prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the advantage of decorrelating the data before running the PLS algorithm?

Read the following text and answer briefly.

Context 1: Paper Info

Title: Efficient nonparametric estimation of Toeplitz covariance matrices
Publish Date: March 20, 2023
Author List: Karolina Klockmann (from Department of Statistics and Operations Research, Universität Wien), Tatyana Krivobokova (from Department of Statistics and Operations Research, Universität Wien)

Figure

Figure 1: Spectral density functions (first row) and autocovariance functions (second row) for examples 1, 2, 3 
Figure 2: Distance between the first atom and the first center of mass of aquaporin (left) and the opening diameter y t over time t (right) 
black line in the left plot) confirms that the covariance matrix estimated with our VST-DCT method almost completely decorrelates the channel diameter Y on the training data set Next, we estimated the regression coefficients β with the usual PLS algorithm, ignoring the dependence in the data Finally, we estimated β with PLS that takes into account dependence using our covariance estimator Σ Based on these regression coefficient estimators, the prediction on the test set was calculated The plot on the right side of Figure 2 shows the Pearson correlation between the true channel diameter on the test set and the prediction on the same test set based on raw (grey) and decorrelated data (black) 
Figure 3: On the left, the auto-correlation function of Y (grey) and of Σ−1/2 Y (black), where Σ is estimated with the VST-DCT method; On the right, correlation between the true values on the test data set and prediction based on partial least squares (in grey) and corrected partial least squares (black) 
Uniform distributionThe observations follow a uniform distribution with covariance matrices Σ 1 , Σ 2 , Σ 3 of examples 1, 2, 3, i e , Y i = Σ 1/2 j X i , j = 1, 3, with X 1 ,    the parameter innov of the R function arima sim is used to pass the innovations X 1 ,    , X n i i d Table4, 5 and 6 show respectively the results for (A) p = 5000, n = 1, (B) p = 1000, n = 50 and (C) p = 5000, n = 10 
(A) p = 5000, n = 1: Errors of the Toeplitz covariance matrix and the spectral density estimators with respect to the spectral and L 2 norm, respectively, as well as the average computation time of the covariance estimators in seconds for one Monte Carlo sample (last column) 
(C) p = 5000, n = 10: Errors of the Toeplitz covariance matrix and the spectral density estimators with respect to the spectral and L 2 norm, respectively, as well as the average computation time of the covariance estimators in seconds for one Monte Carlo sample (last column) 
(A) p = 5000, n = 1: Errors of the Toeplitz covariance matrix and the spectral density estimators with respect to the spectral norm and the L 2 norm, respectively Average computation time of the covariance estimators in seconds for one Monte Carlo sample (last column) 
(B) p = 1000, n = 50: Errors of the Toeplitz covariance matrix and the spectral density estimators with respect to the spectral norm and the L 2 norm, respectively Average computation time of the covariance estimators in seconds for one Monte Carlo sample (last column) 
(C) p = 5000, n = 10: Errors of the Toeplitz covariance matrix and the spectral density estimators with respect to the spectral norm and the L 2 norm, respectively Average computation time of the covariance estimators in seconds for one Monte Carlo sample (last column) 

abstract

A new nonparametric estimator for Toeplitz covariance matrices is proposed  This estimator is based on a data transformation that translates the problem of Toeplitz covariance matrix estimation to the problem of mean estimation in an approximate Gaussian regression  The resulting Toeplitz covariance matrix estimator is positive definite by construction, fully data-driven and computationally very fast 
Moreover, this estimator is shown to be minimax optimal under the spectral norm for a large class of Toeplitz matrices  These results are readily extended to estimation of inverses of Toeplitz covariance matrices  Also, an alternative version of the Whittle likelihood for the spectral density based on the Discrete Cosine Transform (DCT) is proposed 
The method is implemented in the R package vstdct that accompanies the paper 

Introduction

Estimation of covariance and precision matrices is a fundamental problem in statistical data analysis with countless applications in the natural and social sciences  Covariance matrices with a Toeplitz structure arise in the study of stationary stochastic n = 1, to the best of our knowledge, there is no fully data-driven approach for selecting the banding/tapering/thresholding parameter 
suggested first to split the time series into non-overlapping subseries and then apply the cross-validation criterion of   However, it turns out that the right choice of the subseries length is crucial for this approach, but there is no data-based method available for this  In this work, an alternative way to estimate a Toeplitz covariance matrix and its inverse is chosen 
Our approach exploits the one-to-one correspondence between Toeplitz covariance matrices and their spectral densities  First, the given data are transformed into approximate Gaussian random variables whose mean equals to the logarithm of the spectral density  Then, the log-spectral density is estimated by a periodic smoothing spline with a data-driven smoothing parameter 
Finally, the resulting spectral density estimator is transformed into an estimator for Σ or its inverse  It is shown that this procedure leads to an estimator that is fully data-driven, automatically positive definite and achieves the minimax optimal convergence rate under the spectral norm over a large class of Toeplitz covariance matrices 
In particular, this class includes Toeplitz covariance matrices that correspond to long-memory processes with bounded spectral densities  Moreover, the computation is very efficient, does not require iterative or resampling schemes and allows to apply any inference and adaptive estimation procedures developed in the context of nonparametric Gaussian regression 
Estimation of the spectral density from a stationary time series is a research topic with a long history  Earlier nonparametric methods are based on smoothing of the (log-)periodogram, which itself is not a consistent estimator   Another line of nonparametric methods for estimating the spectral density is based on the Whittle likelihood, which is an ap-proximation to the exact likelihood of the time series in the frequency domain 
For example, estimated the spectral density from a penalized Whittle likelihood, while used polynomial splines to estimate the log-spectral density function maximizing the Whittle likelihood  Recently, Bayesian methods for spectral density estimation have been proposed (see , but these may become very computationally intensive in large samples due to posterior sampling 
The minimax optimal convergence rate for nonparametric estimators of Hölder continuous spectral densities from Gaussian stationary time series was obtained by under the L p , 1 ≤ p ≤ ∞, norm  Only few works on spectral density estimation show the optimality of the corresponding estimators  In particular, and derived convergence rates of their estimators for the log-spectral density under the L 2 norm, while neglecting the Whittle likelihood approximation error 
In general, most works on spectral density estimation do not exploit further the close connection to the corresponding Toeplitz covariance matrix estimation  In particular, an upper bound for the L ∞ risk of a spectral density estimator automatically provides an upper bound for the risk of the corresponding Toeplitz covariance matrix estimator under the spectral norm 
This fact is used to establish the minimax optimality of our nonparametric estimator for the Toeplitz covariance matrices  The main contribution of this work is to show that our proposed spectral density estimator is not only numerically very efficient, but also achieves the minimax optimal rate in the L ∞ norm, which in turn ensures the minimax optimality of the corresponding Toeplitz covariance matrix estimator 
The paper is structured as follows  In Section 2, the model is introduced and ap-proximate diagonalization of Toeplitz covariance matrices with the discrete cosine transform is discussed  Moreover, an alternative version of the Whittle's likelihood is proposed  In Section 3, new estimators for the Toeplitz covariance matrix and the precision matrix are derived, while in Section 4 their theoretical properties are presented 
Section 5 contains simulation results, Section 6 presents a real data example, and Section 7 closes the paper with a discussion  The proofs are given in the appendix to the paper 

Set up and diagonalization of Toeplitz matrices

Let Y 1 ,       , Y n i i d  ∼ N p (0 p , Σ), where Σ is a (p × p)-dimensional positive definite covariance matrix with a Toeplitz structure, that is, Σ = {σ |i−j| } p i,j=1 0  The sample size n may tend to infinity or to be a constant  The case n = 1 corresponds to a single observation of a stationary time series, and in this case the data are simply denoted by Y ∼N p (0 p , Σ) 
The dimension p is assumed to grow  The spectral density function f , corresponding to a Toeplitz covariance matrix Σ, is given by so that for f ∈ L 2 (−π, π) the inverse Fourier transform implies Hence, Σ is completely characterized by f , and the non-negativity of the spectral density function implies the positive definiteness of the covariance matrix 
Moreover, the decay of the autocovariance σ k is directly connected to the smoothness of f   Finally, the convergence rate of a Toeplitz covariance estimator and that of the corresponding spectral density estimator are directly related via Σ ≤ f ∞ := sup x∈ |f (x)|, where • denotes the spectral norm (see  
As in , we introduce a class of positive definite Toeplitz covariance matrices with Hölder continuous spectral densities  For β = γ + α > 0, where The optimal convergence rate for estimating Toeplitz covariance matrices over P β (M 0 , M 1 ) depends crucially on β  It is well known that the k-th Fourier coefficient of a function whose γ-th derivative is α-Hölder continuous decays at least with order O(k −β ) (see  
Hence, β determines the decay rate of the autocovariances σ k , which are the Fourier coefficients of the spectral density f , as k → ∞  In particular, this implies that for β ∈ (0, 1], the class P β (M 0 , M 1 ) includes Toeplitz covariance matrices corresponding to long-memory processes with bounded spectral densities, since the sequence of corresponding autocovariances is not summable 
A connection between Toeplitz covariance matrices and their spectral densities is further exploited in the following lemma  Lemma 1  Let Σ ∈ P β (M 0 , M 1 ) and let x j = (j − 1)/(p − 1), j = 1,    , p, then where δ i,j is the Kroneker delta, O(•) terms are uniform over i, j = 1,       , p and divided by √ 2 when i, j ∈ {1, p} is the Discrete Cosine Transform I (DCT-I) matrix 
The proof can be found in Appendix A 1  This result shows that the DCT-I matrix approximately diagonalizes Toeplitz covariance matrices and that the diagonalization error depends to some extent on the smoothness of the corresponding spectral density  In the spectral density literature the discrete Fourier transform (DFT) matrix
, where i is the imaginary unit, is typically employed to approximately diagonalize Toeplitz covariance matrices  Using the fact that introduced an approximation for the likelihood of a single Gaussian stationary time series (case n = 1), the so-called Whittle likelihood (1) The quantity , where F j denotes the j-th column of F , is known as the periodogram at the j-th Fourier frequency 
Note that due to periodogram symmetry, only p/2 data points I 1 ,    , I p/2 are available for estimating the mean f (2πj/p), j = 1,       , p/2 , where x denotes the largest integer strictly smaller than x  The Whittle likelihood has become a popular tool for parameter estimation of stationary time series, e g , for nonparametric and parametric spectral density estimation or for estimation of the Hurst exponent, see e g , ;  
Lemma 1 yields the following alternative version of the Whittle likelihood where W j = (D t j Y ) 2   Note that this likelihood approximation is based on twice as many data points W j as the standard Whittle likelihood  Thus, it allows for a more efficient use of the data Y to estimate the parameter of interest, such as the spectral density or the Hurst parameter 
Equations ( ) or (2) invite for the estimation of f by maximizing the (penalized) likelihood over certain linear spaces (e g , spline spaces), as suggested e g , in or   However, such an approach requires well-designed numerical methods to solve the corresponding optimization problem, since the spectral density in the second term of (1) or ( ) is in the denominator, which does not allow to obtain a closed-form expression for the estimator and often leads to numerical instabilities 
Also, the choice of the smoothing parameter becomes challenging  Therefore, we suggest an alternative approach that allows the spectral density to be estimated as a mean in an approximate Gaussian regression  Such estimators have a closed-form expression, do not require an iterative optimization algorithm and a smoothing parameter can be easily obtained with any conventional criterion 
First Hence, for W j = (D t j Y ) 2 , j = 1,       , p it follows with Lemma 1 that where Γ(a, b) denotes a gamma distribution with a shape parameter a and a scale parameter b  Note that the random variables W 1 ,       , W p are only asymptotically independent  Obviously, E(W j ) = f (πx j ) + O(1), j = 1,      
, p  To estimate f from W 1 ,       , W p , one could use a generalized nonparametric regression framework with a gamma distributed response, see e g , the classical monograph by   However, this approach requires an iterative procedure for estimation, e g , a Newton-Raphson algorithm, with a suitable choice for the smoothing parameter at each iteration step 
Deriving the L ∞ rate for the resulting estimator is also not a trivial task  Instead, we suggest to employ a variance stabilizing transform of that converts the gamma regression into an approximate Gaussian regression  In the next section we present the methodology in more detail for a general setting with n ≥ 1 

