text:
\section{Introduction}

Currently, the prediction of time series has played an important role in many science fields of practical application as engineering, biology, physics, meteorology, etc. In particular, and due to their dynamical properties, the analysis and prediction of chaotic time series have been of interest for the science community. In general, the chaotic time series are usually modeled by delay-differential equations; standard examples are the Mackey--Glass system \cite{mackey1977}, or the Ikeda equation \cite{ikeda1979} (for more examples see \cite{bez2001}).
Also, many methods have been used in the chaotic time series analysis \cite{hamilton1994}.
However, in the last decades different types of artificial neural networks (ANN) have been widely used for forecasting of chaotic time series, for example, back-propagation algorithm \cite{kuruna2006}, radial basic function \cite{chng1996}, recurrent network \cite{zhang2000}, etc.

On the other hand, the analysis of real-life time series requires of taking into account the error propagation of input uncertainties. The observed data could be contaminated for different instrumental noise types as white noise or proportional to signal (the latter mainly arises from instrumental calibration).
In modeling of chaotic time series, the impact of noise can be treated as errors-invariable problem where the noise is propagated into the prediction model. In the literature, the noisy impact on chaotic time series prediction has been barely considered. We can found studies where the algorithms were tested from a theoretical point of view (for example, see \cite{girard2003,sapan2009,haykin1998,li2012,han2013}), and works where the implementation was applied on real-life time series (for example, see \cite{leung2001,sheng2012,sapan2009}).
In addition, some authors have proposed a modification to the standard methods in order to improve the performance prediction in presence of noise \cite{sheng2012,sapan2009}.

In this work, we used the Mackey--Glass chaotic time series in order to study the short-term prediction ($x(t+6)$) with an artificial neural network optimized with a particle swarm algorithm (ANN+PSO).
The method was applied on noiseless and noisy chaotic time series.
In order to carry out the error propagation of the input noise, this hybrid algorithm was complemented with a Gaussian stochastic procedure to compute a new estimator of the predictions and their uncertainties.
Note that ANNs have been used in combination with PSO in several applications. Principally, these applications include: feedforward neural network training \cite{Han2011,WeiChang2013,Zhang,Grimaldi}, design of recurrent neural networks \cite{Juang2004}, design of radial basis function networks \cite{Huang2007}, and neural network control for nonlinear processes \cite{Song2007}. In addition, there are several current versions of PSO available in the literature (for example, see the following reviews \cite{Banks2007,Banks2008,Thangaraj2011}), but our application uses a standard PSO with inertial weight \cite{Shi1998MPSO}.
In this point, the use of a PSO with inertial weight is based on the following reasons: 1) this vesion of PSO is easy to understand and implement due to its simple concept and learning strategy; 2) as pointed out in \cite{Eberhart2000}, the PSO with inertia weight \cite{Shi1998MPSO} and PSO with constriction factor \cite{Clerc2002} are mathematically equivalent, and PSO with constriction factor can be considered as a special case of PSO with inertia weight \cite{Banks2007,Eberhart2000} (note that this equivalence can be applied to other improved PSO algorithms that include a varying the inertia weight schedule); 3) inertia weight PSO algorithm is quite stable to population changes \cite{Banks2008}; 4) the advantages and disadvantages of variants of PSO depend on the problem to solve \cite{Banks2007,Banks2008,Thangaraj2011}; 5) as a first approach for study of noise effect on dynamical systems using an ANN combined with inertia weight PSO algorithm, so the present study may motivate and help the researchers working in the field of evolutionary algorithms to develop new hybrid models or to apply other existing PSO models to solve this problem.
To the best of the authors's knowledge, there is no application for forecasting of noisy chaotic time series such as the one presented here, using a hybrid method that combined ANN with PSO algorithm.

Organization of this paper is as follows. In Section~\ref{sec:ANN+PSO} we present a detailed description of the hybrid ANN+PSO method. Section~\ref{sec:noiseless} and Section~4 present the simulation, algorithm implementation and the principal results obtained for the forecasting of noiseless chaotic time series and noisy time series, respectively. Finally, conclusions are given in Section~5.

\section{Hybrid ANN+PSO algorithm}
\label{sec:ANN+PSO}
Artificial neural networks (ANN) are similar to biological neural networks in performing functions collectively and in parallel using connection nodes.  Thus, ANN are a family of statistical learning algorithms biologically inspired.

In this study, we consider one of the most successful and frequently used types of neural networks: a multilayer feed-forward neural network with a backpropagation learning algorithm (gradient descent error). This ANN was implemented replacing standard backpropagation with particle swarm optimization (PSO).

PSO is a population-based optimization tool, where the system is initialized with a population of random particles and the algorithm searches for optima by updating generations \cite{lazzusj2009}. In each iteration, the velocity of each particle $j$ is calculated according to the following formula \cite{lazzus2010}:

\begin{equation}
v_{j}^{k+1}=\omega v_{j}^{k}+c_{1}r_{1}\left(\psi_{j}^{k}-s_{j}^{k}\right)+c_{2}r_{2}\left(\psi_{g}^{k}-s_{j}^{k}\right)
\label{eq2}
\end{equation}

\noindent where $s$ and $v$ denote a particle position and its corresponding velocity in a search space, respectively. $k$ is the current step number, $\omega$ is the inertia weight, $c_{1}$ and $c_{2}$ are the acceleration constants, and $r_{1}$, $r_{2}$ are elements from two random sequences in the range (0,1). $s_{j}^{k}$  is the current position of the particle, $\psi_{j}^{k}$ is the best one of the solutions that this particle has reached, and $\psi_{g}$ is the best solutions that all the particles have reached. In general, the value of each component in $v$ can be clamped to the range [$-v_{\rm max}$, $+v_{\rm max}$] control excessive roaming of particles outside the search space \cite{lazzusj2009,lazzus2010}. After calculating the velocity, the new position of each particle is:

\begin{equation}
s_{j}^{k+1}=s_{j}^{k}+v_{j}^{k+1}
\label{eq3}
\end{equation}

The procedure to calculating the output values, using the input values are described in detail in \cite{lazzus2009}.

The net inputs ($N$) are calculated for the hidden neurons coming from the inputs neurons. In the case of a neuron in the hidden layer is has:

\begin{equation}
N_{i}^{h}=\sum_{i}^{n}w_{i,j}^{h}p_{i}+b_{i,j}^{h}
\label{eq:ann_neurons}
\end{equation}

\noindent where $p_{i}$ is the vector of the inputs of the training, $w_{i,j}^{h}$ is the weight of the connection among the input neurons with the hidden layer $h$, and the term $b_{i,j}^{h}$ corresponds to the bias of the neuron of the hidden layer $h$, reached in its activation. The PSO algorithm is very different then any of the traditional methods of training \cite{lazzusj2009}. Each neuron contains a position and velocity. The position corresponds to the weight of a neuron $\left(s_{i}^{k}\rightarrow w_{i,j}^{h}\right)$. The velocity is used to update the weight $\left(v_{i}^{k+1}\rightarrow w'_{i,j}\right)$. Starting from these inputs, the outputs ($y_{i}$) of the hidden neurons are calculated, using a transfer function $f^{h}$ associated with the neurons of this layer:
\begin{equation}
y_{i}=f^{h}\left(\sum_{i}^{n}w_{i,j}^{h}p_{i}+b_{i,j}^{h}\right)
\label{eq:ann_out}
\end{equation}

The transfer functions $f^{h}$ can be linear or non-linear. We used one hidden layer with $f^{h}_{i}$ as a tangent hyperbolic function ({\it tansing}) and $f^{h}_{j}$ as a  linear function in the output layer.

\begin{equation}
f(N_{i})=\frac{e^{N_i}-e^{-N_i}}{e^{N_i}+e^{-N_i}}
\label{eq6}
\end{equation}
\begin{center}
\begin{table}[t!!!!]
\caption{Parameters used in the hybrid {\sc ANN+PSO} algorithm.}
\centering
\begin{tabular}{l c}
\hline
& \\ [-2  ex]
 \multicolumn{2}{c}{ANN}        \\ [0.5 ex]
\hline
   & \\ [-2.3  ex]
NN-type & feed-forward           \\
Number of hidden layers & 1      \\
Transfer function & {\it tansig} \\
Number of iterations & 1500      \\
Normalization range & [--1, 1]   \\
Weight range & [--100, 100]      \\
Bias range & [--10, 10]          \\
Minimun error & 1e--3            \\ [0.5 ex]
\hline
   & \\ [-2  ex]
 \multicolumn{2}{c}{PSO}  \\ [0.5 ex]
\hline
   & \\ [-2.3  ex]
Number of particles in swarm ($N_{\rm part}$) & 50\\
Number of iterations ($k_{\rm max}$) & 1500\\
Cognitive component ($c_{1}$) & 1.494\\
Social component ($c_{2}$) & 1.494\\
Maximum velocity ($v_{\rm max}$) & 12\\
Minimum inertia weight ($\omega_{\rm min}$) & 0.5\\
Maximum inertia weight ($\omega_{\rm max}$) & 0.7\\   %
Objective function & RMSE\\
\hline
\end{tabular}
\label{tab:input_ANN_PSO}
\end{table}
\end{center}
All the neurons of the ANN have an associated activation value for a give input pattern, and the algorithm continues finding the error that is presented for each neuron, except those of the input layer. After finding the output values, the weights of all layers of the network are actualized $w_{i,j}\rightarrow w'_{i,j}$ by PSO, using eqs. (\ref{eq2} and \ref{eq3})\cite{lazzus2010}. The velocity is used to control how much the position is updated. On each step, PSO compares each weight using the data set. The network with the highest fitness is considered the global best. The other weights are updated based on the global best network rather than on their personal error or fitness \cite{lazzusj2009}. In this article, we used the mean square error (MSE) to determine network fitness for the entire training set:
\begin{equation}
{\rm MSE}=\frac{\sum_{i=1}^{n}\left(Y_{i}^{\rm true}-Y_{i}^{\rm calc}\right)^{2}}{n}
\label{eq7}
\end{equation}
where $Y_{i}^{\rm true}$ is the real data and $Y_{i}^{\rm calc}$ is the calculated output value obtained from the normalized output ($y_{i}$) of the network. This process was repeated for the total number of patterns in the training set. For a successful process the objective of the algorithm is to modernize all the weights minimizing the total root mean squared error (RMSE):
\begin{equation}
{\rm RMSE}=\sqrt{\rm MSE}
\label{eq:rmse}
\end{equation}
\begin{equation}
\varepsilon=\min ({\rm RMSE}).
\label{eq9}
\end{equation}

