall Av\in L, x^\top Av\in \Bbb{Z}\} = A^{-\top} \Bbb{Z}^n= A M^{-1} \Bbb{Z}^n$$
We find $L'' =(A^{-\top})^{-\top}\Bbb{Z}^n= L$ so that
 $$\forall A^{-\top} v\in L', (A^{-\top} w)^\top A^{-\top} v \in \Bbb{Z} \iff A^{-\top} w\in L'' \iff A^{-\top} w \in L$$
For $A^{-\top}w\in L', \not \in L$ then $$\exists A^{-\top} u\in L',\lambda=\exp(2i\pi (A^{-\top} w)^\top (A^{-\top} u))\ne 1$$
And since $M\in M_n(\Bbb{Z}) \implies L\subset L'$
$$S=\sum_{A^{-\top} v\in L'/L} \exp(2i\pi (A^{-\top} w)^\top (A^{-\top} v))=S\lambda= 0$$
$$\sum_{A^{-\top} w\in L'/L,} \sum_{A^{-\top} v\in L'/L} \exp(2i\pi (A^{-\top} w)^\top (A^{-\top} v))= |L'/L|= |\det(M)|$$


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Bhim Sen Sachar (1 de diciembre de 1894 - 18 de enero de 1978)  fue un político indio . Fue el Ministro Principal de Punjab , tres veces.

Primeros años
Sachar nació el 1 de diciembre de 1894. Hizo una licenciatura y un LLB en Lahore y ejerció la abogacía en Gujranwala, que ahora se encuentra en Pakistán . Se sintió atraído por el movimiento por la libertad y se unió al partido del Congreso Nacional de la India a una edad temprana. En 1921, fue elegido Secretario del Comité del Congreso de Punjab Pradesh. Cuando India obtuvo su independencia en 1947, era un miembro importante del partido.

Años en Pakistán
Alrededor de la época de la independencia, Sachar aceptó la ciudadanía de Pakistán y se convirtió en miembro de la Primera Asamblea Constituyente de Pakistán. Más tarde renunció a la ciudadanía de Pakistán y regresó a la India.

De vuelta en la India
En 1949, el Congreso lo eligió para el cargo de Ministro Principal de Punjab . Prestó juramento el 13 de abril de 1949 y sirvió hasta el 18 de octubre de 1949.  Sin embargo, la amarga política de facciones en la unidad del partido estatal entre Gopi Chand Bhargava y Sachar llevó a la primera imposición del gobierno del presidente en cualquier estado de la India en virtud del artículo 365. de la Constitución de la India.

Las primeras elecciones en la India independiente se celebraron en 1952 y la asamblea legislativa de Punjab se formó por primera vez ese año. El partido del Congreso ganó las elecciones provinciales en ese momento, y Sachar se convirtió en el primer ministro nuevamente, sirviendo del 17 de abril de 1952 al 23 de enero de 1956.

Bhim Sen Sachar era suegro del famoso periodista y embajador de India en el Reino Unido, Kuldip Nayar.

Después de dimitir del cargo (debido a la política interna del partido), Sachar fue nombrado gobernador de Odisha por el gobierno sindical. Sirvió de 1956 a 1957. Luego fue nombrado gobernador de Andhra Pradesh y sirvió de 1957 a 1962.

Durante la Emergencia , fue arrestado y enviado a la cárcel con algunos otros líderes disidentes del partido del Congreso, que pertenecían a la "vieja escuela" del partido y habían hablado contra el creciente autoritarismo de Indira Gandhi y su hijo Sanjay .

Vida personal
Sachar se casó a una edad temprana con una niña de su propia comunidad, en un partido concertado por sus padres. Su hijo, Rajinder Sachar (n. 1923) fue un abogado y juez que se desempeñó como presidente del Tribunal Supremo de Delhi,  y fue el famoso presidente del Comité Sachar que produjo un informe sobre la situación de las minorías religiosas en la India. . Otro hijo, el capitán Vijay Sachar del ejército indio, murió en combate en Gaza, donde estaba sirviendo en el contingente indio de la UNEF .. El veterano periodista indio, activista de izquierda y activista por la paz Kuldip Nayar es yerno de Sachar..

Referencias
Personas de Peshawar
Fallecidos en 1978
Nacidos en 1894
Políticos del Congreso Nacional Indio

redpajama_set_name: RedPajamaWikipedia