Methodology

For Y i ∼ N p (0 p , Σ), i = 1,       , n, it was shown in the previous section that with Lemma 1 the data can be transformed into gamma distributed random variables     , n, j = 1,       , p, where for each fixed i the random variable W i,j has the same distribution as W j given in (3)  Now the approach of Cai et al  ( ) is adapted to the setting n ≥ 1 
First, the transformed data points W i,j are binned, that is, fewer new variables     , T   Note that the number of observations in a bin is m = np/T   In Theorem 1 in Section 4, we show that setting T = p υ for any υ ∈ ((4 − 2 min{β, 1})/3, 1) leads to the minimax optimal rate for the spectral density estimator 
To simplify the notation, m is handled as an integer (otherwise, one can discard several observations in the last bin)  Next, applying the variance stabilizing transform (VST) ∼ where H(y) = {φ(m/2) + log (2y/m)} / √ 2 and φ is the digamma function (see   Now, the scaled and shifted log-spectral density H(f ) can be estimated with a periodic smoothing spline
where h > 0 denotes a smoothing parameter, q ∈ N is the penalty order and S per (2q − 1) a space of periodic splines of degree 2q − 1  The smoothing parameter h can be chosen either with generalized cross-validation (GCV) as derived in or with the restricted maximum likelihood, see   Once an estimator H(f ) is obtained, application of the inverse transform function H −1 (y) = m exp √ 2y − φ (m/2) /2 yields the spectral density estimator f = H −1 H(f )  
Finally, using the inverse Fourier transform leads to the fol- The precision matrix Ω is estimated by the inverse Fourier transform of the reciprocal of the spectral density estimator, i e , Ω = (ω |i−j| ) p i,j=1 with ωk = The estimation procedure for Σ and Ω can be summarised as follows  1  Data Transformation:
where D is the (p × p)-dimensional DCT-I matrix as given in Lemma 1 and D j is its j-th column  2  Binning: Set T = p υ for any υ ∈ ((4 − 2 min{β, 1})/3, 1) and calculate W i,j , k = 1,       , T 

VST:

where k are asymptotically i i d  Gaussian variables  Inverse VST: Estimate the spectral density f with f = H −1 H(f ) , where Note that Σ and Ω are positive definite matrices by construction, since their spectral density functions f and f −1 are non-negative, respectively  Unlike the banding and tapering estimators, the autocovariance estimators σk are controlled by a single smoothing parameter h, which can be estimated fully data-driven with several available automatic methods, which are numerically efficient and well-studied 
In addition, one can also use methods for adaptive mean estimation, see e g , , which in turn leads to adaptive Toeplitz covariance matrix estimation  All inferential procedures developed in the Gaussian regression context can also be adopted accordingly 

Theoretical Properties

In this section, we study the asymptotic properties of the estimators f , Σ and Ω  The results are established under the asymptotic scenario where p → ∞ and p/n → c ∈ (0, ∞], that is, the dimension p grows, while the sample size n either remains fixed or also grows but not faster than p  This corresponds to the asymptotic scenario when the sample covariance matrix is inconsistent 
Let f be the spectral density estimator defined in Section 3, i e , f = m exp{ √ 2 H(f ) − φ(m/2)}/2, where H(f ) is given in (4), m = np/T and φ is the digamma function  Furthermore, let Σ be the Toeplitz covariance matrix estimator and Ω the corresponding precision matrix defined in equations ( ) and (6), respectively 
The following theorem shows that both Σ and Ω attain the minimax optimal rate of convergence over the class and hT → ∞, then with T = p υ for any υ ∈ ((4 − 2 min{β, 1})/3, 1) and q = max{1, γ}, the spectral density estimator f , the corresponding covariance matrix estimator Σ and the precision matrix estimator Ω satisfy sup
For h {log(np)/(np)}   The proof of Theorem 1 can be found in the Appendix A 3 and is the main result of our work  The most important part of this proof is the derivation of the convergence rate for the spectral density estimator f under the L ∞ norm  In the original work, established an L 2 rate for a wavelet nonparametric mean estimator in a gamma regression where the data are assumed to be independent 
In our work, the spectral density estimator f is based on the gamma distributed data W i,1 ,       , W i,p , which are only asymptotically independent  Moreover, the mean of these data is not exactly f (πx 1 ),       , f (πx p ), but is corrupted by the diagonalization error given in Lemma 1  This error adds to the error that arises via binning and VST and that describes the deviation from a Gaussian distribution, as derived in  
Finally, we need to obtain an L ∞ rather than an L 2 rate for our spectral density estimator  Overall, the proof requires different tools than those used in   To get the L ∞ rate for f , we first derive that for the periodic smoothing spline estimator H(f ) of the log-spectral density  To do so, we use a closed-form expression of its effective kernel obtained in , thereby carefully treating various (dependent) errors that describe deviations from a Gaussian nonparametric regression with independent errors and mean f (πx i ) 
Note also that although the periodic smoothing spline estimator is obtained on T binned points, the rate is given in terms of the vector dimension p  Then, using the Cauchy-Schwarz inequality and a mean value argument, this rate is translated into the L ∞ rate for the spectral density estimator f   To obtain the rate for the Toeplitz covariance matrix estimator is enough to note that

Simulation Study

In this section, we compare the performance of the proposed Toeplitz covariance estimator, denoted as VST-DCT, with the tapering estimator of and with the sample covariance matrix  We consider Gaussian vectors Y 1 ,    , (3) such that the corresponding spectral density is Lipschitz continuous but not differentiable: f (x) = 1 44{| sin(x + 0 5π)| 1 7 + 0 45} 
In particular, var(Y i ) = 1 44 in all three examples  Figure shows the spectral densities and the corresponding autocorrelation functions for the three examples  A Monte Carlo simulation with 100 iterations is performed using R (version 4 1 2, seed 42)  For our VST-DCT estimator, we use a cubic periodic spline, i e , q = 2 is set in (4) 
The binning parameters are set to T = 500 bins with m = 10 points for (A) and T = 500 bins with m = 100 points for both (B) and (C)  To select the regularisation parameter for our estimator, we implemented the restricted maximum likelihood (ML) method, generalized cross validation (GCV) and the corresponding oracle versions, i e , as if Σ were known The tapering parameter
where T ap k (Σ ν 2 ) is the tapering estimator of with parameter k  If n = 1, that is, under scenario (A), suggest to split the time series Y into l non-overlapping subseries of length p/l and then proceed as before to select the tuning parameter k  To the best of our knowledge, there is no data-driven method for selecting this parameter l 
Using the true covariance matrix Σ, we selected l = 30 subseries for the example 1 and l = 15 subseries for the exam-ples 2 and 3  The parameter k can then be chosen by cross-validation as above  We employ this approach under scenario (A) instead of an unavailable fully data-driven criterion and name it semi-oracle 
Finally, for all three scenarios (A), (B) and (C), the oracle tapering parameter is computed using grid search for each Monte Carlo sample as kor = arg min k=2,3,   ,p/2 T ap k ( Σ) − Σ , where Σ is the sample covariance matrix  To speed up the computation, one can replace the spectral norm by the 1 norm, as suggested by  
In Tables , the errors of the Toeplitz covariance estimators with respect to the spectral norm and the computation time for one Monte Carlo iteration are given for scenarios (A), (B) and (C), respectively  To illustrate the goodness-of-fit of the spectral density, the L 2 norm f − f 2 is also computed 
The results show that the tapering and VST-DCT estimator perform overall similar in terms of the spectral norm risk  This is not surprising as both estimators are proved to be rate-optimal  Moreover, both the tapering and VST-DCT estimators are clearly superior to the inconsistent sample Toeplitz covariance matrix 
A closer look at the numbers shows that the VST-DCT method has better constants, i e , VST-DCT estimators have somewhat smaller errors in the spectral norm than the tapering estimators across all examples, but especially under scenario (C)  The oracle estimators show similar behaviour, but are slightly less variable compared to the data-driven estimators 
In general, both the tapering and VST-DCT estimators perform best for example 1, second best for example 3 and worst for example 2, which traces back to functions complexity  In terms of computational time, both methods are similarly fast for scenarios (A) and (B)  For scenario (C), the tapering method is much slower due to the multiple high-dimensional matrix multiplications in the cross-validation method 
It is expected that for larger p the tapering estimator is much more computationally intensive than the corresponding VST-DCT estimator  (1) polynomial σ ( (  To test how robust our approach is to deviations from the Gaussian assumption, we simulated the data from gamma and uniform distributions and conducted a simulation study for the same scenarios and examples 
The results are very similar to those of the Gaussian distribution, see supplementary materials for the details 

Application to Protein Dynamics

We revisit the data analysis of protein dynamics performed in Krivobokova et al  (2012) and   We consider data generated by the molecular dynamics (MD) simulations for the yeast aquaporin (Aqy1) -the gated water channel of the yeast Pichi pastoris  MD simulations are an established tool for studying biological systems at the atomic level on timescales of nano-to microseconds 
The data are given as Euclidean coordinates of all 783 atoms of Aqy1 observed in a 100 nanosecond time frame, split into 20 000 equidistant observations  Additionally, the diameter of the channel y t at time t is given, measured by the distance between two centers of mass of certain residues of the protein 
The aim of the analysis is to identify the collective motions of the atoms responsible for the channel opening  In order to model the response variable y t , which is a distance, based on the motions of the protein atoms, we chose to represent the protein structure by distances between atoms and certain fixed base points instead of Euclidean coordinates 
That is, we calculated where A t,i ∈ R 3 , i = 1,       , 783 denotes the i-th atom of the protein at time t, B j ∈ R 3 , j = 1, 2, 3, 4, is the j-th base point and d(•, •) is the Euclidean distance  Figure shows the diameter y t and the distance between the first atom and the first center of mass  It can therefore be concluded that a linear model Y = Xβ + holds, where
  This linear model has two specific features which are intrinsic to the problem: first, the observations are not independent over time and second, X t is high-dimensional at each t and only few columns of X are relevant for Y   have shown that the partial least squares (PLS) algorithm performs exceptionally well on this type of data, leading to a small-dimensional and robust representation of proteins, which is able to identify the atomic dynamics relevant for Y  
Singer et al  ( ) studied the convergence rates of the PLS algorithm for dependent observations and showed that decorrelating the data before running the PLS algorithm improves its performance  Since Y is a linear combination of columns of X, it can be assumed that Y and all columns of X have the same correlation structure 
Hence, it is sufficient to estimate Σ = cov(Y ) to decorrelate the data for the PLS algorithm, i e , Σ −1/2 Y = Σ −1/2 Xβ + Σ −1/2 results in a standard linear regression with independent errors  Our goal now is to estimate Σ and compare the performance of the PLS algorithm on original and decorrelated data 
For this purpose, we divided the data set into a training and a test set (each with p = 10 000 observations)  First, we tested whether the data are stationary  The augmented Dickey-Fuller test confirmed stationarity for Y with a p-value< 0 01  The Hurst exponent of Y is 0 85, indicating moderate long-range dependence supported by a rather slow decay of the sample autocovariances (see grey line in the left plot of Figure ) 
Therefore, we set q = 1 for the VST-DCT estimator to match the low smoothness of the corresponding spectral density  Moreover, the smoothing parameter is selected with the restricted maximum likelihood method and T = 550 bins are used  Obviously, the performance of the PLS algorithm on the decorrelated data is significantly better for the small number of components 
In particular, with just one PLS component, the correlation between the true opening diameter on the test set and its prediction that takes into account the dependence in the data is already 0 54, while it is close to zero for PLS that ignores the dependence in the data  showed that the estimator of β based on one PLS component is exactly the ensemble-weighted maximally correlated mode (ewMCM), which is defined as the collective mode of atoms that has the highest probability to achieve a specific alteration of the response Y  
Therefore, an accurate estimator of this quantity is crucial for the interpretation of the results and can only be achieved if the dependence in the data is taken into account  Estimating Σ with a tapered covariance estimator has two practical problems  First, since we only have a single realization of a time series Y (n = 1), there is no datadriven method for selecting the tapering parameter 
Second, the tapering estimator turned out not to be positive definite for the data at hand  To solve the second problem, we truncated the corresponding spectral density estimator ftap to a small positive value, i e , f + tap = max{ ftap , 1/ log(p)} (see   To select the tapering parameter with cross-validation, we experimented with different subseries lengths and found that the tapering estimator is very sensitive to this choice 
For example, estimating the tapered covariance matrix based on subseries of length 8/15/30 yields a correlation of 0 42/0 53/0 34 between the true diameter and the first PLS component, respectively  Altogether, our proposed estimator is fully data-driven, fast even for large sample sizes, automatically positive definite and can handle certain long-memory processes 
In contrast, the tapering estimator is not data-driven and must be manipulated to become positive definite  Our method is implemented in the R package vstdct 