In PSO, the inertial weight $\omega$, the constant $c_{1}$ and $c_{2}$, the number of particles $N_{\rm part}$ and the maximum speed of particle summary the parameters to synchronize for their application in a given problem.
Then, an exhaustive trial-and-error procedure was applied for tuning the PSO+ANN parameters. Firstly, the effect of population $N_{\rm part}$ is analyzed for values of 25 to 100 individuals in the swarm.
For other applications, some authors have shown that a larger swarm increases the number of function evaluations to converge to an error limit \cite{Ratnaweera2004}.
In addition, Shi and Eberhart \cite{Shi1998} illustrated that the population size has hardly any effect on the performance of a swarm algorithm. The top panel of Figure~\ref{fig:figure_convegency} shows that the best population to solve the problem is of 50 individuals.
Next, the effect of $\omega$ is analyzed for values of 0.1 to 0.9. The bottom panel of Figure~\ref{fig:figure_convegency} shows the values of $\omega$ that favoured the search of the particles and accelerated the convergence. This figure shows that for a linearly decreasing inertia weight starting at 0.7 and ending at 0.5, the PSO+ANN presents a good convergence. In other aspect, a usual choice for the acceleration coefficients $c_1$ and $c_2$ is $c_1$\,=\,$c_2$ \cite{Ratnaweera2004}. The effect of variation of constants was evaluated for the commonly used values of $c_1$ and $c_2$ such as 1.49, and 2.00 \cite{Ratnaweera2004,Shi1998}. For this analysis, $c_1$\,=\,$c_2$\,=\,1.49 presents a better convergence than other values.
Table~1 shows the selected parameters for this hybrid algorithm.

\begin{figure}[t!!!]
\begin{center}
\includegraphics[width= 7.9 cm]{Figure1}
\caption{Illustration of the behaviour of some parameters of the ANN+PSO against the number of iterations. The top and bottom panel correspond to the number of particles in the swarm ($N_{part}$) and the inertia weight ($\omega$), respectively.}
\label{fig:figure_convegency}
\end{center}
\end{figure}

The step-to-step approach of PSO+ANN can be summarized as:

\noindent \textbf{Step 1:} Initialize the positions (weights and biases) and velocities of a group of particles randomly. The particles represents the weight vectors of ANN, including biases. The dimension of the search space is therefore the total number of weights and biases.

\noindent \textbf{Step 2:} The ANN is trained using the initial particles position in PSO. The learning error produced from ANN network can be treated as particles fitness value according to initial weight and bias. The current best fitness achieved by particle $j$ is set as $\psi_{j}^{k}$. The $\psi_{j}^{k}$ with best value is set as $\psi_{g}$ and this value is stored.

\noindent \textbf{Step 3:} Evaluate the desired optimization fitness function (Eq. 7) over a given data set.

\noindent \textbf{Step 4:} Compare the evaluated fitness value of each particle ($F_j$) with its   value. If $F_j < \psi_{j}^{k}$  then $\psi_{j}^{k}=s_{j}^{k}$ is the coordinates corresponding to best particle so far.

\noindent \textbf{Step 5:} The objective function value is calculated for new positions of each particle. If a better position is achieved by an agent, $\psi_{j}^{k}$ value is replaced by the current value. As in Step 1, $\psi_{g}$ value is selected among $\psi_{j}^{k}$ values. If the new $\psi_{g}$ value is better than previous value, it is replaced by the current $\psi_{g}$ value and this value is stored. if $F_j < \psi_{g}$ then $\psi_{g}=s_{j}^{k}$ is the particle having the overall best fitness over all particles in the swarm.

\noindent \textbf{Step 6:} The learning error at current epoch will be reduced by changing the particles position, which will update the weight and bias of the network. Change the velocity and location of the particle according to movement equations (Eqs. 1 and 2). The new sets of positions (weights and biases) are produced by adding the calculated velocity value to the current position value. Then, the new sets of positions are used to produce new learning error in ANN.

\noindent \textbf{Step 7:} This process is repeated until the stopping conditions either minimum learning error or maximum number of iteration are met, then stop; otherwise Loop to Step 3 until convergence.

\noindent \textbf{Step 8:} The optimum weight and biases for ANN model are obtained by PSO. Best training process is obtained for ANN.

In our time series analysis, if the input noise level contribution is available, the RMSE in the training phase shall be computed as follow:
\begin{equation}
{\rm RMSE}= \sqrt{ \frac{1}{n}\sum_{i=1}^{n} \frac{\left(Y^{\rm cal}_{i} - Y^{\rm true}_{i} \right)^2}{\sigma_{N,i}^2}}
\label{eq:rmse_std}
\end{equation}
where $\sigma_{N,i}$ is the noise level of each $i$--element. Note that $\sigma_{N,i} = \sigma_{N}$ for a white noise assumption.

Henceforth, we refer as {\it the standard ANN+PSO} to the hybrid ANN+PSO defined above.

\subsection{The {\it Stochastic} {\sc ANN+PSO}}
\label{sec:ANN+PSO_stochastic}
Up to now, the standard ANN+PSO is not developed to carry out the error propagation of the input noise level contribution.
Nevertheless, once the {\it standard} {\sc ANN+PSO} has been executed and has provided the optimal topology, we can apply an additional method in order to compute uncertainty of the prediction.

Note that once the topology is established (number of hidden layer, neurons in each hidden layer, transfer functions $f^{h}$, and weights and biases ($w^h_{i,j}$ and $b^h_{i,j}$)), the neural network acts as a function (called {\it function ANN}) whose output only depends on the input vector (see, Eq. 4).
The idea is to generate simulations from the input data ($d_i\equiv d(t)$) via Gaussian random number generator in order to propagate the intrinsic data noise through the {\it function ANN}.

For each $i$--element of the input time series we generate $k$--simulations as:
\begin{equation}
d_{i,k} = d_i + GR_k(\sigma_{N,i})
\label{eq:sim_d}
\end{equation}
\noindent where the input noise level $\sigma_{N,i}$ is known. $GR(\sigma_{N,i})$ is a random number generator following a Gaussian distribution with mean zero and standard deviation equal to $\sigma_{N,i}^2$.

Finally, and for the $i$-th element, each $k$ input data $d_{i,k}$ provides an output $y_{i,k}$. These $y_{i,k}$ are used in the estimation of a new estimator of prediction ($\hat{y}_i$) and an error on the prediction ($\sigma_{\hat{y}}$) as follows:
\begin{equation}
\hat{y}_i = <y_{i,k}> \ \ {\rm and} \ \ \sigma_{\hat{y}}= <y_{i,k}^2>^{1/2}.
\end{equation}

\section{Noiseless chaotic time series prediction}
\label{sec:noiseless}
We computed the chaotic time series from the Mackey--Glass time-delay differential system \cite{mackey1977,farmer1982}, which is described as follow:
\begin{equation}
\frac{dx}{dt}=\beta x(t)+\frac{\alpha x(t-\tau)}{1+x(t-\tau)^{10}}
\label{eq10}
\end{equation}
\noindent where $x$ (unitless) is the series in the time $t$, and $\tau$ the time delay.
Here, we assumed $\alpha=0.2$, $\beta=0.1$ and $x(0)=1.2$. Note that, if $\tau\geq$17 the time series shows a chaotic behaviour \cite{mirzaee2009,farmer1982}. The nominal Mackey--Glass time series is obtained from numerical integration by a fourth order Runge--Kutta method. This series was computed with a time sampling of 1 second. Thus, $x(t)$ is derived for $0\leq t \leq t_{\rm h}$ with $x(t)=0$ for $t<0$, where $t_{\rm h}$ is the time horizon considered.

Mackey--Glass chaotic time series with $\tau=$\,17 is considered as the nominal case $x^{\rm Noiseless}$ (without noise contribution). Here, we generate two thousand data points ($t_{\rm h}=2000$).

From this data set, the input is created as a vector using $d$ points of the time series spaced $\Delta$ apart, i.e., ${\bf x}(t)=\left[x(t), x(t+\Delta),\cdots, x(t+(d-1)\Delta)\right]$. The output is generated with the value $x(t+T)$.

According to the standard analysis of the Mackey--Glass chaotic time series, we consider four non consecutive points in the chaotic time series in order to predict the short-term $x(t+6)$:
\begin{equation}
x(t+6)=F\left[x(t), x(t-6), x(t-12), x(t-18)\right]
\end{equation}
where this standard test assumes $d=4$ and $\Delta=T=6$ \cite{chng1996,mirzaee2009}.

\begin{figure}[h!!!]
\begin{center}
\includegraphics[trim= 0cm 1.cm 0cm 0.5cm,clip=true,width= 6.9 cm]{Figure2_top}
\includegraphics[trim= 0cm 1.cm 0cm 0.5cm,clip=true,width= 6.9 cm]{Figure2_bottom}
\caption{Performance of ANN+PSO method on the Mackey--Glass chaotic time series (noiseless). The top and bottom panel show the {\it training} and {\it prediction} performance for the short-term $x(t+6)$ analysis, respectively. The grey and blue lines correspond to the input ($x_{\rm in}$) and output ($x_{\rm out}$) data. The red line with diamond draws the difference between the input and output data (in a factor of $10^{-2}$).}
\label{fig:figure1}
\end{center}
\end{figure}

For this input, the first thousand data were used for learning ({\it training}) while the others were used for the prediction validation ({\it prediction}).
In the ANN+PSO implementation on the nominal case, the optimum value of $N_{\rm HL}$ found was six, i. e., the architecture is described as 4-6-1.