Discussion

In this paper, we proposed a simple, fast, fully data-driven, automatically positive definite and minimax optimal estimator of Toeplitz covariance matrices from a large class that also includes covariance matrices of certain long-memory processes  Our estimator is derived under the assumption that the data are Gaussian 
However, simulations show that the suggested approach yields robust estimators even when the data are not normally distributed  In the context of spectral density estima- , for mixing processes (see Theorem 5 3 of Rosenblatt, 2012), as well as for non-linear processes (see   Since DFT and DCT matrices are closely related, we expect that equation (3) also holds asymptotically for these non-Gaussian time series, but consider a rigorous analysis to be beyond the scope of this paper 
In fact, our numerical experiments have even shown that if the spectral density is estimated from W j = f (πx j ) + j , that is, as if W j were Gaussian instead of gamma distributed, then the resulting spectral density estimator has almost the same L ∞ risk (and hence the corresponding covariance matrix has almost the same spectral norm) 
Of course, such an estimator would lead to a wrong inference about f (πx j ), since the growing variance of W j would be ignored  Since our approach translates Toeplitz covariance matrix estimation into a mean estimation in an approximate Gaussian nonparametric regression, all approaches developed in the context of Gaussian nonparametric regression, such as (locally)
adaptive estimation, as well as the corresponding (simultaneous) inference, can be directly applied  Bayesian tools for adaptive estimation and inference in Gaussian nonparametric regression as proposed in can also be employed 