Figure~\ref{fig:figure1} present a comparison between recorded and predicted values of the Mackey--Glass time series for the training and prediction phases. This figure shows that for training and validation phases, the nominal and reconstructed values are in total agreement.
In fact, and for training, we computed a remainder average, $<x_{\rm in} - x_{\rm out}>$, of $-1.4\times10^{-3}$ and a remainder maximum, max$\{|x_{\rm in} - x_{\rm out}|\}$, of $3.20\times10^{-2}$. Similar results are obtained for the prediction phase; with a maximum of $3.22\times10^{-2}$ and an average of $-1.5\times10^{-3}$.

\begin{center}
\begin{table}[t!!!!]
\caption{Root mean squared error (RMSE) reported for different methods in the Mackey--Glass chaotic time series analysis.}
\centering
\begin{tabular}{l c}
\hline
 Method & RMSE$_{x(t+6)}$ \\
\hline
\multicolumn{2}{c}{}  \\ [-2.0 ex]
Linear model \cite{lazzus2014}& 0.5503  \\
Conjugate gradient ANN \cite{Zhao2014} & 0.2296 \\
Product operator T-norm \cite{Wang1992} & 0.0907 \\
Fuzzy system \cite{Lee1994} & 0.0816 \\
Cascade correlation NN \cite{Chen2005}& 0.0624 \\
Genetic algorithm and fuzzy system \cite{Kim1997} & 0.0490 \\
Backpropagation NN \cite{lazzus2014} & 0.0262 \\
Linguistic Model (20 rules ) \cite{Qin2014}& 0.0256 \\
K-Nearest Neighbor \cite{Yen2006} & 0.0194 \\
This work & 0.0138  \\
\hline
\end{tabular}
\label{tab:noiseless_rmse}
\end{table}
\end{center}

Table~\ref{tab:noiseless_rmse} shows the RMSE (for short term prediction of  Mackey--Glass chaotic time series) from different computational methods obtained from literature, for example, the Back-propagation NN \cite{lazzus2014}, the conjugate gradient ANN \cite{Zhao2014}, the product operator T-norm \cite{Wang1992}, the fuzzy system \cite{Lee1994}, etc (see references in Table~\ref{tab:noiseless_rmse}).
In the ANN+PSO configuration used here, the RMSE\,=\,0.014 indicates that the performance prediction is in good agreement with other methods. Clearly, the inclusion of the PSO approach allows us to improve methods based on ANN without PSO as, for example, the conjugate gradient ANN (RMSE\,=\,0.229) and the back--propagation NN (RMSE\,=\,0.026).

\subsection{Chaotic behaviour}
As the Mackey--Glass time series without noise, it is a known system, is possible to compare the ability of ANN+PSO method of reproducing its chaotic behavior. Figure \ref{fig:figure3} shows a representation of the chaotic attractor studied from Mackey--Glass time series. This Figure shows that with $\tau=17$ the system operates in a high-dimensional regime. The Mackey--Glass system is infinite dimensional (because it is a time-delay equation) and, thus, has an infinite number of Lyapunov exponents ($\lambda_{i}$) \cite{farmer1982}. The Lyapunov exponents of dynamical systems are one of a number of invariants that characterize the attractors of the system in a fundamental way \cite{brown1997}. Table~3 shows a comparison of the first four largest Lyapunov exponents of the Mackey--Glass system reported in \cite{farmer1982}, with the Lyapunov exponents obtained for the ANN+PSO method for $\tau=$17.

\begin{figure}[t!!!!!!!]
\begin{center}
\includegraphics[width= 6.9 cm]{Figure3}
\caption{Chaotic attractor for the Mackey--Glass noiseless chaotic time series ($\tau=17$).}
\label{fig:figure3}
\end{center}
\end{figure}

\begin{center}
\begin{table}[t!!!!]
\caption{Lyapunov exponents reported in Farmer~\cite{farmer1982} versus calculated for the ANN+PSO method.}
\centering
\begin{tabular}{c c}
\hline
\multicolumn{2}{c}{}  \\ [-2.0 ex]
$\lambda_{i}$  & \multicolumn{1}{c}{$\lambda_{i, {\rm ANN+PSO}}$}\\ [0.5 ex]
\hline
0.00860 & 0.00900    \\
0.00100 & 0.00132    \\
--0.03950 & --0.04100\\
--0.05050 & --0.05000\\
\hline
\end{tabular}
\label{tab:par_lyapunov}
\end{table}
\end{center}

An approach to determining an appropriate cutoff value for the number of exponents can be related to the Lyapunov dimension \cite{brown1997}. This idea was originally explored by Kaplan and York \cite{kaplan1979}. Thus, Kaplan and York conjecture that this dimension ($D_{\rm KY}$) is equal to the information dimension \cite{kostelich1989}. In our case $D_{\rm KY}$ is compute as 2.10. Note that in Farmer~\cite{farmer1982}, authors reported a fractal dimension $D_{\rm F}$\,=\,2.13, and a Lyapunov dimension calculated by the Kaplan and York conjecture of $D_{\rm KY}$\,=\,2.10.

\section{Noisy chaotic time series prediction}
\label{sec:noisy}
In the previous section, the ANN+PSO has proven to be an efficient method to the prediction of chaotic time series. Nevertheless, up to now effects of noise on the hybrid ANN+PSO implementation have not been studied.

In order to study the impact of noise on chaotic series time prediction, we constructed the noisy time series as the contribution of a noise level on the nominal case without noise.
The Mackey--Glass noisy chaotic time series, $x_{i} \equiv x(t)$, is generated as:
\begin{equation}
x_{\rm i} = x^{\rm Noiseless}_{\rm i} + \eta_{\rm i}
\label{eq:sim_dat_mg}
\end{equation}
\noindent where $\eta_{\rm i}$ is the particular contribution of noise on the $i$--element. It is estimated as $\eta_{\rm i} = GR(\sigma_{N,i})$, with $GR(\sigma_{N,i})$ a Gaussian random number generator.

Note that $\sigma_{N,i}^2$ corresponds to the noise level considered.
Here, we assume that the original data are effected by a white noise, i. e., the noise level is the same in each $i$--element, $\sigma_{N,i} = \sigma_{N}$~\footnote{In order to clarify, although the noise level $\sigma_{N}$ is the same in each time the noise contribution $\eta_{i}$ is not the same (the latter depend on the Gaussian random number generator).}.
Different white noise levels are considered: $\sigma_{N}=0.01$, $\sigma_{N}=0.04$, $\sigma_{N}=0.06$, $\sigma_{N}=0.08$ and $\sigma_{N}=0.1$.
These values are nearly related with the 1\,\%, 4\,\%, 6\,\%, 9\,\% and 11\,\% of the pick--to--pick amplitude  of nominal case ($ \sim \ x^{Noiseless}_{\rm max} - x^{Noiseless}_{\rm min}$). Figure~\ref{fig:MG_noisydata} shows the noisy chaotic time series for $\sigma_{N}$ equal to 0.01 (green), 0.04 (blue) and 0.1 (red). As expected, the noisy time series with $\sigma_{N}=$\,0.01 is the closest to the nominal case. However, the cases with $\sigma_{N}=$\,0.04 and $\sigma_{N}=$\,0.1 show a slightly more modified shape from the noiseless case, in particular with $\sigma_{N}=$\,0.1.

\begin{figure}[t!!!!!]
\begin{center}
\includegraphics[trim= 1cm 0.1cm 0cm 0.cm,clip=true,width= 8.0 cm]{Figure4}
\caption{Mackey--Glass chaotic time series considered in this work ($\tau=$\,17). The black solid line shows the noiseless case (nominal case). The green, blue and red lines correspond to the Mackey--Glass noisy time series with a white noise level ($\sigma_{N}$) contribution of 0.01, 0.04 and 0.1, respectively.}
\label{fig:MG_noisydata}
\end{center}
\end{figure}

\subsection{Noise effect on ANN+PSO}
\label{sec:noisy_impact}
The {\it standard} {\sc ANN+PSO} is applied on our noisy time series, which provides the optimum topology and the $y_i$ prediction.
Then, the {\it stochastic} {\sc ANN+PSO} is run in order to obtain a new prediction estimator $\hat{y}_i$ and the uncertainty of the prediction ($\sigma_{\hat{y}_i}$).

\begin{figure}[t!!!!!]
\begin{center}
\includegraphics[width= 8.3 cm]{Figure5}
\caption{Impact of the noise on the architecture.}
\label{fig:MG_output_rmse_vs_nn}
\end{center}
\end{figure}

{\it Impact on architecture.} For each noisy time series, and in the {\it standard} {ANN+PSO} implementation, we carry out a detailed study of the architecture characterization.
In the determination of the optimum $N_{\rm HL}$, the RMSE is computed for different number of neurons in the hidden layer (from two up to thirty), which are presented in Figure~\ref{fig:MG_output_rmse_vs_nn}.
For each series, the optimum $N_{\rm HL}$ is obtained when the RMSE reachs a minimum.
As expected, the characterization of the architecture is strongly related  with the noise level in the input data.
In lower noise (as 0.01) the optimum $N_{\rm HL}$ is clearly identified from Figure~\ref{fig:MG_output_rmse_vs_nn}; in contrast, in the most contaminated case ($\sigma_{N}$\,=\,0.1) the selection depends on fourth decimal of the RMSE (0.1292, 0.1291 and 0.1293 for 19, 20 and 21 neurons in the hidden layer, respectively).
The RMSE and the $N_{\rm HL}$ optimum are presented in Table~4.
Using these values, and according to the trend seen in Figure~\ref{fig:MG_output_rmse_vs_nn}, we fit a lineal model, which provides a correlation with a slope of 0.0085.
Although the $N_{\rm HL}$ for $\sigma_{N}$\,=\,0.08 is not well characterized for this model, we can find a clear lineal correlation between the RMSE and the $N_{\rm HL}$ for different noise levels.
In this context, and as illustration, in the overplot  (in top-right side of Figure~\ref{fig:MG_output_rmse_vs_nn}) we show the relation of the $N_{\rm HL}$ and the noise level, whose the best lineal fit model is $N_{\rm HL}$\,=\,146\,$\sigma_{N}$+\,4.7.
Therefore the impact of noise on the architecture of this hybrid neural network, for contributions lower than 0.1, can be characterized by a lineal correlations of the RMSE with the $N_{\rm HL}$, and the $N_{\rm HL}$ with the input noise $\sigma_{N}$.
\begin{center}
\begin{table}[t!!!!]
\caption{Parameters used in the evaluation of the prediction performance of the {\it Standard} and {\it Stochastic} {\sc ANN+PSO} approach.}
\centering
\begin{tabular}{l c c c}
\hline
 & $N_{\rm HL}$ & RMSE & $\xi$ \\
\hline
Noiseless          & 6& 0.0138&  1  \\
$\sigma_{N}=0.01$  & 6& 0.016 &1.2\\
$\sigma_{N}=0.04$  & 11& 0.054&3.9\\
$\sigma_{N}=0.06$  & 14& 0.078&5.7\\
$\sigma_{N}=0.08$  & 15& 0.103&7.5\\
$\sigma_{N}=0.1$   & 20& 0.129 &9.4\\
\hline
\end{tabular}
\label{tab:rmse_results}
\end{table}
\end{center}
\begin{figure}[t!!!!!]
\begin{center}
\includegraphics[trim= 0cm 1.2cm 0cm 0.5cm,clip=true,width= 7.8 cm]{Figure6}
\caption{Predictions of Mackey--Glass noisy chaotic time series with a white noise contribution of $\sigma_N=0.1$. The grey solid line correspond to the original Mackey--Glass noisy chaotic time series.
The red and blue lines identified the results from {\it standard} {\sc ANN+PSO} and {\it stochastic} {\sc ANN+PSO}, respectively.
The upper panel draw the $y_{i}$ and $\hat{y}_{i}$ predictions, and the lower panel the residual contribution ($x_{\rm in} - x_{\rm out}$) of both methods.
}
\label{fig:MG_output_0.1_prediction}
\end{center}
\end{figure}
\begin{figure}[t!!!!!]
\begin{center}
\includegraphics[width= 7.5 cm]{Figure7}
\caption{Impact of the noise on the performance prediction.}
\label{fig:MG_output_rmse_vs_sigma}
\end{center}
\end{figure}

{\it The prediction performance.}
As illustration, the predictions obtained for noisy case $\sigma_{N}=0.1$, from the {\it standard} {\sc ANN+PSO} ($y_i$) and the {\it stochastic} {\sc ANN+PSO} ($\hat{y}_i$) procedures, are presented in Figure~\ref{fig:MG_output_0.1_prediction}.
As expected, even on this high noise level case, the $y_{i}$ and $\hat{y}_{i}$ predictions are in total agreement.
Actually, the RMSE obtained from both methods is same (in the approximation of the third decimal) for each noisy case. For this reason, the RMSE shown in Table~4 represent the RMSE of both methods.