Appendix

Throughout the appendix, we denote by c, c 1 , C, C 1 ,       etc  generic constants, that are independent of n and p  To simplify the notation, the constants are sometimes skipped and we write for less than or equal to up to constants  We embed the p-dimensional Toeplitz matrix Σ = toep(σ 0 ,       , σ p−1 ) in a (2p − 2)dimensional circulant matrix Σ = toep(σ 0 ,      
, σ p−1 , σ p−2 ,       , σ 1 )  Then, Σ = with the conjugate transpose U * , and Λ is a diagonal matrix with the k-th diagonal value for k = 1,    , p given by Furthermore, Σ = V * ΛV , where V ∈ C (2p−2)×p contains the first p columns of U   In particular, b(j, r) = b(j, 2p−r) and c(j, r) = −c(j, 2p−r) for r = p+1,      
, 2p−2  Together, we have (A 1) Some calculations show that for r = 1,       p Using the Taylor expansion of cot(x) for 0 < |x| < π one obtains for r = 1,       p where the O term does not depend on j and the hidden constant does not depend on r, p  If i = j, equations (A 1) -(A 3) imply where the O terms do not depend on j 
Since the complex exponential function is Lipschitz continuous with constant L = 1, it holds λ r = λ j + L r,j |r − j|p −1 where −1 ≤ L r,j ≤ 1 is a constant depending on r, j  Then, , it is sufficient to consider j = 1,    , p − 1  We begin with first sum  For a shorter notation, we use k := r − 1 and l := j − 1 in the following 
Then, summing the squares of the first term in (A 4) for l = 0,    , p−2 on sums of reciprocal powers  If p is even, then the residual terms are given by where φ and φ (1) denote the digamma function and its derivative  If p is odd, similar remainder terms can be derived  To see that R i (l, p) = O(p −1 ) for i = 1, 2, 3 and uniformly in l we use that asymptotically φ(x)∼ log(x)−1/(2x) and
The mixed term are both of the order p −1   Furthermore, since the harmonic sum diverges at a rate of log(p)  Finally, λ j = f (x j )+O{log(p)p −β } by the uniform approximation properties of the discrete Fourier series for Hölder continuous functions (see   All together, we have shown that (DΣD) j,j = where the O terms are uniform over j = 1,    , p 
Case i = j and |i − j| is even In this case, (DΣD) i,j = a i a j uniformly in i, j  To show that a i a j 2p−2 r=1 λ r c(i, r)c(j, r) = O(p −1 ), we proceed similarly as before  Setting k=r−1, l=j−1, m=i−1 and using that l =m and |l−m| is even, one obtains where for even p the residual terms are given by If p is odd, analogous residual terms can be derived 
Using similar techniques as before, one can show that the two residual terms and the remaining mixed and square terms vanish at a rate of the order O(p −1 ) and uniformly in i, j  Case i = j and |i − j| is odd |r − i| and |r − j| are either odd and even, or even and odd  Without loss of generality, assume that |r − i| is even 
Then, (DΣD) i,j = a i a j 2p−2 r=1 λ r b(i, r)c(j, r)  Since b(i, •) is an even function, c(j, •) is an odd function and λ r = λ 2p−r , it follows (DΣD) i,j = 0  The structure of the proof is as follows  First, we derive the L ∞ rate of the periodic smoothing spline estimator H(f )  Then, using the Cauchy-Schwarz inequality and a mean value argument, the convergence rate of the spectral density estimator f is
∞ the first claim of the theorem follows  Finally, we prove the second statement on the precision matrices  For the sake of clarity, some technical lemmas used in the proof are listed separately in A 4  hT → ∞, then with T = p υ for any υ ∈ ((4 − 2 min{1, β})/3, 1), the estimator H(f ) described in Section 3 with q = max{1, γ} satisfies
Proof : Application of the triangle inequality yields a bias-variance decomposition Set T = 2T − 2 and x k = (k − 1)/ T for k = 1,    , T   Using Lemma 4, we can write where Mirroring and renumerating ζ k , η k , k is similar as for Y * k , k = 1,    , T   Using the above representation, one can write First we reduce the supremum to a maximum over a finite number of points 
If q > 1, then W (•, x k ) is Lipschitz continuous with constant L > 0  In this case, it holds almost surely that sup ) is a piecewise linear function with knots at x j = j/ T   The factor (ζ k + ξ k ) can be considered as stochastic weights that do not affect the piecewise linear property  Thus, the supremum is attained at one of the knots x j = j/ T , j = 1,    , T , and (A 7) is also valid for q = 1 
Again with (a + b) 2 ≤ 2a 2 + 2b 2 we obtain We start with bounding   This requires a bound on 1 • ψ 2 denotes the sub-Gaussian norm  In case of a Gaussian random variable the norm equals to the variance  Thus with Lemma 2 and Lemma 4, we obtain Lemma 1 6 of ) then yields Recall that T = p υ for some fixed υ ∈ ((4 − 2 min{1, β})/3, 1) 
Using the inequality log(x) ≤ x a /a one can find constants x υ , C υ > 0 depending on υ but not on n, p such that log(2 T ) log(p) Next, we derive a bound for the second term The exponential decay property of the kernel K stated in Lemma 2 yields The first term in (A 9) can be bounded again with Lemma 1 6 of  
We use the fact that for not necessarily independent random variables X 1 ,    , X N R and R > 0 are constants  This is a consequence of Lemma 1 of which yields , it follows that N i=1 a i X i has a subGaussain distribution and the subGaussian norm is bounded by 2R( N i=1 a 2 i ) 1/2   See for further details on the subgaussian distribution 
T h   For the second inequality Lemma 2(ii) is used  Applying Lemma 1 6 of then yields To bound the second term in (A 9), we use the moment bounds for ξ k derived in Lemma 4  Then, for all integers > 1 Combining the error bounds (A 10) and (A 11) and choosing R=m −1/2 gives By assumption T = p υ and m = np (1−υ) for some fixed υ ∈ ((4 − 2 min{1, β})/3, 1) 
If is an integer such that ≥ 1/(1 − υ), then where we used log(x) ≤ x a /a with a = 1/(4 )  Consider 1/2 < β ≤ 1 and let 0 < χ < 1 be a constant  Applying log(x) ≤ x a /a twice with a = χ/(2 ) yields For any fixed υ∈((4 − 2 min{1, β})/3, 1) one can find an integer which is independent of n, p such that the right side of (A 12) holds 
Since p/n → c ∈ (0, ∞] and thus n/p = O(1) and p −1 = O(n −1 ), it follows for satisfying (A 12) that In total, choosing an integer Using the representation in Lemma 4 once more gives for each x ∈ [0, 1] The bounds on k in Lemma 4 imply Consider the case that β ≥ 1  In particular, q = γ and f (q) is α-Hölder continuous 
Since f is a periodic function with f (x) ∈ [δ, M 0 ] and H(y) ∝ φ(m/2)+ log (2y/m), it follows that {H(f )} (q) is also α-Hölder continuous  Extending g := H(f ) to the entire real line, we get Expanding g(t) in a Taylor series around x and using that h −1 K h is a kernel of order 2q, see Lemma 2(iii), it follows that for any x ∈ [0, 1]
where ξ x,t is a point between x and t  Using the fact that the kernel K h decays exponentially and that g (q) is α-Hölder continuous on [δ, M 0 ] with some constant L, the logarithm is Lipschitz continuous on a compact interval, it follows g = H(f ) is β-Hölder continuous  Expanding g to the entire line and using Lemma 2(iii) with
In a similar way as before, one obtains Note that T −β =o(h β ) as β > 1/2, T h → ∞ and h → 0 by assumption  Since the derived bounds are uniform for x ∈ [0, 1] it holds Putting the bounds A 13 and A 14 together gives If h > 0 such that h → 0 and hT → ∞, then with T = p υ for any υ ∈ ((4 − 2 min{1, β})/3, 1), the estimator f described in Section 3 with q = max{1, γ} satisfies
Proof : By the mean value theorem, it holds for some function g between H(f ) and To show that the second term on the right hand side of (A 15) is negligible we use the moment generating function of H(f ) ∞   In the next paragraph, we derive the asymptotic order of E[exp{λ H(f ) ∞ }] for n, p → ∞, where λ > 0 may depend on n, p or not 
By the exponential decay property of the kernel K stated in Lemma 2 holds First, H(f ) ∞ is bounded with the maximum over a finite number of points  Calculating the derivative of s : Since δ δx s(x) > 0 almost surely for x = x k , the extrema occur at x k , k = 1,    , T   Thus, for λ > 0 the moment generating function of H(f ) ∞ is bounded by
Let M j = ( T h) −1 T k=1 γ h (x j , x k ), which by Lemma 2 is bounded uniformly in j by some global constant M > 0  By the convexity of the exponential function we obtain √ 2 and by assumption 0 ≤ δ ≤ f ≤ M 0   Using Lemma 3, Q k can be written as a sum of m = np/T independent gamma random variables, i e 
The moment generating function of | log(X)| when X follows a Γ(a, b)-distribution is given by where Γ(a) is the gamma function and γ(a, b) is the lower incomplete gamma function  In particular, To derive the asymptotic order of E[exp{λ H(f ) ∞ }] for n, p → ∞ we first establish the asymptotic order of the ratio Γ(a + t)/Γ(a) for a → ∞ 
We distinguish the two cases where t is independent of a and where t linearly depends on a  Thus, for 0 < t < a and t independent of a, equation (A 17) implies for a → ∞ that Γ(a + t)/Γ(a) = O(a t )  Similarly, it can be seen that Γ(a − t)/Γ(a) = O(a −t )  If 0 < t < a and t linearly depends on a, i e  t = ca for some constant c ∈ (0, 1), then we get Γ(a ± t)/Γ(a) = O(a ±t exp{a}) for a → ∞ 
Hence, for a fixed λ not depending on n, p and such that 0 < λ < m/( √ 2M j ) we get for sufficiently large n, p If λ = cm such that 0 < λ < m/( √ 2M j ), then for sufficiently large n, p b∈{cδ/m,cM 0 /m} (bm/2) for some constant L > 1  Set K = min j=1,   , T 1/( √ 2M j ) which is a constant independent of n, p  Altogether, we showed that for 0 < λ < Km and n, p → ∞
Bounding the right hand side of (A 15) for some constants c 0 , c 1 > 0 and n, p → ∞ Since g lies between H(f ) and H(f ), and f almost surely pointwise  Thus, for C > f ∞ = M 0 it holds where c 1 := H(C − M 0 )  Applying Markov inequality for t = cm with c ∈ (0, K) and C = 2L 4/c + M 0 where c, K, L are the constants in gives
Together with Proposition 1 follows Using the fact that the spectral norm of a Toeplitz matrix is upper bounded by the sup norm of its spectral density we get sup According to the mean value theorem, for a function g between H(f ) and H(f ), it holds that some constant c 1 > 0 not depending on n, p  Chosing the same constant C as in section A 3 2 it follows
Noting that 1/f ∞ ≤ 1/δ and 2/m exp {φ(m/2)} ∈ [0 25, 1] for m ≥ 1, (A 18) implies for some constants c 2 , c 3 > 0 and n, p → ∞ Since the derived bounds hold for each Σ(f ) ∈ F β , we get all together sup This section states some technical lemmata needed for the proof of Theorem 1  The proofs can be found in the supplementary material 
The first lemma lists some properties of the kernel K h and its extension K h on the real line  The proof is based on   Lemma 2  Let h > 0 be the bandwith parameter depending on N   (i) There are constants 0 < C < ∞ and 0 < γ < 1 such that for all for x, t ∈ [0, 1] Lemma 3 states that the sum of the correlated gamma random variables in each bin can be rewritten as a sum of independent gamma random variables 
for i = 1,    , n and j = (k − 1)m + 1,    , km, and x j = (j − 1)/(2p − 2)  Finally, Lemma 4 gives explicit bounds for the stochastic and deterministic errors of the variance stabilizing transform  Thus, it quantifies the difference to an exact Gaussian regression setting  This result is a generalization of Theorem 1 of Cai et al 
(2010) adapted to our setting with n ≥ 1 observations and correlated observations  √ 2 can be written as where for the proof of the first statement  Furthermore, for x, t ∈ [0, 1] holds In particular, for some constants C 1 , C 2 > 0 depending on γ ∈ (0, 1) but not on h and x, it holds h (iii) See Lemma 15 of with p = 2q − 1 
It is sufficient to show the statement for n = 1 by independence of the Y i   Then, the number of points per bin is m = p/T   For simplicity, the index i is skipped in the following  First, we write Q k as a matrix-vector product and refactor it so that it corresponds to a sum of independent scaled χ 2 random variables 
In the second step, we calculate the scaling factors  Let E (km) be a diagonal matrix with ones on the (k − 1)m + 1,    , km-th entries and otherwise zero diagonal elements  Then, By Theorem 1 of for the gamma distribution it follows where Wi,j iid  ∼ Γ(1/2, 2 f (x * k )) and such that Cov( Wi,j , Wi,h ) = Cov(W i,j , W i,h ) for j = (k − 1)p/T + 1,    , kp/T and h ∈ {1,    , p} \ {(k − 1)p/T + 1,    , kp/T } 
Let θ be the maximum difference of the observations' means in each bin  Then, θ = max are defined via quantile coupling, it holds Z k = Φ −1 {F Q( Qk )} (see   Furthermore, define the uniform random variables Let ρ = Cov(Z k , Z l )  Then, the identity implies F Z,Z (x, y) − Φ(x)Φ(y) ≥ 0 for all x, y ∈ R ⇐⇒ ρ ≥ 0, (see  
Since Cov( Qk , Ql ) ≥ 0 and the ratio of two densities is non-negative, x = − 2/m, it follows that f Q(x) is monotone decreasing for x ≥ − 2/m  Furthermore, F Q(− m/2) ≤ 0 5 for all m ∈ N as f Q(x) is right-skewed  In particular, − m/2 ≤ F −1 Q (1/2) for all m ∈ N  Finally, since f Q(− 2/m) → φ(0) for m → ∞ there is a constant c > 0 not depending on m such that
The simulation study in Section 5 is performed in the same way, but with the uniform and the gamma distribution instead of the Gaussian distribution 
Context 2: Transport Aircraft for IAF - Page 67 - Bharat Rakshak
Transport Aircraft for IAF
Re: Transport Aircraft for IAF
Postby abhik » 17 Nov 2014 05:55
+1, Air India recently sold their entire fleet of Boeing 777s 
afaik the A330 MRTT does not make any structural mods or add anything internally in cargo or passenger cabin  it just relies on the intrinsic 110 tons of fuel  external refueling pods are added and internally the control station and cameras for the operator i guess 
so its a easy conversion from a passenger layout to the AAR mode - mostly ripping out the passenger cabin of all extra stuff and retuning the FCS for any changes in COG 
this should have been pursued years ago
the IL78 adds a palletized drum tank system inside its cargo bay due to paucity of intrinsic fuel but it can be removed and a/c converted back to cargo hauling or send off to russia for Phalcon structural mods if we want it that way  they will however need to change engines to PS90 as they have the old engines
http://www airplane-pictures net/images     7/5616 jpg
the RAF is already gone that route in 2011
http://www defensenews com/article/2011     -Refuelers
LONDON - Airbus Military has delivered the first of 12 A330-200 airliners due to be converted into in-flight refueling planes for the British Royal Air Force by Cobham Aviation Services 
The aircraft, part of an order of 14 jets, will be modified with aerial refueling pods and other equipment at Cobham's newly refurbished facility in Bournemouth, England  The first two aircraft have already been converted by Airbus in Spain 
The multirole tanker aircraft are being provided to the RAF under a private finance initiative service deal led by Airbus parent EADS 
Seven of the planes will be operated full time by the RAF  The remainder will be available for lease in the third-party market, with the proviso that they can be returned to British military service to meet any surge in demand 
All of the aircraft, to be known as the Voyager in RAF service, will be fitted with two wing-mounted refueling pods, while half the fleet will also be fitted for, but not necessarily with, a center-line mounted unit  The refueling units are being supplied by Cobham 
The first aircraft will become operational in a passenger and freight transport role by the end of this year to start relieving pressure on the RAF's hard-pressed assets 
Despite the increasing fragility of current RAF in-flight refueling operations, the new capability is not contracted to start being used in this role until 2015 
All 14 Voyagers are scheduled to be available for RAF operations by the middle of the decade  The A330 will replace the increasingly ancient Tristar and VC-10 refuelers now in service 
Push the 6 Il-476 from refueler to AEW duty  Phalcon them up
Not sure if that is a good path to follow  For one they all should be sent to pasture in about 8 years  Then if the are to be phalconed up - the requires major structural changes  Not worth that cost 
Whatever happened ot the two new ones that were supposed ot be ordered?
the IL78 can be easily converted back to IL76 cargo hauling  only the fuel tank inside cargo bay needs removal   infact that was even mentioned in initial days as swing role fuel/cargo 
Postby Cybaru » 17 Nov 2014 07:55
I am talking about the new il78 that we ordered recently in refueling role  Sorry for the mix up  They are the same platform, that I why i used 476 or 76 to identify it 
777 carries more internal fuel than the A330  We suck!
From the KC-777 program 
http://www globalsecurity org/military/     kc-777 htm
"the KC-777 would be 209 feet long with a wingspan of 212 feet, 7 inches  That's the same size as the 777-200LR commercial jet  The KC-777 would be able to carry far more fuel, cargo and passengers than either the KC-767 or the Airbus A330 tanker  The KC-767 offers more operational flexibility, while the KC-777 would be better suited for long-range strategic missions in which more cargo needs to be delivered  The KC-777 would be able to carry more than 350,000 pounds (160,000 kilograms) of fuel and offload more than 220,000 pounds (100,000 kg) of it on a mission of 500 nautical miles (900 kilometers)  On the other hand, the KC-767 can lift off with more than 200,000 pounds (90,000 kg) of fuel and offload more than 130,000 pounds (60,000 kg) in a similar mission  The KC-777 would be able to deliver 200 percent more fuel after flying 1,000 nautical miles than older Air Force KC-135s  The KC-777 could carry up to 37 pallets of cargo, compared to the 19 pallets for the KC-767 "
Postby Cosmo_R » 18 Nov 2014 04:31
Viv S wrote: From Ajai Shukla's article -
HAL points out that, since each Avro flies barely 350 hours every year, most of them have a residual life of about 80,000 hours  In a request for information (RFI) released on August 15, HAL has proposed replacing the aircraft’s engines (Rolls Royce Dart) with “modern fuel efficient engines” 
So, the IAF's Avros have a residual life of 228 years at the current rate of usage  Ain't life grand?
At zero up time, it could reach infinity 
Relax Cy  Kc777 has no client  Usaf is going with kc767 and almost everyone else with a330 
We don't have the number of heavies and long missions of usaf else I would say convert an124 
KC777 will be extremely expensive given the demand/backlog for the 777 and the 777x  Any buyer would have to virtually pay for the increase in capacity 
I think the 767 production line is closed  so the proposed KC767 Boeing is supposed to deliver 18 by 2017  that can be managed from mothballed and cargo hauler airframes on the market 
but to meet the final order of around 180 will they not have to open the production line unless such a huge number were available on the market?
I do get the spider feel this program again will be cancelled in favour of a in-production plane like the 777X ?
I wasn't suggesting we get the KC777  All I was doing was comparing what possibly the 777 could offload compared to A330  It carries 171000 liters of fuel versus 130000 liters that the A330 carries  If we had older 777s in stock, we could have quite easily converted them to this config  The cost to us would be miniscule just the refurbishing cost vs acquiring a new type 
Singha wrote: I think the 767 production line is closed  so the proposed KC767 Boeing is supposed to deliver 18 by 2017  that can be managed from mothballed and cargo hauler airframes on the market 
The Line is open, they have a backlog of around 50 (All Fed ex), with Fed Ex placing a small order this year  The Pegasus order is for all new builds, and so will the follow on order  The only reason for any nation to buy the 767 tanker is going to be because of the ability to hard bargain with Boeing given that the commercial future of the 767 is dead  This also allows a potential buyer to purchase cheap spares from the open market, or club its logistical and inventory purchase with that of the USAF  Other than that and perhaps availability (which would be doubtful once USAF pushes through a larger order) there is really no technical reason to purchase the this tanker over the A330 which by all accounts is a superior tanker in addition to being a much much better airliner in general 
IAI is doing conversations for the 767 and its called the 767 MMTT
http://www iai co il/sip_storage/FILES/1/38471 pdf
Cybaru wrote: I wasn't suggesting we get the KC777  All I was doing was comparing what possibly the 777 could offload compared to A330  It carries 171000 liters of fuel versus 130000 liters that the A330 carries  If we had older 777s in stock, we could have quite easily converted them to this config  The cost to us would be miniscule just the refurbishing cost vs acquiring a new type 
The cost of converting a commercial airliner to a tanker, certifying it and running a full fledged test program is by no means small  There is absolutely no justification for that sort of cost over and above the capability that that A330 provides  If it were a certified and tested conversion, that would be a different matter 
Postby Kartik » 21 Nov 2014 12:27
Cybaru wrote:
Why? If the airframe can handle more flight hours, why not?
because it is a very very old airframe as is  Maintenance spares won't be available easily even as of now, then imagine how it'll be 20-30 years from now   and as things stood anyway, the HS-748 offered very little in terms of payload and range versus a C-295 class aircraft  The C-295 offers a very credible light transport, whereas the HS-748's role in the IAF was more akin to a transport trainer and for communication duties with little operational use  Having seen a dozen or so HS-748s parked at Vadodara airport all through my childhood, I never once saw one in the air  They just seemed to be stored out in the open  Upon asking an IAF transport pilot who was my friend's father, he remarked "zyaada kaam ke nahi hain yeh" 
Why would you expend more capital on what is essentially an obsolete airframe, even if theoretically it had not yet reached its service life? You'd have to re-engine it, put new avionics on board and even that wouldn't suffice for para dropping requirements  it was operationally never suitable for para dropping, which is an important mission for transport aircraft and had deficiencies in hot and high climes as well 
Unfortunately, the 748 was never meant to be a military transport  At the request of IAF, its door was enlarged to enable larger cargo items to be loaded and to allow para dropping without hitting the tail plane  However, to load a jeep in it, a 30-ft long ramp was required  The jeep would drive in and insert its front wheels into the aircraft  Then it had to be manually lifted and turned to get it in  Unloading it was just as difficult  Para dropping of troops or cargo even from the aircraft with the enlarged door was considered too dangerous with the risk of hitting the tail plane  The aircraft's performance at hot and high airfields was hopelessly inadequate  Eventually IAF acquired the tail-loading An-32s which were powered specifically for IAF's need for operating in the Himalayas 
BRF article -Avro in IAF service
Now unless you want to overcome all these through a costly, time consuming engineering re-design program, that too without access to original documents since this airplane was designed in the 1960s, there is no question of keeping them going for another 40 years  By which time the original design would be over 80 years old and with no one on earth but the IAF as an operator and HAL as the agency supporting it  Hardly a situation anyone would want 
abhik wrote: +1, Air India recently sold their entire fleet of Boeing 777s 
Only 5 of the Boeing 777-200LR, to Etihad Airways, which IMO was a bad decision  they could have reconfigured the airplanes with just 2 classes and continued to fly them to the US, non-stop 
The remaining 3 777-200LR were offered for lease but are still a part of AI's fleet since they didn't find any takers  This particular model hardly sold much and was developed for ultra-long range flights  it was the least successful 777 model and clearly AI goofed up on the configuration by going for these in place of the 300ER  The economics however didn't make too much sense for AI eventually 
there are 13 777-300ER as a part of their fleet ahd their economics is much better 
Govt  to decide tomorrow on whether to go ahead and allow the IAF to verify the technical details of the C-295 bid by Tata-Airbus instead of scrapping the tender due to single vendor situation 
The government will decide on Saturday whether to press ahead with the Rs 13,000 crore mega project for the private sector to supply 56 medium transport aircraft to the IAF despite only a single bidder, the Tata-Airbus consortium, being in the fray 
Though the defence acquisitions council (DAC) chaired by Manohar Parrikar will take the final decision, MoD sources on Tuesday said the "emerging dominant view" is that green signal should be given to the crucial project designed to promote Indian private sector's entry into the domestic aerospace arena with foreign collaboration 
"The Tata-Airbus technical and commercial bid is a credible offer submitted in a competitive environment  The other seven contenders backed out for one reason or the other," said a source 
IAF has now sought the clearance of the DAC -- the first such meeting to be chaired by Parrikar after becoming defence minister on November 10 -- to begin technical evaluation of the C-295 aircraft offered by Airbus Defence & Space and Tata Advanced Systems 
Though it has become a single-vendor situation, the DAC can approve it if it wants as per existing procurement procedures  Of the eight foreign aviation majors that got the global tender, American Boeing and Lockheed-Martin as well as Brazilian Embraer said they did not manufacture the class of aircraft being sought by IAF 
Refusing to take part in the tender, Russian Rosoboronexport said it wanted a fresh design and development project  Antonov of Ukraine wanted yet another extension of the bid submission deadline due to the ongoing conflict in Crimea  Swedish Saab said it had shut down its assembly line for such aircraft 
Then, Alenia Aermacchi was linked to Italian conglomerate Finmeccanica, which has been slapped with "a partial ban" after the infamous VVIP helicopter scandal  "All this left only the European consortium Airbus  The DAC will have to take a call since re-tendering may lead to the same situation," said the source 
Incidentally, it was the Modi government's first DAC in July -- then headed by Arun Jaitley - which revived the Avro replacement project after it was put on hold by the UPA-2 regime last year due to strong opposition from the powerful PSU lobby and ministers like Praful Patel, as reported by TOI earlier 
Apart from the critical need to encourage the private sector to enter defence production in a big way, especially in the aerospace arena where Hindustan Aeronautics enjoys a monopoly, its felt the defence PSU's order books are already overflowing with projects 
Fingers crossed  Hopefully sense will prevail 
Why was lr got? Er is capable of Dubai to sfo nonstop 
Lr is overkill unless we want Delhi to Peru  
Singha wrote: Why was lr got? Er is capable of Dubai to sfo nonstop 
they wanted it for non-stop routes from India to the west coast of the US  But with fuel prices going higher and with the lower seat count on the 777-200LR, the seat mile costs grew too high  A 3 class configuration only made matters worse  A higher density configuration with more economy class seats and just 12-15 Business class seats would have been better perhaps, especially if they didn't have very high First Class load factors 
LR and ER is better if you want to have a better payload down below for long haul  Ultimately, the best bet is going to come form the 787's that take a fewer people (so you can do the longer routes) with still a competitive CASM, and the B and F class folks will pay good money for newer aircraft 
Postby Kartik » 04 Dec 2014 12:55
Lets see if there is any forward movement on the stalled MTA project once Putin arrives in New Delhi
Major defence deals to be signed during Putin-Modi summit
In this connection, it is expected that during the summit, Russia and India may ultimately resolve several long-delayed agreements on military-technical cooperation projects between the two countries and sign them finally for their implementation  These agreements, above all, include joint Fifth Generation Fighter Aircraft (FGFA) project and joint development of Multi-role Transport Aircraft (MTA) 
A final deal on FGFA for production has been delayed because the Indian Air Force (IAF) did not approve the design and work-share  Now Russia has reportedly agreed that the jet would be a two-seat design, not a one-seater  India’s work-share would also be increased from18 percent to 25 percent, and even up to 40-50 percent in the near future, in view of the steady development of the Indian aviation industry 
Defence and SecurityAccording to the agreement, India’s stealth air-to-air missile “Astra” along with Indo-Russian BrahMos supersonic cruise missile will be mounted on the FGFA 
The preliminary design agreement on FGFA had been signed in 2010 between Indian HAL and Russian Sukhoi Design Bureau to build the jet for the use by both countries
Context 3: 2015-05-14 Assigned to ROVI GUIDES, INC  reassignment ROVI GUIDES, INC  MERGER (SEE DOCUMENT FOR DETAILS)  Assignors: TV GUIDE, INC 