On the other hand, and as expected, the RMSE increases as growing the noise level (see Figure~\ref{fig:MG_output_rmse_vs_sigma}).
For example, we obtained RMSE of 0.0138 and 0.13 for the noiseless and noisy (with $\sigma_{N}$\,=\,0.1) cases, respectively.
From Figure~\ref{fig:MG_output_rmse_vs_sigma}, we observe a linear correlation between the RMSE and the input noise level. The best fit model, without considering the RMSE of the noiseless case, corresponds to RMSE\,$=\,1.3\,\sigma_{N}$, which shows a strong lineal correlation.
Therefore, we confirm that a higher noise level in input data leads to a poor estimation of the prediction estimator, which is related linearly with the input noise level.

Also, the ratio $\xi=$\,RMSE$_{\rm noisy}$/RMSE$_{\rm noiseless}$ (third column in Table~\ref{tab:rmse_results}) can be used to study the impact of noise on the performance efficiency of our implementation (with respect to nominal case).
The bottom-right panel of Figure~\ref{fig:MG_output_rmse_vs_sigma} shows the performance efficiency  against the input noise level.
In the worst case, the performance efficiency ($\xi$) is strongly affected by  one order of magnitude with respect to noiseless case. Even so, the {\it standard} and {\it stochastic} ANN+PSO confirm to be a powerful tools for making predictions of chaotic time series.

In the literature, we do not find a similar implementation (due to the ahead prediction, type and level of noise, etc.) that allows us a straightforward comparison of results.
For example, we can contrast our results with those presented by Sheng et al. 2012 \cite{sheng2012}. They applied the Echo State Network based on dual estimation ({\sc ESN}) on a noisy Mackey--Glass time series (with a sampling of 2 second) with a white noise level of $\sigma=0.1$.
However, the ahead prediction was one, which is considerable lower than ours.
Yet let us carry out a plain comparison.
Depend on the prediction performance, they obtained RMSE of 0.05 for {\sc Generic ESN} (hereafter {\sc GESN}) and 0.04 for {\sc CKF/KF based ESN} (henceforth {\sc CESN}).
In this context, the impact of the noise on the performance efficiency is lower in ANN+PSO implementation (with respect to the ESN).
In fact, we have a performance efficiency $\xi$ of 9.4 while they obtained $\xi$ of 1161 and 33.5 for {\sc GESN} and {\sc CESN}, respectively.

\begin{figure}[t!!!!!]
\begin{center}
\includegraphics[trim= 0cm 1.2cm 0cm 0.cm,clip=true,width= 7.9 cm]{Figure8}
\caption{Predictions and uncertainties from the {\it stochastic} {\sc ANN+PSO} for the Mackey--Glass chaotic time series. This corresponds to case with a white noise of $\sigma_N=0.1$. The grey solid line draws the original Mackey--Glass noisy chaotic time series. The blue points with error bars correspond to the $\hat{y}_{i}$ prediction and their uncertainties $\sigma_{\hat{y}}$. For optimal display of the uncertainties, these are presented in the low panel.}
\label{fig:MG_output_0.1}
\end{center}
\end{figure}
{\it Prediction uncertainties.}
One of a main goals of this work is to estimate the uncertainty on the prediction.  The prediction measurement ($\hat{y}_i$) and the error bars ($\sigma_{\hat{y}_i}$) obtained from the {\it stochastic} {\sc ANN+PSO}, for the noisy time series with $\sigma_{N}=0.1$, are presented in Figure~\ref{fig:MG_output_0.1}.
We confirm that our forecast and the input data, for the strong noise contribution, are in agreement at one-sigma (at 68.5\% of confidential level) when the error bars are considered.
The uncertainties obtained are presented in the low panel of Figure~\ref{fig:MG_output_0.1}.
We found a maximum and minimum uncertainty of 0.024 and 0.13, respectively, with a average of $<\sigma_{\hat{y}_i}>=0.07$.
This value is lower than the input noise level ($ <\sigma_{\hat{y}_i}> / \sigma_{N}= 0.7$), and this show impact of the error propagation in our methods.
According to Figure~\ref{fig:MG_output_0.1}, a relationship between the uncertainties and the times is not appreciated.

Finally, and from Figures~\ref{fig:MG_output_0.1_prediction}~and~\ref{fig:MG_output_0.1}, we have proven that the ANN+PSO (with the {\it standard} and/or the {\it stochastic} implementation) is a robust tool in the predictability (for the short-term prediction) of time series affected by a white noise.
In addition, now the ANN+PSO method can provide, for first time, an estimation of the uncertainty of the prediction.

\section{Conclusions}
\label{sec:conclusion}
In this paper, a hybrid algorithm based on artificial neural network and particle swarm optimization (ANN+PSO) is used in the short-term $x(t+6)$ prediction of Mackey--Glass chaotic time series.
In addition, an study of the impact of the noise on our hybrid method is presented.
Based on the results and discussion presented in this study, we have the following conclusions:

\noindent$\bullet$ The current value $x(t)$ and the past values used have influential effects on the good training and predicting capabilities of the chosen network.

\noindent$\bullet$ In noiseless case, simulation shows that this hybrid ANN+PSO algorithm is a very powerful tool for making prediction of chaotic time series, and the low deviations found with the proposed method show an accuracy comparable with other methods available in the literature.

\noindent$\bullet$ In noisy cases, we have proven that the hybrid {\sc ANN+PSO} is a robust tool in the predictability of the short-term prediction of chaotic time series affected by a white noise.

\noindent$\bullet$ The impact of the noise on the topology and performance efficient of the ANN+PSO is important.
However, this study shows that the error propagation through the ANN+PSO have a linear behaviour, which generates a linear relationship between the RMSE (optimization parameter) and the input noise level. Therefore, the PSO optimization provides a linearity which ensures that the neural network will converge to an appropriate solution, even if a noise level contribution is present.

\noindent$\bullet$ For noisy cases, although a straightforward comparison with literature is unavailable. The performance efficient $\xi$ proves that the {\it standard}/{\it stochastic} ANN+PSO implementation is affected in a lesser degree than other similar performance.

\section*{Conflict of Interests}
The authors declare that there is no conflict of interests
regarding the publication of this paper.

\section*{Acknowlegments}
The authors thank support from the Research Directorship of the University of La Serena (DIULS).

redpajama_set_name: RedPajamaArXiv


This review gives a broad overview of the types of chemical hazards that can occur in foodstuffs, indicating how they arise and how they are measured and controlled. The examples given are representative of the many types of issues that the food industry has to face on a daily basis.
Further information on individual chemicals can be found in Campden BRI Review 52 – Understanding chemical hazards in support of risk assessment. Also, advice on the risk assessment of raw materials will be published in March 2011 in Campden BRI Guideline 65 – Risk assessment and management of raw materials. Meanwhile, analysis is covered in the Campden BRI Key Topic No. 10 Chemical analysis of foods: an introduction. A summary of chemistry and quality management services available to the food industry can be found on the Campden BRI website.
Campden BRI has published several short reviews on different practical aspects of interest to the food industry.
It has been said that 99% of all toxins are naturally occurring, and also that all things are toxic at a high enough concentration. Certainly, many food raw materials contain chemicals, which, if consumed in excess, might lead to health problems. Cooking and processing in general can remove or inactivate many chemicals (e.g. protease inhibitors, lectins) that are either directly toxic or inhibit digestion or absorption of nutrients. However, some chemicals have arisen as problems associated with food processing techniques developed in the last 100 years or so, e.g. trans fatty acids resulting from chemical hydrogenation of unsaturated fats, or 3– monochloropropanediol from the chemical hydrolysis of proteins. One recently publicised example of a processderived chemical hazard in food is the formation of acrylamide in baked products. Although this has been occurring for centuries (e.g. in home baking of bread, potatoes and other starch–based foods), it was not discovered until 2002. A further area of concern is the migration of chemicals from packaging materials into foods, which has recently become a large problem for food manufacturers.