2015-05-14 Assigned to UV CORP  reassignment UV CORP  MERGER (SEE DOCUMENT FOR DETAILS)  Assignors: UNITED VIDEO PROPERTIES, INC 
2015-05-14 Assigned to TV GUIDE, INC  reassignment TV GUIDE, INC  MERGER (SEE DOCUMENT FOR DETAILS)  Assignors: UV CORP 
Methods and systems are described herein for quickly and easily displaying supplemental information about an event occurring in a media asset  In some embodiments, a media application may use a content-recognition module to determine the context of an event and distribute itemized tasks to multiple entities in order to generate the supplemental information about the event 
While viewing media assets (e g , a television program), users may wish to learn more information about an event (e g , a statement made by a person appearing in the media asset, the validity of a claim in an advertisement, etc ) occurring in the media asset  While some media assets allow a user to select additional options or added features (e g , pop-up biographies about the cast and crew), when the added features appear and what topic the added features concern are determined by the content producer and not the user  Furthermore, as the added feature is derived from the content producer, the added feature may be biased or may present limited viewpoints about an event  Therefore, added features provided by a content producer may not provide the added information about an event that a user desires 
In order to gain the added information that a user desires, the user may use additional devices (e g , a laptop computer) to search (e g , using an Internet search engine) for more information about the event  However, without knowing the proper context (e g , who said the statement, what was the tone of the statement, when was the statement said, etc ) of the event or what search terms to use to describe the context of the event (e g , how to describe the tone of the statement), a user may not be able to determine (even using a search engine) more information about the event  Moreover, the use of general search terms may not provide the accuracy or precision needed by the user  Furthermore, even if a user may eventually determine the information, the effort and time required may distract the user from the media asset 
Accordingly, methods and systems are described herein for quickly and easily displaying supplemental information about an event occurring in a media asset  In some embodiments, a media application may use a content-recognition module to determine the context of an event in a media asset and distribute itemized tasks to multiple users in order to generate the supplemental information about the event  The context-recognition module prevents the user from being distracted from the media asset (e g , while the user attempts to describe the context of the event or search for information about the event)  In addition, by distributing tasks to multiple entities (e g , crowd-sourcing), the media application may collect large amounts of information in relatively short periods of time (or in real-time) and aggregate and/or filter the information to generate the supplemental information about the event based on multiple viewpoints and/or sources  By using multiple viewpoints and/or sources, the media application enhances the completeness (e g , by providing unbiased information) and accuracy of the supplemental information 
For example, when a statement or action is made by a character or person appearing on a media asset (e g , a television program), a user may request supplemental information about the statement or action  In response, the media application may determine the context of the statement (e g , who said the statement and to what the statement was referring) or action (e g , what was the reason for the action)  After determining the context of the statement or action, the media application may itemize into tasks the additional information it requires in order to generate the supplemental information  The media application may then transmit requests including the tasks to a plurality of other users  Based on the responses from the plurality of other users, the media application may generate the supplemental information for display to the user 
In some embodiments, a media application may use multiple types of content-recognition modules and/or algorithms to determine the context of an event  For example, the media application may process data associated with the event in order to determine the context of an event  In some embodiments, processing the various types of data may include cross-referencing the data in a database indicating the different contexts the event may have 
In some embodiments, a media application may generate supplemental information about an event in a media asset in response to a user request  In order to generate the supplemental information, the media application may transmit, to multiple users, a request for additional information regarding a context of an event shown in a media asset  Upon receiving messages from the plurality of users that include the requested additional information, the media application may generate the supplemental information associated with the context of the event based on the messages 
It should be noted, the systems and/or methods described above may be applied to, or used in accordance with, other systems, methods and/or apparatuses 
FIG  9 is a flowchart of illustrative steps for generating supplemental information based on additional information provided by a plurality of users in accordance with some embodiments of the disclosure 
Accordingly, methods and systems are described herein for quickly and easily displaying supplemental information about an event occurring in a media asset  The methods and systems described herein alleviate the need for a user to determine the proper context (e g , who said a statement, what was the tone of the statement, when was the statement said, etc ) of an event in a media asset, or the search terms to use to describe the event (e g , the proper search terms to describe the tone of the statement), in order to determine more information about the event  In addition, the methods and systems increase the completeness and accuracy of the information compared to information gathered using traditional searching methods (e g , an Internet search engine), without distracting the user from the media asset 
In some embodiments, a media application may receive a user input from a user device for supplemental information about the context of an event shown in a media asset  The media application may determine additional information required to generate the supplemental information about the context of the event shown in a media asset, and transmit requests for the additional information to one or more users  The media application may receive one or more messages, which include the requested additional information, from the one or more users and generate the supplemental information based on the one or more message  The media application may then instruct the user device to display the supplemental information 
As used herein, “supplemental information” refers to any information related to or associated with an event in a media asset  For example, supplemental information may include, but is not limited to, the verification of a statement or claim in a media asset, further descriptions and/or information about objects or entities shown and/or described in a media asset, and/or any other information, including, but not limited to, a video or audio segment, that may interest a user about an event in a media asset  In some embodiments, the media application may generate supplemental information based on one or more pieces of additional information 
As used herein, “additional information” refers to any information used to generate supplemental information  For example, in an embodiment in which supplement information is the verification of a statement made by a person displayed in a media asset, and a request for the additional information from the media application includes a request for a fact needed to verify the factual basis of the statement, the additional information may be the fact used to verify the statement  For example, if an advertisement claims to have the best product on the market, the media application may use additional information such as the name of the product in question, a list of all other products in the market, and the results of a comparison study of the product in question to all other products to determine whether or not the product is actually the “best” product on the market  Additionally or alternatively, the media application may request industry and/or user reviews related to the event (e g , reviews indicating the quality of the product)  The media application may then use the information in the reviews to generate the supplemental information 
As used herein, an “event” is any action (e g , a verbal statement, opinion and/or physical movement), segment (e g , a portion of a news broadcast featuring a particular topic), or other occurrence during a media asset that may be of particular interest to a user  For example, in some embodiments an event may be a statement or gesture made by a character or person in a media asset affirming or denying a claim 
As referred to herein, the terms “media asset” and “content” should be understood to mean an electronically consumable user asset, such as television programming, as well as pay-per-view programs, on-demand programs (as in video-on-demand (VOD) systems), Internet content (e g , streaming content, downloadable content, Webcasts, etc ), video clips, audio, content information, pictures, rotating images, documents, playlists, websites, articles, books, electronic books, blogs, advertisements, chat sessions, social media, applications, games, and/or any other media or multimedia and/or combination of the same  Media applications also allow users to navigate among and locate content  As referred to herein, the term “multimedia” should be understood to mean content that utilizes at least two different content forms described above, for example, text, audio, images, video, or interactivity content forms  Content may be recorded, played, displayed or accessed by user equipment devices, but can also be part of a live performance 
As referred to herein, the phrase “user equipment device,” “user equipment,” “user device,” “electronic device,” “electronic equipment,” “media equipment device,” or “media device” should be understood to mean any device for accessing the content described above, such as a television, a Smart TV, a set-top box, an integrated receiver decoder (IRD) for handling satellite television, a digital storage device, a digital media receiver (DMR), a digital media adapter (DMA), a streaming media device, a DVD player, a DVD recorder, a connected DVD, a local media server, a BLU-RAY player, a BLU-RAY recorder, a personal computer (PC), a laptop computer, a tablet computer, a WebTV box, a personal computer television (PC/TV), a PC media server, a PC media center, a hand-held computer, a stationary telephone, a personal digital assistant (PDA), a mobile telephone, a portable video player, a portable music player, a portable gaming machine, a smart phone, or any other television equipment, computing equipment, or wireless device, and/or combination of the same 
In some embodiments, the user equipment device may have a front facing screen and a rear facing screen, multiple front screens, or multiple angled screens  In some embodiments, the user equipment device may have a front facing camera and/or a rear facing camera  On these user equipment devices, users may be able to navigate among and locate the same content available through a television  Consequently, media may be available on these devices, as well  The media provided may be for content available only through a television, for content available only through one or more of other types of user equipment devices, or for content available both through a television and one or more of the other types of user equipment devices  The media applications may be provided as on-line applications (i e , provided on a website), or as stand-alone applications or clients on user equipment devices  Various devices and platforms that may implement media applications are described in more detail below 
In some embodiments, a media application may transmit, to a plurality of users, a request for additional information regarding a context of an event shown in a media asset  As used herein, a “plurality of users” may include, but is not limited to any device, entity, or source of information that may process a request for additional information  For example, the plurality of users may include a person operating a user equipment device  In some embodiments, the person may receive (e g , via e-mail, Internet posting, advertisement, or any other applicable information delivery method) the request from the media application for additional information, and in response generate a message (e g , via a return e-mail, an answer to the Internet posting, a user input in the advertisement, or any other applicable method of transmitting information) that includes the additional information  It should be noted that in some embodiments, transmitting a request to a plurality of users may also include querying one or more databases (e g , an Internet search engine or any other storage device, including, but not limited to, databases containing previously generated supplemental information and/or additional information) or consulting one or more data gathering services (e g , a intelligent personal assistant application) for the additional information 
In some embodiments, a media application may use a content-recognition module or algorithm to determine the context of an event and distribute itemized tasks to multiple users in order to generate the supplemental information about the event  The content-recognition module may use object recognition techniques such as edge detection, pattern recognition, including, but not limited to, self-learning systems (e g , neural networks), optical character recognition, on-line character recognition (including but not limited to, dynamic character recognition, real-time character recognition, intelligent character recognition), and/or any other suitable technique or method to determine the objects and/or characteristics in media assets  For example, the media application may receive media assets in the form of a video  The video may include a series of frames  For each frame of the video, the media application may use a content-recognition module or algorithm to determine the context (e



ground_truth: Decorrelating the data before running the PLS algorithm improves the performance of the algorithm.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: Besides the Boeing C-17, what other transport aircraft is the IAF considering for acquisition?

Read the following text and answer briefly.

Context 2:  The final design contract was to be signed in July-August 2012  But the deadline has already passed  According to the Indian media reports, under the programme, India is expected to build 200 fighter jets at the cost of $30 billion 
FGFA is not the only Indo-Russia joint project  The two countries also signed an agreement on the joint development of MTA in 2007, based on Il-214 Russian plane  The cost of the $600 million project is being equally shared by the two countries  The MTA, when developed, will have ready market for 205 aircraft - 45 for the Indian Air Force, 100 for the Russian Air Force, and 60 more for exporting to friendly countries  The international market for MTA is estimated at 390 planes  Under the agreement, thirty percent of the annual production of planes could be exported to third countries 
The MTA was expected to go in service with the Russian and Indian Air Forces in 2015  But the project faced a number of problems, delaying the development of the MTA  The project got into rough weather after India felt there was nothing much for Indian engineers and scientists to do in the design and development of the MTA 
However, all the issues related to the project were resolved with the Russians when the HAL undertook to carry out design and development of its work-share of MTA at Aircraft R&D Centre at Bangalore  Russian Ilyushin Design Bureau and the Irkut Corporation and HAL are participating in the project  The first flight is expected to take place in 2017-18 
The MTA would replace the AN- 32 aircraft being used by the IAF  It will be used for both cargo and troop transportation, para-drop and air drop of supplies, including low-altitude parachute extraction system 
BrahMos missile exports a challenging proposition
Another key deal expected to be signed during the summit, is for the development of “BrahMos mini missile” by the Indo-Russian joint venture BrahMos Aerospace which manufactures supersonic cruise missile  BrahMos’ new CEO Sudhir Mishra recently said he was hopeful that a deal to develop the mini version of the missile will be signed during Putin’s summit with Modi 
“We are hoping to sign a tripartite agreement between DRDO, NPOM lab and BrahMos Aerospace during the planned visit of Russian President in December,” Mishra said 
He said that the new missile will have a speed of 3 5 mach and carry a payload of 300 km up to a range of 290 km  In size, it will be about half of the present missile, which is around 10 metres long  The missile can be integrated with different platforms, including submarines and FGFA  It is planned to be inducted into service by 2017 
Modi-Abbott to upgrade defence ties
A new dimension:
In a first, India and Australia will also set up a mechanism to discuss “synergies in integrating defence system”, including research and development cooperation on integrating defence equipment that both countries currently purchase, for example, U S’s C-17 Globemaster III, according to officials 
^^That report about MTA is fishy  First it says that India has nothing to learn from an existing design (duh) and then says the issue has been resolved  How? Next it says India's need is 45 planes to replace over 100 An-32s  It also speculates about the export potential which may be nonexistent unless we sell it for peanuts 
This is a scam which only aims to create screwdriver jobs at HAL, stall any attempt to introduce private players into the aviation market and continue the Russian gravy train  My fear is the Russkies have our testiments in a firm grip with key components of Brahmos, nuke subs, Su30mki etc and we may be jerked around 
(They need to be more definitive about "MTA" - Multirole vs  Medium)
The Indians had not selected an engine (among other things) for the MTA with the Russians  Perhaps that has been resolved now 
On export numbers, IIRC, it was the responsibility of Rosoboronexport  ?????
Kartik wrote: The MTA would replace the AN- 32 aircraft being used by the IAF  It will be used for both cargo and troop transportation, para-drop and air drop of supplies, including low-altitude parachute extraction system 
Pardon my ignorance  The Avro and An-32 have different upgrade paths  How are the replacements for these venerable aircraft different in terms of use cases in IAF  Cannot one platform replace both these types? (Either MTA or C-295)
In this case, I feel they should have just gone with screwdrivergiri (production tech) and got to market first  There is no jet-powered transporter in this range! Just license produce the IL-214 with the PD-14M, glass cockpit and a state-of-the-art COTS avionics computer 
In my view, it was a low hanging fruit, which they completely messed up! They could have learnt on how to adopt the plane for the 160-200 seater 
indranilroy wrote: They could have learnt on how to adopt the plane for the 160-200 seater 
Yes, the MTA project should fold the Avro, An-32 and the regional transport role and become a conversion project rather a development one  The driving numbers will come from the regional transport (thousands in India itself) rather than the Avro or medium transport roles (max 300 between them)  This changes the ball game and introduces all kinds of possibilities  But I'm pretty sure that the Il-214/MTA is not the way to go because it will take a decade or more to arrive  A good possibility was another Antonov, the An-148 but it has some mechanical glitches apparently besides being bogged down in the Ukraine mess  Maybe the Russians can "relocate" the aircraft to Russia? The other possibility is the BAe-146 which is ironically another Avro  We should remember that both the HS-748 "Avro" and An-32 were regional airliners that were converted to military use, not the other way around  HAL or a private firm will pick up a lot of experience in the conversion process itself 
The Sukhoi Superjet is already in production/orders,with over 100+ for Russian and intl  customers  It is ideal for regional transport,perfect for flights to smaller Tier-2/3 cities from metros  If we really want a regional jet this is the fastest way toi go,we can set up a manufacturing unti here for the same at an HAL unit 
Postby shaun » 05 Dec 2014 15:24
Its an international projects, with components outsourced from different international vendors   Over 30 foreign partnership companies are involved in the project and partly financed by Italy 
Sukhoi is good for passenger use but wont be suitable for military, rough field use  The shoulder wing jets like the An-148 have slower speeds and better ground clearance  The Bae-146 was usedby Druk Air in Bhutan so it should do OK in the ALGs  If we don't fold our requirements then we should go with something like the Superjet which we will at least be able to make in India and also modify to stretched versions  Unless we have a clear path to operational clearance within 10 yrs for the RTA project vetted by our top industrial houses, it is pie-in-the-sky and should be dropped  The RTA will be big enough to keep 2-3 factories humming and leapfrog our capabilities  If we don't get our act together almost immediately, we will miss the boat, just like our trainer fiascos 
I don't think Superjet fits into our scheme of things  We should think as a country and see to it that our programs don't trample on each other 
First, the more certain ones:
1  Mahindras NM5 and Airvans can care of the low-cost but sturdy 5,8,10 and 18-seater section 
2  Saras had such great potential for being the high performance 14-18 seater  But I have almost given up on it  This section will most probably be taken up by the Tata-built Do-228 NG 
3  We should standardize the C-295 as the Avro/An-32 replacement and create a 70-80 seater variant out of it 
And then the more wishful ones:
1  If the RTA is going to be a jet, then make it a 100-130 seater  I don't expect the first prototype to take the sky before 2025  I feel it is too big of a jump where we don't even have a base  With LCA, at least we were at least license producing other fighters 
4  Building on the IL-214, the MTA was on a more sure footing  But, I can't see how the first prototype can to take to the sky before 2019(more than 10 years since MTAL was formed)! If the transport plane materializes, then one can imagine making a civilian 150-200 seater version of the same  But this program needs a push  Will Putin's visit be able to galvanize this into the next symbol of Indo-Russian cooperation  Probably not!
Postby GeorgeWelch » 12 Dec 2014 23:39
http://www ctvnews ca/canada/defence-de     -1 2144472
The Defence Department intends to purchase a Boeing C-17 Globemaster III, a large military transport plane that comes with a price tag of just under $200 million, CTV News has learned
It's difficult to get a good count, but by some sources, if this and the 4 Australia planes go through, there will only be 5 left 
X-Posting from FGFA thread 
Despite Putin’s visit, two pacts on military aircraft still in doldrums
President Vladimir Putin may have come and gone but stalemate largely persists over two key long-pending India-Russian defence projects, the fifth-generation fighter aircraft (FGFA) and military multirole transport aircraft (MTA) 
The deadlock over the MTA, which were initially envisaged to gradually replace IAF's ageing fleet of the medium-lift AN-32 aircraft, seems to be much more serious  India now wants to ascertain the cost viability of the twin-engine transport aircraft in comparison to similar planes available in the market 
There are also questions about the MTA's "predicted timelines for delivery" as well as its failure to meet the high-altitude requirements, which need to be answered before India even thinks of inking the full-scale contract for the project, said sources 
Postby Gyan » 13 Dec 2014 12:29
indranilroy wrote: I don't think Superjet fits into our scheme of things  We should think as a country and see to it that our programs don't trample on each other 
1  Mahindras NM5 and Airvans can care of the low-cost but sturdy 5,8,10 and 18-seater section  Righto
2  Saras had such great potential for being the high performance 14-18 seater  But I have almost given up on it  This section will most probably be taken up by the Tata-built Do-228 NG  We need future extended variants of presurrized aircraft like 30 seater Saras and say 30 seater unpressurized Do-328 NG 
3  We should standardize the C-295 as the Avro/An-32 replacement and create a Civilian turboprop pressurized cabin 70-80 seater variant out of it 
1  If the RTA is going to be a jet, then make it a 100-130 seater  Agreeeeeed I don't expect the first prototype to take the sky before 2025  I feel it is too big of a jump where we don't even have a base  With LCA, at least we were at least license producing other fighters  Though I think that we should participate in Russian MS-21 and also the wide body follow on 
4  Building on the IL-214, the MTA was on a more sure footing  But, I can't see how the first prototype can to take to the sky before 2019(more than 10 years since MTAL was formed)! If the transport plane materializes, then one can imagine making a civilian 150-200 seater version of the same  Though I think that we should participate in Russian MS-21 and also the wide body follow on  But this program needs a push  Will Putin's visit be able to galvanize this into the next symbol of Indo-Russian cooperation  Probably not!
Absence of any specifics on Sukhoi Superjet, MS-21, Wide body aircraft, Mi-38, MRTA, FGFA, even after Putin visit is very disappointing 
FlightGlobal- Boeing sitting on 8 unsold C-17s
By: Dan ParsonsWashington DCSource: Flightglobal com
This story is sourced from Flightglobal com 12 hours agoBoeing has sold two more C-17 transports to an undisclosed customer, but it will likely end the year with eight unsold white tails 
There are 10 Boeing C-17 airlifters in various stages of assembly at the company’s Long Beach, California, production facility 
Two of the aircraft are spoken for by an unnamed customer, Boeing says  Boeing is trying to sell off the other eight white tails, which will be the last produced before the factory is shuttered sometime in the summer of 2015 
The 279th – and final – C-17 fuselage will be mated to its wings in January or February, programme spokeswoman Tiffany Pitts tells Flightglobal  The operation is California’s last remaining aircraft production line and the lone widebody military aircraft production line in the USA, according to Boeing 
At least two countries – Australia and Canada – have publicly announced an intention to purchase a C-17, though neither factor into Boeing’s future planning, Pitts says  Until contracts are finalised, the number available remains eight, she says  The Royal Canadian Air Force already has four C-17As, according to Flightglobal’s World Air Forces 2014 directory 
Canadian news outlets reported earlier in December that the air force would buy one C-17 with money left over at the end of 2015 
Australia is further along with its bid to purchase C-17s  The US Defense Security Cooperation Agency in November announced Australia was approved to buy up to four C-17s and support equipment for $1 6 billion 
Boeing has plans to store any unsold C-17s following closure of its production line, Pitts says 
“I’m hoping they all will be sold before then, but we’ve had plans in place for a very long time to store and maintain the aircraft if that doesn’t happen,” she says 
the IAF will need to factor in the demand vs availability of C-17s and stock up with a follow-on order quickly  The initial plan to have 16 C-17s may not fructify, considering that there are just 8 left now, with Australia having announced plans to buy 4 more 
why are they closing the line if it has demands ???
Real estate sales tactics probably  Buy now last 8 3bhk flats Saar 
krishnan wrote: why are they closing the line if it has demands ???
It requires 3 years lead time to order raw materials/parts from all of its sub-vendors  All current firm orders have been fulfilled, and no new orders have come  Anticipating a need for a few more aircrafts, they produced 10 extra (self-funded) units before production winded down  Bottom line is they don't make money keeping an idle plant around with all its employees and infrastructure  At most what they will likely do is keep a limited infrastructure around for a few more years in case a bunch of new orders come  They can then see if it makes business sense to re-open the plant 
Postby Aditya_V » 17 Dec 2014 12:19
Wish this can be brought to the notice of Journos/ Poster when slamming LCA/ Arjun and other indigenous projects  If there are no orders there will be no efficiency 
Dec 10, 2014 :: Russia launches Il-76MDM upgrade programme
Russia's Ilyushin has started to upgrade a first Russian Air Force (VVS) Ilyushin Il-76MD 'Candid' military transport aircraft to Il-76MDM standard, company officials have told IHS Jane's   The main features of the upgrade include refurbished engines and upgraded avionics 
The modernisation is being conducted at the VVS's Military Transport Aviation (MTA) maintenance facility based at the Ilyushin division in Zhukovsky city near Moscow 
A senior Ilyushin official told IHS Jane's that the upgrade of the first aircraft will be finished in 18 months  Subsequent aircraft will take less time to complete the process, however  When the modernisation is finished the initial Il-76MDM will undergo state trials  The upgrade process for subsequent aircraft will begin when the trials programme is completed 
IHS Jane's was previously told by a VVS senior official that the modernisation of 41 MTA Il-76MDs is planned by 2020  While the Il-76MDM upgrade retains the old D-30KP engine (compared with the PS-90A engine equipping the new Il-76MD-90A/Il-476), the modernisation effort should match the aircraft's onboard electronics with those of the newbuild Il-76MD-90A  This and other efforts mean the cost of modernising the Il-76MD to Il-76MDM is only a third of that of a newbuild Il-76MD-90A 
The existing D-30KP engines are to be enhanced to increase their service life  The overall aircraft's service life will be extended by 15 years 
The upgrade works are planned to be conducted in an aviation repair factory or in the MTA's aircraft maintenance facility  As a result, the Ulyanovsk-based Aviastar-SP plant, which is building the Il-76MD-90A, is not involved in the Il-76MD to Il-76MDM modernisation programme 
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Context 3: g , the person that is speaking or a facial gesture affirming or denying a statement) of an event occurring during the frame or series of frames 
In some embodiments, the content-recognition module or algorithm may also include speech recognition techniques, including but not limited to Hidden Markov Models, dynamic time warping, and/or neural networks (as described above) to translate spoken words into text  The content-recognition module may also use other techniques for processing audio and/or visual data  For example, the media application may monitor the volume of a statement in a media asset to determine the tone of the statement (e g , a high volume may indicate an angry tone) 
In addition, the media application may use multiple types of optical character recognition and/or fuzzy logic, for example, when determining the context of a keyword(s) retrieved from data (e g , media data, translated audio data, subtitle data, user-generated data, etc ) associated with the media asset (or when cross-referencing various types of data with databases indicating the different contexts of events as described below)  For example, the particular data field may be a textual data field  Using fuzzy logic, the system may determine two fields and/or values to be identical even though the substance of the data field or value (e g , two different spellings) is not identical  In some embodiments, the system may analyze particular data fields of a data structure or media asset frame for particular values or text  The data fields could be associated with characteristics, additional information, and/or any other data required for the function of the embodiments described herein  Furthermore, the data fields could contain values (e g , the data fields could be expressed in binary or any other suitable code or programming language) 
As used herein, the “context” of an event refers to the set of circumstances or facts that surround a particular event that influence or affect the meaning of the event  For example, when determining the context of a written and/or spoken statement, the media application may determine who or what authored/stated the statement, the written and/or spoken words and/or other statements that preceded and/or followed the statement, the tone of the statement, and/or any other conditions that may alter the connotation of the statement 
FIG  1 shows an illustrative example of a media application that may be used to display supplemental information in accordance with some embodiments of the disclosure  Display 100 illustrates a display on a user device displaying a media asset  Display 108 illustrates a display featuring supplemental information as described and/or generated in FIGS  6-9  It should be noted that display 100 and display 108 may be presented on any of the devices shown in FIGS  3-4  For example, in some embodiments, display 100 and display 108 may be displayed on user equipment 402, 404, and/or 406 (FIG  4) 
In FIG  1, display 100 represents a display of a media asset (e g , a streaming television program) on a user device (e g , user equipment 402, 404, and/or 406 (FIG  4))  Display 100 includes entity 102 and entity 104  In display 100, entity 104 is currently speaking as indicated by event 106  As shown in FIG  1, event 106 is a statement (e g , “We export a lot of coal”) by a person in the media asset 
In some embodiments, display 108 represents the continued display of the media asset on a user device, after a user has requested supplemental information about event 106  For example, a media application may have received a user input (e g , via user input interface 310 (FIG  3)) while entity 104 was speaking  Using the systems and methods described herein (e g , FIGS  6-9), the media application generated supplemental information 110  Supplemental information 110 represents more information about event 106 
For example, the media application (e g , media application 206 (FIG  2)) may have determined the context of event 106  Specifically, the media application may determine via a content-recognition module or algorithm the words spoken and/or actions by the person during the event  Additionally or alternatively, the media application may analyze the words and/or action during a predetermined amount of time (e g , ten seconds) before and/or after the event (e g , in order to better understand the context of the event)  Furthermore, by cross-referencing the words and/or other information obtained by the content-recognition module (e g , as discussed below in relation to FIG  5) with a database, the content-recognition module determines that the term “we,” the person in the media asset refers to an organization or body  The content-recognition module or algorithm may also determine that the term “export” refers to shipping goods out of a country  The content-recognition module or algorithm may also determine that the term “a lot” refers to a particular numerical amount  Finally, the content-recognition module or algorithm may also determine that the term “coal” refers to a mineral of fossilized carbon 
The content-recognition module or algorithm may also determine the relationships between words and/or other information obtained by the content-recognition module  For example, by processing the relationship between the words, the media application determines that event 106 is a statement regarding a particular amount of a particular substance shipped out of a particular country  Therefore, the media application determines that the request for supplemental information is likely a request to determine the validity of the statement  The media application then generates the supplemental information 
The media application may also have stored supplemental information generated by previous requests (e g , supplemental information generated in response to the same or different user viewing the media asset at an earlier date), and display the supplemental information again during the event (either in response to a user input requesting supplemental information or automatically without a user requesting supplemental information) 
FIG  2 shows an illustrative example of a system that may be used to generate supplemental information (e g , supplemental information 110 (FIG  1)) based on additional information provided by a plurality of users in accordance with some embodiments of the disclosure  For example, in some embodiments, system 200 may be used to generate supplemental information (e g , supplemental information 110 (FIG  1)) on a display (e g , display 108 (FIG  1)) of a user device (e g , user equipment 402, 404, and/or 406 (FIG  4))  It should be noted that in some embodiments, the devices shown in FIG  2 may correspond to one or more devices in FIGS  3-4 
FIG  2 shows system 200  In system 200, a user is currently accessing a media asset on display 202  In some embodiments, display 202 may correspond to display 100 (FIG  1))  During an event (e g , event 106 (FIG  1)) a user may have requested supplemental information about an event (e g , event 106 (FIG  1)) in display 202 using user device 204  Media application 206, which in some embodiments, may be implemented on user device 204 or at a remote location (e g , supplemental information source 418 (FIG  4)), receives the request for supplemental information 
Media application 206 determines the context of the event (e g , who said the statement making up the event and to what the statement was referring)  After determining the context of the statement, the media application may itemize into one or more tasks, additional information (e g , facts) it requires in order to generate the supplemental information (e g , a verification or correction of the factual basis of the statement)  For example, if the event is a statement about the amount of coal that is exported from the United States (e g , as described in relation to FIG  1 above), media application 206 may determine the fact required to generate the supplemental information is the exact numerical amount of coal that is exported from the United States  The media application may then transmit requests for the additional information (e g , a request for the exact numerical amount of coal that is exported from the United States) to a plurality of other users 
In FIG  2, users operating user device 208, user device 210, and user device 212 represent a plurality of users  Having determined the additional information it requires in order to generate the supplemental information, media application 206 requests the additional information from the plurality of users  In system 200, media application 206 has transmitted the same task (e g , the same question) to each of the plurality of users  In some embodiments, one or more of the users may receive different tasks  For example, by breaking the additional information into small, independent tasks, media application 206 may increase the speed (e g