text:
Supreme Court leaves consumer regulator standing but backs president's ability to fire director
The Supreme Court in a ruling Monday allowed the Consumer Financial Protection Bureau to continue operating, but said that the director of the watchdog can be removed by the president of the United States "at will." The decision, written by Chief Justice John Roberts, agreed with a California-based law firm's argument that the CFPB's leadership by a sole director who was removable "only for cause" violated the separation of powers rule under the U.S. Constitution...
Current Events|

redpajama_set_name: RedPajamaCommonCrawl


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Now that the whole world knows who is the new successor of St. Peter, there will be a rush to find out more about this man, where his priorities lie, the nature of his theological and political views, etc. As such, I have compiled the following links to biographies and analysis of Jorge Bergoglio, Pope Francis I.
I will update this post regularly as new material appears online. If you know of any that I should add to the list, please leave a comment.
UPDATE (3/17/2013): I have decided to organize these articles by when they were written so that the reader can see how the commentary on Pope Francis has developed over time. Also, please note that while this compilation is extensive, it is by no means exhaustive. I am sure that there are some great articles that I have missed. Thirdly, I will only be chronicling the first week of his papacy. It would be too much of a burden to keep this up after that. Finally, the inclusion of an article to this list does not necessarily indicate an endorsement on my part.
The Cardinals of the Holy Roman Church: Biographical Dictionary, "BERGOGLIO, S.J., Jorge Mario"
Andrea Tornielli, Vatican Insider: "Careerism and vanity: Sins of the Church"
Vatican Radio: Who Is Pope Francis?
Terry Mattingly, Get Religion: Yes! Pope Francis is not from Europe!
Matthew Archbold, National Catholic Register: Gay Groups Rush to Label New Pope "Hateful" and "Harsh"
Amy Welborn, Charlotte Was Both: Who Is Pope Francis?
Dr. Taylor Marshall, Canterbury Tales: Traditionalists and Pope Francis: Can We Take a Deep Breath and Please Calm Down?
Fr. Dwight Longenecker, Standing on My Head: Why Did Pope Francis Go to St. Mary Major?
Francis Phillips, Catholic Herald: Pope Francis - what's in a name?
Simcha Fisher, National Catholic Register: Papamoon!
Rocco Palmo, Whispers in the Loggia: On Day One, Pope Rides the Bus and Pays the Bills | Francis' Agenda: "To Walk, To Build, To Profess Christ Crucified"
Jeff Miller, The Curt Jester: Liturgical Doomsday! | What's in a name?
Terry Mattingly, Get Religion: Flooding the papal coverage zone | Pope Francis and the "Hand of God"
Fr. C. John McCloskey, National Catholic Register: Orphans No More!
Emily Stimpson, Catholic Vote: Pope Francis and St. Francis: "Preach the Gospel Always. And for the Love of God, Use Words."
Taylor Marshall, Canterbury Tales: Pope Francis: Devotion to Mary and the "New Evangelization"
Patrick J. Reilly, Catholic Education Daily: Can Pope Francis renew Jesuit education?
Edward Pentin, National Catholic Register: Pope: "How I Wish for a Church That is Poor and For The Poor!"
Jeff Miller, The Curt Jester: What's in a nickname?
Fr. Dwight Longenecker, Standing on My Head: Is Pope Francis a Liturgical Liberal?
Rocco Palmo, Whispers in the Loggia: From the Window, "God Never Gets Tired of Forgiving!"
Kevin Tierney, Common Sense Catholicism: Why do Traditionalists Care So Much About the Latin Mass?
Jeannie DeAngelis, American Thinker: Did Hugo Chávez Pick the New Pope?
Selwyn Duke, American Thinker: Is Pope Francis Liberal or Conservative?
Jimmy Akin, National Catholic Register: Should We Be Concerned About Pope Francis' Inaugural Mass?
Stephen White, Catholic Vote: Pope Francis: Protect Creation, It Points to God!
Taylor Marshall, Canterbury Tales: Pope Francis: Reviving the Gospel Reading in Greek?
Michael Barber, The Sacred Page: A Catholic Meme I'm Not Thrilled About. Don't Forget, Benedict Emphasized "Charity"
Deacon Greg Kandra, The Deacon's Bench: Pope greets Jesuit superior general: "He insisted I treat him like any other Jesuit"
Damian Thompson, The Telegraph: Pope Francis inaugural Mass: can this extraordinary man save the Catholic Church?
Mollie Hemingway, Get Religion: Was Pope Francis 'anointed' today?
I will update each day with new links as I find the time. This is still a work in progress.
UPDATE (4/3/2013): If I happen to come across one, I'll add it, but I don't plan on actively seeking any more links to add to this collection. Of course, if you know of one that I should add, you are free to leave a comment and I will add it (unless I don't like it for some reason).
Russel responded to my previous post. As before, his words will be indented and italicized.
You asked if the followers of John the Baptist were wrong in calling him (i.e., John) "Rabbi / Teacher." I would have to say yes they were, according to Jesus, but they probably did this in ignorance, since Jesus addressed this topic AFTER John the Baptist's death (Matthew 14:1-12).
Concerning the title "King," this is not a SPIRITUAL title, which is what Jesus was addressing in Matthew 23.
That is partly true, but Jesus didn't say, "Call only those with the RIGHT ATTITUDE "Father," or only those who DESERVE it "Rabbi." He said to give those spiritual titles to NO HUMAN (Matthew 23:8-10).
Russell ... thank you for your response. Your debate style is much like mine, calm and thorough. I appreciate that.
Regarding your first point, I think that if it was wrong of them to address John the way they did, then John himself would have objected to it. He is after all the model of humility. "His sandals I am not worthy to carry" (Mt 3:11) or "to stoop down and untie" (Mk 1:7). "He must increase, I must decrease" (Jn 3:30).
I guess you'll say that John was ignorant of Jesus' teaching as well. While I find it hard to believe that John would not have intuited the wrongness of these titles if indeed they were wrong, since neither of us can really know the mind of the baptist on this point, let us consider this particular argument a draw.
Regarding your second point, I think the title of "King" -- at least as it applies to the Davidic kings -- is very much a spiritual title. The Davidic king was God's anointed steward of His people, and the mediator of God's covenant relationship with them. The new Davidic king was the great hope of all of Israel. So, perhaps the references to Herod, Agrippa, and Aretas don't apply, but the ones to Saul, David, Solomon, and Adonijah do.
Regarding your final point, you say that we are to give spiritual titles to "NO HUMAN". I really think you're missing the point. Read everything in Mt 23 that is before and after the passage in question. "The scribes and the Pharisees sit on Moses' seat; so practice and observe whatever they tell you" (vs. 2-3). Jesus' wants the people to continue to respect the authority of the scribes and Pharisees. Using titles such as "father", "rabbi", and "master" is how you show this respect for someone in a position of authority. Yet, by your interpretation, Jesus told the people to respect their authority one minute, then disrespect it the next. That makes no sense.
Jesus issues 7 woes against them in this chapter for being the "hypocrites" and "blind guides" that they are. You have to understand vs. 8-10 in light of this context. Jesus' whole point is that the scribes and Pharisees exhibit a dastardly conduct that should not be imitated and they do not live up to the honor that they receive. God alone is the great and perfect Father, Rabbi, and Master. We can only fulfill these positions in a derivative sense.
Finally, think about it, Jesus is pissed off and fed up. He is angry, filled with righteous indignation. It makes perfect sense that He would use hyperbolic language. "You have ONE teacher" (vs. 8), "you have ONE father" (vs. 9), "you have ONE master" (vs. 10) ... yet obviously we have all had more teachers and fathers and masters than simply God. Thus, Jesus is NOT speaking literally, He is using exaggerated language. Verse 24 from this same chapter ("You blind guides, straining out a gnat and swallowing a camel!") is obviously hyperbolic. Verses 8-10 are said in the same vein.
Like I said before, the Catholic interpretation is the only one that squares with the context of the passage and the greater body of Scripture. I humbly submit that your bias against Catholicism is causing you to misinterpret this passage. If you will simply put that aside, even just for a moment, I think you will see that what I am saying about this passage is true.
PS: From here you may proceed to Part Three.
Scripture says very little about Mary, the mother of Jesus, compared to the other great figures in the formative years of the Church, yet Catholics believe that she is the greatest woman who ever lived. Let's take a closer look at the Scriptural evidence and see if perhaps more is said about Mary than what first meets the eye.
There are five doctrines about Mary. The first one proclaims that Mary is the Mother of God. The logic here is simple: If Mary is the mother of Jesus and Jesus is God, then Mary is the Mother of God. In giving Mary this title, the Church follows in the example of Elizabeth, who exclaimed upon seeing Mary, "And why is this granted to me that the mother of my Lord should come to me?" (Lk 1:43).
Note that this doctrine says more about Jesus than it does about Mary. If Jesus is not God, then Mary is not the Mother of God. By affirming this doctrine, the Church affirms the divinity of Jesus. At the Council of Ephesus in 431 AD, the Church officially referred to Mary as the theotokos (Gk. "God-bearer"), not to exalt Mary but to combat the heresies of the day that denied that Jesus was truly God.
To really grasp the full depth of meaning in this passage, we have to look at the original Greek language in which it was written. The Greek word translated as "full of grace" is kecharitomene. This is a difficult word to translate. For one, in the entire New Testament and the entire Greek Old Testament, it only appears once: right here in Luke 1:28. Clearly, something extremely unique is being described here.
Secondly, the construction of the word is peculiar. Without getting too bogged down by Greek grammar, looking closely at the voice and the verb tense of kecharitomene, one finds that this word literally means, "You who were and continue to be full of and completed in grace." Blass and DeBrunner's Greek Grammar of the New Testament states: "It is permissible, on Greek grammatical and linguistic grounds, to paraphrase kecharitomene as completely, perfectly, enduringly endowed with grace."
How remarkable! Mary wasn't just given grace like we receive grace. She was filled with grace, completed in grace, perfected in grace, and this fullness of grace persisted, it continued up to and through the present. Sin and grace are opposed (cf. Rom 5:20-21), and grace saves us from sin (cf. Eph 2:5, 8). Where there is fullness of grace there is no room for sin.
These were the holiest of all Jewish relics and represented the very presence of God to the Jewish people. As such, the container or "ark" that held them had to be made of the purest, most perfect materials. The Ark itself was considered so holy that no one was allowed to even touch it, lest they die (cf. 2 Sam 6:7; 1 Chron 13:9-10).
We see in Scripture that there are many parallels between Mary and the Ark (compare Lk 1:35, 39, 41, 43, 56 with Exo 40:35 and 2 Sam 6:2, 9, 11, 16) but space permits us to only address one. We already know what the Ark was built to contain. What was Mary built to contain, but Jesus Christ? And Who is He but the new Word of God (cf. Jn 1:1), the Manna from Heaven (cf. Jn 6:51), and the great High Priest (cf. Heb 5:4-5)?
Catholics believe that Mary remained a virgin her entire life. This may seem odd at first, considering that there are many Scripture passages that refer to the "brothers" of Jesus (cf. Mt 12:46; 13:55-56; Mk 3:31; Lk 8:19; Jn 7:1-10; Acts 1:14; Gal 1:19). It is not necessary, however, to believe that these "brothers" were actually His siblings.
Considering the broad meaning of the word, we can just as easily say that these "brothers" of Jesus were related to Him in some other way. Scripture tells us that at least four of them – James, Joseph, Simon, and Judas – were actually Jesus' cousins, since their mother was Mary's sister (cf. Mt 27:56, 61; 28:1; Mk 15:47; Jn 19:25).
Also, note that it was Jewish custom for the eldest son to care for his mother once his father died. When the eldest son died, this responsibility fell on the next son, and so on. Yet, Jesus gave His mother to the Apostle John, not to any of His "brothers" (cf. Jn 19:26-27).
It appears from these peculiar details that Jesus was in fact the only son of Joseph and Mary. And, since the Jews considered it a serious sin to prevent the marital act from bearing fruit (cf. Gen 1:22; 9:1; 38:8-10), we can rightly infer from the lack of other children that Mary remained a virgin.
Typically, when a human being dies, his body is buried or cremated and his soul receives its eternal reward. It is only once Jesus comes again that this soul will receive its body back and experience heaven or hell as a completed human being.
The concept of persons being assumed, body and soul, into their eternal reward is not foreign to Scripture. Enoch (cf. Gen 5:24; Heb 11:5) and Elijah (cf. 2 Ki 2:11-12) experienced this. Paul said that a third man may have as well (cf. 2 Cor 12:2-4). The "two witnesses" in the last days (Rev 11:1-12) also were taken up bodily to heaven. Thus, there is precedent for what we believe happened to Mary.
Our first indication that Mary was assumed into heaven comes from the Revelation of John the Apostle. John looked up, expecting to see the Ark, and what did he see? A woman clothed with the sun (cf. Rev 11:19-12:1). We have already seen how Mary is the Ark of the New Covenant. That this woman is Mary is further confirmed later in chapter 12, where we see the woman giving birth to a son who will rule the nations with a rod of iron (vs. 5). This son is obviously Jesus, therefore the woman is Mary, whom John has seen, body and soul, in heaven. "Arise, O LORD, and go to thy resting place, thou and the ark of thy might" (Ps 132:8).
Beyond this, the assumption of Mary follows from who Christ is. During the reign of David and his descendants, the queen of the kingdom was actually the mother of the king, not his wife (cf. 1 Ki 2:19; 15:13; 2 Ki 10:13; Ps 45:9; Jer 13:18; 29:2). As soon as the king was crowned, the queen was likewise crowned, and she was seated on a throne right beside him (cf. 1 Ki 2:19).
Now, who is Jesus? He is the new king of David (cf. Mk 11:10; Lk 1:32). It makes perfect sense that from the moment He ascended into heaven and took up His throne, Jesus would assume Mary into heaven and install her as His queen mother. In the Davidic kingdom, there is no king without a queen.
The final Marian doctrine of the Church declares that Mary is the "Mediatrix" of God's grace. By this we mean that Mary cooperated in an extraordinary way in the saving mission of Christ, who alone is the unique mediator between God and man.
It may seem peculiar at first to think of a human being working with God to bring us grace, but Scripture says that all Christians are called to contribute to this vital work. It bears repeating: Jesus alone is the Savior and Redeemer of all mankind. Yet, it is also true that He wishes to involve us in His work.
For example, St. Paul said, "I have become all things to all men, that I might by all means save some" (1 Cor 9:22). He considered himself a steward of God's grace that was given to him for others (Eph 3:2; cf. Rom 11:13-14; 1 Cor 7:16; 1 Tim 4:16; 2 Tim 2:10; Jas 5:20; 1 Pet 3:1; 4:10; Jude 1:22-23). We are "God's fellow workers" (1 Cor 3:9), "working together with Him" (2 Cor 6:1).
Now, Mary played her part just as Paul did, but her cooperation was and is uniquely exemplary. Why? Consider her amazing life. Mary's "yes" to God was the occasion for the Son to enter human history and take on our human nature. She gave Him the flesh that He nailed to the Cross for our salvation. And, since she was sinless, she was able to stand at the foot of the Cross and unite her will and her suffering perfectly with the will and the suffering of her Son. No other human being can claim to do what Mary did.
This was undoubtedly rewarded with a tremendous outpouring of grace for the benefit of the Church. How do we know this? Because we see from Scripture that whenever someone suffers for the sake of the Church, the Church is rewarded with an application of the grace of the Cross.
These five doctrines, and the Scripture passages that support them, point to Mary as uniquely blessed by the fruit of her womb. If God had not chosen her to be His mother, then none of her other unique qualities would have existed. He made her the most extraordinary woman who has ever lived, and it is with good reason that "all generations will call her blessed" (Lk 1:48).