ground_truth: The IAF is considering the acquisition of the Airbus A330 MRTT (Multi-Role Tanker Transport) besides the Boeing C-17.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How does a media application determine the context of an event?

Read the following text and answer briefly.

Context 3: , multiple users may work concurrently to solve different parts of a problem) and accuracy (e g , reducing the tasks to smaller, less complex problems reduces the chance of human error) of the additional information returned by the plurality of users 
In addition, by breaking the additional information into small, independent tasks, the plurality of users may not know to what they are contributing (enhancing the privacy of the user that requested the supplemental information), however, the plurality of users can still be effective in their individual tasks  In addition, by breaking the additional information into small, independent tasks, the media application may more easily outsource the requests for additional information  For example, one or more of the tasks used to generate the additional information may be the same as one or more of the tasks used to generate other additional information (e g , additional information used to generate different supplemental information in response to a request for supplemental information about the same or a different event issued by the same or a different user)  The response to each of the request and/or the additional information may be stored (e g , on any of the devices accessible by communications network 414 (FIG  4)) for subsequent retrieval 
Based on the responses, transmitted as messages including the additional information, from the plurality of other users, media application 206 may generate the supplemental information (e g , supplemental information 110 (FIG  1)) for display to the user on the user device 204  For example, media application may aggregate, append, and/or compare the additional information in each of the messages received from the plurality of users  The supplemental information may then be generated based on the aggregated, appended, and/or compared additional information (e g , as described in FIG  9 below) 
In some embodiments, the plurality of users may receive summary information about the event with the request for additional information  (e g , a video clip of a portion or segment of the media asset, a textual description, etc ), which may help the plurality of users provide additional information  For example, in some embodiments, the media application may instead of (or in addition to) determining the context of an event, determine a particular portion of the event that would be needed for the plurality of users to provide additional information about the event 
For example, the media application may use progress information associated with the progress of the media asset (e g , line 506 (FIG  5)) to determine at what point during the progression of the media asset the event occurred, and in response, transmit a portion of the media asset beginning ten second before that point and ending ten seconds after that point  For example, if the event is a statement made by a character or person in a media asset, the media application may determine when the statement began (e g , the point of progress of the media asset in which the statement began) and ended  The media application may then include the portion containing the entire statement (and the event) in the request for additional information sent to the plurality of users 
The selected portion may include any amount of summary information that the media application determines is necessary for the user or any one of the plurality of users to understand the main action sequence  This summary information (e g , a portion of the media asset) may be included with the request for additional information (e g , in a file transmitted with the request), or may be included with the generated supplemental information as a reference for the user  For example, the media application may select a segment of the play length of the media asset or a particular scene of the media asset, which includes the event, for to display to the plurality of users along with the request for additional information 
For example, if an event (e g , a statement) was in response to a question, the media application may also determine when the question began and ended, and send the entire question (or the play length of the media asset corresponding to the question) to the plurality of users as well  After determining the portion to provide to the plurality of users (e g , a segment including the ten seconds before and the ten seconds after the event), the media application may provide the summary information of the event and any other material needed by the plurality of users to understand the event and/or request for supplemental information from the user 
In some embodiments, a portion of the media asset containing the event, as selected by the media application, may also include any amount of the play length of the media asset, or any amount of scenes or segments from the media asset  In some embodiments, the portion may include segments of the play length of the media asset or scenes from the media asset that are not adjacent during the normal playback of the media asset  For example, in some embodiments, a portion of the media asset may include one or more sequences or scenes of interest to the plurality of users, even though the particular sequences or scenes are featured at different points in the play length of the media asset  The media application may determine the segments or scenes to include based on a content recognition file (e g , data structure 500 (FIG  5)) describing the media asset  For example, if a plot point or other information, which may be relevant to an event is displayed earlier in the media asset, the summary information may include a portion of the media asset displaying the plot point 
In some embodiments, the length of a portion may be determined based on the genre of the media asset  In some embodiments, the length of the portion may depend on a user profile for the user or for anyone of the plurality of users  For example, a user profile and/or a content recognition file (e g , data structure 500 (FIG  5)) may indicate that a particular user may require more or less additional content  For example, the user may be aware of particular characters or plot points in the media asset and, therefore, may not require the additional content to introduce those aspects 
In some embodiments, the plurality of users may receive a particular user interface, which organizes the data about the event (e g , a clip of the actual event, summary information about the event, information about the request for supplemental information issued by the user, etc )  The interface may also include an automatic submission form, which may be used to generate a message, which is sent to the media application 
In some embodiments, the media application may also receive user input from the user requesting the supplemental information that further affects the generation of supplemental information by the media application  For example, the user may request the supplemental information includes particular information (e g , the factual basis of a statement), may request a multimedia format of the supplemental information (e g , textual description, a video clip, etc ), may request a form of the supplemental information (e g , a short description about the event, an Internet link to other sources of information on the event, or a true or false designation about the event) by entering user inputs (e g , via user input interface 310 (FIG  3)) 
It should be noted that any information or process referred to in this disclosure that is referred to as being in response to a user input may alternatively and/or additionally be performed automatically by the media application (e g , via control circuitry 304 (FIG  3))  For example, in some embodiments, a user may request a true or false designation (e g , an on-screen pop-up box indicating whether an event was true or false)  Additionally and/or alternatively, in some embodiments, the true or false designation may appear automatically based on predetermined settings indicating to the media application to display a true or false designation in response to detecting an event 
In some embodiments, an indicator that supplemental information has previously been generated or is currently ready to generate (e g , a plurality of users are available) may be displayed to a user (e g , on display 100 (FIG  1) during the event)  The indicator may also indicate the particular information, the multimedia format, and/or the form of supplemental information that is available  An indicator may also appear with the supplemental information (e g , supplemental information 110 (FIG  1)), which allows the user to request additional supplemental information or provide feedback/responses (e g , rating the quality of the supplemental information) to the media application and/or plurality of users 
In some embodiments, a user may also access (e g , via selection of an indicator and/or automatically upon the supplemental information being generated) summary information about the event  For example, in some embodiments (e g , when the supplemental information is not generated in real-time), the media asset may have progressed to a different point by the time the supplemental information is ready for display  Therefore, the media application may need to provide a video clip of the event or other summary information, so that the user remembers about what or why the supplemental information was requested 
FIG  3 is a block diagram of an illustrative user equipment device in accordance with some embodiments of the disclosure  It should be noted that the components shown in FIG  3 may be used to store, receive, transmit, and/or display the media assets, additional information, and/or supplemental information as described herein  For example, media application 206 (FIG  2) may be implemented on user equipment device 300, and may issue instructions (e g , displaying supplemental information 110 (FIG  1)) via control circuitry 304 
Users may access media assets and the media application (and its display screens described above and below) from one or more of their user equipment devices  FIG  3 shows a generalized embodiment of illustrative user equipment device 300  More specific implementations of user equipment devices are discussed below in connection with FIG  4  User equipment device 300 may receive content and data via input/output (hereinafter “I/O”) path 302  I/O path 302 may provide content (e g , broadcast programming, on-demand programming, Internet content, content available over a local area network (LAN) or wide area network (WAN), and/or other content) and data to control circuitry 304, which includes processing circuitry 306 and storage 308  Control circuitry 304 may be used to send and receive commands, requests, and other suitable data using I/O path 302  I/O path 302 may connect control circuitry 304 (and specifically processing circuitry 306) to one or more communications paths (described below)  I/O functions may be provided by one or more of these communications paths, but are shown as a single path in FIG  3 to avoid overcomplicating the drawing 
Control circuitry 304 may be based on any suitable processing circuitry such as processing circuitry 306  As referred to herein, processing circuitry should be understood to mean circuitry based on one or more microprocessors, microcontrollers, digital signal processors, programmable logic devices, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), etc , and may include a multi-core processor (e g , dual-core, quad-core, hexa-core, or any suitable number of cores) or supercomputer  



ground_truth: It uses a content-recognition module or algorithm.