text:
Neill Blomkamp is making a funny robot movie starring District 9's Sharlto Copley
For those concerned that Neill Blomkamp hiring the likes of Matt Damon and Jodie Foster for Elysium meant he'd only be working with the most famous of movie stars going forward—his mad sense of entitlement growing until he's demanding the studio dig up Jimmy Stewart to placate him—you can stop worrying and being insane. Blomkamp has confirmed that, like Elysium, his next film, Chappie, will also feature his old District 9 pal Sharlto Copley, this time back in the leading role. As per usual with Blomkamp, not much else is known about Chappie, other than it will again be a science-fiction film "in an unusual setting"—though as the director been saying for nearly two years now, it will be more of a "science-fiction comedy thing," and it's apparently far more "simplistic" and lighthearted than his other two films. Blomkamp also tells Empire it involves a "ridiculous robot character"—though of course, we're pretty sure that goes for all movies, now that we live in the future.


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How to refund your skill points and reset your character
The passive skill tree of the Road of Exile has more than 1,200 nodes to choose from. You need to use all the skill points obtained when upgrading to reach remote and powerful nodes. And, if you make a mistake in your build, there are only a few ways to fix it. PoECurrency.com has a large amount of POE Currency, and it will update the relevant POE Items for each update in a timely manner, efficiently and safely.
Can I completely reset my skill tree?
The Road to Exile does not allow you to completely reset the passive skill tree. If you are above level 20 and are not happy with your build, most players recommend that you start over.
If you are still early and don't want to make mistakes that destroy the passive skill tree, we recommend that you choose a version. For example, Marauder built from PoE Vault comes with a complete classification of the skills you need. You can follow the production guides of other players to make sure you don't mess up the passive skill tree.
There is only one case where you can completely reset the Passive Skill Tree. If Grinding Gear Games drastically changes the skill tree between seasons, the studio may offer players a completely free reset.
This is not a completely reliable situation. If you are desperate for a more powerful version, the best advice is to start over.
Can I change personal skills on the tree?
On the road to exile, you can unlock refund points for characters. After completing the main story of the game, you will get about 20 refund points. You can also earn a few more refund points with a rare consumable called the Sorry Orb. PoECurrency.com will also update the content simultaneously. When players need to POE Currency, they can place an order directly at PoECurrency.com.
If you have refund points, you can activate them at the top of the Passive Skill Tree and then deselect the skills that have been unlocked. However, you can only return the node at the end of the unlocking branch-you cannot return a skill that also combines the other two skills. If you want to take your character in a completely different direction, it's almost impossible to get a limited number of refund points in your campaign.
Passive skill trees can be very punishing in Road to Exile. If you don't like to start from scratch, the best way is to find a guide and stick with it until you learn to make it yourself.
Lu Fan Yesterday, 04:13 · Tags: poe currency, poe currency ps4, poe items, poe orbs
Path of Exile 2 will be available in 2020, more information aroun...
We have confirmed that Grinding Gear Games has no plans to release Path of Exile 2 in 2020. No matter how it changes, for players, they always need to get more POE Currency in exchange for more items.
The team's latest development update states that Path of Exile will again receive significant quarterly expansion in the coming year, but this does not include sequels.
As revealed at ExileCon last November, Path of Exile 2 will no longer be a traditional sequel. Instead, the game will be a major update to the existing platform in version 4.0.0.
The team noted that public testing of this version is expected to take place by the end of 2020, but this much depends on how well we can expand the team this year to complete the remaining behaviors and new systems, 19 new courses and major adjustments to equipment and skills systems.
Grinding Gear Games hopes to be able to publicly display the content of Path of Exile 2 in the middle of this year, maybe around E3. PoECurrency.com will also update the content simultaneously. When players need to Buy POE Currency, they can place an order directly at PoECurrency.com.
At the same time, the group plans to announce the next expansion of the Path of Exile in late February. At the same time, the studio is currently building console staff to develop the features that console users expect more quickly.
Lu Fan Jan 16 · Tags: poe currency, poe currency ps4, poe items, poe orbs
The Path of Exile: Multiplayer Cooperation and Predatory Sharing
Multiplayer games are key elements like mobile RPGs, such as Path of Exile. You and your friends can participate in group gatherings of 2 to 6 people to travel through the game world and participate in later game events. However, there are some key factors to consider when gathering, such as making monsters more difficult or how to affect loot drops. Players must collect POE Currency, which will bring you great convenience in the game.
Gathering together is one of the simplest aspects of the Path of Exile. Enter the name of a friend's role in the space to add it to your friend's list. Then, when they are online, you can choose their name and invite them to join your forum. You will not be able to meet your friends in certain areas, such as before touching the Lions Eye watch at the start of the game. It may take you a while to enter the new area.
It is also possible for you to enter a version (example) of a town other than your friend, which means you will never meet again, but once you enter the mission area, they will appear in the world with you. If you and your friends are in the task area, but you can't find them, click the small portal next to their avatar to teleport to their instance.
Players can create their public parties, join other people's public parties, or turn private parties into public parties. Public gatherings are essentially a public invitation to other Path of Exile players without having to join your friend's list. You can even set descriptions for the activities you plan to do. If you want to Buy POE Currency, please pay attention to my website POECurrency.com imprinting to help you get it as quickly as possible.
Path of Exile: POE transactions and transaction prices
Suppose I found an excellent item while playing a casino game, but I don't require it at this time (maybe it won't fit my current character, or even I currently have a better character). Normally, I would make an effort to "sell" it-publicly listing it desires to trade it with players so they could earn some currency. The idea is, much like in any truly free market, the commodity will not be valuable to me-but it can have value to others, therefore we can make both of us better via an exchange (assuming he does it to me Provides some value) in turn).
In principle, I can try and replace it with another device (not some POE Currency) that I require, but, much like in real life, this barter trade has lots of disadvantages and is also rarely used.
As generally RPGs, two players have to be in the same play area to be able to trade. This seemingly insignificant requirement caused natural friction within the trading process. Usually, when I am from the game I am playing the action-so every time a potential buyer sends me a message saying he could be interested in what I am selling, I have to halt what I am doing and head over to participate The buyer of the place (an urban area or one on the player's hide). If both players are widely-used to trading in POE, the operation is usually just one minute, but it is a bit annoying and partially interrupts the overall game flow.
So ever before, I decided to prevent selling these devices for a price below some price (1 Chaos Orb) and believed that the smaller profit wasn't worth my time-I prefer to continue playing the experience. If after a while it sells for no less than 1, then I can get rid of it to regain store storage.
I have defined how the exchange must produce a net profit of at the very least 1 chaos or shouldn't happen at all-this is my transaction price (naturally, it can vary between participants).
In awareness of, this result can be compared to the transaction costs Buy POE Currency in real-life stock market-in real life, the exchange itself runs on the small part of each transaction as brokerage fees, creating friction.
Survival Guide in Path of Exile Metamorph
Some time ago, GGG released the latest extension of Path of Exile and a new private Metamorph alliance, which provides a lot of new content, but also brings some difficult challenges to players. Therefore, I think it is necessary to provide a survival guide in POE Metamorph to help you beat your boss faster and get rewarded by learning these skills faster.
Chaos resistance about equipment. Since Metamorph is the leader you build, you can clearly understand their power and cannot guarantee that they can kill all enemies, but to increase the kill rate, it is best to equip Chaos resistance to prevent the transformed leader from attack Chaos damage is used in the process, causing it to cause poison or blasphemy when it dies. At the same time, this update adds the point that you can alliance with friends in the game. Fighting with friends from any alliance can bring you huge benefits. With their help, you can easily defeat the Metamorph boss faster and even get enough experience points.
It's worth noting that you are not always lucky to get all the POE Currency in the game. At this point, you need to carefully craft the content you need to enhance your character, while it can also make more powerful and valuable items, keep them for your use or sell in exchange for POE Currency, which can bring you huge Booty.
Regarding the construction of the Path of Exile, it is well known that POE construction is very important in games. If you don't know any good builds, I suggest you google for some related guides about it. For example, IGGM is a very good website that can provide you with a lot of guides on POE, especially the POE currency production guide, which is the topic we will discuss next.
There are many ways to make POE currency, complete basic challenges, auction houses, and transactions with others, but these will waste a lot of time, so why not try some more convenient methods? IGGM also offers POE Currency sale service, which is a very reliable store, and everything it offers is safe and cheap, so if you need Path of Exile Currency, you can give it a try.
Bale Jan 13 · Tags: poe currency, poe items, poe orbs
Path of Exile 3.9 ignites the world BD gameplay strategy
The Path of Exile 3.9 Lights the World BD Advanced gameplay is a very popular version of the latest version. This latest gameplay is very good, with very high power damage. Many players are interested in this BD, take a look at the Path of Exile 3.9 How to ignite the world BD, S10 ignites the world BD gameplay strategy.
From the beginning of the revision, I have sought new ideas in the change of bow skills. The initial set of explosive arrows, the experience of drug man explosion arrows, chief explosion arrows, are not satisfactory. Level 36 barbarian deaths 108+, use life to push Illustration. Players must accumulate POE Currency, which is the only currency in circulation in the game. POE Orbs are also important.
The deepest points so far this season:
1. Synthesize the regular ground effect. If there is no second return, dodge + MOM BD, it is easy to violently.
2. Synthetic monsters often hit children with a series of skills, which leads to a problem that they will infinitely faint.
3. The strange combination of blood-sucking and blood-sucking is very desperate.
Finally selected the skill of burning arrows.
Borrowed from the idea of ??Taiwanese big brother Z, the mainline is the same, mainly adding a lot of personal understanding and improving ideas. If you are looking for an online store to Buy POE Currency, you can come to POECurrency.com here to help you a lot.
The Path of Exile 3.9.2 patch notes are here
Extensive patch notes and improvements to Atlas are included in the extensive patch notes for Path of Exile 3.9.2. The full list of patch notes is long. Perhaps the most important part involves deformation and improvements in the atlas.
Added new vendor formula for Metamorph organs. Any three organs can be given to receive random organs different from the organs provided, and given random rewards. Players must pay attention to the accumulation of POE Currency.
Fixed a bug that caused Metamorph bosses to fail to freeze. They can be frozen again, but their disease threshold is higher compared to map leaders with similar lives.
Adjusted some transformation skills, including Sage's Firestorm, Shavronne and Brutus Hover Slams, tentacle miscreation projectile skills, tracking mortar skills (including those used by Oriath Zombies and Kitava's pioneers), burning and harsh Ground creation skills and a few other skills. Overall, these will now cause less damage or be easier to avoid.
Increased the timeout for Tane's lab area to close when empty.
Fixed rare cases where deformed organs were missing after clearing the area.
Fixed a bug where players could sometimes get stuck in a vat in Tarn Labs.
Fixed some call options for Tane being available at the wrong time.
The visual effects of monsters that cause organ death are now properly retained instead of being removed shortly after.
Atlas improvements include:
Fixed an issue that displayed incorrect Atlas task information after migrating roles.
Fixed a bug where the castle was still hidden when unable to meet the boss.
Fixed a bug where influence items would not drop from monsters in maps affected by Atlas Conquerors (they might drop from boxes).
Fixed a bug that sometimes failed to properly complete the "Conditional Defeat Conqueror" challenge condition.
Fixed a bug where the conqueror of the Atlas leader would be retargeted after being mocked.
Added new lore targets to conquerors in the Atlas Boss area.
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The path of exile: A Secret to Survival Metamorphosis
The ppath of exile recently released one of the largest expansions to date. The conquerors of Atlas eliminated endgames by adding new bosses, completely overhauled the endgame system, and brought new loot and rewards to do the harder things.
With this new extension, The path of exile is easy to have one of the best post-game systems of any video game currently available. In the game, as soon as the player collects POE Currency, POE Orbs, and other items, the better, this will help you a lot later.
The conquerors of Atlas also launched for the first time a temporary challenge alliance called Metamorph. This alliance allows players to use the organs of killed monsters to create scary bosses, thus providing awesome rewards. The challenges these monsters bring (and the full expansion of the conquerors) make it difficult for some players to enjoy.
When you fight Metamorphs, the first thing you will notice is how deadly they are. Some will kill you immediately, and some will not be so scary.
This may be because you are not very resistant to chaos. A large number of Morphling bosses use Chaos damage in their attacks, causing poison or creating blasphemy when they die. Unless you run Chaos Inncoluation and you need to gain Chaos Resistance on your gear, these things will kill you immediately. Also, you can check if each organ uses this mod and choose not to use it, but this can be time-consuming.
Although this may seem obvious, playing with friends can potentially streamline content. As long as you and your friends have a building that can cope with yourself, you might kill the boss more easily. If you don't have enough time to stream in the game, you can also Buy POE Currency through POECurrency.com to get the game items you need to help you pass the level easily.
Lu Fan Jan 9 · Tags: poe currency, poe currency ps4, poe items, poe orbs
Path of Exile: A Beginner's Guide to PoE Currency
The Path of Exile challenges players by injecting unique elements into ordinary RPG elements. Players exchange each other by exchanging PoE Orbs. Although these spheres have a certain function, they are easy to collect and they will gain a lot throughout the Wraeclast journey. They are also used in transactions with NPCs, so they are the official Path of Exile Currency of the game.
Just entering the game starts with accumulating your treasure. Do not use the Orbs for any purpose at this time. Focus on finding your gear. Once the build is complete, worry about equipment and gems later. Then you can spend the Orbs.
Other ways to get money
There are several ways to continuously obtain spheres and other POE Currency. They are perfect for restocking after some handcrafting or getting enough spheres to buy the equipment you need.
One is to study. Obtain sufficient kyanite to limit dark resistance and light radius in low-level areas. However, don't run out of sapphires, as you will also buy torches and explosives. As you delve into it, try to find the broken wall in the dark. Here you will find fossils that can sell up to 200 Chaos Orb. However, this price only applies to very special prices, and you are more likely to find many products at much lower prices.
Another method is to make items for sale. Ask or look around for more popular mods on your device and make them. Otherwise, you can sell services for making custom items or other services. You can browse some public channels to see which services are profitable for you.
Path of Exile 2: Great concept art for the new armor models
Path of Exile becomes the successor to Path of Exile 2 from the ARPG. A mountain of conceptual art shows how pretty armor looks, for example.Many players don't know how to get more POE Currency in the game. Now the opportunity is here. You can buy especially cheap virtual items on PoECurrency.com. Including POE Currency, POE Orbs and POE Items
Path of Exile 2 was unveiled at Exilecon in November, but it may be a while before the release. The developers have announced a beta of the mega update of the ARPG for the end of 2020. Until then, those responsible at Grinding Gear Games always want to publish new information snippets. Right at the beginning of the freshly started the year 2020, there is a mountain of concept art for the new armament designs.
These demonstrate that the Path of Exile clothing, which is getting on in years, is being retired and is making room for detailed clothing. The images also show that in PoE we still have to make do with shredded, moth-eaten scraps. Only later will there be visually impressive outfits.Players can get 6% off on POEurrency.com with the discount to Buy POE Currency. Very cheap!
Ascendancy classes with their own armor sets in Path of Exile 2
It is remarkable that the ascendancy classes (specializations) also come with special armor sets that visually match this style of play. The Champion set looks like we can use it to bring troops directly into battle. The chief armor presents the bearer as an honorable member of the Karui tribes. As the Inquisitor, the bearer naturally relies on religious symbols, chain mail, sacred scripture, and ornaments. And the colossus (Juggernaut) is in enough metal to withstand even the toughest hits.
smrtsmith Jan 6 · Tags: poe currency, poe currency ps4, poe items, poe orbs
Recap of what happened on the Path of Exile in 2019
With the arrival of 2020, the Path of Exile will also summarize what has been achieved in the past year. A lot can happen in this short year. Let's take a look at the meaningful things that happened on the Path of Exile in 2019 and what was interesting.In the game, Path of Exile Currency plays a great role, and players must not despise it.
In 2019, the first stream amplification conference (commonly known as Exile-con) was launched, with more than 1,400 participants. Exile-con found that many announcements were public, such as The Path of Exile 2 that was eventually introduced, the safest assumption is to post to Path of Exile on a mobile device. Cosplay and discussion groups abound throughout the long weekend, where fans can discuss who made the design decision.
The Way of Exile received four separate extensions last year, and the recently released Atlas Conqueror is the largest of these four. Comprehensive, Legion and Withering extensions were also released, all of which provide extensions and improvements to the mechanics and knowledge found throughout War Destruction.
Path of Exile was successfully released on PlayStation 4, and eventually coincided with the pace set by the Xbox One, which was introduced to the game console in August 2017. Action RPGs expanded the audience's horizons, which set a record number. The Path of Exile has a total of 45 updates and patches, with an average of about three-quarters of a week updated throughout the year.
In terms of courses and skills, Grinding Gear Games has redesigned Necromancer, archery, mage, and melee combat in 2019 alone, making it more in line with its grand plan and winning vision. Atlas has also been completely redesigned in the latest update, and Lioneye's Watch has also experienced some break-ins.You POE Currency Buy on PoECurrency.com and it will definitely make you a repeat customer because the service is really great.
The Path of Exile will continue to increase resources for Exile in the future, the game has been 6 years old. With the release of Path of Exile 2 and PoE Mobile, no matter which platform you like, Path of Exile will continue to innovate and develop for better user experience.
The founder of path of exile 2 is confident and fearless
The birth of popular gameplay is good for every game developer. If someone can bring an additional 20 million players to a brand new popular gameplay, the entire game industry will benefit.In path of exile, poe currency is the only Path of Exile Currency in circulation, with more POE Orbs, POE Items can save you a lot of time.
Nowadays, games are gradually transitioning to cross-platform online, focusing on interaction with community players. path of exile 2 is very willing to do this if it supports cross-platform online. However, there are still some problems across platforms, such as how to update content on different platforms at the same time. Despite some difficulties, we are still optimistic that we can find a solution in 2020.
As a free game that includes micro-transactions, many players feel that The path of exile is a model in free games. How to prevent the micro-transaction system from affecting the game balance?
Everyone knows that the game concept of the path of exile is that it does not allow microtransactions to affect the game system. In this way, there will not be any consideration related to game design, so the game development team does not need to consider the business model of game profit, but only needs to focus on making the game fun.
For this reason, the sneak attack only sells micro-transaction items that allow players to dress up the character's appearance, and provides some convenient storage space.Players who POE Currency Buy and other goods on PoEcurrency can enjoy a 6% off with the discount code "XMAS", as of January 5.
The mobile R & D team spends a lot of time chatting with players on mobile phone projects and soliciting feedback when players complete the game. This has generated a lot of feedback on the current version, and the R & D team is still processing the feedback and making changes as a result. We haven't announced how the player will get the next iteration, but their feedback is very important to our process, so we will do more game testing in the community.
If the mobile version of path of exile is a good game for players, we will release it. So far, it looks promising, but there is no hard requirement for revenue from mobile projects in our financial plan, so we can spend time and make sure it is what we need before we launch.
123 Dec 31 '19 · Tags: poe currency, poe currency ps4, poe items, poe orbs
What new changes can be expected in Path of Exile 2
Developers want to contact PoE 2 with rival game Diablo IV. Can GGG bring new features that have not yet be completed? Will PoE currency and POE Currency PS4 be as important as they are now? Let's find out together.
Beta testing will begin in late 2020
There is no exact release date yet, and since Path of Exile 2 has been shown at ExileCon, it has been available to the conference participants. It can be predicted that the first beta version of PoE 2 will start in late 2020, but so far, there is no way to use it.
Path of Exile 2 is not simply a sequel
Path of Exile 2 will implement a new skill system. If you are an old player on the Path of Exile, you will continue to have all the cosmetics in the game. The same goes for items and characters you already have.
Path of Exile 2 is probably one of the biggest updates the community has ever made, and it's free. This is not surprising, as The Path of Exile itself is a free game that will launch seven new action battles for players to experience and will be held 20 years after the death of Kitava the Endless.
Path of Exile 2 will feature a new coating that looks like a major improvement over the already good ARPG. What do you think of this highly anticipated update? Will the way of breeding PoE currencies such as POE Currency Xbox change? As a third-party trading platform for PoE, PoECurrency.com will update the virtual currency you need as soon as possible. Come and buy POE Currency on PoECurrency.com now you can enjoy Christmas 6% off.
Path of Exile 2 developers talk about Diablo 4
Grinding Gear Games founder Chris Wilson discussed their reaction to the unveiling of Blizzard Entertainment's next issue of Diablo 4. Blizzard is more like gambling, and the game design decisions it makes may be of great benefit to their games, and may also harm the development of the games. Players will not know the answer until they play the released game.
Regardless, players always enjoy mysterious adventures and stay curious. However, storing more Path of Exile Currency in your hand will greatly help players in the game.
Comparing Diablo 4 to their video game, its popularity proves that claim, as well as millions of viewers watching the ExileCon event, and 1,400 diehard fans flying to New Zealand to watch it in person. The changes developers make for their games are carefully designed to increase the number. The new campaign is much better than the old one.
The new skill system allows players to do everything previously impossible while making it easier to understand and solve many confusing problems. Competitors may release brand new games, but this is an untested global decision and it is entirely possible that some wrong decisions.
Does the developer want to attract a wider group? The answer is yes. But when the game experience of loyal and veteran players is destroyed to attract other groups, this situation is not what developers want to see.
If that doesn't in any way compromise what makes their game very suitable for hardcore players, then they will try to attract a wider player base. If you don't want to spend too much time in the game, then you can POE Currency Buy from PoECurrency.com, here is a third-party transaction service platform for PoE, which guarantees your safety!
mick jaens Dec 28 '19 · Tags: poe currency, poe currency ps4, poe items, poe orbs
The idea of the path of exile is to distinguish MTX from the main...
Microtransactions are a relatively young monetization method in the history of games, but their rapid expansion is a good indicator of their effectiveness. The path of exile developers discovered a golden formula.
As a third-party transaction service platform for POE, PoECurrency.com has always silently supported players to help them complete Path of Exile Currency transactions.
Grinding Gear Games co-founder Chris Wilson said in a speech to Gamepot that the magic formula of the path of exile is to ensure that game development and monetization remain in their corner.
"Our philosophy is not to allow microtransactions to affect the game system. That way, there will be no game design considerations related to it, so the game development team does not need to think about how to monetize the game and can focus on making it It's fun. "
Micro-transactions on the path of exile are charged by deposit, not a win-win situation, which means that they are purely cosmetics and do not affect the gameplay. Balancing fairness and finances is always a daunting task, but GGG makes it stand out.
The discussion quickly turned to Tencent, one of GGG's major shareholders, and the mere mention of the name Tencent did seem to disturb some people, but we haven't found any praise other than Western investment. Wilson emphasized that the plan will remain until then. Chinese publishers have given them sufficient freedom and support.
If you are also a Poe enthusiast and haven't found a secure game vendor to help you POE Currency Buy, Come on! PoECurrency.com not only saves you money but also makes you the best in time Service.
ms wang Dec 27 '19 · Tags: poe currency, poe currency ps4, poe items, poe orbs
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There are many sides to The Islands of Tahiti. Yet they are all connected by Mana. Mana is a life force and spirit that surrounds us. "You can see it. Touch it. Taste it. Feel it." And from the moment visitors arrive, they will understand why locals say the islands are embraced by Mana.
Mana is a mythical and essential concept, a fundamental truth. It's both tangible and intangible, expressive yet imperceptible, revealing but enigmatic, so natural but also mysterious and esoteric.
Mana lives, animates, raises up, ennobles and transcends every thing, every being, every element in every dimension; it can also annihilate, ruin and destroy until the last vital vibration. Mana is purity, it arises from the life, humility, respect, dignity, love, sharing, beauty, goodness and peace of the beings and things that merge harmoniously in this ma'ohi universe.
Mana is wisdom; it emanates from the empirical, technical and ancestral knowledge, from the common sense arising out of the inalienable link between man and his environment, from the faith in the divine, the state of grace that every thing and every being can reach through a spiritual, cultural and profane quest for the universal Mana, the promise to be reborn wiser, purer and more powerful.


Global Delivery Model (GDM) in the software services space has evolved (highly) over time and has gained acceptance across customers as the benefits far exceed the perceived risks. A significant one among the many known advantages (cost, investment, and geo-spread) this model presents is access to talented & skilled technical resources with experience in latest technology-stacks.
In this instance, typically, the service provider sends skilled and experienced consultants to the client's company. Since the service provider and client are at the same location, there is more communication and face-to-face interaction, which means the client's business requirements are better understood. This type of delivery model is suitable for projects where more face time is required, and it is not easy to capture all requirements in a document.
When it comes to offshore delivery model, all the work is done at the service provider's location. Often times, the service provider is chosen from a country where costs are competitive and has some time-zone advantage as well. With regards to the process, the client's needs are understood in detail at the beginning and the project time-line and scope of work are agreed upon. After this, there is reasonable (ongoing) interaction between the client and service provider – say, check-point or review meetings. So, it becomes imperative that the communication that takes place initially is clear and documented thoroughly. Best practice from the service provider's end is to assign an Account/Client Service Manager to manage and guide the team, so that the client does not have to worry about the day-to-day aspects of the project. This is quite a popular and successful model, as the client gets the project done without incurring heavy on-site infrastructure and resource costs.
As the name suggests, this is a mix of on-site and offshore delivery models. Here the project team sits in more than one location. Based on the type and scope of the project, the work is distributed between resources in both teams. You have the best of both worlds here, as there is face-to-face interaction, planning and information gathering on-site, combined with cost savings, access to skilled staff and higher productivity achieved through an offshore development team.
As in life, every model has its pros and cons. There is no 'one size fits all' solution. One needs to take a careful look at their priorities and challenges (technical, finance, resources) and decide on the model that fits well for them. Companies can also migrate from one model to the other – say, you start with the on-site model and as you get comfortable with the team, you could move to a hybrid model and at some point in future, go fully offshore.
At Asahi Technologies, we work with clients predominantly on a hybrid delivery model. Consult with our experts and who are happy to help you pick the right approach/model.


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"I just didn't want to get caught up in something that wasn't real."
Ella Cerón
Photo: Courtesy of Apple Music
Between the fact that it's nearly the one-year anniversary since Zayn Malik left One Direction, and the fact that his new album, Mind of Mine, drops on Friday, March 25, it's safe to say that we are most definitely in the era of Zayn. His interview with Complex dropped on Monday, but the singer wasn't done quite yet, as NME also booked him for their new cover, and he's diving a little further into the process of saying goodbye to the band that first made him a mega-star.
He told the magazine that he's "still probably the closest to Liam. We talk on the phone. He congratulated me on my single, which was nice. I congratulated him on his Brit Award. It was a good chat. We haven't met up in a long time so we want to meet up." He added that he's "tried to have contact" since he boarded his plane and flew home "but nobody's reached out. So...whatever."
(To be fair, Liam has said that he didn't have the rest of his bandmates' cell phone numbers for the longest time because they saw each other every day anyway, but still, that kind of icing out has to hurt.)
And Zayn also further clarified being seen as the dark and mysterious member of the group, saying that "I've kept a bit of my sanity, I know how the media works. I think that's why it came across as being mysterious or detached. I just didn't want to get caught up in something that wasn't real." Granted, he's likely talking about how the eye of the media isn't real, but we'll wait for people to interpret that as a dig at his former band in three...two...
Related: You Need to Hear JoJo's Amazing Cover of Zayn's "Pillowtalk"
Keywordszayn malikOne direction